Modelling polymers with side chains: MEH-PPV and P3HT

This article was downloaded by: [Francisco Lavarda]On: 12 October 2012, At: 07:24Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Molecular SimulationPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/gmos20

Modelling polymers with side chains: MEH-PPV andP3HTA. Batagin-Neto a , E. F. Oliveira a , C. F.O. Graeff a b & F. C. Lavarda a ba UNESP, Univ. Estadual Paulista, POSMAT, Programa de Pós-Graduação em Ciência eTecnologia de Materiais, Bauru, SP, Brazilb DF-FC, UNESP, Univ. Estadual Paulista, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01,17033-360, Bauru, SP, Brazil

Version of record first published: 12 Oct 2012.

To cite this article: A. Batagin-Neto, E. F. Oliveira, C. F.O. Graeff & F. C. Lavarda (): Modelling polymers with side chains:MEH-PPV and P3HT, Molecular Simulation, DOI:10.1080/08927022.2012.724174

To link to this article: http://dx.doi.org/10.1080/08927022.2012.724174

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form toanyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses shouldbe independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims,proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly inconnection with or arising out of the use of this material.

Modelling polymers with side chains: MEH-PPV and P3HT

A. Batagin-Netoa, E.F. Oliveiraa, C.F.O. Graeffa,b and F.C. Lavardaa,b*

aUNESP, Univ. Estadual Paulista, POSMAT, Programa de Pos-Graduacao em Ciencia e Tecnologia de Materiais, Bauru, SP, Brazil;bDF-FC, UNESP, Univ. Estadual Paulista, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01, 17033-360 Bauru, SP, Brazil

(Received 17 June 2012; final version received 11 August 2012)

Modelling polymers with side chains is always a challenge once the degrees of freedom are very high. In this study, wepresent a successful methodology to model poly[2-methoxy-5-(20-ethyl-hexyloxy)-p-phenylenevinylene] (MEH-PPV) andpoly[3-hexylthiophene] (P3HT) in solutions, taking into account the influence of side chains on the polymer conformation.Molecular dynamics and semi-empirical quantum mechanical methods were used for structure optimisation and evaluationof optical properties. The methodology allows to describe structural and optical characteristics of the polymers in asatisfactory way, as well as to evaluate some usual simplifications adopted for modelling these systems. Effectiveconjugation lengths of 8-14.6 and 21 monomers were obtained for MEH-PPV and P3HT, respectively, in accordance withexperimental findings. In addition, anti/syn conformations of these polymers could be predicted based on intrinsicinteractions of the lateral branches.

Keywords: MEH-PPV; P3HT; electronic structure calculation; modelling branched polymers

1. Introduction

Polymeric materials have been used in a great variety of

technological applications due to their interesting optical–

electronic and mechanical properties, easy processing

and relatively low cost. In particular, conjugated organic

polymers have attracted great attention in the manufacture

of semiconductor devices such as light-emitting diodes,

solar cells, transistors, optocouplers, photodiodes, triodes,

voltage regulators and lasers [1]. The usefulness of these

materials comes from the fact that small changes in the

constitution of their monomeric units can result in profound

changes in their physicochemical properties, allowing a

wide adjustment range [2].

A significant increase in experimental and theoretical

studies involving not only polymers but also other organic

materials has been recently observed. Molecular model-

ling studies involving computational chemistry and

theoretical physics have enabled significant advances in

understanding the basic properties of these materials, as

well as in the development of more efficient devices/sys-

tems.

Since most of the organic-based devices are structured

in a thin film form, it is interesting that polymeric materials

present good solubility and stability in organic solvents in

order to obtain films with reasonable homogeneity and

good adhesion to substrates [3]. In this sense, polymers with

lateral chains have been employed for the manufacture of

devices.

It is known that polymers’ solubility in organic solvents

depends on several factors mainly associated with the

chemical structure of the polymer, such as molecular

weight, polarity, cross-linking degree, crystallinity and the

presence/absence of side branches [4]. Generally, the

presence of lateral chains renders greater solubility, since it

allows a better interaction between polymer and solvent

molecules. On the other hand, it is also expected that very

long branched chains present high entanglement degree,

hampering the solvation of the polymer and reducing its

solubility. Thus, more soluble materials are supposed to

have relatively short branches.

The presence of these lateral chains, which at the same

time provides higher solubility to the compounds, sets an

additional problem for conformational studies of these

polymers via electronic structure calculations. The high

flexibility of the side chains, combined with possible steric

interactions between branches of adjacent monomeric

units, allows a great variety of distinct conformations

relatively close in energy, resulting in a high number of

structures by considering just one repeating unit.

There is no concern with the conformation search of

these side chains in most of the molecular modelling studies

of polymers reported in the literature. In general, a shorter

lateral chain is chosen to study the conformation of the main

chain [5]. This procedure is based on the fact that the

optical–electronic properties of polymers are directly

associated with the structural characteristics of the main

chain. However, although it is a valid approach, it ignores

situations where there is a significant interaction between

the side chains of adjacent monomeric structures. Such

steric interactions are, in fact, barriers that can influence the

ISSN 0892-7022 print/ISSN 1029-0435 online

q 2012 Taylor & Francis

http://dx.doi.org/10.1080/08927022.2012.724174

http://www.tandfonline.com

*Corresponding author. Email: [email protected]

Molecular Simulation

iFirst article, 2012, 1–13

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

conformation of the polymer’s main chain and significantly

alter its conjugation length and optical properties.

The work described here presents a methodology for

molecular modelling of polymers by employing semi-

empirical calculations, considering the influence of side

branches in the conformational study of oligomers.

Interactions between distinct polymers chains were not

considered in this model. Although these interactions

presumably influence optical and structural properties of

the system, a secondary hole is expected in solutions

(frequently employed in films manufacturing) where

interchain interactions are not supposed to be relevant. In

addition, interactions between adjacent backbones are

expected to be hindered in polymers with large side chains

[6]. In these systems, stronger interactions are expected

between lateral ramifications of adjacent repeating units

which somewhat shield the main chain.

Two conjugated conducting polymers widely used in

opto-electronic devices were evaluated in order to illustrate

the methodology: poly[2-methoxy-5-(20-ethyl-hexyloxy)-

p-phenylenevinylene] (MEH-PPV) and poly[3-hexylthio-

phene] (P3HT). The method, besides being computation-

ally feasible, has shown to be effective in obtaining

optimised structures and allowing the prediction of some

properties of these polymeric materials in solution.

In the following sections, the methodology used for the

polymer modelling is presented, followed by the results of

the study of MEH-PPV and P3HT oligomers employing

the described methodology. It is important to emphasise

that the methodology described here aims to evaluate

medium-sized systems with lateral ramifications; thus, it is

not a general approach to deal with large systems (as

proteins and DNA chains). For this purpose, the reader

may refer to Refs [7–10].

2. Methodology

2.1 Theoretical methods

In this study, we have employed molecular dynamics (MD)

simulations in order to obtain structures with different

conformations of the side chains of the polymers. The

MM þ force field [11] implemented in Hyperchem

computer package was employed.1 Details of MD

simulations are discussed in Section 2.2.

For optimisation of all structures (monomer, dimer,

tetramer and oligomers), we have employed the semi-

empirical parametric methods 3 and 6 (PM3 and PM6)

[12,13] (for MEH-PPV and P3HT, respectively)

implemented in the computational package MOPAC2009

[14,15] in a restricted Hartree–Fock (RHF) approach. The

presence of the solvent was simulated by conductor-like

screening model (COSMO) [16]. Interchain interactions

were not considered.

The choice of a semi-empirical method to structure

optimisation is justified by the size of the considered

systems, since an ab-initio approach would be computa-

tionally expensive, or even unfeasible, given the large

number of conformations evaluated (see Section 2.2). In

addition, it is known that steric interactions, such as van

der Waals interactions (expected to exist between the

lateral chains), are not well described by many ab-initio

and density functional theory approaches [17,18]. PM3

semi-empirical method has been chosen to study MEH-

PPV since barrier torsion studies of poly( p-phenylene-

vinylene) (PPV) employing this method have shown

superior geometries in comparison with similar methods

[19–21]. On the other hand, a relative lack of studies can

be noted on P3HT polymer employing semi-empirical

methods. In this sense, we have opted to use the PM6 semi-

empirical method since it has been already satisfactorily

employed in the study of photovoltaic properties of P3HT

derivatives [22,23].

The theoretical optical absorption spectra of the

structures were all calculated using the ZINDO/S semi-

empirical method in conjunction with configuration

interaction approach for single excitations implemented

in Orca computational package [24,25]. We have

considered the first 10 transitions (roots) for each structure

(considering only singlet state transitions).

MD and geometry optimisations were performed on an

Intel Coree 2 Quad 2.40 GHz computer. Typically, 15 s

were taken for MD simulations of each structure; the

geometry optimisations were performed from 2 s to 42 h

depending on the oligomer size. Optical absorption spectra

calculations were made using Intel Xeon 2.83 GHz

machines, demanding between 24 s and 2 h 30 min for

each structure depending on the oligomer considered.

2.2 Conformational studies approach

Figure 1 shows the repeating units of MEH-PPV and

P3HT polymers.

As can be seen, both structures present side chains

entirely composed of single bonds between carbon atoms.

In fact, high conformation flexibility of these branches can

result in a large number of different conformers with

relatively close energies.

Figure 2 exemplifies possible variations that lateral

chains can perform in these polymers. Since the rotations of

these single bonds require relatively little energy to occur, it

is difficult to obtain unique lower energy structures.

Obtaining geometries that adequately describe the

polymer is extremely important in electronic structure

calculations, since the electronic Hamiltonian depends

parametrically on the position of the atoms of the system

studied. A systematic search of different angles illustrated

in Figure 2 becomes impracticable, since the initial number

of possible conformations would be very high. Consider-

ing, for example, a systematic study with 908 steps, it would

be possible to construct about 65,536 (48) distinct structures

A. Batagin-Neto et al.2

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

for each monomeric unit of MEH-PPV and 4096 (46)

structures for P3HT.

Given the impossibility of a systematic analysis of the

hyper-surface generated by varying the angles illustrated

in Figure 2, it is an attractive option to scan regions of this

hyper-surface, considering low correlated structures with

different conformations of the side chains.

In order to obtain these initial structures, MD

simulations at high temperatures have been performed.

The main chain of the polymer is maintained (locked) in a

specific configuration (discussed later) while side chains

could change its conformation during MD. The dynamics is

performed supposing the system in contact with a thermal

reservoir at an initial temperature of 1000 K. After 1 ps of

simulation (simulation step of 0.001 ps), the dynamics is

stopped and the resulting structure is stored for further

optimisation. Subsequently, the MD is restarted and

another structure is obtained (after 1 ps of simulation) and

so on. In order to obtain weakly correlated structures, the

reservoir temperature is increased by 500 K for each five

conformations.

The MD simulations were performed only to generate

random structures for further optimisation employing

quantum methods. In this sense, unusual parameters were

employed in the simulations: (i) high temperatures to obtain

weakly correlated conformations and (ii) relatively short

simulation time (just to describe ‘randomic’ bonds’

rotations).

Aiming to ensure that optimisation using quantum

mechanical methods (RHF-PM3/PM6-COSMO) does not

present convergence problems, a pre-optimisation with

molecular mechanics methods was previously performed

for all the initial structures (MMþ with gradient norm#1).

In optimisations via RHF-PM3/PM6-COSMO methods the

gradient norm employed was 0.05, higher than the

commonly used in calculations made in the absence of

solvent [26,27].

The conformational study was divided into topics to

identify relevant aspects of the polymer structure: (i)

monomers, (ii) dimers, (iii) tetramers and (iv) oligomers

(five or more repeating units). In all optimisation

calculations, the same parameters pointed above were

employed.

(1) Monomers study: Given the high conformational

flexibility of polymers’ side chains (Figure 2), a large

variety of conformers is expected. The study of the

monomer was conducted aiming to evaluate possible

lower energy configurations of the isolated branches.

The monomers were obtained by hydrogenating the

ends of the polymer’s repeating unit. Freezing the

main structure on a planar conformation, MD

simulations were performed on the side chains to

obtain distinct structures. Thus, 50 different initial

structures were obtained for further optimisation (for

each polymer). The optimisation was also performed

with the monomer’s main chain locked in a planar

conformation.

(2) Dimers study: A natural step in the search for

equilibrium conformation of a polymer is the study of

dihedral angles formed between adjacent monomers.

In polymers having large lateral branches, this kind of

study is not easy, since a large number of freedom

degrees is expected. With this concern, the study is

generally carried out considering a specific confor-

mation of the side chains. This analysis, however, does

not provide reliable results, since it is restricted to a

specific conformation of the chains. In this approach, it

is not possible to evaluate steric interactions between

them, which probably have a great influence on the

equilibrium conformation of the polymer.

To better evaluate these interactions, we chose to

conduct the study of the angle between adjacent

monomeric structures by sampling, considering the

angles between the adjacent rings of the dimer (see

Figure 3).

Initial structures were obtained by blocking the main

chain of the dimer in four different configurations

(presenting 0, 90, 180 and 2708 for dihedral angles

between adjacent rings) and by employing the MD

approach for obtaining random structures. About 50

different conformations were obtained for each

blocked main chain configuration of MEH-PPV and

Figure 1. Structural formulae of MEH-PPV and P3HT.

Figure 2. Degrees of freedom of side chains’ single bonds forMEH-PPV and P3HT.

Molecular Simulation 3

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

40 for the P3HT, totaling about 200 structures for

MEH-PPV and 150 for P3HT. The structure optimis-

ation was then carried out (RHF/PM3 or

PM6/COSMO), allowing that all distances, angles

and dihedrals be optimised.

The analysis of the angles was carried out by a specific

program developed in Fortran 90, calculating the angle

observed between the planes defined by adjacent rings

of the optimised dimer (i.e. dimer angle). Figure 3

presents the atoms defining the rings (ring A: atoms 1,

2 and 3; ring B: atoms 4, 5 and 6). The results were

compared with those obtained through similar analysis

using Molden 5.0 [28] and Gabedit 2.3.9 [29]

softwares. The relative angle between the vectors

r21 ¼ r22r1 and r54 ¼ r52r4 was also considered in

order to distinguish between u and 1808 2 u angles.

Finally, to evaluate the influence of the lateral chain

extension in the polymer conformation, we studied the

structures with smaller lateral branches (CH3 group).

In this case, around 100 initial structures were

generated for each polymer using the same approach

described above for obtaining the initial structures and

optimisation.

For the purpose of evaluating the average angle

between the repeating units of the polymers consider-

ing the optimised dihedrals angles (Ai) obtained for

each dimer, we used Equation (1).

Ah i ¼

PiAi exp ð2DEi=kTÞPi exp ð2DEi=kTÞ

; ð1Þ

where kAl represents the average angle between

adjacent units of the polymer, Ai is the dihedral angle

found for ith dimer, exp(2DEi/kT) is the Boltzmann

factor and DEi ¼ Ei 2 E0, whereas Ei represents the

energy of the ith dimer and E0 represents the average

energy obtained by considering all the optimised

dimers. For such calculations, a temperature of 300 K

was adopted.

(3) Tetramers study: The tetramer study was carried out to

obtain a structure in which steric interactions between

the side chains were considered. By blocking the main

chain in a specific configuration (dictated by the dimer

study), a series of MD simulations were performed

with the lateral chains to achieve different structures

(similar to that made for the monomers). Thus, 30

different initial conformations were obtained, which

were optimised in an RHF-PM3/PM6-COSMO

approach. During optimisation, the main chain was

also maintained in the configuration of lower energy

obtained from the dimers study.

(4) Oligomers study: To evaluate whether the approach

allows to reproduce relevant properties of the polymer,

a theoretical optical absorption spectrum study of

different oligomers was carried out. The structures

studied were obtained by joining multiple confor-

mations of the more stable tetramer (following the

pattern established by the dimer study). All structures

were then optimised in an RHF-PM3/PM6-COSMO

approach (allowing the optimisation of all structural

parameters).

In order to evaluate the main peak position of the

absorption spectrum in an infinite chain, the exponential

relationship proposed by Meier et al. [30] was employed:

lðnÞ ¼ l1 2 Dl exp ½2aðn2 1Þ�; ð2Þ

where n represents the number of repeating units of the

polymer; Dl ¼ l1 2 l1 represents the total displacement

of the absorption peak caused by the conjugation extension,

where l1 refers to the optical absorption peak for one

repeating unit (n ¼ 1) and l1 refers to the optical

absorption peak for n ! 1. Dl can also be related to the

overall effect of conjugation [30]. The parameter a

indicates how fast the limit of convergence is achieved.

Using Equation (2) the effective conjugation length

(ECL) of the polymers can also be accessed. Meier et al.

suggest a way to evaluate nef assuming a detection limit of

,1 nm so that:

l1 2 lef # 1nm; ð3Þ

where lef is the value of the optical absorption peak for the

ECL (n ¼ nef).

3. Results and discussion

3.1 Poly[2-methoxy-5-(20-ethyl-hexyloxy)-p-phenylenevinylene]

Figure 4 shows the heat of formation of various monomers

obtained using the methodology outlined above. The

dotted lines subdivide the graph into intervals of kT energy

at room temperature ( , 0.5765 kcal/mol).

A relatively large energy variation can be observed in

the conformers studied (9.7 kcal/mol, ,17 kT at 300 K)

which is exclusively due to the conformations of the side

chains. Figure 5 illustrates the monomers of lower (08, 38

Figure 3. Atoms defining the evaluated ring planes for MEH-PPV and P3HT.

A. Batagin-Neto et al.4

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

and 47) and higher energy (46 and 49) obtained. In

general, no side chain patterns may be observed.

Table 1 shows some selected electronic structure data

of the structures shown in Figure 5 as well as the standard

deviation of these properties regarding the average value

of all optimised structures.

As can be seen, the properties considered present a

relatively small variation which asserts that these structures

have a similar electronic structure. Larger dispersion is

observed in the dipole moment and can be easily understood

since it is quite probable that different conformations of the

side chains induce dipole alterations in the molecules. In

fact, it is well known that opto-electronic properties of

conjugated polymers are almost exclusively related to the

main chain features of these systems [31]. However, this

fact does not discard the concern about the conformations of

the side chains of the polymer, since strong steric

interactions between adjacent branching units could

appreciably influence its backbone conformation.

In order to evaluate these interactions, the study of the

angles between the adjacent rings of monomers was

carried out. Figure 6(a) shows the heat of formation as a

function of the angles between the adjacent rings obtained

after optimisation (grid lines spacing of 2 kT), and Figure

6(b) illustrates the percentage distribution of structures in

the angles at intervals of 208.

Note that there is a tendency of planar conformations

of the units since the highest concentration of structures is

found near 08. The lowest energy conformers are also in

this region, suggesting that the formation of the p system

stabilises the compound.

Another important characteristic is the absence of

lower energy structures at 1808. It indicates that such

arrangement despite facilitating the p system formation is

less likely observed. This result suggests that steric

interaction between the side chains plays an important role

in the conformation of the polymer.

Figure 7 illustrates some lower energy conformations

obtained. Note that the interaction between side chains is

evident.

The results show that polymer conformation is, in fact, a

balance between the stability (promoted by the p system

Table 1. Selected properties of the MEH-PPV monomers.

ConformerHeat of formation

(kcal/mol)Total electric dipole

(D)HOMO

(eV)LUMO

(eV)LUMO2HOMO

(eV)

08 274.803 2.159 28.984 20.338 8.64623 269.352 1.578 29.013 20.364 8.64938 275.233 2.420 29.022 20.353 8.66946 266.233 2.214 28.931 20.370 8.56147a 275.948 2.004 29.015 20.350 8.66549 267.690 1.490 28.938 20.337 8.601Average value 272.662 1.856 28.978 20.360 8.618Standard deviation 1.749 0.517 0.091 0.026 0.070

a Most stable structure.

Figure 4. Heat of formation of the 50 optimised MEH-PPVmonomers.

Figure 5. Structure of monomers 08, 38, 46, 47 and 49 of MEH-PPV.

Molecular Simulation 5

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

formation) and the interaction between side chains of

neighbouring monomer units. Actually, the widespread

distribution around 08 (Figure 6(b)) is probably the result of

this balance.

An average angle around 21.68 is obtained by using

Equation (1) (with the average energy of the conformers

set, E, of 2164.06 kcal/mol), near the planar conformation

of the polymer. In addition, it is possible to observe an

average dispersion of s <418 around 08 (the standard

deviation between 2908 and 908), lightly superior to the

dispersion proposed for PPV polymers (308) [19].

In order to evaluate the ECL of MEH-PPV, we have

generated 100,000 different polymeric structures as the

angle between adjacent units (u) has been randomly

dictated by a Gaussian probability distribution (GPD):

P uð Þ ¼1

s 2pð Þ1=2exp 2

u2 u0ð Þ2

2s2

� �; ð4Þ

where u0 represents the most probable angle between

adjacent units (obtained from the dimer study, i.e. u ¼ 0),

and s is the standard deviation of the distribution. No

correlation was considered between 2nd neighbours

(similar to a 1D random walk problem [32]).

The polymer chains were constructed by adding

monomer units in a sequential manner, with dihedral

angles of adjacent units governed by P(u) distribution. The

ECL was then evaluated by counting the average number of

units required to achieve a total torsion angle of 908 in the

polymer main chain (relative to the first repeat unit). Thus,

an ECL of approximately eight units has been obtained in

agreement with the literature [33].

In general, Figure 6 illustrates the difficulties related to a

structural optimisation study of branched polymers con-

sidering only a specific side chain configuration. As can be

seen, lateral chains significantly alter the structure of the

main chain of the polymer (standard deviation of ,418)

influencing, for example the optical properties of the system.

An approach frequently employed in the studies of

polymers with side branches is the use of reduced lateral

chains. Such simplification is widely used since a

significant reduction in the computational costs is achieved.

In order to evaluate this approach we have studied the dimer

of poly[(2,5-dimethoxy-p-phenylene) vinylene] (DM-

PPV) derivative. The structure of DM-PPV was obtained

by reducing the side chain group by CH3 substituents.

Figure 8(a),(b) shows the heat of formation (as a function of

the angles between adjacent rings after the optimisation)

and the percentage distribution of the structures at angle

intervals of 208, respectively (grid lines spacing of 1 kT).

An average angle of ,5.88 is obtained from Equation

(1) for DM-PPV dimer (E ¼ 290.6 kcal/mol), which also

suggests a planar conformation of the polymer. The

deviation of the planarity can be attributed to the presence

of low energy structures at 1208 (discussed later) and the

consideration of a reduced number of structures in the

Figure 6. (a) Heat of formation obtained as a function of the angles between adjacent rings of the monomers and (b) percentagedistribution of structures of MEH-PPV dimers after optimisation.

Figure 7. Lowest energy conformations for some planar MEH-PPV dimers.

A. Batagin-Neto et al.6

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

calculation (compared to MEH-PPV). In addition, a

smaller dispersion is observed (,16.78) as well as an

absence of structures at 1808, resulting in an ECL of ,36

units (by GPD random walk study), different from that

obtained for larger lateral chains.

The results suggest that the lateral branches’ simplifica-

tion sets a good approximation in the study of the main

chain conformation of PPV derivatives in solution.

However, we must stress the relevance of the optimisation

study by sampling even within this approach. As can be

seen in Figure 8(a), the lowest energy structures obtained

are close to 1208 and 21208 angles, which are not the most

probable conformation (Figure 8(b)). By the way, this fact

is also observed in the study of the dimer with the original

branches, where the lowest energy structure is located close

to 2808. Figure 9 shows the mentioned structures.

Figure 8. (a) Heat of formation obtained as a function of the angles between adjacent rings of the monomers and (b) percentagedistribution of structures of DM-PPV dimers after optimisation.

Figure 9. Lowest energy structures obtained for MEH-PPV and DM-PPV dimers.

Molecular Simulation 7

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

As can be seen, the structures present a very specific

side chains’ configuration, which promote the stabilisation

of the compound. However, it is reasonable to assume that

these settings are not actually observed at room

temperatures due to the high degree of freedom of these

branches. In this sense, Figure 8(a) illustrates the possible

risk of considering only an initial structure for geometry

optimisation since unrealistic local minima can be

achieved.

Although the results obtained for the study of MEH-

PPV and DM-PPV dimers are reasonable, it is important to

consider that the use of only two monomeric units in the

analysis of dihedral angles overestimates the values

obtained, since the influence of the p system is not

satisfactorily considered in these structures. In this way, the

study of properties of the oligomers is still relevant to

structure evaluation.

Figure 10(a) shows the heat of formation of several

optimised structures of the MEH-PPV tetramer, and

Figure 10(b),(c) shows the structure of the lowest energy

tetramer (conformer 05).

Note that complex interactions are observed between

the side chains of adjacent polymer repeating units, which

stabilise the structure. This conformation was employed to

build larger oligomers.

In order to evaluate whether the approach allows to

reproduce relevant properties of the polymer, theoretical

optical absorption spectrum of MEH-PPV oligomers was

calculated. Figure 11 shows the relationship between the

main peak position of the theoretical optical absorption

spectrum and the number of monomeric units in the

oligomer. Table 2 presents the best fit obtained for

Equation (2).

As can be seen, in the infinite chain limit (n ! 1 in

Equation (2)) we obtain the main peak position of the

theoretical absorption spectrum at 445.95 nm with a

deviation of around 10% for the experimental result

(496 nm) [33]. This deviation is consistent with those

obtained with the ZINDO/S method [34]. In addition, the

discrepancy can also be attributed to specific polymer–

Table 2. Exponential fit data for MEH-PPV.

Equation: l(n) ¼ l1 2 Dl exp[2a(n 2 1)]

Parameter Value Error

l1 445.948 0.839Dl 117.858 8.038a 0.351 0.024Correlation (R2) 0.998 –

Figure 10. (a) Heat of formation and (b), (c) lowest energy structure (conformer 05) obtained for optimised MEH-PPV tetramers.

Figure 11. Relationship between the main peak position of thetheoretical optical absorption spectrum and the number of MEH-PPV monomeric units.

A. Batagin-Neto et al.8

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

solvent and polymer–polymer steric interactions that have

not been explicitly considered in this study and are

frequently responsible for red shifts in the absorption

spectrum [35].

Finally, to evaluate the ECL of the polymer, we used

Equation (3). Thus, an average value of nef ¼ 14.6 units

can be obtained for MEH-PPV.

Note that the ECL estimation performed employing

both a Gaussian distribution (8 units) and the extrapolation

of the main peak position of the MEH-PPV oligomers (14.6

units) are compatible to other works which suggest the

presence of around 10 planar substructures in the polymer

[33], which reinforces the methodology proposed for

geometry evaluation. Moreover, note that the dimer study

really overestimates the angles between adjacent rings,

resulting in a reduced ECL value (as discussed above).

3.2 Poly[3-hexylthiophene]

In order to better evaluate the proposed methodology, we

also studied the P3HT-conjugated organic polymer using

the same approach described for MEH-PPV.

Figure 12 illustrates the heat of formation of various

conformers obtained. The dotted lines divide the graph into

kT energy intervals (at room temperature: , 0.5765 kcal/

mol). It was noted that the most stable conformers present

similar heat of formation values (the lowest points in

Figure 12), with a very similar conformation (Figure 13)

despite the geometry optimisation employing different initial

structures. Figure 13 shows the structures of the conformers

that presented the lower (06, 10, 21 and 29) and higher energy

(23 and 34). Note that most stable conformations present a

ladder type lateral chain structure.

Table 3 presents some electronic structure data of the

monomers (lower and higher energy structures) as well as

the standard deviation of these properties (compared to the

average value of all optimised structures).

As can be seen, small deviations are also observed,

indicating that branches’ position does not affect the

electronic structure of the monomer. One can also observe

the great similarity between the most stable conformers

obtained.

Figure 14(a) shows the heat of formation as a function

of the angle between adjacent thiophenics rings of

Table 3. Selected properties of the P3HT monomers.

ConformerHeat of formation

(kcal/mol)Total electric dipole

(D)HOMO

(eV)LUMO

(eV)LUMO2HOMO

(eV)

06 26.226 1.839 29.006 20.107 8.89910 26.232 1.744 29.006 20.095 8.91121 26.235 1.721 29.030 20.121 8.90929a 26.236 1.792 29.007 20.096 8.91123 23.602 1.763 29.028 20.122 8.90634 23.601 1.754 29.009 20.097 8.912Average value 25.201 1.762 29.013 20.106 8.906Standard deviation 0.605 0.044 0.018 0.016 0.005

a Most stable structure.

Figure 12. Heat of formation of the 50 optimised P3HTmonomers.

Figure 13. Structures of the monomers 06, 10, 21, 29, 23 and 34of P3HT, respectively.

Molecular Simulation 9

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

optimised P3HT dimers, and Figure 14(b) illustrates the

percentage distribution of structures at intervals of 208.

Note that, despite the large number of initial random

structures, a sharp distribution is observed between 1008

and 1208 after optimisation. By using Equation (1) (with

E ¼ 215.037 kcal/mol) an average dimer angle of about

110.58 could be obtained, in agreement with in vacuo

Hartree–Fock (6-31G and 6-31G*) studies [36] where a

dihedral angle of 1088 is suggested.

Since the average angle obtained is larger than 908, it is

impossible to estimate the ECL, with a similar approach

that was performed for MEH-PPV (1D random walk). In

this case, the study of oligomers has shown to be more

efficient for ECL determination.

Figure 15 illustrates some of the lowest energy

conformations obtained in the dimer study. Apparently,

conformations of side chains on the opposite sides of the

polymer result in a more stable conformer, contrarily to that

observed for MEH-PPV. Note also a ladder-type confor-

mation of the side chains.

Similar to MEH-PPV, we also carried out the dimer

study on P3HT-reduced main chain derivative, poly

(3-methylthiophene) (P3MT). The structures of P3MT

dimers were obtained by replacing P3HT hexyl chains

with methyl substituents. This study was carried out

aiming to evaluate whether variations of the side chains

length are relevant for the simulation of this polymer.

Figure 16(a) shows the heat of formation and the value

of the dihedral angles obtained for P3MT dimers after the

optimisation. Figure 16(b) shows the percentage distri-

bution of structures in intervals of 208.

It can be observed that the more stable dimers present

angles near to 1208. An average angle of 119.28 can be

obtained through an analysis similar to that performed for

the P3HT dimer.

The results suggest that the simplification of P3HT

side chains leads to an overestimation of repeating units’

angles (approximately 108), which can be attributed to the

interaction of lower lateral chains, resulting in a structure

closer to 1808 (more planar) for P3MT dimers.

Contrary to MEH-PPV, the P3HT did not show a

considerable dispersion around the most probable value

(,10.188), suggesting that the interaction between the side

chains is more specific. In fact, the optimisation of the

monomer has already suggested a most likely conformation

of the side chain, which apparently is not strongly affected

by interaction with other chains. This result shows that

considerable interactions of side chains are observed in

P3HT polymers providing main chain structural changes.

Figure 17(a) shows the heat of formation of P3HT

tetramers after optimisation. Figure 17(b) shows the most

stable tetramer structure obtained (conformer 10), which

illustrates a repulsive interaction between the side chains.

Small deviations of the initial angles of the main chain

could be observed after optimisation; however, these angles

remain within the ranges predicted in the dimer study (near

to 1158). This result can be attributed to an increased

Figure 14. (a) Heat of formation obtained as a function of the angles between adjacent rings of the monomers and (b) percentagedistribution of structures of P3HT dimers after optimisation.

Figure 15. Lowest energy conformations of some P3HTdimers.

A. Batagin-Neto et al.10

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

repulsion between the branches due to the additional

neighbouring units. Such interactions, however, are not able

to induce significant alterations on the backbone

conformation.

Figure 18 shows the relationship between the position

of the optical absorption main peak and the number of

monomeric units for P3HT polymer. Table 4 presents the

best-fit curve data obtained for Equation (2).

In the infinite chain limit, we find the main peak around

385 nm, with a deviation of around 14% of the experimental

result (446 nm) [37]. We believe that the result is reasonable

given the number of approximations made. In addition, the

deviations can be partially attributed to the same steric

interactions discussed for MEH-PPV. Moreover, in this

case thermal effects can also be pointed out as an important

deviation factor. In fact, it could bring the polymer

backbone for a more planar mean conformation, promoting

an appreciable red shift in the spectrum.

Using Equation (2), an ECL of 21 units could be

obtained for P3HT, according to that suggested for

thiophene derivatives in the literature [38].

4. Conclusions

In this study, we have described a methodology for the study

of polymers with side branches, which allows a reasonable

description of side chains’ steric interactions and their

influence on the polymer main chain conformation. In order

Figure 16. (a) Heat of formation obtained as a function of the angles between adjacent rings of the monomers and (b) percentagedistribution of structures of P3MT dimers after optimisation.

Figure 17. (a) Heat of formation and (b) lowest energy structure (conformer 10) obtained for optimised P3HT tetramers.

Molecular Simulation 11

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

to illustrate it, the structural and optical properties of two

widely studied polymers were evaluated.

The methodology allows to evaluate the properties of

polymers in a satisfactory way as the effective conjugation

length, main peak position of the optical absorption

spectrum as well as inherent structural characteristics.

The dihedral angles’ analysis suggest that the

simplification of the side branches is an interesting approach

for MEH-PPV only if certain precautions are taken during

optimisation. Moreover, significant deviations were

obtained for P3HT, suggesting that such simplification is

inadequate for this polymer.

In summary, the methodology allows to satisfactorily

assess the structural and optical properties of polymers. In

addition, it was possible to evaluate commonly adopted

simplifications of these systems.

Acknowledgements

We would like to thank the Brazilian agencies CAPES (INCTMN),FAPESP (Proc. 2012/03116-7) and CNPq for financial support.This research was also supported by resources supplied by theCenter for Scientific Computing (NCC/GridUNESP) of the SaoPaulo State University (UNESP).

Note

1. Hypercube, HyperChemTM, Hypercube, 2002.

References

[1] S. Gunes, H. Neugebauer, and N.S. Sariciftci, Conjugated polymer-based organic solar cells, Chem. Rev. 107 (2007), pp. 1324–1338.

[2] E. Bundgaard and F.C. Krebs, Low band gap polymers for organicphotovoltaics, Sol. Energy Mater. Sol. Cells. 91 (2007),pp. 954–985.

[3] S. Richter, M. Ploetner, W.-J. Fischer, M. Schneider, P.-T. Nguyen,W. Plieth, N. Kiriy, and H.-J.P. Adler, Development of organic thinfilm transistors based on flexible substrates, Thin Solid Films 477(2005), pp. 140–147.

[4] B.A. Wolf, Solubility of polymers, Pure Appl. Chem. 57 (1985),pp. 323–336.

[5] B. Milian Medina, A. Van Vooren, P. Brocorens, J. Gierschner,M. Shkunov, M. Heeney, I. McCulloch, R. Lazzaroni, and J. Cornil,Electronic structure and charge-transport properties of polythio-phene chains containing thienothiophene units: A joint experimentaland theoretical study, Chem. Mater. 19 (2007), pp. 4949–4956.

[6] L.-O. Palsson, C. Wang, D.L. Russell, A.P. Monkman, M.R. Bryce,G. Rumbles, and I.D.W. Samuel, Photophysics of a fluorene co-polymer in solution and films, Chem. Phys. 279 (2002),pp. 229–237.

[7] S.A. Adcock and J.A. McCammon, Molecular dynamics: Survey ofmethods for simulating the activity of proteins, Chem. Rev. 106(2006), pp. 1589–1615.

[8] A. Perez, F.J. Luque, and M. Orozco, Frontiers in moleculardynamics simulations of DNA, Acc. Chem. Res. 45 (2012),pp. 196–205.

[9] S. Shenoy, W. Bates, H. Frisch, and G. Wnek, Role of chainentanglements on fiber formation during electrospinning of polymersolutions: Good solvent, non-specific polymer–polymer interactionlimit, Polymer 46 (2005), pp. 3372–3384.

[10] G.M. Foo and R.B. Pandey, Conformation of interacting polymerchains: Effects of temperature, bias, polymer concentration, andporosity, Phys. Rev. E. 55 (1997), pp. 4433–4441.

[11] A. Hocquet and M. Langgard, An evaluation of the MMþ forcefield, J. Mol. Model. 4 (1998), pp. 94–112.

[12] J.J.P. Stewart, Optimization of parameters for semiempiricalmethods I. Method, J. Comput. Chem. 10 (1989), pp. 209–220.

[13] J.J.P. Stewart, Optimization of parameters for semiempiricalmethods V: Modification of NDDO approximations and applicationto 70 elements, J. Mol. Model. 13 (2007), pp. 1173–1213.

[14] J.J.P. Stewart, MOPAC Molecular orbital package, StewartComputational Chemistry, 2009; Available at http://www.openmopac.net/MOPAC2009.html (2009).

[15] J.J.P. Stewart, MOPAC: A semiempirical molecular orbitalprogram, J. Comput.-Aided Mol. Des. 4 (1990), pp. 1–103.

[16] A. Schafer, A. Klamt, D. Sattel, J.C.W. Lohrenz, and F. Eckert,COSMO implementation in TURBOMOLE: Extension of an efficientquantum chemical code towards liquid systems, Phys. Chem. Chem.Phys. 2 (2000), pp. 2187–2193.

[17] N. Kurita and H. Sekino, Ab initio and DFT studies for accuratedescription of van der Waals interaction between He atoms, Chem.Phys. Lett. 348 (2001), pp. 139–146.

[18] R. Peverati and K.K. Baldridge, Implementation and performance ofDFT-D with respect to basis set and functional for study ofdispersion interactions in nanoscale aromatic hydrocarbons,J. Chem. Theory Comput. 4 (2008), pp. 2030–2048.

[19] D.S. Galvao, Z.G. Soos, S. Ramasesha, and S. Etemad, A parametricmethod 3 (PM3) study of trans-stilbene, J. Chem. Phys. 98 (1993),pp. 3016–3021.

[20] R. Vendrame, V.R. Coluci, and D.S. Galvao, Comparativeparametric method 5 (PM5) study of trans-stilbene, J. Mol. Struct.686 (2004), pp. 103–108.

[21] A. Camilo, R.P.B. dos Santos, V.R. Coluci, and D.S. Galvao,Comparative parametric method 6 (PM6) and Recife model 1(RM1) study of trans-stilbene, Mol. Simul. 38 (2011), pp. 1–7.

[22] R.C. Hiorns, E. Cloutet, E. Ibarboure, L. Vignau, N. Lemaitre,S. Guillerez, C. Absalon, and H. Cramail, Main-chain fullerenepolymers for photovoltaic devices, Macromolecules 42 (2009),pp. 3549–3558.

[23] R.C. Hiorns, P. Iratcabal, D. Begue, A. Khoukh, R. De Bettignies, J.Leroy, M. Firon, C. Sentein, H. Martinez, H. Preud’homme, and

Table 4. Exponential fit data for P3HT.

Equation: l(n) ¼ l12Dl exp[2a(n 2 1)]

Parameter Value Error

l1 385.335 0.408Dl 68.464 1.629a 0.211 0.008Correlation (R 2) 0.998 –

Figure 18. Relationship between the main peak position of thetheoretical optical absorption spectrum and the number of P3HTmonomeric units.

A. Batagin-Neto et al.12

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2

C. Dagron-Lartigau, Alternatively linking fullerene and conjugatedpolymers, J. Polym. Sci. Part A: Polym. Chem. 47 (2009),pp. 2304–2317.

[24] F. Neese, ORCA: An ab initio, DFT and semiempirical SCF-MO,Available at http://www.thch.uni-bonn.de/tc/orca (2010).

[25] F. Neese, The ORCA program system, Wiley Interdiscip. Rev.Comput. Mol. Sci. 2 (2012), pp. 73–78.

[26] J. Tomasi, B. Mennucci, and R. Cammi, Quantum mechanicalcontinuum solvation models, Chem. Rev. 105 (2005),pp. 2999–3093.

[27] M.A. Watson, D. Rappoport, E.M.Y. Lee, R. Olivares-Amaya, andA. Aspuru-Guzik, Electronic structure calculations in arbitraryelectrostatic environments, J. Chem. Phys. 136 (2012), pp. 024101-1–024101-14.

[28] G. Schaftenaar and J.H. Noordik, Molden: A pre- and post-processing program for molecular and electronic structures,J. Comput.-Aided Mol. Des. 14 (2000), pp. 123–134.

[29] A.-R. Allouche, Gabedit-A graphical user interface for compu-tational chemistry softwares, J. Comput. Chem. 32 (2011),pp. 174–182.

[30] H. Meier, U. Stalmach, and H. Kolshorn, Effective conjugationlength and UV/vis spectra of oligomers, Acta Polym. 48 (1997),pp. 379–384.

[31] J. Gierschner, J. Cornil, and H.-J. Egelhaaf, Optical bandgaps of p-conjugated organic materials at the polymer limit: Experiment andtheory, Adv. Mater. 19 (2007), pp. 173–191.

[32] F. Reif, Introduction to statistical methods, in Fundamentals of

Statistical and Thermal Physics, 2nd ed., Boston, McGraw-Hill,

1965, pp. 1–37.

[33] B.J. Schwartz, Conjugated polymers as molecular materials: How

chain conformation and film morphology influence energy transfer

and interchain interactions, Annu. Rev. Phys. Chem. 54 (2003),

pp. 141–172.

[34] L.E. Friedrich and J.E. Eilers, Progress toward calculation of the

hues of azomethine dyes, J. Imaging Sci. Technol. 38 (1994),

pp. 24–27.

[35] A.K. Baveja and V.K. Gupta, Spectrophotometric determination of

vanadium in complex materials using N-m-TMBHA and Thiocya-

nate, Int. J. Environ. Anal. Chem. 17 (1984), pp. 299–306.

[36] M.A. de Oliveira, W.B. Almeida, and H.F. dos Santos, Structure and

electronic properties of alkylthiophenes coupled by Head-to-Tail

and Head-to-Head regioselectivity, J. Braz. Chem. Soc. 15 (2004),

pp. 832–838.

[37] L. Huo, Y. Zhou, and Y. Li, Alkylthio-substituted polythiophene:

Absorption and photovoltaic properties, Macromol. Rapid Com-

mun. 30 (2009), pp. 925–931.

[38] H. Nakanishi, N. Sumi, Y. Aso, and T. Otsubo, Synthesis and

properties of the longest Oligothiophenes: The Icosamer and

Heptacosamer, J. Org. Chem. 63 (1998), pp. 8632–8633.

Molecular Simulation 13

Dow

nloa

ded

by [

Fran

cisc

o L

avar

da]

at 0

7:24

12

Oct

ober

201

2