Jonathan Diploma Work Report_final

Quaternary Ammonium Surfactants Adsorbed at the Solid-Liquid Interface

A VSFS-Study

Jonathan Liljeblad

Master of Science Thesis at the Royal Institute of Technology

Stockholm 2007

Denna avhandling är skyddad enligt upphovsrättslagen. Alla rättigheter förbehålles. Copyright © 2007 by Jonathan Liljeblad. All rights reserved. Royal Institute of Technology Department of Chemistry, Surface Chemistry Drottning Kristinas väg 51 SE-100 44 Stockholm Sweden

Abstract The aim of the research presented in this Master of Science Thesis, was to study the adsorp-tion of quaternary ammonium surfactants at the hydrophilic solid-liquid interface with Vibra-tional Sum Frequency Generation Spectroscopy (SF-spectroscopy). Studies of both the H-bonded water region and the hydrocarbon region of the SF spectral window have been per-formed in an attempt to distinguish between a range of different proposed structures for the adsorbed aggregates.

The adsorption of tetradecyltrimethylammonium bromide, TTAB, with and without NaCl and didodecyldimethylammonium bromide, DDAB, at the solid-liquid (S/L) interface of alumina and water was studied at concentrations above the cmc. It has earlier been indicated by AFM-imaging that those surfactant systems form spherical and cylindrical micelles and a flat bi-layer on quartz at concentrations above the cmc and it is assumed that the same applies to alumina. Our results show a very weak, if any, signal in the CH-region for all three systems and may indicate a slightly more loosely ordered water structure at the S/L interface for the case of cylindrical and spherical micelles compared to the planar bilayer. This indicates that SF-spectroscopy can probably not discriminate between flat bilayers, spherical micelles and cylindrical micelles formed by adsorption of ammonium surfactants at a charged surface.

The adsorption of TTAB at the S/L interface of alumina and water along the adsorption iso-therm at high pH was also studied. The SF-spectra did not display any CH-signals of strong intensity at any concentrations. The OH-signals gradually decreased to an almost flat line, as the surfactant concentration increased. The OH-region remained flat also at surfactant concen-trations above the point of zero charge and at the cmc where signal was expected. We postu-late that adsorption of TTAB might not form a homogeneous layer at the interface; resulting in regions within the probed area, possessing opposite charges (negatively charged sapphire, and positively charge TTAB) aligning water molecules in opposite orientations. This could result in a total net orientation that is zero and a loss of SF signal.

For all experiments conducted using sapphire at high pH, a strong peak at ~3700 cm-1 was continually observed, especially for the pure water samples. This peak is associated to a non hydrogen bonded OH-group, a “Free-OH” and is not expected to be present at the S/L inter-face of alumina and water. We have proved by isotope exchange experiments that this peak originates from the S/L interface, but can not provide any explanation for the reason behind.

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Abstract in Swedish / Sammanfattning Målet med den forskning som presenteras i detta examensarbete var att studera adsorption av kvarternära ammoniumtensider på en hydrofil gränsyta mellan fast fas och vätska med vibra-tionsspektroskopi som utnyttjar sumfrekvensgenerering (SF-spektroskopi). Såväl det väte-bundna vattenområdet som kolväteområdet studerades för att söka efter skillnader mellan en rad föreslagna strukturer som tensiderna kan tänkas forma på gränsytan.

Adsorptionen av Tetradecyltrimetylammoniumbromid, TTAB, med och utan NaCl och dido-decyldimetylammoniumbromid, DDAB, på gränsytan mellan fast aluminiumoxid (Safir) och vatten studerades vid koncentrationer högre än cmc. Avbildning med AFM har tidigare visat att dessa tensidsystem bildar sfäriska och cylindriska miceller samt ett dubbelskikt på kvarts vid koncentrationer högre än cmc, vilket kan antas vara fallet även på aluminiumoxid. Våra resultat visar en mycket svag, om ens någon, signal i kolväteområdet för alla tre systemen, samt möjligen för cylindriska och sfäriska modeller en något mera löst bunden vattenstruktur vid gränsytan jämfört med det plana dubbelskiktet. Detta antyder att SF-spektroskopi troligen inte kan särskilja de tre diskuterade tensidstrukturerna.

Även adsorption av TTAB på gränsytan mellan aluminiumoxid och vatten för koncentrationer längst adsorptionsisotermen studerades. Starka kolvätesignaler förekom inte vid några kon-centrationer. Signalerna i det vätebundna vattenområdet avtog gradvis till en plan linje då tensidkoncentrationen ökades. Vattensignalerna återkom inte vid koncentrationer högre än ”nolladdningspunkten” (pzc) eller högre än cmc där vattensignaler förväntades. Vi föreslår att TTAB inte bildar ett homogent lager vid adsorptionen, vilket ger upphov till områden med olika laddning (negativt laddad aluminiumoxid och positivt laddad TTAB) på den studerade ytan som riktar vattenmolekylerna i motstående riktningar. Detta skulle kunna resultera i för-lust av nettoorienteringen hos vattenmolekylerna vilket leder till en förlust av SF-signalen.

I alla försök, särskilt med vatten utan tensid, som genomförts med aluminiumoxidsubstrat vid ph 10 syns i spektra en stark signal vid ungefär 3700 cm-1. Denna signal härrör från en icke vätebunden OH-grupp, en ”Fri OH-grupp” och förväntas inte genereras av en gränsyta mellan aluminiumoxid och vatten. Vi har med isotoputbytesförsök visat att signalen kommer från gränsytan mellan aluminiumoxid och vatten, men kan inte ge någon förklaring till dess upp-komst.

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Table of contents Introduction ................................................................................................................................ 4

General ................................................................................................................................... 4 Background ............................................................................................................................ 4 Surfactants.............................................................................................................................. 5 Adsorption of surfactants on a charged surface ..................................................................... 7

Thermodynamics................................................................................................................ 7 Mechanisms and structures ................................................................................................ 7 Adsorption isotherms ......................................................................................................... 9

Studying adsorption behavior with SF-spectroscopy........................................................... 10 Hydrocarbon stretching region......................................................................................... 10 Water stretching region .................................................................................................... 11

The alumina surface ............................................................................................................. 13 Theory and methods ................................................................................................................. 15

Sum frequency generation.................................................................................................... 15 Sum frequency spectroscopy................................................................................................ 16 Analysis of spectroscopic data and modeling of spectra...................................................... 17

Experimental ............................................................................................................................ 19 The Stockholm vibrational sum frequency spectrometer..................................................... 19 Substrates and the liquid cell................................................................................................ 19 Chemicals and preparation of solutions ............................................................................... 20 Liquid exchange and the measurement of isotherms ........................................................... 21 Normalization of spectra from isotherm two ....................................................................... 21

Results ...................................................................................................................................... 23 Control experiments ............................................................................................................. 23 Adsorption structures, TTAB and DDAB............................................................................ 23 SF Spectra for Adsorption Isotherm..................................................................................... 25 Possible time dependence..................................................................................................... 27

Discussion ................................................................................................................................ 28 Conclusions .............................................................................................................................. 31 Acknowledgements .................................................................................................................. 32 References ................................................................................................................................ 33 Appendix 1 Modeling SFG spectra with Lorentzian functions.................................................. 1

Real Lorentzian functions and polar coordinates................................................................... 1 Complex Lorentzian functions and Cartesian coordinates..................................................... 5 Curve fitting ........................................................................................................................... 6

Appendix 2 Liquid exchange in the fluid cell ............................................................................ 1

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Introduction

General The aim of the research conducted and presented in this Master of Science Thesis, was to study the adsorption of cationic surfactants at the hydrophilic solid-liquid (S/L) interface with Sum Frequency Generation Spectroscopy (SF-spectroscopy). Surfactant molecules self as-semble both in bulk solution and at interfaces between two media. However, symmetric struc-tures such as spheres, rods, and bilayers which are observed in bulk may not be conserved when adsorbed at the solid-liquid interface. The ultimate goal of this research was to use SF-spectroscopy to determine whether they absorb at an interface as asymmetric structures. For example, do surfactants adsorb as hemispherical caps on top of a monolayer, or as spherical micelles. As SF-spectroscopy is both technically and theoretically challenging the project was carried out in close corporation with Clayton McKee, a postdoctoral researcher at the division of surface chemistry at KTH.

Background An improved understanding of adsorption of surfactants on solid surfaces is important in many different areas of surface chemistry. For example froth flotation, which is used primar-ily for enrichment of ore and paper recycling, is strongly affected by surfactant adsorption at the solid-liquid interface. Detergency, wetting and penetration in for instance food products and stabilization of colloidal particles in solution are other important areas.1,2

A variety of techniques such as neutron reflectivity, Atomic Force Microscopy (AFM), fluo-rescence spectroscopy, ellipsometry and QuartzCrystal Microbalance (QCM) as well as Vi-brational Sum Frequency Spectroscopy (SF-spectroscopy) may be utilized to study the ad-sorption of surfactants at a solid surface SF spectroscopy was chosen for this work as it is highly specific to the structure of only those molecules which are adsorbed at the interface between two media.

SF-spectroscopy, which is a combination of IR- and RAMAN-spectroscopy, relies on nonlin-ear optical effects present in a material at high irradiation energies. The main advantage of SF-spectroscopy is that it is surface specific and enables the determination of molecular spe-cies present at an interface as well as their orientation.

As with other spectroscopic techniques, it is very informative to review sum frequency spec-tra that have been collected for surfactants adsorbed at a variety of surfaces, when trying to interpret our results. The interface of silica (fused quartz, SiO2)3, 4 is probably the most exten-sively studied, but alumina (Al2O3)5,6 and CaF2

7,8 have also been studied.

1 Hopkins, A. J., et al., Investigations of the solid-aqueous interface with vibrational sum-frequency spec-troscopy. Current Opinion in Solid State & Materials Science 2005, 9, (1-2), 19. 2 Tiberg, F., et al., Adsorption and surface-induced self-assembly of surfactants at the solid-aqueous inter-face. Current Opinion in Colloid & Interface Science 1999, 4, (6), 411. 3 Ostroverkhov, V., et al., Vibrational spectra of water at water/alpha-quartz (0001) interface. Chemical Physics Letters 2004, 386, (1-3), 144. 4 Du, Q., et al., Surface Vibrational Spectroscopic Studies of Hydrogen-Bonding and Hydrophobicity. Science 1994, 264, (5160), 826. 5 Yeganeh, M. S., et al., Vibrational spectroscopy of water at liquid/solid interfaces: Crossing the isoelec-tric point of a solid surface. Physical Review Letters 1999, 83, (6), 1179. 6 Fan, A. X., et al., Adsorption of alkyltrimethylammonium bromides on negatively charged alumina. Langmuir 1997, 13, (3), 506.

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One of the first systems studied were self assembled monolayers of octadecyltrichlorosilane, OTS. The SF spectrum is dominated by the presence of methyl stretches from the hydrocar-bon chains of the OTS molecule. The chains of the OTS monolayer are well ordered, with a minimum number of gauche defects. In addition, it is found that water molecules adjacent to the hydrocarbon layer are at times not able to hydrogen bond with other water molecules; which results in a very strong, well defined SF signal.

Surfactants physisorbed (not covalently bound) at the solid-liquid interface at substrates of silica, and CaF2, have also been studied with SFG.,, The adsorption of SDS at the CaF2 sur-face was investigated by Becraft et al. At low pH, below the isoelectric point of CaF2, a bi-layer formed as the surfactant concentration increased, while monomer adsorption dominated at low concentrations. Becraft and Richmond also studied carboxylate surfactants at CaF2 and found that the monolayers were more tightly packed for longer hydrocarbon chains.9 The ad-sorption of positively charged polyelectrolytes at the silica/water interface has been studied by Kim et al.10 and protein adsorption at the silica/water interface by Chen and Somorjai.11

However, little seems to have been done with SF-spectroscopy when it comes to the adsorp-tion of cationic ammonium surfactants on alumina. This is an interesting observation as alu-mina is a widely used material in a variety of surface chemistry applications.

Surfactants A surface active agent, or surfactant, is a molecule with the ability to enrich at the interface between two different media and change the energy associated with the interface. This ability arises because the surfactants have a charged or polar part and a non polar hydrocarbon part. Many surfactants consist of a single charged or polar group, the head, attached to one or a few non polar hydrocarbon chains, the tails.

Surfactants can be classified by their charged or polar part. If the headgroup is ionic, the sur-factant is named anionic or cationic depending on the charge. Non-ionic surfactants have a polar non-ionic part and zwitter-ionic surfactants have ionic components of both charges within the head group.

The ammonium surfactants used in this study belongs to the cationic type. The hydrophobic part consists of one or two hydrocarbon chains and the head is an ammonium, N+, group. Tet-radecyltrimethylammonium bromide, TTAB, (Figure 1) has one C14 hydrocarbon chain, while didodecyldimethylammonium bromide, DDAB (Figure 2) has two C12, chains, almost dou-bling the hydrophobic volume. The counter ion, bromine, is sometimes exchanged with other halides such as chlorine.

7 Becraft, K. A.; Richmond, G. L., In situ vibrational spectroscopic studies of the CaF2/H2O interface. Ibid.2001, 17, (25), 7721. 8 Becraft, K. A., et al., In-situ spectroscopic investigations of surfactant adsorption and water structure at the CaF2/aqueous solution interface. Physical Chemistry Chemical Physics 2004, 6, (8), 1880. 9 Becraft, K. A.; Richmond, G. L., Surfactant adsorption at the salt/water interface: Comparing the confor-mation and interfacial water structure for selected surfactants. Journal of Physical Chemistry B 2005, 109, (11), 5108. 10 Kim, J., et al., Investigations of polyelectrolyte adsorption at the solid/liquid interface by sum frequency spectroscopy: Evidence for long-range macromolecular alignment at highly charged quartz/water interfaces. Journal of the American Chemical Society 2002, 124, (29), 8751. 11 Kim, G., et al., Investigations of lysozyme adsorption at the air/water and quartz/water interfaces by vi-brational sum frequency spectroscopy. Langmuir 2002, 18, (7), 2807.

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N +Br-

C14H33N+Me3Br-

Figure 1 Tetradecyltrimethylammonium bromide, TTAB.

N +Br-

(C12H25)2N+Me2Br-

Figure 2 Didodecyldimethylammonium bromide, DDAB.

The Critical Packing Parameter, (1) uses geometrical considerations of the molecules to pre-dict what kind of structures can be formed in bulk phases when monomers come together to form aggregates. In (1), v equals the volume of the hydrophobic tail, l equals the length of the tail and a equals the head group area in an aggregate. The packing parameter is equal to one for bilayers. A value above one indicates a preference for inverse structures (hydrophobic parts are pointing out from the center) and a value less than one is related to normal struc-tures. A CPP value less than 1/3 indicates a preference for spherical micelles, 1/3 < CPP < 1/2 cylindrical micelles and 1/2 < CPP < 1 a preference for vesicles or bilayers.

vCPPl a

=∗

(1)

As the concentration of monomers of surfactant in solution increase, a critical concentration is reached where the number of monomers in solution remains constant and the number of mi-cellar aggregates increases. This is termed the critical micelle concentration (cmc). The cmc-value of a specific surfactant depends in part on the ionic strength of the solution, the tem-perature and the counter ion. The cmc values for the surfactants used in this research are put together in Table 1.

Table 1 Cmc-values for TTAB and DDAB.12

Surfactant cmc (mM) cmc (mM) 10 mM salt

TTAB 3.6 2.1 DDAB 0.05

12 Atkin, R., et al., Mechanism of cationic surfactant adsorption at the solid-aqueous interface. Advances in Colloid and Interface Science 2003, 103, (3), 219.

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Adsorption of surfactants on a charged surface

Thermodynamics

The thermodynamics of adsorption is best described using the surface tension, γ, as the start-ing point. Surface tension is defined as the reversible work, w, required to create a unit of new surface area, A, (2).

dw dAγ= (2)

The Gibbs free energy, G, gives a measure of the maximum amount of work achievable from a system at constant temperature, pressure and amount of a substance, and is one of the most used potential energy functions in chemistry.

The surface tension is the partial derivative of G with respect to the surface area.

, ,T P n

GA

γ ∂⎛ ⎞= ⎜ ⎟∂⎝ ⎠ (3)

The driving force for adsorption is a decrease in the free energy of the surface. This leads to a decrease in the surface tension. The adsorption creates an excess, Γ, of the adsorbed substance at the interface. The surface excess is usually defined so that the excess of the solvent at the interface, Γ1, is zero and Γi>0 (the adsorbed species treated) is the concentration of the respec-tive substance in excess of its concentration in the solution. It must be noted that Г can be negative as well, corresponding to a depletion of the concentration of the species. The Gibbs equation of adsorption, (4), is an expression for the change of the surface tension due to ad-sorption.13 If the adsorption process is carried out at constant temperature the entropy term is neglected.

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i

Si

d S dT diγ μ=

= − − Γ∑ (4)

In (4), Ss is the surface entropy per unit area and μ is the chemical potential of the adsorbing species.

Mechanisms and structures

The adsorption of cationic surfactants on negatively charged surfaces (Illustrated in Figure 3) is at low concentrations driven by the electrostatic attraction between the charged head group and the surface. It is believed that the hydrocarbon tails are pointing in arbitrary directions into the liquid or along the surface, resulting in an isotropic surface (Step I). Continued ad-sorption of the charged surfactant to the interface decreases the net surface charge, until the surface is “neutralized” by the adsorbing surfactant (Step II). This is termed the “point of zero charge” or pzc. To accurately determine the point of zero charge AFM force measurements or electrophoretic techniques have to be utilized.14 As the amount of hydrophobic material at the surface increases a second layer of surfactant molecules start to rapidly adsorb in the opposite direction, driven by hydrophobic attraction between the tails. This leads to a recharging of the surface. The decreased slope in step III could be because of electrostatic repulsion. The transi-tion between step III and IV occurs at the cmc or when the surface is fully covered by a bi-layer. It must however be kept in mind that this is a simplified model. Especially the change 13 Fuerstenau, et al., Some aspects of flotation thermodynamics. In Froth flotation: a Century of innovation, C., M., Ed. SME, cop.: Littleton, 2007; pp 95-99. 14 Veeramasuneni, S., et al., Measurement of interaction forces between silica and alpha-alumina by atomic force microscopy. Journal of Colloid and Interface Science 1996, 184, (2), 594.

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between step one and two is probably taking place in a gradual manner, since to our knowl-edge no measurements have indicated the formation of a complete monolayer before partial bilayer formation takes place.

Figure 3 The four step adsorption process as described by Bitting and Harwell.15

Depending on the nature of the surfactant, and the properties of the solution the surfactant is dissolved in, different structures such as spheres, rods or bilayers can form in the bulk at the cmc. Apart from the traditional view16 of adsorption at a charged surface forming structure-less bilayers recent investigations with AFM-imaging, indicate that structural features identi-cal to what form in the bulk also form at the surface. In this report the term “adsorption struc-ture” will be used to describe what kind of structure the surfactant forms by adsorbing at the solid-liquid interface. However AFM images are strictly top down images, therefore asymme-try in the adsorbed layer would not be discernable.

Adsorbed layers of TTAB and DDAB on silica were imaged with AFM in 1995 by Manne and Gaub.17 The images indicated that spherical micelles and a double layer were formed. In 2001, adsorbed TTAB layers on quartz, with and without salt and adsorbed DDAB, were im-aged with AFM by Schulz, Warr et al.18 Their images indicated visually similar structures as previously found on silica for TTAB and DDAB and cylindrical micelles for TTAB with salt. We expect that similar structures will form on sapphire as well.

15 Bitting, D.; Harwell, J. H., Effects of Counterions on Surfactant Surface Aggregates at the Alumina Aqueous-Solution Interface. Langmuir 1987, 3, (4), 500. 16 Bijsterbosch, B. H., Characterization of silica surfaces by adsorption from solution. Investigations into the mechanism of adsorption of cationic surfactants. Journal of Colloid and Interface Science 1974, 47, 186. 17 Manne, S.; Gaub, H. E., Molecular-Organization of Surfactants at Solid-Liquid Interfaces. Science 1995, 270, (5241), 1480. 18 Schulz, J. C., et al., Adsorbed layer structure of cationic surfactants on quartz. Physical Review E 2001, 6304, (4).

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Figure 4 The upper part shows illustrations of spherical and cylindrical micelles and a bilayer. The lower part shows AFM-images of the corresponding adsorption structures.18

Adsorption isotherms

An adsorption isotherm consists of a series of measurements of the surface excess as a func-tion of concentration of surfactant at constant temperature. The adsorption isotherm for TTAB on alumina was measured in 1996 by Fan et al. (Figure 5) using adsorption depletion. To measure the concentration at the S/L interface, alumina particles with a known surface to mass ratio were mixed into a surfactant solution with a known concentration. The particles were removed by centrifugation and the surfactant concentration in the supernatant was de-termined by titration. Adsorption to the solid sapphire interface depletes the bulk solution, and so the surface excess can simply be calculated from the difference in the amount of surfactant present in the supernatant and the starting surfactant solution.

The correlation between the chain length (CTAB has C16 tail and DTAB has C12 tail) and the adsorption density is explained by the increasing hydrophobic attraction as the hydrophobic mass increases.19 As the cmc is reached the adsorption density levels off because the chemical potential of the monomers in solution is almost constant above cmc. As more surfactant is added above cmc, the micelle concentration increases but the monomer concentration remains approximately constant.

19 Atkin, R., et al., The influence of chain length and electrolyte on the adsorption kinetics of cationic sur-factants at the silica-aqueous solution interface. Journal of Colloid and Interface Science 2003, 266, (2), 236.

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Figure 5 An adsorption isotherm for TTAB at pH 10 and 30 mM NaCl.6 A comparison with the four step model in Figure 3 reveals that region III seems to be absent.

The adsorption isotherm in Figure 5 does not completely resemble the model described in the previous section. Especially step III seems to be absent, but by comparing with results ob-tained by other techniques the authors came to the conclusion that the adsorption was follow-ing the four step model.

Studying adsorption behavior with SF-spectroscopy For readers without previous experience of SF-spectroscopy it is advisable to go through the Theory and Methods section before proceeding.

When studying the adsorption behavior of surfactants at the solid-liquid (S/L) interface it is necessary to bear in mind that not only the surfactant itself, but also the surrounding liquid and surface species may reveal information about the surfactant. At the S/L interface between water and a charged interface the surface charge will align water molecules with their dipoles oriented in their lowest energy configuration. This was neatly demonstrated through SF-spectroscopy by Yenegha et al. in a study of water at different pH adsorbed at an Alumina surface. If the surface is positively charged the free electron pair of the oxygen will point to-wards the surface and if the surface charge is negative the opposite applies. This gives rise to a net orientation of the water molecules. This net orientation is a necessary condition for a vibrational mode to be sum frequency active. Without a net orientation the contribution from each independent molecule will be averaged out by another molecule with an opposite orien-tation. This means that a hydrogen ion, which is a potential determining ion, can affect the intensity of a SF-signal in the water stretching region, i.e. the SF-intensity is pH-dependent.

Hydrocarbon stretching region

In the methyl and methylene CH-stretching region between 2800 cm-1 and 3000 cm-1 TTAB and DDAB have methyl and methylene groups that can give rise to a SF-signal. The stretch-ing modes observed in SF-spectroscopy20 are listed in Table 2. The signals associated with the CH2-groups are highly dependent on the conformation of the hydrocarbon chain. If all the 20 Lambert, A. G., et al., Implementing the theory of sum frequency generation vibrational spectroscopy: A tutorial review. Applied Spectroscopy Reviews 2005, 40, (2), 103.

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bonds are in a trans conformation, the methylene groups are in a locally centrosymmetric en-vironment and SFG is prohibited. This is the case for a densely packed layer of hydrocarbons such as OTS, where in the all trans conformation the hydrocarbon chains occupy the least space. If the dihedral angle between two adjacent carbons is changed (especially 120°, so called gauche defect) local centrosymmetry is broken and the methylene groups will be SFG active (Figure 6). This is possible in hydrocarbon layers with low packing density.20 Thus the relative intensity of the methyl and methylene signals can be used to obtain a measure of the monolayer order.

Figure 6 Illustration of gauche defects in a hydrocarbon layer adsorbed to a surface.

Table 2 Assignments and wave numbers for CH-stretching modes observed by SF-spectroscopy. In air the wavenumbers would shift slightly to higher energies.Fel! Bokmärket är inte definierat.

Designation Description Wavenumber [cm-1] In water

r- CH3, anti-symmetric stretch 2962

FRr+ CH3, symmetric stretch (Fermi resonance) 2933

d- CH2, anti-symmetric stretch 2916

FRd + CH2, symmetric stretch (Fermi resonance) 2890-2930

r+ CH3, symmetric stretch 2874

d+ CH2, symmetric stretch 2846

Water stretching region

The SF-spectra of the OH-stretching region of the liquid-air (L/V) interface of water was first recorded by Du, Shen et al. in 1993.21 Two main features are exhibited in the OH-region of SF-spectra (SSP) at the L/V-interface (Figure 7) of water. There is a broad profile located between 2900 cm-1 and 3600 cm-1 and a narrow peak at ~3700 cm-1. The broad profile origi-

21 Du, Q., et al., Vibrational Spectroscopy of Water at the Vapor Water Interface. Physical Review Letters 1993, 70, (15), 2313.

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nates from hydrogen bonded surface water. It is commonly resolved into three peaks, one centered at ~3170 cm-1 corresponding to the optimum hydrogen bonding in surface water (ice-like), a second centered at ~3310 cm-1 corresponding to the more loosely associated hydrogen bonded structure of water and a third at 3450 – 3500 cm-1. The first and second peaks are commonly referred to as the “ice” and “water” peaks. Generally, peaks at higher wave num-bers (higher energy) are associated with a less optimal hydrogen bonding structure. The peak at ~3700 cm-1 has been described as non hydrogen bonded OH-group directed towards the vapor phase, referred to as the “Free-OH peak”. The fitting of vibrational modes and interfer-ence effects in the SF-spectra of the L/V interface of water was extensively treated by Brown et al. (Table 3). 22 However the assignment of the water stretching region and the water struc-ture at the surface is still a matter of considerable debate.23 A different approach for the as-signment is to fit only two peaks to the low wavenumber OH-region.21 One centered at ~3200 cm-1, close to the ~3150 cm-1 peak observed at the surface of ice24 and another peak centered at ~3450 cm-1, referred to as “water-like”. The commonly accepted structure for the liquid water has been a network of tetrahedrally hydrogen bonded molecules.25 However recently performed X-ray spectroscopy and computational chemistry modeling have indicated hydro-gen bonds of two different strengths.26,27

Table 3 Summary of vibrational modes fitted to the SF-spectra (SSP) of the air / water interface.

Designation Wave num-ber [cm-1] Origin

Ice OH 3170 Symmetric Stretch (SS) of tetrahe-drally bonded water.

Water OH 3310 SS as above, more loosely bonded.

AS - “bonded H2O” 3510 Asymmetric stretch (AS), loosely coordinated bulk water.

SS - vapor 3662 SS, surface vapor

Free OH 3710 Narrow, non hydrogen bonded OH.

AS - vapor 3763 AS, surface vapor

22 Brown, M. G., et al., The analysis of interference effects in the sum frequency spectra of water interfaces. Journal of Physical Chemistry A 2000, 104, (45), 10220. 23 Tyrode, E. Vibrational Sum Frequency Spectroscopy Studies at the Air-Liquid Interface. Doctoral Thesis, Royal Institute of Technology, Stockholm, 2005. 24 Wei, X., et al., Sum-frequency spectroscopic studies of ice interfaces. Physical Review B 2002, 66, (8). 25 Chandler, D., Hydrophobicity: Two faces of water. Nature 2002, 417, (6888), 491. 26 Wernet, P., et al., The structure of the first coordination shell in liquid water. Science 2004, 304, (5673), 995. 27 Kuo, I. F. W.; Mundy, C. J., An ab initio molecular dynamics study of the aqueous liquid-vapor interface. Ibid.303, (5658), 658.

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Figure 7 Example of a SF-spectrum of the S/V interface of water.28

The alumina surface Alumina (Al2O3) is an extensively studied material with importance as a catalyst,29 and as a common constituent in soils and atmospheric particles.30 It is also a main constituent in the exhausts from solid fuel rocket motors.31 The surface is of specific importance in catalytic applications and when adhesives are used to connect aluminum parts when used as a construc-tion material.

The thermodynamically most stable form is α-alumina (corundum, sapphire). It has a trigonal unit cell with D3d symmetry. At high temperatures the surface is completely dehydrated32 and displays coordinatively unsaturated, Lewis acidic, Al-ions.33 At lower temperatures water is readily adsorbed to the Al-ions and at room temperature the surface is fully covered.32

It has been found that water can dissociate at the alumina surface, giving rise to two different OH vibrational modes, OHads and OHs.

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The first mode originates from adsorbed surface wa-ter molecules and the second from surface oxygen bonded to alumina.

28 Wei, X.; Shen, Y. R., Motional effect in surface sum-frequency vibrational spectroscopy. Physical Re-view Letters 2001, 86, (21), 4799. 29 Knözinger, H.; Ratnasamy, P., Catalytic Aluminas: Surface Models and Characterization of Surface Sites. Catal. Rev. Sci. Eng. 1978, 17, (1), 31. 30 Ma, G., et al., Piperidine adsorption on hydrated alpha-alumina (0001) surface studied by vibrational sum frequency generation spectroscopy. Langmuir 2004, 20, (26), 11620. 31 Turco, R. P., et al., Space-Shuttle Ice Nuclei. Nature 1982, 298, (5877), 830. 32 Ballinger, T. H.; Yates, J. T., Ir-Spectroscopic Detection of Lewis Acid Sites on Al2O3 Using Adsorbed Co - Correlation with Al-Oh Group Removal. Langmuir 1991, 7, (12), 3041. 33 Hass, K. C., et al., The chemistry of water on alumina surfaces: Reaction dynamics from first principles. Science 1998, 282, (5387), 265.

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Apart from this, hydrogen bonding can take place between adjacent OH groups on the surface which may also have different charge depending on their coordination. According to the most accepted model of the surface, put forward by Knözinger and Ratnazamy in 1978,29 the dif-ferent charges are explained by different coordination of Al3+ and O2- ions (terminal or bridg-ing coordination) at different sites at the surface, Figure 8. These surface species generate a variety of different IR peaks in the OH region or when modeled with computational chemis-try.33 Vibrational modes from oriented water molecules in close proximity to the surface are also present when a submerged, charged alumina surface is studied with SF-spectroscopy.5,30

Figure 8 Illustration of the model of the Alumina surface postulated by Knözinger and Ratnazamy. To the left is the aluminol OH-groups with different charge depending on the coordination of the oxygen atom, to the right the hydrogen bonding network at the alumina surface and below the proposed wavenumbers for the vibrational modes of the different species.34

The isoelectric point (iep) of alumina, which is the pH value at which the surface has a net charge of zero, is approximately 8.5 This is close to neutral pH which makes it easy to achieve either a positively or negatively charged surface. Silica, SiO2, another commonly used sub-strate for surface adsorption studies has an iep of ~2, making only a neutral or negatively charged surface practically available.

It has been argued that alumina may be contaminated by silica if laboratory glassware is used for handling.30, , 35 36 Contamination of the surface can be assessed by performing elementary analysis by XPS. It has been indicated that silica contamination can affect the SF-spectra in the OH-region i.e. the Free OH or aluminol OH peak.30

34 Mawhinney, D. B., et al., Infrared spectroscopic study of surface diffusion to surface hydroxyl groups on Al2O3: 2-chloroethylethyl sulfide adsorption site selection. Langmuir 2000, 16, (5), 2237. 35 Furlong, D. N., et al., The Adsorption of Soluble Silica at Solid-Aqueous Solution Interfaces.1. Leaching from Glass - an Electrokinetic Study. Journal of Colloid and Interface Science 1981, 80, (1), 20. 36 Polat, M., et al., Effect of pH and hydration on the normal and lateral interaction forces between alumina surfaces. Ibid.2006, 304, (2), 378.

14

Theory and methods

Sum frequency generation When two electrical fields of sufficient intensity to generate a non-linear response overlap in space and time at the interface between two media a third field with the sum of the frequen-cies of the overlapping fields is generated.

Sum frequency generation was first described in 1962 by Bloembergen and Parshan.37 To fully comprehend the phenomena it is necessary to go through a quantum mechanical deriva-tion based on second order time dependent perturbation theory. However a simplified classi-cal model is also available.20

When electrons in a molecule are subjected to an applied electromagnetic field, whose strength is of the same order, or larger than that from the molecule itself, higher terms in the bulk polarization need to be included. A time dependent polarization acts as a source of an electromagnetic field. One simple way to demonstrate the origin of SFG is to study part of the series expansion of the polarization vector at a surface where two electrical fields overlap in space and time, (5).20

(5) (2) (2) 20 1 1 2 2... ... ... ( cos cos ) ...t tε χ ω ω= + + = + + +P P E E

SFG is resultant from the second order term, PP

+

(2). Expanding the squared parenthesis and us-ing trigonometry gives rise to six terms, one of them accounting for the sum frequency, . (6)

(6) (2) (2)0 1 2 1 2cos(( ) )SF tε χ ω ω∝P E E

Among the others, are terms accounting for second harmonic generation (SHG) and differ-ence frequency generation, which will not be discussed in this thesis.

The second order non-linear susceptibility, χ(2) in the above equations is a 3rd rank tensor that is related to the corresponding molecular hyperpolarizability tensor, β(2) (also 3rd rank) aver-aged over all possible orientations, (7). In (7), N is the number of molecules and ε0 is the di-electric permittivity.

(2) (2)

0

Nχ βε

= (7)

The magnitude of χ(2 )is a related to how “well” a molecule interacts with an incoming photon. Most importantly the magnitude of χ(2) depends on the orientation of surface molecules in relation to the polarization of the incoming beams. As such, to properly define χ(2), we need to define a surface coordinate system of x, y, and z for a molecule at an interface, which leads to a total of 27 tensor elements needed to describe the non-linear response of a molecule. For the tensor to take a non zero value the molecules must be in a non centrosymmetric environment, as is the case for surfaces where the inversion symmetry is broken. Symmetry constraints also reduce the number of independent, nonzero tensor elements from 27 to 4 for surfaces with C∞ symmetry i.e. isotropic surfaces.

By polarizing the incident fields and selecting the sum frequency field perpendicular (S) or parallel (P) to the plane of incidence in different combinations, it is possible to selectively probe the four nonzero tensor elements. Table 4 lists those non zero elements.

37 Bloembergen, N.; Pershan, P. S., Light waves at the boundary of nonlinear media. Phys. Rev. 1962, 128, 606.

15

Table 4 Polarization combinations and corresponding susceptibility tensor elements for isotropic surfaces.

χ(2) element Polarization combination (SF, VIS, IR)

(2) (2) (2) (2)zzz zxx xzx xxzχ χ χ χ= = = PPP

(2)yyzχ SSP (2)yzyχ SPS (2)zyyχ PSS

Sum frequency spectroscopy Vibrational sum frequency vibrational spectroscopy (VSFS) is a surface specific method. It is based on the concept of Sum Frequency Generation (SFG) first described 1962.37 However the first spectra was not recorded until 1987, by Shen, when lasers giving sufficiently high energy were developed.20

Sum frequency generation is described in the previous section. In sum frequency spectros-copy (SF-spectroscopy) the incident fields are two pulsed, high energy laser beams, one fixed visible, Evis and one tunable infrared, EIR. In the most common setup the two incident beams are directed to the surface from the same side, and the reflected sum frequency (SF) beam, ESF, is detected (Figure 9).

ESF

Evis

EIR

Figure 9 Incident and reflected beams in the most common setup for a SFG experiment.

As the IR wavelength is scanned over a substrate, a sum frequency signal will be generated when the vibrational frequency of a molecular bond is in resonance with the frequency of the IR radiation. Importantly, for a molecular vibration to be sum frequency active it has to be both IR and RAMAN active. The selection rule for IR activity is that the dipole moment, μ, must be altering with respect to the normal coordinate of the vibration, Q.

0Qμ⎛ ⎞∂

≠⎜ ⎟∂⎝ ⎠ (8)

A corresponding selection rule for RAMAN activity is that the polarizability, α has to alter with respect to the normal coordinate in the same way.

16

0Qα⎛ ⎞∂

≠⎜ ⎟∂⎝ ⎠ (9)

If the underlying substrate is SF active itself, this has to be taken into account by introducing a so called non resonant susceptibility, (2)

NRχ . For most dielectric materials this value is close to zero while for metals and crystalline materials it can be of considerable magnitude and is treated as a complex constant.

Analysis of spectroscopic data and modeling of spectra To be able to make quantitative statements (and even qualitative if the spectra are not ex-tremely simple) a modeling function has to be fitted to the spectra and the fitting parameters (wavenumber, amplitude and damping constant) for each peak need to be collected. To do this it is necessary to have a mathematical model for the SF-intensity as a function of the wavenumber. Such a model is described briefly here. For a more elaborate treatment of the modeling of SF-spectra see Appendix 1.

It must be stressed that in most cases it is not possible to deduce the number of peaks and the intensity of a specific peak simply by visual inspection. The resonant (surface molecular vibra-tions) and non resonant background can interact both constructively and destructively depend-ing on the phase difference between them. This can lead to misinterpretation of spectral fea-tures. A literature search for both RAMAN and IR active vibrational modes should be con-ducted and used as a starting point when fitting spectra. If RAMAN literature data is not available, an IR spectrum is a useful starting point. All possible vibrations have to be included in the modeling function, even if they are not obvious in the spectra.

The intensity of the sum frequency (SF) signal is proportional to the absolute square of the sum of the non-resonant and the resonant susceptibilities, (10).

2

(2) (2)vSF NR R

vI χ χ∝ +∑ (10)

It has to be noted that the susceptibilities are complex quantities. They can be treated both in Cartesian and in polar coordinates. Although polar coordinates are the most common in publi-cations about SF spectroscopy the mathematical treatment is simplified if Cartesian coordi-nates are used. The non resonant susceptibility, χNR, can be treated as a complex constant, whereas the resonant susceptibilities, χR, are independent functions of the wave number, (11).

(2)v

vR

Rv IR v

Ai

χω ω

=− − Γ

(11)

In equation (11) which describes a Lorentzian peak shape A is a constant accounting for the amplitude and Г is a damping constant describing the homogenous broadening of the peak, i.e. the peak width.

An equation (12) describing the SF intensity, based on both the real and imaginary component of χR is obtained by combining equation (10) and (11). This function is then fitted to the spec-tra by using any computational program featuring curve fitting capabilities. Sometimes con-straints have to be applied for some of the constants in order to facilitate the fit or exclude unphysical values.

17

( )( )

( )( )

( )

2

2 2

2 22 2Re Im

v

v

SF NR Nv

v R IR v vNR NR

v vRv IR v Rv IR v

I

A A

χ χ

ω ωχ χ

ω ω ω ω

∝ + =

⎛ ⎞ ⎛ ⎞− Γ⎜ ⎟ ⎜ ⎟= + + +⎜ ⎟⎜ ⎟− + Γ − +Γ⎝ ⎠⎝ ⎠

∑

∑ ∑ (12)

The peak width is mainly governed by two different broadening phenomena, homogenous and inhomogeneous broadening. In must thus be noted that the peak can not be infinitely narrow, but is limited to the “natural peak width” by the Heisenberg uncertainty principle. The ho-mogenous broadening is mainly related to the lifetime of the exited states, so that

1

rTΓ = (13)

where TR is the relaxation time. A short relaxation time results in a less well defined vibra-tional frequency giving rise to a broader line shape.

The inhomogeneous broadening arises because atoms in a studied ensemble have different local environments. The variables describing the local environment obey some statistical dis-tribution function and a method to account for this is to convolute (11) with a Gaussian distri-bution of vibrational frequencies, giving a Voigt-like peak shape.38 This approach is espe-cially useful for modeling broad peaks like in the 3000 cm-1 to 3600 cm-1 region of the water spectru3 and does not exhibit the overestimation of interference between widely separated peaks as with the Lorentzian peak shape.22 This overestimation arises because the Lorentzian function decays less rapidly at wavenumbers far away from the resonance frequency com-pared to the Voigt function.

38 Bain, C. D., et al., Quantitative-Analysis of Monolayer Composition by Sum-Frequency Vibrational Spectroscopy. Langmuir 1991, 7, (8), 1563.

18

Experimental

The Stockholm vibrational sum frequency spectrometer The vibrational sum frequency spectrometer and normalization procedures are described more elaborately elsewhere.39 Here only a brief description of the key parts is given.

The pulsed Nd:YAG laser is an EXPLA PL2143A20 generating a 1064 nm beam with a pulse length of ~20 ps, a repetition rate of 20 Hz and an energy per pulse of 40 mJ.

This laser pumps an OPG/OPA (Optical Parameter Generator / Optical Parameter Amplifier) (Laser Vision) generating two beams. One, fixed at 532 nm is used as the visible (green) and the second is the IR-beam, tuneable in a range from 1000 cm-1 to 4200 cm-1.

The green and the IR-beams are overlapped in time and space at the sample by a system of mirrors and a spatial time delay in the green beam-path. Polarizers fitted in the beam paths enable the selection of P or S polarization for the incident beams. The intensity of the green beam can be reduced with a half-wave plate to avoid damaging the sample by local heating. The green and the IR-beams strike the sample with incident angles of 55° and 63° respec-tively to the surface normal.

The generated sum frequency beam is directed via a polarizer to a monochromator and de-tected with a photomultiplier tube (PMT). Irises are used to spatially filter scattered light and facilitate directing the beam to the PMT by a mirror system. The tuning of the monochroma-tor as well as the OPG and the signal acquisition is performed by a computer with a LabView program.

To account for variations in the green and IR intensity at the sample position both intensities are measured at representative places and used for normalization of the SF signal intensity.

The output file from the spectrometer system contains wave number and the corresponding intensities of SFG, IR and Green stored in Microsoft Excel files. Commercial software (Igor Pro version 6) is used to process the data. All data presented in diagrams have been smoothed using moving average over eleven data points. (Igor Pro version 6, Box algorithm, 11 points.)

Substrates and the liquid cell Our sample cell features a cylindrical Teflon chamber holding two circular windows parallel to one another with a separation of about 1 cm. The internal volume is 7 ml. Tubes for ex-changing the liquid can be fitted to the cell. In the setup for measuring the TTAB isotherm an upper (directed to the incident beams) window of alumina and a lower window of fused IR-grade silica was used. The windows were obtained from ISP optics corp., type Al-W-38-3 and QI-W-38-3. Alumina is not transparent for wavelengths above 4 μm (2500 cm-1) giving a lower boundary for the wavenumber range that can be studied at 2500 cm-1. The reason for using a lower window of silica was that its composition was not assumed to affect the ex-periments and thus a cheap and robust material was chosen.

39 Johnson, C. M., et al., A vibrational sum frequency spectroscopy study of the liquid-gas interface of ace-tic acid-water mixtures: 1. Surface speciation. Journal of Physical Chemistry B 2005, 109, (1), 321.

19

Figure 10 The liquid cell used for all measurements. The windows are held in position by the grooves visi-ble in the bore. The cell was machined from a single peace of Teflon by the KTH workshop.

The sample cell and tubing were cleaned before each experiment by rinsing with MQ-water and ethanol. The sapphire and silica windows were rinsed the same way and treated five min-utes in a low-pressure RF-plasma generator (Herrick, PDC-3XG) on a “high” setting. This generates a clean hydrophilic surface with a negative charge in water. The cell was immedi-ately put together after cleaning, to limit contamination of the windows, and was filled with the first solution to prevent further contamination by exposure to the surroundings.

Chemicals and preparation of solutions TTAB, CAS 1119-97-7 (Sigma, 99%, Batch 124K0594) was purified by two recrystalliza-tions from a mixture of 25 % ethanol and 75 % acetone.40 The crystals were dried at 60°C and reduced pressure for approximately four hours. This drying reduced the mass of the sample by ≈ 30%. The final yield of the purification was 18 %.

DDAB, CAS 3282-73-3 (Eastman Kodak Company, Lot D5T) was used as received.

The water used for all cleaning and sample preparation (MQ-water) was purified with a Milli-pore RiOs-8 and MilliQ PLUS 185 system and filtered with a 0.2 μm Millipak filter unit. The conductivity and the organic content were constantly monitored and never exceeded 18.2 MΩ/cm and 6 ppb respectively.

Water with pH 10 was prepared by diluting a small amount of concentrated NaOH solution to a final volume of one dm3 and verifying the pH by measurement with a Metrom 713 unit with a Metron 6.0253.100, 3 M KCl electrode.

For the first isotherm NaOH from the laboratory stock (Aldrich, ACS 97+ %) was used as received. For the second isotherm Sigma-Aldrich, 99.998 % (Batch 08731KE) was used.

NaCl for the first isotherm was taken from the laboratory stock. For the second isotherm Sigma-Aldrich, 99.999 % (Batch 01504DE) was used.

40 Matsubara, H., et al., Effects of alkyl chain length on synergetic adsorption and micelle formation in homologous cationic surfactant mixtures. Langmuir 2005, 21, (18), 8131.

20

The solutions were prepared in glass volumetric flasks by dilution from a stock solution with a TTAB concentration of 4 mM. One dm3 of water with pH 10 and 30 mM NaCl was pre-pared and used for the solutions.

All glassware used was cleaned by soaking in a >5 % NaOH solution for several hours and then rinsed several times with MQ-water and high purity ethanol, blown off with nitrogen and dried in a laminar flow hood.

Liquid exchange and the measurement of isotherms SF-spectra of different concentrations of TTAB along the adsorption isotherm was recorded on two different occasions, referred to as isotherm one and isotherm two. All spectra were recorded at the SSP polarization combination unless otherwise stated. Control experiments were also performed to try to determine the effect of organic contaminations from the sur-rounding on the outside of the alumina window.

After the cell was cleaned and the first solution, which was usually a control sample of water with the same pH and salt concentration as the rest of the samples the liquid cell was put in the spectrometer setup and aligned. The solution exchange was carried out by injecting the solution with the desired concentration in one of the tubes connected to the Teflon chamber. At least three times the cell volume was injected. This procedure for liquid exchange is dis-cussed in detail in Appendix 2.

The adsorption isotherm of any surfactant depends strongly on the starting interfacial energy of the substrate that is being coated. As such, we believe that the fluid cell should not be dis-mantled and cleaned after every solution concentration; rather the isotherm should be con-ducted on a substrate that has not been recleaned between each concentration. This procedure is fine when using a technique that can acquire the necessary data, to collate an adsorption isotherm, in a sufficiently short period of time. However, each measured SF spectra between 2700-3900 takes approximately 30 minutes; combined with the necessity of averaging many spectra and the number of concentrations studied means that to measure an entire isotherm takes multiple days to complete. Being certain that the alumina substrate does not become contaminated over this length scale is difficult.

Normalization of spectra from isotherm two The SF-intensity is highly dependent on the alignment of the cell, and the condition of the laser and OPA/OPG. This is problematic as the time required to measure an entire isotherm is several days. Drift in laser efficiency or IR output from the OPA/OPG can make comparison of results collected on day one of the experiment with results collected on day two impossible. To try and minimize this effect, and enable at least a rough comparison of spectra recorded different days, the last sample scanned at the end of a day was scanned again in the morning of the next day, and used for normalization. However this was only done for isotherm two. If no time dependent effects are present, the spectrum of the last sample scanned day one, spec-trum one and the spectra of the same sample scanned again in the next morning, spectrum two, will have the same relative peak heights, i.e. be identical except from the multiplication of all the data-points in either of them by a constant. However, it turned out that this was not the case and a different approach had to be chosen. Instead, the 3500 cm-1 region where only weak signal was expected, was used for normalization. The normalization was done by multi-plying the data points in spectrum two with a constant, while comparing it visually with spec-tra one, aiming at getting identical intensities in the 3500 cm-1 region. As great care was taken not to move the sample cell between the measurements and our experience is that the drift in laser efficiency and OPA/OPG output power is small during one workday it seemed reason-

21

able to use the constant determined for the normalization of spectra two for normalizing the subsequent spectra recorded the same day as spectrum two. This procedure was then repeated again for the next day.

22

Results

Control experiments To rule out the possibility that organic contamination on the outer surface of the alumina win-dow give rise to a SF-signal, a control experiment was performed. This was done by injecting a sample of neutral MQ-water into the cell and recording the spectra of the CH region and comparing it to scans at 1.5 h and 2.25 h exposure times. No signal from the CH region was measured at the initial or subsequent scan times. The reason this experiment was conducted, is due to the possibility that a signal could be generated form the opposite face of the window we are using for study. The geometry of the setup combined with the high refractive index of alumina makes the green and IR-beams overlap at the outer as well as on the inner surface of the upper window. This could lead to a SF signal, generated at the outer surface mixing with the SF signal of the inner surface. However it must also be taken into account that contami-nants have to adsorb in an ordered manner to be SFG-active. We are thus reasonably confi-dent that the results obtained from this setup are reliable.

Adsorption structures, TTAB and DDAB It has been shown with AFM imaging that TTAB and DDAB at concentrations above the cmc, give rise to spherical aggregates, and planar bilayer respectively when adsorbed to a quartz surface. In addition, the structure of the adsorbed TTAB molecules can be changed from spheres to cylinders with the addition of 200 mM NaCl. SF-spectra in CH and OH stretching regions from these three systems are compared in Figure 11 and Figure 12. There are no obvious peaks in the CH-region in any of the systems, although there might be a peak at ~2950 cm-1 in all three (Figure 12). This indicates that the hydrocarbon chains are disor-dered regardless of the adsorption structure.

There is also considerable difference between the ratios of the peaks when comparing the DDAB and TTAB systems in the 3000 cm-1 to 3600 cm-1 region, but it has to be noted that the measurements took place at different pH. An important observation is that the peaks at ~3200 cm-1 and ~3450 cm-1 in the case of planar DDAB are at about the same wavenumbers as for a planar, charged interface of silica, while for TTAB, which adsorbs as spheres and rods, they are shifted to slightly higher energies, i.e. indicating more loosely associated interaction be-tween the water molecules.

The narrow peak at ~3700 cm-1 is associated with a “Free OH” group and is only expected to be present at the L/V-interface or at hydrophobic interfaces. It is surprising that it is present at the alumina-water interface at all. The first assumption was that it was an artifact residing from the S/V-interface at the outside of the cell. To determine which side it was originating from a control experiment was performed (Figure 13). This was done by injecting a D2O sample in the cell. When the OH and OD regions of the D2O sample were recorded the strength of the OH-peak at 3700 cm-1 was considerably reduced and a peak identical to the OH-peak of a H2O sample showed up at 2730 cm-1. This indicates that a large contribution of the 3700 cm-1 peak of the water originates from the S/L interface. The residual 3700 cm-1 sig-nal can originate from the S/V-interface of from “buried” OH-groups at the S/L-interface not accessible to the liquid.

23

Figure 11 SF-spectra for TTAB with and without salt and DDAB. DDAB is believed to form a plane, rigid bilayer. TTAB with and without salt is believed to form cylindrical and spherical surface micelles respec-tively.

Figure 12 A magnification of the CH-region in Figure 11. A peak seems to be present at ~2950 cm-1 in all three graphs.

24

Figure 13 ”Free-OH” peak (~3700 cm-1) at the S/L liquid interface of alumina and H2O. An isotope ex-change experiment was used to prove the origin of the peak.

SF Spectra for Adsorption Isotherm Two adsorption isotherm experiments were conducted, and the results are shown in Figure 14 and Figure 15. It must be stated that the intensity of any peak cannot be compared between the two experiments; only the relative intensities of peaks measured during the same experi-ment are roughly comparable. An attempt was made to normalize the spectra in Figure 15 as described in the experimental section.

The peak at 3700 cm-1 discussed in the previous section is present in the isotherm experiments as well and seems to keep about the same shape throughout the concentration gradient in both isotherms suggesting that it could be used for comparison of the intensity of other features.

In the CH-region no obvious peaks are present in the neat water sample in any of the iso-therms. This indicates that the sample cell was properly cleaned from start. As the concentra-tion of surfactant increases a peak appears at ~2950 cm-1 in both isotherms and remains throughout the concentration range. In the second isotherm a peak at ~2900 cm-1 also appears. For the second isotherm both the discussed peaks in the CH-region appears after leaving the sample cell overnight with the 0.07 mM sample inside and remains throughout the isotherm. This raises the question if they are a result of a time dependent rearrangement or from con-tamination of the cell.

In the OH-region, the peaks in the low wavenumber range quickly decreases to almost a flat line as the surfactant concentration increases, while the peak at ~3450 cm-1 seems to shift to higher wave numbers and the intensity seems to increase slightly.

A striking observation is that the broad peak at ~3200 cm-1 does not return at higher concen-trations as expected. This peak also has different shapes at low concentrations in the two ex-periments.

25

Figure 14 SF-spectra for different concentrations of TTAB along the adsorption isotherm.

Figure 15 Repeat of TTAB concentrations along the adsorption isotherm.

26

Possible time dependence As discussed in the Normalization of spectra from isotherm two section, to enable the nor-malization of SF-spectra recorded at different days, the final sample scanned at the end of one day was left overnight and rescanned the next morning. It was believed that the two scans would give spectra with the same shape and relative intensities between the different peaks. However this was, as indicated in Figure 16, not the case.

Figure 16 shows two SF-spectra of 0.07 mM TTAB solution recorded 30 minutes and 12 hours after injection. The major difference is in the CH-region where two new peaks showed up at ~2900 cm-1 and ~2950 cm-1 but the ratio between the 3700 cm-1 peak and the 3200 cm-1 peak had also changed considerably. This may indicate a time dependent rearrangement of surfactant at low concentrations. As seen in Figure 15 the peaks in the CH-region remained roughly the same throughout the rest of the adsorption isotherm. This is consistent with a slow formation of a more ordered monolayer that persists as the surfactant concentration is in-creased, but can also be the result of contamination. However, this experiment has not been repeated.

Figure 16 Time dependence of adsorption. TTAB, 0.07 mM 30 minutes and 12 h after injection.

27

Discussion The first aim of this project was to test the assumption that SF-spectroscopy can be used to distinguish between different adsorption structures on a surface by observing the CH-region. Based on these results we hoped to determine whether or not self assembled structures at the solid-liquid interface are symmetric, i.e. a full spherical micelle or a hemispherical cap ad-sorbed to a monolayer of surfactant. To test this it was necessary to find suitable substrate-surfactant systems with known adsorption structures. Cationic ammonium surfactants ad-sorbed to a negatively charged substrate seemed to be a suitable starting point. They are well characterized in terms of adsorption isotherms and behavior and the adsorption structures had been imaged with AFM. The ideal experiment would be to transform the adsorbed surfactant structure from a sphere to bilayer as a function of bulk salt concentration or pH. However we could not find a surfactant that demonstrated this transition on silica or alumina. In the ab-sence of this ideal experiment, we chose to look at the difference in SF spectra between an adsorbed layer of TTAB, which form spheres and rods, and DDAB which forms flat bilayers, both at an alumina substrate.

We made the assumption that a rigid bilayer would not give any SF-signal in the CH-region, due to the symmetry of the system. Essentially the inversion symmetry of the matter must be broken, as is the case in an interface, for a SF-signal to be generated (See Theory and methods section). In effect, a mirror plane would bisect the inner and outer layer of the adsorbed struc-ture. This applies in the direction perpendicular to the substrate surface. In the plane parallel to the surface the bilayer is isotropic. By a similar argument spherical micelles adsorbed to the surface would not give rise to any signal, but hemimicelles on top of a monolayer would.

The results presented in Figure 11 however seem to contradict those assumptions. First, all three systems show a weak signal at ~2950 cm-1, This signal could be the anti symmetric methyl stretch or the Fermi resonance of the symmetric methyl stretch. Both the TTAB and DDAB have methyl groups on the head and at the end of the hydrocarbon tail. The methyl groups at the headgroup immediately adjacent to the solid interface may be sufficiently differ-ent from headgroup methyls pointing towards solution to give rise to a SF signal. We believe it is less likely that the tail group methyls, which are directly adjacent to one another, both in a hydrocarbon environment will contribute to this signal. Future studies with selectively deuter-ated compounds will answer this question. Most importantly though, the signal intensity for all the systems is low and it is hard to distinguish any signal difference in the CH-region.

Visual inspection indicates a shift of the peaks in the OH-region at ~3200 cm-1 and ~3450 cm-1 to higher wavenumbers for the case of cylindrical and spherical micelles compared to the planar bilayer. This is consistent with the idea that a “coarse” water structure at the interface generates a more loosely associated water structure associated to a higher energy.

We conducted the adsorption isotherm of TTAB on alumina to try and better understand the adsorbed structure of surfactants as a function of concentration. This experiment was per-formed twice, shown in Figure 14 and Figure 15. The most interesting result is that we never measured a strong SF signal at the CH-region in the adsorption isotherms. It was expected that below and up to the point of zero charge, the SF signal would increase as the density and therefore the order of the adsorbed surfactant increased. This would be followed by a decrease in signal as the surfactant continued to adsorb in a reversed orientation as the outer layer formed. The fact that this was not observed would suggest that regardless of the adsorbed surfactant structure, the chains of the hydrocarbon tail are in a liquid like, disordered envi-ronment or that monolayer adsorption does not take place, i.e. closed aggregates.

28

The effect of surfactant adsorption in the water region also showed interesting features. Initial adsorption of surfactant results in a decrease in the surface charge density of the sapphire. This results in a decrease in the intensity of the 3200 cm-1 and 3450 cm-1 peaks, which should continue until the pzc is reached. At this point it would be expected to be a minimum in the orientation of water molecules and the SF-signal should be a minimum. As the surfactant concentration increases, the surface recharges, and the 3200 cm-1 and 3450 cm-1 peaks should return. The result from the two experiments was thus rather surprising. The expected behavior with a decreasing intensity was initially present, but as the concentration of TTAB increased, the 3200 cm-1 peak did never return. The surface charge is not independently measured, but the pzc is assumed to be at the surfactant concentration related to the minimum amount of oriented water, i.e. the minimum OH-signal. As no such minima occurred, the pzc can not be determined. The simplest explanation of this is incorrect concentrations of TTAB in the solu-tions used. If only the concentration range below and up to the pzc was actually studied the result would be consistent. However, as the experiment was repeated and the preparation of the surfactant solution thoroughly checked this seems less likely.

The physical meaning of why the peak at 3200 cm-1 did not return after recharging the surface is not obvious and is still being studied. To detect this peak, the water must have a total net orientation in the volume close to the surface where the inversion symmetry is broken. We postulate that adsorption of TTAB might not form a homogeneous layer at the interface; re-sulting in regions within the probed area, possessing opposite charges (negatively charged sapphire, and positively charge TTAB) aligning water molecules in opposite orientations. This could result in a total net orientation that is zero and a loss of SF signal.

Apart from this the screening length is also changing as the surfactant concentration increases because the surfactant itself is an ionic species and also carries a counter-ion, Br-. An in-creased screening because of increasing ionic strength throughout the isotherm will reduce the distance from the surface containing oriented water molecules. When the surface is positively charged at high surfactant concentrations the charge will be balanced by OH- and Br- ions screening the surface in a larger extent than for the case of the negatively charged surface at lower concentrations.

The large time frame over which the adsorption isotherms were conducted combined with the many times liquid is injected in the cell increases the risk of contamination. Provided the ki-netics for the adsorption to the surface is reasonably fast the experiments can be performed in a different manner by cleaning the liquid cell between each measurement and record a water spectrum prior to injecting the surfactant to asses the purity and enable normalization.

For all experiments we have conducted using sapphire, we continually observed a strong peak at ~3700 cm-1, especially for the pure water sample. We did not expect this signal to be pre-sent. The peak associated with a “Free OH” group (3700 cm-1) is only expected to be present at the L/V-interface or at hydrophobic interfaces. It seems very unlikely that there would be any non hydrogen bonded water present at a hydrophilic surface next to bulk water, as the bulk water must present numerous opportunities for hydrogen bonding. This suggested that the peak at 3700 cm-1 was an artifact caused by resonances between the outer and inner alu-mina surface or purely emanating from the outer surface.

To try to determine the origin of the 3700 cm-1 peak we used D2O to create an asymmetry between the surface on the inside of the cell, which we want to study, and the outside of the cell. Filling the dry cell with a D2O sample results in an exchange of all hydrogen atoms at the alumina surface in contact with D2O. When we conducted SF-spectroscopy on this system we observed a free OD peak at ~ 2750 cm-1 and a dramatic decrease in the free OH region. This demonstrates that the Free OH we measured did not originate from water within the window

29

itself and that any signal from the outside of the window is minimal. The Free OD signal was consistent with literature values from free OD observed at solid-vapor interfaces.41,42 This raises a very interesting question; why are water molecules at the hydrophilic solid-liquid in-terface of sapphire constrained in an energetically unfavorable conformation? We do not yet have a full answer for this. A literature search revealed that the Free OH-peaks have been ob-served at alumina both at the S/V-interface with high intensity and at the solid-neat water in-terface with low intensity.30 The Free OH signal has also been observed at the solid-liquid interface at CaF2.7 A possible explanation put forward for the origin of the Free OH peak at the CaF2 surface was that it was caused by the dissolvation of CaF2 in bulk water.7 The dis-solvation was believed to give rise to surface bound Ca-OH oscillators uncoupled to the water at the surface-liquid boundary. It was further indicated that the intensity of the Free-OH signal was related to the pH and the concentration of F- ions in the solution. However this explana-tion seems less likely for alumina, as the solubility in water is extremely low, but a more elaborate study of the pH dependence of the Free-OH signal at the alumina–water interface would be a possible continuation of the performed studies to further investigate this possibil-ity.

Experiments were performed to determine if any correlation with the amount of dissolved gas in the water was present for the Free OH signal. There was no obvious difference in the 3700 cm-1 region between samples of degassed water and non degassed water. Another explanation that can not be ruled out completely is that the Free OH-peak is caused by vapor or gas bub-bles induced through local laser heating. Attempts were made to try to relate the strength of the OH-signal to the intensity of the green beam and IR beam, but no such correlation could be observed.

At the time when the experiments in this report were performed the issue with contamination of silica on the sapphire surface30,35,36 was not known by us. Laboratory glassware was used for all cleaning and preparation of solution. The dissolvation of silica from the glassware is pH dependent and increases at high pH. Also a silica window was used as part of the liquid cell in the setup. It seems unlikely that the alumina surface was not contaminated by silica. Any such contamination will probably lower the isoelectric point of the sapphire, making the surface more negatively charged than expected at high pH and affect the adsorption isotherm as well as the thickness of the layer of oriented water dipoles associated with the surface. In future work, great care will be taken to isolate our sapphire substrates from silica contamina-tion by preparing solutions in teflon containers and only using sapphire in the fluid cell.

41 Kubota, J., et al., Transient responses of SFG spectra Of D2O ice/CO/Pt(111) interface with irradiation of ultra-short NIR pump pulses. Chemical Physics Letters 2002, 362, (5-6), 476. 42 Ogasawara, H., et al., Direct observation of the molecular interaction between chemisorbed CO and water overlayer on Pt(111). Surface Science 1997, 386, (1-3), 73.

30

Conclusions The studied surfactants, TTAB and DDAB, adsorbed to the S/L interface of alumina and wa-ter and probably other ammonium surfactants as well, gave a low intensity SF-signal, if any, in the CH region for concentrations above the cmc. If a methyl signal is detected it can not be assigned specifically to the head group or tail. Our results indicate that SF-spectroscopy can not discriminate between flat bilayers, spherical micelles and cylindrical micelles formed by adsorption of ammonium surfactants at a charged surface. The absence of strong CH-signals indicates that the hydrocarbon chains are in a disordered environment regardless of the ad-sorption structure. The results may also indicate a slightly more loosely ordered water struc-ture at the S/L interface for the case of cylindrical and spherical micelles compared to the pla-nar bilayer.

The SF-spectra of TTAB adsorbed to a charged alumina surface at different concentrations along the adsorption isotherm does not display any CH-signals of strong intensity, and the signals from the two different isotherm experiments are different. The data indicates that the hydrocarbon chains are in a disordered environment at submonolayer/monolayer coverage.

For all experiments conducted using sapphire at pH 10, a strong peak at ~3700 cm-1 was con-tinually observed, especially for the pure water samples. This peak is associated to a non hy-drogen bonded OH-group, a “Free-OH” and is not expected to be present at the S/L interface of alumina and water. We have proved by isotope exchange experiments that this peak origi-nates from the S/L interface, but can not provide any explanation for the reason behind.

In the TTAB isotherm experiments, except for the ~3700 cm-1 peak that remains unchanged, the OH-signals gradually decreases to an almost flat line, as the surfactant concentration in-creases. The OH-region remains flat also at surfactant concentrations above the point of zero charge and at the cmc where signal is expected. We postulate that adsorption of TTAB might not form a homogeneous layer at the interface; resulting in regions within the probed area, possessing opposite charges (negatively charged sapphire, and positively charge TTAB) aligning water molecules in opposite orientations. This could result in a total net orientation that is zero and a loss of SF signal.

31

Acknowledgements First I would like to thank Professor Emeritus Jan Christer Eriksson for directing my eyes to the field of Surface Chemistry and VSFS, and also for mentoring, interesting and valuable discussions and advices about the recrystallization of TTAB. I would also like to thank the following persons: Professor Mark Rutland for giving me the opportunity to perform this diploma work with large freedom in his group. Clayton McKee for project suggestions, for taking care of me the first time and teaching me the basics of surface chemistry research, laboratory methods and VSFS and valuable help with reviewing this thesis. I will miss working with you and will never forget the “oily fish”. Jonas Hedberg for the introduction to VSFS the first days. Torbjörn Petterssson for discussions about programming and computer issues. All the remaining members of the Fundamental Surface Science Group for help and good company. Mikael Danielsson and Margareta Hellström for advices concerning Swedish copyright legis-lation.

32

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Bain, C. D., et al., Quantitative-Analysis of Monolayer Composition by Sum-Frequency Vibrational Spectroscopy. Langmuir 1991, 7, (8), 1563.

Ballinger, T. H.; Yates, J. T., Ir-Spectroscopic Detection of Lewis Acid Sites on Al2O3 Using Adsorbed Co - Correlation with Al-Oh Group Removal. Langmuir 1991, 7, (12), 3041.

Becraft, K. A.; Richmond, G. L., In situ vibrational spectroscopic studies of the CaF2/H2O interface. Langmuir 2001, 17, (25), 7721.

Becraft, K. A., et al., In-situ spectroscopic investigations of surfactant adsorption and water structure at the CaF2/aqueous solution interface. Physical Chemistry Chemical Physics 2004, 6, (8), 1880.

Becraft, K. A.; Richmond, G. L., Surfactant adsorption at the salt/water interface: Compar-ing the conformation and interfacial water structure for selected surfactants. Journal of Physical Chemistry B 2005, 109, (11), 5108.

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Brown, M. G., et al., The analysis of interference effects in the sum frequency spectra of water interfaces. Journal of Physical Chemistry A 2000, 104, (45), 10220.

Chandler, D., Hydrophobicity: Two faces of water. Nature 2002, 417, (6888), 491.

deSainteClaire, P., et al., Simulations of hydrocarbon adsorption and subsequent water penetration on an aluminum oxide surface. Journal of Chemical Physics 1997, 106, (17), 7331.

Du, Q., et al., Vibrational Spectroscopy of Water at the Vapor Water Interface. Physical Review Letters 1993, 70, (15), 2313.

Du, Q., et al., Surface Vibrational Spectroscopic Studies of Hydrogen-Bonding and Hydro-phobicity. Science 1994, 264, (5160), 826.

33

Fan, A. X., et al., Adsorption of alkyltrimethylammonium bromides on negatively charged alumina. Langmuir 1997, 13, (3), 506.

Fuerstenau, et al., Some aspects of flotation thermodynamics. In Froth flotation: a Century of innovation, C., M., Ed. SME, cop.: Littleton, 2007; pp 95-99.

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Hass, K. C., et al., The chemistry of water on alumina surfaces: Reaction dynamics from first principles. Science 1998, 282, (5387), 265.

Hopkins, A. J., et al., Investigations of the solid-aqueous interface with vibrational sum-frequency spectroscopy. Current Opinion in Solid State & Materials Science 2005, 9, (1-2), 19.

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Kubota, J., et al., Transient responses of SFG spectra Of D2O ice/CO/Pt(111) interface with irradiation of ultra-short NIR pump pulses. Chemical Physics Letters 2002, 362, (5-6), 476.

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Lambert, A. G., et al., Implementing the theory of sum frequency generation vibrational spectroscopy: A tutorial review. Applied Spectroscopy Reviews 2005, 40, (2), 103.

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Mawhinney, D. B., et al., Infrared spectroscopic study of surface diffusion to surface hy-droxyl groups on Al2O3: 2-chloroethylethyl sulfide adsorption site selection. Langmuir 2000, 16, (5), 2237.

34

Ogasawara, H., et al., Direct observation of the molecular interaction between chemisorbed CO and water overlayer on Pt(111). Surface Science 1997, 386, (1-3), 73.

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Shen, Y. R., The Principles of Nonlinear Optics. Wiley: New York, 1984.

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35

Appendix 1

Modeling SFG spectra with Lorentzian func-tions

By Jonathan Liljeblad and Clayton McKee, autumn 2007.

Real Lorentzian functions and polar coordinates The method described here is outlined by Lambert & Davies.1

The intensity of the sum frequency (SF) signal is proportional to the absolute square of the sum of the non-resonant and the resonant susceptibilities, (1). Here the susceptibilities are given in polar form, by magnitude and phase factor.

2(2) (2) v

v

iiSF NR R

vI e δεχ χ∝ +∑ e (1)

Because non-linear susceptibilities used in the calculations for SFG-spectroscopy are gener-ally of second order, the “(2)” is hereafter omitted. For one resonance, v = 1, expanding (1) yields:

)cos(2

)cos(2

)(

22

22

)()(22

δεχχχχ

εδχχχχ

χχχχ εδδε

−++=

=−++=

=+++∝ −−

NRRNRR

NRRNRR

iiNRRNRRSF eeI

(2)

Similarly two resonances yield:

)cos(2)cos(2

)cos(2

21

21222

21

2121

δεχχδεχχ

δδχχχχχ

−+−+

+−+++∝

NRRNRR

RRNRRRSFI (3)

It is important to note that the non-linear susceptibility itself is a complex quantity, but the absolute value and the absolute value squared are real valued. The Lorentzian line function is given by:

22

2

wxhwy+

= (4)

where h is the peak height at x = 0 and w is half the width at half the maximum height.

1 Lambert, A. G., et al., Implementing the theory of sum frequency generation vibrational spectroscopy: A tutorial review. Applied Spectroscopy Reviews 2005, 40, (2), 103.

1

The frequency dependent part of the second order susceptibility derived from second order time dependent perturbation theory2, with a constant, A, accounting for the line amplitude is given by (5).

( )Γ−−=

iA

IRRR ωω

χ (5)

Here ωR is the wave number of the resonance, ωIR is the wave number of the tunable IR-beam and Γ is a damping constant, describing the homogenous broadening of the resonance, i.e. the width of the peak. Taking the absolute value, ( )zzz ⋅= , of equation (5) yields:

( ) 22

2

Γ+−=

IRRR

Aωω

χ (6)

Comparing equation (6) with the equation for the Lorentzian peak, (4), and identifying the variables, shows that w=Γ , ( ) xIRR =−ωω and whA = . The frequency dependent part of the second order susceptibility can now be rewritten in Lorentzian parameters:

( )iWWH

IRRR −−=

ωωχ

2

(7)

Equation (7) is separated into its real and imaginary components (needed later) by multiplying it with the complex conjugate:

( )( )( )

( )( ) ( ) 22

2

22

2

WWHi

WWH

iWiW

iWWH

IRRIRR

IRR

IRR

IRR

IRRR

+−+

+−

−=

+−+−

⋅−−

=ωωωω

ωωωωωω

ωωχ

(8)

For the non resonant contribution, χNR, the magnitude and the phase are constant over the whole range of wave numbers, but the phases of the resonances are each independent func-tions of the wave number, i.e. )( IRωδδ = . By studying the first quadrant of an Argand diagram of the complex plane it can be deduced that the phase, δ, can be expressed as the arcustangens of the ratio of the imaginary and real parts of the susceptibility:

[ ][ ]⎟⎟⎠

⎞⎜⎜⎝

⎛=

vR

Rv χ

χδ

ReIm

arctan 1 (9)

At this stage it must be noted that the expression (9) is only valid in the first quadrant, where the phase is varying between 0 and π/2 (and 0 and - π/2 for negative amplitudes described later). To define the phase in the entire complex space the atan2, (10), function must be used instead. This allows the phase to vary between –π and π. Due to typographic reasons, atan2 is hereafter denoted as arctan”.

2 Shen, Y. R., The Principles of Nonlinear Optics. Wiley: New York, 1984.

2

(10) This enables a function for the phase valid in the entire complex space:

( )( )

( )2

2 2 2arctan" , v

v v

v v R IRv vv

R IR v R IR v

H WH W

W W

ω ωδ

ω ω ω ω

⎛ ⎞−⎜ ⎟=⎜ ⎟⎜ ⎟− + − +⎝ ⎠

2 (11)

However, it is easy to realize from equation (11) that the imaginary component is constrained to be positive, thus allowing values on δv between 0 and π. Finally, by putting together the equations (3), (7) and (11) the full expression for the SF inten-sity in the two peak case is obtained (12).

( ) ( )

( ) ( )( )

( )

( ) ( )( )

2 221 1 2 2

2 22 21 1 2 2

221 1 11 11 1

2 22 21 1 1 1 1 1

222 2 22 22 2

2 22 22 2 2 2 2

2 cos arctan" ,

2 cos arctan" ,

SF NRIR IR

IRNR

IR IR IR

IRNR

IR IR

H W H WIW W

H WH WH WW W

H WH WH WW W

χω ω ω ω

ω ωχ ε

ω ω ω ω ω ω

ω ωχ ε

ω ω ω ω ω

= + + +− + − +

2 2W

⎡ ⎤⎛ ⎞−⎢ ⎥⎜ ⎟+ ⋅ ⋅ ⋅ − +

⎜ ⎟⎢ ⎥− + − + − +⎝ ⎠⎣ ⎦

−+ ⋅ ⋅ ⋅ −

− + − + −( )

( ) ( )

( )( )

( )

( )( )

( )

2 22

2 21 1 2 2

2 22 21 1 2 2

22 2 22 2

2 22 22 2 2 2

21 1 11 1

2 22 21 1 1 1

2

arctan" ,

cos

arctan" ,

IR

IR IR

IR

IR IR

IR

IR IR

W

H W H WW W

H WH W

W W

H WH W

W W

ω

ω ω ω ω

ω ω

ω ω ω ω

ω ω

ω ω ω ω

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ +

⎜ ⎟⎢ ⎥+⎝ ⎠⎣ ⎦

+ ⋅ ⋅ ⋅− + − +

⎡ ⎤⎛ ⎞−⎢ ⎥⎜ ⎟ −

⎜ ⎟⎢ ⎥− + − +⎝ ⎠⎢ ⎥⋅⎛ ⎞⎢ ⎥−⎜ ⎟−⎢ ⎥⎜ ⎟− + − +⎢ ⎥⎝ ⎠⎣ ⎦

(12)

This, however, is not sufficient to completely model the SFG intensity. The line amplitude, A, (see equation (5)), is allowed to take both positive and negative values as it is obtained by transforming the corresponding molecular hyperpolarisability, β, from the molecular coordi-

3

nates to the laboratory frame. Depending on the sign of A the peak adds in a constructive or destructive way to the total signal.3

However this is not compatible with the model outlined above, as whA = can not take negative values as both w and h are constrained to be positive. Looking at (12), it is obvious that H, the peak height, in the first two terms, accounting for the absolute square of the resonances may be allowed to be negative. Comparing with equation (3) shows that those terms are the squared modulus of the resonant susceptibilities and hence has to be positive. This is accomplished by using the absolute values of the two first terms in equation (12) in the modeling equation. When it comes to the cross-terms between different resonances and the non resonant back-ground the situation is a bit more complicated. Here the square root of H appears. One way to handle this is to simply use the absolute value of H in the part of the cross term corresponding to the absolute value of the resonant and move the sign outside the square root in the arctan” part. Doing so enables the cosine factor of the cross-term to govern the sign of it and thus give rise to the desired constructive or destructive interference. This leads to the final expression for the two peak case, (13). However the method to use Cartesian instead of polar coordinates described in the next part simplifies the modeling considerably.

( ) ( )

( ) ( )( )

( )

( )

2 221 1 2 2

2 22 21 1 2 2

221 1 1 1 1 1 11 1

2 22 21 1 1 1 1 1

222 2 22 2

2 22 2

( ) ( )2 cos arctan" ,

( )2 cos arctan"

SF NRIR IR

IRNR

IR IR IR

NRIR

H W H WIW W

sign H H W sign H H WH W

W W

sign H H WH W

W

χω ω ω ω

ω ωχ ε

ω ω ω ω ω ω

χ εω ω ω

= + + +− + − +

⎡ ⎤⎛ ⎞−⎢ ⎥⎜ ⎟+ ⋅ ⋅ ⋅ − +

⎜ ⎟⎢ ⎥− + − + − +⎝ ⎠⎣ ⎦

+ ⋅ ⋅ ⋅ −− + ( )

2 2W

( )( )

( ) ( )

( )( )

( )

( )

2 2 2 22 22 2

2 2 2 2

2 21 1 2 2

2 22 21 1 2 2

22 2 2 2 2 2 2

2 22 22 2 2 2

21 1 1

2 21 1

( ),

2

( ) ( )arctan" ,

cos( )

arctan"

IR

IR IR

IR IR

IR

IR IR

IR

sign H H W

W W

H W H W

W W

sign H H W sign H H W

W W

sign H H W

W

ω ω

ω ω ω

ω ω ω ω

ω ω

ω ω ω ω

ω ω

⎡ ⎤⎛ ⎞−⎢ ⎥⎜ ⎟ +

⎜ ⎟⎢ ⎥− + − +⎝ ⎠⎣ ⎦

+ ⋅ ⋅ ⋅− + − +

⎛ ⎞−⎜ ⎟−⎜ ⎟− + − +⎝ ⎠⋅

−− +

( )( )

1 1 1 12 2

1 1

( ), IR

IR

sign H H W

W

ω ω

ω ω

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎛ ⎞−⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟− +⎝ ⎠⎣ ⎦

(13)

It has been found useful for the polar coordinate model to include the following constrains in the fit to exclude fits with unphysical values.

3 Wolfrum, K.; Laubereau, A., Vibrational Sum-Frequency Spectroscopy Of An Adsorbed Monolayer Of Hexadecanol On Water - Destructive Interference Of Adjacent Lines. Chemical Physics Letters 1994, 228, (1-3), 83.

4

0

00

n

NR

W

H

π ε πχ

>

− < ≤>

>

Complex Lorentzian functions and Cartesian coordinates Another by far simpler method is to use Cartesian instead of polar coordinates. Starting from (5) and separating it into its real and imaginary parts by multiplication with the complex con-jugate yields:

( )( )( )

( )( ) ( )2 22 2

R IR R IRR

R IR R IR R IR R IR

iW AA AiiW iW W W

ω ω ω ωχ

ω ω ω ω ω ω ω ω

− + −= ⋅ = +

− − − + − + − +

W (14)

It is evident from (1) that the intensity of the sum frequency signal is proportional to the squared absolute value of the sum of the resonant susceptibilities and the non resonant back-ground. Using equation (14) in equation (1) and modeling the non resonant background with constant real and imaginary components yields an expression for the total intensity.

( ) ( ) ( ) ( )

( )( )

( )( )

( )

2

2 2

2 2

2 22 2

Re Re Im Im

Re Im

v

v v

v

SF NR Nv

NR N NR Nv v

v R IR v vNR NR

v vRv IR v Rv IR v

I

A A WW W

χ χ

χ χ χ χ

ω ωχ χ

ω ω ω ω

∝ + =

⎛ ⎞ ⎛ ⎞= + + + =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞−⎜ ⎟ ⎜ ⎟= + + +

⎜ ⎟⎜ ⎟− + − +⎝ ⎠⎝ ⎠

∑

∑ ∑

∑ ∑(15)

The main advantage of this model is to avoid using a number of trigonometric expressions, reducing the computational time for the curve fitting program. This model is also mathemati-cally easier to understand. The real and imaginary parts of the non resonant background may easily be transformed to polar form if desired. A drawback is that the amplitude, A, is not immediately related to the actual peak height as in the polar model. Using Cartesian coordi-nates enables the modeling of negative amplitudes and a non resonant background with arbi-trary phase without any modification of (15). Also in this model it is of course useful to try to apply as tightly held constraints as possible to facilitate the curve fitting.

5

Curve fitting Equations like (12) and (15) are used together with a curve fitting program to fit the intensity equation to the spectra. We have used the computer program “Igor Pro, version 6.0”, featuring an iterative routine, the Levenberg-Marquardt algorithm, to minimize chi-square, (16).

∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

v i

iyysquarechi

2

_σ (16)

This is a form of non-linear, least-squares fitting, utilizing a different way to calculate the difference between the fitting function and the data points, accounting for the standard devia-tion, σ.

6

Appendix 2Liquid exchange in the fluid cell

By Jonathan Liljeblad, autumn 2007. The liquid cell used for SFG spectroscopy at the solid-liquid interface features a sealed cham-ber with a volume in the order of 7 ml. Inlet and outlet tubing are fitted to the chamber. The concentration of surfactant in the cell is changed by injecting liquid with the desired final concentration by the inlet tube. Simultaneously the same amount is led out by the outlet tube. It is assumed in this model that the injected surfactant immediately diffuses within the cell to a complete mixing and that the injected surfactant is inert, i.e. no adsorption or reactions takes place within the cell. The first assumption holds if the injection flow is slow compared to the time needed to achieve mixing within the cell. The second assumption holds if the area of the surface where adsorption takes place is small compared to the cell volume and the concentra-tion within the cell. The validity of both this assumptions remains to be checked.

Fluid cell Vcell = vol-ume ccell = con-centration in cell

Vin = injected volume

cin = concen-tration in injected li-quid

Vout = rejected volume

Figure 17 Model system of fluid cell.

In a closed cell filled with liquid it is obvious that Vin = Vout as the compressibility of most liquids are very low. According to the assumptions made earlier the concentration in the re-jected liquid, cout, equals the concentration in the cell, ccell. Now, a differential equation, (1), for the system can be put together.

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( ) ( )cell in in in cell in in

in cell in cell in

dc V c V c V VmoldV l V V V V

∗ ∗⎡ ⎤ = −⎢ ⎥ ∗ ∗⎣ ⎦ (1)

As an extra check the units for the terms are compared.

2 2

1 1mol mol molll l l l l

∗ = ∗ ∗ − ∗ ∗1ll

(2)

1

Rearranging (1) gives:

( ) ( )cell in cell in in

in cell cell

dc V c V cdV V V

+ = (3)

with the common solution cc and the particular solution cp.

in

cell

VV

c

inp cell in

cell

c Decc V

V

−

=

c= ∗ = (4)

The beginning condition ccell(0) = cstart is used to determine the constant D:

(5) (0)cell start start in start inc c c c D D c= ⇒ = + ⇒ = − c Finally the solution to the differential equation can be put together:

( ) ( )in

cell

VV

cell in in start inc V c c c e−

= + − (6)

Graph 1 This graph illustrates how the concentration in the cell, ccell, changes as a function of the injected volume at three different starting concentrations, cstart.

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