Photophysics of Conjugated Polymers · Photophysics of Conjugated Polymers Tieneke E. Dykstra Doctor of Philosophy, 2008 Graduate Department of Chemistry University of Toronto Abstract

Photophysics of Conjugated Polymers

by

Tieneke E. Dykstra

A thesis submitted in conformity with the requirementsfor the degree of Doctor of PhilosophyGraduate Department of Chemistry

University of Toronto

c© Copyright by Tieneke E. Dykstra 2008

Photophysics of Conjugated Polymers

Tieneke E. Dykstra

Doctor of Philosophy, 2008

Graduate Department of Chemistry

University of Toronto

Abstract

Poly (para-phenylenevinylene) (PPV), and its derivatives such as poly [2-methoxy,

5-(2’-ethyl-hexoxy)-1,4-phenylene vinylene] (MEH-PPV), are typical conjugated poly-

mers. In order to implement conjugated polymers into processable electronics tech-

nologies, we must first understand their complex photophysical properties as their

efficiencies depend on the balance between exciton recombination and charge carrier

formation. The inherent complexities of these materials arise from entanglement of

the pi-electron system with disorder and nuclear motions of the polymer backbone.

This disorder breaks the polymer chain into conformational subunits which can couple,

giving rise to a set of delocalized states formed by Coulombic interactions between

proximate subunits. Characteristics of PPVs include high quantum yields, non-mirror

image absorption and fluorescence line shapes, and large apparent Stokes’ shifts. These

properties are discussed in the context of the relationships between polymer conforma-

tion, electronic structure, coupling, disorder and polymer photophysics.

These important influences are often manifest in the dynamics of what happens af-

ter photoexcitation. In this work, we present 3-pulse photon echo peak shift (3PEPS)

studies of conjugated polymers in both solution and film. To elucidate timescales char-

acteristic of relaxation processes, we have simulated the 3PEPS data simultaneously

with absorption and fluorescence, observing a rapid localization of the exciton in the

initial ∼ 20 fs. Additional contributions to the decay of the peakshift are discussed.

We also present transient anisotropy data for PPV polymers and oligomers which is

compared to dynamics simulation for isolated chains of PPVs. This work demonstrates

ii

the influence of microscopic structure on ultrafast dynamics. We show that relaxation

between exciton states can lead to rapid depolarization of the anisotropy, even though

the spatial extent of exciton migration may be small. Generally, the connection be-

tween conformation and electronic structure is a theme throughout this thesis.

iii

Acknowledgments

I would like to thank all of those people who supported me throughout this adventure.

You know who you are.

iv

Contents

List of Figures vii

List of Tables x

1 Introduction 11.1 Conformational Subunits and their Interactions . . . . . . . . . . . . . 31.2 Coupling to Nuclear Motions . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Conjugated Polymers-The Picture So Far 92.1 Properties of Conjugated Polymers . . . . . . . . . . . . . . . . . . . . 10

2.1.1 Nature of Photoexcitation in Conjugated Polymers . . . . . . . 112.1.2 Site Selective Techniques . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Dynamics Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Comparison with modified polymers . . . . . . . . . . . . . . . 15

2.3 Single Molecule Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 192.4 Energy Transfer- Interchain and Intrachain Dynamics . . . . . . . . . . 22

2.4.1 Extent of Interchain Interactions and Energy Transfer . . . . . . 232.4.2 Enhancement of Intrachain Energy Transfer . . . . . . . . . . . 25

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Relevant Spectroscopies 273.1 Why go non-linear? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Why do we need the 3PEPS experiment? . . . . . . . . . . . . . 273.2 Three-Pulse Photon Echo Peak Shift (3PEPS) . . . . . . . . . . . . . . 283.3 Third Order Spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 The Response Function Formalism . . . . . . . . . . . . . . . . 343.3.2 The Brownian Oscillator Model- A Model M(t) . . . . . . . . . 38

3.4 Simulations Involving the 3PEPS . . . . . . . . . . . . . . . . . . . . . 393.5 Experimental Section- How the Experiment was Actually Done . . . . . 413.6 Polarization Anisotropy Experiments . . . . . . . . . . . . . . . . . . . 43

3.6.1 Pump-Probe as a Measure of Depolarization . . . . . . . . . . . 463.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

v

Contents

4 MEH-PPV and Disorder and all that Jazz 494.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 The Stokes’ Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.1 Molecular Stokes’ Shift and Spectral Diffusion . . . . . . . . . . 564.2.2 Coupled Chromophores and Dynamic Localization . . . . . . . . 584.2.3 Resonance Energy Transfer . . . . . . . . . . . . . . . . . . . . 59

4.3 Simulation of the data . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.1 Multiphonon Model . . . . . . . . . . . . . . . . . . . . . . . . . 604.3.2 Two-level electronic system approach . . . . . . . . . . . . . . . 634.3.3 Three-Stage Relaxation Model . . . . . . . . . . . . . . . . . . . 67

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.1 Comparison to Oligomers . . . . . . . . . . . . . . . . . . . . . 814.4.2 Conformation in Solution vs. Films . . . . . . . . . . . . . . . . 824.4.3 Localization and Energy Transfer . . . . . . . . . . . . . . . . . 844.4.4 Effect of Breaking Conjugation . . . . . . . . . . . . . . . . . . 854.4.5 Lineshape and Stokes’ Shift . . . . . . . . . . . . . . . . . . . . 86

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5 Exciton Dynamics in PPV Polymers: The Ultrafast Decay 935.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.2.1 Simulation of Absorption and Fluorescence . . . . . . . . . . . . 985.2.2 Dynamics Simulations . . . . . . . . . . . . . . . . . . . . . . . 1015.2.3 Simulation of the Anisotropy . . . . . . . . . . . . . . . . . . . . 103

5.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6 Additional Contributions to the Peakshift 1226.1 Importance of “Non-rephasing” terms . . . . . . . . . . . . . . . . . . . 1226.2 Higher Excited States in PPVs . . . . . . . . . . . . . . . . . . . . . . 1246.3 Excited State Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 1246.4 Vibrational Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.5 Further Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7 Conclusions 132

References 134

vi

List of Figures

1.1 Molecular structures of relevant polymers. . . . . . . . . . . . . . . . . 21.2 Absorption and Photoluminescence spectra for Rhodamine 6G (a) and

MEH-PPV (b) in solution. . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Schematic of the dynamical processes important in disordered conju-gated polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 The ray optics analogy for the three pulse photon echo (3PE) experiment. 303.2 3PE signal versus coherence time for population times T = 0, 20, and

50 fs, for both a PPV pentamer (upper panels) and MEH-PPV (lowerpanels) in chlorobenzene. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3 3PE as function of both delays t1 (the coherence time) and t2 (the pop-ulation time). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4 Two-level systems double-sided Feynman diagrams for the third ordernonlinear optical spectroscopies. . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Time ordering of pulses. . . . . . . . . . . . . . . . . . . . . . . . . . . 373.6 Simulated 3PEPS data. Effect of disorder in the system. . . . . . . . . 403.7 Simulation of (a) absorption and (b) 3PEPS data in the high tempera-

ture limit using the Brownian Oscillator model. . . . . . . . . . . . . . 423.8 Experiment setup and pulse sequence for the 3PEPS experiment. . . . 443.9 Schematic of the depolarization by energy migration in conjugated poly-

mers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1 Absorption and photoluminescence spectra of MEH-PPV (a) and pen-tamer (b) in chlorobenzene solution. . . . . . . . . . . . . . . . . . . . . 51

4.2 Experimental absorption and fluorescence spectra for dilute MEH-PPVsolutions and film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 3PEPS data, τ ∗ vs population time for the pentamer (a) and MEH-PPV(b) in chlorobenzene. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.4 Room temperature 3PEPS data for dilute solutions of MEH-PPV andfilm cast from chlorobenzene. . . . . . . . . . . . . . . . . . . . . . . . 55

4.5 Spectral density obtained using simulation parameters listed in table 4.1for MEH-PPV in chlorobenzene solution. . . . . . . . . . . . . . . . . . 57

vii

List of Figures

4.6 Simulation of MEH-PPV absorption lineshape by the multiphonon model(equation 4.10.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.7 Three Stage Relaxation Model. . . . . . . . . . . . . . . . . . . . . . . 694.8 Simulation of absorption (equation 4.22) and fluorescence (equation 4.23)

lineshapes using the three-stage relaxation model for MEH-PPV (a) andthe pentamer (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.9 Experimental and simulated absorption and fluorescence lineshapes. . . 754.10 Experimental and simulated 3PEPS lineshapes. . . . . . . . . . . . . . 764.11 Comparison between fully conjugated MEH-PPV and that with 28%

broken conjugation by intentional introduction of chemical defects. . . . 87

5.1 Conformations of three representative chains. The radii of gyration ofchains are Chain A: 300 A, Chain B: 210 A, and Chain C: 154 A. . . . 97

5.2 Calculated absorption spectrum and inverse participation ratio for chainC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.3 For efficient relaxation amongst states in the exciton manifold, the ener-gies of the two states must be sufficiently similar according to equation5.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.4 The effect of the excitation energy on the early-time fluorescence. . . . 1075.5 The simulated anisotropy decays for the three chains shown in figure 5.1. 1085.6 Anisotropy decays for chain C when only one state is initially excited. . 1095.7 Absorption spectrum for MEH-PPV in chlorobenzene solution. The nor-

malized laser spectra are also shown, with centre wavelengths of 493 nm,510 nm and 540 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.8 Pump-probe data for MEH-PPV in chlorobenzene solution. Transientsfor the VV and VH polarizations, collected simultaneously. . . . . . . . 111

5.9 a)Experimental pump-probe anisotropy of MEH-PPV in dilute chloroben-zene solution. Pump/probe wavelengths were 540 nm, 510 nm and 493nm.b) Pump-power dependence where the dynamics are different for ex-citation energies of < 5 nJ and 20 nJ. Excitation wavelength was 493nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.10 Comparison between polymers of different molecular weight (Mw=150000vs Mw=900000). Excitation wavelength was 510 nm. . . . . . . . . . . 113

5.11 Experimental POPV oligomers’ anisotropy decay for n=4,6,8. . . . . . 1145.12 The rotation of the dipole moment upon localization for the 3 chains

shown in figure 5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.1 The contribution of rephasing and non-rephasing response functions tothe peakshift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

viii

List of Figures

6.2 Feynman diagram for excited state absorption. . . . . . . . . . . . . . . 1256.3 The effect of coupling strength in ge′e(t) on the peakshift decay. . . . . 1286.4 The effect of decay rate in ge′e(t) on the peakshift decay. . . . . . . . . 129

ix

List of Tables

4.1 Simulation parameters in the three-stage relaxation model for the pen-tamer (a) and the polymer (b). . . . . . . . . . . . . . . . . . . . . . . 73

4.2 Simulation parameters using the three-stage relaxation model for theMEH-PPV solutions and the film cast from chlorobenzene. . . . . . . . 77

x

List of Acronyms

Abs Absorbance

DOS density of states

EET Electronic Energy Transfer

Em Emission

ET Energy Transfer

eV electron volt

FFT Fast Fourier transform

FLN Fluorescence Line Narrowing

fs femtosecond

IPR inverse participation ratio

LH Light Harvesting Complex

LPPP ladder poly (paraphenylenes)

MEH-PPV poly [2-methoxy, 5-(2’-ethyl-hexoxy)-1,4-phenylene vinylene]

NOPA Non-collinear Optical Parametric Amplifier

OD Optical Density

OLED Organic Light Emitting Diode

PE photon echo

3PEPS Three-pulse photon echo peak shift

PL photoluminescence

PPV poly(para-phenylenevinylene)

xi

List of Acronyms

RET Resonance Energy Transfer

SMS Single Molecule Spectroscopy

SSF Site-selective fluorescence

TG transient grating

xii

1 Introduction

Conjugated polymers and conducting polymers were discovered by Shirakawa, MacDi-

armid, and Heeger for which they received the 2000 Nobel prize in Chemistry. The

distinguishing feature of these macromolecules was the discovery that conjugation ex-

tends along a fairly rigid, long backbone. That led to much debate over how to think

of the electronic structure of conjugated polymers: semiconductors or molecules? This

question is still under debate, however most ascribe to the molecular picture. A cru-

cial experimental observation was the report of electroluminescence by Friend and co-

workers that demonstrated that semiconductor like properties are certainly exhibited

by these easily processed “plastics”.

Poly (para-phenylenevinylene) (PPV), its derivatives, such as poly [2-methoxy, 5-

(2’-ethyl-hexoxy)-1,4-phenylene vinylene] (MEH-PPV) (structures are shown in figure

1.1), and its oligomers are typical conjugated polymers. They represent new types

of materials compared to small organic molecules. [1–5] Organic semiconductors are

of interest for applications in electronic devices such as organic light-emitting diodes

(OLEDs), photovoltaics and transistors. [6] Understanding of the elementary excita-

tions and dynamics in conjugated polymers appears to be a central subject enabling

design, optimization and tuning at the molecular level of devices based on conjugated

polymers. For example, controlling conformational disorder or length of polymer chain

can profoundly affect the luminescence yield and charge transport efficiency and there-

fore the overall efficiency of OLED devices. [7–15] Characteristics of some conjugated

polymers and oligomers are high luminescence quantum yields, large apparent Stokes’

shifts, broad absorption bands, and non-mirror image absorption and fluorescence spec-

tra.

This non-mirror image symmetry between absorption and fluorescence is one of the

most obvious differences between a disordered conjugated polymer, like MEH-PPV,

1

1 Introduction

CH3

CH3

O

CH3

CH3

O

CH3

n

MEH-PPV

n

CH3

CH3

PPV

PPV pentamer

n=2

CH3

OC8H17

OH17C8

SCH3 CH3

n

polythiophene

SCH3 CH3

CH3

n

P3HT

CH3

CH3

R

R1

R1

R

n

LPPP

n

CH3

RR1

CH3

polyfluorene

CH3CH3

n

poly (para-phenylene)

Figure 1.1: Molecular structures of relevant polymers.

2

1 Introduction

and a model two-electronic-level system. Normally, in a (multi-vibronic) two-level sys-

tem, there is mirror image symmetry as Kasha’s rule is obeyed and fluorescence occurs

from the lowest vibrational level of the excited state. In MEH-PPV, there are other

phenomena at play that give rise to the anomalous absorption spectra. Investigation

of the origins of this lineshape is a motivation for this work. The electronic origin and

dynamics will be a theme throughout this thesis. The spectral differences between a

model laser dye, Rhodamine 6G, and MEH-PPV are shown in figure 1.2.

1.1 Conformational Subunits and their Interactions

The optical properties and dynamics of conjugated polymers are strongly influenced by

chain conformation. [16–19] Although they share some similarities with inorganic semi-

conductors, they differ in that the properties of conjugated polymers are characterized

by an interplay of π-system conjugation lengths and conformational disorder owing to

the relatively low energy barrier for disruptive small angle rotations around σ-bonds

along the backbone of conjugated chains. [20–29] The breaks in conjugation can arise

from chemical defects, configurational imperfections, and torsional disorder (which is

dynamic). [17] Conformational disorder in the polymer backbone is of utmost impor-

tance as it directly dictates the electronic properties of the polymer by disruption of

the intrinsic π-system conjugation. [20–29] The distribution function of different conju-

gation lengths takes an approximately Gaussian form with the center estimated to be

five-ten subunits. [30–33] This conformational disorder can be seen in the spectroscopy

of conjugated polymers as a kind of inhomogeneous line broadening.

Such information is contained in the linear absorption spectrum together with the

homogeneous absorption lineshape contribution manifested by the coupling between

electronic transitions and nuclear motions, causing fluctuations and relaxations of elec-

tronic transition energies. [1, 34] The time scales and amplitude of these fluctuations

together dictate dephasing processes and characterize the dynamical width of fluctua-

tions of the electronic energy gap (absorption lineshape). [35] A detailed understanding

of the absorption lineshape for small organic molecules in the condensed phase has been

3

1 Introduction

Ab

sorb

an

ce (

arb

. u

nits

)

24x103

2220181614

Energy (cm-1)

Photo

lum

inesce

nce

(arb

. units)

Ab

sorb

an

ce (

arb

. u

nits

)

26x103

242220181614

Energy (cm-1)

Photo

lum

inesce

nce

(arb

. units)

a)

b)

Figure 1.2: Absorption and Photoluminescence spectra for Rhodamine 6G (a) andMEH-PPV (b) in solution. The Rhodamine 6G spectra are very symmetric,indicative of a two-level system. This is not the case for the polymer.

4

1 Introduction

ascertained. [36–43] Previous work has shown that the origin of lineshape in conjugated

polymers differs fundamentally from such model two level systems. [1, 30–33] For ex-

ample, it is possible that interplay between conformational subunits predicted by the

Coulomb interaction affects the optical properties and electronic structure of conju-

gated polymers.

Experiments such as site-selective fluorescence (SSF) and single molecule spectroscopy

(SMS) have shown that the excitation of a polymer chain can take on a range of en-

ergies depending on the nature of the absorbing conformational subunit/chromophore.

This energy is subsequently funneled to lower-energy sites on the chain by electronic

energy transfer (EET) prior to emission. Experimental evidence for this energy transfer

has been obtained from analysis of the polarization anisotropy decay, the conclusion

of which is that energy migration is a complex process which occurs over a few to

100s of picoseconds. [44–47] Interchain energy transfer is more efficient than intrachain

EET [48, 49] owing to more favourable electronic coupling between cofacial segments

that give rise to enhanced π− π interactions [28,50]. For example, films cast from sol-

vents like chlorobenzene are likely to have close-packed regions that have many long,

parallel chains, facilitating energy transfer along those chains. [50–53]

Conformational subunits can interact, forming delocalized collective states of nanoscale

excitons. [54] Extending the π system over more than one conformational subunit is pos-

sible either along the chain (intrachain) or between subunits that are nearby through-

space (interchain). Such interchain excitons can be a consequence of coupling between

adjacent polymer chains as in a film or between segments of a chain that is folded back

on itself. Experimental evidence for both of these types of excitations with differing

energies has been drawn from single molecule spectroscopy and from observing con-

formational change in mixed solvents. [55–57] Both of these studies have observed two

distinct types of chromophores with “red” or “blue” emission energies, possibly corre-

sponding to interchain/aggregate and intrachain/isolated chromophores respectively.

Further quantum chemical calculations have endeavored to clarify our understanding

of the nature of conformational subunits in conjugated polymers. It has been predicted,

even in simple dipole-dipole models, that adjacent conformational chromophores should

be electronically coupled. However, recent work has shown that it is difficult to pin

5

1 Introduction

down a definition of conformational subunit with respect to torsional disorder. [58,59]

It is difficult to define when the conjugation is “broken” or when the π − π interac-

tion is only weakened somewhat. Thus, even the notion of a conformational subunit is

complex. However, this remains a useful model – the conjugated polymer as a set of

chromophores of differing sizes and energies which couple electronically, determining

the overall photophysical properties.

1.2 Coupling to Nuclear Motions

Theoretical studies have suggested the importance of intramolecular motions and changes

in molecular structure that underlie dynamical processes induced upon photoexcita-

tion. [60] Beenken and Pullerits, through a deep quantum chemical analysis, have con-

cluded that conformational subunits arise concomitantly with the self-trapping of the

exciton (dynamic localization) in polythiophene. [58, 59] It is noted, though, that the

polythiophenes seem to differ from the PPVs with respect to the relationship between

conformation and spectroscopy.

Exciton-phonon coupling is often manifest in conjugated materials as vibronic pro-

gressions. For delocalized , rigid structures, these effects are on the order of 1/N (where

N is the number of atoms) [61]. That is, the more atoms present, the lesser the effect

of an electron’s excitation. However, because of the self-localization know to exist in

more flexible conjugated polymers, vibronic structure is observed, even in polymers.

Furthermore, π electrons are highly delocalized and polarizable, leading one to expect

electron-electron correlation effects. (the π electrons can easily redistribute in the pres-

ence of charges). [61] The prototypical example is the Peierls distortion in conjugated

polymers, giving rise to bond-length alternation.

The non-mirror image symmetry of the absorption and fluorescence spectra are often

attributed to torsional modes. This is supported by comparison to both oligomers [62],

which rule out significant disorder-related effects, and ladder type poly(paraphenylenes)

(LPPPs), which have no torsional degrees of freedom and exhibit absorption/emission

symmetry [63]. It has also been suggested that torsions couple to excitons which plays

6

1 Introduction

a role in exciton self-trapping. [60, 64–66]

Self-trapping occurs on an ultrafast timescale. Time-resolved absorption and emis-

sion spectroscopy has provided some information on the initial relaxation processes

occurring after photo-excitation [67–69], such as the strong coupling between elec-

tronic and vibrational states in excited state dynamics. The fastest dynamics are

complicated and likely attributable to numerous entangled processes. These can in-

clude relaxation through delocalized exciton states or vibrational cooling. These fast

dynamics are discussed extensively in chapters 4 and 5. Subsequent dynamics are dom-

inated by electronic energy transfer (EET) between chromophores on the same chain

and between chains. This EET is prior to emission which is generally from localized,

low-energy sites.

Throughout this thesis, various theoretical studies and experimental results will be

discussed, building up a picture of the electronic structure and the dynamical processes

that occur in conjugated polymers. We show that the basic characteristics of conju-

gated polymers are derived from those of conformational subunits. However, they are

not simply a superposition of contributions from each subunit; these conformational

subunits couple to contribute collective electronic states to the absorption spectrum.

Owing to the interaction between subunits, it is clear that there will be a profound

dependence of the photophysics on conformation/morphology. Subsequent to absorp-

tion, these collective states are rapidly localized by conformational relaxation. Relax-

ation through the exciton manifold occurs very quickly. EET transfers excitation to

longer segments prior to emission. EET can also occur to defects but they are usually

non-emissive traps. Observation of such processes are obscured by disorder and line

broadening in the steady-state spectra.

Chapter 2 provides an overview of the work that laid the foundations for our under-

standing of the photophysics of conjugated polymers and a discussion of more recent

work that adds to this picture. The original work presented in this thesis served to

guide the model of polymer behaviour discussed in this chapter. Following this is a

more detailed explanation of the experimental techniques that I have used to charac-

terize MEH-PPV and other samples in chapter 3. Chapter 4 is a discussion of the

results of the photon echo experiments and simulations of these experiments using

7

1 Introduction

three phenomenological models. This is followed by a comparison of these results to

polarization anisotropy decays along with simulations and theoretical work on PPV

chains in Chapter 5. The peak shift is revisited briefly looking at transient absorption

in Chapter 6. The thesis is then summarized briefly.

8

2 Conjugated Polymers-The Picture So Far

With the notion that conjugated polymers like MEH-PPV consist of a distribution of

chromophores, the length of which is determined by breaks in conjugation, which in-

teract strongly, giving rise to the coupled collective states, we can now explore further

their nature and properties, structure and dynamics. In order to understand these com-

plex systems, researchers have used a wide variety of experimental techniques. Because

of sensitivity to conformation and disorder, careful sample preparation, experiment de-

sign and analysis of results are extremely important.

Performing a number of experiments on the same sample allows for direct compar-

ison. Many complementary experiments must be done to characterize the complex

nature of conjugated polymers. Absorption and fluorescence steady state measure-

ments can tell about the transition energy, extinction coefficients (oscillator strengths),

and Stokes’ shift (includes structural relaxation and energy transfer). [70] Varying ex-

perimental parameters can include wavelength dependence, time delays, polarization

dependence, and temperature, among others. One can change the wavelength to look

at the different energy regimes, change the delay between pulses to look at how the

populations and interactions in these different energy regimes evolve or change the

temperature to look at the effects of phonons/vibrational modes. Judicious choice of

experiment can yield information about the desired phenomena while being insensitive

to other processes, imparting a degree of selectivity.

The other option is to perform the same experiment on various samples with well

defined differences. Smart choices include comparison to oligomer analogues (to probe

the role of conformational disorder), ladder type polymers - LPPPs, (effect of torsions),

and polymers with broken conjugation (effect of exciton delocalization). Employing

creative synthetic strategies to modify specific features in the conjugated polymer ar-

chitecture allows a deeper understanding of the influence of microscopic structure on

9


the electronic states (spectra) and how they interact (dynamics).

2.1 Properties of Conjugated Polymers

The absorption spectra of disordered conjugated polymers should be viewed as inho-

mogeneously broadened with contributions from coupled quasi-localized chromophores

arising from breaks in conjugation. [71–73] This is supported by comparison to oligomers

of varying length. It is important to note that the disorder in conjugated polymers

is dynamic. That is, a chromophore is not a static entity. The size and nature of

an individual chromophore can change with time [74] as evidenced by the reversible

switching between narrow and broad emission corresponding to isolated and aggregated

behaviour.

The asymmetry between the absorption and fluorescence arises from torsional disor-

der along the polymer backbone. [57] This is supported by the asymmetry observed in

oligomers [13, 62, 75] as well as the mirror-image symmetry observed in polymers like

ladder poly-(paraphenylene) (LPPP) where there is no torsional disorder [63]. Disorder

in conjugated polymers is dynamic, at room temperature torsional motions can give rise

to large dihedral angles, effectively breaking (or weakening) conjugation and changing

the conjugation length of that chromophore. At low temperatures, when these torsional

motions are frozen out, MEH-PPV indeed exhibits mirror-image symmetry between ab-

sorption and fluorescence. Emission spectra tend to reflect the spectral properties of

the exciton traps (lowest energy chromophores) rather than a randomly selected chro-

mophore along the chain. The emission is generally from a more localized/self-trapped

exciton whereas the absorption is into a delocalized exciton state. [66]

The Stokes’ shift arises from the intramolecular reorganization energy associated

with a geometry change in going from the ground to the excited state in conjugated

polymers and oligomers. The planarization upon excitation has been shown theoreti-

cally by, notably, Tretiak et al. [60] The more planar structure of the relaxed excited

state is also consistent with the sharper fluorescence spectra (as compared to absorp-

tion) because of a decrease in torsional disorder. [70] The true Stokes’ shift is much

10


smaller than the apparent Stokes’shift between the absorption and fluorescence max-

ima. This apparent Stokes’ shift is made larger because it reflects energy migration

to the longest, red-most chromophores in the ensemble. The Stokes’ shift is discussed

further in Chapter 4.

2.1.1 Nature of Photoexcitation in Conjugated Polymers

It is now generally accepted that the dominant primary photoexcitation in conjugated

polymers is a Coulombically bound electron-hole pair, an exciton [76–79] (also referred

to as a polaron-exciton owing to the coupling to the lattice deformations in the poly-

mer backone [28, 61]). Photoluminescence (PL) is attributed to the radiative decay

of this species. There is ample evidence from a wide variety of experimental tech-

niques [80] and theoretical calculations [28]. The exciton was first assigned by looking

very carefully at the quantum efficiency and the time-dependence of PL on the same

samples. The exciton binding energy is ∼0.4 eV in PPV type polymers according to

experimental and theoretical results. [81–85] This has been measured, for example, by

looking at the dependence of the E-field strength on PL quenching [81], the magnetic

field dependence on conductivity [82] and by scanning tunneling microscopy (STM) of

MEH-PPV on gold [84].

Polarization-dependent ultrafast dynamics were elucidated from stretch-oriented films

of PPV, delving into the nature of the photoexcitations in such conjugated poly-

mers. [86] “Spatially indirect” excitations are shown to be unimportant in this case,

with the majority of excitons forming intrachain. Polaron pairs (or charge transfer

excitons), where the electron and the hole are on different chains but are still bound,

can be a secondary bi-product of the breaking up of initially created excitons. [82] It is

possible that some are photogenerated directly but in small yield. [78] Conversely, other

groups have attributed larger percentages of the photoexcitations to polaron pairs [2].

This effect is even more pronounced in photo-oxidized samples. It should be noted

that, because conformation is so strongly linked to the photophysical properties of con-

jugated polymers, differences in sample preparation would most likely lead to differing

proportions of photoexcitations, [28] as would photo-oxidation. It also well established

11


that the photoexcitation density (pump intensity) is a crucial parameter in pump-probe

measurements, as the decay dynamics in both films and solutions have been shown to

vary strongly with changing intensity, through a combination of nonlinear decay and

formation mechanisms. [87]

In films, which are of interest because of their use in device applications, polaron

pair formation may be quite significant. [57] Pump-probe dynamical studies have been

used to attribute various processes to polaron pairs. Rothberg and co-workers use the

model of polaron pair formation to explain the difference between stimulated emis-

sion (from singlet excitons) and excited state absorption (proposed to be from polaron

pairs) dynamics. [57] In addition, non-emissive interchain species may be required to

explain the lower PL quantum yields in films compared to solutions. Quenchers formed

by photochemical reactions are a possibility but the lower PL is also present in “pris-

tine” films. The long-lived PL has been attributed to polaron pairs that are formed

and then slowly recombine to form singlet excitons which are, in turn, responsible for

the emission. [57] Possibly other interchain species also provide satisfactory explana-

tions to these phenomena, however it may be difficult to differentiate between these

with real certainty. The difficulty of sample preparation remains, as does the fact that

many experiments require radically different excitation conditions, possibly giving rise

to differing proportions of excited species. Also, some experiments are not sensitive to

polaron pair formation as these species are dark, with very little oscillator strength.

The existence of these species is not incompatible, however, with these experiments as

discussed briefly in chapter 4.

2.1.2 Site Selective Techniques

Site-selective fluorescence (SSF) is a powerful technique where a spectrally narrow laser

makes it possible to excite only “selected” chromophores from amongst the entire en-

semble. [17, 79, 88] Such experiments have revealed that there is only a small Stokes’

shift between absorption and fluorescence in LPPPs. [89] This is consistent with the

assertion that planarization in the excited state is responsible for the larger reorgani-

zation energy in PPVs. [60] The fluorescence spectra obtained from SSF will be only

homogeneously broadened as long as the interchromophore interactions are vanishingly

12


small. [89] This can be achieved by exciting on the red-edge of the ensemble absorp-

tion, thereby exciting only the lowest-energy chromophores which will then emit. The

absorption and fluorescence spectra can then be obtained for the same small sub-set of

the ensemble.

Friend and his colleagues used SSF to probe the energy transfer as a function of tem-

perature in PPV derivatives. [90] They report a threshold energy above which emission

is independent of excitation energy. That is, energy transfer to an emitter is rapid

and occurs prior to emission. Below this threshold, the emission is correlated to the

excitation energy in that the energy transfer will be less efficient given fewer acceptors

with suitably low energy. They refer to this energy as the localization threshold below

which excitons do not migrate. Looking at these data they are able to separate out the

effects of exciton migration from other relaxation processes.

2.2 Dynamics Studies

In conjunction with the work done in determining what happens upon absorption and

fluorescence, researchers have also delved into connecting the two with a picture of

the dynamical processes. We can think of the instance of absorption as starting the

clock. Emission signals the end– for our purposes, time equals infinity then. In order

to understand what phenomena occur during this time, time resolved and non-linear

optical techniques have been used.

Drawing from many kinds of experiments [2, 91–96], including those presented as

part of this thesis, we are able to put together a picture of the important processes

that occur in conjugated polymers. The relative importance of these effects depends

strongly on the degree of interaction between chromophores in the polymer. This in

turn depends on a number of factors both external: solvent, chromophore concentra-

tion (solution vs film), temperature, and intrinsic: polymer degrees of freedom,bridged

vs more flexible with torsional motions, intentional chemical breaks in conjugation.

Absorption is into delocalized collective states. Many experiments are insensitive to

the degree of delocalization, however, the 3PEPS peakshift is thought to decrease upon

localization. [62,97] We expect these delocalized states to be very short lived owing to

13


the large reorganization energies characteristic of individual conformational subunits

and self-trapping of the exciton by coupling to the nuclear motions as has been pre-

dicted theoretically, driven by geometrical relaxation of a conformational subunit [60].

Although it might seem counterintuitive, this localization lowers the total energy of

the system by interacting with the bath. This localization can be on one side of a

defect [58] or in the middle of an extended segment [60,98].This may be responsible for

the early decay observed in anisotropy measurements provided the localization rotates

the transition moment significantly [47] in addition to the 3PEPS decay. Also on a

<100fs timescale, rapid spectral diffusion though the exciton manifold occurs. This is

a consequence of the strong coupling between chromophores and conformational disor-

der. Owing to the large degree of disorder, the exciton is confined to a smaller segment

of the polymer chain in MEH-PPV than in a polymer like LPPP where the torsional

disorder is blocked by bridging between repeat units. Short times are dominated by

cooperative processes and will be addressed further in subsequent chapters.

On a tens to hundreds of picosecond timescale, Forster resonance energy transfer

is the dominant process. Polarization anisotropy provides a direct measure of the ex-

citon migration on this timescale. [99] During migration, the dipole moment changes

orientation which results in a change in the anisotropy. As an exciton migrates, the

dipole orientation becomes different than that of the originally excited chromophore.

The technique does not itself distinguish between inter- and intrachain energy transfer,

but, when combined with knowledge of the polymer structure, is an excellent tool for

studying energy transfer. Both intrachain and interchain energy transfer are thought

to occur in conjugated polymers [50],with comparisons between film and solution shed-

ding light on the nature of the EET. [16, 97] There is competition between intrachain

EET which occurs along the polymer backbone and interchain EET which occurs pri-

marily through space where the chromophores are very close but not neighbours on

the polymer chain. Interchain refers to EET between chromophores on separate chains

or on the same chain in the case of folding. Owing to the favourable cofacial orienta-

tion of transition moments, the coupling between subunits is larger and the interchain

mechanism is much faster. [50,97,100–102] The hopping occurs between segments un-

til the exciton resides on a low-energy chromophore trap from which it cannot escape

14


before recombination. A chromophore is a trap when all of the nearby chromophores

have higher energy because EET to a state with higher energy is thermally activated

and therefore a slow process. The exciton diffusion length is reported to be 20 nm

for PPVs. [103, 104] These essential dynamical processes are presented schematically

in figure 2.2.

Time-resolved fluorescence studies show a strong excitation (and emission) energy

dependence. [105] Excitation further to the blue results in faster decay dynamics owing

to the large number of acceptor chromophores (those with lower energy), driving energy

transfer towards the bottom of the DOS. Thermally activated energy transfer is much

slower and is manifest in the slower decays upon excitation to the red (where there are

fewer acceptors). The decays are highly non-exponential. This may be because, upon

initial excitation, there are many acceptors which gives rise to a rapid energy transfer.

As the mean energy is decreased (with time), the average energy transfer rate will slow

as the number of potential acceptors is decreased. Eventually, the excitation will reside

on a low-energy trap site with little probability of transfer to another site. [105] The

nature of the fluorescing species may be different with time. Excited chromophores

can have different PL lifetimes depending on their conformation (isolated vs aggregate

species). Changing relative numbers of these species will change the PL decays, adding

to the non-exponential behaviour. [57]

2.2.1 Comparison with modified polymers

In order to test and strengthen various models that have emerged to explain the unique

optical properties of conjugated polymers, many researchers compare the optical re-

sponse of MEH-PPV to those that have controlled differences and similarities. For

example, MEH-PPV with intentional breaks in conjugation have been used to look at

the effects of delocalization length. pLPPP is used extensively to probe the role of

disorder in MEH-PPV. The two molecules have the same π conjugated backbone,but

owing to bridging between subunits, there is very little torsional freedom in the ladder

polymer. Oligomers are frequently used to assess the roles of disorder and intramolec-

ular vibrational modes in polymers.

15


Time

10s of fsof fs

100s of fsof fs

100s

10s of p

s

1s of p

s

al diffusion/

ion in

manifold

interchain

self-trapping

3002001000 fs

0

µ

µµ

energy transfer

incoherent hopping

energy transfer

intrachain

Figure 2.1: Schematic of the dynamical processes important in disordered conjugatedpolymers. Self-trapping occurs on a timescale of approx. 25 fs. Spectraldiffusion through the DOS (not necessarily localizing) occurs on a similarlyrapid timescale. Both interchain and intrachain Forster energy transferoccur. Interchain is much faster owing to more favourable coupling betweensubunits. Eventually, the exciton will recombine. It has been shown thataverage exciton diffusion length for PPVs is 10-20 nm. [103,104]

16


Oligomers are an essential model system to establish the relationship between struc-

ture and photophysical properties in their polymer analogues. Comparison between a

series of oligomers with increasing length reveals a convergence of their spectroscopic

properties. [106] The notion of the “effective conjugation length” is especially helpful

when comparing poly- and oligomers. This is the chain length when the size of the

π-conjugated system is big enough that the optical and electronic properties are no

longer size dependent. [106] This is usually approximately the persistence length of the

polymer. [107]

PV oligomers generally show more vibrational structure in their spectra than the

corresponding polymer. It is thought that the increase in intramolecular modes with

increase in chain length leads to a dampening of these vibronic progressions by torsional

disorder in the ground state. This is also consistent with the decrease in fluorescence

quantum yield upon increasing chain length with an approximately constant radiative

lifetime of ∼1.3 ns which can be attributed to the increase in the intramolecular modes

suitable for energy dissipation. [70]The nonradiative decay from polaron pairs to the

ground state can also contribute to this. [57]

The extent of delocalization of the exciton strongly influences excited state dynam-

ics and depends on electronic coupling, site energy disorder and electron-phonon cou-

pling. [47] Breaking conjugation by insertion of chemical defects (sp3 defects) can give

insight into the average degree of conjugation and the extent of coupling between

chromophores. Decreasing the conjugation from “fully conjugated” 2-methoxy-5-3,7-

dimethyloctoxy-PPV (MDMO-PPV), nominally 100%, to less than 60% conjugated

dramatically blue shifts the absorption maximum and broadens the lineshape, indica-

tive of the increasing contribution from absorption by high-energy (short) conforma-

tional subunits. [70] Below 80% conjugation, there is a blue shift but not nearly to

the extent seen in the absorption owing to energy transfer to the red-most segments in

the broken-conjugation polymers as well. Similar results have been reported for other

polymers in the PPV family. [108]

The dynamics following photoexcitation have also been studied for MEH-PPV with

broken conjugation. [47] The ultrafast depolarization of fluorescence and transient ab-

sorption was compared in samples of fully conjugated polymers and those that were

17


80% conjugated. Both the fully conjugated and broken conjugation samples display

decays with ∼ 1 ps time constants. This is in line with hopping timescales for Forster

energy transfer. [44] This dynamic is also seen as a PL rise time on the red-edge of the

spectrum, both of these results are consistent with incoherent energy transfer, which

decreases the average chromophore energy. Interestingly in the fully conjugated poly-

mer, there is an additional fast timescale, <100 fs. [47] They attribute this to dynamic

localization of the exciton in the fully conjugated case. This ultrafast timescale appears

in the anisotropy only when exciting to the blue and it is difficult to say why the self-

trapping would have a wavelength dependence. Most likely there are other processes

at work here, also. Regardless, it is clear that this must be some sort of cooperative

effect, a result of better coupling and stronger interaction between chromophores. The

nature of the ultrafast decay component seen in the anisotropy of PPV polymers will

be discussed at length in chapter 5.

The extreme case is a “perfect” polymer chain. This ideal is very difficult to re-

alize owing to the typically folded, disordered conformation of conjugated polymers.

Through clever synthetic and sample preparation techniques, researchers have devised

ways to circumvent this problem and are able to simulate ideal 1-D wires, with long

conjugated segments and controllable alignment of chains. [109] In stretch oriented

films of MEH-PPV, the exciton was measured to have a diffusion length of 50 repeat

units, much more so than in disordered films. [109]

Dendrimers are an interesting model system for comparison. Careful variation in

the degree of branching makes studies on energy transfer possible [110] and allows for

study of the origins of spectral broadening. Some dendrimers show enhancement of

optical properties as compared to their analogous linear compounds. [111, 112] This is

thought to be because of better delocalization of the exciton and interaction between

branches. Even though well-defined, dendrimers still show signatures of inhomogeneity

in the absorption lineshape and as a residual peakshift in the 3PEPS experiment.

18


2.3 Single Molecule Spectroscopy

While ensemble techniques are able to give insight into the elementary photophysi-

cal processes in conjugated polymers, they are generally unable (with the exception

of photon echo type experiments) to distinguish between intrinsic (homogeneous) and

disorder-related (inhomogeneous) effects. Owing to the unique ability of single molecule

spectroscopy to delve deeply into the complex relationship between structure and dy-

namics, it has now been widely used to investigate the nature of conjugated polymers,

adding to the wealth of information obtained from ensemble-based experiment and the-

ory. [51, 55, 56, 74, 113–116] Using this combined spectroscopic/microscopic technique,

researchers have been able to collect spectral and kinetic data that are not obscured

by sample heterogeneity, however it is important to note that each polymer chain can

included hundreds of chromophores. Since they look at one polymer at a time in a

very dilute matrix, they can look at spectral signatures that are not complicated by

ensemble averaged values.

Paul Barbara and his group of researchers have been on the forefront of research into

the structure and nature of the emitting states in conjugated polymers like MEH-PPV.

Significantly, they observed blinking of polymer fluorescence and discrete emission lev-

els for single polymer chains comprised of hundreds of chromophores, raising some

interesting questions about the nature of interchromophore interactions. [113] This in-

termittency is only observed for chains cast from poor solvents, suggesting a strong

link between conformation and photophysical properties.

As is clear from this and various other investigations, the conformation of polymer

chains is intimately related to its electronic and optical properties. From a theoret-

ical perspective, Hu et al. simulated the conformations adopted by a polymer using

a bead-on-a-chain model. [51] They showed the different types of conformations that

are expected depending on the strength of interaction between chain segments. A

random coil is most stable only for flexible polymers with little attractive interaction.

Conjugation imparts stiffness to polymer chains, which are expected to collapse into

conformations with some long-range order. Using their simulations in conjunction with

polarization-dependent single molecule spectroscopy (SMS), they are able to determine

19


the conformation adopted by, for example, isolated MEH-PPV chains in an inert ma-

trix. Comparing the intensity of polymer fluorescence as excitation light was modulated

between 0◦ and 180◦ with results from Monte Carlo anisotropy simulations,they con-

clude that the chain adopts an ordered, collapsed conformation. This is different from

ideal rod or toroid structures in that the presence of defects and intersegment attrac-

tions are taken into account in the formation of this conformation, referred to as the

defect cylinder. There is a degree of long-range order in this typical structure, where

the bulk of the chains are roughly aligned along the long axis of the cylinder shape.

Their experimental anisotropy agrees well with the simulated anisotropy distribution of

this roughly cylindrical conformation. [51]. This shape, where there are many parallel

chain interactions, is also a useful model to explain the anisotropy decay dynamics we

have observed in an ensemble measurement and in calculations on single chains of PPV

which will be discussed in Chapter 5. Within the model of this conformation, we can

explain the efficient interchain energy transfer in MEH-PPV, the large anisotropy and

the unique optical properties of the polymer.

In chains that coil more tightly, for example those cast from toluene solution [117],

the following explanation has been proposed for the conformation dependence and on-

off blinking. [115] The closer proximity of chromophores allows for greater interaction

and, thus, more efficient energy transfer/exciton migration. This results in energy mi-

gration to the longest segments, manifest as a red shift in fluorescence as these are

the major emissive species. Since only the red segments will be populated after the

first few ps, these are the only segments that can undergo photochemistry, forming

defects. Once these are bleached, a blue shift is observed, consistent with this pic-

ture. If the defect is reversible, this is seen as blinking with discrete levels as only a

few chromophores dominate the photophysics. [56] In more extended conformations,

energy transfer is much less efficient and emission is observed from a distribution of

chromophore sizes. There is, therefore a more uniform photobleaching, as seen in an

initial exponential decrease in PL.

Further experimental evidence for this model was obtained by quantifying the effect

of oxygen quenching on fluorescence [19]. In this work, the temporal evolution of the

fluorescence from single polymer chains was elucidated. Under oxygen-free conditions,

20


MEH-PPV chains exhibit a time-independent fluorescence intensity and spectral shape

(low-intensity excitation). Blinking of the fluorescence intensity is attributed to forma-

tion of a quencher on the polymer chain. The probability of forming such a quencher

is dependent on the oxygen concentration. Most likely, the oxygen reacts with the ex-

citon such that the molecule temporarily goes to a long-lived “dark” state (e.g., triplet

state) where it cannot fluoresce. [116] The position of the fluorescence quencher along

the polymer chain is dictated by singlet exciton migration, funneling excitons to the

trap sites. Regions where there are parallel chain segments should favour rapid en-

ergy transfer owing to favourably aligned transition moments and close proximity. The

relationship between quenched and unquenched emission helps to build an energy land-

scape, which along with time-resolved fluorescence data, shows that this energy funnel

is “permanent” on the timescales of the experiment, and is related to the structure of

the polymer chain.

Taking advantage of the narrower lineshapes at low temperatures (fwhm decreasing

from ∼ 37 nm /1120 cm−1 at 300 K to 10 nm/300 cm−1 at 20 K), researchers were able

to resolve two different types of emission spectra [55]. They refer to these as “single

chromophoric type” and “multichromophoric type” spectra where more than one peak

is evident. The observation of more than one emitting site is evidence for the pres-

ence of multiple energy transfer channels in a single MEH-PPV chain. This type of

measurement would be very difficult to do in a disordered ensemble of polymer chains.

Many of the single chains possess red chromophores arising from interchain interac-

tions which act as low-energy exciton traps to which energy is very efficiently funneled.

Emission is from these states when they are present. Otherwise emission is to the blue.

Rothberg makes use of the notion of distinct red and blue chromophores in his “2 state

model” [57]. In films of bulk MEH-PPV, nearly all the emission occurs from red sites,

indicative of efficient energy transfer to these sites within the exciton lifetime. The

nearly identical emission spectra for samples excited at various wavelengths is further

evidence for efficient energy transfer to these sites prior to emission. [118]

Other researchers have modified this technique, using it to observe conjugated poly-

mers in “host matrix free” environments. [116] The energetic extent of spectral diffusion

is found to be much greater in such films where the polymer chains interact. To reach

21


this conclusion, the temporal evolution of the fluorescence spectra along with the max-

imum position and the linewidth was analyzed. They showed that conformational

changes are possible even at low temperatures, explaining that these single chains have

more freedom for fluctuations than those in a host matrix. [116]

Combining the well established fluorescence technique with simultaneous measure-

ment of surface enhanced Raman scattering (SERS) provides an effective probe of the

absorbing and emitting parts of the polymer. [119] Looking at the vibrational signa-

tures of the chromophores also provides a distinction between two relaxation processes:

intramolecular exciton self-trapping and energy transfer between chromophores. When

the Raman and PL signals are correlated, the absorption and emission are from the

same chromophore. In the majority of cases, energy transfer occurs prior to emission,

with the Raman and PL being uncorrelated.

2.4 Energy Transfer- Interchain and Intrachain

Dynamics

The view that singlet excitons execute a random walk between conjugated segments,

statistically relaxing in energy, until they become trapped on a low-energy segment from

which they cannot escape within their lifetime is supported by direct measurement of

spectral diffusion in time-resolved measurements that show a red-shift with increasing

time. [120] This is also seen in the large apparent Stokes’ shift between absorption and

fluorescence and the narrowing of the distribution of conjugation lengths towards a

red-dominated ensemble [62]. The nature of the energy transfer can be discussed in

terms of the location of the donor and acceptor species. That is, does energy transfer

occur along the chain or between chains?

In dilute solutions, intrachain energy transfer along isolated chains dominates as

there are relatively few chain-chain contacts. [121] Interchain energy transfer is faster

and more efficient owing to the favourable alignment of transition moments and delocal-

ization effects. [50,97,100–102,122] Energy transfer in conjugated polymers is complex

22


and depends not only on the electronic structure of the materials but also on their

mesoscopic organization.

It has been proposed that the rate of energy transfer is affected by torsional relaxation

on a picosecond timescale. Westenhoff et al. demonstrate that the exciton size increases

upon torsional relaxation in polythiophenes and that accounting for this is necessary

to correctly simulate the energy transfer dynamics. Using a site-selective experiment

where EET cannot contribute, they attribute a red shift in the PL to this relaxation.

The red shift is not observed in samples where the torsions are blocked. [123] The re-

organization associated with the relaxation of some intramolecular modes is likely on

a timescale similar to that of energy transfer in MEH-PPV as well. [46] In MEH-PPV,

however, the importance of these effects may be obscured or diminished by the larger

conformational disorder and disorder related localization. [44]

2.4.1 Extent of Interchain Interactions and Energy Transfer

Using polarization anisotropy, Herz et al. have recently demonstrated experimentally

the effect that interchain interactions can have on the ultrafast decay component in

films of conjugated polymers [101]. They used a polydiphenylenevinylene derivative

(PDV) for which they have precise control over the chain packing, achieving this control

by supramolecular complexation with a matrix polymer that disrupts the interaction

between neighboring conjugated chains and also by surrounding parts of the polymer

chain with bulky insulating molecules. [101] Because the isolated chains show only slow

decay, they conclude that the ultrafast PL depolarization dynamics are directly cor-

related with the initial delocalization of the excitation across more than one polymer

chain. The sample in which interchain contact is allowed shows an anisotropy decrease

to ∼ 0.1 in 100 fs (a rotation of ∼ 43◦) demonstrating that stronger intermolecular

coupling promotes an ultrafast depolarization of the transition dipole moment. The

relaxation in conjugated polymer solution is likely mediated by intrachain interactions

such as localization [47] where a bent chromophore would cause a rotation in the dipole

moment. [58] The microscopic origins of rapid anisotropy decay are discussed in Chap-

ter 5.

23


The faster energy transfer in films as compared to solution has been attributed

to more interchain energy transfer as facilitated by improved chain-chain contact.

[50,53,97,100] Initial energy transfer dynamics from polymer chains to an energy trap

are thought to be rapid and diffusion-assisted. [48] Only at longer times after photoex-

citation and as excitons relax through the DOS do other transfer mechanisms become

important. This is because EET depends on both the spectral overlap and the distance

separating donor and acceptor. In films, there is more contact between chromophores,

reducing the distance. Tightly packed ordered chains, as expected for MEH-PPV cast

from chlorobenzene, allow for greater excitonic interaction than in more loosely packed

films, increasing the possibility for exciton-exciton annihilation [16], lowering the quan-

tum yield versus solution. There are other mechanisms which may contribute to this

lowering of the quantum yield including formation of non-emissive interchain species.

Previous research has shown that the emission intensity and quantum yield of films

cast from chlorobenzene (ordered films) are significantly lower than for those cast from

THF (less ordered films). Annealing causes further reduction and red-shifts, in agree-

ment with more ordered, longer segments and more efficient energy transfer. [124,125]

Energy transfer in MEH-PPV has been shown to be three time faster than in poly-

thiophenes previously studied. [44] This is attributed to the greater flexibility in MEH-

PPV which allows for greater chain-chain contact, facilitating efficient energy transfer.

This is because when the chains are able to interact in a cofacial manner, the coupling

between chromophores is larger than along the chain, increasing the rate of energy

transfer. Chemical modification of polyfluorene derivatives was used to examine the

effect of sidechain substitution. It was found that the sidechains affect the chain pack-

ing in films and the extent to which aggregates with many chain-chain contacts were

formed. [126] Changing solvent from which films are cast is also an option to con-

trol the degree of interchain contact. [117] Single molecule work comparing rigid

rod polymers to the more common folded polymers shows that the overall process of

energy transfer is different in these two systems. In rigid rods, where interchain mi-

gration is blocked, migration of thermalized excitons along the polymer backbone is

inefficient. [33] Huser and Yan demonstrate that extended chains show emission from

multiple segments whereas tightly coiled chains emit from a few distinct sites (indica-

24


tive of energy transfer to these sites). [114]

2.4.2 Enhancement of Intrachain Energy Transfer

Researchers have made use of specially designed poly(p-phenylene ethynylene)s that

display chain-extended conformations when dissolved in nematic liquid crystalline sol-

vents. [121] In these solutions, the polymers show a substantial enhancement in the

intrachain exciton migration rate, which is attributed to their increased conjugation

length and better alignment. There is little opportunity for interchain migration, owing

to the extended conformation. By capping the ends with lower energy chromophores,

they demonstrated the increased energy migration along the chain when the conjuga-

tion was increased by alignment within a nematic liquid crystal. When un-aligned, the

same capped polymers exhibit fluorescence mostly from the polymer itself. [121]

Schwartz et al. have shown that directed energy transfer is possible in MEH-PPV

aligned in mesoporous silica. [49] Polarization spectroscopy shows excitons migrate uni-

directionally from randomly oriented polymer segments to isolated, aligned polymer

chains within the pores. Once the aligned chains were excited, the energy migration

along the chains embedded in the pores was slower than EET between chains. This

is the only channel of EET after the initial migration to the aligned chains. This is

shown by an increase in the anisotropy as the system becomes more aligned rather than

more randomized. Eventually it plateaus as there is no further rotation in the dipole

moment because all of the dipole moments are (nearly) fully aligned.

2.5 Summary

From this chapter, it is clear that the photodynamics of MEH-PPV and other conju-

gated polymers is complex. The relationship between conformation and dynamics is

strong. Interplay between π-conjugation and disorder determines the spectral dynam-

ics. Different sized chromophores and varying degrees of coupling between them will

25


contribute to very different photophysics. These themes and how they relate to the

specific experiments and simulations I have done will be considered in the following

chapters.

There has been much work done on studying the optical response and energy mi-

gration on the 10s to 100s of picoseconds timescale. What happens at earlier times is

less well studied. Specifically, I will address the role that conformational disorder plays

in the optical response of MEH-PPV by looking at the ultrafast decay of the 3PEPS

experiment. I will also present experimental and theoretical work that examines the

microscopic nature of conformational subunits and their interaction on the ultrafast

decay in polarization anisotropy experiments.

26

3 Relevant Spectroscopies

In this chapter I will discuss the motivations for pursuing non-linear optical spec-

troscopy. The three pulse photon echo peak shift experiment will be explained. In order

to understand the 3PEPS results and to be able to compare the information obtained

from this experiment with others, the response function and theoretical framework in

which we analyze our experimental data will be outlined. The key features of this

theory are discussed. Simulations using this theoretical model are presented and our

particular experimental set-up will be explained briefly.

3.1 Why go non-linear?

Given the experimental and theoretical challenges in doing non-linear optical spec-

troscopy, there have to be compelling reasons to choose these over simpler linear ab-

sorption and fluorescence experiments. Non-linear spectroscopy allows us to access

information that is obscured under the lineshapes of absorption and fluorescence. By

varying the number of pulses and their sequence, wavelength, experimental geometry

and polarization, a wealth of information can be obtained, including population dy-

namics and the electronic energy gap correlation function.

3.1.1 Why do we need the 3PEPS experiment?

The three-pulse photon echo peak shift (3PEPS) experiment allows the origins of spec-

tral lineshapes to be elucidated and has been used successfully to decipher the signa-

tures of solvation dynamics. The experiment measures spectral diffusion and can re-

27


trieve the timescales of processes that broaden spectral lines or change the microscopic

nature of the excited state, e.g. resonance energy transfer and localization of excitation

in molecular aggregates. The experiment is sensitive over a large dynamic range–from

femtoseconds to nanoseconds– and can go beyond the time resolution typical of pulse-

width limited responses. [36, 38–43, 127–130] This is because this experiment depends

on the difference between the centre position of the pulses, which greatly enhances

time resolution. The 3PEPS experiment retrieves information related to absorption

and fluorescence spectroscopies, enabling us to elucidate the origins of line broaden-

ing which are obscured in spectral line shapes. The peak shift reflects the rephasing

and echo formation capability of the medium. Thus 3PEPS is capable of providing

much valuable information, such as all the time scales of dephasing processes that are

coupled to an electronic transition, by providing a lineshape function and separating

homogeneous and inhomogeneous broadening [35–39,131,132]. Using this spectroscopy

we have been able to elucidate the details of lineshape broadening as a correlation func-

tion. The 3PEPS experiment has been shown to track with the system-bath correlation

function. [39] Experimental results will be discussed in Chapter 4.

3.2 Three-Pulse Photon Echo Peak Shift (3PEPS)

The 3PEPS experiment is a very powerful technique which is sensitive to correlations in

the system. It is a measure of the system’s memory of the initially prepared state (the

transition frequency/excitation energy of the chromophore) and follows the electronic

transition frequency correlation function. As the population time (the experimentally-

controlled delay between the second and third pulses) is increased, the system is less

able to refocus. The time-integrated 3PE signal S(T, τ) measured in the laboratory is

expressed in terms of response functions R(t, T, τ) that involve third order polarizations,

[133] with τ being the time delay between the first two pulses (the coherence period),

T the time delay between the last two pulses (the population period) and t the time

28


evolution of nonlinear polarization after the third pulse:

S(T, τ) =

∫ ∞

0

dt∣∣∣P (3)(t, T, τ)

∣∣∣2

(3.1)

At first, photon echoes are often difficult to understand conceptually. Fleming uses

a ray optics analogy to explain the phenomenon [134] which is illustrated in figure 3.1.

The first pulse creates a coherence (superposition between two quantum levels, |g〉 and

|e〉) which evolves with an oscillatory component e−iωegt, where Eeg = hωeg is the energy

difference between the two levels (the excitation energy). We can define a phase factor

ωegt, and the phase evolves linearly in time with a slope ωeg. Because chromophores are

not necessarily in identical environments, they will have different transition frequencies.

For n molecules with a distribution of energy levels, there will be n lines with different

slopes fanning out from the initial value (where the coherence is driven at the frequency

of the laser pulse). The second pulse produces a population, during which the frequency

difference between the bra and the ket, ωeg = 0 and the phase is constant. That is,

there is no phase evolution during this time period. The third pulse produces another

coherence with phase factor −ωegt. The sign changes because the second coherence is

the Hermitian conjugate of the first. The final interaction refocuses the rays at a time

t equal to the first time τ . The refocused beam is the photon echo.

This picture is in an ideal case. Of course, the chromophores are interacting with

the environment, changing the energy of the quantum states. This is illustrated as

fluctuations in the lower portion of figure 3.1. In this case, the phase factor is ωeg−〈ωeg〉.Dephasing processes are those that change the slope during the coherence times, τ and

t, while spectral diffusion and homogeneous dephasing (randomizing) occur during the

population period T.

The 3PE signals in the −k1+k2+k3 and k1−k2+k3 phase matching directions are

spatially isolated and measured simultaneously. The peak shift τ ∗ for each population

time T corresponds to the coherence time τ when the time-integrated photon echo

signals peak. With normal time-ordering, the last pulse, with eigenvector k3, converts

the population into a coherence which generates an echo in the ks = −k1 + k2 + k3

29


t1=τ t3=tt2=T

Figure 3.1: The ray optics analogy for the three pulse photon echo (3PE) experiment.The first pulse creates a superposition of ground and excited states. Becauseall of the chromophores are different, there is rapid dephasing illustratedas the rays spreading out from the first “lens”. The second pulse createsa population which is allowed to evolve for a time T. The third pulse cre-ates a coherence which is the complex conjugate of the first. This causesrephasing and an echo signal to be emitted. In the lower panel, the effectof interactions with the bath is shown as fluctuations in the phase. Thesefluctuations cause the system to become randomized, losing the memoryof the initially prepared state (at the time of the first pulse). That is, therephasing ability of the system is diminished.

30


phase matching direction. Simultaneously, we measure the signal with wave vector

ks′ = +k1 − k2 + k3 (with pulse sequence k2,k1,k3). Peak positions of the measured

echo signal are obtained by fitting each of the two data traces with a Gaussian function.

The peak shift is expressed by τ ∗ = (|τ ∗1 |+ |τ ∗2 |)/2.

Figure 3.2 shows the time integrated 3PE signal at various population times for a

PPV pentamer and MEH-PPV in chlorobenzene solutions. The 3PE data in upper

panels for the pentamer are obtained using laser pulses with center wavelength at

485 nm, and pulse duration of 45 fs FWHM. For MEH-PPV the excitation center

wavelength is 538 nm, with a laser pulse duration of 25 fs FWHM. The 3PE signals

are pulse-width limited, and the actual peak shift is affected by pulse duration. [39]

The effect of pulse duration on peak position is accounted for in the simulation of the

signals. Clearly as the population time is increased, the peak shift decreases as the

systems loses the ability to rephase.

This loss of rephasing ability is also reflected in the magnitude of the photon echo

signal in addition to the effects of population relaxation. A 3PE scan is shown in figure

3.3 as a function of both delays t1 (the coherence time) and t2 (the population time).

As the delay between the second and third pulses is increased, allowing population

dynamics to evolve for a longer period of time, the rephasing ability of the system is

diminished. That is, the system loses memory of the initially prepared state. This

is seen experimentally as a smaller signal which decays rapidly. The peakshift is the

difference between the maximum of signal intensity and t1=0 which is drawn as a

vertical line for clarity.

3.3 Third Order Spectroscopies

In order to compare the multitude of experiments, all of which have different interac-

tions, a common formalism is required, ensuring direct comparison without confusion.

Nonlinear (in addition to linear) spectroscopic signals (including 3PEPS) can be calcu-

lated using the response function formalism. Here, I consider a two-level system with

electronic states |g〉 and |e〉 that are coupled to external electromagnetic fields through

dipole interactions. [39]

31


-200 -100 0 100 200 -200 -100 0 100 200-200 -100 0 100 200

-100 -50 0 50 100 -100 -50 0 50 100 -100 -50 0 50 100

T = 0 fs

Coherence time (fs)

T = 50 fs

Coherence time (fs)

T = 20 fs

Coherence time (fs)

T = 0 fs

Coherence time (fs)

3P

E s

ignal in

tensity

T = 20 fs

Coherence time (fs)

T = 50 fs

Coherence time (fs)

Figure 3.2: 3PE signal versus coherence time for population times T = 0, 20, and 50 fs,for both a PPV pentamer (upper panels) and MEH-PPV (lower panels) inchlorobenzene. Open circles are the data for the phase matching directionk1 − k2 + k3 and the filled circles are for the phase matching direction−k1 + k2 + k3. The solid lines represent the Gaussian fit of the echo datapoints. As the population time is increased, the peak shift decreases.

32


t1

t2

Norm

aliz

ed Int

ensity

0 fs

Figure 3.3: 3PE as function of both delays t1 (the coherence time) and t2 (the popula-tion time). The signal intensity decreases with population time reflectingthe loss of the system’s ability to rephase completely and owing to pop-ulation loss during this time. The peakshift is the difference between themaximum of signal intensity and t1=0 which is drawn as a vertical line forclarity. This is experimental data for MEH-PPV in chlorobenzene solution.

33


We can write the time-dependence of the energy gap as

ωi(t) = 〈ω〉+ δωi(t) + εi (3.2)

where 〈ω〉 is the average transition frequency of the ensemble. δωi(t) is a dynamic

fluctuation and εi is the static offset of the chromophore from the ensemble average.

[132] The correlation function of the fluctuations of the normalized transition energy

gap is contained in M(t):

M(t) =〈∆ω(0)∆ω(t)〉

〈ω2〉 (3.3)

This correlation is very important. It has been shown that it contains all the informa-

tion needed to fully describe the optical response of the system.

3.3.1 The Response Function Formalism

Once M(t) is known, it can be used to determine the lineshape function g(t). The

lineshape function g(t) is defined via

g(t) = −iλ

∫ t

0

dt1M′(t1) + 〈δω2〉

∫ t

0

dt1

∫ t1

0

dt2M′′(t2) (3.4)

where λ is the reorganization energy, 〈δω2〉1/2 is the coupling strength and

M ′(t) =1

π∆2

∞∫

0

dωC(ω) coth(βhω

2) cos(ωt) (3.5)

M ′′(t) =1

πλ

∞∫

0

dωC(ω)

ωcos(ωt) (3.6)

∆2 =1

π

∫ ∞

0

dωC ′′(ω) coth( hω

2kBT

)(3.7)

34


and

λ =1

π

∫ ∞

0

dωC ′′(ω)

ω(3.8)

Equations 3.5 and 3.6 demonstrate the relationship between the correlation function

and the spectral density C(ω). Often it is convenient to work in the frequency- rather

than time- domain. It is possible to interchange the two keeping the same information

because the correlation function is related to the spectral density by Fourier transform.

These two approaches have been shown to be equivalent. [39]

The third order polarization requires three field-matter interactions. These occur

at time ti with electric field Ei(ti, ωi,ki). ωi and ki are the frequency and the wave

vector of the ith pulse. The third order polarization signal is emitted in all of the

phase matching directions ±k1 ± k2 ± k3 allowed by one interaction with each pulse.

Other combinations are possible if there is more than one interaction with the same

pulse, as in pump-probe experiments for example. I’ll only consider the −k1 +k2 +k3

direction in this discussion. The Feynman diagrams that describe the pulse ordering

and interactions contributing to that phase-matching direction are presented in figure

3.4.

The Feynman diagrams provide a useful shorthand for describing the field-matter

interactions that take place. For the diagrams shown, the rotating wave approximation

has been made, that is, only resonant transitions are considered. [133] In the Feynman

diagrams, time goes up. An inwards pointing arrow signifies absorption; outward means

emission. The left hand side represents interactions with the ket. The right is for

interactions with the bra. Either the bra or the ket is promoted to the excited state

following interaction with the radiation field (laser pulse). When the bra and the ket

are in different states (either eg or ge) the system is said to be in a coherence state which

has a certain phase as described earlier. Because every chromophore in the ensemble is

different, these coherences will interact destructively as they are out of phase, causing

the coherence to decay quickly. Once the system is in a population state (ee or gg)

after interaction with a second laser pulse, there is no energy gap between the bra

and ket, any non-zero phase is a result of nuclear degrees of freedom or vibrational

coherences. The third pulse returns the system to a coherence. At some time, t, later a

signal is emitted. R1-R4 create excited state populations after the second pulse. R5-R8

35


ge

ee

eg

t1'

t3'

t2'

eg

ee

eg

eg

ee

eg

ge

ee

eg

ge

gg

eg

eg

gg

eg

eg

gg

eg

ge

gg

eg

k2

k2

k2

-k1

ks

k3

ks

k3

-k1

k2

ks

k3

-k1

ks

ksks

k3

-k1

ks

-k1

k2

ks

k3

-k1

k3

-k1

k3

k2

k3

k2

R 1

-k1

k2

R 2 R 3

R 4 R 5 R 6

R 7 R 8

Figure 3.4: Two-level systems double-sided Feynman diagrams for the third order non-linear optical spectroscopies. [39] In these diagrams, the third order polar-ization is in the −k1 + k2 + k3 phase matching direction. Time increasesgoing up. The arrows on the left and right indicate field-matter interac-tions of the ket and bra states respectively. Arrows pointing in representabsorption of the field. Arrows pointing out are emission.

36


Pulse 1 Pulse 3Pulse 2 P(3)(t')

0-T-T-τ

t1

t1' t2' t3't2

t3 t

time

Figure 3.5: Time ordering of pulses. τ , T and 0 are the centres of pulses 1, 2 and 3respectively. The ti are the times of field-matter interaction and the t′i arethe delays between the interactions. [39]

create ground state populations. The four field-matter interactions (pulses 1,2,3 and

the signal) are the reason that this type of third order spectroscopy is sometimes called

four wave mixing. [135] The pulse sequence for the relevant experiments is given in

figure 3.5 along with the definitions of the delay times. In the limit of delta function

pulses, t1’=τ , t2’=T and t3=t. [39]

The response functions corresponding to the Feynman diagrams can be calculated

with a second order cumulant expansion [133,136] if g(t) is known:

R1(= R4) = exp{−g∗(t′1) + g(t′2)− g∗(t′3)− g∗(t′1 + t′2)

−g(t′2 + t′3) + g∗(t′1 + t′2 + t′3)} (3.9)

R2(= R3) = exp{−g(t′1)− g∗(t′2)− g∗(t′3) + g(t′1 + t′2)

+g∗(t′2 + t′3)− g(t′1 + t′2 + t′3)} (3.10)

R5(= R8) = exp{−g∗(t′1)− g∗(t′2)− g(t′3)− g∗(t′1 + t′2)

−g∗(t′2 + t′3) + g∗(t′1 + t′2 + t′3)} (3.11)

R6(= R7) = exp{−g(t′1)− g(t′2)− g(t′3) + g(t′1 + t′2)

+g(t′2 + t′3)− g(t′1 + t′2 + t′3)} (3.12)

37


The relevant response functions for the photon echo are those that cause rephasing

(R1, R4, R5, R8). For those that do not (R2, R3, R6, R7) the decay in the third order

polarization signal is more like a free induction decay (FID). [39] If the delay between

the first two pulses, t′1, is zero, all response functions yield an FID because the rephasing

depends on the correlation between the evolution during times t′1 and t′3 as defined in

figure 3.5.

The third order polarization is

P(3)(t, T, τ) =i

h

3 ∫ ∞

0

dt′3

∫ ∞

0

dt′2

∫ ∞

0

dt′1

4∑i=1

Ri(t′1.t

′2, t

′3)

×E∗1(k1, t1)E2(k2, t2)E3(k3, t3) (3.13)

where Ei is the electric field of the ith pulse with eigenvector ki. The third order

polarization is related to the experimentally measured signal by equation 3.1.

With an understanding of the basics of third-order spectroscopies, we can per-

form simulations looking at the effect of different parameters on the magnitude and

timescales of optical response.

3.3.2 The Brownian Oscillator Model- A Model M(t)

The fluctuations of the transition energy gap are used to define a correlation function as

in equation 3.3. Fluctuations of transition frequencies in the system are instrumental

in the decay of the peakshift, and the timescales of the fluctuations can give insight

to their origins. The contributions to M(t) include intramolecular vibrational motions

and system-bath dissipative processes. It is usually difficult to separate these processes.

In fact, the nuclear motions of the polymer chain itself can be coupled to the electronic

energy gap. [39]

Fluctuations can be modeled by a bath of Brownian oscillators coupled to the elec-

tronic transition. Using the overdamped Brownian Oscillator model in the high tem-

38


perature limit the line broadening function g(t) is:

g(t) = 2λkBT/hΛ2[exp(−Λt) + Λt− 1]− i(λ/Λ)[exp(−Λt) + Λt− 1] (3.14)

where λ is the bath reorganization energy and Λ is the frequency of the bath fluc-

tuations. [133] The high temperature limit is likely to hold in most systems because

the solvent spectral density is near 60 cm−1. [137] Only two adjustable parameters,

Λ and ∆, are required to implement the model. ∆ is the variance of the frequency

fluctuations and is related to λ. κ ≡ Λ/∆ = (hΛ2/2λkBT)1/2 is a convenient way to

look at the interplay between these two factors. When κ ¿ 1, dynamics are slow (with

long timescales Λ−1) compared to the magnitude of the coupling (λ). In this limit, the

absorption lineshape is Gaussian. In the fast modulation (homogeneous) limit, when

κ À 1, the molecular Stokes’ shift disappears and line lineshape becomes Lorentzian.

3.4 Simulations Involving the 3PEPS

If g(t) is known, then the coupling to the bath of nuclear motions can be elucidated.

Linear spectroscopies do not uniquely reveal the microscopic form of g(t) owing to the

complicated interplay of phenomena at different timescales - fluctuations of the bath

and intramolecular vibrational modes. [62, 133] Photon echo spectroscopies, however,

are well-suited to providing insights into g(t) via a correlation function.

The 3PEPS experiment gives us the information that is contained in the three pulse

photon echo (3PE) signals in a compact form. 3PEPS reveals information about the

timescales of dephasing and is sensitive to a correlation function. In order to understand

the rather complicated data, we must perform computer simulations. However, it is

possible to interpret the 3PEPS data qualitatively. Disorder in the system is manifested

in the 3PEPS data as an asymptotic peak shift, as the system always retains some

memory of the initially prepared state. Although influenced by pulse-width and solvent

effects, a higher initial peak shift is associated with weaker coupling, as shown in

figure 3.6. Increasing the coupling to the bath, λ, changes the value of the asymptotic

39


14

12

10

8

6

4

2

0

Pea

k S

hift

(fs)

101

102

103

104

Population Time (fs)

Figure 3.6: Example of 3PEPS data. The peakshift provides a measure of the in-homogeneity of the frequency distribution. Strong coupling to the bathincreases the homogeneous broadening, correspondingly reducing the peak-shift. These data were simulated using the full response function. The solidline are 3PEPS data simulated using an exponential M(t) with τe = 100 fsand λe = 900 cm−1. To demonstrate the effect of disorder in the system,a static Gaussian contribution is added to the same M(t), with σ = 1000cm−1. This simulated 3PEPS data are shown by the dotted line. Note thatnow a long-time, asymptotic peak shift is evident. The effect of increasedcoupling to the bath is demonstrated by simulating the 3PEPS data withthis same M(t), but now with λe = 1100 cm−1. There is a decrease in theinitial peak shift and the asymptotic offset (dash-dot line).

peakshift, but, more significantly, it reduces the initial peakshift.

The relationship between asymptotic peak shift and T , the population time, can be

understood using the following equation for the asymptotic peak shift: [35]

τ ∗(T →∞) =σ2

in

√Γ + σ2

in + λ2

√π[Γ(Γ + 2σ2

in + λ2) + σ2inλ

2] (3.15)

where Γ = 2λ/(hβ) and β = 1/kT . λ is the total reorganization energy divided by

h. σin is the static inhomogeneity of the system. When σin 6= 0 a non-zero peak shift

40


is observed. It can also be shown that the peak shift decays as M(t), the correlation

function for fluctuations of the electronic energy gap, in the absence of static inhomo-

geneity. [35,39] Figure 3.6 shows that if static disorder is included in a simulation, the

peak shift is, indeed, non-zero.

Figure 3.7 shows simulated data for absorption lineshapes and 3PEPS decays gen-

erated by varying the couplings and timescales. The continuous change of lineshape

from Gaussian to Lorentzian is evident when comparing the broadest peak to the nar-

rowest. Increasing the coupling broadens the absorption lineshape appreciably while

decreasing the initial peakshift. In the slow modulation (inhomogeneous) limit, there

is inhomogeneity on the timescale of the experiment. Thus, increasing the timescales

(making the bath “slower”) is observed as an inhomogeneous broadening of the absorp-

tion spectra. An asymptotic peakshift is observed when in the static inhomogeneity

limit, that is, there is disorder in the system. In simulations of polymer relaxation,

I include the conformational disorder (causing inhomogeneous line broadening) as a

constant since the magnitude of the disorder is essentially static on the time scale of

the experiment.

3.5 Experimental Section- How the Experiment was

Actually Done

A Ti:sapphire regeneratively amplified laser system that generates ∼140-fs pulses at

775 nm and 1 kHz repetition rate was used to pump a tunable nonlinear optical para-

metric amplifier (NOPA). The tunable visible output of the NOPA was used for ex-

citation. [138] The excitation wavelength was centered on the absorption peak of the

sample. (However, other wavelengths are used for comparison.) Low excitation in-

tensity was controlled by using a half-wave plate/polarizer combination. Two quartz

prisms were used to precompensate for dispersion. The duration of the resulting pulse

was measured by autocorrelation of the intensity FWHM of the sum frequency genera-

tion in a 50 µm BBO crystal (assuming a Gaussian pulse shape) at the sample position.

41


Figure 3.7: Simulation of (a) absorption and (b) 3PEPS data in the high temperaturelimit using the Brownian Oscillator model. The line broadening functionis given in eq. 3.14. The broadest peak, the dotted-dashed line to λ =250cm−1 and Λ−1 ≈ 1060 fs (κ ≈ 0.015) and the narrowest, the dotted linecorresponds to λ = 25cm−1 and Λ−1 ≈ 11 fs (κ ≈ 5.0). The bold black lineis simulated using λ = 25cm−1 and Λ−1 ≈ 1060 fs (κ ≈ 0.05). The blackline corresponds to λ = 250cm−1 and Λ−1 ≈ 11 fs (κ ≈ 1.5). Increasedcoupling to the bath is seen as a lowering of the initial peakshift and abroadening of the absorption lineshape. Short timescales give rapid decaysof the peakshift and narrow absorption spectra. The absorption maximaare set at 495 nm.

42


The laser spectrum was measured using a CCD spectrometer.

3PEPS measurements were performed using three beams of equal intensity ( ∼ 5 nJ

/beam at the sample). The three S-polarized beams were aligned to form an equilateral

triangle (1 cm sides) [1] and were focused into the sample using a silver-coated spherical

mirror (f = 25 cm). Two beams were independently delayed to scan pulse delays from

negative τ , pulse sequence k2,k1,k3, to positive τ , pulse sequence k1,k2,k3, such that

the population time T is fixed between pulses 1 and 3 at τ < 0 and then between 2

and 3 at τ > 0. The set-up and pulse sequence are shown in figure 3.8.

The temporal overlap between the three pulses was set initially by autocorrelating

each of the three pulse pairs. Accurate T = 0, and τ = 0 stage positions were set ac-

cording to overlap of the pulses in the sample by measuring all three three-pulse echo

signals and using the symmetry of the echo signals along the τ time axis. The time

delay between pulse 1 and 2 was set using −k1 +k2 +k2 and k1−k2 +k3 signals. The

delay between pulse 2 and 3 was set using k1− k2 + k3 and k1 + k2− k3 signals. The

echo signals are symmetric along the τ axis at room temperature, so the peak shift τ ∗

for each τ -scan at a fixed T was accurately determined by taking half the separation

between the peaks of the Gaussian fits for the two signal directions.

3.6 Polarization Anisotropy Experiments

Polarization anisotropy experiments are useful in determining the extent of exciton

migration (as evidenced by a rotation in the transition dipole moment) in samples like

conjugated polymers. When a system of randomly oriented polymer chains interacts

with polarized light, only those chromophores with absorption transition moments with

non-zero vector projection onto the exciting electric field vector will absorb light. That

is, when the sample is excited by polarized light, the dipole will be oriented (at least

partly) in the direction of polarization. Measurement of the signal in the perpendicular

polarization provides a measure of the degree of dipole moment rotation. The rotation

of transition dipole moment in a conjugated polymer sample is illustrated in figure 3.9.

The polarization anisotropy is defined as [140]:

43


from NOPA /compressor

sample

POL HWP

BS-67% BS-33%

BS-0%

focusing

mirror

delay: k3 delay: k2 fixed: k1

-k1+k

2+k

3k1-k2+k

3

1+k

2-k3

k2

k1

k3

3PE

t1

t

t2

k

Figure 3.8: Experiment setup and pulse sequence for the 3PEPS experiment. POLrefers to a polarizer; HWP refers to half wave plate; BS refers to beamsplitter. See the text for further details.

44


polarized

excitation

partially depolarized

emission

depolarizes the

transition dipole

E*E*

exciton migration

Figure 3.9: Schematic of the depolarization by energy migration in conjugated poly-mers. Figure after ref. [139]

45


r =I‖ − I⊥I‖ + 2I⊥

(3.16)

where I‖ is the signal intensity when the observing polarizer is parallel to the excita-

tion source. When the polarizers are perpendicular, the obtained signal is I⊥. This

expression can be used for a wide variety of experiments that probe the polarization

dependence of chromophore optical response. Fluorescence up-conversion and pump-

probe spectroscopy are popular examples.

The anisotropy of an ensemble of chromophores is given by [140]

r0 =2

5

(3 cos2 θ − 1

2

)(3.17)

where θ is the angle between the absorption and emission dipoles. When looking at

the depolarization as a function of time, the anisotropy, r, tells about the average

rotation of the dipole moment during the course of the experiment. Equation 3.17

includes the effect of photoselection. That is, the chromophores with dipole moments

best aligned with the axis of polarization will be excited with the highest probability.

Because scattered light is completely polarized, θ = 0 and r0 = 0.4. This is also the

theoretical value for two-level systems at zero delay time between pump and probe in

the transient absorption experiment (commonly referred to simply as pump-probe) for

linear transitions.

3.6.1 Pump-Probe as a Measure of Depolarization

Pump-probe spectroscopy has been applied successfully to the investigation of ultrafast

processes in a variety of relevant systems including dyes, light harvesting pigments and

conjugated polymers. [141, 142] The temporal evolution of the depolarization process

can be monitored as a function of the delay between the pump and probe pulses.

The depolarization of dipole moments is often studied in conjugated polymers as

it yields useful information on the dynamics of exciton migration in both films and

solution. [47,101]

46


Following excitation for a model two-level system in dilute solution, the anisotropy

decay follows an exponential decay:

r(t) = r0 exp(−t/τrot) (3.18)

where the decay only depends on the rotational correlation time, τrot. In more complex

systems, the anisotropy may be fit to a sum of exponentials, the time constants of

which correspond to the different processes contributing to the decay, such as energy

transfer. In larger molecules, including proteins and polymers, the rotational diffusion

contribution to the anisotropy decay is negligible compared to other, much faster, de-

cay processes.

In the pump-probe experiment, the system interacts twice with the first pulse. Re-

ferring to the Feynman diagrams in figure 3.4, this is equivalent to the first time delay

being set to zero, with the appropriate adjustment of wavevectors. Since the first two

interactions are with the same pulse, they necessarily have the same wavevector. Thus,

the signal is radiated in the −k1 + k1 + k3 = k3 phase matching direction where k3 is

the wavevector of the probe pulse [39]. In this experiment, the third-order polarization

is heterodyned against the probe pulse which acts as a local oscillator. In this way,

the detected signal is different than in the 3PEPS or other homodyned third order

spectroscopies where the signal is proportional to the third-order polarization squared

(cf equation 3.1).

The signal intensity is linear with respect to the third-order polarization:

I(T ) ∝∫ ∞

−∞dt′{|Epr(t

′) + E(3)(t′)|2 − |Epr|2}

= 2 Im ωpr

∫ ∞

−∞dt′Epr(t

′)P (3)(0, T, t′) (3.19)

where Epr(t′) is the time-dependent electric field associated with the probe pulse. To

measure the anisotropy, the pump beam was vertically polarized. The probe polarizer

was set to 45◦ and a polarization cube before the detectors allowed for simultaneous

measurement of the parallel (VV) and perpendicular (VH) signals. The decay of the

difference between the two signals is normalized by the isotropic response (equivalent

47


to the signal at the magic angle) as in equation 3.16. Thus, population dynamics do

not influence the anisotropy decay.

3.7 Summary

In this chapter, I have outlined the experiments that I have used to examine the

photophysics of conjugated polymers. The techniques and the theoretical framework

necessary to understand and compare these experiments was discussed. Some examples

of simulated data were presented. Later chapters will use this framework to interpret

experimental data.

48

4 MEH-PPV and Disorder and all that Jazz

In this chapter, investigations of the origins of line broadening and excited state dynam-

ics for the conjugated polymer poly[2-methoxy,5-(2-ethyl-hexoxy)-1,4-phenylenevinylene]

(MEH-PPV) and a model pentamer, p-bis{[o,m-di(2-ethylhexy)oxy-p-methylstyryl]styryl}benzene are reported (structures shown in fig 1.1). The time-integrated three-pulse pho-

ton echo peak shift (3PEPS) experiment is employed to elucidate dephasing, spectral

inhomogeneity arising from conformational disorder, and dynamical processes, other-

wise obscured by ensemble averaging. I progressively discuss three dynamical models

to describe the experimental data. The multiphonon model describes coupling of the

electronic transitions to high frequency vibrational modes, and is able to fit the absorp-

tion spectra well, highlighting the importance of a distribution of conjugation length.

However, it fails to model the 3PEPS data. A two-level system approach is found

to reproduce the absorption lineshapes as well as 3PEPS data, however, it cannot si-

multaneously describe the fluorescence data as the homogeneous line width is grossly

overestimated. In light of these analyses, we propose the three-stage relaxation model,

that (1) describes absorption into delocalized states that arise from electronically cou-

pled conformational subunits; (2) explains the fast decay of the 3PEPS data as a rapid

dynamic localization/self-trapping of excitation; and (3) provides a homogeneous line

broadening that is consistent for both the absorption and fluorescence processes. Si-

multaneous modeling of the 3PEPS, absorption, and fluorescence data, establishes a

consistent picture to understand the line broadening, dephasing mechanisms, and ex-

cited state dynamics for conjugated polymers and oligomers.

49


4.1 Results

Absorption and photoluminescence spectra of dilute MEH-PPV and pentamer solu-

tions (chlorobenzene solvent) at room temperature are shown in figure 4.1. Both the

pentamer and MEH-PPV have broad, unstructured absorption bands and narrower,

structured fluorescence spectra. The maximum of the absorption band of the pentamer

solution is located at ∼ 435 nm (2.85 eV) while the apparent Stokes’ shift between the

absorption and fluorescence band peaks is ∼ 2600 cm−1 (322 meV). MEH-PPV has a

broader, redshifted absorption band compared to the pentamer. The absorption max-

imum is at ∼ 500 nm (2.48 eV) in chlorobenzene, the apparent Stokes’ shift is ∼ 2330

cm−1 (289 meV). The similarity of the spectra for the two samples suggests that the

primary origins of the line broadening in the absorption spectra do not differ greatly.

This is somewhat surprising given that static inhomogeneity reflecting conformational

disorder is anticipated to contribute significantly to the MEH-PPV absorption spec-

trum. This conformational disorder is further discussed in section 4.3.

Room-temperature absorption and photoluminescence spectra of dilute MEH-PPV

solutions (THF, toluene, chlorobenzene solvents) and an MEH-PPV film cast from

chlorobenzene are shown in figure 4.2. The spectra exhibit the broad, unstructured

absorption bands and narrower, structured fluorescence typical of this class of conju-

gated polymers. The peaks of the film spectra are significantly broader than those

of the solution. The lineshapes are quite similar in all of the solutions, the primary

difference being that the transition energy gap decreases from THF, to toluene, to

chlorobenzene (most red-shifted). The film spectra are markedly red-shifted versus

the solutions, especially the fluorescence. The absorption maxima are located at 495

nm (20240 cm−1), 498nm (20080 cm−1), 499 nm (20040 cm−1), and 504 nm (19840

cm−1) for THF, toluene, chlorobenzene solvents and the film, respectively. The appar-

ent Stokes’ shift between the absorption and the fluorescence maxima are 2220 cm−1,

2140cm−1, 2230 cm−1, and 2970 cm−1 for THF, toluene, chlorobenzene solvents and

the film, respectively. The film shows a notably larger apparent Stokes’ shift than

the solutions. In aligned films, the Stokes’ shift increases further and the absorption

red-shifts by about 0.1 eV, indicative of better conjugation. [143,144]

50


Abs

orba

nce

(arb

. uni

ts)

700600500400Wavelength (nm)

Photolum

inescence (arb. units)

Figure 4.1: Absorption and photoluminescence spectra of MEH-PPV (a) and pentamer(b) in chlorobenzene solution. Slit widths were 1.5 nm. Excitation wave-lengths were 520 nm and 450 nm respectively.

51


Abs

orba

nce

(arb

. uni

ts)

700600500400Wavelength (nm)

Photolum

inescence (arb. units)

Chlorobenzene Solution

THF Solution Toluene Solution Film

Figure 4.2: Experimental absorption and fluorescence spectra for dilute MEH-PPV so-lutions and film. The film is significantly red-shifted and broadened withrespect to the solutions. This is attributed to both the presence of low-energy aggregates and more efficient energy transfer which red-shifts thefilm fluorescence.

52


The time integrated 3PE signal is measured by scanning the time delay τ . The

maximum of this signal for each experimentally controlled population time T is found

for a coherence time (first time delay) labeled τ ∗(T ). The behaviour of τ ∗(T ) is closely

related to the transition frequency correlation function M(t). [35,39] The form of M(t)

provides a useful means of characterizing the bath and will be discussed below. 3PEPS

data τ ∗ versus population time, T for the pentamer and MEH-PPV in chlorobenzene

solution are plotted in figure 4.3. The amplitude of the peak shift data for both pen-

tamer and MEH-PPV rapidly decays within T = 500 fs, attaining a persistent offset

at a population time of 5 ps. It is clear that MEH-PPV has a higher asymptotic offset

than that of pentamer. This result is reproducible under different sample, pulse-width,

and experimental setup conditions. The nonzero persistent peak shift is attributed

to the degree of structural defects along the conjugated backbone. Looking at the

T < 500 fs population time region, it is evident that the pentamer 3PEPS data decays

more slowly compared to MEH-PPV. The clear and slowly diminishing oscillations in

the pentamer 3PEPS data are due to the coherently excited intramolecular vibrations

that are weakly damped by the bath. The oscillations for MEH-PPV are washed out

by many averaged excited vibrational modes since the frequency of these vibrations

depends on the size of the conformational subunits. [145,146] That is, there is inhomo-

geneous dephasing.

In all of the experiments performed, solutions of MEH-PPV and pentamer in chloroben-

zene were filtered to remove insoluble impurities. The absorbance was adjusted to be

∼ 0.2 in a 100-µm cell. The solutions were circulated through a 100-µm path length

flow cell using a gear pump. The film was spin-cast from a solution of MEH-PPV in

chlorobenzene onto a quartz slide. All measurements reported here were conducted at

294 K. Chlorobenzene, tetrahydrofuran (THF) and toluene (spectroscopic grade) were

obtained from Aldrich Chemical Company. MEH-PPV was purchased from Aldrich.

The model pentamer was provided by Prof. Lewis Rothberg, University of Rochester

and was synthesized by Mary Galvin.

Experimental 3PEPS data for solutions in various solvents and the film are plotted

in figure 4.4. The MEH-PPV solutions all have higher initial peak shifts and asymp-

totic offsets than the film. The peak shift of the film decays to zero at long population

53


Figure 4.3: 3PEPS data, τ ∗ vs population time for the pentamer (a) and MEH-PPV(b) in chlorobenzene. Solid lines are simulated data using the three-stagerelaxation model (equation 4.20). The insets show the same data on a logscale.

54


10

8

6

4

2

0

Pea

k S

hift

(fs)

101

102

103

104


Chlorobenzene Solution

THF Solution Toluene Solution Film

Figure 4.4: Room temperature 3PEPS data for dilute solutions of MEH-PPV and filmcast from chlorobenzene. The solutions attain a persistent off-set at ∼ 5ps, owing to conformational disorder. In the film, the initial peak shift islower and peak shift decays to zero, indicative of strong electronic couplingand efficient energy transfer.

times. The long-time peak shift is associated with the degree of structural defects along

the backbone and whether all states of the ensemble are sampled by energy migration

within a given population time. The amplitude of the peak shift decays rapidly and

attains a persistent offset at a population time of ∼ 5 ps for the solutions. This is

indicative of persistent disorder in the system. The peak shift for the film decays to

zero because of efficient interchain energy transfer, which allows the system to sample

all of the electronic states, some of which are not accessible to the isolated polymer in

solution. It is important to model these data in order to further interpret their meaning.

55


4.2 The Stokes’ Shift

There has been much investigation into the non-mirror image relationship between ab-

sorption and fluorescence and the large difference between the absorption and emission

maxima observed in conjugated polymers. In the following section, I will introduce

three major contributors to the apparent Stokes’ Shift, some of which also affect the

mirror image/lineshape, and which can be examined using different spectroscopic tech-

niques. They are the true molecular Stokes’ shift arising from exciton-bath coupling,

an ultrafast localization component, and spectral diffusion through energy transfer.

4.2.1 Molecular Stokes’ Shift and Spectral Diffusion

The coupling of electronic transitions to a bath of fluctuating nuclei in any chromophore

effects line broadening and the Stokes’ shift. Often we consider the characteristic

timescales of bath fluctuations to label line broadening as homogeneous or inhomoge-

neous. Homogeneous line broadening results from a fluctuating frequency distribution

on a fast timescale; inhomogeneous broadening denotes an effectively static frequency

distribution. It is also illustrative to consider the spectral density, to gain insight into

the connection between reorganization energy and the Stokes’ shift via fluctuation-

dissipation. This spectral density is essentially the distribution of timescales (frequen-

cies) weighted by coupling constants. [132]

The energy gap for an electronic transition of a chromophore is influenced by the

fluctuations in the environment and the chromophore itself. Assuming that the fluc-

tuations are similar for all chromophores in the system, the time-dependent Stokes’

shift

S(t) =〈δVSB(t)δVSB(0)〉

〈δV 2SB〉

(4.1)

with δVSB as the system-bath fluctuation, can be expressed in terms of the spectral

density as follows [38]

S(t) = h/λ

∫ ∞

0

dωρ(ω) cos ωt (4.2)

56


500

400

300

200

100

0

Spectr

al D

ensit

y

1000080006000400020000

Frequency

Figure 4.5: Spectral density obtained using simulation parameters listed in table 4.1for MEH-PPV in chlorobenzene solution.

where ω is the frequency of the fluctuations, ρ(ω) is the spectral density. The spec-

tral density calculated using the simulation parameters for MEH-PPV shown in table

4.1. is plotted in figure 4.5. λ is a renormalization constant which is identical to the

reorganization energy

λ = h

∫ ∞

0

dωωρ(ω) (4.3)

The lineshape function can be expressed in the frequency domain as [35,133]

g(t) = −iλt/h +

∫ ∞

0

dωρ(ω) coth[hωβ/2

](1− cos ωt) + i

∫ ∞

0

dωρ(ω) sin ωt (4.4)

where β = 1/kt.

These expressions yield the Stokes’ shift and lineshapes in the absence of energy

transfer and generally pertain to isolated chromophores. Clearly, there is a fundamental

relationship between homogeneous line broadening and the Stokes’ shift (2λ). On the

other hand, inhomogeneous line broadening does not contribute to fluctuations of each

57


chromophore transition frequency and therefore does not affect the Stokes’ shift. In

order to obtain molecular Stokes’ shifts in more complex systems such as conjugated

polymers, special spectroscopic techniques must be used. For example, by selectively

exciting only the red-most chromophores, site selective fluorescence techniques reveal

the molecular Stokes’ shift, unaffected by spectral diffusion associated with energy

transfer. [17,88,147]

4.2.2 Coupled Chromophores and Dynamic Localization

The ideas of localization and delocalization of electronic states [148,149] are known to

be important in the study of photosynthetic systems. I will demonstrate in this chapter

that they also play a role in the photophysics of conjugated polymers. The absorp-

tion of excitation onto the B850 band of the light harvesting complex LH2 of purple

bacteria and the subsequent localization onto a single dimer pair is an illustrative ex-

ample. [150] In this well studied system, there have been numerous experiments and

discussions as to the extent of delocalization observed. The answer seems to be that

different experiments interrogate different timescales and thus show different degrees

of localization of excitation. It has been calculated that there are strong electronic

couplings between the 18 chromophores in the B850 band and thus absorption excites

excitonic states. Circular dichroism experiments (CD) provide an incisive probe of the

instant of excitation, and thus absorption of a photon into delocalized states of the

B850 ring, for example. In fact, in order to account for experimentally determined CD

spectra, delocalization over at least half the ring system is required. [151, 152] On the

other hand, the extent of delocalization is found to be much less when calculating the

superradiance from fluorescence experiments in the same systems. [153] Fluorescence

measurements are sensitive to timescales on the order of the fluorescence lifetimes,

suggesting a localization of excitation before emission. It is predicted, therefore, that

emission would occur from localized states while absorption is into delocalized exciton

states. [154] In MEH-PPV , where there is significant coupling between subunits, on

the order of ∼ 100 cm−1, it is reasonable to expect that absorption is into collective,

delocalized states. Also, given the much larger disorder, which tends to localize exci-

58


tation, in MEH-PPV than in the quite ordered LH2 system, dynamic localization is a

reasonable expectation.

The 3PEPS experiment has a sufficiently large dynamic range to be sensitive to

all of these timescales. [36–43, 127–130, 155] We are, therefore, able to monitor the

dynamics of localization as well as other, slower processes, such as resonance energy

transfer. [156,157]

4.2.3 Resonance Energy Transfer

There are two distinct regimes of energy transfer important to the study of conju-

gated polymers. The first is the rapid localization, already discussed, whose associ-

ated spectral diffusion gives rise to part of the apparent Stokes’ shift. The second,

slower process is likely to operate via a generalized-Forster mechanism where energy is

transferred from a localized excitation on the donor to a delocalized “aggregate chro-

mophore” state. [102, 158–160] Owing to the separation of timescales, energy transfer

(from donor chromophore to delocalized aggregate acceptor) occurs well after the ini-

tial localization of excitation. Multiple energy transfer to delocalized acceptor and

subsequent localization steps may occur before fluorescence is observed from excitation

localized on the lowest energy chromophores in the system. [17,88,147]

4.3 Simulation of the data

I have simulated the data using three models. The multiphonon model gives a phys-

ical picture of conjugated polymers and conformational subunits. It is able to fit the

absorption lineshape. However, this model, in its present form, is unable to fit the

3PEPS, reinforcing the issue of the insensitivity of linear absorption to the origins of

line-broadening. To simulate the 3PEPS and absorption simultaneously, we have used

a two-level electronic system approach derived from studies of solvation. However, this

approach does not satisfactorily fit the fluorescence lineshape. To incorporate spectral

59


diffusion through the inhomogeneously broadened density of states, we move to the

three-stage relaxation model. Within this model, we are able to simulate the 3PEPS

signal as well as the absorption and fluorescence lineshapes.

4.3.1 Multiphonon Model

Previous work suggests that the distribution of conjugation lengths of phenylene-based

molecular systems is determined by conformational disorder in the system and that

the distribution function is Gaussian [30]. In this section, we present and discuss the

simulations of the absorption spectrum of MEH-PPV by a theoretical approach [30]

that is derived from molecular radiationless transition theory. [161,162] The simulation

of absorption is based on the properties of each conjugation segment which, when

superimposed, form the MEH-PPV absorption profile. [163] A Gaussian distribution

function was assumed on the basis of quantum chemical calculations and because it

fit the experimental data better than an exponential distribution. [30] In the Frenkel

exciton theory, a conjugated system with N units can have energies

El = E0 + 2β( πl

N + 1

)(4.5)

where l = 1, 2, ...N , E0 is the energy of excited state of each unit and β is the interaction

strength between nearest-neighbour conjugation units. The corresponding transition

dipole moment is

|~µlN | =

2|~µ|2N + 1

[cot

( πl

2N + 2

)]2

(4.6)

where the monomer dipole moment |~µ|2 = 1. The absorption coefficient αeg(ω) for the

electronic transition g → e of each conjugation segment is given by

αeg(ω) =2πω

3ach|µeg|2

∫ ∞

−∞dt exp

[it

h(Ee − Eg − hω)− 1

2d2t2

]

× exp[−∏

j

Gj(t)] (4.7)

60


where µeg denotes the electronic transition moment; a is the factor which describes the

medium effect; c is the speed of light; d is the width of inhomogeneity of electronic

states, and here∏

j Gj(t) corresponds to the lineshape function, which is defined via

Gj(t) =2βjβ

′′j sinh(hωj/2kT )

sinh λj sinh µ′′j× (4.8)

exp[− β2

j β′′2j ∆2

j/[β′′2j coth(λj/2) + β2

j coth(µ′′j /2)]]

[β′′2j coth(µ′′j /2) + β2j coth(λj/2)]1/2[β′′2j tanh(µ′′j /2) + β2

j tanh(λj/2)]1/2

In equation 4.9, βj = (ωj/h)1/2, λj = itωj + hωj/2kT , µ′′j = −itω′′j , where ωj and

ω′′j are the oscillator frequencies of the jth mode in the electronic states g and e,

respectively, ∆j denotes the normal coordinate displacement which is chosen so that the

conjugation length (N) dependent Huang-Rhys factor Sj = ωj∆2j/2h = ai + bi/(N +1)

with ai and bi being adjustable, as described by Chang et al.. [30] We take the Gaussian

function D[N ] deduced from the disorder to describe the distribution of conjugation

segments of MEH-PPV backbone with center N0 and width Bav as fitting parameters.

In our calculation, the best fit for the absorption spectrum of MEH-PPV gives us

N0 = 5 and Bav = 6.3.

D[N ] = B− 1

2av exp

[− (N −N0)2/Bav

](4.9)

Thus, the molecular absorption coefficient for MEH-PPV is given by

α(ω) =∑N

D[N ]αeNgN(ω) (4.10)

The calculated absorption spectrum of MEH-PPV is shown in figure 4.6 with contri-

butions from conjugation segments consisting of one to nine subunits compared with

experimental data. As in Ref. [30], the blue tail of the absorption spectrum is fitted by

choosing 1400 (1550), 700 (700), and 200 (200) cm−1 for the three vibrational modes

of the ground (excited) state of each conjugation segment. The slight discrepancy be-

tween the experimental data and the simulation is probably due to underestimating the

contribution from the short conjugation length segments in the Gaussian distribution.

61


1.6 104

1.8 104

2 104

2.2 104

2.4 104

2.6 104

Norm

aliz

ed a

bsorb

ance

Wavenumber (cm-1

)

Figure 4.6: Simulation of MEH-PPV absorption lineshape by the multiphonon model(equation 4.10.) (Dotted line). Solid line is experimental data for dilutesolution in chlorobenzene.

The width of inhomogeneity d is taken as 900 cm−1 for all segments.

The multiphonon model can fit the absorption lineshape well. However, the cal-

culation of Gj(t) includes only high frequency modes, since we do not have detailed

information on the distribution of low frequency torsional modes. This means that the

homogeneous broadening, influenced by low frequency modes in the spectral density,

is not taken into account in this model. Thus the lineshape function∏

j Gj(t) of Eq.

4.9 cannot fit our 3PEPS data to obtain the line broadening response function, which

is indispensable to differentiate between homogeneous and inhomogeneous broaden-

ing. Moreover, there seem to be subtleties missing from the multiphonon model, in

its present form, that are necessary to understand the pentamer data. The following

two-level electronic system approach allows this differentiation by describing these low

frequencies in the bath spectral density according to a Brownian oscillator model.

62


4.3.2 Two-level electronic system approach

Assuming that the coupling between the electronic transition of each conjugation seg-

ment is coupled to a bath of nuclei which are undergoing Brownian motion, we use

a two-level electronic system to model the chromophore-bath system. The theoreti-

cal treatment of third-order nonlinear optical signals has been described elsewhere in

detail [133,135] and briefly in chapter 3. The basis for our model to describe the pho-

tophysical properties of MEH-PPV, or any conjugated polymer with conformational

disorder, is to consider each polymer chain as consisting of a series of conformational

subunits. Each of these conformational subunits acts as a chromophore i in the zeroth-

order picture. At this point in the model we can define the excitation frequency of each

conformational subunit as the sum of an average transition frequency for the ensemble

〈ω〉 and a static offset,εi, from this mean that designates the difference between the

transition frequency ωi of chromophore i from the mean.

ωi = 〈ω〉+ εi (4.11)

The distribution of ωi reflects the distribution of conjugation lengths in the polymer

at the time of absorption- inhomogeneous line broadening. This model is expanded

to accommodate the homogeneous line broadening by adding a fluctuating frequency

component δωi(t) so that

ωi(t) = 〈ω〉+ δωi(t) + εi (4.12)

The time-integrated 3PE signal S(T, τ) measured in the laboratory is expressed in

terms of response functions R(t, T, τ) which generate third order polarizations, [133]

with τ being the time delay between the first two pulses (the coherence period), T the

time delay between the last two pulses (the population period) and t the time evolution

of nonlinear polarization after the third pulse:

S(T, τ) =

∫ ∞

0

dt∣∣∣P (3)(t, T, τ)

∣∣∣2

(4.13)

63


For a 3PEPS experiment, the peak shift τ ∗(T ) at a particular time T is defined as the

coherence time at which the integrated echo signal is a maximum. The behaviour of

τ ∗(T ) is closely related to the transition frequency correlation function M(t). [35, 39]

We must use a correlation function formalism in order to properly fit/simulate 3PEPS

data, simple fitting to a multiexponential decay is not sufficient.

From this correlation function, we obtain absorption and fluorescence lineshape func-

tions:

σA(ω) =

∫ ∞

−∞dt exp

[− i(ω − ωeg)t

]exp

[− g(t)

](4.14)

σF (ω) =

∫ ∞

−∞dt exp

[− i(ω − ωeg + 2λ)t

]exp

[− g∗(t)

](4.15)

In order to obtain information concerning the amplitude and time scales of the

fluctuations of the bath, as well as the inhomogeneity of the system, we have modeled

our data using the unnormalized correlation function M(t) as a sum of components as

follows:

M(t) =∑

λe exp(−t/τe) + λvib exp(−t/τvib) cos(ωvibt + φ) + σ2i (4.16)

where λe are the reorganization energies associated with exponential contributions that

model Brownian fluctuations with timescales (correlation times) τe; λvib is the reorga-

nization energy associated with the vibrational mode with damping time τvib. The

reorganization energy, λ is related to the amplitude of the fluctuations at temperature

T by:

λ =〈δω2〉2kT

(4.17)

The coupling of low-frequency vibrational modes to the electronic transition is taken

into account to fit the data according to exponential terms in equation 4.16. It has

been determined in previous analysis of Raman spectra that the low frequency mode

has large a Huang-Rhys factor S, and hence the sum of Sωvib controls the large ap-

parent Stokes’ shift of phenylenevinylene oligomers. [164] Leng et al. ascribe the low

frequency modes to torsional modes of PPV polymer and its derivatives [92]. In

64


general, the inertial motion in solvation is caused by the small angle free rotation of

a few solvent molecules, and has been shown to be well approximated by a Gaussian

component of M(t) [38,137,165]. We cannot include a Gaussian contribution to M(t)

and retrieve an acceptable simulation of the experimental 3PEPS data. The absence

of this component in the simulations of the polymer and pentamer is an indication

that dephasing in both these materials is not governed by solvation, but has a different

origin.

Static inhomogeneity owing to the distribution of conjugation lengths and isomers

derived from conformational disorder is assumed to follow a Gaussian distribution, and

is included in the correlation function according to a standard deviation σi. This is an

important contributor to broadening of the absorption lineshape, and as we will show

in the following section, helps to explain the different width in absorption and emission

spectra.

3PEPS data for the pentamer in chlorobenzene were found to be fit best by M(t)

with two exponential components λej exp(−t/τej), with λe1 = 170 cm−1 and τe1 = 25

fs; λe2 = 1130 cm−1 and τe2 = 690 fs. The sum of the coupling strength was fixed to be

1300 cm−1 according to the experimentally determined apparent Stokes’ shift for the

pentamer in chlorobenzene (2600 cm−1). The coherently excited intramolecular vibra-

tions were simulated as damped cosines λvib exp(−t/τvib) cos(ωvibt + φ), with λvib = 40

cm−1 and τvib = 4 ps, ωvib = 80 cm−1, and φ = 1.8 rad. The static inhomogeneity

required to reproduce the data was found to be σi = 1200 cm−1 The appearance of

slowly damped oscillations indicates weak coupling between electronic transition and

the solvent bath.

3PEPS data for MEH-PPV in chlorobenzene were modeled using the response func-

tion M(t), which is best represented by three exponentials λej exp(−t/τej). We obtained

λe1 = 250 cm−1 and τe1 = 5 fs; λe2 = 610 cm−1 and τe2 = 70 fs; λe3 = 300 cm−1 and

τe3 = 1 ps; The total coupling strengths were also constrained to be 1160 cm−1 in order

to equal half of the Stokes’ shift estimated from the difference in the peak maxima of

the absorption and emission spectra (1160 cm−1). The small offset shown in the data

required a static inhomogeneity: σi = 1000 cm−1. The vibrational contribution with

a frequency 80 cm−1 for the pentamer is assigned to torsional motion. Analogous vi-

65


brations are damped out in the polymer data owing to the superposition of vibrational

modes from the distribution of conjugation lengths.

Discrepancies between calculated and experimental spectra and the form of energy

gap transition correlation function prompted us to scrutinize contributions to the 3PE

signal. According to the 3PEPS data and simulations for either pentamer or MEH-

PPV, we conclude that any inertial solvation effect is insignificant. The huge coupling

strengths and very rapid time constants for all exponential components also exclude

diffusive solvation effects typical of dilute chromophore solutions. These observations

clearly differentiate the spectroscopy of conjugated polymers from that of rigid dye

molecules in solution, for example, rhodamine 6G. An important observation was that

using this two-level system model we were unable to fit the fluorescence lineshape,

which we should have been able to do, given the M(t) obtained from the 3PEPS ex-

periment.

It is well accepted that the torsional barrier around single bonds in conjugated chains

is very low (on the order of kT ), and the conformational rotation of a conjugation seg-

ment is strongly coupled to the electronic transition. Even in films, it is unlikely that

the torsions are completely frozen out, though they will be hindered. For example,

Tretiak et al. calculated energy profiles of ground and excited states of PPV conju-

gated polymers, and modeled the excited state of PPV by a planar structure relative

to a torsionally disordered ground state conformation [60]. Thus the large apparent

Stokes’ shift can be interpreted in terms of the conformational change upon excitation,

and hence the origin of fluctuation and relaxation of transition energies contained in

M(t) is mostly connected to these conformational changes. On the other hand, the

static offsets may represent an extremely long lifetime component that is also related

to different conformational changes, such as cis-trans transitions along polymer back-

bone. [59]

The time scales of correlation between conjugation segments that cause dephasing,

as well as the coupling between torsional motions and electronic transitions enter the

3PEPS signal. Therefore the dephasing processes of conjugated PPV oligomers and

polymers need to be further interpreted by a detailed model for third-order response

of a many-body disordered system. In the following section we describe how we can

66


implement this in a phenomenological model which captures the fundamental physics

of the exciton dynamics following photoexcitation.

4.3.3 Three-Stage Relaxation Model

It is apparent from the above analysis that the lineshape of MEH-PPV is poorly de-

scribed as a simple two-level electronic system coupled to nuclear motions of a solvent

bath. Thus, even individual conformational subunits, or the model pentamer, are very

much unlike typical chromophores in the condensed phase. We describe here a refined

physical model that explains all our observations. This model accounts for (1) ab-

sorption into delocalized electronic states; (2) implicit incorporation of the coupling of

fluctuations to electronic transitions, and therefore dynamic self-trapping of excitation;

(3) coupling to torsional motions and bath fluctuations that provide homogeneous line

broadening; (4) inhomogeneous line broadening owing to a distribution of conforma-

tional subunits. A particularly significant result is that different manifestations of (1)

and (2) in absorption, 3PEPS and other transient spectroscopies, [46] has, up to this

point, obfuscated analysis of excited state dynamics.

An understanding of conjugated polymers begins with a clear description of the

sources of inhomogeneous line broadening. The physical picture of the polymer is a

chain of “wormlike” conjugated segments separated by breaks in conjugation (caused

by a large dihedral angle). [25, 31] As a result, there is a distribution of conjugation

lengths, and for MEH-PPV the average value for conjugation length is approximately

seven repeat units. [30–33] The distribution of conjugation lengths is influenced by the

degree of conformational disorder in the system. [166]

Our experiments suggest that there is another type of disorder manifest in the ab-

sorption spectrum. This disorder, represented by standard deviation σ1, reflects a

set of delocalized states formed by Coulombic interactions between proximate con-

formational subunits, the simplest form being a dipole-dipole type interaction. For

polyindenofluorene, for example, intrachain electronic couplings are estimated to be in

the range 1 to 900 cm−1; depending on the length of the conformational subunits. [102]

Smaller conformational subunits couple more strongly than larger conformational sub-

67


units. Interchain couplings are larger owing to greater coupling between subunits with

favourable cofacial geometries. Thus it is not unreasonable to consider several coupled

conformational subunits to constitute a primary absorbing unit. This idea is examined

further in chapter 5.

However, we expect these delocalized states to be very short lived owing to the large

reorganization energies characteristic of individual conformational subunits. [50, 60]

The excitation is self trapped as a result of random nuclear fluctuations. Thus 3PEPS

decays according to localization of the excitation, driven by relaxation of a confor-

mational subunit. Fluorescence emission derives from a relaxed, equilibrated geome-

try. Thus we introduce the notion that conjugated polymers contain dynamic chro-

mophore/fluorophore units as a consequence of the strong dependence of electronic

structure on nuclear coordinates.

Within the framework of a three-stage relaxation model, the inhomogeneity seen in

an absorption spectrum is derived from two sources: σ1, an inhomogeneously broad-

ened density of exciton states and σ2, the conformational disorder. They are related

to the total inhomogeneity, Σ, by: [150]

Σ2 = σ21 + σ2

2 (4.18)

The two types of disorder are uncorrelated because they arise from different distribu-

tions. The conformational disorder, σ2, is a consequence of the distribution of confor-

mational subunits and their associated energies. σ1, on the other hand, arises from the

distribution of chromophores that are near to a given chromophore. It is the distri-

bution of coupling strengths to neighbouring chromophores which helps to determine

the manifold of exciton states. The density of states and conformational disorder are

shown in figure 4.7, which shows the extent of delocalization and labels the absorption,

localization and fluorescence stages of the dynamical evolution of conjugated polymer

excited states.

The absorption lineshape is governed by the correlation function:

M(t) =∑

λe exp(−t/τe) + λvib exp(−t/τvib) cos(ωvibt + φ) + Σ2 (4.19)

68


12

10

8

6

4

2

00 50 100 150 200 250

Population time, T (fs)

Peak s

hift, τ

* (f

s)

(a)

(b)

(c)

Absorption

3.5

3.0

2.5

2.0

Energ

y (

eV

)

2.5

2.0

1.5Fluorescence intensity

Energ

y (

eV

)

}

}

}

Σ

σ2

σ2'

�

�

�

Figure 4.7: Three Stage Relaxation Model. The three columns show (from left to right): aschematic of the extent of delocalization of the chromophore (dashed ellipse), atransition energy diagram, and corresponding experimental data for MEH-PPVin toluene solution. Absorption (a) occurs from the ground state (dashed line)into a delocalized exciton (over more than one subunit) state (solid lines), Σ beingthe standard deviation of the distribution of transition energies in this manifold.Subsequent to photoexcitation, there is spectral diffusion (b) through this densityof states which is associated with localization of excitation, leaving a smallerdistribution of transition energies, characterized by a standard deviation σ2. Thislocalization is driven by the large reorganization energy. σ1 is thus removed onthe timescale of this localization, while σ2 remains as the standard deviation ofthe inhomogeneous broadening associated with conformational disorder. We areable to observe this spectral diffusion as the rapid decay of the 3PEPS data.Lastly, fluorescence (c) occurs from a sub-set of the ensemble of localized states,narrowed as a result of resonance energy transfer. σ′2 represents the standarddeviation of such transition energies.

69


where the λe are the intramolecular reorganization energies for relaxation with timescales

τe. As used by Mukamel and others, and consistent with Kubo’s stochastic theory of

lineshape, we use an Ohmic spectral density and exponential M(t). [133,167,168] Simu-

lations showing the effect of coupling terms (reorganization energy, λ) and timescales,τ ,

are shown in chapter 3. Briefly, the larger the variance in the amplitude of fluctuation,

the larger the coupling to the bath/ reorganization energy. That is, when there is

stronger coupling, the bath fluctuations will have a larger effect. The coherent vibra-

tional component is damped out in MEH-PPV, but in general, λvib is the reorganization

energy of the vibrational mode with the damping time τvib. The large geometrical re-

organization associated with photoexcitation of conjugated polymers gives rise to the

homogeneous lineshape. Thus, we posit that homogeneous line broadening is dom-

inated by fluctuations due to the changes in geometry associated with the torsions

within conformational subunits. A key assumption in our analysis is that the homo-

geneous lineshape function—the exponential component in M(t)—is the same in each

measurement. Since absorption pertains to a delocalized excitation and 3PEPS and

fluorescence to localizing/localized excitation, this approximation amounts to assuming

the local and non-local fluctuations are correlated. A considerably more sophisticated

model is necessary to account properly for changes in g(t) during localization of exci-

tation. [169,170]

The change in geometry associated with photoexcitation of conjugated polymers and

oligomers gives rise to the homogeneous lineshape. For PPV oligomers, the transition

to a mainly planar excited state from a ground state with large torsional disorder [60]

can help to further explain the non-mirror image symmetry of the absorption and flu-

orescence lineshapes. There is less torsional disorder in the excited state owing to

the higher frequency of such modes as compared to the ground state [13, 75]. At a

given temperature, fewer of these modes will be populated in the geometrically relaxed

excited state. This large geometry change, which is also very likely observed upon

excitation of MEH-PPV and the model pentamer to the first singlet excited state, may

be viewed as a type of “reaction” as a function of nuclear degrees of freedom. [60,171]

Subsequent to excitation into a delocalized manifold of electronic states, ultrafast

relaxation, associated with localization of excitation, is observed in the 3PEPS experi-

70


ment. The ultrafast relaxation may be interpreted via a random walk within the inho-

mogeneously broadened density of states. [71] Chromophore fluctuations and dynamics

are related to a correlation function, to which the 3PEPS experiment is sensitive, by

the fluctuation-dissipation theorem. [172] Owing to the significant difference between

ground and excited state equilibrium geometries, an initially photoexcited conforma-

tional subunit is far from equilibrium. In response to that, the polymer backbone

relaxes through nuclear degrees of freedom into a new equilibrium position. There is a

concomitant change in intermolecular configuration. [73] Rather than simply “rolling

down” the potential energy surface, the fluctuations and small angle torsions are in-

strumental in the relaxation process. [173,174] This is manifested as the very fast decay

in this stochastic 3PEPS signal. To account for this rapid spectral diffusion we use the

phenomenological correlation function given by:

M(t) =∑

λe exp(−t/τe)+λvib exp(−t/τvib) cos(ωvibt+φ)+σ21 exp(−t/τloc)+σ2

2 (4.20)

The homogeneous contribution remains as in the absorption correlation function. The

relaxation through the distribution of delocalized states is a dissipative process, thus

the additional time-dependent component with amplitude σ21. Hence it is clear that

the inhomogeneity σ1 is removed by dynamic localization on a timescale τloc. The

inhomogeneity associated with conformational disorder is σ2, which is responsible for

the asymptotic offset in the 3PEPS data.

Fluorescence occurs from a small subset of localized states because energy migration

through the polymer transfers population to the larger conformational subunits. [16,

17, 49, 88, 147] Thus σ2 narrows to σ′2 prior to emission.The time-evolution of σ2 → σ′2is not accounted for explicitly in our simulations because it occurs on longer timescales

than we are focussing on. Simulation of the fluorescence also gives an upper limit for

the homogeneous broadening as it will be the same in the absorption and emission

spectra, ensuring that this is not overestimated as it has been previously [62,175]. The

fluorescence lineshape is determined by the correlation function:

M(t) =∑

λe exp(−t/τe) + λvib exp(−t/τvib) cos(ωvibt + φ) + σ′22 (4.21)

71


where the prime denotes fluorescence from a sub-set of the entire ensemble. This con-

formational disorder is much smaller than that required to fit the absorption lineshape.

In polymers, this may be attributed to resonance energy transfer from the shortest

chromophores to the longest (lowest energy) ones. [100] Thus, fluorescence is only ob-

served from this low energy subset of the entire ensemble of chromophores, narrowing

the distribution. The picture may be different in the pentamer. Fluorescence is still

observed only from a subset of the ensemble, but the origin of this subset can arise

from different processes. The poor photostability of the pentamer suggests that pho-

toproducts may be produced. Reaction with oxygen may form ketonic defects, which

have been shown to quench fluorescence by migration of energy to the defect. [176–178]

Thus, if those pentamers with defects do not fluoresce, the ensemble size of fluorophores

is effectively reduced.

Additionally, in order to fit the experimental data, keeping in mind our physi-

cal picture of the chromophores, high-frequency modes were added to the simula-

tions of the absorption and fluorescence lineshapes. They were incorporated using

the following equations for the area-normalized absorption and fluorescence lineshapes

[62,158,179,180]:

ai(ε) =

⟨ ∑i

Na|µi|2∑

k

P (k)×

Re

∫ ∞

0

dt〈k|k(t)〉 exp[i(ε− εk

i − λ)t/h]exp[−g(t)]

⟩ε/n (4.22)

fi(ε) =

⟨ ∑i

Nf |µi|2∑

k

P (k)×

Re

∫ ∞

0


i + λ)t/h]exp[−g∗(t)]

⟩ε3 (4.23)

where g(t) is the line broadening function, λ is the reorganization energy associated

with the Stokes’ shift, µ is the transition moment, εki is the transition frequency of the

ith chromophore adjusted for thermal population of the kth vibrational mode. It is

weighted by the Boltzmann weighting P (k). The time-dependent overlap of the initial

72


Table 4.1: Simulation parameters in the three-stage relaxation model for the pentamer(a) and the polymer (b).

a) Pentamer b) MEH-PPVλe, cm−1 τe, fs λe, cm−1 τe, fsλ1 = 250 400 λ1 = 210 85λ2 = 150 690 λ2 = 177 1500σ, cm−1 τloc, fs Σ, cm−1 σ, cm−1 τloc, fs Σ, cm−1

σ1 = 350 60 σ1 = 416 25σ2 = 455 574 σ2 = 425 595σ′2 = 175 σ′2 = 10

vibration k with its evolution in the excited state is represented by〈k|k(t)〉 and Nf (Na)

is a normalization constant. The angular brackets indicate an ensemble average over Σ

or σ′2 for the absorption and fluorescence, respectively. In the absence of high frequency

modes, these equations reduce exactly to Mukamel’s lineshape functions, equation 4.14

and 4.15.

With the three correlation functions in hand, we simultaneously fit the absorption,

fluorescence and 3PEPS lineshapes. The 3PEPS fits are shown in figure 4.3. The

parameters are listed in Table 1. The absorption and fluorescence fits are shown in

figure 4.8. The different timescales of relaxation shown in M(t) arise from a variety of

intramolecular interactions. The ultrafast component (1) observed in both MEH-PPV

and the pentamer may be attributed to the intramolecular motion of the chromophores

themselves, which has a direct effect on the conjugation of the π-electron system. Slower

relaxations (2) are due to slower, larger angle torsions and the rearrangement between

ground and excited state geometries. These resulting linewidths and Stokes’ Shifts

are calculated in the high temperature limit. However, a knowledge of M(t) permits

lineshapes to be calculated at any temperature.

Conformational disorder plays a role in the behaviour of the polymer, and even

the pentamer, via σ2. This was predicted previously,for oligomers that approach, or

are greater than, the conjugation length. [31] The three-stage relaxation model has

incorporated this effect, along with a distribution of exciton states, to simulate the

absorption, fluorescence and 3PEPS data simultaneously.

73


Figure 4.8: Simulation of absorption (equation 4.22) and fluorescence (equation 4.23)lineshapes using the three-stage relaxation model for MEH-PPV (a) and thepentamer (b). Dashed lines are simulated data. Solid lines are experimentaldata.

The simulations and experimental data for the 3 solutions and films are presented

in figures 4.9 and 4.10.

The high frequency modes (displacements) that were used in the simulations were 1600

cm−1 (0.2), 1200 cm−1 (0.9), and 700 cm−1 (0.2) for solutions in chlorobenzene, THF

74


Figure 4.9: Experimental and simulated absorption and fluorescence lineshapes. Dot-ted lines are experimental data. Solid lines are simulated using correlationsfunctions (equation 4.19 and equation 4.21) and high frequency modes.

and the film. 1600 cm−1 (0.2), 1250 cm−1 (1.0), and 700 cm−1 (0.2) were used for

the solution in toluene solvent. Chang et al. used similar discrete high frequency

modes when fitting the blue edge of MEH-PPV absorption and were attributed to C-C

double bond stretch, C-H deformation/ring stretch and a C-H out of plane bend, re-

spectively. [164]

The 3PEPS data and our analysis suggest two distinct regimes of energy migration.

The first, fast timescale, corresponds to the rapid localization of excitation. Small angle

rotations of the polymers may be instrumental in this relaxation. The origins of the

rapid relaxation are discussed further in chapter 5. Relaxation on a ≥ 1 ps timescale

likely represents resonance energy transfer to longer conjugation chromophores.

Larger angle torsions and rearrangements between ground and excited state geome-

tries can give rise to slower relaxations. It is likely that the middle timescale present

75


Figure 4.10: Experimental and simulated 3PEPS lineshapes. Dotted lines are experi-mental data. Solid lines are simulated using the correlation function givenin equation 4.20. It is difficult to fit the early time region due to pulseoverlap, where additional pathways can contribute to the signal.

in the solutions arises from a non-polar solvation effect. [43] This is the bath response

to changes in geometry of the probe chromophore when excited. Motion of the sol-

vent molecule centre-of-mass predominates. We are unable to fit the experimental data

using a Gaussian contribution to the lineshape function. [62] The Gaussian contribu-

tion is associated with inertial solvation (dipolar reorientation of solvent molecules) in

isolated chromophores. [36] Perhaps we are unable to observe such a Gaussian contri-

bution because the geometry change is large and the system is so far from equilibrium

that the bath response is no longer inertial and requires moving the bath molecules.

It is difficult to fit the early time of the 3PEPS decay. [169, 170] Previous studies

76


Table 4.2: Simulation parameters using the three-stage relaxation model for the MEH-PPV solutions and the film cast from chlorobenzene.

Solvent λe, cm−1 τe, fs σ, cm−1 τloc, fs Σ,cm−1

THF λ1 = 200 55 σ1 = 454 33λ2 = 155 900 σ2 = 390 599

σ′2 = 10chlorobenzene λ1 = 210 85 σ1 = 416 25

λ2 = 177 1500 σ2 = 425 595σ′2 = 10

toluene λ1 = 220 85 σ1 = 416 25λ2 = 177 1800 σ2 = 300 513

σ′2 = 80film λ1 = 280 100 σ1 = 542 25

λ2 = 300 1200 σ2 = 300 668σ′2 = 85

have shown that the simulation of the initial ∼ 50 fs of the 3PEPS data are more

significantly overestimated in polar solvents than in less polar solvents. Perhaps fur-

ther contributions to line broadening from solvent or thermal effects play a role on this

timescale. [43] Additionally, within the pulse-overlap region, many additional pathways

can contribute to the signal when the pulses are not properly time-ordered. Within

this region, coupling to high-frequency modes may also affect the signal.

4.4 Discussion

Compared to single molecules with two level states, the properties of conjugated poly-

and oligomers are quite different. The origin of the absorption lineshape lies in the

nuclear motion coupled to the electronic degrees of freedom. The collective properties

of the chromophores give rise to distinct features which differ from a superposition of

contributions from individual conjugation segments.

The 3PEPS experiment has been widely used to study solvation effects and dynam-

77


ics of proteins. [36–43, 127–130] In this work, the technique was employed to reveal

the similarities in conjugated polymer excited state dynamics in various solvents, in

direct contrast to the film, and a model oligomer. The similarities suggest further that

structural reorganizations within the polymer itself dominate the homogeneous line-

shape [62] rather than the interaction of the chromophores with the solvent bath which

is typical of isolated dye molecules in solution. The lineshape is closely tied to the

coupling of nuclear motion to electronic degrees of freedom. In the case of conjugated

polymers, the lineshape is not simply a superposition of contributions from individual

conformational subunits, but is comprised of distinct features which arise from the

collective properties of chromophore aggregates. For example, at the instance of exci-

tation, there is a large extent of delocalization in the excited state according to recent

Near-Field Scanning Optical Microscopy (NSOM) solvatochromism experiments. [16]

This is consistent with our picture of a manifold of delocalized excited states.

Although the multiphonon model can fit the absorption lineshape of MEH-PPV phe-

nomenologically, the lineshape function equation 4.9, in its present form, is not effective

when faced with the task of explaining the 3PEPS data. The reason is that we have

used a bath spectral density involving only discrete high frequency vibrational modes.

This is not representative of the actual spectral density of the conjugated polymers and

oligomers, since their electronic transitions appear to be strongly coupled to a distribu-

tion of low frequency intramolecular modes—presumably torsions. [147] Nonetheless,

this multiphonon model provides a clear connection to the coupling between electronic

transitions and intramolecular motions, that provides the most satisfactory explana-

tion for the homogeneous lineshapes retrieved from analysis of the 3PEPS data using

the three-stage relaxation model. Furthermore, if the multiphonon model is modified,

as described recently, [46] to include electronic interactions between conformational

subunits, then it becomes closely related to our three-stage relaxation model, however,

it must first be incorporated into the response function formalism to model the 3PEPS

data.

We noticed that the Gaussian distribution function used to model inhomogeneous

broadening may under-represent the shortest conformational subunits which contribute

to the blue edge of the absorption, causing a deviation from a Gaussian lineshape. This

78


is perhaps due to the fact that the shortest units can have greater oscillator strength

than their longer counterparts and therefore contribute more strongly to the absorption

spectrum. Some research has shown a distribution function with the shortest repeat

units most heavily weighted to be successful in simulation of the absorption spectra in

linear polyenes. [26,27] This is the function used when considering a chain with abrupt

breaks in conjugation only, rather than considering weakening of the conjugation by

small angle deviations from planarity. [25] Perhaps this would be a better representa-

tion and an improvement over the current model. The actual distribution is probably

a superposition of the two. However, the longer side chains on both MEH-PPV and

the pentamer would hinder movement more so than in the polyenes, leading to a dis-

tribution function somewhat less weighted toward the shortest chromophores.

The two-level system approach works well for other classes of materials, molecular

dyes for example, and was used to simulate the experimental data for MEH-PPV and

the pentamer. It provides an approximate description of the low frequency intramolecu-

lar modes by assuming them to be continuously distributed and in the high temperature

limit. In this model, the distribution of conformational subunits is directly related to

the inhomogeneous line broadening of the absorption spectrum and the asymptotic off-

set of the 3PEPS data. We are able to fit the absorption and 3PEPS lineshapes well,

however, this model clearly fails when attempting to fit the fluorescence lineshape be-

cause the homogeneous line broadening is far too large. The two-level system approach

does not incorporate relaxation through a broadened density of states. Although, since

the time dependence of that localization is exponential, the 3PEPS data can still be

simulated by addition of an exponential term to the homogeneous component of the

correlation function. However, use of this correlation function is unsatisfactory for sim-

ulation of fluorescence data.

The short falls of the two-level system model are remedied by inclusion of a distribu-

tion of exciton states in a three-stage relaxation model. Theoretical frameworks have

calculated exciton states that derive from the large number of π electrons in conju-

gated oligomers, although states at the band edge are discrete. Mukamel’s collective

electronic oscillator approach and the quantum chemical calculations of Beljonne and

Bredas are examples [72, 181–183]. We define the manifold of states that leads to

79


the distribution characterized by σ1 as collective states formed by electronic coupling

among conformational subunits. [1]

The three-stage relaxation model is a phenomenological model that captures the

essential physics of absorption into a delocalized manifold of electronic states, and sub-

sequent evolution to a localized emissive state. It incorporates two types of disorder

into the simulations of the absorption, fluorescence and 3PEPS data. In the context

of this model, it is apparent that conformational disorder is ultimately responsible for

each of these categories of disorder as (i) a distribution of transition frequencies dis-

tributed over the polymer; and (ii) a distribution of delocalized exciton states arising

from electronic coupling among these subunits. The standard deviation of the distri-

bution of transition frequencies (owing to conformational disorder) is related to the

distribution function used in the multiphonon model. Spectral diffusion through an

inhomogeneously broadened density of exciton states is included in the simulation of

the 3PEPS data to model dynamic localization of excitation. We find this dynamic

localization occurs in ∼ 25 fs for the polymer. Possible mechanisms by which excita-

tion localizes in conjugated polymers have been discussed recently. [58, 98] Although

the model is complicated, it provides a physical picture of what is happening. There

are relatively large error bars on

The significant geometry change upon photoexcitation (and subsequent relaxation)

is intimately related to many of the lineshape features of the system. This geometry

change itself is large and has a direct and profound influence on the electronic structure

of the polymer by the disruption of π orbitals with nuclear motion. Some SSF studies

have shown smaller intrinsic Stokes’ shifts for PPVs. However, SSF, by its nature,

excites only the reddest chromophores in the ensemble, which are likely the most pla-

nar and, therefore, have the smallest geometry change between the ground and excited

states. The reorganization energy associated with this geometry change is large for

most chromophores and accounts for much of the observed Stokes’ shift. However, this

may occur on a timescale much slower than that associated with dynamic localization.

Through the three-stage relaxation model we were able to separate the rapid dynamic

localization of excitation from the molecular lineshape. We obtain a Stokes’ shift corre-

sponding to 2λ ≈ 750 cm−1 for MEH-PPV that is comparable to the molecular Stokes’

80


shift reported for PPV of 500 cm−1. [17] The reorganization energy, λ is related to the

homogeneous lineshape by the fluctuation-dissipation theorem. There are relatively

large error bars on our estimate as this model is intended to give a physical picture,

rather than being entirely quantitative.

4.4.1 Comparison to Oligomers

Comparing the steady state spectra and 3PEPS data of MEH-PPV and a model PPV

oligomer (which, although is not exactly an analogue of MEH-PPV, has long side-chains

providing a similar degree of steric hindrance) can shed light onto the relative impor-

tance of the dynamic processes which are manifest in the 3PEPS and as a broadening of

the spectra. Their electronic transitions appear to be strongly coupled to a bath of low

frequency intramolecular modes—presumably torsions. [147] Bassler and co-workers

have attributed the non-mirror image spectra of both the polymer and oligomer to

these torsional modes. [17,147] The persistent peakshift may suggest a disorder in the

pentamer as well. We have calculated ( as discussed in the next chapter) that many

chromophores are delocalized over fewer than five repeat units. This opens up the

possibility that an oligomer does not necessarily behave as a single unit.

The significant geometry change upon photoexcitation (and subsequent relaxation)

is intimately related to many of the lineshape features of the system. It has been cal-

culated that the torsional potential is steeper in the planarized excited state than in

the ground state [75], which may be reflected in the narrowing of the fluorescence. The

absorption/emission mirror symmetry is broken when the ground state and excited

state frequencies differ. Gierschner et al. have calculated the potential energy surfaces

for trans-stilbene as a function of torsional angle. [75] They clearly demonstrate how,

at finite temperatures, torsional modes will broaden the absorption spectra much more

than the fluorescence and how a blue tail arises as a direct consequence of these modes.

This argument is extended to multiple torsional modes in longer phenylenevinylene

oligomers. Both absorption and fluorescence narrow at low temperatures. [184,185]

81


4.4.2 Conformation in Solution vs. Films

Choice of solvent is crucial to the conformation that is adopted by a polymer in so-

lution and the morphology of any film cast from that solution. [16] Using the 3PEPS

experiment, we are unable to quantify the precise differences arising from polymer con-

formation in different solvents. Any solvent that is able to dissolve sufficient polymer

to allow us to perform measurements is a good enough solvent that we are unable to

observe the subtle differences in polymer-polymer interaction. Of course, the solvent

largely determines the conformation of the polymer, yet we see very little solvent de-

pendence in the dynamics [97], nor is there a molecular weight dependence. Mixed

solvent studies have shown that it is possible for two distinct species (aggregate and

isolated) to be present in the solution and the spectra are a superposition of both. The

ratio of these species can be changed by changing the solvent composition. [57] It seems

that as long as the polymer chain is longer than the persistence length, which is 6 nm

(10 repeat units)in MEH-PPV [107], it can form a coil or defect cylinder in solution

and the overall length becomes unimportant. As long as the solvent is ‘good enough’

to dissolve enough polymer, the photophysics are dominated by intramolecular modes

and EET (electronic energy transfer) between subunits that are close in space but not

necessarily adjacent along the chain. The rate of energy transfer may be influenced by

the packing of chromophores, however we are not sensitive to slight differences on this

timescales. The early time dynamics are not appreciably affected by solvent choice.

Also, excitation further to the blue might enhance different energy transfer rates, mak-

ing the difference between tightly coiled and loose open chains more pronounced. On

the other hand, the films are clearly different as evidenced by their lower initial peak

shift and decay to zero peak shift at long times.

Monte-Carlo simulations by Barbara and co-workers convincingly show that rigid

conjugated polymers are likely to collapse into a defect cylinder conformation when de-

fects and inter-segment attraction are incorporated. The defect cylinder and defect coil

conformations are supported by single molecule studies as well. [51,52] MEH-PPV has

the necessary tetrahedral defects to adopt these conformations. In a nonpolar solvent

such as toluene, MEH-PPV is expected to form a defect coil to minimize solvent-solute

interactions. [19] Additionally, the hydrodynamic radius of MEH-PPV is significantly

82


larger in chlorobenzene than in THF [117] and, most likely, toluene. The larger radius

suggests that the chains are relatively open and straight in conformation. This is con-

sistent with the absorption and fluorescence spectra shown in figure 4.2 as the THF and

toluene solutions are blue-shifted with respect to the chlorobenzene solution. The film

is red-shifted compared to the chlorobenzene solution, suggesting that chlorobenzene

is not a very good solvent. PL spectra of Films cast from good solvents seem to be

blue shifted with respect to the solution spectra. [114]

In the film, an ordered, collapsed chain with many parallel chain segments likely facil-

itates energy transfer along the polymer chain since such segments are more favourably

oriented. [50, 100] Spin-coating tends to deposit polymer chains flat against the sub-

strate [186] and films cast from chlorobenzene are thought to be tightly packed. The

extent of conjugation is the predominant difference between the solutions and the film.

The solutions have individual polymer chains coiled to varying degrees which interrupts

conjugation. This allows for coupling between subunits to form chromophores while

still limiting energy transfer to mainly intrachain. The film’s more ordered, closely

packed morphology allows for more efficient energy transfer by facilitating interchain

energy transfer as well. This is observed as red-shifted fluorescence and a large appar-

ent Stokes’ shift. The differences in chromophore size are observed as a red-shift of

the film absorption compared to the solutions. The film line shape is also broadened,

perhaps due to absorption by aggregates (electronically coupled conjugation segments),

the prevalence of which is determined by morphology, on the red side of the absorption

spectrum .

Since the system is dynamic, the conformation of a polymer chain in solution will

differ from one instant to the next, even while the time-averaged distribution of con-

formation lengths remains constant, giving rise to inhomogeneous broadening [187]. It

is important to note that the because the disorder in conjugated polymers is dynamic,

a chromophore is not a static entity. The size and nature of an individual chromophore

can change with time [74] as evidenced by the reversible switching between narrow and

broad emission corresponding to isolated and aggregated behaviour. The fluorescence

from a single chromophore has been observed to drift with time to both lower and higher

energies. [175] This further calls into question the picture of a static chromophore with

83


a well-defined conjugation length. Thus, the inhomogeneity in conjugated polymers

differs from the static inhomogeneity observed in, for example, inorganic semiconduc-

tor quantum dots [131].

4.4.3 Localization and Energy Transfer

Absorption into the inhomogeneously broadened density of states (DOS) ultimately

leads to energy migration to lower energy chromophores. [73] The initial dynamics,

however, are dominated by rapid localization or self-trapping of the excitation onto a

conformational subunit. The localization of excitation is typically thought to be driven

by the geometrical relaxation of a conformational subunit. Recently, possible localiza-

tion mechanisms for conjugated polymers have been discussed. [58, 98] The ultrafast

relaxation component cannot be attributed to intramolecular relaxation because the

associated very large Stokes’ shift and homogeneous line broadening are absent.

Signatures of polaron pair formation were first directly observed as a long-lived

component in a pump-probe experiment. [188] Since then, polarons have been im-

portant in the discussion of photoexcitation and relaxation of conjugated polymers.

[61,98,189–192] Polarons refer to spatially separated electrons or holes which are cou-

pled to the lattice distortions. Miranda et al. present evidence for the formation

of polarons in both solutions and films of MEH-PPV. [193] They propose that most

electrons and holes form neutral bound states upon excitation. However, after ther-

malization, a small percentage of them remain spatially separated by many repeat

units (polarons). Concentration dependent studies of dilute solutions establishes the

polarons as intra-chain in solution. [193] Recombination is a slow process because the

polarons must diffuse over large distances before there is sufficient wavefunction over-

lap. We cannot differentiate between excitons and polarons or polaron pairs using

3PEPS because polaron pairs are dark in our experiments owing to their small oscilla-

tor strength. However, polaron pairs (or other interchain species, like charge transfer

excitons) are compatible with our model because they can be explained by an initially

highly delocalized state from which the electron and hole localize on separate subunits.

Some small fraction of the initial delocalized population is trapped as polaron pairs.

84


Also consistent is the observation that there are more polaron pairs formed in films

versus solutions. [57] This may be because, owing to stronger interactions between ad-

jacent subunits, the initial extent of delocalization can be larger in films, facilitating

localization of hole and electron on different regions of the chain.

The narrow steady state emission spectrum of MEH-PPV at low temperature has

been shown to be independent of excitation wavelength. [55] Yu et al. propose a

mechanism whereby the electronic energy is rapidly funneled to the same low energy

segments. [19,55] We suggest that this funneling mechanism is mediated, in large part,

by the initial localization of excitation (∼ 25 fs). Other works have also found very fast

depolarization timescales that may be explained by this mechanism as they are too fast

to be explained by Forster hopping. They are attributed to relaxation between collec-

tive excited states of the aggregate and changes in delocalization of excitation. [194]

Other theoretical studies have had to go to non-Forster or generalized Forster mecha-

nisms in order to satisfactorily replicate experimental data. [59,102,122,176]

It is apparent that the peak shift of the film of MEH-PPV does, in fact, decay to

zero as predicted by the efficient energy transfer in these systems. [156] Energy transfer

is unable to remove all of the inhomogeneity from the polymers in solution. However,

the distribution of conformational subunits is reduced from σ2 to σ′2. Many single

molecule experiments on tightly coiled chains point to emission from a single chro-

mophore, giving further evidence for the efficiency of energy transfer in conjugated

polymer systems. [19,52,108,114,115] Consistent with conformation-dependent energy

transfer, the Stokes’ shift of MEH-PPV is much lower in aligned/oriented samples than

in typical MEH-PPV samples, [143, 144] although some of this reduction may be due

to a red-shift in absorption as inhomogeneity is reduced.

4.4.4 Effect of Breaking Conjugation

In order to qualitatively check the effect of conjugation on things like energy transfer

and delocalization, we compared the “fully conjugated” MEH-PPV to one with ∼28%

of the vinylene linkages replaced with single bonds. The 3PEPS data is shown for

the polymer with broken conjugation in figure 4.11. Normal MEH-PPV is shown for

85


comparison. Clearly the broken conjugated polymer has a lower initial peak shift with

a higher asymptotic offset. This is indicative of stronger coupling to the bath and more

static disorder. This is likely because at chemical defects, the break in conjugation is

permanent, making it difficult for an exciton to visit all parts of the ensemble on the

timescale of the experiment. This is also manifest in the change of dynamic Stokes’

shift. In fluorescence depolarization experiments on the fully conjugated polymer, there

is an additional fast timescale, <100 fs [47], in line with the rapid decay of the peakshift.

They attribute this to dynamic localization of the exciton in the fully conjugated case

and say that this is more difficult in the broken conjugation polymer, consistent with

the slower peakshift decay. The states are initially more localized on average in the

broken polymer so the effect of dynamic localization is less pronounced. They also show

that there is a significant blue shift of the absorption spectra when chemical defects

are introduced, consistent with the picture of a collection of chromophores, separated

by breaks in conjugation.

4.4.5 Lineshape and Stokes’ Shift

The geometry change upon photoexcitation is large and has a direct effect on the

electronic structure of the polymer by the disruption of the π-orbital system. We

are able to retrieve Stokes’ shifts (2λ) of ∼ 700-800 cm−1 for solutions and ∼ 1160

cm−1 for the film. These are comparable to the molecular Stokes’ shift reported for

poly(phenylphenylenevinylene) of 500 cm−1. [17] The reorganization energies associ-

ated with the geometry changes are primarily responsible for the homogeneous line

broadening. This reorganization energy is related to the homogeneous lineshape by

fluctuation-dissipation.

In our simulations, the maximum value for the sum of the λs was fixed at half of the

energy difference between the absorption and fluorescence maxima. This is the apparent

Stokes’ shift. In an isolated two-level system, this would correspond to the molecular

Stokes’ shift arising from electron-bath coupling. In a more complex system, such as

MEH-PPV, there are further contributions which must be considered. These include

an ultrafast localization component and spectral diffusion through energy transfer. [62]

86


12

10

8

6

4

2

0

Peak

Shift

(fs

)

1000080006000400020000Population Time (fs)

12

10

8

6

4

2

0

Pea

k S

hift

(fs)

0.1 1 10 100 1000Population Time (fs)

Figure 4.11: Comparison between fully conjugated MEH-PPV (black line) and thatwith 28% broken conjugation by intentional introduction of chemical de-fects (grey line). The broken polymer has a lower initial peakshift.

87


Site selective fluorescence techniques, by excitation of the red-most chromophores, re-

veal the true molecular Stokes’ shift, without these contributions. [17, 88,147,195]

Both the nature of the single chromophore and the conformation of an entire chain

comprised of many chromophores dictate the photophysical properties of conjugated

polymers. In MEH-PPV and similar systems, disorder plays a large role. However,

comparison to LPPPs shows a surprising similarity on a chromophoric level. As ex-

pected, the two types of polymers exhibit different behaviour on a single molecule

level. [19,115,196] Schindler et al. also show that single chromophores exhibit spectral

diffusion that gives rise to dynamic disorder. It has been observed that fluorescence

from single molecules “drifts and jumps” [175], consistent with our picture of a dynamic

chromophore.“Switching” between aggregate and free chromophore type emissions in

single molecules, suggests further that emission from within the same polymer chain

may be both molecular (isolated chromophore, although dynamic) or more delocalized

(more than one chromophore) depending on the coupling strength between adjacent

sub-units at the time of fluorescence. [175]

The broader, red-shifted absorption and fluorescence observed from the film [197]

are probably due to the formation of aggregates in the film, leading to emission from

interchain excitons. [108] This, in addition to the faster, more efficient energy transfer

in films differentiates them from the behaviour of rigid conjugated polymers in solution.

Our analysis has shown that the homogeneous broadening is grossly overestimated by

modeling polymer systems as a two-level system similar to isolated chromophores. [62]

The three-stage relaxation model is more in line with the single molecule work, assum-

ing that the single molecule fluorescence sets an upper limit for homogeneous broad-

ening. [175]

We view the line broadening in MEH-PPV and the pentamer as arising primar-

ily from coupling to substantial geometry changes, and as such it differs from typical

molecules in the condensed phase. Such geometry changes are the main contribu-

tions to the homogeneous line broadening and are included as exponential terms. (We

are unable to retrieve a Gaussian component associated with inertial solvation.) We

can consider these nuclear motions to be a bath of overdamped Brownian oscillators.

The Stokes’ shift, due to relaxation, can only be observed when the oscillators are

88


overdamped. Mukamel shows that in this limit, M(t) is exponential in nature. [133]

Mathies and co-workers have used such an exponential M(t) in the analysis of the

photophysics of bacteriorhodopsin by modeling the photoisomerization coordinates as

a low-frequency vibrational mode with a large Huang-Rhys factor. [171] The transi-

tions of bacteriorhodopsin are strongly coupled to this isomerization coordinate. The

example of bacteriorhodopsin is especially relevant given the structural similarity to

polyenes.

Mathies and co-workers have shown that the cis-trans photo-isomerization of bacte-

riorhodopsin is extremely fast. [171] This is also true of stilbene, the cis-trans photo-

isomerization of which is nearly barrierless along the reaction coordinate. [198,199] In

more complex systems, such as conjugated polymers and oligomers in solution, there

are many chemically-unique double bonds around which photo-isomerization may oc-

cur. This results in an ensemble of isomers, increasing the inhomogeneity of the system.

Vibrational dephasing is expected to occur on a slower timescale and involves coupling

of the isomerization coordinate to a wavepacket. [198]

It is worthwhile to note that the time-averaged distribution of conjugation lengths

remains constant while a “snapshot” of one conformation will differ from the previous,

since the system is dynamic. The fluctuations of nuclear coordinates in the chro-

mophores can give rise to inhomogeneous broadening. [187] This is different from the

static inhomogeneity observed in other systems such as molecular dyes and inorganic

semiconductors. The inhomogeneity that provides the asymptotic peak shift observed

for both the pentamer and MEH-PPV, may also be caused by a sub-population of

cis-isomer photoproducts. Photoisomerization is known to occur in many conjugated

systems. Isomerization at any of the carbon sites along the backbone would add to

conformational disorder which is manifested as the long-time peak shift offset. The

slow interchange between conformations may be another contributor to the residual

peak shift observed on the timescale of the experiment. In addition, chains of different

conformations have been observed in single molecule studies of MEH-PPV. [19] The

presence of cis-isomers would support the model that polymers adopt a defect cylinder

conformation in solution. [51] Hairpin turns necessary to form the defect cylinder con-

formation are easily formed when cis-defects are present and are perhaps less accessible

89


by sp3 defects alone.

Additional experiments on complementary systems are consistent with the three-

stage relaxation model outlined above. Data for films of MEH-PPV show that the peak

shift does, in fact, decay to zero as predicted by the extremely efficient energy transfer

in these films. [156] This energy transfer allows the system to explore all states of the

ensemble. [132] The coupling of the electronic transitions to the solvent bath appears

to be negligible compared to coupling to intramolecular modes, however, the solvent

cannot be disregarded as unimportant. The solvent is known to affect the conforma-

tion of the polymer in both solution and film. [19,51,117,200] Furthermore, ladder-type

poly-paraphenylenes have been shown to obey the mirror-image rule, suggesting that

the change in lineshape is indeed due, at least in part, to the large geometry change

in the less rigid polymers studied in this chapter. The smaller Stokes’ shift observed

in LPPPs is consistent with the model, as well. LPPPs are an ideal model system to

study the Stokes’ shift as it is unobscured by disorder and energy transfer. [89,196]

Some of the deviations from experimental data are readily explained. In figure 4.8,

the simulated absorption spectrum does not follow the experimental lineshape on the

red-edge. In this model, we have used a Gaussian distribution of exciton states. More

rigorous simulation would have us use a distribution with a steeper than Gaussian rise,

which is what is observed experimentally. Also, the 3PEPS experiments are performed

using laser pulses that excite on the red edge of the absorption spectrum. The blue-

edge is so far off-resonance that we are not sensitive to that area of the spectrum. It

has been well documented that the initial part of the ultra-fast decay of the 3PEPS

signal is difficult to fit. [169,170] The underlying reason is that within the pulse-overlap

region, several additional signal pathways contribute to the signal when the pulses are

not properly time-ordered. This is especially important in multichromophore systems

and semiconductors. Coupling to high-frequency modes also affects the early time be-

haviour of the 3PEPS signal. We are also unable to resolve accurately the frequencies

of coherently excited vibrational modes that add to the 3PEPS signal. [201]

The implications of these results for resonance energy transfer in conjugated poly-

mers are that there are two distinct regimes of energy migration. During the first ∼ 25

fs, delocalized states populated during excitation—effectively occupying more than one

90


conformational subunits—are localized to a single conformational subunit. Associated

spectral diffusion explains the unexpectedly rapid decay of the 3PEPS data. This re-

laxation is a highly complex dynamical process, wherein electronic and nuclear degrees

of freedom are inseparable. [46] In the second, longer time scale regime prior to photo-

luminescence, excitation energy migrates to a sub-distribution of longer conformational

subunits, thus narrowing their associated spectral inhomogeneity from σ2 = 425 cm−1

to σ′2 = 10 cm−1. However, because absorption occurs to delocalized states, resonance

energy transfer, in turn, operates by a non-Forster mechanism; whereby localized ex-

citation on a donor conformational subunit transfers energy to an aggregate state.

The separation of time scales between the rapid localization (25 fs) and resonance en-

ergy transfer (> 1 ps), suggests that such energy migration can be usefully modeled

by the Generalized Forster Theory (GFT) models proposed recently. [158,159,202–204]

4.5 Conclusions

The origins of many optical properties of conjugated polymers differ greatly from those

of molecular dyes and inorganic semiconductors. It is the interplay between conjuga-

tion and the conformational disorder that disrupts it that gives rise to many of these

properties. We have shown that the conformational disorder in these systems results in

large spectral inhomogeneity. Homogeneous line broadening results from coupling to

intramolecular motions modeled by an overdamped Brownian oscillator. No evidence

was found for inertial solvation. An important conclusion of our analysis was that ab-

sorption occurs from the ground state to a delocalized set of states, that we suggested

originate from electronic coupling between conformational subunits. That set of states

appears as an additional inhomogeneous broadening of the absorption spectrum. The

strong coupling of electronic transitions to the nuclear coordinate was suggested to

be of the utmost importance in determining dynamics subsequent to photoexcitation

of conjugated polymer systems. The highly nonequilibrium geometry produced upon

photoexcitation—and subsequent relaxation—has a direct effect on the electronic struc-

ture of the conjugated polymer, and promotes rapid localization of excitation. This

91


relaxation is observed in the 3PEPS experiment as a type of spectral diffusion, with

τloc ≈ 25 fs for MEH-PPV. The fluorescence derives from a localized state, explaining

the main reason for the narrow fluorescence, as well as the large apparent Stokes’ shift.

We have used the 3PEPS experiment with absorption and fluorescence to compare

MEH-PPV solutions with film. The experiments and simulations show the marked

difference in conjugated polymer excited state dynamics between the solutions and the

film. This is an effect of polymer conformation and disorder. Excitation is initially

more delocalized in the polymer film because of the presence of longer conjugation

segments and stronger Coulombic coupling between adjacent subunits. This excitation

energy is rapidly localized onto a conformational subunit. Longer conjugation length

segments are manifest in a red-shifted absorption lineshape which is broadened by the

presence of aggregates. The film is also able to transfer energy more efficiently owing

to its more-ordered, packed morphology as shown in the peak shift’s decay to zero and

its large apparent Stokes’ shift. The line shapes of the polymer are very similar in all of

the solvents studied, suggesting that the response is dominated by the polymer itself,

rather than interaction with the solvent bath. We have used a three-stage relaxation

model to simulate the experimental data. The peak shift, absorption and fluorescence

together give a picture of the importance of conformation of polymer chain in that the

energy transfer and coupling strengths are much more pronounced in the film versus

solution.

92

5 Exciton Dynamics in PPV Polymers: The

Ultrafast Decay

5.1 Introduction

Conjugated polymers are being used in novel optoelectronic devices. In such appli-

cations the interplay between free charge carriers and rather strongly bound excited

electronic states is used. For example, in a light emitting device it is the combination of

charge carriers to a bound state (an exciton), and the high yield of photoluminescence

from that state that are important. On the other hand, for photovoltaic applications,

we need to discover how excitons are irreversibly dissociated into carriers. That pro-

cess might happen instantaneously upon photo-excitation, or it can occur subsequent

to exciton relaxation and migration (perhaps to a trap or interface). Thus the evo-

lution of photoexcitation over quite a large time span (from femtoseconds to 100s of

picoseconds) needs to be understood. The difficulty in addressing these processes is

that they depend sensitively on the structure and organization of the polymer. [7–13,15]

To elucidate these processes, the question “What happens after photoexcitation?” is

of utmost importance and should be considered in conjunction with the design, opti-

mization, and tuning at the molecular level. Numerous phenomena must be considered

when examining the dynamics and conjugated polymer photophysics in general. In this

chapter, we will focus on a discussion of the fastest dynamics, those that happen in the

first 100 fs or so. This time window has not been deeply explored previously, mainly

because the necessary incisive experimental probes of ultrafast exciton dynamics are

not commonly available and phenomena on this timescale tend to be complex owing

to entanglements among electronic and nuclear degrees of freedom.

At any fixed nuclear configuration, it is energetically favourable for excitons to de-

93

5 Exciton Dynamics in PPV Polymers: The Ultrafast Decay

localize and, in systems where there is little disorder (ladder type polyphenylenes,

oriented films), excitons may delocalize over large sections of the polymer, with a

diffusion length of ∼ 50 repeat units for oriented poly[2-methoxy-5-(2’-ethylhexyloxy)-

p-phenylene vinylene] (MEH-PPV). [109, 205] This was demonstrated experimentally

with polydiacetylene chains dispersed in their monomer single crystal matrix forming

an ideal 1-D quantum wire. [206,207]

In flexible polymers like MEH-PPV, excitation is (de)localized onto only a few re-

peat units. To understand these polymers we think in terms of a hierarchy of structural

disorder that dictates the interplay of π-system conjugation and nuclear degrees of free-

dom. Firstly, owing to the relatively low energy barrier for small angle rotations around

σ-bonds along the backbone of conjugated chains, the chain is broken into conforma-

tional subunits. [20–29] It is these conformational subunits that constitute the primary

absorbing units. We have calculated the average conjugation length for PPV polymer

chains to be 7 repeat units (approx 1.7-2 chromophores with an average of 4.7 PV units

per chromophore), in line with the experimental predictions for exciton delocalization

in MEH-PPV. [30, 208] There is a distribution of conformational sizes as is evident

in the broad, mostly featureless absorption spectra of many species. This breadth is

considerably greater in films and aggregates than in dilute solution. [97]The basic char-

acteristics of conjugated polymers are derived from those of conformational subunits.

However, these conformational subunits couple to contribute collective electronic states

which influence the polymer optical properties.

Theoretical works have calculated exciton states that derive from the large number

of π electrons in conjugated oligomers/polymers, although states at the band edge

are discrete. Coulombic interactions between proximate conformational subunits are

important to the dynamics of conjugated polymers. [62, 97] In polyindenofluorene, for

example, intrachain electronic couplings are estimated to be in the range 1 to 900 cm−1

depending on the length of the conformational subunits. [102] Interchain couplings are

larger yet. [50]

With this picture of conjugated polymers as chromophores comprised of coupled col-

lective states, we can realize an understanding of the dynamical processes that occur

and the length scale over which they are important. It is important to note that these

94


phenomena can compete and are obscured by ensemble averaging. A schematic of these

processes was presented in figure 2.2. Initially, upon photoexcitation, absorption occurs

into the exciton manifold. It is widely understood that nanoscale excitons constitute

the primary photoexcitations in conjugated polymers. [54, 79] On the shortest time

scales we suggest these excitons are somewhat delocalized over a few conformational

subunits owing to the intersubunit electronic coupling. However, we expect these delo-

calized states to be very short lived owing to the reorganization energies characteristic

of individual conformational subunits. [50, 60] Thus, conjugated polymers contain dy-

namic chromophore units as a consequence of the sensitive dependence of electronic

structure on nuclear coordinates

Time-resolved absorption and transmission spectroscopy has provided some infor-

mation on the initial relaxation processes occurring after photo-excitation [67–69].

Femtosecond fluorescence experiments have revealed an ultrafast relaxation of optical

excitations within an inhomogeneously broadened density of states (DOS). [47] Self-

trapping by disorder and vibrational relaxation can contribute to the rapid timescales

as observed in the 3PEPS experiment [1, 62, 97] and in anisotropy decay or low initial

anisotropies (both pump-probe and fluorescence upconversion) [47,95,101,209]. In ad-

dition to self-trapping of excitation, there can also be relaxation within the manifold

of collective states which is manifest as a localization. [194,210]

On a longer timescale, and covering a larger spatial extent, electronic energy transfer

(EET) is a significant event occurring after photoexcitation. This has been the topic of

much discussion on conjugated polymers and will only be mentioned briefly in this chap-

ter. Experimental evidence of energy transfer is obtained by probing certain spectral re-

gions or time delays like in site-selective photoluminescence spectroscopy [17,88,90,147]

or time-resolved polarization anisotropy measurements. [44, 209, 211]. Both intrachain

and interchain energy transfer are thought to occur in conjugated polymers [50], with

comparisons between film and solution shedding light on the nature of the EET. [16,97]

Fluorescence occurs from a small subset of localized states because energy migration

through the polymer transfers population to the larger conformational subunits prior to

emission. [16,17,49,88,147].Thus, fluorescence is only observed from this low energy sub-

set of the entire ensemble of chromophores, narrowing the distribution. Time-resolved

95


fluorescence measurements revealed that the 0-0 Stokes’ shift changes by 350 cm−1 in

3 ns for poly[(2-methoxy-5-hexyloxy)-p-phenylenevinylene] (MH-PPV) and 180 cm−1

for PPV. [95] In this ensemble measurement, the shape of the spectra changed as well,

reflecting the change in the relative contributions from the long and short chromophores

with time. The steady state emission spectrum is significantly narrower than the ab-

sorption, with less inhomogeneity, [17, 62,97] reflecting this EET.

Many investigations have addressed the linear and nonlinear optical properties of

conjugated polymers. [1, 2, 62, 91–97] We build on these in an attempt to understand

the fastest dynamics. We report theoretical studies of excitation relaxation in indi-

vidual chains and ensemble non-linear polarization dependent experiments. We found

that on a timescale <100 fs, the anisotropy decays rapidly in single chains as a re-

sult of relaxation among exciton states (spectral diffusion). Interestingly, the exciton

does not translate along a significant length scale, unlike in Forster energy transfer.

Nonetheless, the effect on anisotropy is significant. This effect is obscured in an en-

semble measurement where disorder is likely to dominate. We compare the theoretical

predictions to experimental studies.

5.2 Theory

Molecular dynamics simulations were performed to determine a number of suitable

conformations for PPV chains. These chains were “broken up” into chromophores of

conjugated segments separated by large dihedral angles. The cut-off angle was adjusted

to give experimentally relevant conjugation lengths. A cut-off of around 55◦ was typi-

cally used. Comparison of different cut-off angles shows that there is little dependence

on this value. This insensitivity is because all of the chromophores are coupled (and the

couplings are included explicitly) there is no discernable difference between one large

chromophore with central conjugation break or two smaller chromophores which are

strongly coupled. INDO/SCI calculations were performed to determine the site ener-

gies of the chromophores and the couplings between them. Chromophores shorter than

two repeat units are not included in subsequent calculations. The MD and INDO/SCI

96


A B C

Figure 5.1: Conformations of three representative chains. The radii of gyration of

chains are Chain A: 300 A, Chain B: 210 A, and Chain C: 154 A. Theconformations of the chains were generated by MD simulations. The siteenergies and the couplings between sites were calculated using INDO/SCItechniques.

calculations were performed by our collaborators at the University of Mons.

The conformations of three representative chains are shown in figure 5.1. The radii of

gyration of these polymer chains are estimated to be 300 A, 210 A, and 154 A according

to the equation:

R2g =

1

2N2

∑i,j

(ri − rj)2 (5.1)

where N is the number of monomers. The sum is over all pairs of monomers, i, j, and

(ri − rj) is the distance between monomers i,j. We begin in a multi-chromophoric

picture where the basis self consists of conformational subunits with excitation energies

Hnn and electronic coupling among them Hmn. To obtain the collective exciton states

ν in terms of the mixing coefficients λνn, the secular equations were solved

∑n

(Hnm − EνSnm)λνn = 0 (5.2)

97


where the energies Eν are defined relative to the ground state energy of the aggre-

gate, E0, matrix elements are Hnm = 〈φm|H − E0|φn〉 and the overlap integrals are

Snm = 〈φn|φm〉. The N exciton states are obtained:

Ψν =∑

n

λνnφn (5.3)

It is in this eigenstate basis that we simulate the absorption/participation ratio and

the early-time dynamics. Unless otherwise noted, Greek characters (µ, ν) represent

eigenstates and Roman characters (m,n) are chromophores in the site representation.

5.2.1 Simulation of Absorption and Fluorescence

We have simulated the absorption and fluorescence spectra for the single PPV chains

using the equations below. High frequency vibrational modes are included explicitly in

the simulation of absorption and emission. They were incorporated using the following

equations for the area-normalized absorption and fluorescence spectra [158,179,180]:

ai(ε) =

⟨ ∑ν

Na|µν |2∑

k

P (k)×

Re

∫ ∞

0


ν − λ)t/h]exp[−g(t)]

⟩ε/n (5.4)

fi(ε) =

⟨ ∑ν

Nf |µν |2∑

k

P (k)×

Re

∫ ∞

0


ν + λ)t/h]exp[−g∗(t)]

⟩ε3 (5.5)

where g(t) is the line broadening function, λ is the reorganization energy associated

with the Stokes’ shift, εkν is the transition frequency of the νth chromophore adjusted

for thermal population of the kth vibrational mode. The spectrum is weighted by the

Boltzmann weighting P (k). 〈k|k(t)〉 is the time-dependent overlap of the initial vibra-

tion k with its evolution in the excited state. This overlap gives the time-domain picture

98


of the vibrational absorption spectroscopy, the Fourier transform of which corresponds

to the vibrational component of the absorption. [179, 180] Nf (Na) is a normaliza-

tion constant. The angular brackets indicate an ensemble average over the density of

states. µν is the transition moment vector, given by the vector sum of the site-localized

transition dipole moment vectors:

µν =N∑

n=1

λνnµn (5.6)

The specific form of the line broadening function, g(t) includes experimentally de-

termined bath fluctuations and coupling magnitudes [62] as discussed in chapter 4. In

the absence of high frequency modes, equations 5.4 and 5.5 reduce exactly to the stan-

dard lineshape functions [133], equations 4.14 and 4.15. The coupling of low-frequency

vibrational modes to the electronic transition is taken into account through the bath

spectral density. Leng et al. ascribe the low frequency motions to torsional modes in

PPV polymer and its derivatives [92]. The time-resolved fluorescence was calculated

using the Master equation approach described below and equation 5.5 with |µ2ν | re-

placed by the cumulative ground state population produced by emission from state ν,

P ′ν(t).

The inverse participation ratio (IPR) is a measure of the extent of exciton delocalization

and was calculated by [212]:

L(ε) = 〈∑

ν

∆(ε− εν)

( N∑n=1

(λνn)4

)〉/ρ(ε) (5.7)

where ρ represents the density of states. The IPR ranges from 1 where the exciton is

completely localized on a single chromophore to 0 where the exciton is delocalized over

the entire polymer. The average value obtained was found to be 0.7 which corresponds

to a conjugation length of around 7 repeat units for PPV. The IPR is plotted in figure

5.2.

99


36x103

3432302826

Wavenumber

0.95

0.90

0.85

0.80

0.75

Inve

rse P

articip

atio

n R

atio

Ab

sorb

an

ce (

Arb

itra

ry U

nits

)

Figure 5.2: Calculated absorption spectrum and inverse participation ratio for chain C.The inverse participation ratio is a measure of the extent of delocalization. 0corresponds to completely delocalized. 1 is when the exciton is localized ona single subunit. The calculated spectra for all the chains are qualitativelysimilar (not shown).

100


5.2.2 Dynamics Simulations

In order to understand the ultrafast dynamics of conjugated polymers unobscured by

ensemble averaging, we perform theoretical simulations on single PPV chains. The

dynamics of delocalized exciton states will be discussed in the basis of an electronic

eigenstate representation. It is reasonable to consider the excitons as delocalized as we

are only interested in the early time dynamics in this framework. In order to look at

equilibrium energy migration, we would need to change to a localized representation.

We examine the dynamics of the exciton relaxation in isolated PPV chains by solving

the Master Equation:

Pν = −γνPν +∑

µ

(WνµPµ −WµνPν) (5.8)

P ′ν = −γνPν (5.9)

where γν is the radiative decay rate constant of |ν〉 The W are the transfer rates and P

is the population. P ′ν are the ground state populations produced by emission from each

state |ν〉. These coupled differential equations are solved numerically,passing from the

differential to the integral form of the equations. [213]

Pν(t) = Pν(0) exp(−Wνt) +∑

µ

Wνµ

∫ t

0

dt′ exp[−Wν(t− t′)]Pµ(t′) (5.10)

where Wν = γν +∑

µ Wµν . This is solved iteratively by:

Pν(t + δt) = Pν(t) exp(−Wνδt) +1

Wν

[1− exp(−Wνδt)]

×∑

µ

Wνµ −Wν(t− t′)Pµ(t′) (5.11)

avoiding divergence at small Wν by expanding:

1

Wν

[1− exp(−Wνδt)] = δt(1− 1

2Wνδt) (5.12)

101


The rate is calculated by [213–215]:

Wµν = D(|Eµ − Eν |)Oµν (5.13)

×{

1 + n(Eν − Eµ), Eν > Eµ

n(Eµ − Eν), Eµ > Eν

where D(∆E) is the bath spectral density, n = (exp(∆E/kBT )−1)−1 is the mean ther-

mal occupation (Boltzmann distribution) and Oµν is the probability overlap between

the two states |µ〉 and |ν〉. Equation 5.13 satisfies the principle of detailed balance.

The bath spectral density is defined as:

D = ω0ω

ωc

exp(− ω

ωc

) (5.14)

when using an Ohmic spectral density [167, 168]. ω0 is the exciton-phonon coupling

constant; ωc is a cut-off frequency. The overlap probability is given by:

Oµν =N∑

n=1

|λµn|2|λν

n|2 (5.15)

In this simulation, γν = |µν |2γ0. That is, an average single-chromophore radiative

rate, γ0, is weighted by the oscillator strength (transition dipole moment squared) of

the exciton state of interest. γ0 was set to be 0.0031 ns −1. This corresponds to an

excited state lifetime of ∼ 700 ps to 1 ns (neglecting non-radiative decay) when excited

by a laser pulse. The actual value depends on the microscopic nature of the individual

chain. The value of the radiative lifetime has been shown experimentally to be approx-

imately 1 ns in PPVs. [70, 216] Our simulations are insensitive to the specific value of

this rate, as we are probing only the early time dynamics where ¿1% of the initial

population is lost due to emission. A cut-off frequency of 60 cm−1 was used in addition

to an exciton-phonon coupling parameter of 500 cm−1 in the bath spectral density.

For relaxation between states to be efficient, the states must be energetically similar.

However, this is not sufficient to ensure relaxation. The relaxation rate is also depen-

dent on the overlap probability between two exciton states. That is, spatial extent and

102


Position on Chain

En

erg

y

Figure 5.3: For efficient relaxation amongst states in the exciton manifold, the energiesof the two states must be sufficiently similar according to equation 5.13.The relaxation between states in the exciton manifold is also dependenton the overlap probability between states Oµν . When this is included,the relaxation is not simply down the energetic ladder but also dependsstrongly on the spatial extent of the exciton. [215] The solid arrows indicatetransitions that are quick owing to both energetic and overlap conditionsbeing met. The dotted arrow indicates a slow relaxation step owing to poorenergy match. The dashed lines show slow transitions where the overlap ispoor.

proximity are important. A schematic of the energy relaxation is presented in figure

5.3.

5.2.3 Simulation of the Anisotropy

When a system of randomly oriented polymer chains interacts with polarized light,

only those chromophores with absorption transition moments with non-zero vector

projection onto the exciting electric field vector will absorb light. That is, when the

103


sample is excited by polarized light, the dipole will be oriented (at least partly) in the

direction of polarization. This is the initially prepared state; from this distribution of

states relaxation will occur. If that relaxation involves a change in transition dipole

orientation, then a change of anisotropy is observed. The anisotropy is defined in

equation 3.16. We have calculated the anisotropy using the following equation which

takes into account loss of anisotropy due to photoselection and angular displacement

of transition dipoles [140] for an isotropic ensemble of polymer chains:

r0(t) =1

5(3 cos2 θ(t)− 1) (5.16)

where θ is the angle between absorption and emission transition moments. We are look-

ing solely at anisotropy changes induced by spectral diffusion and exciton migration.

To this end, rotational effects are ignored and static chains are considered because the

rate of rotational diffusion is much slower than that which we probe experimentally or

are concerned with in our simulations. Additionally, there is no wavelength/energy bias

in detection in these simulations. Emission from all states is included. Because many

states may be initially populated by absorption of a laser pulse, a weighted anisotropy

is used. [140] This is determined by calculating the anisotropy decay under each initial

condition (where only one state is excited at time, t=0). Then we calculate a weighted

average of all of these decays. The weighting is determined by the overlap of the single

state absorption spectrum with the excitation source (the probability that this state

would be populated in an ensemble of eigenstates). Those states which are more pop-

ulated will contribute to the overall anisotropy decay more than the states which have

poor overlap. This weighted anisotropy is expressed by:

r0(t) =∑

ν

fνrν0(t) (5.17)

where the summation is over all states |ν〉 and fν is the fractional contribution of the

νth state to the absorption.

104


5.3 Experimental

Briefly, a tunable nonlinear optical parametric amplifier (NOPA) was pumped by 200

µJ of the output of a Ti:sapphire regeneratively amplified laser system that generates

∼140-fs pulses at 775 nm and 1 kHz. The tunable visible output of the NOPA was

used for excitation. [138] Dispersion was precompensated using a pair of quartz prisms.

The laser spectrum was measured using a CVI SM-240 CCD spectrometer. Depend-

ing on the laser center frequency, pulse durations of 30 to 45 fs were obtained from

autocorrelation measurements at the sample position. The intensities of the excitation

beams were controlled by using a half-wave plate/polarizer combination. Both pump

and probe beams were attenuated until the early-time signal shape was independent

of pulse energy, <5 nJ per pulse (fluence of 140 µJ/cm2) at the sample position. To

measure the anisotropy, the pump beam was vertically polarized. The probe polarizer

was set to 45◦ and a polarization cube before the detectors allowed for simultaneous

measurement of the parallel (VV) and perpendicular (VH) signals. The polarization

was verified by ensuring that the initial anisotropy for a laser dye was 0.4.

Chlorobenzene (spectroscopic grade) was obtained from Aldrich Chemical Company.

MEH-PPV was obtained from American Dye Source. POPV oligomers were a gift from

Johannes Gierschner. Solutions of MEH-PPV or POPV in chlorobenzene were filtered

to remove insoluble impurities. The absorbance was adjusted to be ∼0.3 at the ab-

sorption maximum in a 1mm cell. The solutions were circulated through a 1mm path

length flow cell using a gear pump. All measurements reported here were conducted

at 294 K. To ensure that there was no photodegradation, the absorption spectrum of

each sample was recorded before and after the anisotropy measurements.

5.4 Results

Our simulations demonstrate the effect of excitation wavelength on the early-time (first

100 fs) emission spectra as shown in figure 5.4. The shifting of early time fluorescence

with excitation wavelength is consistent with that reported previously. [217] There is

105


a small shift between 100 fs and 3 ps in fully conjugated MEH-PPV in solution. This

shift is much larger in polymers with broken conjugation [47], in keeping with the

larger proportion of shorter (blue) segments. The effect of excitation wavelength on

the anisotropy decay is shown in figure 5.5 for single PPV chains.

In order to gain a better understanding of the role that microscopic conformation

plays in the dynamics of the PPV chain, another simulation where individual eigen-

states were initially excited was performed. This is analogous to very narrow linewidth

excitation. The results of these simulations demonstrate how disorder in single poly-

mer chains can blur information regarding processes ongoing in the polymer chain by

averaging over all (or a sub-set of) chromophores in the ensemble. Figure 5.6 shows

the various types of effective chromophores possible which may be excited by the same

laser pulse. These excitons range from delocalized/strongly coupled with associated

fast anisotropy decays to very isolated chromophores which are localized and only very

weakly coupled to others. These exhibit no fast anisotropy decay. Interchain excitons

are also formed, as shown in figure 5.6c) where the conformational subunits which form

the exciton are not adjacent along the chain but interact through-space.

Redistribution/relaxation of the exciton density (the probability distribution of find-

ing a proportion of the exciton on a site n at a given time) clearly decays the anisotropy

even though the extent of spatial migration can be very small as shown in the figures

5.6. This can happen on a very rapid time scale. As seen the figure 5.6, the excitation is

quickly redistributed among the chromophores which comprise the collective electronic

state when there are several contributing chromophores. When the exciton is mostly

localized on one conformational subunit, there is almost no decay in the anisotropy, as

that chromophore will be coupled to others only very weakly.

Turning to experimental results, the raw data for the VV and VH polarized pump-

probe transients for MEH-PPV in chlorobenzene solution are presented in figure 5.8.

The polarization anisotropy is defined as [140]:

r(t) =IV V (t)− IV H(t)

IV V (t) + 2IV H(t)(5.18)

106


4035302520x10

3Wavenumber

Absorbance (A

rbitrary Units)

Flu

ores

cenc

e (A

rbitr

ary

Uni

ts)

Figure 5.4: The effect of the excitation energy on the early-time fluorescence. Calcu-lated absorption and steady-state fluorescence spectra are shown in blackfor chain A. The excitation pulse is shown as a green gaussian. The emis-sion at 100 fs is shown in red. The early-time fluorescence clearly changesdepending on excitation energy. The DOS is shown in blue at the top ofeach figure as a reference. In (c) the abnormal shape of the early time fluo-rescence is due to the fact that even though the states nearest in energy tothe excitation each contribute significantly to the early-time fluorescence,the higher density of states further to the red sums to give a greater overallcontribution, even though the contribution from each state is small. Thisaccounts for the appearance of the peak at lower energies. Also, these statescan be excited directly when the coupling to the higher frequency modesis considered. This increases the overlap between these red-states and theexcitation pulse. 107


0.40

0.35

0.30

0.25

0.20

0.15

0.10

Ani

sotr

opy

8006004002000Time (fs)

0.40

0.35

0.30

0.25

0.20

0.15

0.10

Ani

sotr

opy

8006004002000Time (fs)

0.40

0.35

0.30

0.25

0.20

0.15

0.10

Ani

sotr

opy

8006004002000Time (fs)

R=300 Å

R=210 Å

R=154 Å

Figure 5.5: The simulated anisotropy decays for the three chains shown in figure 5.1.Each chain is excited at several wavelengths as shown. Bold dashed linescorrespond to excitation at 30000 cm−1 by a Gaussian pulse of 500 cm−1

fwhm; grey is 28000 cm−1; dashed is 27500 cm−1; bold is 26000 cm−1.There is a more rapid decay in the anisotropy as the radius of gyration isdecreased.

108


0.4

0.3

0.2

0.1

0.0

Ani

sotro

py

12080400Time (fs)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Exc

iton

Den

sity

12080400Time (fs)

1.0

0.8

0.6

0.4

0.2

0.0

Exc

iton

Den

sity

12080400 Time (fs)

0.8

0.6

0.4

0.2

0.0

Exc

iton

Den

sity

12080400Time (fs)

case 3

case 2

case 1

a) b)

c) d)

case 1

case 2

case 3

Figure 5.6: a) Anisotropy decays for chain C when only one state is initially excited.Each trace corresponds to one of the following cases: Case 1- Initially de-localized, strongly interacting exciton; Case 2- Interchain exciton; Case 3-Initially localized, weakly interacting exciton. b) The redistribution of exci-ton density (between sites) for the initially delocalized exciton. Each tracecorresponds to a different site/conformational subunit, n, on the polymerchain. c) An interchain exciton. The two traces correspond to confor-mational subunits that couple through-space. d) An isolated state. Thisexciton is localized on one conformational subunit which is only weakly cou-pled to others. These neighbours are shown as slight increases in excitondensity at the bottom of the plot.

109


600550500450400350

Wavelength

Ab

sorb

an

ce (

Arb

itra

ry U

nit

s)

Figure 5.7: Absorption spectrum for MEH-PPV in chlorobenzene solution. The nor-malized laser spectra are also shown, with centre wavelengths of 493 nm,510 nm and 540 nm.

Figure 5.9a) demonstrates the excitation wavelength dependence of the anisotropy de-

cay of MEH-PPV in chlorobenzene as measured by one-colour pump-probe. Excitation

wavelengths are 540 nm, 510 nm and 493 nm. Figure 5.9b) shows a power dependence

of the anisotropy decay. The insensitivity to polymer molecular weight is demonstrated

in figure 5.10. The anisotropy decay of a series of POPV oligomers is shown in figure

5.11 for comparison.

110


5x10-3

4

3

2

1

0

Sig

nal I

nten

sity

(m

V)

100806040200Time (ps)

VV

VH

Figure 5.8: Pump-probe data for MEH-PPV in chlorobenzene solution. Transients forthe VV and VH polarizations, collected simultaneously.

111


0.5

0.4

0.3

0.2

0.1

0.0

-0.1

Anis

otr

opy

20151050Time (ps)

<5 nJ/pulse ~20nJ/pulse

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

Anis

otr

opy

100806040200Time (ps)

Figure 5.9: a)Experimental pump-probe anisotropy of MEH-PPV in dilute chloroben-zene solution. Pump/probe wavelengths were 540 nm, 510 nm and 493nm.b) Pump-power dependence where the dynamics are different for exci-tation energies of < 5 nJ and 20 nJ. Excitation wavelength was 493 nm.

112


0.5

0.4

0.3

0.2

0.1

0.0

Ani

sotr

opy

2520151050Time (ps)

Figure 5.10: Comparison between polymers of different molecular weight (Mw=150000vs Mw=900000). Excitation wavelength was 510 nm.

113


0.5

0.4

0.3

0.2

0.1

0.0

Anis

otr

opy

100806040200Time (ps)

8POPV

4POPV

6POPVH7C3O

OC3H7

H7C3O

OC3H7

n

Figure 5.11: Experimental POPV oligomers’ anisotropy decay for n=4,6,8. Excitationwavelength was 493 nm. Initial anisotropies are approximately 0.4 for4POPV and 6POPV. The initial anisotropy is slightly lower for 8POPV.The structure is shown as an inset.

114


5.5 Discussion

There has been much discussion as to the nature of the ultrafast decay component ob-

served in polarization anisotropy experiments on conjugated polymers. [1,47,62,97,101]

The complex photophysical response of conjugated polymers makes it difficult to as-

cribe this decay to any single phenomenon. Indeed, multiple competing processes likely

contribute to varying degrees, including self-trapping/localization of the excitation and

relaxation within the exciton manifold. It is illustrative to compare the pump-probe

depolarization anisotropy decays with the 3PEPS experiment which was discussed at

length in chapter 4. It is the fastest timescales in these experiments that are of in-

terest here. The 3PEPS shows an ultrafast decay when exciting near the absorption

peak whereas the polarization anisotropy does not. The anisotropy will only decay

by a process which rotates the transition dipole moment. Conversely, the 3PEPS is

sensitive to a correlation function and will decay by any process which induces spectral

diffusion, destroying memory of the initially prepared frequency distribution. Spectral

diffusion/relaxation through the exciton density of states will be seen as a decay in

both of these experiments. [132,218] It is less clear what the effect of localization/self-

trapping would be.

Self-trapping/localization of excitation has been observed in photosynthetic light

harvesting complexes (LH1 and LH2) [219, 220] and discussed in the context of local-

ized/delocalized electronic states [148,149]. The absorption into the B850 band of LH2

of purple bacteria and the subsequent localization of excitation onto a single dimer pair

is an illustrative example. [150] It is not unrealistic, then, to expect self-trapping of the

exciton to be very rapid in conjugated polymers where disorder dominates. Possible

mechanisms by which excitation localizes in conjugated polymers have been discussed

recently. [58,98]

Experimental evidence for self-trapping has been found for single poly(phenylene-

ethynylene-butadiynylene) chains. [119] For PPV oligomers, Tretiak et al modeled the

transition to a mainly planar excited state from a ground state with large torsional

disorder [60]. This large geometry change, which is also very likely upon excitation of

MEH-PPV, lowers the equilibrium free energy and may contribute to self-trapping as

115


the electronic transitions are coupled to this nuclear coordinate. [60, 171] Experimen-

tally, it is difficult to separate out the fluorescence shifting due to vibrational relaxation

and that due to energy transfer. Steady-state anisotropy experiments comparing poly-

mers to related oligomers have shown that the anisotropy in polymers can be attributed

to some internal mechanism rather than molecular rotation. [211]

We have calculated that localization of the exciton alone will reduce the anisotropy to

0.35 on average for single chains. This value is valid when broad-band excitation is used

and corresponds to a rotation of the transition dipole of 17◦, which is an average over all

the excitation energies (evenly weighted) and over a number of chains. Of course, this

is an average value and will depend on the microscopic nature of the polymer chain.

For an individual exciton/chromophore this value can range from approximately 0◦

to 90◦ in a few cases. The rotation of the dipole moment upon localization is shown

in figure 5.12 for the 3 chains drawn in figure 5.1. Although this effect is small in

the pump-probe anisotropy measurements presented, it most likely contributes to the

rapid decay of the peakshift in the 3PEPS experiment [1, 62, 97] where we see the

transition frequency change accompanying self-trapping. This observation is consis-

tent with the picture of the polymer chain forming a defect cylinder formation, with

domains of chromophores aligned along the long axis, rather than a random coil. [19]

In a defect cylinder conformation, localization would not rotate the transition moment

greatly but would decrease the peakshift. Westenhoff et al. show significantly greater

loss of polarization in disordered polymers than between low-lying, relatively straight

segments. [221]

The experimental wavelength dependence of the anisotropy decays is consistent with

this picture. Our experiments show that the initial decay is relatively slow (hundreds

of fs) when exciting on the red-edge of the absorption spectrum. As excitation is swept

across the region, towards higher energies, this rate increases slightly. This is consistent

with the fact that it is energetically favourable for EET to go downhill whereas uphill

EET is thermally activated. As excitation is further to the blue, the states which are

excited are of higher energy and, therefore, there are more acceptors on average.

The power dependence of the anisotropy decay is also good evidence for exciton-

exciton annihilation effects at high pump-intensities. At high intensities, two excitons

116


80

60

40

20

0

120100806040200State Number

80

60

40

20

0

Dip

ole

Ro

tatio

n U

po

n L

oca

liza

tion

(d

eg

ree

s)

140120100806040200State Number

80

60

40

20

0

140120100806040200State Number

A

B

C

Figure 5.12: The rotation of the dipole moment upon localization for the 3 chains shownin figure 5.1. The majority of the dipoles are rotated by fewer than 10◦

upon localization. However, a few chromophores may be rotated by asmany as 85-90◦.

117


on the same polymer chain may encounter each other and annihilate. Multi-exciton

states are generally short lived in polymers and other macromolecules because excita-

tions on nearby but distinct chromophores annihilate very effectively, forming a local-

ized higher electronic state that rapidly relaxes through internal conversion [222,223].

This rapid relaxation is observed in the high intensity anisotropy decay shown in fig-

ure 5.9b). Care must be taken to avoid such power dependent effects if one hopes to

investigate the dynamics of single excitons.

Ultrafast (< 100 fs or faster) decays are observed with excitation very far to the blue

at approx. 400 nm, [47, 101] which can be qualitatively explained by conformational

disorder shortening the effective conjugation length. Short, blue segments are found in

parts of the chains where there are lots of kinks and bends, breaking up the conjugation.

Moving away from those segments will result in greater depolarization then if straight

(red), parallel segments are initially excited. [221] This rapid depolarization cannot be

explained within the framework of incoherent hopping. This ultrafast component is

not observed in the anisotropy decay of broken conjugation MEH-PPV [47], suggesting

that this effect is dependent on the degree of coupling between chromophores, giving

rise to collective exciton states. If this decay were due to EET by an incoherent hopping

mechanism, it would appear in the spectroscopy of both the fully conjugated polymer

and the broken MEH-PPV [47]. Additionally, there exists the possibility of forming

free charge carriers by overcoming the exciton binding energy with such high energy

excitation.

The anisotropy decays for the POPV oligomers presented in figure 5.11 are strong

evidence that interchromophore interaction plays a role in the ultrafast depolarization

in polymers. The depolarization is not simply due to vibrational relaxation because this

would occur in the oligomers as well. If geometric relaxation contributes to this decay,

it is only when accompanied by localization of the exciton (see figure 5.12). Much previ-

ous work has demonstrated the importance of torsional motions on the spectroscopy of

conjugated poly- and oligomers, most obviously in the asymmetry between absorption

and PL spectra. [13, 57, 62, 75] It is unlikely that relaxation of these modes contribute

significantly to the ultrafast dynamics because of the very low frequency. However,

they are clearly important on a longer timescale. It has been proposed that the rate

118


of energy transfer is affected by torsional relaxation on a picoscecond timescale [123].

Westenhoff et al. demonstrate that the exciton size increases upon torsional relaxation

in polythiophenes and that accounting for this is necessary to correctly simulate the

energy transfer dynamics. Using a site-selective experiment where EET cannot con-

tribute, they attribute a red shift in the PL to this relaxation. The red shift is not

observed in samples where the torsions are blocked. [123] The reorganization associated

with the relaxation of some intramolecular modes is likely on a timescale similar to that

of energy transfer in MEH-PPV as well. [46] In MEH-PPV, however, the importance

of these effects may be obscured or diminished by the larger conformational disorder

and disorder related localization. [44]

As shown in figure 5.4 the early time-fluorescence derives from a sub-set of the ensem-

ble of states that is near in energy to that of the excitation source. That is, absorption

and fluorescence are from nearly the same set of chromophores; there is little spectral

migration. However, the anisotropy can change greatly on this timescale as shown in

figures 5.5 and 5.6 without a large average energy change. Still, at early times the fluo-

rescence depends on excitation wavelength. As time progresses, a small time-dependent

Stokes’ shift is indeed observed. Intramolecular reorganization and energy transfer on a

longer timescale is responsible for the rest of the large apparent Stokes’ shift observed

in MEH-PPV [97] and other conjugated polymers. Again, this phenomenon is even

more apparent in films, where interchain energy transfer dominates. [97, 101]

A systematic excitation wavelength dependence is difficult to establish in single

chains. When excitation is far from resonance, very few states are excited and those

are often very energetically different from other states, that is the states are further

apart (see figure 5.4) . Thus, there is little interaction between them and the rate of

transfer is estimated to be slow in the present simple model (see equation 5.13). This

results in a very slow anisotropy decay. Higher excited states are not included in the

simulations and will most likely contribute to the experimentally observed anisotropy

decays when exciting in the blue.

At excitation energies nearer to resonance, there is still a strong dependence on the

microscopic conformation of the single chain. Chromophores which are energetically

similar do not necessarily have the same conformation or the same degree of coupling

119


to other chromophores. Therefore, the dynamics of a single chain reflect the micro-

scopic nature of the chromophores which are directly excited. Therefore, the degree

of anisotropy decay will change depending on the chain. In practice, the averaging

done in an ensemble experiments is over many more chains and can give good average

values which do not reflect the nature of every state. Looking at the radii of gyration

of the various chains it is clear that, on average, the size dependence shown in figure

5.5 is consistent with the present model of polymer dynamics where conformation is

important. This reflects the tendency for certain types of chain conformations to have

certain types of chromophores more often. The chain with the largest radius of gyra-

tion, that is the most extended conformation with a lesser degree of coupling between

subunits, has the slowest anisotropy decay on average. The smallest chain, where the

chromophores are the most strongly coupled, has the fastest decay.

The work on fluorescence depolarization by Grage et al. shows that there is an

anisotropy-decay dependence on chain conformation [44]. By changing the average con-

jugation length or the distribution of site energies, differences in simulated anisotropies

could be obtained. Our work presented here also shows that there is a strong de-

pendence on the microscopic molecular structure. These subtleties are often lost in

ensemble measurements. Our simulations show that the overall fluorescence decay rate

is different for each chain. This microscopic difference could help explain the difficulty

in fitting fluorescence decays to sums of exponentials. Additionally, the dynamics differ

greatly for exciton states of very similar energy. They may be in very different local

conformations in the chain and coupled to varying degrees to neighbours. Both ener-

getic compatibility and spatial proximity must be taken into account. Excitation on

chromophores that are spatially separated from other chromophores (for example at

the ends of the chain) and therefore only weakly coupled will not quickly relax through

the exciton manifold (ref figure 5.6d). There is very little associated anisotropy decay.

On the other hand, if a chromophore is strongly coupled to others, there will be rapid

relaxation and anisotropy decay. Our results are consistent with those that show that

interchain species can play a role in ultrafast depolarization. [101] In dilute solution,

there will be far fewer interchain species than in films [97]. The dynamics follow more

closely those of isolated chains in films.

120


Overall, we have demonstrated that relaxation through the manifold of exciton states

can lead to rapid depolarization of the anisotropy. This is not necessarily accompanied

by large energetic or spatial migration of the exciton but is a consequence of the disor-

der inherent in polymer chains. Even though the spatial extent of exciton translation

is very small, the effect on the anisotropy decay, for example, can be profound. Simula-

tions and calculations were necessary to obtain these insights because the subtleties of

these effects are hidden by the large degree of disorder in the ensemble which is probed

by experiment. In fact, even single molecule studies are affected by the microscopic

nature of the numerous chromophores on a single polymer chain.

121

6 Additional Contributions to the Peakshift

It is very difficult to fit the initial experimental peakshift when simulating the 3PEPS

data. This is because, at short times, additional pathways can contribute to the signal

and are not properly accounted for in the picture of a two-level system. In this chapter

I will briefly revisit the contributions to the 3PEPS decay by considering the role that

a higher excited state would play in the relaxation dynamics following photoexcitation.

Simulations in this chapter make use of code that was written by Mayrose Salvador.

Beginning with the formalism presented in chapter 3 for a two-level system, I expand

this to look at the effect of excited state absorption on the peakshift.

6.1 Importance of “Non-rephasing” terms

Before considering higher excited states, it is necessary to understand the contributions

in a two-level system. The relevant response functions for the photon echo are those

that cause rephasing (R1, R4, R5, R8). For those that do not (R2, R3, R6, R7) the decay

in the third order polarization signal is more like a free induction decay (FID). [39] If

the delay between the first two pulses, t′1, is zero, all response functions yield an FID

because the rephasing depends on the correlation between the evolution during times

t′1 and t′3 as defined in figure 3.5. Because it is impossible to differentiate between

pathways that give rise to a ground state population and those that propagate on the

excited state using the 3PEPS experiment, only R1 − R4 are considered. These four

important response functions are included in these simulations.

The effect of including non-rephasing terms is shown in figure 6.1. These diagrams

R2 and R3 (ref. figure 3.4) contribute echoes to the signal in the −k1 + k2 + k3 when

the pulse ordering is k2,k1,k3 or k3,k1,k2. That is, they are only important when

122


20

10

0

-10

Peak S

hift

(fs)

10008006004002000Population Time (fs)

Figure 6.1: The contribution of different response functions to the peakshift. The solidline was simulated using R1 − R4 as defined in figure 3.4. This includesboth rephasing and non-rephasing contributions. The dotted line includesonly R1 and R4 – the rephasing diagrams. The dashed line includes onlyR2 and R3 – the non-rephasing diagrams.

the delay between the first two pulses, τ , is negative. Clearly these contribute to the

signal at all values of T (at negative τ) and must be included with their corresponding

rephasing term. It has been shown that this experiment follows the correlation function

closely. [39] This gives us a check to ensure that our simulations are sensible. When

there is no disorder included in the correlation function, the peakshift will decay to

zero. This is the case when both the rephasing and non-rephasing terms are included

as shown in figure 6.1.

123


6.2 Higher Excited States in PPVs

In this chapter, we examine the contribution of a higher-lying state to the 3PEPS de-

cay. First, we must know the about the excited states. Vardeny and coworkers have

done extensive research into the nature of higher lying excited states. [224] Generally,

the electronic states have been found to be similar to those of large centro-symmetric

molecules. The photophysics of many conjugated polymers is therefore determined by

an alternation of odd- (Bu) and even- (Ag) parity excited states. [23] Usually we only

consider the transition between ground (1Ag) and the first excited state (1Bu) because

Ag-Ag transitions are one-photon symmetry-forbidden.

6.3 Excited State Absorption

We consider the possibility of excited state absorption to a higher state (f) as a con-

tributor to the 3PEPS signal. This requires the inclusion of additional signal pathways

to the simulation of the 3PEPS signal. This additional term was proposed as a possible

contributor to the rapid decay of the peakshift in the polymer and oligomer experi-

ments discussed in chapter 4 as suggested previously [1]. The Feynman diagram for

this response function is shown in figure 6.2.

The relevant correlation functions are as follows:

ξee(τ2) = 〈δωeg(τ2)δωeg(0)〉ξff (τ2) = 〈δωfg(τ2)δωfg(0)〉ξef (τ2) = 〈δωeg(τ2)δωfg(0)〉ξfe(τ2) = 〈δωfg(τ2)δωeg(0)〉 (6.1)

where the first is the normal e-g energy gap correlation function used in simulation

of the two-level system. The others are the correlation functions for the fluctuations

between the f-state and ground state and the cross-correlation functions, respectively.

It has been shown experimentally that two different excitation pulses can successively

124


ge

ee

fe

t1'

t3'

t2'

eg

ee

fe

k2

ks

k3

-k1

k2

ks

k3

-k1R ESA - r R ESA - nr

Figure 6.2: Feynman diagrams for excited state absorption into a higher excited state.RESA−r is the rephasing contribution to the echo signal. RESA−nr is non-rephasing.

generate odd-parity (1Bu) excitons and then reexcite them to higher Ag states. [224]

Since this higher state can be seen as being formed by the sequential excitation of two

one-exciton states, it is reasonable to assume that the transition can be written as the

sum of the time-independent and fluctuating terms associated with each of the one

exciton energies, δωeg and δωe′g. The fluctuations are assumed to be the same as for

the one-exciton states |e〉 and |e′〉. Thus,

δωfg(t) ∼= δωeg(t) + δωe′g(t) (6.2)

Substituting equation 6.2 into equations 6.1, we get

1

2ξff (τ2) = ξef (τ2) = ξfe(τ2) = ξee(τ2) + ξe′e(τ2) (6.3)

The cross-correlation function ξe′e(τ2) tells about exciton-exciton interaction induced

dephasing processes. We consider that the fluctuations in the exciton states may not

be perfectly correlated, hence we use these separate correlation functions and their

associated lineshape functions. The response functions associated with figure 6.2 are

listed below. Here the ts refer to the delays between the pulses. That is, primes have

125


been omitted for clarity.

RESA−r(t3, t2, t1) = − exp[−∫ t1+t2

t1

dτ1

∫ τ1

t1

dτ2ξee(τ1, τ2)

−∫ t1+t2+t3

t1+t2

dτ1

∫ τ1

t1+t2

dτ2ξff (τ1, τ2)

−∫ t1+t2+t3

0

dτ1

∫ τ1

0

dτ2ξ∗ee(τ1, τ2)

−∫ t1+t2

t1

dτ1

∫ t1+t2+t3

t1+t2

dτ2ξ∗ef (τ1, τ2)

+

∫ t1+t2

t1

dτ1

∫ t1+t2+t3

0


+

∫ t1+t2+t3

t1+t2

dτ1

∫ t1+t2+t3

0

dτ2ξ∗fe(τ1, τ2)] (6.4)

RESA−nr(t3, t2, t1) = − exp[−∫ t1+t2

0

dτ1

∫ τ1

0

dτ2ξee(τ1, τ2)

−∫ t1+t2+t3

t1+t2

dτ1

∫ τ2

t1+t2

dτ2ξff (τ1, τ2)

−∫ t1+t2+t3

t1

dτ1

∫ τ1

t1


−∫ t1+t2

0

dτ1

∫ t1+t2+t3

t1+t2

dτ2ξ∗ef (τ1, τ2)

+

∫ t1+t2

0

dτ1

∫ t1+t2+t3

t1


+

∫ t1+t2+t3

t1+t2

dτ1

∫ t1+t2+t3

t1

dτ2ξ∗fe(τ1, τ2)] (6.5)

We can write the response functions in terms of the lineshape functions gαβ(t) by

making use of the relationship between lineshape function and a correlation function,

equation 3.4, as discussed in chapter 3. The rephasing contribution to the excited state

126


absorption is given as an example:

RESA−r(t3, t2, t1) = exp{−gff (t3)− gee(t3) + gef (t3) + gfe(t3)

+gef (t2)− gee(t2)− g∗ee(t1)− gef (t2 + t3)

+gee(t2 + t3)− g∗fe(t1 + t2) + g∗ee(t1 + t2)

+g∗fe(t1 + t2 + t3)− g∗ee(t1 + t2 + t3)} (6.6)

Making use of relation 6.3, we are able to fully define the response function in terms of

only two lineshape functions – gee(t) and ge′e(t). gee(t) describes the two-level system

response. ge′e(t) can take on any form but is likely to exhibit a rapid decay because of

the dephasing inherent when two non-identical exciton states |e〉 and |e′〉 are excited.

In this study, we use the general case that the excitons are weakly correlated. There

are three extreme sub-cases, each of which simplify the relationship between all of the

correlation functions, equation 6.3. The cases are: the excitons are independent; they

are perfectly correlated; they are anti-correlated. In any of these extremes, the response

functions may be written using only the lineshape function gee(t) which is used in the

two-level system simulations and is related to the fluctuations in the eg energy gap. In

these cases, ge′e(t) does not contribute.

The effect of changing the coupling in ge′e(t) is illustrated in figure 6.3. The effect

of changing the decay rate is shown in figure 6.4. Clearly neither of these parameters

can be adjusted to induce a lowering of the initial peakshift and an ultrafast decay in

the 3PEPS. Other contributions must be considered to fully characterize the early part

of the 3PEPS data.

6.4 Vibrational Cooling

Vibrational cooling would contribute to the 3PEPS signal if the cooling induces de-

phasing. That is, the fluctuations are different in vibrationally excited states than

in lower vibrational states: memory is lost as spectral diffusion occurs. The simplest

thing to model that includes cooling is to look at a “one step down” process, looking

127


50

40

30

20

10

Peak S

hift

(fs)

102 3 4 56

1002 3 4 56

10002 3


Figure 6.3: The effect of the coupling strength in ge′e(t). The coupling was variedfrom 100 cm−1 (dashed line) to 200 cm−1 (dotted line) to 300 cm−1 (solidline). All other parameters were kept constant. The long-time peakshift isdecreased with increased coupling.

128


50

40

30

20

10

Peak S

hift

(fs)

10 100 1000Population Time (fs)

Figure 6.4: The effect of the decay rate in ge′e(t). The time constant was varied from2000 fs (dashed line) to 200 fs (dotted line) to 20 fs (solid line). All otherparameters were kept constant. Neither the initial peakshift nor the long-time offset were significantly affected.

129


at the relaxation down one rung on the ladder of vibrational states. This was included

as a detuning during the population period. That is, the average energy of the chro-

mophores interrogated by the experiment moved further from resonance with the laser

pulse. There was no effect on the peakshift due to vibrational cooling even for large

detuning.

6.5 Further Contributions

In order to fully understand the initial peakshift and fast decay dynamics, we need to

further refine the model of what may contribute both in terms of the response function

formalism and from the viewpoint of polymer photophysics. Localization likely does

not fully explain the ultrafast decay observed in the oligomer 3PEPS data. The poly-

mer, on the other hand, probably shows the effects of localization to a greater extent.

As shown in this chapter, the fastest decay cannot be explained by excited state ab-

sorption either. Exciton-exciton annihilation perhaps contributes, where one exciton

is returned to the ground state and another gains its energy, becoming an effective

potential energy donor.

We have shown experimentally in chapter 5 that exciton-exciton annihilation can

occur in polymers when there is more than one excitation per chain by looking at the

energy dependence in figure 5.9b. It is reasonable that a coherence between excitons

can also occur. In polymers, this has an intuitive interpretation. Spatially separated

conformational subunits are excited to |e〉 states. Because they correspond to separate

chromophores on the same chain, the excitations are unlikely to form a population,

|e〉〈e|. Instead, during the “population period”, a second coherence is more likely to

exist between |e〉 and |e′〉, which continues the dephasing during this time period. In

this case, it is difficult to see how the system could ever rephrase completely. Thus,

inclusion of this effect would likely cause dephasing and a concomitant rapid decay in

the peakshift.

Perhaps it is also necessary to revisit the role that torsions may play in the ultrafast

photophysics of conjugated polymers and oligomers. Because they behave differently

130


than other vibrational modes, torsions are not included properly in the Brownian os-

cillator model. Additionally, energy relaxation between different torsional levels may

have to be included. It is still not clear what role torsional relaxation has on the extent

of exciton delocalization. Torsions may change the extent of delocalization by coupling

to excitons [60,64–66] as has been suggested previously. Further analysis must include

an in-depth study of these modes.

The initial peakshift remains difficult to fit. However, we have shown that inclusion

of excited state absorption does not contribute to the rapid decay of the peakshift.

We have also proposed other possible explanations specific to conjugated polymers and

oligomers. This can provide direction for further study of the ultrafast component in

the peakshift experiment and for conjugated polymer photophysics more generally.

131

7 Conclusions

In this thesis, I have discussed the complex photophysics of conjugated polymers. As

discussed throughout the thesis, the optical properties and dynamics of conjugated

polymers are strongly influenced by chain conformation. The properties of conjugated

polymers are characterized by an interplay of π-system conjugation lengths and con-

formational disorder owing to the relatively low energy barrier for disruptive small

angle rotations around σ-bonds along the backbone of conjugated chains. The breaks

in conjugation can arise from chemical defects, configurational imperfections, and tor-

sional disorder (which is dynamic). Conformational disorder in the polymer backbone

is of utmost importance as it directly dictates the electronic properties of the polymer

by disruption of the intrinsic π-system conjugation. This conformational disorder can

be seen in the spectroscopy of conjugated polymers as a kind of inhomogeneous line

broadening.

By simultaneous modeling of the peakshift with the fluorescence and absorption line-

shapes, we have shown that the basic characteristics of conjugated polymers are derived

from those of conformational subunits. However, they are not simply a superposition

of contributions from each subunit; these conformational subunits couple to contribute

collective electronic states to the absorption spectrum. Owing to the interaction be-

tween subunits, it is clear that there will be a profound dependence of the photophysics

on conformation/ morphology. Subsequent to absorption, these collective states can be

rapidly localized. Relaxation through the exciton manifold occurs very quickly. Energy

transfer between subunits occurs on a longer timescale. This narrows the distribution

of chromophores which are excited. Fluorescence occurs from the lowest energy seg-

ments.

Comparison of the 3PEPS to polarization anisotropy experiments allowed for deeper

analysis of the competing ultrafast processes. The fastest dynamics are complicated

132

7 Conclusions

and likely attributable to numerous entangled processes. Simulations performed on

single chains of PPVs allowed us to show that the local conformation of chains is very

important, dictating the coupling and relaxation between exciton states. The effect of

this relaxation on the anisotropy is marked, even when the spatial extent of migration

is small. These simulations were crucial as most of this detail is obscured by disorder

in ensemble experiments.

Overall, we have used complementary experimental and theoretical techniques to

elucidate the optical properties and dynamics of conjugated polymers. We have shown

that conformation dictates electronic properties, which in turn, strongly influence the

optical properties and dynamics. Understanding of these phenomena are necessary to

further develop technologies based on conjugated polymers.

133

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Photophysics of Conjugated Polymers · Photophysics of Conjugated Polymers Tieneke E. Dykstra Doctor of Philosophy, 2008 Graduate Department of Chemistry University of Toronto Abstract

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