16030
J. Phys. Chem. B 2004, 108, 16030-16039
Interference Effects in Sum Frequency Vibrational Spectra of Thin Polymer Films: An Experimental and Modeling Investigation Sarah J. McGall and Paul B. Davies* Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
David J. Neivandt Department of Chemical and Biological Engineering, UniVersity of Maine, Orono, Maine 04469 ReceiVed: April 23, 2004; In Final Form: August 2, 2004
Sum frequency (SF) vibrational spectra in the C-H stretching region of polydimethyl siloxane (PDMS) and of the comb copolymer cetyl dimethicone copolyol (CDC), consisting of a PDMS backbone with grafted poly(ethylene oxide) and cetyl side chains, have been recorded in air after deposition onto a gold-coated substrate. The polymers were deposited over a range of thicknesses (up to 70 nm) by spin coating from chloroform solutions of different polymer concentrations. Film thicknesses were determined by ellipsometry. The methyl symmetric (r+) stretching modes appeared as peaks in the SF spectra of both polymers at all film thicknesses investigated, indicating that the constituent methyl groups have a net orientation toward the air. However, the phase of the methyl anti-symmetric (r-) stretching mode displayed a dependence upon film thickness, changing from a peak (positive phase) to a dip (negative phase) as film thickness was increased. The phase behavior of the r- methyl resonance has been successfully modeled by the extension of a previously developed interference theory to include multiple reflections and a resonant contribution from the polymer/ gold interface.
Introduction The surface characteristics of polymeric films, such as their hydrophilicity, chemical functionality, and molecular level interfacial order, are of fundamental importance in defining film properties for applications in a diverse array of industrial and biomedical processes.1 Recently, the nonlinear optical technique of sum frequency vibrational spectroscopy (SFS), an interfacially specific probe of molecular orientation and conformational order, has emerged as an important tool in the study of polymeric surfaces.1,2 SFS was first applied to synthetic homopolymers such as polyethylene, polypropylene,3 poly(methyl methacrylate),4 poly(vinyl alcohol),5 and polyimide6 approximately eight years ago. Considerable work has since been performed in the area of synthetic biocompatible polymers, with a focus on polyurethanes. Zhang et al. studied the surface properties of a polyurethane modified with grafted polydimethyl siloxane (PDMS) end groups.7 The PDMS segments were found to migrate to the surface when the polymer film was exposed to air and to reorient into the bulk when the film was immersed in water, behavior which is consistent with the hydrophobic nature of the PDMS end groups. The same group reported SFS studies of the surface composition of blends of the grafted polymer with polyphenol, an additive typically used to enhance bulk properties such as the glass transition temperature, thereby making the blend more attractive for biomedical applications.8 Recently, Clarke et al. investigated the effect on surface composition and structure of plasticizers added to polyurethanes to improve bulk properties.9 Evidence was found for migration of plasticizer to the polymer surface when the film was exposed * To whom correspondence should be addressed. Tel: +44 1223 336460. Fax: +44 1223 336362. E-mail:
[email protected].
to both air and water, a finding with significant ramifications for biocompatibility. In the past two years the field has expanded to studies of interfacial properties of biological polymers, with a particular emphasis on protein adsorption. Wang et al. have studied bovine serum albumin (BSA) adsorption in a number of systems, including at aqueous/air, aqueous/silica, and aqueous/polystyrene interfaces.10-12 The relative intensities and phases of the C-H resonances of BSA displayed a marked dependence upon the interface employed, indicating significant surface specific changes in the adsorbed conformation of the protein. In a subsequent publication the same group performed a complementary study of the effect of protein adsorption on the conformational order of a polymeric substrate.13 Kim et al. have probed the effect of pH on the conformation of hen egg white lysozyme and its associated water at both the quartz/water and air/water interfaces.14 Somorjai and co-workers have studied the interaction of fibrinogen with various synthetic polymeric surfaces15 and the molecular packing of lysozyme, fibrinogen, and BSA on silica and polystyrene.16 In a significant development, Watry et al. recently demonstrated the applicability of SFS for determining interfacial orientation and conformational information of nucleic acid based polymers at an oil/water interface.17 Despite the rapid growth in SF applications to a diverse range of polymeric systems, few studies have been reported on comb copolymers, which are of both industrial and biomedical interest. Oh-e et al.18 investigated the surface orientation and conformation of alkyl side chains of polyimides, discussing the effects of side chain length and mechanical rubbing of the surface on SF spectra at the polymer/air interface. Gautam and Dhinojwala19 used SFS to determine the orientation and degree of
10.1021/jp048218l CCC: $27.50 © 2004 American Chemical Society Published on Web 09/18/2004
Interference Effects in SF Vibrational Spectra
Figure 1. Molecular structures of CDC and PDMS.
order of the octadecyl side chains of poly(vinyl octadecyl carbamate-co-vinyl acetate) at the polymer/air interface. In both studies the spectra arose from a single type of side chain and there was no evidence of SF activity attributable to the polymer backbone itself. Recently we recorded and interpreted the SF spectrum of a comb copolymer cetyl dimethicone copolyol (CDC, Figure 1), in the C-H stretching region in air after solvent casting of a film of the polymer onto a gold substrate.20 Resonances attributable to the cetyl side chains and the polydimethyl siloxane (PDMS) backbone of the polymer were observed, while no evidence of resonances attributable to the PEO containing side chains was obtained. CDC resonant assignment was achieved through comparison of its SF, FTIR, and Raman spectra with those of the PDMS polymer backbone and various structural analogues with and without each type of side chain. All resonances in the SF spectrum of CDC occurred with a positive phase (as spectral peaks). Such an observation is consistent with the capacity of SF spectroscopy to provide orientational information of interfacial species on substrates with strong nonresonant susceptibility, such as gold,21 and indicates an orientation of backbone methyl groups and cetyl side chains of the polymer into air. Similarly the SF spectrum of PDMS contained a methyl symmetric (r+) stretching mode with a positive phase (spectral peak); however, the methyl antisymmetric (r-) resonance was observed in the spectrum as a dip (negative phase). The opposite phase of the r- resonance to that of the r+ in the same spectrum is highly suggestive of interference related phenomena. Interference effects have previously been reported in sum frequency spectra by Lambert et al.22 and Briggman et al.23 The latter group studied thin polystyrene films on oxidized silicon substrates.23 The relative phases of the styrene aromatic C-H resonances were determined as a function of polystyrene layer thickness and compared to theoretical simulations for the buried (polystyrene/SiO2) and free (polystyrene/air) interfaces. The similarity of the experimental data and the theoretical simulations for the free interface as a function of polystyrene thickness indicated that the dominant source of the resonant SF contribution was the polystyrene/air interface. Recording spectra under different infrared, visible, and sum frequency beam polarization combinations allowed the polar orientation of the styrene groups at the polystyrene/air interface to be determined. In a subsequent publication by the same group,24 interference effects in sum frequency spectra of a two layer system of polystyrene deposited onto hydrogen silsesquioxane spin-on glass (SOG) on gold were
J. Phys. Chem. B, Vol. 108, No. 41, 2004 16031 investigated both experimentally and theoretically. Selecting specific SOG film thicknesses resulted in the spectra being dominated by either the polystyrene/air or polystyrene/SOG interface, thereby allowing unambiguous orientational analyses to be performed that were specific to each interface. Lambert et al. characterized interference effects in SF spectra of a composite substrate consisting of a silane monolayer on mica backed with gold.22 Changes in the measured phase of the methyl symmetric, r+, and anti-symmetric, r-, stretching modes of the silane monolayer were observed as a function of mica thickness. The periodicity of the interference effect of the r+ resonance was observed to be 3.4 (0.2 µm;25 however, the relationship between the mica thickness and the phase of the r- resonance was less clear. Theoretical simulations revealed that the r- interference effect contained a dominant nanometer scale periodicity (of 162 nm) coupled with a weaker micron scale effect (3.01 µm periodicity), a finding broadly consistent with the experimental observations of a micron scale periodicity overlaid with a much shorter but unquantifiable periodicity. The theoretical simulations revealed that the nanometer scale effect was related to interference of an SF beam generated at the mica/ air interface emitted into air and an SF beam generated at the mica/gold interface emitted into mica and refracted into air. The micron scale periodicity, however, was shown to originate from interference of an SF beam generated at the mica/air interface emitted into mica, reflected off the mica/gold interface, and refracted into air, with an SF beam generated at the mica/gold interface and refracted into air. The predicted nanometer scale interference effect of Lambert et al. could not be validated experimentally employing the composite mica substrate due to practical limitations concerning the minimum thickness of mica that could be cleaved. However, such effects have subsequently been investigated by Holman et al. employing Langmuir-Blodgett multilayer fatty acid films on gold substrates.26,27 SF spectra recorded as a function of multilayer thicknesses allowed the periodicity of the nanometer scale r- interference effect to be characterized. Highly satisfactory agreement with the predictions of Lambert et al. was found. Furthermore, the dominant resonant contribution to the SF signal was found to arise from the uppermost fatty acid layer, with a weaker contribution derived from the hydrocarbon/gold interface. Polymer films provide a more challenging, applied experimental system for comparison to the modeling work of Lambert et al. since the positions of SF generation, tilt angles of resonanting groups and refractive indices are less well known. Furthermore, development and application of the theory to polymeric systems offers the potential to elucidate the origin of the dual phase of the methyl resonances observed previously in SF spectra of PDMS films.20 In the present work, SF spectra of spin-coated CDC and PDMS films on gold substrates have been recorded as a function of film thickness, the latter determined by ellipsometry. Spin coating was employed in preference to solvent casting to permit the polymer film thickness to be systematically varied, while also providing a more controlled surface morphology for SF and ellipsometric analysis. In parallel, theoretical work has been performed to develop and extend the model of Lambert et al. into a form more applicable to thin polymer films. Experimental Section The Cambridge nanosecond sum frequency (SF) spectrometer has been described in detail elsewhere.28,29 Briefly, a fixed frequency visible laser pulse (λ ) 532 nm) and a variable
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Figure 2. Ray diagram to illustrate the generation of (a) the SF1 beam, (b) the SF2 beam and (c) the SF3 beam, in a multi-reflection model (for simplicity only one reflection of each beam within the polymer film is illustrated).
frequency mid-IR pulse are overlapped both spatially and temporally on a surface. The high energy electric field established induces a nonlinear response in interfacial species, resulting in the emission of a pulse of light at the sum of the frequencies of the two incident beams (≈ 461 nm for spectra in the 2800-3000 cm-1 region). The SF emission is detected by a photomultiplier tube, the output of which is recorded by a digital oscilloscope interfaced to a computer. Recording the SF intensity as a function of the IR frequency produces a vibrational spectrum of the interfacial species. Spectral modeling of the experimental data is performed via normalization by the nonresonant background signal of the gold substrate and the
fitting of Lorentzian resonance line profiles using a LevenbergMarquardt least-squares fitting routine.28 Polymer films were spin coated onto approximately 150 nm thick gold layers thermally evaporated onto silicon wafer supports. A thin layer of chromium (≈10 nm thick) was evaporated onto the silicon wafer substrate prior to the gold coating to improve adhesion. The substrates were stored in methanol and subjected to a UV-ozone cleaning procedure prior to polymer deposition.30 Polymer samples were spin coated from a range of solution concentrations (∼0.01% w/w to ∼1% w/w) in chloroform (HPLC grade, Aldrich) using a drop volume of 10 µL. The samples were spun for approximately 30 s at 4000
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J. Phys. Chem. B, Vol. 108, No. 41, 2004 16033
rpm immediately after the chloroform solution was deposited and stored in a desiccator prior to analysis. Polymer film thicknesses were determined using an ELX02C DRE single wavelength ellipsometer operating at a wavelength of 632.8 nm and an angle of incidence of 70°. The reported values of the thickness are an average of six measurements recorded across each substrate. Modeling of the ellipsometric data was performed assuming a two-layer system with a polymer layer refractive index of 1.43 (as reported in ref 31) and a gold substrate refractive index calculated from reference data recorded from a bare gold substrate prior to polymer deposition. The polymer layer refractive index may vary from that quoted above for the specific polymer chain length and range of film thicknesses used here. In addition, the refractive index of CDC is expected to differ from that of PDMS due to the additional cetyl and poly(ethylene oxide) side chains of the polymer. Consequently, the value employed for the polymer refractive index was varied between 1.40 and 1.45, resulting in uncertainties in calculated film thicknesses of approximately 10%. This uncertainty is represented as error bars on the data of Figures 4-7. The CDC (MW ∼ 12400) and PDMS (MW ∼ 7400) polymers were supplied by Procter & Gamble Technical Centers Limited, UK. The molecular structures of CDC and PDMS are given in Figure 1. CDC was custom synthesized by randomly grafting a known average number of side chains onto the PDMS backbone. The polymers were used as received. The sum frequency intensity for a single resonance, ISF, is given by (2) (2) ISF ∝ ||χR,ijk |eiδ + |χNR,ikj |ei|2 (2) (2) (2) (2) ∝ ||χR,ijk |eiδ + |χNR,ijk |ei|‚||χR,ijk |e-iδ + |χNR,ijk |e-i| (2) 2 (2) (2) (2) ∝ |χR,ijk | + |χNR,ijk |2 + 2|χR,ijk ||χNR,ijk |cos[ - δ]
(1a)
where |χNR| represents the magnitude and the phase of the nonresonant background signal to which the spectrum was normalized, and |χR| is the magnitude and δ the phase of the resonant signal. Spectral simulations as a function of polymer layer thickness were carried out in Mathematica at 1 nm thickness increments from 0 to 100 nm. The simulated and experimental spectra were fitted with Lorenzian line profiles following the procedure of Lambert et al. in ref 25. That is, the sum frequency intensity can be described in terms of the Lorenzian parameters H (height of the curve on resonance) and W (its half width at half-maximum), as given in eq 1b for a single SF resonance:
HW2 2 + |χ(2) ISF ∝ NR| + (ωv - ωIR)2 + W2 2
x
[
Theory Initial Model. Simulations of the sum frequency (SF) response of a polymer film on a gold substrate were initiated employing the model developed by Lambert et al. for a silane monolayer on a thin mica sheet backed with gold.22 In the present study the polymer film replaces the mica sheet of the model composite substrate while the silane monolayer at the mica/air interface is replaced with the segment of the polymer film in contact with air. Lambert et al. considered the detected SF signal to be a superposition, at a point of coherent addition, of three sources of SF light: light generated from the silane monolayer at the mica/air interface and emitted into air, SF1, light generated at this interface emitted into the mica film and reflected from the gold substrate to refract through the mica/air interface into air, SF2, and light generated at the mica/gold interface and refracting through the mica/air interface into air, SF3. Both SF1 and SF2 arise from resonant sum frequency generation from the silane monolayer, while SF3 is nonresonant light from the gold substrate. A schematic ray diagram is shown in Figure 1 of ref 22. The mathematical expressions for the electric fields, polarizations, and linear32 and nonlinear Fresnel factors of the three SF beams are given by eqs 1-10 in ref 22. Model Including Multiple Reflections. A second generation model was developed in the present work to account for multiple reflections of the visible, IR, and SF beams within the polymer film, as illustrated in Figure 2. The initial model of Lambert et al. considered the electric field of the infrared or visible beam at the polymer/air interface to consist of the sum of the relevant incident and reflected beams, labeled EI and ER respectively in eqs 2 and 3. A linear Fresnel factor, rp, for p polarized incident light, was incorporated to account for intensity losses in the reflected beam (ER). θI represents the appropriate visible or infrared incident beam angle (relative to the surface normal):
Ez ) (EIz + ERz + EM ˆ z )z ) (EIz + rpEIz + mEIz)zˆ ) EIp sinθI (1 + rp + m)zˆ
(2)
ˆ Ex ) (EIx + ERx + EM x )x ) (EIx + rpEIx + mEIx)xˆ
(
)]
HW -W |χ(2) |cos - arctan 2 2 NR (ω (ωv - ωIR) + W v - ωIR) (1b) 2
incorporated into the optimized value for generated by the least-squares fitting routine. This modified value is termed the “interference phase” in ref 25 and has been extracted here for the r+ and r- resonances separately to quantify the observed changes in resonance line-shapes as a function of film thickness.
The values of the variables H, W, ωv, |χNR|2, and are then varied in a least-squares fitting routine in order to minimize the error between the profile produced by eq 1b and the experimental or simulated data. In this way a value for the nonresonant phase can be extracted from experimental data. The additional phase offset existing between the resonant and nonresonant SF signals as a result of thin film interference is
) EIp cosθI(1 - rp - m)xˆ
(3)
Equations 2 and 3 incorporate additional terms introduced in the present work to account for multiple reflections of the IR and visible beams. Specifically, the term EM is introduced for incident infrared and visible beams that are initially transmitted through the polymer/air interface and reflected one or more times within the polymer layer at the polymer/gold and polymer/air interfaces. The factor m allows for the summation of E fields generated by multiple reflections following the general principles first introduced by G. B. Airy in 1833 to describe thin film interference effects in layered media.33 As such, m takes into account reflection and transmission losses
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though linear Fresnel factors and an additional polymer thickness dependent phase term R1
m ) t12t21r23eiR1 + t12t21r223r21ei2R1 + t12t21r323 r221ei3R1 + .... )
account for multiple reflections of the incident visible and IR beams.
Ep,SF2 ∝ |Ex,SF2| + |Ez,SF2| (2) (2) | + |Lt,zPz,SF2 | ∝ |Lt,xPx,SF2
t12t21r23eiR1
(4)
1 - r21r23eiR1
mod mod ∝ |(mSF2Lt,xχ(2) xxz Kx,vis Kz,IR + mod mod i(∆vis1+∆IR1) |+ mSF2Lt,xχ(2) xzx Kz,vis Kx,IR )e
where R1 is given by
R1 )
(
)
4πd n2 - n1 tan θ23 sin θ12 λ cosθ23
mod mod |(mSF2Lt,zχ(2) zzz Kz,vis Kz,IR +
mSF2 ) r23t21eiR2 + r223r21t21ei2R2 + r323 r221t21ei3R2 + ...
The parameter R1 includes the polymer layer thickness, d, the refractive index of the polymer layer, n2, the refractive index of the ambient medium (air), n1, the incident angle of the beam at the polymer/air interface, θ12, the incident angle of the beam at the polymer/air interface from within the polymer film, θ23, and the wavelength of the visible or IR beam, λ (or SF beam when applied to SF2 and SF3 later). R1 takes into account the phase of the IR or visible beam relative to the planes of reference defined by Lambert et al. and indicated in Figure 1 of ref 22 and Figure 2 in this article. A rigorous derivation of R1 is provided in the Supporting Information. It follows that the K factors which relate the incident visible and infrared beams to the surface-bound E fields are modified from those of the initial model to eqs 6-9. mod ) cosθI,vis(1 - rp - m) Kx,vis
(6)
mod ) sinθI,vis(1 + rp + m) Kz,vis
(7)
mod ) -cosθI,IR(1 - rp + m) Kx,IR
(8)
mod ) sinθI,IR(1 + rp + m) Kz,IR
(9)
The sum frequency beam SF1 (Figure 2a) is then described by
Ep,SF1 ∝ |Ex,SF1| + |Ez,SF1| (2) (2) | + |LzPz,SF1 | ∝ |LxPx,SF1 mod mod ∝ |(Lr,xχ(2) xxz Kx,vis Kz,IR + mod mod i(∆vis1+∆IR1) Kz,vis Kx,IR )e |+ (2) mod mod |(Lr,zχzzz Kz,vis Kz,IR + mod mod i(∆vis1+∆IR1) | Lr,zχ(2) zxx Kx,vis Kx,IR )e
mod mod i(∆vis1+∆IR1) | (11) mSF2Lt,zχ(2) zxx Kx,vis Kx,IR )e
(5)
)
r23t21eiR2 1 - r23r21eiR2 R2 )
4πn2d cosθ23λ
(12)
Finally an expression for the nonresonant sum frequency beam generated at the polymer/gold interface, SF3, must be derived (to include the effects of multiple reflections of the visible, IR, and SF beams within the polymer film, Figure 2c). Lambert et al. used a simple description of nonresonant SF generation at this interface involving arbitrary magnitude (ENR) and phase () terms. However, to include the multiple reflection factors relevant in the present work, a more complex description is necessary. Specifically, via the assumption that nonresonant SF generation is dominated by surface plasmon excitation of gold, (in accordance with Liebsch34 and Mendoza35) it is possible to consider nonresonant generation in a manner analogous to resonant generation involving χzzz (visible, IR, and SF beams polarized along the surface normal). The equation developed to account for multiple reflections of the SF3 beam (equation 13) consequently includes, in addition to the relevant nonlinear Fresnel factor (Lr,z), Fresnel factors for the IR and visible beams (Kgold, eqs 14 and 15). The K factors account for refraction through the polymer/air interface and multiple reflections within the polymer film via an mgold term (equation 16). Multiple reflections of the resultant SF beams are incorporated into eq 13 through an mSF3 term, given in eq 17, that implicitly includes a ∆SF3 phase term. (2) | Ep,SF3 ∝ |Lr,zPz,SF3
Lr,xχ(2) xzx
(10)
The ∆ terms in eq 10 are equivalent to those defined by Lambert et al. in their model (see Appendix A, ref 28). Multiple reflections must also be considered for the SF2 beam (Figure 2b), which is emitted into the polymer film and may undergo multiple reflections within the polymer before being transmitted into air. An additional factor, mSF2, is therefore included in the description of SF2 generation (equations 11 and 12) in a manner analogous to that outlined above for the incident beams that generate SF1. It is noted that the mSF2 term implicitly includes a phase factor to account for the offset of the point of generation of SF2 from the point of coherent addition. Equation 11 also includes the modified K factors described above to
gold gold ∝ |mSF3Lr,zENRei(+∆vis3+∆IR3)Kz,vis Kz,IR |
(13)
gold ) sinθI,vismgold (1 + rp) Kz,vis
(14)
gold ) sinθI,IRmgold (1 + rp) Kz,IR
(15)
mgold )
mSF3 )
t21 1 - r23r21eiR1 t21ei∆SF3 1 - r23r21eiR2
(16)
(17)
Substitution of the multiple reflection expressions for SF1, SF2, and SF3 (equations 10, 11, and 13) into eq 1 of ref 22 gives an expression for the total intensity of detected SF light.
Interference Effects in SF Vibrational Spectra
J. Phys. Chem. B, Vol. 108, No. 41, 2004 16035
Figure 3. Sum frequency vibrational spectra of spin-coated (a) CDC and (b) PDMS of different film thicknesses on a gold substrate. Spectra were recorded with p polarized visible, IR, and SF beams and are displaced vertically for clarity.
Multiple Reflections and a Resonant Contribution from the Polymer/Gold Interface. Several workers, including Briggman et al.23 and Holman et al.,27 have shown in related experimental systems that although the dominant resonant contribution arises from the polymer/air interface, a resonant contribution from the polymer/gold interface may be expected. Consequently, the model incorporating multiple reflections has been extended to include an additional resonant sum frequency contribution from the polymer/gold interface, SF4. The modified K factors and comparable multiple reflection terms to those developed for SF3 (eqs 14-17) were employed for SF4. Additional second order susceptibility terms relevant for the symmetric and anti-symmetric methyl resonances on a gold surface are also included. It should be noted that only χzzz and χxxz are included because on a gold surface the z component of the IR field dominates.28 The resulting expression for Ep,SF4 is given by eq 18:
Ep,SF4 ∝ |Ex,SF4| + |Ez,SF4| (2) (2) ∝ |Lr,xPx,SF4 | + |Lr,zPz,SF4 | gold gold ∝ |(mSF3Lr,xχ(2) xxz Kx,vis Kz,IR + gold gold i(∆vis3+∆IR3) mSF3Lr,zχ(2) | (18) zzz Kz,vis Kz,IR )e
The total intensity of the generated SF light may consequently be expressed as
Ip,SF ) |Ex,SF1 + Ex,SF2 + Ex,SF3 + Ex,SF4|2 + |Ez,SF1 + Ez,SF2 + Ez,SF3 + Ez,SF4|2 (19) Results Sum frequency spectra of PDMS and CDC solvent cast onto gold are given in ref 20. The SF spectrum of PDMS (Figure 4a in ref 20) contains two resonances that have been assigned to the r+ symmetric (2908 cm-1) and r- anti-symmetric (2963 cm-1) stretching modes of the methyl moieties of the polymer.7
The SF spectrum of CDC (Figure 4e in ref 20) contains methyl and methylene resonances arising from both the PDMS backbone and the cetyl side chains of the polymer.20 The resonances of specific relevance to the present work are the r+ mode of the PDMS backbone at 2908 cm-1 and the resonance at 2968 cm-1, which has been assigned to a combination of the r- modes of the backbone and the cetyl side chains of the polymer. To investigate interference effects arising from different quantifiable polymer layer thicknesses, a method of polymer deposition that is more controlled than solvent casting was required. Consequently, SF spectra of CDC and PDMS films spin coated onto gold substrates were recorded. The film thickness of the samples was governed by the polymer concentration of the chloroform solution employed for coating and was determined by ellipsometry. The spectra and their corresponding film thicknesses are presented in Figures 3a and 3b (CDC and PDMS, respectively). Inspection of the SF spectra of Figure 3 reveals that the 2908 cm-1 r+ resonance of the methyl groups in both PDMS and CDC remains a spectral peak (positive phase) over the thickness range investigated. Conversely, for both PDMS and CDC the r- resonance appears as a spectral peak (positive phase) at small polymer film thicknesses, changes to a differential shape as the film thickness increases, and finally becomes a spectral dip (negative phase) for the thickest samples investigated. The r- interference phase, obtained by modeling the spectra in Figures 3a and 3b as discussed earlier, is plotted as a function of film thickness for both polymers in Figure 4. At CDC film thicknesses approaching zero, the r- interference phase tends toward a limiting value of 90°, consistent with that typically observed for monolayer coverage of an alkyl chain terminating in methyl groups on a gold substrate, oriented into air.21 As the CDC film thickness increases, a monotonic rise in the phase of the r- resonance occurs, reaching a maximum value of 180° at a film thickness of approximately 11 nm. An abrupt phase change then occurs at greater film thicknesses, indeed a near complete phase reversal from 180° to -150° takes place when the CDC film thickness
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Figure 4. Experimentally determined r- interference phases for CDC and PDMS, as a function of polymer film thickness. b PDMS, 4 CDC.
is increased from 11 to 16 nm. Raising the film thickness further from 16 to 63 nm results in a monotonic increase in the phase of the r- CDC resonance from -150° to -100°. The PDMS r- interference phase displays a polymer film thickness dependence comparable to that of CDC, with the exception that the magnitude of the measured negative phase values for film thicknesses greater than 11 nm are on average approximately 20° less than those determined for CDC at comparable thicknesses. In addition, the phase reversal from positive to negative phase occurs at a slightly lower film thickness (between 7 and 12 nm). The error bars in Figure 4 represent the uncertainty in thickness and phase of each data point. As discussed earlier, the dominant uncertainty in determining the polymer film thickness by ellipsometry was found to be the uncertainty in the value of the polymer refractive index. Consequently, error bars on each data point indicate the range of thickness values obtained as a result of altering the polymer layer refractive indexes from 1.40 to 1.45. The error in the interference phase has been estimated to be (10 degrees and arises from the subjective nature of choosing the spectral baseline when modeling. Methyl r+ and r- interference phases, predicted from spectral simulations based on the model of Lambert et al. are plotted as a function of polymer film thickness in Figures 5a and 5b respectively, overlaid on the experimentally derived data for PDMS (5a,b) and CDC (5b) of Figure 4. The refractive index of the polymer layer was set to 1.42 for the visible and SF beams36 and 1.40 for the average IR wavelength37 as reported in the literature. The tilt angle of the methyl groups of PDMS to the surface normal at the polymer/air interface is quantitatively undetermined in the literature, although Zhang et al. state from SF measurements that the methyl groups lie “more or less along the surface normal”.7 The tilt angle of the methyl groups of CDC is also undetermined. Consequently, these values were initially set to 34.5°, corresponding to the tilt angle of a terminal methyl group on a hydrocarbon chain with the chain axis oriented parallel to the surface normal. Finally, the phase of the nonresonant SF signal arising from the gold surface was optimized to produce an r+ interference phase tending toward a value of 90° as the polymer layer thickness approached zero. The simulated r+ interference phase of approximately +90° shows only a weak dependence upon polymer film thickness over the range investigated (solid line, Figure 5a). This result is in good agreement with the experimental r+ phases of PDMS. The corresponding data for CDC are not shown since the 2908 cm-1 resonance of CDC is convoluted with nearby resonances at 2933 and 2877 cm-1, therefore its phase cannot be accurately determined. Nonetheless, it can be deduced by examining the spectra of Figure 3a that the CDC r+ interference phase does
Figure 5. (a) Simulations of the methyl r+ interference phase as a function of polymer film thickness, based on the model of Lambert et al. Solid line (-), methyl group tilt angle of 34.5°; dashed line (- - -), methyl group tilt angle optimized to 50° for PDMS r- data; dotted line (‚‚‚), methyl group tilt angle optimized to 53° for CDC r- data. Experimental data for the r+ interference phase of PDMS is overlaid (9). (b) Simulations of the methyl r- interference phase as a function of polymer film thickness, based on the model of Lambert et al. Solid line (-), methyl group tilt angle of 34.5°; dashed line (- - -), methyl group tilt angle optimized to 50° for PDMS r- data; dotted line (‚‚‚), methyl group tilt angle optimized to 53° for CDC r- data. Experimental data for the r- interference phases of CDC (4) and PDMS (b) are overlaid.
not alter significantly with increasing layer thickness, in broad agreement with the spectral simulation. The simulated rinterference phase (solid line, Figure 5b), is negative over the entire thickness range investigated and decreases significantly in magnitude with increasing film thickness. At polymer film thicknesses greater than approximately 16 nm, the simulated r- phase correlates well with the experimental CDC and PDMS data. However, at film thicknesses less than 16 nm the simulated r- phase remains negative, in contrast to the phase inversion to positive values observed in the experimental spectra. In addition to the simulations performed at methyl tilt angles of 34.5°, Figures 5a and 5b display simulations in which methyl tilt angles have been varied in order to more closely correlate the position of phase inversion in the simulation to that in the PDMS and CDC experimental data for the r- resonance. Specifically, optimized tilt angles of 50° and 53° are depicted for PDMS (broken line) and CDC (dotted line), respectively. Positive values of the r- phase below approximately 16 nm film thickness are predicted by both simulations, thereby significantly improving the correlation with the experimental r- data. However the large tilt angles have a detrimental effect on the correlation between the r+ simulation and the experimental results for PDMS resonant phases at larger film thicknesses, which are lower than observed experimentally. More significantly, in a publication on SF interference effects in LangmuirBlodgett fatty acid multilayer films on a gold substrate, Holman et al. observed that the r- resonance appeared as a peak up to
Interference Effects in SF Vibrational Spectra
Figure 6. (a) Simulations of the r+ interference phase as a function of polymer film thickness, based on the multiple reflection model. Solid line (-), methyl group tilt angle of 34.5°; dashed line (- - -), methyl group tilt angle optimized to 13° for PDMS r- data; dotted line (‚‚‚), methyl group tilt angle optimized to 16° for CDC r- data. Experimental data for the r+ interference phase of PDMS is overlaid (9). (b) Simulations of the r- interference phases as a function of polymer film thickness, based on the multiple reflections model. Solid line (-), methyl group tilt angle of 34.5°; dashed line (- - -), methyl group tilt angle optimized to 12° for PDMS r- data; dotted line (‚‚‚), methyl group tilt angle optimized to 16° for CDC r- data. Experimental data for the r- interference phases of CDC (4) and PDMS (b) are overlaid.
approximately 30 nm, whereupon a phase reversal to a dip was observed.26,27 The multilayer films studied by Holman et al. represent a very well-defined experimental system with known methyl group tilt angle (34.5°) and refractive index (1.45), the values of which are almost identical to those used in the initial simulations depicted in Figure 5. The lack of agreement of the initial simulation performed in this work with the data of Holman et al. provides additional evidence that the model of Lambert et al. does not adequately describe experimental observations at thicknesses on the nanometer scale. It should be noted that this length scale was not experimentally accessible for the gold-backed mica substrate employed by Lambert et al., as described in the Introduction section. The Lambert et al. model was therefore extended in the present work to address shortcomings and assumptions implicit in the model and to account specifically for features of the polymer system that were absent in the mica substrate system. Figures 6a and 6b depict interference phase simulation results for the r+ and r- resonances respectively, obtained using the multiple reflection model described in the Theory section. Simulations employing the initial refractive indices (1.42 and 1.40) and tilt angle (34.5°) of Figure 5 are reported as solid lines, overlaid on the experimental data of Figure 4. It is evident from investigation of Figure 6b that, unlike the initial model, the model incorporating multiple reflections captures the experimentally observed phenomenon of r- interference phase inversion at film thicknesses in the range of 10-16 nm. Also,
J. Phys. Chem. B, Vol. 108, No. 41, 2004 16037 the slight curve in the experimental data points at larger thicknesses is broadly reproduced in the simulation. However, the multiple reflection model predicts r- phases that remain positive up to a film thickness of approximately 21 nm, a prediction contrary to experimental observations. In addition, an examination of Figure 6a reveals that the predicted phase of the r+ resonance is in broad agreement with the experimental results (although the simulation diverges slightly from the experimental results at larger film thicknesses). In addition to the multiple reflection simulations employing a tilt angle of 34.5°, Figures 6a and 6b present simulations employing the multiple reflection model where the methyl group tilt angle at the polymer/air interface has been optimized relative to the experimental data (as performed for the initial model depicted in Figure 5). Simulations optimized with respect to the PDMS and CDC r- experimental phases are depicted by the broken and dotted lines and correspond to methyl tilt angles of 13° and 16° respectively. The optimized r- simulation for CDC (at a tilt angle of 16°) displays an improved correlation with the experimental data compared to the original multiple reflections simulation (solid line). However, on decreasing the tilt angle in the simulation further in order to align the point of phase inversion with that of the PDMS data, the correlation with the experimental data generally worsens compared with that of CDC. In contrast, decreasing the methyl group tilt angle in the r+ simulations improves the correlation with the experimental results of PDMS, although the effect is negligible compared with the influence of tilt angle on the r- simulations. In an attempt to improve the correlation with the experimental data of PDMS the model was further refined to include a second resonant contribution arising from methyl groups at the polymer/ gold interface, as discussed in the Theory section. Optimization of the r- simulations for PDMS and CDC was performed through altering the methyl group orientation at the polymer/ gold interface to point toward or away from the gold surface and subsequently through variation of the tilt angle at the polymer/air interface. The results of this process are given for CDC and PDMS in Figures 7a and 7b, respectively. Examination of Figures 6 and 7 reveals that the inclusion of a second resonant contribution improves the correlation of the r- simulations with the experimental results for both PDMS and CDC, particularly for film thicknesses below approximately 30 nm where the curve of the data is better reproduced by the optimized simulation. Furthermore, examination of Figure 7b reveals that the correlation of the r+ simulations with the PDMS data has not been detrimentally affected by optimization of the parameters for the r- simulation. Comparison of Figures 5a, 6a, and 7a and b clearly shows that the best agreement with the experimental results is obtained using a model that takes into account multiple reflections of the visible, IR, and SF beams and a second resonant contribution from methyl groups at the polymer/gold interface. Discussion The overall correlation observed between the phase behavior of the SF spectra of spin-coated PDMS and CDC and the theoretical simulations clearly suggests that interference effects are present in the polymer spectra. The results of the present work also provide a definitive explanation for the opposing rphases observed in the solvent cast spectra of CDC and PDMS (Figure 4, reference 20). It was previously noted20 that the unexpected r- dip in the PDMS spectrum could potentially be attributed to the existence of methyl groups in two different average orientations at the PDMS/air interface, one set directed
16038 J. Phys. Chem. B, Vol. 108, No. 41, 2004
Figure 7. (a) Simulations of the r+ (- -) and r- (-) interference phases of CDC as a function of polymer film thickness for the multiple reflections model incorporating a second resonant contribution from methyl groups at the polymer/gold interface, oriented toward the gold surface. The methyl group tilt angle at the polymer/air interface was optimized to 26°. Experimental data for the r- interference phase of CDC is overlaid (2). (b) Simulations of the r+ (- -) and r- (-) interference phases of PDMS as a function of polymer film thickness for the multiple reflections model incorporating a second resonant contribution from methyl groups at the polymer/gold interface, oriented toward the gold surface. The methyl group tilt angle at the polymer/air interface was optimized to 21°. Experimental data for the r+ (0) and r- (b) interference phases of PDMS are overlaid.
along the surface normal away from the substrate and the other oriented toward the substrate. However, if the r- dip in the PDMS solvent cast spectrum was due to the specific conformation of PDMS, then the r- phase in the spin-coated spectra of the present work would appear opposite to that in the CDC spectra at all film thicknesses (although in both cases they would show a thickness/phase periodicity characteristic of r-). This is clearly not the case experimentally. Consequently, it is concluded that the difference in r- phase for the original solvent cast CDC and PDMS spectra is due solely to different film thicknesses in the solvent cast samples. The simulations performed to reproduce the interference effect as a function of polymer film thickness were found to correlate satisfactorally with the experimental results for the interference phase of both the r+ and r- resonances. The closest agreement with the experimental data was obtained when the original model of Lambert et al. was modified to include multiple reflections of the visible, IR, and SF beams within the polymer layer and a second resonant contribution to the SF spectrum from polymer molecules at the polymer/gold interface. The optimal methyl group orientation at this interface was found to be toward the gold surface, which is reasonable since freshly coated gold becomes hydrophobic almost immediately upon exposure to air. Changing the refractive index of the polymer layer over a reasonable range, i.e., from the lowest reported literature value for spin-coated PDMS of 1.4038 up to 1.45, was found not to significantly affect the simulated spectra. In addition, the
McGall et al. incorporation of a factor to take into account attenuation of the IR beam within the polymer layer was found not to significantly improve the simulation (data not shown). Variation of the final simulation parameters to optimize the agreement with the CDC r- experimental data resulted in a predicted tilt angle of the methyl group to the polymer/air surface normal of 26° (where the tilt angle was varied in increments of 1°). Optimization of the methyl group tilt angle to fit the PDMS experimental data at the same interface resulted in a predicted angle of 21°. The observation of different methyl group tilt angles for the two polymers is not unreasonable since a significant proportion of the r- SF resonance signal of CDC is known to originate from the cetyl side chains,20 with the remainder derived from methyl groups comprising the PDMS backbone. The observation of an orientation of PDMS methyl groups into air and approximately 21° off the surface normal is broadly consistent with the work of Zhang et al.7 who concluded that methyl groups of PDMS in air were oriented “more or less along the surface normal”. While the agreement of the simulations with the experimental results is satisfactory, it is reasonable to expect that the model simulations should show slight deviation from the experimental data for such a complex system in which a significant number of variables exist. Although a variety of parameters have been considered in the modeling work, others have by necessity been omitted. For example, the influence of the methyl group tilt angle at the polymer/gold interface and the effect of a distribution of tilt angles at the polymer/air and polymer/gold interfaces have not been included. Other factors that could influence the spectra include the degree of surface roughness, which may act to obscure the interference effect, and the possibility of a minor contribution from the bulk polymer film in regions of imperfect centrosymmetry. The present analysis has concentrated on the phase behavior of the interference phenomenon. The r+ and r- interference phases are relative to a common reference point of 90° for the r+ resonance of a polymer monolayer and can therefore be directly compared. However, the predicted changes in resonant intensity as a function of film thickness have no such defined reference since the relative magnitudes of the r+ and rresonances in a monolayer depend on the specific tilt angle of the methyl groups, in addition to the overlap between Raman and IR transition moments. Consequently, the r+ resonant intensity cannot be directly compared with the r- resonant intensity within each simulated spectrum. Furthermore, any changes in the predicted resonance intensities as a function of film thickness would not necessarily be reflected by corresponding changes in the experimental data since additional factors affect SF resonant intensities. For example, the exact experimental conditions of beam overlap and pulse energies are difficult to control reproducibly for consecutive spectra on different samples, making quantitative comparisons of resonant strengths impractical. Finally, the applicability of the model to the prediction of the phase behavior of resonances present in the SF spectrum of CDC but not considered here should be discussed. Such resonances include an r+ resonance at 2877 cm-1 attributable to the methyl groups of the cetyl side chains and an r+ Fermi resonance at 2933 cm-1. The phase of both of these resonances would be expected to display the same dependence on polymer film thickness as the r+ resonance at 2908 cm-1, with which they have equivalent symmetry and hence the same expressions for their resonant susceptibilities. In addition, the CDC SF spectrum displays a methylene symmetric stretching resonance
Interference Effects in SF Vibrational Spectra (d+), which occurs in a different symmetry environment. The model could potentially be extended to predict the behavior of the d+ resonance and the resulting simulations compared to the experimentally observed phase behavior. However, the development of such a model would be complicated by the difficulty in predicting a value for the average tilt angle of the SF active methylene groups since SF signals from methylene groups are only predicted to occur at gauche defects where methylene groups may assume one of several different conformations.39 As such, no attempt to generate such a model has been made in the present work. Conclusions Thickness dependent changes in the sum frequency vibrational spectra of thin films of the polymers CDC and PDMS deposited on a planar gold surface have been shown to arise from interference effects between different sources of sum frequency light generated in the composite interfacial system. For nanometer thick films the interference effect is primarily observed as a change in the phase of the r- C-H resonance of the methyl groups of the polymer as the film thickness is varied. The present observations on a nanometer film thickness scale complement the phase changes measured previously for the r+ resonance on a micrometer thickness scale for the analogous interfacial system of a silane monolayer on mica backed by gold. Interference effects of the r+ and r- phases were predicted by Lambert et al. for SF generation from the composite silane/ mica/gold interfacial system. The model was based on interference between three sources of SF generation, two at the air/ mica interface and one at the mica/gold interface. In the present work, this model has been modified and extended to obtain satisfactory agreement between phase predictions and experimental phase measurements for the more complex system comprising a thin polymer film on a planar gold substrate. The model which gave the best agreement with experiment incorporated multiple reflections of the incident and emitted beams. The dominant SF signal was determined to arise from the polymeric methyl groups at the polymer/air interface orientated into air, with a lesser contribution from the same groups at the polymer/gold interface oriented toward the gold surface. These methyl group orientations at the two interfaces are physically reasonable. The optimized model yielded a methyl group tilt angle closer to the surface normal for PDMS than for CDC. The correlation between the predicted and measured r- phase values as a function of polymer film thickness permits application of the model to unambiguously determine the orientation of resonant groups in polymer films of known thickness on gold substrates. Acknowledgment. S.J.M. is grateful to Procter & Gamble Technical Centers Limited, UK, and the EPSRC for the award of a CASE studentship. We thank Dr. Mark Edwards and Dr. Chris White of Procter & Gamble Technical Centers Limited for useful discussions and for supplying the PDMS and CDC. Dr A. G. Lambert provided useful guidance on developing the modeling program, for which we are very grateful. Supporting Information Available: Full derivation of the mulitreflection (m) and phase (R) terms described in the text. This material is available free of charge via the Internet at http:// pubs.acs.org.
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