Spectral Interference and Molecular Conformation at Liquid Interface

8726

J. Phys. Chem. C 2007, 111, 8726-8738

Spectral Interference and Molecular Conformation at Liquid Interface with Sum Frequency Generation Vibrational Spectroscopy (SFG-VS)† Wei Gan,‡,§ Zhen Zhang,‡ Ran-ran Feng,‡ and Hong-fei Wang* State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, The Chinese Academy of Sciences, Beijing, China, 100080 ReceiVed: October 27, 2006; In Final Form: January 28, 2007

In this report, we present an analysis of the interference effects in the SFG-VS spectra of the vapor/ethanol interfaces with normal and deuterated liquid ethanol. Crucial information on the ethanol molecular orientation can be obtained from analyzing the interference effects between the different SFG-VS spectral features. With the strength-coupled orientational functional dr(θ) of the different spectral features from the same or different molecular groups, and with the phase information contained in the SFG spectra measured under different polarization combinations, the detailed orientational conformation structure of the ethanol molecule at the vapor/ethanol interface can be obtained. The ethanol molecule is found to possess an orientational conformation with its CH3- group pointing away from the liquid phase at an orientational tilt angle of about 45°, its -CH2group away from the liquid interface around 10°, and the C-C-O plane is near perpendicular to the plane of interface. Here, the conclusion that the -CH2- group has to tilt away from the liquid phase can only be reached with the knowledge of the spectral overlap and the analysis of the interference between the overlapping spectral features. The details of the molecular orientation angle and the orientational distribution width were discussed with novel approaches. These results suggested that studying coherent interference effects in the polarization analysis in SFG-VS can provide novel understanding of the interfacial molecular structure and interactions. The tools and the concepts of SFG-VS analysis developed in this study can be applied to more complex molecular interfaces and thin films.

1. Introduction In this report, we present a study of the molecular conformation of the ethanol molecule at the vapor/ethanol interface by using deuterated samples and analyzing the interference effects in the SFG-VS spectra. Molecules are generally oriented or aligned at the interface because of the asymmetric forces experienced by the molecules in such an environment. Consequently, the orientation and conformation of molecules at the interface are uniquely different from those of the molecules in the bulk or gas phases, and thus the unique properties of the molecular interfaces arise. The interfacial properties such as the surface potential or the surface wettability, and the surface processes such as the surface reaction or the surface adsorption, are all directly influenced by the interfacial molecular structure and conformation. The detailed information of the molecular orientational structure and conformation at the interface is not only important in order to manipulate the interfacial properties but also crucial for revealing the interaction and dynamics of molecules at the interfaces.1-3 For example, it has been demonstrated in recent reports that the ability to accurately determine the molecular orientational change is the steppingstone for the determination of the antiparallel double-layer structure and the adsorption energetics of the Gibbs adsorption layers at the vapor/aqueous mixture †

Part of the special issue “Kenneth B. Eisenthal Festschrift”. * Corresponding author. E-mail: [email protected]. Tel: 86-1062555347. Fax: 86-10-62563167. ‡ Also graduate students of the Graduate School of the Chinese Academy of Sciences. § Current address: Department of Biological Sciences and Department of Chemistry, Columbia University, 2960 Broadway, New York, NY, 10027.

solution interfaces.4,5 There have been many experimental6-13 and theoretical14-28 investigations of the detailed molecular structure of various model liquid interfaces using state-of-theart experimental techniques and simulation methods. Among the many experimental techniques that can be used to probe molecules at various interfaces, second harmonic generation (SHG) and sum frequency generation vibrational spectroscopy (SFG-VS) have been proven to be the most powerful spectroscopic techniques because of their unique interface selectivity and submonolayer sensitivity.10,29 SHG and SFG-VS can provide direct spectroscopic measurement of the liquid interface that no other technique can match.6,7 Using SHG and SFG-VS, the molecular spectroscopy, structure, and dynamics of an interface can be interrogated at the detailed molecular level.30-33 In an SFG-VS experiment, a visible laser beam (frequency ω1, incident angle β1) and a tunable infrared (IR) laser beam (frequency ω2, incident angle β2) are generally employed to interact with a molecular interface simultaneously, and by varying the IR frequency ω2, the vibrational spectrum of the molecules at the interface is obtained by measuring the signal generated at the sum of the frequencies of the two laser beams (frequency ω ) ω1 + ω2, outgoing angle β) in the direction determined by the momentum conservation relationship. Through analyzing the polarization dependence of the intensities of the spectral peaks in SFG-VS, information, such as the interfacial molecular orientation, structure and ordering, and so forth, can be obtained.34 On the basis of the SHG null angle method,35,36 a more accurate method of employing the measurement of the angle at the null SFG intensity was developed recently.32,37-40 This so-called polarization null angle

10.1021/jp0670642 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/23/2007

Spectral Interference and Molecular Conformation

J. Phys. Chem. C, Vol. 111, No. 25, 2007 8727

Figure 1. Strength-coupled orientational functional dr(θ) for the methyl group (left) and the methylene group (right) plotted against the orientational angle, θ. The symmetric modes are solid lines, and the asymmetric modes are dashed lines. All curves are symmetric and with opposite signs centered at θ ) 90°.

(PNA) method can be used to measure slight changes of the orientation of a particular molecular group at the interface.4,5,41 To determine the conformation of the whole molecule at an interface, knowledge of the orientation of each individual molecular group in the same molecule needs to be known. Zhuang et al. first described a way of using SHG and SFG-VS techniques to measure the orientational angles of the different parts of the 4′′-n-pentyl- 4-cyano-p-terphenyl [5CT, CH3(CH2)4(C6H4)3CN] molecule in the Langmuir film at the vapor/water interface. Thus, the 5CT molecular conformation structure was obtained.33 Very recently, Rao et al. also reported an approach to obtain the absolute orientation of the m-tolunitrile molecule through PNA measurements of the orientational angle of both the methyl and cyano groups in the m-tolunitrile molecule at its vapor/liquid interface.42 These examples have demonstrated the potential of SFG-VS and SHG in interfacial molecular conformation analysis. In these studies, however, the SFG-VS spectra and the polarization dependence of each molecular group were measured separately because there was no spectral overlap or interference between the methyl and cyano groups. It would be much more difficult to interpret the SFG-VS spectra if the spectral features of the different molecular groups overlap and interfere with each other. It is well known that the stretching vibrational spectra of the methyl and methylene groups generally overlap and interfere with each other. This fact makes it difficult to analyze the C-H stretching vibrational spectra and even harder to interpret the orientation and conformation of the carbon chain at the interface, except for some simple cases. Even for the simplest normal chain alcohols and diols, interpretation of the overlapping C-H spectra has never been an easy job, and many confusions and ambiguities have existed before the very recent developments of the polarization selection rules for spectral assignments in SFG-VS.32,43-45 With these developments, it is now possible to understand the complex chain conformation at the liquid interface using SFG-VS. Here we intend to study the conformation analysis of the ethanol molecule at the vapor/ethanol interface using the overlapping and interference nature of the methyl and the methylene spectral features in the SFG-VS spectra. We chose ethanol as the subject for such studying not only because it is the simplest long chain alcohol with both methyl and methylene groups but also because the detailed features of the complex vibrational spectra of the ethanol molecule have been unraveled recently.45,46 Prior to the full knowledge of the ethanol

vibrational spectra, the orientation of its CH3- group has been studied with SFG-VS at the vapor/liquid interface.47,48 These studies were not in full agreement with each other, and they have to be reexamined and reevaluated with the new knowledge of the ethanol spectra. Besides these, the ability to obtain the conformation of the ethanol molecule at the interface can provide a general approach for understanding the conformation of the carbon chain in the longer-chain normal alcohol or other longchain molecules. The key idea is that because their spectral features can be differentiated in the SFG-VS spectra the relative orientation between the end methyl group and the first methylene group attached to the hydroxyl group in the long-chain alcohol molecules provides unique conformational information of the chain. The vibrational spectral features of the ethanol molecule had not been clearly understood until very recently,45,46 even though the ethanol molecule has been used widely as the model molecule for vibrational spectra analysis, vibrational energy relaxation studies, as well as surface structure investigations.47-53 With the recent detailed polarization analysis of the SFG-VS spectra of the vapor/CH3CH2OH, vapor/CH3CD2OH, and vapor/ CD3CH2OH interfaces, the overlapping vibrational modes of the CH3- and -CH2- groups were uniquely determined.45 These new assignments were further confirmed by a detailed Raman and stimulated Raman study that appears in this issue of this journal.46 As shown in Figure 2, the 2875, 2930, and 2970 cm-1 peaks in the ethanol SFG-VS spectra are assigned to the overlapping CH3-SS and CH2-SS modes, Fermi resonance of the CH3-SS mode, and the overlapping CH3-AS and the CH2SS-Fermi resonance modes, respectively. In these SFG-VS spectra, the details of constructive and destructive interference effects between the spectral features of the CH3- and -CH2groups also need to be fully understood. They shall provide unique information on the relative orientation of the CH3- and -CH2- groups at the vapor/ethanol interface. The interference effect is a unique property in the coherent electromagnetic processes and in the quantum phenomena. It is especially important and useful in the coherent spectroscopy analysis.12,31,32,54-75 For example, quantum beat spectroscopy and two-dimensional nonlinear spectroscopy can be used to obtain detailed information on the structure and interactions of different energy levels and molecular groups in complex molecules.54-59 The interference effect has been employed in phase measurement in nonlinear spectroscopy, especially in sum frequency

8728 J. Phys. Chem. C, Vol. 111, No. 25, 2007

Gan et al.

Figure 2. SFG-VS spectra of the vapor/CH3CH2OH, vapor/CH3CD2OH, and vapor/CD3CH2OH interfaces taken at β1 ) 62° and β2 ) 55°. The spectra of ssp and ppp polarization combination are offset for better view. The pss spectra are not listed because they are essentially the same as the sps spectra.

generation vibrational spectroscopy (SFG-VS) or second harmonic generation (SHG).12,60-69,76 The relative phase between the different spectral features in the interference can also be determined through the analysis of the SFG spectra measured in different polarization combinations.12,31,32,61 The interference between the resonant contributions of adsorbed molecules and the nonresonant contribution of the metal substrate has also been used to study the adsorption behavior of the molecules on different metal surfaces.62-64,71,72,77 The interference effect was also used to extract information about the multilayer thin films coated on the substrate surfaces.70 In SHG and SFG-VS, the analysis of the interference effects can provide information on the relative phases of the effective susceptibilities with different origins. The relative phases can also be directly related to the orientation of the contributing molecular groups.78,79 When the absolute phase and structure of one of those involved in the interference are known, the absolute phases of the rest can be deduced from the known relative phases.32 Generally, spectral fitting in SFG-VS can give good agreement on the relative phases (signs) for different spectral features, unless the spectral quality is generally poor and spectral detail cannot be discerned.12,80 The absolute phases (signs) for different spectral features can also be directly measured.76 The interference effects in SFG-VS spectra can be well-correlated to the molecular details of the interface using the recently developed formulation of the general orientational parameter c and susceptibility strength factor d in different experimental polarizations and configurations.32,81,82 In this work, we developed certain concepts in order to analyze the interference effects in the SFG-VS spectra of the vapor/ethanol interface. We carried out these analyses with the simulation of the orientational dependence of the SFG-VS intensities for the methyl and methylene groups in different polarizations and different experimental configurations. We then studied the detailed orientational structure of the ethanol molecule at its vapor/liquid interface. From such conformation analyses, the ethanol molecule is found to possess an orientational conformation with its CH3- group pointing away from the liquid phase with an orientational tilt angle of about 45°, its -CH2- group tilting away from the liquid interface around 10°, and its C-C-O plane being nearly perpendicular to the interface plane.

2. Theoretical Background 2.1. Basic SFG-VS Theory. The principle for the SFG vibrational spectroscopy was described in detail in the literature.32,33 The formulation and procedures for quantitative calculation and simulation of SFG-VS intensities or field strengths in different polarization combinations were also available.32,44 The SFG intensity I(ω) measured in a certain polarization combination and an experimental configuration from the interface region is a square function of the effective second32,33 order sum frequency susceptibility χ(2) eff .

I(ω) )

8π3ω2 sec2 β 2 |χ(2) eff | I(ω1) I(ω2) 3 c n1(ω) n1(ω1) n1(ω2)

(1)

As defined previously,32 here c is the speed of the light in the vacuum; ω, ω1, and ω2 are the frequencies of the SFG signal and visible and IR laser beams, respectively; nj(ωi) is the refractive index of bulk medium j at frequency ωi, and n′(ωi) is the effective refractive index of the interface layer at ωi; βi is the incident or reflect angle from the interface normal of the ith light beam; and I(ωi) is the intensity of the SFG signal or the input laser beams, respectively. Because χ(2) eff depends on the infrared frequency ω2, then one has

χ(2) eff

)

χ(2) NR,eff

+

∑q ω

2

(2) χq,eff

- ωq + iΓq

(2)

(2) (2) in which χNR,eff is the nonresonant contribution and χq,eff is the susceptibility strength factor for the qth vibrational mode in the SFG spectra centered at the vibrational frequency ωq and with (2) (2) a damping constant Γq. Both χNR,eff and χq,eff are ensemble average values over molecules with different orientations. Because there is more than one vibrational mode (q > 1), the observed SFG-VS spectra are subject to the interference effects from the different vibrational modes. Such interference effects can be understood by fitting the observed SFG spectra with multiple modes following eq 2. The relative values and the signs of the



TABLE 1: cq and dq Values for the Symmetric Stretching (SS) Mode and the Asymmetric Stretching (AS) Mode of the Methyl Groups at the Vapor/Ethanol Interfacea polarization

sspss

spsss

pssss

pppss

sspas

spsas

pssas

pppas

c d

-0.55 0.53

1 -0.32

1 -0.31

1.8 0.39

1 -0.24

∞ -0.26 (d‚c)

∞ -0.26 (d‚c)

1.0 0.59

a The notation such as sspss indicates the ssp polarization combination of the SS mode and so forth. The dq value bears the unit βccc for the SS mode and the unit βaca for the AS mode.

(2) (2) χNR,eff and χq,eff factors, as well as the spectral parameters ωq and Γq, can be determined from such a spectral fitting.31,73 For a rotationally isotropic liquid interface (C∞V), the effective (2) sum frequency susceptibility χq,eff is related to the seven nonzero macroscopic susceptibility tensors and can be expressed into the linear combination of the following four independent and experimentally measurable terms.32

(2),ssp χq,eff ) Lyy(ω) Lyy(ω1) Lzz(ω2) sin β2χq,yyz (2),sps χq,eff ) Lyy(ω) Lzz(ω1) Lyy(ω2) sin β1χq,yzy (2),pss χq,eff ) Lzz(ω) Lyy(ω1) Lyy(ω2) sin βχq,zyy (2),ppp χq,eff ) -Lxx(ω) Lxx(ω1) Lzz(ω2) cos β cos β1 sin β2χq,xxz

-Lxx(ω) Lzz(ω1) Lxx(ω2) cos β sin β1 cos β2χq,xzx +Lzz(ω) Lxx(ω1) Lxx(ω2) sin β cos β1 cos β2χq,zxx +Lzz(ω) Lzz(ω1) Lzz(ω2) sin β sin β1 sin β2χq,zzz (3) It is so defined that the xy plane in the laboratory coordinates system λ(x,y,z) is the plane of the interface, with z as the surface normal; Lii (i ) x,y,z) is the Fresnel coefficient determined by the refractive index of the two bulk phases and the interface layer, and the incident and reflected angles.32,33,83 The p polarization is defined as within the xz plane, and the s polarization is perpendicular to the xz plane. The polarization combination ssp indicates that the SF signal, the visible beam, and the IR beam are in the s, s, and p polarizations, respectively; and so on. The mode-specified χq,ijk tensors are related to the mode-specified molecular hyperpolarizability tensor βq,i′j′k′ in the molecular coordinates system λ′(a,b,c) through the ensemble average over all of the possible molecular orientations, which can be described as32,33,83

χq,ijk ) Ns

∑ 〈Rii′Rjj′Rkk′〉βq,i′j′k′

(4)

i′j′k′

where Ns is the number density of the interface moiety under investigation and Rλλ′ is the element of the Euler rotational transformation matrix from the molecular coordination λ′(a,b,c) to the laboratory coordination λ (x,y,z).81,84 The expressions of the relationship between the χq,ijk tensors and the microscopic (molecular) hyperpolarizability tensor βq,i′j′k′ for the molecular groups with C2V, C3V, and C ∞V symmetry were well-described in the literature.32,39,43,44,85-87 (2) The dependence of χq,eff in different polarization combinations on the molecular orientation can be evaluated easily using the following unified functional form of molecular orientation.81,82 The vibrational mode specific parameters cq (general orientational parameter) and dq (susceptibility strength factor) can be calculated for each vibrational mode according to its symmetry categories.31,32,44 (2) ) Nsdq(〈cos θ〉 - cq〈cos3 θ〉) ) Ns dq rq(θ) χq,eff

(5)

Here rq(θ) is the mode-specific orientational field functional for the qth vibrational mode, which contains all of the molecular orientational information at a given SFG experimental configuration of that mode. The dimensionless parameter cq for the qth vibrational mode determines the orientational response of rq(θ) to the molecular tilt angle θ; and dq is the mode specific susceptibility strength factor for the qth vibrational mode, which is a constant for a certain experimental polarization combination. Both the dq and cq values are functions of the related Fresnel coefficients including the refractive index of the interface and the bulk phases, the experimental geometry, and the symmetry of the qth vibrational mode. On the basis of these formulations, the complex molecularorientation-dependent interference effects between the different vibrational modes in the four polarization combinations can be simulated and quantitatively evaluated with the magnitude and phase (or sign) of the dq rq(θ) functional in each experimental configuration. The simulation results and the evaluations can be compared directly with the SFG-VS experimental data in different polarization combinations under different experimental configurations. The symmetry properties of the vibrational modes and detailed orientational information of a particular molecular group at the interface can also be obtained accordingly.31,75 2.2. Simulations of the CH3- and -CH2- Modes of the Vapor/Ethanol Interface. Simulation of the orientational dependence of the SFG-VS intensity in different polarization combinations from the above formulation depends on the knowledge of the related parameters. The issues concerning the accuracy and reliability of these parameters were discussed thoroughly in the recent literature.32 Quantitative empirical corrections of these parameters were also discussed and tested in detail recently.88 Our simulation showed that besides experimentally determined parameters, the uncertainty of all of the parameters were usually very limited in order to be consistent with some apparent trends in the experimental data in different polarization combinations and experimental configurations. This certainly assured the robustness of the simulation and the conclusions. With the known procedures,32,43,44 the parameters cq and dq for methyl groups can be calculated as listed in Table 1. (Because the CH3-AS mode is generally considered doubly degenerate as discussed previously,44 the d values for the CH3AS mode listed here are twice as large as the values presented in previous reports, where the values were for only one of the degenerate modes.32,44 In the plots in the previous reports, the degeneracy was already included.32,44 The d values calculated from eq 28 in the previous report32 already included the degeneracy of the CH3-AS mode. Careful readers may notice this difference. In order not to cause possible confusion, from now on, we shall list the d value for the CH3-AS mode as calculated from eq 28, instead of the single-mode value.) The incident angle of the visible and the IR laser beams are 62° and 55°, respectively. Other parameters used in the simulation are the same as those used in our recent reports;32,43,44 that is, the hyperpolarizability tensor ratio R ) βaac/βccc ) 3.4, the


Gan et al.

empirically corrected ratio βccc/βaca ) 0.22,88 the refractive index in liquid phase n2(ωi) ) 1.36, and in the interface n′(ωi) ) 1.16, which is calculated with the method presented by Shen et al.32,33 However, determination of parameters cq and dq for ethylene groups is more complicated because the -CH2- group in the ethanol molecule cannot rotate freely in the molecular frame. In this case, the macroscopic susceptibility for the -CH2- group is both θ (the tilt angle) and ψ (the twist angle) dependent.32,44,89 For the symmetric stretching (SS, a1) vibrational mode of the -CH2- group

1 (2),ss 2 2 χ(2),ss xxz ) χyyz ) Ns[〈cos ψ〉βaac + 〈sin ψ〉βbbc + βccc] 2 1 〈cos θ〉 + Ns[〈sin2 ψ〉βaac + 〈cos2 ψ〉βbbc - βccc]〈cos3 θ〉 2 (2),ss (2),ss (2),ss χ(2),ss xzx ) χzxx ) χyzy ) χzyy 1 ) - Ns[〈sin2 ψ〉βaac + 2 〈cos2 ψ〉βbbc - βccc][〈cos θ〉 - 〈cos3 θ〉] 2 χ(2),ss zzz ) Ns[〈sin ψ〉βaac +

TABLE 2: cq and dq Values for the SS (a1) and AS (b1) Mode of the Methylene Group at the Vapor/Ethanol Interface with the Euler Twist Angle ψCH2 ) 0a polarization sspss spsss pssss c d

pppss sspas spsas pssas

0.19 1 1 1.4 0.29 0.061 0.060 -0.081

1 0

pppas

0 0 0 0.072 0.071 -0.00082

a The dq value bears the unit βccc for the SS mode and βaca for the AS mode.

different polarization combinations, the strength-coupled orientational functional dqrq(θ) against the orientational tilt angle, θ, can be plotted for each polarization combination, as shown in Figure 1. With these plots, the relative strength and the phase of the orientation-dependent dqrq(θ) in different polarizations are visualized and can be directly evaluated. Because the SFGVS intensities in different polarization combinations are directly proportional to the square of the summed term χ(2) eff in eq 2, the interference effect between different vibrational modes of different molecular groups can be readily evaluated. In section 4, we shall frequently come back and discuss the simulations in Figure 1. 3. Experimental Section

〈cos2 ψ〉βbbc]〈cos θ〉 - Ns[〈sin2 ψ〉βaac + 〈cos ψ〉βbbc - βccc]〈cos θ〉 (6) 2

3

And for the asymmetric stretching (AS, b1) vibrational mode of the -CH2- group 2 3 (2),as χ(2),as xxz ) χyyz ) -Nsβaca〈sin ψ〉[〈cos θ〉 - 〈cos θ〉] (2),as (2),as (2),as χ(2),as xzx ) χzxx ) χyzy ) χzyy

1 ) Nsβaca[〈cos2 ψ〉 2 〈sin2 ψ〉]〈cos θ〉 + Nsβaca〈sin2 ψ〉〈cos3 θ〉 2 χ(2),as zzz ) 2Nsβaca〈sin ψ〉[〈cos θ〉 -

〈cos3 θ〉] (7) Besides, the hyperpolarizability tensor ratios between the βi′j′k′ terms need to be determined from the known Raman depolarization ratios as well as the Raman and IR intensity ratios. Such procedures were fully described in the literature.32,88 As discussed in section 4.2.3, the hyperpolarizability tensors for the -CH2- group can be deduced from the bond polarizability of a single C-H bond and the bond angle between the two C-H bonds.32,88,90 The typical single-bond hyperpolarizability tensor ratio for the C-H bond directly connected to the O-H group is r ) 0.28. This value was also confirmed from the Raman depolarization measurement of the CD3CH2OH molecule.46 With r ) 0.28, one has the following ratios: βaac ) 1.46βccc; βbbc ) 0.54βccc; and βaca ) 0.94βccc.32,88 Following the procedure in the literature,31,44 the cq and dq values for the SS and AS modes of the -CH2- group are calculated for ψ ) 0°, and the values are listed in Table 2. ψ ) 0° means that the C-C-O plane in the ethanol molecule is perpendicular to the plane of the interface. We shall show below that the molecular conformation centered at ψ ) 0° is the only possible conformation that can satisfy the observed SFG-VS spectra. According to the cq and dq values for the symmetric and asymmetric modes of the methyl and methylene groups in

The experimental setup has been described previously.43,44 Briefly, the 10 Hz and ∼23 ps SFG spectrometer laser system from EKSPLA was with a copropagating configuration. Some SFG polarization optics were rearranged from the original design to improve the polarization control in the SFG experiment.39 The visible wavelength is fixed at 532 nm, and the full range of the IR tunability is from 1000 to 4300 cm-1. The specified spectral resolution of this SFG spectrometer is 99.8%) was from Fluka, and the deuterated liquid CD3CH2OH (>98%) and CH3CD2OH (>98%) were from the Cambridge Isotope Laboratory. The samples were used as received. 4. Results and Discussions 4.1. Interference Effect in the Vapor/Ethanol Interface SFG-VS Spectra. The interference effect in the SFG-VS spectra of the vapor/ethanol interface is complicated and interesting. With interface SFG-VS spectra of both the normal and deuterated ethanol molecules, such an interference effect can be elucidated. There were several previous studies on the SFG-VS spectra of the vapor/ethanol interface, with both the C-H stretching spectra44,45,47,48,53,91 and the O-H hydrogen bond spectra.92 It turned out that the C-H vibrational spectra of the normal



TABLE 3: Fitting Results χeff,q of the SFG Spectra of the Vapor/Ethanol Interface, the Vapor/CH3CD2OH Interface, and the Vapor/CD3CH2OH Interfacea CH3CH2OH

CH3CD2OH

CD3CH2OH

position width polarization

ωq Γq ssp ppp sps


ωq Γq ssp ppp sps


ωq Γq ssp ppp sps

χNR

peak 1

-8E-4 ( 4E-5 -8E-4 ( 2E-5 6E-4 ( 5E-5

2878.6 ( 0.4 12.9 ( 0.6 0.022 ( 0.001 0.004 ( 0.002 ?

-8E-4 ( 2E-5 -7E-4 ( 2E-5 -4E-4 ( 2E-5

2872.3 ( 0.4 7.7 ( 0.6 0.009 ( 0.001 0.002 ( 0.002 ?

-2E-3 ( 2E-4 ? ?

2886.1 ( 1.8 20.2 ( 1.5(??) 0.011 ( 0.001 ? ?

peak 2

2904.8 ( 1.4 13.7 ( 2.9 0.006 ( 0.001 ? ?

peak 3

peak 4

2929.7 ( 0.2 8.8 ( 0.3 0.024 ( 0.001 0.006 ( 0.001 ?

2974.7 ( 0.2 8.5 ( 0.2 -0.005 ( 0.002 0.017 ( 0.001 0.009 ( 0.001

2934.5 ( 0.2 7.0 ( 0.2 0.023 ( 0.001 0.007 ( 0.001 ?

2971.2 ( 0.2 8.1 ( 0.2 -0.008 ( 0.001 0.018 ( 0.001 0.010 ( 0.001 2974.1 ( 1.3 7.5 ( 2.2 0.002 ( 0.002 ? ?

a The spectra are fitted with Lorentzian line-shape functions. The peak position of the vibrational modes ωq, the peak width Γq, and the strength of each vibrational mode in different polarizations are listed. The unit for ωq and Γq is cm-1. χ NR is the nonresonant background. The ? sign indicates that the peak is at the noise level, and its sign cannot be identified explicitly. The ?? sign indicates that the fitted width cannot be ascertained completely.

alcohols are much more complicated than what was understood previously.44,45 The most surprising part of the story is that with the recent SFG-VS measurement of the vapor/deuterated ethanol interfaces we learned that the 2875 cm-1 peak contains contributions from both the CH3-SS and CH2-SS modes, the 2930 cm-1 peak contains the CH3-SS-Fermi, and the 2970 cm-1 peak contains both the CH3-AS and CH2-SS-Fermi contributions.45 These findings, which were confirmed by a new Raman and stimulated Raman study with gaseous and liquid ethanol,46 not only put forth new questions on the general Raman and IR spectral assignment of the C-H stretching modes of the normal alcohols93,94 but also put forth new questions on the SFG-VS interpretations47,48,53 as well as the ultrafast vibrational dynamics studies.52 The SFG spectra of the vapor/CH3CH2OH, the vapor/CH3CD2OH, and the vapor/CD3CH2OH interfaces at the C-H vibrational stretching range are measured and plotted in Figure 2. The details of the spectral assignment were reported elsewhere,45 and it is not going to be repeated. It is straightforward to see that the 2875 cm-1 peak in the ssp polarization combination of the SFG-VS spectra at the vapor/CH3CH2OH interface is mostly the contribution of the CH3-SS, which can be clearly identified in the ssp SFG-VS spectra of the vapor/ CH3CD2OH interface as in Figure 2. It is also clear that there is contribution to this same peak from the CH2-SS mode, which can be clearly identified from the ssp SFG-VS spectra of the vapor/CD3CH2OH interface. The contributions of the two spectral features to the 2875 cm-1 peak in ssp polarization combination of the vapor/CH3CH2OH are clearly constructive. The CH2-SS peak on the ssp spectra of the vapor/CD3CH2OH interface is positioned at about 2886 cm-1 on the blue side of the CH3-SS peak position of about 2872 cm-1. This simple fact already provided important information on the CH2-SS vibrational spectra. We have known from the textbooks and previous studies that the CH2-SS peak is generally around 2850 cm-1, that is, on the red side of the CH3-SS peak around 2875 cm-1.44,95 Now we see that the CH2-SS mode of the CH2- group directly connected to the O-H group is on the blue side of the CH3-SS peak in the ethanol molecule. This fact further complicates the 2870-2880 cm-1 region of the vibrational spectra for normal alcohol molecules with longer chains. This shall make it more difficult to interpret the SFG-VS spectra, such as calculating the orientation of the CH3- group47,48,53 as

well as interpreting the ultrafast vibrational dynamics of the related molecules.52 Another surprising feature in the ethanol spectra is that the 2970 cm-1 peak contains contributions from both the CH3-AS and CH2-SS-Fermi modes.45 The symmetry of the CH2-SSFermi mode is determined from the polarization selection rules, which stated that under such copropagating geometry any CH 2SS mode at the liquid or molecular surfaces, including the CH2SS-Fermi mode, should have a stronger intensity in the ssp polarization combination than in the ppp polarization combination.32,43,44 Therefore, from the vapor/CD3CH2OH SFG-VS spectra in Figure 2, it is evident that the peak at about 2970 cm-1 in the ssp polarization combination belongs to CH2-SSFermi. This finding certainly makes the analysis of the CH3AS mode of the normal alcohols more difficult. We shall show later that the experimental configuration dependence of the CH3AS and CH2-SS-Fermi modes are very different. Therefore, any analysis of the polarization dependence in SFG-VS spectral features is subject to possible misinterpretations without such knowledge. Table 3 lists all of the fitted peak positions and oscillator strengths with the overlapping Lorentzian lineshapes according to eq 2. In this table, the oscillator strength with the ? signs indicates that this peak is almost at the noise level and no reasonable numbers can be obtained from the fitting. Fortunately, those stronger peaks do give very reliable numbers, and the constructive (in phase) or destructive (opposite phase) interference between the different modes at the overlapping spectral regions can be determined easily from the tabulated values. For example, the constructive interference between the CH3-SS and CH2-SS modes in the ssp polarization combination in the peak 1 region (2870-2880 cm-1) has the three respective oscillator strengths as 0.22 ≈ 0.009 + 0.011, whereas the destructive interference between the CH3-AS and CH2-SS-Fermi modes around the peak 4 (2970 cm-1) region has -0.005 ≈ -0.008 + 0.002. Analysis of the orientational dependence of the interfering relative oscillator strength and signs of the overlapping spectral features can provide information on the details of molecular orientation as well as the molecular conformation at the interface. Fitting the SFG-VS spectra in different polarizations of the normal and deuterated molecular surfaces provided us with the experimental values of these strengths. The orientational

8732 J. Phys. Chem. C, Vol. 111, No. 25, 2007 analysis can be carried out with the simulation procedures described in section 2.2. 4.2. Orientation and Distribution of Ethanol Molecule at Vapor/Ethnaol Interface. 4.2.1. Orientation Angle of the Methyl Group. The orientation of the CH3- group at the vapor/ ethnaol interface was studied in previous SFG-VS studies.47,48 However, the conclusions for the tilt angle value were diverse, with one giving θ ≈ 30° 47 and another giving θ ≈ 50°.48 In the meantime, both speculated a relatively very broad orientational distribution. However, the analyses in these works were based on the calculations of the polarization-dependent intensity of the 2930 cm-1 peak because the 2930 cm-1 peak was then assigned to CH3-SS.47,48,53 Now we know that the ethanol vibrational spectra is much more complicated than that simple assignment. Both the 2875 cm-1 and 2930 cm-1 peaks in the SFG-VS spectra mainly belong to the CH3- group, and they form a pair of Fermi resonance peaks.45,46 Conventionally, one can call the 2875 cm-1 peak the CH3-SS, and the 2930 cm-1 peak the CH3-SS-Fermi. Such assignment implies that the 2875 cm-1 peak contains more contributions from the fundamental vibration, whereas the 2930 cm-1 peak contains more contributions from the first overtone of the bending vibration. Generally speaking, the peak with more contributions from the fundamental vibration has a stronger transition dipole, that is, stronger IR spectral intensity. However, this may not be the same in the Raman spectra, as well as in the SFG-VS spectra, because Raman or SFG-VS spectral intensity is not a direct measurement of the transition dipole.63,88,96 Nevertheless, because the Fermi pair possesses the same symmetry, the same symmetry analysis is applicable to both, only with slightly different depolarization parameters that can be determined empirically for each peak.46,51,88 As discussed in section 4.2.3, the orientational analysis with the CH3-SSFermi mode peak is with problems because it has different hyperpolarizability tensor ratios from those of the CH3-SS mode, even though they belong to the same symmetry category. With the new knowledge of the vibrational spectra assignment of the ethanol molecule, it is clear that the orientation of the CH3- group at the vapor/CH3CH2OH interface is better to be deduced from the SFG-VS spectra of the vapor/CH3CD2OH interface, instead of the vapor/CH3CH2OH interface, because in CH3CD2OH the CH3- group peak is free from the spectral interference effect as in CH3CH2OH. Recently, the polarization null angle (PNA) method was developed for SFG-VS studies,32,39,40 and it has been used successfully to measure the CH3- group orientational angle at the vapor/methanol and vapor/acetone interfaces as well as the small orientational angle changes at the vapor/liquid interfaces of their aqueous mixtures.4,5,38 In these cases, the null angles of the SFG-VS spectral peaks of the CH3-SS mode were directly measured. Here we are not using the PNA method for the vapor/ CH3CD2OH interface because from Figure 2 one can see that the CH3-SS peak is not as far away from the neighboring peaks as in the methanol and acetone cases. Thus, in applying the PNA method, spectral deconvolution of the neighboring peaks is generally needed for the vapor/CH3CD2OH interface, unlike the cases for the vapor/methanol and vapor/acetone interfaces.40 Such a requirement needs the SFG-VS spectra to be taken in many different polarization combinations, and this is not only experimentally undesirable but also subject to other errors. Therefore, the PNA measurement was not employed here. Here we show that the orientational angle of the CH3- group can be calculated accurately from the convergence of the multiple intensity ratios as shown below. It has been known

Gan et al.

Figure 3. Using the dr(θ) ratio to calculate the orientational tilt angle of CH3- group. The solid curve is the simulated pppas/spsas ratio read on the left axis, and the dashed curve is the simulated sspss/pppas ratio read on the right axis. The horizontal solid lines with arrows are the ratio from experimental fittings, and the horizontal dashed lines with arrows indicates their errors. The tip of the arrow indicates the actual value on the corresponding axis. The vertical double arrows indicate the size of the experimental error bars, respectively. The vertical lines with arrows give the range of the orientational angle of the CH3- group, which is 45° ( 6°. The two tilted arrows indicate the lower and upper boundary of the angle.

previously that the intensity ratios between different two polarization combinations have different sensitivities on molecular orientation.43 For example, for the CH3- group, the intensity ratio of pppas/spsas is more sensitive to the CH3- tilt angle in a fairly broad range than the ratio of pppas/sspas. This can be evaluated easily from the dr(θ) simulation curves for the CH3- group in Figure 1. Of course, the sensitivity of the intensity ratios also depends on the hyperpolarizability tensor ratios of the group, as well as the experimental configuration. Here, as shown in Figure 3, both the pppas/spsas and sspss/ pppas dr(θ) ratios are quite sensitive to the CH3- group orientational angle θ. Using these two ratios and the corresponding experimental values in Table 3 for the SFG-VS spectra of the vapor/CH3CD2OH interface, namely, 1.8 ( 0.3 for the pppas/spsas ratio and 0.50 ( 0.08 for the sspss/pppas ratio, the orientational angle of the CH3- group is θ ) 45° ( 6°, if a δ orientational distribution is assumed. In terms of the orientational parameter D ) 〈cos θ〉/〈cos3 θ〉 value, this tilt angle value corresponds to D ) 2.0 ( 0.4. This result does have a much larger error bar than that determined with the normal PNA method, whose error bar is usually less than 0.1 unit.39 However, such an orientational angle value is fairly accurate, and the error bar is not outrageously big. The two sets of intensity ratios gave overlapping θ values, that is, 42° ( 3° from the pppas/spsas ratio, and 45° ( 5° from the sspss/pppas ratio, as shown in Figure 3. The convergence of these two sets of the θ values indicated the reliability and usefulness of this kind of multiple ratio method. To calculate the sspss/pppas ratio, the empirically corrected βaca/βccc ratio 0.22 of the CH3- group was used. If the uncorrected bond polarizability model value 0.30 was used, then the experimental sspss/pppas ratio will give θ ) 54° ( 6°. This latter value shall not overlap with the value from the pppas/spsas value. This fact certainly indicates the quantitative agreement of the treatment of the empirical correction for the βaca/βccc ratio with the SFG-VS experiment results.88 4.2.2. Orientational Distribution of the Methyl Group. Unlike the orientational angle θ, determination of the orientational distribution width of the surface CH3- group is not as straightforward. For interfaces where the molecular number density is



Figure 4. sec(β) dr(θ,σ) of the CH3-SS and CH3-AS modes in different polarization combinations with β1 ) 62° and β2 ) 53° experimental configuration with the orientational parameter of the CH3- group as D ) 2.0. Here sec(β) is used for the comparison between different experimental configurations, and it is a constant for a given experimental configuration. The solid black curve represents the possible θ0 and σ pair values.

accurately known, such as the Langmuir monolayer, both the orientational angle and the distribution width can be determined from polarization analysis.30,82 However, this is not the case for the liquid interfaces. Generally, in previous SFG-VS studies, the orientational distribution was discussed but the best one can do is to estimate its upper limit.5,31,38,40,83,97,98 Here, in order to better understand the ethanol molecular conformation at the interface, we also try to find the range of possible orientation distributions of the CH3- group. The possible orientational angle and orientational distribution width are limited by the orientational parameter D obtained from the experimental polarization analysis. With D ) 2.0 ( 0.4 from above, simulation of the dr(θ,σ) of the CH3-SS and CH3-AS modes in different polarization combinations with the β1 ) 62° and β2 ) 53° experimental configuration are plotted in Figure 4. As one can see, the black solid line is the possible value for the pair of the orientational angle θ and the standard deviation σ with D ) 2.0, which satisfies the following Gaussian distribution function.

f(θ) )

1

x2πσ2

e-(θ-θ0) /2σ 2

2

(8)

As one can see in Figure 4, when D ) 2.0, σ cannot have a real value larger than 42°. This can be best understood with the Simpson and Rowlen’s famous “magic angle” plot.30,99 It is also evident from Figure 4 that the center orientational angle, θ0, remains almost unchanged when σ is smaller than 20°, and all of the dr(θ,σ) values in different polarization combinations remained almost unchanged (about 17%) in this range. Because all of them change by a very similar percentage with the same σ value, this indicates that mathematically one generally cannot determine the exact value of σ from the experimental measurement, as long as σ is smaller than 20°. However, the following analysis tells us that, despite the uncertainty in the determination of the orientational distribution width, the value of the θ0 can be determined very accurately. In Figure 1, the dr(θ) value in some polarization combinations, such as the pppss, changes rather dramatically when θ is changed. As one can understand, for each σ value, there is a calculated Figure 1, with its horizontal axis as θ0 instead of θ. Therefore, Figure 4 indicates that when σ is less than 20° Figure

1 remains almost unchanged for all different σ values. However, if the θ0 value changes from 45° to 40°, then the sign of the corresponding value on the pppss curve has to be reversed, just the same as in the original Figure 1 where a δ distribution of θ0 is assumed. As shall be discussed in section 4.3, this sign has to remain positive from the experimental configuration measurement results. Therefore, the θ0 value, which is essentially the θ value determined in section 4.2.1, can be determined accurately for a broad range of σ values. This is a very important conclusion because it was generally believed previously that only the orientational parameter, D, could be determined accurately, but both the corresponding θ0 and the σ values could not be determined accurately except for a few special cases.5,38,99 Now we conclude that with the assistance of the analysis of the interference effect the θ0 value can be determined accurately from experiment, and the σ value cannot be determined as accurately, but it can be known to be below a certain upper limit value. This simply means that the orientational distribution has to be centered in an accurately determinable orientational angle, which can be as accurate as within a few degrees. This fact also provides support for the reliability of the phase analysis as well as the robustness of the polarization selection rules in a broad range of orientational distribution widths.32 Another important conclusion concerning the ability to determine the orientational distribution width can also be made. In Figure 4, the θ0 versus σ curve with D ) 2.0 is nearly flat when σ is smaller than 20°. This is because the apparent θ value when σ ) 0° is close to the so-called SHG or SFG magic angle of 39.2°.99 If the D value is significantly away from the magic angle region, then the θ0 versus σ curve is not going to remain flat within such a large range of σ values. This means that for such D values the upper limit value of σ is much smaller; that is, the mathematically allowed distribution width is much smaller. Given the fact that the average orientational angle, θ0, of the CH3- group is determined accurately, the conclusion for θ ≈ 30° in the literature is therefore not possible from the phase analysis from the experimental data.47 With the accurately determined θ0 value for the CH3- group, the orientational angle, θ0, of the CH2- group of the interface ethanol molecule can thus be determined fairly accurately. With the analysis presented in Figure 4, we conclude that the θ0 value with a certain distribution width is essentially the same as the θ value when a δ distribution is assumed and that the distribution width has a upper limit, which is about 20° for the CH3- group at the vapor/ethanol interface. Such analysis and argument can be generally applied in other SFG-VS orientational analyses. 4.2.3. Orientation Analysis with the CH3-SS-Fermi Resonance Peak. In section 4.2.1, we mentioned that the orientational analysis with the 2930 cm-1 CH3-SS-Fermi peak was with problems. Here we present a discussion of these problems. The problem simply came from the unknown hyperpolarizability tensor ratios of this 2930 cm-1 peak. If one uses the experimental oscillator strength ratio in Table 3 between the values obtained for the ssp and the ppp polarization combination spectra of the vapor/CH3CD2OH interface, which is 0.023/0.007, to calculate orientational angle θ of the CH3- group, then one ends up with a value of 57°, when the same hyperpolarizability tensor ratios for the CH3-SS peak are used. This θ value is obviously inconsistent with the θ ) 45° ( 6° value obtained in section 4.2.1 using two pairs of experimental ratios, which are in nice agreement between themselves. Further examination


Figure 5. Strength-coupled orientational functional dr(θ) of pppss mode with different hyperpolarizability tensor ratio R for the methyl group. When θ is between 42° and 50°, the dr(θ) value is positive, and increases with the decrease of the hyperpolarizability tensor ratio, R.

of the problem indicated that the ppp SFG-VS intensity is also unproportionably higher for the 2930 cm-1 CH3-SS-Fermi peak than the 2875 cm-1 CH3-SS peak in the same polarization, as shown in Figure 2. If we examine Figure 1 closely, then we find that when the orientational angle of the methyl group is about 45° the SFG intensity of the CH3-SS mode in the ppp polarization combination should be nearly zero. In Figure 2, the CH3-SS mode at about 2872 cm-1 is indeed near the noise level, and this agrees well with the simulation curves in Figure 1. However, the Fermi resonance mode of the CH3-SS mode, which bears the same symmetry category with the CH3-SS mode, possesses an apparent SFG intensity at about 2930 cm-1 in the ppp polarization combination. This clearly indicates that there is some difference between the CH3-SS and CH3-SS-Fermi mode. Because both of them belong to the same symmetry category, the only thing that can be different in the calculations of these two modes is the hyperpolarizability tensor ratios that can be derived from the Raman depolarization ratio, F. Colles and Griffiths reported the Raman depolarization ratio of both the 2875 cm-1 (F ) 0.053) and the 2930 cm-1 (F ) 0.056) peaks for liquid CH3CH2OH at room temperature.51 However, using these two values to calculate the corresponding hyperpolarizability tensor ratios for these two peaks, assuming that they both possess the same C3V symmetry,32,88 one can only expect an even smaller ppp/ssp intensity ratio in the SFG-VS experiment for the 2930 cm-1 peak than that of the 2875 cm-1 peak. This is obviously in contradiction with the experimental observations as listed in Table 3 obtained from the experimental results in Figure 2. To make everything consistent with these experimental results, the F value for the 2930 cm-1 peak needs to be smaller than that of the 2875 cm-1 peak for the CH3CD2OH molecule. However, such a F value is not available in the literature. This fact is clearly illustrated in the orientation-dependent pppss oscillator strength simulation for the CH3- group in Figure 5. The pppss intensity increases several times as the R ) βaac/ βccc value becomes smaller when the tilt angle θ of the CH3group is a few degrees smaller than 50° and larger than 42°. Because the R value for the CH3-SS mode is 3.4, the R value for the CH3-SS-Fermi mode needs to be about 2.0 to 2.5 in order to produce a consistent ppp intensity for the 2930 cm-1 peak in the vapor/CH3CD2OH interface SFG-VS spectra. This

Gan et al. simulation also requires that as long as the CH3-SS-Fermi ppp intensity is to be explained successfully the tilt angle of the CH3- group has to be between 42° and 50°. This is in excellent agreement with the 45° CH3- group orientational angle obtained in section 4.2.1. A recent study on the photoacoustic stimulated Raman spectroscopy of CH3CH2OH, CH3CD2OH, and CD3CH2OH molecules in the gaseous phase46 not only confirmed above simulation results but also confirmed the vibrational spectral assignment of the ethanol molecule from SFG-VS studies.45 In this new Raman study on ethanol,46 the Raman depolarization ratios obtained for the 2885 and 2940 cm-1 peaks were the same as those reported previously by Colles and Griffiths, with the F value of the former slightly smaller than that of the latter peak.51 However, the F values for CH3CD2OH had the opposite trend; that is, the F value for the 2940 cm-1 peak is smaller than that of the 2885 cm-1 peak, consistent with the prediction above about the trend for the R value. Here, one needs to note that in the gas phase there is almost a 10 cm-1 blue shift of all of the spectral peaks from those peaks in liquid or at the vapor/liquid interface. It is also surprising that the gaseous Raman spectra peak position as well as the Raman spectra peak width closely resemble those of the corresponding SFG-VS vibrational spectra. Here, the slight difference between the CH3-SS and CH3SS-Fermi modes are clearly exhibited in the detailed analysis of the SFG-VS spectra. People have recognized the difference between these two modes by their different intensities before, and now we also understand their difference from their polarization dependence in the SFG-VS spectra. The polarization analysis of the SFG-VS spectra of the CH3-SS-Fermi peak requires that the CH3- group orientation is between 42° and 50°. This again confirms the θ0 ) 45° ( 6 ° obtained above. 4.2.4. Orientation of Methylene Group and Conformation of the Ethanol Molecule. With the above accurately determined θ0 value for the CH3- group, the orientational angle, θ0, of the CH2- group of the interfacial ethanol molecule can be determined fairly accurately using the interference effects in the SFGVS spectra. In the ethanol molecule, the angle between the C2 axis of the CH2- group and the C-C bond is about 125°. Now with the CH3- group θ0 ) 45° ( 6°, the θ0 of the CH2- group should be 80° ( 6° or 170° ( 6° from the surface normal if the C-C-O plane is perpendicular to the interface plane. θ0 ) 170° ( 6° is highly impossible because this would have made the O-H group above the interface, and furthermore all of the interference effects between the CH2- group spectral features, and the CH3- group spectral features should have been in contradiction to the experimentally determined relative phase in the SFG-VS spectra. For example, from the simulation in Figure 1, the CH2-SS in ssp at 170° would interfere destructively with the CH3-SS in ssp with any possible CH3- group θ (between 0° and 90°), whereas the CH2-SS-Fermi in ssp at 170° would interfere constructively with the CH3-AS in ssp. All of these defy the basic features of the SFG-VS experimental data as listed in Table 3. Simply put, because of the interference between the CH3-SS and CH2-SS in the ssp polarization combination spectra, according to Figure 1, the C2 axis of the CH2- group has to point above the interface. Here we see how the interference effects between different groups in a molecule are helping the determination of the molecular configuration at the interface. The interference effect further indicates that the C-C-O plane of the ethanol molecule is close to perpendicular to the interface plane. In keeping the θ0 ) 45° value of the CH3- group,


Figure 6. Orientational structure at the vapor/ethanol interface. The orientational angles for the methyl and methylene groups are deduced to be θCH3 ≈ 45° and θCH2 ≈ 80°. The value of ψCH2 and ψCH3 are very small; that is, the C-C-O plane in the ethanol molecule is nearly perpendicular to the interface.

rotation of the C-C-O plane along the C-C bond (ψCH3) can change the C2 axis orientation of the CH2- group. Such rotation can only make the θ0 of the C2 axis larger than 80°, that is, resulting in a smaller SFG-VS strength for the CH2- contributions. Analytical geometry calculation shows that when the C-C bond rotates about 43° the C2 axis would be lying completely flat at the interface; that is, zero SFG-VS contribution. This roughly equals to a 4.3° rotation for every 1° increase of the θ0 value of the C2 axis from 80°. Further rotation would change the sign of the CH2- SFG-VS strengths and also make the O-H bond above the interface. As one can see from the simulation in Figure 1, each degree increase of the θ0 of the C2 axis can reduce the oscillator strength by 10%, that is, 20% of the SFGVS intensity. Therefore, in order to have enough CH2- group contribution to the SFG-VS strength, ψCH3 can never be close to 43°. In fact, for the CH2- group strength observed in the SFGVS spectra, as shown in Figure 2 and the oscillator strength as listed in Table 3, this rotation has to be much less than half of the 43° value. This certainly keeps the C-C-O plane closer to the perpendicular position relative to the interface plane, even though one may not know whether it is completely perpendicular or not. Thus, the minimum energy configuration of the O-H bond can be determined. The O-H bond of the ethanol molecule shall tilt down at an angle about 130-135° from the interface normal. The determination of the conformation of the whole ethanol molecules is the result of the different constrains involved. Here we see that the orientation of the CH3- group limits the ranges of the orientation and the twist angle of the -CH2- group. And they are further limited by the relative phase of their SFG fields determined from the SFG spectral interference. Analysis of the orientational and twist-angle dependence of the SFG-VS intensity in different polarizations is adequate when no spectral interference is involved.89,100 Here it is clear that the analysis of the orientational and twist-angle dependence of the SFG-VS field strength is necessary when spectral interference is present. In this section, we demonstrated how the interference effects between the molecular groups helped to identify the relative orientation of the interfering molecular groups in the SFG-VS spectra. Thus, the conformation of the whole ethanol molecule at the vapor/ethanol interface is obtained, as illustrated in Figure 6. This conformation is certainly qualitatively expected for the ethanol molecule at the vapor/ethanol interface. However, using the interfacial spectroscopic technique to nail down the details of this structure certainly bears some significance.

J. Phys. Chem. C, Vol. 111, No. 25, 2007 8735 Such a well-positioned conformation of the interfacial ethanol molecule indicates that the interface ethanol molecule is generally well-ordered at the vapor/ethanol interface. So far, it has been shown that the simple liquid interfaces, such as the vapor/methanol and the vapor/acetone interfaces, and so forth, are generally ordered with relatively narrow orientational distributions,4,5,38,39,103 in contrast to the belief that they are generally very dynamic and disordered.7,101 With such an ordered first layer, it is also likely to form an ordered second layer, as in the recently reported antiparallel double-layer structure at the vapor/methanol, vapor/acetone, methanol/quartz as well as the vapor/acetonitrile interfaces.4,5,38,91 Recent SFGVS studies also reported the similar adsorption isotherm of the vapor/ethanol aqueous solution interfaces, such as that of the vapor/methanol and vapor/acetone interfaces.48,53 Despite the unlikely alternative qualitative explanations that were offered for these data,53,102 we surmise that this can be the evidence for a double-layer structure similar to those of the vapor/methanol and vapor/acetone interfaces. Therefore, as long as the disagreements exist, further experimental or theoretical studies are certainly needed in order to understand the interfacial structure and conformation at the molecular level. 4.3. Interference Effects in Different Experimental Configurations. There is more to be learned in the analysis of the interference effects in SFG-VS spectra in different experimental configurations. The experimental configuration study in SFGVS was discussed in detail elsewhere.104 Here we shall discuss the details of the interference effect in the vapor/ethanol interface SFG-VS spectra in different experimental configurations. Figure 7 presents the SFG-VS experimental spectra in different polarization combinations of the vapor/ethanol interface in two experimental configurations, that is, configuration I with β1 ) 62° and β2 ) 53°, and configuration II with β1 ) 37° and β2 ) 51°. Also plotted in Figure 7 are the simulations of the SFG-VS oscillator strength in different polarization combinations for the CH3-SS, CH3-AS, CH2-SS, and CH2-AS modes. As discussed elsewhere and mentioned above,104 the phase change of the 2930 cm-1 CH3-SS-Fermi peak in the ppp polarization combination in the two experimental configurations is a clear indication that the orientational angle, θ, of the CH3group is above 42°. Furthermore, the significant drop of the spectral intensity of the 2970 cm-1 peak from configuration I to configuration II clearly indicates the interference effects between the overlapping CH3-AS and CH2-SS-Fermi modes. If this peak is assigned only to the CH3-AS mode as in the previous literature,45 then the more than five times difference of the intensity of this peak in the two experimental configurations cannot be explained from the simulation in the pppas curves of the CH3- group, where a difference of only less than two times can be expected. Therefore, the previous assignment is further denied by the experimental-configuration-dependent analysis and the experimental data in the two different experimental configurations. Alternatively, from the simulations in Figure 7, the sspas curve is always negative for the CH3-AS mode, and the pppas and spsas curves are always positive for all CH3- group orientations in both experimental configurations; whereas for the CH2-SS-Fermi mode, which has essentially the same orientational dependence as the CH2-SS mode but with smaller amplitude as evident from the ssp SFG-VS spectra of the vapor/ CD3CH2OH interface, the sspss and the spsss curves are positive for all of the orientational angles in both experimental configurations, but the pppss curve changes sign around 40° in configuration I, and keeps being negative with a higher


Gan et al.

Figure 7. Left: SFG-VS spectra of the vapor/ethanol interface in two experimental configurations. The solid lines are fittings with the Lorentzian line shapes. The phase of each fitted peak is marked near the spectral peak position. The ? sign indicates that the peak is at the noise level, and its sign cannot be identified explicitly. Middle: simulation of the SFG-VS intensity for the CH3-SS and CH3-AS mode from the vapor/ethanol interface in different orientational angles. Right: simulation of the SFG-VS intensity for the CH2-SS and CH2-AS mode from the vapor/ethanol interface in different orientational angles. Here the twist angle of the CH2- group is set at 0°, as discussed above. In the simulation plots, the symmetric modes are solid lines, and the asymmetric modes are dashed lines. The factor sec(β) in eq 1 was included for comparison of the SFG-VS strength and phase in different experimental configurations.

amplitude in configuration II than in configuration I. With the knowledge of the orientational angle of the CH3- (45° ( 6°) and the CH2- (80° ( 6°) groups, as well as the relative amplitude of the pppss curves of both CH3-AS and CH3-SS-Fermi modes, one can see from Figure 7 that the destructive interference between these two modes is much larger in configuration II than in configuration I. Thus, the five times difference of the 2970 cm-1 peak in the ppp spectra of the two configurations can be explained satisfactorily. A quantitative simulation confirms that this intensity difference is between 5 and 10 times, consistent with the experimental measurement. The destructive interference of these two modes around 2970 cm-1 in the ssp polarization combination is also evident in Figure 2. From the simulation, it is clear that the sspas curve of the CH3- group bears a sign opposite of that of the sspss curve of the CH2- group. This is why even though the amplitudes of both are not very small; an even smaller SFG-VS spectral intensity was observed at this peak position in the ssp polarization combination for the vapor/CH3CH2OH interface. The above discussions indicate that the experimental configuration analysis may be used to determine the existence of overlapping spectral features when deuteration of the molecule is not achievable. Through studying of deuterated samples, the overlapping features originating from different molecular groups buried in a single peak can be clearly identified.45 This is the starting point for our interference analysis in this report. However, in many cases, deuteration of some groups in a molecule, especially when the molecule is more complex, is usually not achievable. Fortunately, in such cases the experimental configuration and polarization dependence of certain peaks in SFG-VS spectra can only be explained when the interference effect of overlapping peaks is assumed. Here the behavior of the intensities of the 2970 cm-1 peak in the two experimental configurations in Figure 7 is a convincing example. Therefore, applications of the SFG-VS experimental configu-

ration analysis in discerning the overlapping spectral features in the SFG-VS spectra can be expected for complex molecular interfaces. A fact that also needs to be addressed is that in both experimental configurations the CH2-AS spectral feature was essentially not observed. However, the simulation in Figure 7 indicates that it can be as strong as one-half of the CH2-SS mode, given the bond additivity model value βaca ) 0.94βccc. Such intensity should have been observed even with a tilt angle as flat as 80° ( 6°. Here the explanation lies in the fact that the simple bond additivity model values for the CH2-SS and CH2AS modes may not be accurate, and it has to be empirically corrected as discussed elsewhere.88 An estimation based on the empirical correction formula gives a βaca value about three times smaller than the βccc value for the CH2- group in ethanol and other molecules in which the CH2- groups were connected directly to the O-H group. This ensures an 8-10 times drop of the simulated CH2-AS SFG-VS intensity after the empirical correction. Strong CH2-AS SFG-VS intensity was indeed observed for the CH2- groups not connected directly to the O-H group, such as the center CH2- groups in the 1,3-propanediol and 1,5-pentanediol molecules at their vapor/liquid interface.43 Therefore, in the SFG-VS spectra, the spectral features of the different kinds of the CH2- groups can be clearly identified. Therefore, SFG-VS can also be used to interrogate such spectral details as well as intramolecular interactions at the interface.32 The interference effects in the SFG-VS spectra can be understood thoroughly with the SFG-VS data from different experimental configurations, along with the assistance of the simulations of the orientational dependence of the SFG-VS spectral strength in different polarization combinations. Here, we have shown that through such analysis the spectral details of the vapor/ethanol interface SFG-VS spectra can be clearly understood.

Spectral Interference and Molecular Conformation 5. Conclusions In this report, the conformation of the ethanol molecule at the vapor/ethanol interface was determined from the SFG-VS spectra interference effects and polarization analysis. Qualitative understanding of the interface molecular conformation was derived from many traditional methods, such as surface tension and surface potential measurement and so forth. X-ray and neutron diffraction also provided structural information, such as the thickness and depth profile of the various interfaces.105,106 However, quantitative knowledge of the interfacial molecular orientational conformation can be better studied with interface-specific spectroscopic methods, such as the SHG and SFG-VS techniques. Previous SHG and SFG-VS studies have demonstrated that interfacial molecular conformation can be determined by separate measurements of the orientational angles for different parts or molecular groups of an interfacial molecule.33,42 In this work, the detailed interference spectral features of different molecular groups and vibrational modes in the SFGVS spectra were used to provide quantitative information on the interfacial molecular conformation. Such study is possible because SHG and SFG-VS are coherent spectroscopic techniques. Therefore, analysis of the orientation-dependent phase information of the SFG field is not only possible but can also provide rich information on the molecular orientational conformation at the interface. For example, for the interfacial ethanol molecule, not only the orientational angles of the methyl and methylene group in one ethanol molecule are tightly correlated but their strengths and phases in the SFG-VS spectra are also tightly correlated and are dependent on their orientational angles and orientational distribution widths. Therefore, such correlation can be used to determine the orientational angles and the orientational distribution widths of both the methyl group and the methylene group. Such analysis can be carried out with the calculation and simulation of the SFG-VS mode-specific strength-coupled orientational functional for different molecular groups in different polarization combinations and different experimental configurations. Comparison of the strength and the sign (or phase) information contained in the strength-coupled orientational functional with the SFG-VS spectral data can provide detailed knowledge of the interference effects between different spectral features and detailed knowledge of the orientational structure of the different molecular groups. We carried out polarization analysis and experimental configuration analysis on the SFG-VS spectra of the vapor/ethanol and vapor/deuterated ethanol interfaces. We concluded that at the vapor/ethanol interface the CH3- group tilts at about 45° from the surface normal, pointing away from the liquid phase; the C2 axis of the -CH2- group tilts at about 80° from the surface normal, also pointing away from the liquid phase; and the O-C-C plane in the ethanol molecular posits nearly perpendicular to the liquid interface. The detailed analysis of the orientational distribution widths and twist angles of related molecular groups was also presented. Here the conclusion that the -CH2- group has to tilt away from the liquid phase can only be reached with the knowledge of the spectra overlap and the analysis of the interference between the overlapping spectral features. This clearly indicates the importance of the methodology and ideas presented in this report. We also presented the detailed discussions on how and to what extent the molecular orientation and orientational distribution width can be determined, how details of the SFG-VS spectral features can be quantitatively explained, and how experimental configuration analysis can be employed in spectral

J. Phys. Chem. C, Vol. 111, No. 25, 2007 8737 interference analysis. Such ideas and procedures can be applied to assist in the analysis of the SFG-VS spectra of more complex interfaces. Because details of the molecular vibrational spectroscopy can be obtained with SFG-VS from the molecular interface, one can use these advantages of SFG-VS to understand complex molecular vibrational spectral features in the condensed phase that are unable to be resolved with incoherent IR and Raman spectroscopy. These developments have demonstrated that SFG-VS is not only a powerful surface analytical technique but also a unique spectroscopic method for interpreting molecular spectroscopy, structure, and dynamics in general. These shall ensure broad applications of the SFG-VS technique, and all of these are possible because SFG-VS is an intrinsically coherent polarization spectroscopic technique. Acknowledgment. H.F.W. is thankful for support from the Natural Science Foundation of China (NSFC, No.20373076, No.20425309, No.20533070). References and Notes (1) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley-Interscience: New York, 1997. (2) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet, 2nd ed.; Wiley-VCH: New York, 1999. (3) Myers, D. Surfaces, Interfaces, and Colloids: Principles and Applications; VCH: New York, 1999; Chapter 8.1. (4) Chen, H.; Gan, W.; Wu, B. H.; Wu, D.; Guo, Y.; Wang, H. F. J. Phys. Chem. B 2005, 109, 8053-8063. (5) Chen, H.; Gan, W.; Lu, R.; Guo, Y.; Wang, H. F. J. Phys. Chem. B 2005, 109, 8064-8075. (6) Eisenthal, K. B. Acc. Chem. Res. 1993, 26, 636-643. (7) Miranda, P. B.; Shen, Y. R. J. Phys. Chem. B 1999, 103, 32923307. (8) Braslau, A.; Deutsch, M.; Pershan, P. S.; Weiss, A. H.; Als-Nielsen, J.; Bohr, J. Phys. ReV. Lett. 1985, 54, 114-117. (9) Wilson, K. R.; Schaller, R. D.; Co, D. T.; Saykally, R. J. J. Chem. Phys. 2002, 117, 7738-7744. (10) Eisenthal, K. B. Chem. ReV. 1996, 96, 1343-1360. (11) Faubel, M.; Steiner, B.; Toennies, J. P. J. Chem. Phys. 1997, 106, 9013-9031. (12) Shen, Y. R.; Ostroverkhov, V. Chem. ReV. 2006, 106, 1140-1154. (13) Gopalakrishnan, S.; Liu, D. F.; Allen, H. C.; Kuo, M.; Shultz, M. J. Chem. ReV. 2006, 106, 1155-1175. (14) Croxton, C. A. Statistical Mechanics of the Liquid Surfaces; Wiley: New York, 1980. (15) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: Reading, MA, 1994. (16) Smit, B. In Computer Simulation in Chemical Physics; Allen, M. P.; Tildesley, D. J., Ed.; Kluwer Academic Publishers: Boston, MA, 1993; pp 173-210. (17) Townsend, R. M.; Rice, S. A. J. Chem. Phys. 1991, 94, 22072218. (18) Klein, M. L. J. Chem. Soc. Faraday Trans. 1992, 88, 1701-1705. (19) Benjamin, I. Chem. ReV. 1996, 96, 1449-1475. (20) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407-451. (21) Kuo, I. F. W.; Mundy, C. J. Science 2004, 303, 658-660. (22) Duque, D.; Vega, L. F. J. Chem. Phys. 2004, 121, 8611-8617. (23) Stewart, E.; Shields, R. L.; Taylor, R. S. J. Phys. Chem. B 2003, 107, 2333-2343. (24) Taylor, R. S.; Shields, R. L. J. Chem. Phys. 2003, 119, 1256912576. (25) Patel, S.; Brooks, C. L. J. Chem. Phys. 2005, 123, 164502. (26) Jungwirth, P.; Tobias, D. J. Chem. ReV. 2006, 106, 1259-1281. (27) Mundy, C. J.; Kuo, I. F. W. Chem. ReV. 2006, 106, 1282-1304. (28) Chang, T. M.; Dang, L. X. Chem. ReV. 2006, 106, 1305-1322. (29) Shen, Y. R. Nature 1989, 337, 519-525. (30) Zhang, W. K.; Wang, H. F.; Zheng, D. S. Phys. Chem. Chem. Phys. 2006, 8, 4041-4052. (31) Gan, W.; Wu, D.; Zhang, Z.; Feng, R. R.; Wang, H. F. J. Chem. Phys. 2006, 124, 114705. (32) Wang, H. F.; Gan, W.; Lu, R.; Rao, Y.; Wu, B. H. Int. ReV. Phys. Chem. 2005, 24, 191-256. (33) Zhuang, X.; Miranda, P. B.; Kim, D.; Shen, Y. R. Phys. ReV. B 1999, 59, 12632-12640. (34) Sionnest, P. G.; Hunt, J. H.; Shen, Y. R. Phys. ReV. B 1987, 59, 1597-1600.

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Spectral Interference and Molecular Conformation at Liquid Interface

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