J. Phys. Chem. C 2007, 111, 1783-1787
1783
Fast Motion of the Surface Alcohol Molecules Deduced from Sum-Frequency Vibrational Spectroscopy Jaeho Sung and Doseok Kim* Department of Physics and Interdisciplinary Program of Integrated Biotechnology, Sogang UniVersity, Seoul 121-742, Korea ReceiVed: September 29, 2006; In Final Form: NoVember 13, 2006
Sum-frequency generation (SFG) vibrational spectroscopy was used to investigate the surface of the homologue series of alcohols from methanol to octanol. It was found that SFG signal strengths from the terminal methyl group of short-chain alcohols cannot be explained by assuming the surface molecules are fixed in time. Introduction of the rotational motion with time scale comparable to the dephasing time of the vibrational mode of the terminal methyl group (∼0.7 ps) was able to explain the reduction of the SFG signal by motional averaging effect (Wei, X.; Shen, Y. R. Phys. ReV. Lett. 2001, 86, 4799). This time scale of motion increased with the increase in the molecule size and bulk viscosity.
Introduction Molecules in liquid are constantly moving very fast. Their translational motion is responsible for diffusion and Brownian motion. They also rotate about their center-of-mass position. This rotational motion, in particular, has been studied using various techniques including Rayleigh scattering, NMR, pumpprobe, and dielectric relaxation.2-6 For molecules in common liquids like water and methanol, the time scale of rotational motion is in the picosecond range.2-6 For example, femtosecond pump-probe spectroscopy found that the rotation time of water molecule ranges from ∼0.7 ps to ∼13 ps depending upon its hydrogen-bonding strength with the neighboring molecules.2 Molecular dynamics simulation has also found that rotation time of the molecule in room-temperature liquid methanol is a few picoseconds.4 On the other hand, the rotation time deduced from Rayleigh scattering was ∼2 ps for ethyl bromide molecules in the liquid, which increased to ∼840 ps for 1-hexadecil bromide.5 The above trend of increase in the rotation time is expected from the Einstein-Stokes relation utilizing viscosity change with the increase in the chain length of the molecule. Most of the reports up to now have studied the motion of the molecules in bulk liquid. As surface molecules are in a very different environment from those of the bulk, it would be interesting to study the motion of the surface molecules as compared to the molecules in bulk. However, there have been hardly any reports which studied experimentally the motion of the surface molecules. Lack of a proper experimental tool to probe specifically the molecules at the liquid surface has been the main difficulty. The only previous studies utilized the surface sensitivity of the second-order nonlinear optical process, and rotational motion of dye molecules adsorbed at the air-water interface was studied by orientational hole burning followed by surface second-harmonic generation (SHG) with a time-delayed probe pulse.7-9 The results showed that the rotational motions of rhodamine 6G and Coumarin 314 are slower at the interface than in bulk water,7,8 whereas that of eosin B was 90 ps, faster than the rotational motion in bulk water.9 * To whom correspondence should be addressed.
For common and more relevant molecules such as water and alcohol, their motion is expected to be much faster than that of the above dye molecules. However the experimental difficulty has not yet allowed us to understand much about the surface motion of these common molecules. To probe specifically the molecules at the surface, techniques utilizing second-order nonlinear optical processes are the most suitable. On the other hand, analysis of the results from these experiments to find out the surface molecular conformation up to now has assumed the molecules are fixed in place within the observation time. The only exception is the report by Xing and Shen,1 where they proposed fast rotation of surface molecules can affect the strength of the specific sum-frequency signal. They applied this idea to the stretch mode of free OH bond of the water molecule at the surface and suggested that peak strength of that mode in a certain polarization combination vanishes for the rapid-motion limit. In this report, we investigated the surface of several alcohols using surface sum-frequency generation (SFG) vibrational spectroscopy. For small molecules like methanol, the sumfrequency signal of CH3 antisymmetric stretch (r-) mode for certain polarization combinations was nearly zero, and it grew as the molecule became bigger. Analysis of the data indicated that the motional averaging effect must be considered for the SFG spectra of small molecules. Specifically, the SFG spectra of methanol in which the absence of the r- signal has been a mystery10 could be understood by introducing the fast rotational motion of the surface methanol molecules. The detailed simulation shows the specific SFG peak strength was indeed reduced by introducing the motion of the surface molecules. This peak strength was analyzed to find out the time scale of motion semiquantitatively, showing that the small surface molecules move very fast while the motion slows down as the molecular size increases. Theoretical Background A brief theoretical description of the surface SFG is given for the convenience of later discussion. From the basic theory of the surface SFG,11 the SFG output intensity in the reflection direction with visible and infrared input beams is given by
10.1021/jp0664263 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/06/2007
1784 J. Phys. Chem. C, Vol. 111, No. 4, 2007 iφ I(ωSF) ∝ |χ(2) NRe +
Sung and Kim
(2) 2 | ∑q χijk,q
(1)
iφ where χ(2) NRe is the nonresonant part of the nonlinear suscep(2) tibility with its phase factor eiφ, and the resonant part χijk,q in eq 1 is related to the molecular hyperpolarizabiliy and a timedependent direction cosine between the laboratory coordinates and the molecular coordinates as1
χ(2) ijk )
(2) λµν ) Ns∑∑aq,λµν〈Θq,ijk 〉 ∑q χijk,q q λµν
(2)
where
∫0∞Dkν(t - τ)ei(ω
λµν (ωIR,t) ) -iDiλ(t) Djµ(t) Θq,ijk
IR-ωq+iΓq)τ
dτ (3)
Here aq,λµν, ωq, and Γq are the amplitude, resonance frequency, and line width of the qth molecular vibrational mode, respectively, and Ns is the surface number density of molecules. Diλ(t) ) ˆı‚λˆ (t) is a time-dependent direction cosine between the laboratory coordinates i ) (X,Y,Z) and the molecular coordinates λ ) (ξ,η,σ). We assumed the terminal methyl mode under investigation is mainly homogeneously broadened as suggested from ref 12 and also assumed the visible input is far from resonance. In the limit where molecular motion becomes much slower such that Diλ(t) can be taken out of the integration, eq 2 becomes the more familiar equation as follows.
χijk,q(ω2) ) Ns
∑q ∑ λµν ω
2
aq,λuν
〈DiλDjµDκν〉 - ωq - iΓq
(4)
In this study, the SFG signal strength of the terminal methyl symmetric stretch mode (r+) was compared with that of the antisymmetric stretch mode (r-). As both modes consist of three C-H stretch vibrations, we can construct the hyperpolarizability components for each mode starting from each single C-H mode using the bond-additive model.13 The single bond depolarization ratio R is defined as follows.
∂R(1) ∂R(1) ⊥ | )R ∂x ∂x
(5)
where R⊥ and R| refer to the polarizabilities parallel and perpendicular to the single C-H bond, respectively, and x is the distance between the carbon and the hydrogen. This single bond depolarization ratio has been obtained theoretically for a C-H bond as R ) 0.14,14 which yields the known depolarization ratio for the methyl symmetric stretch mode15
r)
R(2) ξξσ(r+) R(2) σσσ(r+)
)
(3/2) cos Θ(sin2 Θ + R(1 + cos2 Θ)) 3 cos Θ(cos2 Θ + R sin2 Θ)
) 2.3 (6)
where σ is along the symmetry axis of CH3 and ξ is the unit vector normal to σ as in Figure 1. Θ is an angle between the single C-H bond and the symmetry axis of the methyl group. Finally, the nonvanishing molecular hyperpolarizability (2) Rσηη (r-) for the methyl antisymmetric stretch mode can be compared with R(2) σσσ(r+) for the symmetric stretch mode as
R(2) σηη(r-) R(2) σσσ(r+)
)
(3/4) cos Θ sin2 Θ 3 cos Θ(cos2 Θ + R sin2 Θ)
) 0.97
(7)
Experimental Section The SFG experiment employed a home-built optical parametric generator/amplifier (OPG/OPA) system pumped with a
Figure 1. Molecular coordinates (ξ,ζ,η) attached to the methyl group shown with respect to the laboratory coordinates (X,Y,Z).
picosecond Nd:YAG laser (Continuum PY61-10, 10-Hz repetition rate).16 The OPG/OPA based on a LiNbO3 crystal generated a tunable IR pulse from 2.5 to 4 µm, and the second harmonic of the Nd:YAG laser fundamental beam was used as the visible input beam. Typical input energies were 1 mJ/pulse and ∼150 µJ/pulse, and incident angles were θvis ) 49° and θIR ) 60° for the visible and the tunable infrared beams, respectively. The pulse widths of the input beams were about 30 ps. The two beams were focused and overlapped at the air/liquid interface, and the sum-frequency output in reflection direction was spatially and spectrally filtered and detected by using a photomultiplier tube. Typically, the data for the spectrum were taken at every 5 cm-1, and at least 200 laser shots were averaged for each data point. The spectrum was normalized to the sumfrequency spectrum from a z-cut quartz sample. The frequency of the infrared beam was calibrated by measuring the absorption spectrum from a polystyrene film. Alcohols (CnH2n+1OH with n ) 1-8) purchased from Aldrich had a purity exceeding 99.5% and were used without further purification. The sample temperature was room temperature (21 °C) for all the experiments. Results and Discussion Shown in Figure 2 are the representative SFG spectra from various alcohol (methanol, propanol, pentanol, and heptanol) surfaces at the CHx stretch vibration region. Parts a-c of Figure 2 represent SFG spectra of alcohols with different polarization combinations: (a) SSP (S, sum-frequency light; S, visible light; P, infrared light), (b) PPP, and (c) SPS. These spectra are similar to the ones from previous papers, except for small differences due to change in the local field factors resulting from the different experimental geometry.10,17,18 The SSP spectrum from the methanol surface shows strong signals from CH3 symmetric stretch (r+) mode at 2830 cm-1 and Fermi resonance around 2945 cm-1,19,20 while overall signal intensities for PPP and SPS spectra are very low. SSP spectra from other alcohol surfaces show strong signals from r+ and Fermi resonance modes at 2880 and 2947 cm-1, respectively.10,17,21 A notable feature is the CH3 r- mode at 2970 cm-1 for PPP and SPS, which becomes appreciable for propanol and shown to grow further with the increase in the chain length. The appearance of the peak around ∼2850 cm-1 starting from heptanol indicates that the gauche defects develop as the alkyl chain gets longer.10,17 Figure 3 represents the SFG peak ratios A(r+, PPP)/A(r+, SSP), A(r-, PPP)/A(r+, SSP), and A(r-, SPS)/A(r+, SSP) deduced from fitted results of the alcohol spectra. A(r+, PPP)/
Fast Motion of Surface Alcohol Molecules
J. Phys. Chem. C, Vol. 111, No. 4, 2007 1785
Figure 2. Surface SFG spectra of methanol, propanol, pentanol, and heptanol. (a) SSP, (b) PPP, and (c) SPS. Each spectrum is shifted vertically for clarity, and dashed lines in the spectra indicates the peak positions of r+ (for SSP) and r- (PPP and SPS) modes used for the analysis.
A(r+, PPP)/A(r+, SSP), A(r-, PPP)/A(r+, SSP), and A(r-, SPS)/A(r+, SSP) are all different. This inconsistency becomes the most serious for methanol. The analysis based on comparing the r+ peak strengths predicts the methyl group is tilted ∼45° from the interface normal, while from A(r-, PPP)/A(r+, SSP) ∼ 0 dictates the molecule should be nearly upright. Finally A(r-, SPS)/A(r+, SSP) ∼ 0 from the experiment along with the theory in the inset of Figure 3c indicates the molecule should be lying almost flat at the surface. This contradiction illustrates that we could not fully explain the molecular orientation by assuming the molecules are frozen in time. On the other hand, the peak strengths seem to agree better with theory as the chain gets longer. For heptanol, A(r+, PPP)/ A(r+, SSP) suggests the methyl groups are tilted ∼40° from the surface normal, and r- peaks in PPP and SPS spectra are only slightly larger than the prediction.22 For very bulky molecules like the hexadecanol monolayer on water or ionic liquid molecules like 1-butyl-3-methylimidazolium tetrafluoroborate, ([BMIM]BF4), r+ and r- peak strengths also agree reasonably well with the theory assuming slow motion of the surface molecules.15,25,26 Thus the analysis assuming molecules are fixed in time can be applicable at least for large molecules As the above difficulties cannot be resolved easily, we then tried to analyze the SFG spectra taking into account the fast motion of the surface molecules.1 In the extreme case of very fast rotation of molecules within the time scale of 1/Γq, eqs 2 and 3 would yield the following nonlinear susceptibility.
∑q ∑ λµν ω
χijk(ω2) ≈ Ns
2
Figure 3. SFG peak ratios extracted from fitted results of various alcohol spectra. (a) A(r+, PPP)/A(r+, SSP), (b) A(r-, PPP)/A(r+, SSP), and (c) A(r-, SPS)/A(r+, SSP). Insets represent the corresponding calculated ratio values vs molecular tilt angle (θ, shown in Figure 1) for δ-function-like polar distribution (σ ) 0), and a Gaussian distribution with σ ) 15°.
A(r+, SSP) is constant, but the other ratio values are shown to increase with increasing chain length. The insets in Figure 3 show the corresponding ratio values from theory as a function of the tilt angle θ of the terminal methyl group (shown in Figure 1). We assumed the molecules are fixed in time and used eqs 6 and 7 from the bond-additive model to compare the peak strengths of r+ and r- modes.13,14 Contradiction between the data and the theory is obvious, as the tilt angles deduced from
aq,λµν - ωq - iΓq
〈DiλDjµ〉〈Dκν〉
(8)
In this fast motion limit, second-order susceptibility is proportional to the product of time-averaged directional cosines of the Raman tensor 〈DiλDjµ〉 and dipole transition moment 〈Dκν〉, and it could make the SFG vanish for certain modes. We can apply this idea to the r- mode, whose dipoles lie close to η-ξ plane as in Figure 1. For s-polarized input beam, the direction cosine Diλ(t) ) ˆı‚λˆ (t) for the infrared dipole of the r- mode in eq 8 would change sign under the fast rotation of the molecule in the φ or ψ direction and would average out to zero. Thus it seems plausible that the vanishing r- peak in the SPS spectrum is caused by the fast rotation of the molecule. It can be shown that, for PPP, the terms consisting of A(r-, PPP) would all average out to zero under the rotation of the molecule in the ψ-direction. The appropriate time scale in this case is 1/Γq ∼ 0.7 ps, the dephasing time of the methyl group stretch vibration, over which the SFG signal is generated by free-induction
1786 J. Phys. Chem. C, Vol. 111, No. 4, 2007
Sung and Kim estimated the time scale of the rotational motion is
