Distinguishing and correlating surface and bulk behaviour using linear and nonlinear vibrational spectroscopy

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by Sandra Roy

M.Sc., University of Victoria, 2013 B.Sc., Universit´e Laval, 2010

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY in the Department of Chemistry

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Sandra Roy, 2017 University of Victoria

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Distinguishing and correlating surface and bulk behaviour using linear and nonlinear vibrational spectroscopy

by Sandra Roy

M.Sc., University of Victoria, 2013 B.Sc., Universit´e Laval, 2010

Supervisory committee

Dr. Dennis K. Hore, Supervisor (Department of Chemistry)

Dr. Fraser Hof, Departmental Member (Department of Chemistry)

Dr. Irina Paci, Departmental Member (Department of Chemistry)

Dr. Stephanie Willerth, Outside Member (Department of Mechanical Engineering)

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ABSTRACT

Thorough understanding of interfaces requires an assessment of both the surface and bulk properties through the use of multiple techniques. In this thesis, infrared absorption, Raman scattering and sum frequency generation were used as vibrational probes of different features of interfacial systems including the ability to measure surface and bulk effects. Two-dimension correlation analysis was used to study the relationship between the spectral response of the different techniques. Attenuated total reflection absorption, bulk Raman scattering and sum frequency generation were used to study the adsorption of ethanol–water mixture on fused silica. With the use of two-dimension correlation analysis, interesting results were observed concerning the behavior of the surface in respect to the bulk. Surface concentration of ethanol were concluded to be higher than in the bulk indicative of competitive adsorption. Furthermore, at low concentration ethanol was shown to adsorb to the surface in dimers, to then form a bilayer of strongly oriented ethanol molecules at higher concentration. At highest concentration, this bilayer is disturbed, leaving only one layer at the surface of oriented ethanol molecules. The same spectroscopic techniques were applied to pressure sensitive adhesives of different composition while drying on a sapphire surface. The presence or absence of acrylic acid in the material was shown to alter the reorientation at the surface while drying. In the case where no acrylic acid is present, the orientation of the polymer at the surface was driven by the packing of the molecules at the surface. When acrylic acid was present in the pressure sensitive adhesive, reorientation occurred much faster and was caused by strong hydrogen bonding with the surface of the sapphire. An increase in acrylic acid composition, increased the rate of reorientation. An experimental set up was constructed to specifically study interfaces with a nonuniform distribution within the plane of the surface. This allows for concomitant measurement of polarized total internal reflection Raman scattering and sum frequency generation spectroscopy along with bright field imaging and cross polarized imaging.

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This set up was used to study the L-histidine crystal in situ adsorbed on fused silica. The polarized experiments along with calculations allowed for a more in-depth analysis of the crystal orientation effect on the birefringence, the Raman and the sum frequency generation.

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List of Tables

2.1 Parameters used to model the 7 peaks for the IR absorption, |χ(2)|2_{, and}

Im[χ(2)] spectra. The initial amplitude A0 and final amplitude A0 is listed,

along with the fraction of total time that the amplitude remains at A0before

it increases or decreases towards A0. . . 24 2.2 Assignment of the vibrational modes that contribute to the adsorbed Leu

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List of Figures

1.1 Examples of different interface length scales. Adapted from Ref. 1. . . 1 1.2 Jablonski diagram of the different spectroscopic techniques. From left to

right: infrared absorption, stokes and anti-Stokes Raman scattering and sum frequency generation. The dashed lines represent virtual states. . . 7 1.3 Example of a total internal reflection geometry for Raman spectroscopy. . . 15 1.4 SFG setup with prism cut at 70◦. . . 19 2.1 Evolution of the amplitudes A2 in the case of the IR and |χ(2)|2 _(narrow

lines), and A in the case of the Im[χ(2)] (thick lines) for the peaks at 2860 cm−1 (red) and 2880 cm−1 (blue). The end of the delay before any changes in amplitude occur is indicated by vertical dashed lines. . . 26 2.2 Top row: evoluation of the spectra for the IR absorption (left), |χ(2)|2

(middle), and Im[χ(2)_{] (right) lineshapes with Γ = 5 cm}−1_{. The spectrum}

at t = 0 is shown with a bold line. Middle row: synchronous correlation maps, with positive contours drawn in red and negative contours in blue. Bottom row: asynchronous correlation maps. The traces on the edges of the correlation maps are the average (reference) spectra. . . 28

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2.3 Top row: evoluation of the spectra for the IR absorption (left), |χ(2)|2

(middle), and Im[χ(2)] (right) lineshapes with Γ = 10 cm−1. The spectrum at t = 0 is shown with a bold line. Middle row: synchronous correlation maps, with positive contours drawn in red and negative contours in blue. Bottom row: asynchronous correlation maps. The traces on the edges of the correlation maps are the average (reference) spectra. . . 29 2.4 (a) x-polarized and (b) z-polarized IR absorption spectra of Leucine

adsorbed to surfaces of varying hydrophobicity. The Im[χ(2)] spectra are shown for the (c) xxz, (d) xzx and (e) zzz elements. The legend at the top of the figure indicates the colours used to plot the spectra generated for the specific hydrophobic surface, labelled according to the water contact angles. 30 2.5 Results obtained for the x-polarized (left) and z-polarized IR absorption

spectra. The top row shows the adsorbed leucine spectral features as a function of the surface hydrophobicity as indicated by the water contact angle, plotted as a difference from the average spectrum. Darker red colors (positive differences) indicate that the features are stronger than those in the reference spectrum; darker blue colors (negative differences) indicate that the spectral features are weaker than those in the reference spectrum. The synchronous correlation maps are shown in the middle row, and asychronous in the bottom row, with the same color conventions as for the previous 2DCOS analysis. . . 35

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2.6 Results obtained for Im[χ(2)] spectra in the (left) xxz, (center) xzx, and (right) zzz polarization combinations. The top row shows the adsorbed leucine spectral features as a function of the surface hydrophobicity as indicated by the water contact angle, plotted as a difference from the average spectrum. The synchronous correlation maps are shown in the middle row, and asychronous in the bottom row, with the same color conventions as for the previous 2DCOS analysis. . . 36 3.1 Top row: subset of raw data; bottom row: subset of data to be used in

the correlation analysis. Water spectra shown in blue, ethanol spectra in red, intermediate mole fractions in black. (a) ATR reflection-absorbance, relative to the dry ZnSe crystal. (b) Im[χ(1)_{] spectra, obtained from}

the ATR data using Eq. 3.2. (c) Raman scattered intensity. (d) Raman scattering cross section, proportional to Im[χ(3)]. (e) SFG intensity, corrected only for the transmission of the fused silica. (f) Im[χ(2)] spectra, obtained from a combination of local field corrections, other dispersion corrections, and MEM analysis. Larger representations of this data, including all mole fractions of ethanol used in this study, are shown in Figs. 3.2–3.5. . . 42 3.2 (a) ATR absorbance data and (b) Im[χ(1)_{] data for ethanol-water mixtures}

for the bulk ethanol mole fractions as indicated in the inset. . . 43 3.3 (a) Raman scattering data and (b) Im[χ(3)] data for ethanol-water mixtures

for the bulk ethanol mole fractions as indicated in the inset. . . 44 3.4 (a) Region 1 SFG data and (b) Im[χ(2)] data for ethanol-water mixtures for

the bulk ethanol mole fractions as indicated in the inset. . . 45 3.5 (a) Region 2 SFG data and (b) Im[χ(2)] data for ethanol-water mixtures for

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3.6 Optical constants and spectral corrections as a function of IR wavenumber and ethanol mole fraction. (a) real part of the refractive index, (b) imaginary part of the refractive index, (c) IR evanescent wave penetration depth, (d) ATR correction from Eq. 3.2, (e) magnitude squared and (f) phase of the SFG correction factor in Eq. 3.9. . . 47 3.7 Synchronous homospectral correlation maps for (a) the IR absorption data

transformed into Im[χ(1)],and (b) the Raman scattering data transformed into the scattering cross section. Red contours indicate positive values; blue contours indicate negative values. . . 52 3.8 (a) Synchronous (b) asynchronous Im[χ(1)]–Im[χ(1)] corellation maps

obtained from the IR absorption data. Red contours indicate positive values; blue contours indicate negative values. . . 53 3.9 (a) Synchronous (b) asynchronous Im[χ(3)_]–Im[χ(3)_{] corellation maps}

obtained from the Raman scattering data. Red contours indicate positive values; blue contours indicate negative values. . . 54 3.10 Synchronous Φ and asynchronous Ψ homospectral correlation maps for

the SFG data transformed into Im[χ(2)] for (a,b) Region 1, EtOH mole fractions 0–0.81, and (c,d) Region 2, EtOH mole fractions 0.82–1. Red contours indicate positive values; blue contours indicate negative values. The percentage in the inset of the asynchronous map indicates the ratio of the largest signal in Ψ compared to Φ. . . 56 3.11 Synchronous Φ and asynchronous Ψ heterospectral correlation maps for

(a,b) the IR–SFG data, and (c,d) the Raman–SFG data for Region 1, 0 < xEtOH < 0.81. Red contours indicate positive values; blue contours

indicate negative values. The percentage in the inset of the asynchronous map indicates the ratio of the largest signal in Ψ compared to Φ. . . 60

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3.12 Synchronous Φ and asynchronous Ψ heterospectral correlation maps for (a,b) the IR–SFG data, and (c,d) the Raman–SFG data for Region 2, 0.82 < xEtOH < 1. Red contours indicate positive values; blue contours

indicate negative values. The percentage in the inset of the asynchronous map indicates the ratio of the largest signal in Ψ compared to Φ. . . 62 4.1 In ATR-IR absorption spectroscopy, the reflectance of an IR probe beam

is altered by transfer of energy from the evanescent wave into the PSA in contact with the Ge prism. In visible-infrared SFG spectroscopy, a new colour of light is created from regions of the PSA-sapphire interface where molecules are oriented in a polar manner. . . 68 4.2 A subset of the reflection absorbance spectra (collected every 30 min for

10 h) as measured in the ATR-IR experiment following a simple ATR correction that renders the data proportional to Im[χ(1)] for the sample containing (a) no acrylic acid, (b) 2% acrylic acid and (c) 4% acrylic acid as a function of the drying time as indicated in the inset to the top panel. . . 72 4.3 A subset of the |χ(2)ppp| spectra (collected every hour for 10 h) as measured

in the SFG experiment for the sample containing (a) no acrylic acid, (b) 2% acrylic acid and (c) 4% acrylic acid as a function of the drying time as indicated in the inset to the top panel. The axes are broken at 3050 cm−1 so as to magnify the CH stretching region in the 2800–3050 cm−1region. . 73 4.4 Heterospectral synchronous (Φ, top row a,c,e) and asynchronous (Ψ,

bottom row b,d,f) correlation maps that relate SFG to IR spectral changes during the drying process. Results are shown for (a,b) 0% acrylic acid, (c,d), 2% acrylic acid, and (e,f) 4% acrylic acid. Positive contours are drawn in red; negative contours in blue. Percentages in the inset of the Ψ plots indicate the fraction of the largest synchronous signal found in the corresponding asynchronous plot. . . 75

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5.1 Schematic of the experimental set up. . . 80

5.2 Photograph of the flow cell design from top and side view. . . 81

5.3 SFG and TIRR spectra of ethanol, water and histidine in solution. . . 83

5.4 SFG signal of Aluminum coated prism. . . 84

5.5 Spectrum of the narrowed 800 nm laser beam. . . 84

5.6 SFG (A) and TIRR (B) spectra of histidine crystal grown ex situ and place on the prism perpendicular(1) and parallel(2) to the plane of incidence. Bright field images (top) ,y-in x-out cross polarized images (middle) and images with polarizer rotated by 45◦(bottom) are presented on a same scale for crystal perpendicular(C, D and E) and parallel (F, G and H) to the plane of incidence. . . 86

5.7 SFG (A) and Raman (B) spectra of crystals probed in situ with their respective bright field images (1: C , 2: D , 3: E ) and cross polarized images (1: F, 2: G, 3: H). . . 87

5.8 SFG (A) and Raman (B) spectra of crystal growth in situ with their respective bright field images (1: C , 2: D ) and cross polarized images (1: E, 2: F). The time elapsed between the two measurements was about 20 min. . . 88

6.1 Scanning SFG spectra of Caulobacter crescentus growth (A) and normal-ized intensity of two frequency variation with time (B) . . . 97

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List of Symbols and Definitions

symbol definition units

α polarizability Cm2V−1

α(2) _{hyperpolarizability} _Cm3_V−2

λ wavelength m

χ electric susceptibility a.u.

χ(2) second order nonlinear susceptibility a.u.

ω wavenumber cm−1

t time s

µ electric dipole moment C · m

Γ spectral linewidth cm−1

SFG sum frequency generation TIRR total internal reflection Raman

IR infrared

2DCOS 2D correlation spectroscopy PSA pressure sensitive adhesive

θi, φ, ψ Euler angles for tilt, azimuth and twist deg or rad

xyz laboratory coordinate system unit vector

ijk place holders for any of the x, y or z coordinates abc molecular coordinate system unit vectors

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ACKNOWLEDGEMENTS

I would like to thank:

Dennis Hore, for being the best advisor there is. From amazing brainstorming sessions, to hands on help in the lab, to moral support through challenges, you have made this PhD a truly amazing learning experience.

My mom, dad and sister, Linda, Marcel and Samanta, for the support through all my endeavors.

Andrew Schildroth and Tasha Jarisz, for having the proof-reading skills that I do not. Paul Covert, Tasha Jarisz, William FitzGerald, Sean Yang and Sagnik Datta, for making life in the basement more interesting.

Andrew Schildroth, Alex Nadon, Derek Book, Kristen Scott, Katherine King, Carl Constantine and all my friends and neighbours, for the interesting discussions, the mental and moral support, the occasional drink, and all of the laughs. Life in Victoria wouldn’t have been as interesting without you in my life to brighten every day of it. NSERC and UVic, for financial support.

Compute Canada, for the use of the Westgrid clusters.

“La physique est une science qui devient chimie lorsqu’on la chauffe a l’air libre” Jean-Louis Marcel-Charles

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Chapter 1 Introduction

1.1 Motivation

Elucidating the structure of molecules at interfaces is a fundamental aspect of understand-ing and optimizunderstand-ing the characteristics of biosensors [2, 3], catalytic systems [4], chemical separations [5–8], and environmental monitoring [9].The lengthscale or depth of the interfacial region may differ depending on the point of view of the observer. Fig. 1.1 shows an example where a simple interface such as rust on a metal surface can possess different definitions. To the naked eye, one can consider the rust being millimeters thick, the depth to which the substance will need polishing. If analyzed through topographic techniques, one might observe different height variations between the metal and rust and consider the interface to be on a micron lengthscale. If rust is analyzed through computational chemistry, one might consider the interfacial region to be defined by the top most layer of atoms at the interface, which can then be described in Angstroms. Study of different length scales will contribute complementary information about the interface.

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For solid–liquid interfaces, the profile as a function of distance into the bulk phase may be described in terms of composition, density, or molecular orientation. These properties can be significantly different between the bulk and surface. Furthermore, the molecular interaction at the surface may alter the behaviour of the system as a whole. For example, the adsorption of molecules on surfaces can alter the adsorption properties of other molecules in the immediate environment. Not only is it important to be able to distinguish the surface and bulk behavior at the interface, but the correlation of those two behaviors is the key to better understand the interfacial properties.

1.2 Surface structure of small molecules

Adsorption of small molecules from solution onto a surface is governed by the strength and nature of intra and intermolecular interactions between all the components present in solution. This includes the interactions of molecules with the surface, with themselves and with other molecules in solution. The relative adsorption strength of other molecules in solution must also be taken into consideration. The adsorption process is thus not only dependent on what is happening at the surface, but also in the bulk solution.

One of the simplest of small molecule adsorption processes is water adsorption, yet it is still a topic of great interest. Water has been the subject of countless studies of its bulk and surface behavior [10–12]. The structure of water on solid surfaces is a critical component for mediating adsorption of other molecules—ions, synthetic surfactants, proteins and cells [13,14]. Experimental and theoretical studies have demonstrated that water at surfaces may be substantially different from bulk water in terms of orientation and the nature and degree of hydrogen bonding [15–18]. However, the same studies reveal that these differences extend over a distance of approximately 1 nm, after which the water structure resembles that of isotropic bulk water.

Molecules in aqueous solution will also behave differently in the presence of a solid surface. Competitive adsorption can occur if solutes have different affinities to the surface.

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This difference in affinity to the solid is the basis of separation techniques such as liquid chromatography. The competitive adsorption might also cause the surface concentration to differ from the bulk. For processes that are concentration dependent such as chemical reaction, a change in concentration near the surface may mean a change in reactivity. In other cases, like amino acids in solution, it is the specific orientation at the surface that is of interest. Proteins have been shown to denature when adsorbing to surfaces [19]. For example, insulin has been shown to unfold when adsorbed to certain surfaces and thus lose its efficacy. Since amino acids are the building block of proteins, understanding their adsorption and orientation preference on a surface might lead to a better insight into surface induced protein unfolding. Because of this, the adsorption and surface orientation of amino acid on solid surfaces has been studied extensively [20, 21].

For small molecules adsorbing on a surface from a liquid solution, the overwhelming contribution of the bulk to spectral response can make the analysis of the interface really challenging as the interfacial region can be considered quite small. If only a monolayer of molecules is adsorbed on the surface, this corresponds to an interfacial region depth in the order of a few nanometers. The use of techniques that can probe this small region of the interface can be a great asset in these systems. Furthermore a comparison with spectral response of a bulk techniques could lead to some insight of concentration gradient of the system.

1.3 Adhesion

Adhesion studies are of critical importance in a broad range of applications, from biological to industrial. In biomedical devices, the control of interfacial adhesion is crucial. For artificial implants, two completely different strategies are being used [22]. One strategy focuses on a material that will not interact with any biological material and will not promote adhesion. This is in the hope of preventing cell death and to discourage blood coagulation on the surface. Additionally this approach seeks to prevent bacterial cell adhesion which

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can lead to infections [23]. Modifying the hydrophobicity, roughness, stiffness and charge of the surface have been useful methods to control cell adhesion to the material [24, 25].

A more complex but superior solution is to have a material that will be biocompatible through integration with the body over time as it minimizes the risk of rejection. This requires promoting the adhesion of the proper cells and proteins on a surface. This process is akin to building a scaffold, upon which the body can begin work to heal itself. A non-artificial example of this is a bone graft. In this case, a foreign but biocompatible bone is surgically inserted to promote healthy bone growth. Artificial materials used as scaffolds in tissue engineering are often based on ceramics, synthetic polymers and natural polymers [26, 27]. Examples of these materials include hydroxyapatite, polystyrene and collagen.

In biological applications, the study of cell adhesion on surfaces has been of interest to allow for better understanding of the mechanism of adhesion and cell growth [28]. Fundamental adhesion studies of model systems has been the focus of many recent studies. In bacterial adhesion, Escherichia coli is the most common gram negative model bacteria studied. This is due to E. coli’s presence in the gut flora as well as its problematic presence in contaminating medical devices [29–31]. These studies have led to a growing understanding of bacterial adhesion and biofilm growth. Other examples where bacterial adhesion would need to be controlled can be observed in the sea. Bacteria in the ocean adhere to ships’ hulls, allowing for biofilms to grow. These biofilms become a perfect anchor for barnacles to attach. When a ship’s hull is covered in barnacles, it creates a great deal of drag and this results in more fuel being spent at significant financial cost. Over $200 billions are being spent in the united state every year to deal with biofouling and biocorrosion [32]. This is just one example of benign mircoorganism adhesion making a major impact in the human world.

Strong adhesives also occur in nature. Some examples include: the Notaden bennetti frog which secretes a sticky substance when provoked [33, 34]; mussels that produces proteins capable of strong adhesion in wet conditions [35, 36]; gastropods such as slugs

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whose mucus is strong and flexible [37]; and bacteria who can secrete substances to allow for irreversible adhesion [38, 39].These naturally formed compounds brought about innovative research into bio-inspired adhesives [40, 41].

The adhesion process is governed by the interaction of two surfaces and the strength of the adhesion lies at the interface of these two materials. Therefore, it is important to properly understand the interfacial interactions at work to truly understand any adhesion process. Adhesion is governed by mechanical, physical and chemical properties of the materials employed [42, 43]. Adhesion can be assessed by examining both surfaces in consideration, and the region in which they interact. However, there is ambiguity in defining at what point two materials become an interface. This can range anywhere from millimeter to sub-nanometer depending on the point of view of the research.

In industrial applications, adhesion is often measured through mechanical properties. Mechanical deformation extends beyond millimeter from the interface and thus has a broader definition of interface [44, 45]. Alternatively, if the interfacial region is defined through physical properties, such as the 3D scaffold used in tissue engineering, an interface can be thought to be only microns deep. In the case of chemical properties and intermolecular interactions, then the interface can be considered Angstroms to nanometers thick. None of these definitions are false, as they all contribute valuable assessments of the interface.

In some cases the interfacial region is delimited by the scale of the material itself. The scale of bacterial adhesion [46], for example, can be drastically reduced to the orders of microns due to the size of the microbe. Atomic force microscopy [47, 48] and traction force microscopy [49] have proven to be useful techniques in assessing adhesion strength in microscale and nanoscale systems. When the composition is unknown, other techniques need to be employed to asses the interface. By example, in order to isolate and characterize the region of interest within a micron size system, such as bacterial adhesion, studies have employed different invasive techniques. These techniques include cell mutation to break

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down the cell into its constituent parts, which can then be separately examined through analytical techniques, such as capillary electrophoresis and liquid chromatography - mass spectrometry (LC-MS) [50]. However, in the study of living organisms, techniques that are less invasive or destructive would be more appropriate.

One of the current challenges into studying the interfacial behavior of adhesives stems from the fact that they are often viscous materials that tend to have a gradient of concentration and orientation extending deeper within the bulk. The use of multiple techniques that would probe different depths of the interface would be an asset for better understanding the behavior of adhesives at surfaces.

1.4 Organic nonlinear crystals at the solid-liquid interface

Most amino acids when crystallized tend to form highly ordered structures due to their strong intermolecular hydrogen bonding capabilities. These often have strong nonlinear properties [51]. Organic nonlinear optical (NLO) crystals have higher nonlinear susceptibility, are structurally more diverse and have a higher response rate than their inorganic counterpart [52, 53]. This makes them interesting for use in applications such as frequency conversion in lasers (to obtain SFG, DFG or OPG), optical switching and optical data storage. Monitoring the growth of a crystal in situ is of interest to better understand the crystal formation and crystal growth. To achieve this, a crystal must first be isolated, this can be achieved by having the crystal adhere onto a solid surface. However, the study of the crystal can still be a challenge as in an oversaturated solution the concentration in the bulk liquid can easily overwhelm signal arising from small crystals at the surface. In this case it is important to have a technique capable of distinguishing between bulk crystal and bulk solution and this can be achieved by limiting the probed depth at the interface.

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1.5 Useful probes of interfacial properties

Vibrational spectroscopy is a valuable family of techniques to study surfaces, owing to the fine structural detail and non-invasive nature of the methods, requiring only that the interfaces be accessible to light. Of the many vibrational techniques available, ones capable of addressing buried interfaces, that is between two condensed phases whether solid–liquid, liquid–liquid, or solid–solid, are particularly valuable. Common vibrational spectroscopic techniques include infrared absorption spectroscopy, stokes and anti-stokes Raman scattering, and sum frequency generation (SFG). These are all represented in the Jablonski diagram in Fig. 1.2. The dipole moment of a molecule µinduced induced by an

Figure 1.2: Jablonski diagram of the different spectroscopic techniques. From left to right: infrared absorption, stokes and anti-Stokes Raman scattering and sum frequency generation. The dashed lines represent virtual states.

external field E can be described as the sum of the effect of all nth-order polarizabilities (α(n)). µinduced = α(1)E + 1 2α (2)_{EE +}1 6α (3)_{EEE + ... +} 1 n!α (n)_En _(1.1)

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The susceptibility χ(n)is the macroscopic analogue of the polarizability, so the polarization of a material P may be expressed in terms of susceptibility tensor elements

Pi = ε0 χ(1)_ij Ej + 1 2χ (2) ijkEjEk+ · · · + 1 n!χ (n)_En (1.2)

where χ(n) _{is the n-th order susceptibility and ε}

0 is the vacuum permittivity. Here

i, j, k refer to any of the laboratory-frame Cartesian x, y or z components. The linear susceptibility χ(1) is responsible for IR absorption, while SFG and Raman rely on the second and third order susceptibility respectively.

When two atoms are covalently bonded, the repulsive and attractive forces acting along the bond when disturbed from its equilibrium length (req) can be thought of as two masses

attached by a spring. The force acting along the bond by displacement (r − req) can then

be described by Hooke’s law,

f = −k(r − req) (1.3)

where k is the force constant. This model is called the simple harmonic oscillator model. In this ideal case, the energy F of the system takes a parabolic form,

F = 1

2k(r − req)

2 _(1.4)

The vibrational frequency (ω) of the bond can then be derived from the shape of the parabola which lies in the force constant k and the reduced mass µ,

µ = m1m2 m1+ m2 (1.5) w = 1 2π s k µ (1.6)

Following quantum mechanics, the vibrational energy can be redefined in terms of quantum number v,

F = (v + 1

2)hw (1.7)

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For a molecule containing N atoms, there exist 3N degrees of freedom (for all three Cartesian coordinates). If we remove the full translation or rotation of the molecule, we end up with 3N − 6 different internal vibrations. For linear molecules, only two axis are needed to define the rotation of the molecule, leaving 3N − 5 different internal vibrations. These vibrations can be stretching modes (symmetric and antisymmetric) or bending modes.

1.5.1 Electric fields at surfaces

The choice of probe ultimately depends on the length-scale of the interface. This can have many definitions in vibrational spectroscopy, even for the same system, since the profile as a function of distance into the bulk phase may be described in terms of composition, density, or molecular orientation. Due to the large ratio of bulk to surface contribution, it can be difficult to investigate smaller regions of the interface. Total internal reflection can help in controlling the depth of the probed interface.

When light passes through an interface of two different refractive indices, some of the light will be reflected and some will be transmitted. The angle of the transmitted light θtis

correlated with the angle of the incident light θithrough Snell’s law

nisin θi = ntsin θt (1.8)

where niand ntare the real part of the complex refractive index N.

N = n + ik (1.9)

The ratio of the reflected/transmitted field to the incident field differs for different polarizations and is dependent on the refractive indices of the materials as well as the

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incident angle through the Fresnel equations rs = nicos(θi) − ntcos(θt) nicos(θi) + ntcos(θt) (1.10a) rp = nicos(θt) − ntcos(θi) nicos(θt) + ntcos(θi) (1.10b) ts = 2nicos(θi) nicos(θi) + ntcos(θt) (1.10c) tp = 2nicos(θi) nicos(θt) + ntcos(θi) (1.10d)

Where r and t are the reflection and transmission coefficient, respectively, and p and s subscripts indicate the light polarized parallel and perpendicular to the plane of incidence, respectively. The resulting surface field is a sum of both the incident and reflected field and can be expressed in terms of its individual Cartesian coordinate component x, y, z

Ex = Epcos(θi)(1 − rp) (1.11a)

Ey = Es(1 + rs) (1.11b)

Ez = Epsin(θi)(1 + rp) (1.11c)

In total internal reflection geometry, the incident light approaches from a material of higher refractive index than the adjacent material at an angle higher than the critical angle

θc = arcsin

nt

ni

. (1.12)

In TIR, all light is reflected and none is transmitted. There is however an electric field on the low refractive index side which exponentially decays as the distance from the interface increases. This is called the evanescent wave. The corresponding evanescent wave penetration depth is related to both the refractive index of the materials ni and ntas

well as the wavelength λ of the probe beam and the incident angle. The evanescent wave penetration depth dphas the form

dp = λ 2πn1 p sin2θ − (nt/ni)2 (1.13)

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where ni is the refractive index of the prism, and nt is the refractive index of the sample.

Total internal reflection techniques have been widely used to study interfaces [54] utilizing the low penetration depth of the evanescent wave as a surface-limiting probe. By using different incident angles, probed beam wavelength and material refractive index, one can control the probed depth of the TIR techniques.

1.5.2 Infrared absorption spectroscopy

Infrared absorption spectroscopy is well suited to analyze vibrational modes as their frequency usually spans in the infrared region. In transmission infrared spectroscopy, an infrared source goes through a sample; the molecules in the path will absorb light with energy matching their specific vibrational energy. The transmitted light will then be diminished at those specific wavelengths. It is important to note that for light to be absorbed a change in dipole moment (µ) needs to occur along the vibration. This can mathematically be expressed as dµ dQ Q=0 6= 0 (1.14)

where Q is the normal mode coordinate. This is commonly called the IR selection rule. The vibrational frequency can span between 1 µm to 100 µm but are often categorized into two main groups: the fingerprint region and the functional group region. The fingerprint region, from 500 to 1500 cm−1 arises from the backbone of organic molecules. This includes most CC, CN and CO bonds. The functional group region, from 2200 to 4000 cm−1 includes vibrations from all CH, NH and OH bonds.

Infrared absorption data is often presented in absorbance (A), which is calculated from the transmittance and corrected with a reference transmittance.

A = − log(T /T0) (1.15)

The absorbance of a material is directly proportional to the thickness of the material and the absorption coefficient .

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This makes this vibrational spectroscopic technique not only useful for qualitative purposes but also for analytical measurements. The absorption coefficient can be related to the imaginary part k of the complex refractive index.

Measurements. The simplest way to do an IR absorption measurement would be to illuminate the sample with monochromatic light and then examine the absorption before changing to another wavelength. An alternative approach is to use Fourier transform infrared spectroscopy (FTIR). In this experiment, the sample is irradiated with a broadband light source to collect the whole spectrum at once. When using a an integrating photodetector, the photons from all wavelengths are collected as one value. To be able to differentiate between them a Michelson interferometer is used. The light is split, half of it is reflected on a fixed mirror, while the other half is reflected on a moving mirror. The two beams are then recombined and interfere with each other. Since the light interference is wavelength dependent, the resulting interferogram can then be transformed back to get the spectrum. This mathematical transformation is called Fourier transformation. This technique allows for fast broadband measurement with good signal to noise ratio, reproducibility and high spectral resolution.

In transmission IR absorption, when a solid has to be measured, the absorbance of the probed volume has to be considered so as not to absorb all the light. For example, for bulk solid, it often necessitate dilution in an IR transparent matrix. KBr is the most common matrix used as once compacted properly in a pellet form it becomes clear. However, this is a somewhat tedious process. A way to circumvent this problem is to do the IR absorption measurement in TIR geometry, generally called attenuated total reflection infrared spectroscopy (ATR-IR), where only the electric field brought on by the evanescent wave will probe the sample. This allows for one to probe only microns from the surface [55]. As a result, in ATR-IR the pure solid can be compacted directly on the surface of the ATR crystal without absorbing all the light. For materials with lower absorption coefficients, multiple reflections on the ATR crystal allows for greater

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sensitivity by multiplying the ATR absorption by the number of reflections. ATR-IR was first demonstrated in the early 1960s [56, 57]. The probe depth of a few microns makes this technique also useful for studying interfaces.

For ATR-IR, certain care needs to be taken when analyzing the spectra. In fact the resulting absorption spectral intensity and peak position will be different than its transmission counterpart. The spectral intensity and shape differences stem from the wavelength dependence of the refractive index, which in turn will affect the penetration depth. The path length in Eq. 1.16 is now replaced with a refractive index dependent effective length, deff.

deff =

nt|t|2d

2nicos θi

(1.17) The other consideration is the peak position shift. This is due to the refractive index shape. Near an absorption band, with an increase in imaginary refractive index, the real part of the complex refractive index changes considerably, which in turn affects the penetration depth and surface field. This results in a shift of the observed absorbance to lower wavenumbers. Both of these changes in spectral shape can be corrected for as long as the refractive index is known for the wavelengths studied.

Implementation. In this work, ATR-IR data was collected using a Bruker Vertex 70 FTIR spectrometer with a KBr beamsplitter, wire-grid polarizer on a BaF2 substrate

(Thorlabs, Newton NJ) and a deuterated triglycine sulfate (DTGS) detector. Measurements were performed with Pike HATR accessory fitted with a 80 mm × 10 mm × 4 mm ZnSe or Ge crystal cut at 45◦ to yield 10 ATR reflections. Raw data was corrected with a baseline reflectance R0measured using a dry crystal.

AATR = − log(R/R0), (1.18)

Different data processing procedures were implemented for the different projects and will be discussed in the corresponding chapters.

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1.5.3 Raman scattering

When light interacts with a material, small portions will be scattered in all directions. Most of this scattered light will be of the same energy as the incoming beam. This elastic scattering is called the Rayleigh scattering. As represented in the Jablonski diagram (Fig. 1.2), some of the energy will be scattered at lower and higher energy, corresponding to Stokes and anti-Stokes Raman scattering, respectively. The frequency shift between the incident light and collected scattered light in this inelastic scattering corresponds to the vibrational frequency.

The Raman scattering process is related to the probed molecule’s polarizability. Analogous to the IR selection rule (Eq. 1.14), to obtain Raman scattering, the probed molecule must have a non-zero polarizability change through the vibration,

dα(1)

dQ

Q=0

6= 0 (1.19)

The small amount of scattered light means that a high intensity of the incoming light is necessary. In a standard Raman scattering set up, a microscope objective is often used to tightly focus the light onto or into the sample. This assures a high intensity to produce more scattered light, and can also be used to achieve some depth profiling by changing the position of the focus. Since the scattering occurs in all directions, the collection can be done with the same or different lenses. The two most commonly measured positions for the scattered light are back-scattered light or light scattered in the opposite direction of the incident beam, since these are usually the most intense. A high numerical aperture (NA) of the microscope objective will allow for the light to be focused on a smaller volume, as well as allowing for more scattered light to be collected.

Stokes and anti-Stokes measurements both have advantages and disadvantages. The difference in population of the ground and excited vibrational states leads to a significant difference in intensity between the two Raman measurements with the Stokes scattering being stronger. Therefore, the probed region of choice is usually within the Stokes shift.

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Fluorescence is another non directional process that shows up at lower energy than the probed beam. Fluorescence bands are wide and depending on the sample studied, they can be stronger than the Stokes scattering. When the fluorescence does not fully obscure the Raman signal , data processing can be used to extract the proper information. As the energy of the anti-Stokes is higher then the probed light, no fluorescence is interfering with the spectra. On the other hand, the signal is so low from the anti-Stokes that it is often undetectable, and requires strong Raman scattering materials in conjunction with a sensitive detector to be able to collect a proper spectrum.

The choice of wavelength can be important when dealing with fluorescent samples as the Raman scattering is inversely proportional to the fourth power of the wavelength. Decreasing the wavelength can give more Raman signal but organic materials often fluoresce strongly in the visible region. Thus, increasing the wavelength to the near-IR might be a better option in some cases. On the other hand, detectors are more sensitive in the visible region.

Figure 1.3: Example of a total internal reflection geometry for Raman spectroscopy.

Total internal reflection Raman (TIRR) can be useful in limiting the volume probed by use of an evanescent wave. As the evanescent wave penetration depth is correlated to the wavelength of the light (see Eq. 1.13), TIRR using a visible wavelength has a considerably

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smaller penetration depth than ATR-IR for the same incident angle and prism. This can prove useful for buried interfaces where the signal at the interface would get lost from overwhelming bulk signal in a standard bulk Raman scattering experiment. In a TIRR experiment, the incident light is focused tightly on a prism at an incident angle higher than the critical angle, and the scattered light is then collected at the bottom of the prism (see Fig. 1.3). This technique was first demonstrated over 40 years ago [58], but had limitations due to the high fluorescence emanating from prisms other than silica. Limitations of fused silica stems from its relatively low refractive index, which allows for TIR only with samples of refractive index lower than 1.45. The development of higher refractive index prisms containing fewer impurities has given this technique a boost in popularity [59–63].

Implementation Bulk Raman data were collected using a lab-built semi-confocal instrument. A 50 mW 532 nm diode laser (B&W Tek. BWN-532-50E) was attenuated with an OD 1 neutral density filter, and then incident on a dichroic mirror oriented at 45◦ transmitting wavelengths greater than 550 nm (Thorlabs DMLP550). This directed the 5 mW beam to a 10× infinity-corrected microscope objective with a working distance of 9.6 mm. The reflected Raman signal was collected by the same objective, transmitted by the dichroic mirror. The Rayleigh line was further rejected with a 532 ± 17 nm notch filter (Thorlabs NF533-17) before the light was focused onto the 200 µm entrance slit of a 750 mm spectrometer (Acton SP-2500i) fitted with a 1200 groove/mm grating blazed at 750 nm. Spectra were collected using a CCD camera (Princeton Instruments Pixis 400B) operating at −80◦C, averaging 5 spectra with an exposure time of 1 s.

For TIRR, the same 532 nm laser was brought to a 15 mm diameter with a beam expander then tightly focused with a 100 mm BK7 lens to the center of a 5 mm radius fused silica hemisphere. The laser size at the prism is approximately 80 µm wide. The laser was brought at an 80◦ incident angle. With this angle of incidence and the use of a fused silica prism (n = 1.49), this assures TIR geometry for samples with refractive index up to 1.43. The scattered Raman signal is then collected at the bottom of the prism with a

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50× infinity corrected objective and redirected to the same spectrometer for data collection. One long pass dichroic and one 532 nm notch filter (Thorlabs NF533-17) was used to get rid of the Rayleigh scattering within the collected signal.

1.5.4 Visible-Infrared Sum Frequency Generation

A central challenge associated with the characterization of molecules at interfaces is ac-quiring sufficient specificity so as to discriminate between nearby molecules in an adjacent bulk phase, as these generally outnumber interfacial species by orders of magnitude. This is where second-order nonlinear optical techniques can make a contribution [64–66]. The ith component of the second-order polarization is given by the 27-element nonlinear susceptibility tensor χ(2) and the j and k components of the applied fields according to the second term of Eq. 1.2. The surface specificity arises from the fact that, under the electric dipole approximation, all elements of χ(2) vanish in centrosymmetric materials [65, 67]. In achiral isotropic phases, the only place where the centrosymmetry is broken is at the interface. Of the various second-order nonlinear processes, visible-infrared sum-frequency generation has gained recent attention as a structural probe [68–71]. In this process, a fixed frequency visible laser (with wavelength typically 532 nm from a doubled YAG laser or 800 nm from a Ti:sapphire oscillator and a tunable or broadband IR laser (ωIR = 1000–4000 cm−1) are annihilated to produce a component of the polarization at the

sum-frequency (ωSFG = ωvis+ ωIR). The momentum-conserving direction determines the

reflected angle of the SFG,

nSFGωSFGsin(θSFG) = nvisωvissin(θvis) + nIRωIRsin(θIR). (1.20)

The intensity of the SFG signal can be correlated to the intensity of the IR beam IIR,

the intensity of the visible beam Ivis and the magnitude squared of nonlinear susceptibility

tensor χ(2)

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The susceptibility tensor can in term be divided into two different contributions, the resonant χ(2)_R and non–resonant χ(2)_NR.

χ(2)_R = χ(2)_R + χ(2)_NR (1.22)

As the IR laser frequency ωIR is tuned over vibrational resonances frequency ωQ,

an enhancement in χ(2)_R (ωIR) is observed that may be linked directly with structural

information. χ(2)(ωIR) = X Q AQ ωQ− ωIR− iΓQ . (1.23)

Where AQ and ΓQare the amplitude and linewidth of the vibrational mode Q respectively.

The component of the nonlinear polarization is given by the second term of Eq. 1.2, where the two electric fields E are from the visible and IR beam. It is interesting to note that even if the SFG doesn’t need the TIR geometry to be surface specific, the electric fields enhancement at the surface is often taken advantage of in SFG [72].

Picosecond Implementation. Visible 532 nm beam for the SFG experiment was created using the doubled output from a 10 Hz, 20 ps Nd:YAG laser (Ekspla PL2241). Mid infrared light was generated by difference frequency generation in AgGaS2, mixing

the 1064 nm YAG fundamental with the idler from parametric generation using some of the 532 nm beam in a Beta barium borate (BBO) crystal. This created tuneable IR in the range ωIR = 2800–3700 cm−1. Both beams, s or p-polarized visible and p-polarized IR,

were temporally and spatially overlaped at the sample. Incident light of the visible and IR were 70◦ and 65◦, respectively. The reflected SFG was separated from the reflected visible beam by two 532 nm notch filters (Thorlabs NF533-17), and was focused onto the slit of a 200 mm monochromator (SOL MS2001) equipped with a 2400 groove/mm grating and a photomultiplier tube (Hamamatsu R7899). Internal reflection geometry was achieved using a prism cut at 70◦ to minimize reflection loss.

Femtosecond Implementation. A Ti:Sapphire amplifier system (Spectra-Physics Hurricane-i) was employed to achieve 800 nm femtosecond beam with 1 kHz repetition

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Figure 1.4: SFG setup with prism cut at 70◦.

rate. This beam was then directed through an optical parametric amplifier (OPA) system to create signal and idler which in turn are focused through a AgGaS2 crystal to create

a broadband infrared signal (2700-3100 cm−1). The 800 nm from the OPA was passed through a bandpass filter (Thorlabs FB800-40) and then spectrally narrowed using an etalon nominally centered at 800 nm with a 1 nm FWHM (CVI Optic). The polarization of the 800 nm was controlled through the use of a half wave plate (Thorlabs WPH10M-808). For the IR beam, a periscope was used to permanently change the beam to p-polarized light to achieve ssp polarization. The IR and 800 nm were both focused to the sample using a 200 mm BaF2 and a 1000 mm BK7 focus lens, respectively. This leads to a beam size

of approximately 150 µm for both beams with an energy of about 3-4 µJ for both IR and 800 nm.

1.5.5 Bright field imaging

For complex, non homogeneous samples, such as bacteria, it is important to be able to visualize the sample probed by the different vibrational techniques. A bright field microscope was therefore constructed. The use of a home made microscope instead of a commercial one allows for easier integration with other techniques and more flexibility. The important components of a microscope include a light source, a collector lens, field and aperture diaphragm, a condenser lens, and a lens tube. The combination of these components in a K´’ohler illumination geometry allow for an even illumination of the sample without imaging the shape of the light source. In this research, a camera was used instead of a eye piece to be able to record the image.

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conjunction with 500 nm short pass filter (Thorlabs FES500) then roughly collimated with a 25.4 mm lens. These are followed by two irises used in placement of the field diaphragm and the aperture diaphragm. A 50 mm lens was used as a condenser. In this configuration, the light illuminated the top of the hemispherical prism. The light is collected through an infinity corrected 50× objective at the bottom of the prism and reflected from a long pass filter. A 75 mm lens tube was used to focus the collected light to a CMOS camera (Thorlabs DCC1645C). The probed region has a radius of approximately 100 µm.

1.6 Scope of thesis

SFG experiments have proven to be extremely valuable in isolating the response of interfacial molecules, especially when the same species are present in an adjacent bulk phase. This applies to water in the bulk aqueous phase, solutes in the aqueous phase, or substrate molecules (such as polymers) in the bulk substrate. In many cases, changes that occur in the bulk during surface adsorption are negligible. However, there are situations in which adsorption events occur as a result of significant changes in bulk solution conditions. In such cases, vibrational SFG spectroscopy continues to offer unparalleled selectivity and sensitivity to surface structure, but it cannot offer any insight into bulk effects. It is then useful to combine SFG with other methods, such as IR absorption or Raman scattering. In order to thoroughly analyze the results of those multiple techniques, a way to correlate the data is necessary. Generalized two-dimensional correlation spectroscopy (2DCOS), first proposed by Noda [73–77], has seen a widespread and growing application for studying changes due to a perturbation such as time, temperature, concentration, pH, or any other external variable of interest. In chapter 2, I will be showing how 2D correlation analysis can be applicable and useful to better understand SFG spectra along with other vibrational spectroscopy.

In chapter 3, I will discuss the competitive adsorption process of ethanol and water on fused silica through analysis of bulk and surface behavior. Ethanol and water are both

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simple molecules, but with complex and strong surface activity due to their hydrogen bonding capabilities. Because of its application in surface chemistry, industry and chromatography, ethanol-water mixture adsorption has been the focus of many studies [78, 79]. In this study, I will focus on the use of SFG, ATR-IR and Raman scattering in conjunction with 2D correlation analysis to study the interfacial properties with respect to the bulk properties.

In chapter 4, the analysis of the adhesion process of different pressure-sensitive adhesives (PSA) will be presented. In industrial pressure-sensitive adhesives, adhesion is typically characterized by evaluating shear, peel, and tack properties. These properties are strongly correlated to the chemical composition of the PSA. In this study, I will assess the importance of one of those components (acrylic acid) to adhesion by analyzing the interfacial region using ATR-IR and SFG.

In chapter 5, I will outlined the construction of an experimental set up capable of sequential measurement of SFG, TIRR and imaging. This will allow for better understanding of heterogeneous samples as well as samples that evolve with time. I will demonstrate this powerful combination of techniques on the study of nonlinear crystal formation. Amino acids tend to form highly ordered crystal with nonlinear properties due to their strong intermolecular hydrogen bonding and L-histidine has shown to be a promising material for producing nonlinear crystals for optical purposes [51]. I will use polarized SFG, polarized TIRR and cross-polarized bright field imaging to have a better insight into the crystal growth behaviour of L-histidine.

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Chapter 2 2D correlation analysis

It is natural that vibrational SFG spectroscopy should seek to take advantage of techniques that have been established in other forms of vibrational spectroscopy, such as polarization analysis for the quantification of bond orientation distributions [80–83], multidimensional techniques for observing coupling between modes [84, 85], isotopic labelling for the selective study of particular moieties [86, 87], and two-dimensional correlation analysis (2DCOS) [73–77]. Although generalized 2DCOS is applicable to a broad range of measurements extending beyond spectroscopy, it has been most developed and applied by the vibrational spectroscopy community. The basic idea—to investigate how the spectral response at one frequency ω1 is correlated to that at another frequency ω2 in response

to an external perturbation—has several advantages. First, it may effectively enhance the spectral resolution in cases where two or more overlapping peaks behave differently. The observation of cross peaks then provides the clue to these band components and their frequencies. Second, it may reveal trends that are not evident in the raw spectra. Third, when the complex cross correlation X(ω1, ω2) is expressed in terms of synchronous

Φ(ω1, ω2) and asychronous Ψ(ω1, ω2) correlation maps

X(ω1, ω2) = Φ(ω1, ω2) + iΨ(ω1, ω2), (2.1)

Noda’s rules [73] may be used to interpret the cross peaks in order to arrive at the causality relationship between events. Finally, the intensity of autopeaks in the synchronous map are a direct measure of the degree to which a particular feature in the spectrum is

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changing, irrespective of the extent to which that component is represented in the overall spectrum. These appealing aspects of 2DCOS applied to vibrational spectroscopy have found recent applications in the discrimination of water solvation environments [88, 89], polymer dynamics [90–92] protein structure determination [93–98], the quality control of pharmaceuticals [99, 100], and in the study of the 2DCOS signatures of cells [101, 102].

It would be appealing to extend the toolbox of techniques that have been applied to vibrational SFG to include 2DCOS. The resolution enhancement in particular would be most welcome, as most current SFG experiments are typically ≈ 5 cm−1 resolution for scanning instruments (picosecond pulses) and ≈ 10–15 cm−1 for broadband instruments (femtosecond pulses). Although recent developments increase the spectral resolution [103, 104], a fundamental obstacle has to do with the SFG lineshape as obtained in a homodyne experiment that measures |χ(2)_|2_(ω

IR). On account of the fact that the

contribution from participating vibrational modes are summed before the response is squared, interferences may lead to odd features in the raw spectra, particularly in cases where the peaks are overlapping or the spectral resolution is not sufficiently high. In the following section we will demonstrate that, compared to an IR absorption experiment, 2DCOS applied to homodyne SFG has advantages and disadvantages. We then consider a heterodyne experiment where the SFG field generated by the sample is interfered with a reference SFG (local oscillator) field, to provide information on the complex-valued χ(2)_(ω

IR) that may then be expressed as its imaginary component [16, 105–116]. We

will show that 2DCOS applied to Im[χ(2)(ωIR)] has clear advantages and overcomes all

of the obstacles encountered in |χ(2)|2 _{correlation analysis. In the final section, we will}

provide a demonstration of the application of 2DCOS-SFG spectroscopy to the study of leucine adsorption onto surfaces of varying hydrophobicity. Here we will consider the hydrophobicity of a model surface to be the external perturbation, and study the adsorbed leucine polarized IR absorption and Im[χ(2)_(ω

IR)] response as generated from molecular

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ω / cm−1 A0 / a.u. A0 / a.u. delay / period 2820 0.34 0.71 0.00 2840 0.00 −0.50 0.50 2860 −0.64 0.53 0.10 2880 0.34 −0.64 0.25 2900 −0.87 −0.34 0.00 2920 0.00 0.50 0.00 2940 0.87 0.34 0.00

Table 2.1: Parameters used to model the 7 peaks for the IR absorption, |χ(2)_|2_{, and Im[χ}(2)_]

spectra. The initial amplitude A0and final amplitude A0is listed, along with the fraction of

total time that the amplitude remains at A0before it increases or decreases towards A0.

2.1 Application of Correlation Analysis to Vibrational

Sum-Frequency Generation Spectra

2.1.1 Spectral Line Shapes

To illustrate the application of 2D correlation analysis, we have generated dynamic spectra for an IR absorption lineshape

IAbs(ωIR, t) ∝ 7 X j=1 A2 j(t)Γj (ωj − ωIR)2+ Γ2j (2.2)

where Aj(t) is the time-dependent amplitude, ωj is the frequency, and Γj is the width of

each resonant mode. Here we are considering a time evolution of the spectral shape in response to an arbitrary perturbation with Aj(t) = sin aj(t), where a range of aj were

generated such that Aj(t) varies from A0 at t = 0 to A0 at t = t0 according to the values of

these parameters as given in Table 2.1. For the SFG spectra, we concern ourselves with the second-order nonlinear susceptibility

χ(2)(ωIR, t) = 7 X j=1 Aj(t) ωj − ωIR− iΓj . (2.3)

A trigonometric function was used for the amplitude since, as will be discussed further below, we wish to consider positive and negative values of A(t). In a homodyne SFG experiment, the measured intensity is proportional to the squared magnitude of the second

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order susceptibility |χ(2)|2 |χ(2)_|2_(ω IR, t) = 7 X j=1 Aj(t) ωj− ωIR− iΓj 2 . (2.4)

In a heterodyne SFG experiment, one has access to the imaginary component of χ(2)_{. These}

spectra have a simpler lineshape

Im[χ(2)(ωIR, t)] = 7 X j=1 Aj(t)Γj (ωj− ωIR) + Γ2j (2.5)

as the dispersive component has been removed. Seven resonances were selected in order to best illustrate the differences between these two experimental lineshapes. In order to additionally compare these three different spectroscopic techniques in terms of their effect on the asynchronous component of the correlation, we have delayed the time evolution of some spectral features with respect to others. This delay is shown in the last column of Table 2.1 in terms of the fraction of the time period. For example, a delay of quarter period for the feature at 2880 cm−1 indicates that the evolution of this band does not start until a quarter of the measurement time has elapsed in comparison to a band with no delay, such as the one at 2820 cm−1. As an example, we illustrate the evolution of the peak amplitudes of the 2860 cm−1and 2880 cm−1features in Fig. 2.1. Here we can see that, after a short (10%) delay, the amplitude of the 2860 cm−1 band (red) starts off as negative for the Im[χ(2)_]

spectra (bold line), and then becomes more positive, eventually crossing zero and ending with a positive amplitude. The 2880 cm−1 band (blue) has a larger (25%) initial delay, during which time it maintains its positive amplitude in the Im[χ(2)]. This amplitude then decreases, crossing zero and ending up with a negative value (see Table 2.1). In the case of the IR absorption and homodyne |χ(2)|2 _{lineshapes, there are no negative peaks, and the}

corresponding evolution of the amplitudes in indicated with the thin red (2860 cm−1) and blue (2880 cm−1) lines.

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Figure 2.1: Evolution of the amplitudes A2 _{in the case of the IR and |χ}(2)_|2 _(narrow

lines), and A in the case of the Im[χ(2)_{] (thick lines) for the peaks at 2860 cm}−1 _(red)

and 2880 cm−1 (blue). The end of the delay before any changes in amplitude occur is indicated by vertical dashed lines.

2.1.2 High Spectral Resolution

The top row of Fig. 2.2 shows the spectra that are obtained using the parameters in Table 2.1 for a line width of Γ = 5 cm−1, for the case of IR absorption (Eq. 2.2) in the first column, the magnitude squared of the nonlinear susceptibility |χ(2)|2_{(Eq. 2.4) as would be obtained}

in a homodyne SFG experiment in the middle column, and the imaginary component of χ(2) _{(Eq. 2.5) in the last column. In all cases, the initial spectrum (t = 0) is drawn in bold.}

As our seven bands are spaced 20 cm−1 apart, this resolution is not extremely high, but is typical of what would be observed in an experiment, and is sufficiently high in order for us to make our case in our first comparison of the three techniques.

The middle row of Fig. 2.2 shows the synchronous correlation map, and the bottom row displays the asynchronous correlation. Even though the lineshape of the IR (squaring amplitudes, then summing over modes) and |χ(2)|2 _{(squared sum of amplitudes) are}

significantly different, in the case of this relatively narrow line width, the correlation maps are very similar for these two cases, and identical in the sign of all the cross peaks. This is expected as there is relatively little interference between the peaks. Closer inspection reveals that the detailed shape of the cross peaks display slight differences caused by the two different line shapes. In the case of the Im[χ(2)] synchronous map, special attention

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needs to be given to the sign of the cross peaks in accordance with the sign of the peak in the raw Im[χ(2)] spectrum. Similar to what is observed in the case of IR dichroic difference or VCD spectra, the Im[χ(2)] spectrum can have positive and negative peaks. The synchronous cross peak will be positive if both peaks are becoming more positive or more negative; if one peak is becoming more positive while the other is becoming more negative, the synchronous cross peak will be negative. For example, if two peaks are growing in intensity (their magnitudes are both increasing), but one is positive and one is negative, the cross peak will be negative. This situation does not occur in the case of the IR absorption experiment, as the magnitudes always translate into positive peaks.

All of the details of the autopeaks and cross peaks in the synchronous maps, and cross peaks in the asynchronous maps may be accounted for by the spectra that we have generated with the parameters in Table 2.1. For example, the largest change in the IR and |χ(2)_|2 _{spectra occurs for the peaks at 2900 cm}−1 _{and 2940 cm}−1_{, and this is seen}

in the large autopeaks in the corresponding synchronous spectra. As they both decrease in intensity at similar rates, they have strong synchronous cross peaks. As there is no time delay associated with the response of these peaks, we see no asychronous cross peaks. The strongest autopeaks for the Im[χ(2)] spectra are observed at 2860 cm−1 and 2880 cm−1. This is noteworthy, as the Im[χ(2)] spectra are generated from the same set of parameters as the |χ(2)_|2 _{spectra, illustrating the substantial difference between the results}

of the homodyne and heterodyne SFG experiments.

Continuing our discussion of the 2860 cm−1 and 2880 cm−1 peaks, we illustrate a unique aspect of the SFG response, especially as revealed in a heterodyne experiment that can measure Im[χ(2)]. These two peaks both change their sign during the perturbation— the 2860 cm−1 peak starts with a negative amplitude, passes through zero, and ends up with a positive amplitude; the 2880 cm−1 peak does the opposite, starting off positive and ending negative. (In the case of the IR absorption and |χ(2)_|2 _{experiment, this is seen as a}

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Figure 2.2: Top row: evoluation of the spectra for the IR absorption (left), |χ(2)|2 _(middle),

and Im[χ(2)] (right) lineshapes with Γ = 5 cm−1. The spectrum at t = 0 is shown with a bold line. Middle row: synchronous correlation maps, with positive contours drawn in red and negative contours in blue. Bottom row: asynchronous correlation maps. The traces on the edges of the correlation maps are the average (reference) spectra.

where a chemical functional group starts off with a tilt angle (measured with respect to the surface normal) of 0◦ < θ < 90◦ that then increases to θ ≈ 90◦ with the funtional group nearly in the plane of the surface, followed by a continued transition where the group flips its orientation, now in the range 90◦ < θ < 180◦ [117, 118]. These two peaks change with similar rates so they produce strong synchronous cross peaks. As we have described above, one peak is becoming more negative as the other is becoming more positive, so we observe the cross peak to be negative. As seen in Table 2.1, the 2880 cm−1 response is delayed with respect to the time evolution of the 2860 cm−1 peak, and this therefore shows

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Figure 2.3: Top row: evoluation of the spectra for the IR absorption (left), |χ(2)|2 _(middle),

and Im[χ(2)] (right) lineshapes with Γ = 10 cm−1. The spectrum at t = 0 is shown with a bold line. Middle row: synchronous correlation maps, with positive contours drawn in red and negative contours in blue. Bottom row: asynchronous correlation maps. The traces on the edges of the correlation maps are the average (reference) spectra.

up as a cross peak in the asynchronous spectrum. Even though special care is required in the interpretation of the signs of the synchronous cross peaks, note that Noda’s rules for assigning the causality from the asynchronous peaks still applies, as they are defined in reference to the sign of the synchronous peaks. The asychronous peak at (2880, 2860) is negative, and derived from a negative synchronous peak at the same location, indicating that the change in the response at 2860 cm−1occurs before that at 2880 cm−1. This feature also illustrates the utility of the Im[χ(2)_{] spectra, as no strong (2880, 2860) cross peak is}

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Figure 2.4: (a) x-polarized and (b) z-polarized IR absorption spectra of Leucine adsorbed to surfaces of varying hydrophobicity. The Im[χ(2)_{] spectra are shown for the (c) xxz, (d)}

xzx and (e) zzz elements. The legend at the top of the figure indicates the colours used to plot the spectra generated for the specific hydrophobic surface, labelled according to the water contact angles.

evolution of the amplitudes have roughly the same magnitude, leading to a net cancellation of the synchronous correlation based on the squares.

2.1.3 Lower Spectral Resolution

Using the same parameters (Table 2.1) as we have described for the narrow peaks above, we repeat our simulation, but this time with a width of Γ = 10 cm−1 for each of the 7

Distinguishing and correlating surface and bulk behaviour using linear and nonlinear vibrational spectroscopy

Contents

List of Tables

List of Figures

List of Symbols and Definitions

Chapter 1

Introduction

1.1

Motivation

1.2

Surface structure of small molecules

1.3

Adhesion

1.4

Organic nonlinear crystals at the solid-liquid interface

1.5

Useful probes of interfacial properties

1.5.1

Electric fields at surfaces

1.5.2

Infrared absorption spectroscopy

1.5.3

Raman scattering

1.5.4

Visible-Infrared Sum Frequency Generation

1.5.5

Bright field imaging

1.6

Scope of thesis

Chapter 2

2D correlation analysis

2.1

Application of Correlation Analysis to Vibrational

Sum-Frequency Generation Spectra

2.1.1

Spectral Line Shapes

2.1.2

High Spectral Resolution

2.1.3

Lower Spectral Resolution