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Measuring Complex Sum Frequency Spectra with a Nonlinear Interferometer Jing Wang, Patrick J. Bisson, Joam M. Marmolejos, and Mary Jane Shultz* Laboratory for Water and Surface Studies, Chemistry Department, Tufts University, Medford, Massachusetts 02155, United States S Supporting Information *

ABSTRACT: Currently, the only techniques capable of delivering molecular-level data on buried or soft interfaces are the nonlinear spectroscopic methods: sum frequency generation (SFG) and second harmonic generation (SHG). Deducing molecular information from spectra requires measuring the complex componentsthe amplitude and the phaseof the surface response. A new interferometer has been developed to determine these components with orders-of-magnitude improvement in uncertainty compared with current methods. Both the sample and reference spectra are generated within the interferometer, hence the label nonlinear interferometer. The interferometer configuration provides experimenters with wide latitude for both the sample enclosure and reference material choice and is thus widely applicable. The instrument is described and applied to the well-studied octadecyltrichlorosilane (OTS) film. The OTS spectra support the interpretation that variation in fabrication solvent water content and substrate preparation account for differences in OTS spectra reported in the literature.

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accurate on the nanometer scale. Uncertainty in positioning results in phase uncertainty of ±π.13 In this Letter, we report creation of a nonlinear interferometer designed to overcome the phase accuracy and positional challenges of current techniques. The interferometer is demonstrated with application to an octadecyltrichlorosilane (OTS, CH3(CH2)17SiCl3) film on fused silica. OTS has become a defacto standard test surface, despite the OTS SFG spectral variations in the literature.10,17−22 The superior accuracy of a truly interferometric technique reveals the likely source for this variation. The basic interferometer layout is illustrated in Figure 1. The nonlinear interferometer contains several features that result in orders-of-magnitude improved phase resolution. (a) Positional accuracy and stability are facilitated by the embedded, linear Mach−Zehnder interferometer (segments A−D). In use, a tracker beam inserted along with the visible excitation beam provides interferometric positional accuracy. Incorporating the interferometric tracker beam signal into a position-control feedback loop provides active stabilization. Because the nonlinear and linear interferometers share common optics, when the tracker signal is stable, so is the SF signal. Typical long-term phase stability is better than 1°. (b) Interfering SF signals are generated in the combiner and detected at both detectors I and II. Signals at detectors I and II are complementary (see below); the sum is independent of interference, thus providing normalization. (c) Once calibrated, an intensity and phase measurement can be obtained in a single

oft, buried, and highly dynamic interfaces play key roles in settings as diverse as the environment, biology, and energy production. Probing such surfaces at the molecular scale without perturbing the interface is a challenging quest. It is thus not surprising that the only techniques currently capable of delivering data on this scale, sum frequency generation (SFG) and second harmonic generation (SHG), have attracted considerable attention and experimental effort.1−4 Long ago (1965),5 it was recognized that the nonlinear nature of SFG that renders it surface sensitive also means that the measured spectra are inherently complex (in the mathematical sense); the measured response is the square of the complex amplitude. Hence, deducing molecular-level information such as surface coverage, orientation, or interactionsinformation typically determined in analogous linear, bulk spectroscopyrequires measuring the complex components. Realization and measurement were separated by decades, reflecting the challenges associated with measurement and analysis. Measurement of the complex response was first demonstrated (1986) for second harmonic generation.6 Due to the greater molecular information content, there remained abundant interest in measuring the complex response for vibrational SFG. This was first reported in 2007 by Shen and co-workers.7 Since then, several reports have followed with labels such as phase or heterodyne measurement.8−13 All exploit wave interference between the SF beams generated by a reference and that generated by a sample. Current complex response measurement techniques fall into two broad categories: scanning7,9,14 and broad-band.8,11,12,15,16 In both cases, the most stringent requirement is that the sample must be positioned at the same location as the surface used in calibration. The sum frequency (SF) beam wavelength is on the order of a few hundred nm; therefore, the replacement must be © XXXX American Chemical Society

Received: April 13, 2016 Accepted: May 9, 2016

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DOI: 10.1021/acs.jpclett.6b00792 J. Phys. Chem. Lett. 2016, 7, 1945−1949

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The Journal of Physical Chemistry Letters

often, the reference phase is declared to be zero, though recent work23 has questioned this assumption; furthermore, it has been shown to be incorrect for z-cut quartz.24 The spectra reveal resonances as follows. The SF response is well-known25 to consist of real and imaginary parts Re = Re NR +

∑ q

Im = Im NR −

Aq(ω − ωq) (ω − ωq)2 + Γq 2

∑ q

(ω − ωq)2 Γq 2

(3)

where Aq, ωq, and Γq are the amplitude, resonant frequency, and bandwidth of the qth resonance. Re NR (Im NR) is the real (imaginary, often assumed to be zero) part of the nonresonant signal. (Note that in the case of resonances forming a continuous band, the sums are replaced with integrals over the density of vibrational states.) The literature is not explicit about how these real and imaginary components relate to the amplitude and phase of the SF signal. This relationship is discussed here. The SF amplitude is related to the Euler phase, φe, and amplitude, ( .

Figure 1. Nonlinear interferometer schematic showing the infrared beam splitter (IR-BS), visible beam splitter (Vis-BS), reference (R), sample (S), and beam combiner (BC). Beams include the infrared (ω2) and visible (ω1) driving beams and the generated reference (ωSF(R)) and sample (ωSF(S)) SF. A−F label the various path lengths; I and II indicate detectors.

scan rendering full complex vector measurement no more timeconsuming than a normal intensity (hereafter labeled scalar) SFG measurement. (d) Duplicates of any optical elements (lenses or windows) required by the sample (in segments C, D, or F) can be introduced into the corresponding reference (A, B, or E) segment, making the interferometer extremely adaptable. Specifically, it allows an enclosed cell sample. (e) Similarly splitting ratios can be modified to ensure that the sample and reference generate comparable intensity signals. (f) The phase of weak sample signals can be accurately determined via a direct measurement of the interferogram (described in the Supporting Information). Single scan phase measurement is achieved following calibration that uses the phase reference surface in both sample and reference positions. Use of the same material ensures that the relative phase between the sample and reference is zero. Calibration produces the reference intensity spectrum, ΣR, the combiner reflectance, rC, and transmittance, tC, and any instrument phase, δresid. All are functions of the frequency; in principle, once these are determined for a given set of optics, they do not change and thus are characteristic of the interferometer. The final factor is an optical overlap, M. M is the ratio of the interferogram amplitude to 4 rCtCΣ R ΣS . M describes the relative interferogram amplitude and is determined with a reference material in both sample and reference positions. Due to the relative reflected π phase shift at the combiner, beams directed to detectors I and II are complementary; the sum, Σ, is independent of interference. This provides normalization as well as the sample intensity spectrum, ΣS

ΣS = Σ − Σ R

Aq Γq

(eiφe = Re + i Im

(4)

where the real and imaginary parts are given by eq 3. As detailed in the Supporting Information, the Euler amplitude and phase are given by a linear superposition of the component waves. This simplifies in the case of a single resonance as (=

Ao (ω − ωo) + Γo 2

⎫ ⎧ ⎪ ⎪ (ω − ωo) ⎬ φe = arccos⎨ ⎪ 2 2 ⎪ ⎩ (ω − ωo) + Γo ⎭ ⎧ ⎫ ⎪ ⎪ Γo ⎬ = arcsin⎨ ⎪ 2 2 ⎪ ⎩ (ω − ωo) + Γo ⎭

(5)

The sign ambiguity in the square root is resolved by adopting the convention that all phases are positive;7 a negative measured phase indicates a negative amplitude, A. This Letter reports results of measuring an OTS film with a scanning, nonlinear interferometer. Unlike current scanning measurements, this interferometer uses a surface-generated reference beam. In contrast to all current methods, this instrument simultaneously generates the sample and reference beams (see Figure 1). The surface, OTS, is well-studied with both scalar and so-called phase-sensitive SFG.10,17−22,26,27 Phase and spectra of the film used in the present study are shown in Figure 2. All OTS spectra in the literature contain two main peaks, but they differ in relative intensity from 1:0.6 to nearly 1:1. Smaller features also differ. With the exception of one study discussing water in the fabrication process,20 these variations have been unremarked in the literature. Spectral analysis (below) supports the view that water in the fabrication solvents, prefabrication surface preparation, and the condition of the OTS precursor all affect the final film. To our knowledge, the phase spectrum reported in Figure 2 is the first full-band phase spectrum reported in the literature. Note that the measured phase varies from −90 to +90° due to calculation via eq 2, the inverse sine. Procedures found in the literature use an

(1)

Operating the interferometer with a built-in 90° phase shift between the sample and reference ensures a sine dependence on the phase difference between the sample, δS, and the reference, δR. Letting Δ be the difference between the detector I and II signals {(rC − tC)(Σ R − ΣS) + 4M rCtCΣ R ΣS sin(δS − δresid − δ R )} Δ = (Σ R + ΣS) Σ

(2)

Thus, if the reference phase is known or chosen by convention, the sample phase is determined via an arcsine function. Most 1946

DOI: 10.1021/acs.jpclett.6b00792 J. Phys. Chem. Lett. 2016, 7, 1945−1949

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example of differing film preparation conditions resulting in films with differing spectra and hence different properties. Figure 4 illustrates the effect of interference between these

Figure 2. Experimental scalar (left axis, blue squares) and phase (right axis, wine half triangles) spectrum of the OTS film relative to +xoriented, z-cut, α-quartz. Note that both scales are chosen to vertically offset the two spectra. The scalar (dark blue line) and phase (red line) are modeled according to eq 3. Resonances are indicted by arrows.

Figure 4. Re parts of the 2875 cm−1 CH3 symmetric stretch (orange solid line) and the 2884 cm−1 α-CH2 antisymmetric stretch (blue solid line) compete to generate a peak in the Re (red half circles) spectrum. Similarly, the Im parts of the 2875 cm−1 CH3 symmetric stretch (orange dashed line) and the 2884 cm−1 α-CH2 antisymmetric stretch (blue dashed line) compete to generate a dip and peak in the Im (magenta stars) spectrum. Resonances to either side also add, resulting in the deduced Re and Im spectra shown.

inverse tangent, problematic near strong resonances for which the phase is ±90°. The phase and spectra are difficult to interpret directly because the scalar intensity is the square of the real and imaginary parts; the phase is a weighted combination of the component phases. Both experimental spectra thus result from interferences among resonances. The real and imaginary parts, however, are linear combinations of the component resonances, as shown in eq 3. Thus, the motivation for and goal of measuring the complex (or vector) SFG response is to generate the real and imaginary spectra so that the component resonances can be identified. Real and imaginary spectra of OTS are shown in Figure 3.

opposite amplitude, neighboring peaks generating features in the Re and Im spectra. The interference produces an asymmetric shape in the scalar spectrum, appearing as a steep drop on the blue side of the first prominent peak. The second prominent peak in the scalar spectrum at 2940 cm−1 also results from interference, not so clear in the intensity spectrum but quite obvious in the Re and Im spectra. The literature agrees on assignment of the 2931 cm−1 resonance as the CH3 Fermi resonance.7,18 Agreement between the symmetry and the sign of the amplitude supports this assignment. There is no agreement on either the frequency or assignment of the higher-frequency peak. It has been observed as a weak feature at 2958 cm−1 and assigned to the CH3(as)7 and at 2948 cm−1 assigned to the α-CH2(a).18 We observe an additional peak that aids in resolution of this assignment, the peak at 2901 cm−1 with positive SF amplitude. This resonance sits in a valley between the two pairs of prominent peaks, resulting in a cancellation that renders it difficult to observe in previous studies (although vestiges are visible). The sign of the amplitude supports assignment of this peak as the α-CH2(as), implying that the 2946 cm−1 peak is due to the CH3(as). The CH3(as) is doubly degenerate, a degeneracy that is partially lifted giving rise to a weaker companion resonance at 2962 cm−1. This companion peak is quite clear in the phase spectrum. Finally, the large bandwidth of the CH3 and CH2 resonances suggests a broad orientation distribution, reflective of the high water content in film fabrication leading to greater molecular-level disorder. A consistent set of C−H assignments is given in Table 1. The remaining component required for an excellent fit is a broad resonance to the blue end of the C−H stretches. This spectral location is consistent with hydrogen-bonded OH stretches. Due to its width, this feature disappears into the baseline beyond 2975 cm−1; however, its effect on boosting the amplitude of the intensity spectrum at high frequency makes it relatively easy to identify. This feature is reasonable given the

Figure 3. Real (red half circles) and imaginary (magenta stars) spectra generated from data in Figure 2. (Details are contained in the Supporting Information.) Identified resonances are indicated by arrows.

A clear example of two interfering resonances is illustrated by the major OTS peak in the scalar spectrum at 2875 cm−1. Fitting shows that the peak consists of the CH3(ss) stretch at 2875 cm−1 and a resonance at 2884 cm−1. The latter resonance is often weak and has contradictory assignments as the antisymmetric7 and symmetric stretch18 of the α-CH2 group (the CH2 group attached to the Si). For the measured film, it is a strong resonance. On the basis of the sign of the amplitude, the remaining spectrum, and an isotope study,18 it is assigned as the α-CH2(ss). The contrasting strength of this resonance is an 1947

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Table 1. Amplitude, Frequency, and Bandwidth for the Seven Identified Resonances Plus the OH Tail from High Frequency A ωo Γ

1

2

3

4

5

6

7

8

0.32 2847 14 gauche defects

0.63 2875 12 CH3(ss)

−0.3 2884 8 α-CH2(ss)

0.09 2901 7.5 α-CH2(as)

0.17 2931 8 CH3(FR)

−0.48 2946 10 CH3(as)

−0.22 2962 13 CH3(as)

−2.8 3050 60 OH

high water content during fabrication and storage of the film in a 55% relative humidity environment. The final feature of the nonlinear interferometer is its ability to sensitively determine the magnitude and phase of the nonresonant component even when the amplitude is small. The scaler spectrum shows a constant intensity from 2600 to 2750 cm−1, indicative of a nonresonant response. Because the signal in this region is quite small, the difference technique (eqs 1 and 2) is dominated by noise. The interferometer provides an easy method to determine the nonresonant amplitude and phase via direct inspection of the interferogram, discussed in the Supporting Information. The data clearly reveal a −90° nonresonant phase of the sample relative to the +x oriented, z-cut quartz reference. The nonresonant amplitude is small, −0.034. These parameters are used in the fitting shown in Figure 2. In summary, this Letter reports creation of a nonlinear interferometer. The instrument produces order-of-magnitude (from ±π to better than 1°) improved measurement of the SF phase. The instrument is versatile, supporting a wide range of sample configurations as well as choices of the phase reference. Applying it to an OTS film supports the suggestion that surface preparation and water in the fabrication solvent explain variations in the OTS spectra reported in the literature.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Partial support by the United States National Science Foundation, Grant Number CHE1306933 is gratefully acknowledged. Financial support by Schlumberger and by the Tufts University Faculty Research Fund is also gratefully acknowledged.

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REFERENCES

(1) Shen, Y. R. Principles of Nonlinear Optics; John Wiley & Sons: New York, 2002. (2) Shen, Y. R. Fyndamentals of Sum Frequency Spectroscopy; Cambridge University Press: Cambridge, U.K., 2016. (3) Shen, Y. R.; Ostroverkhov, V. Sum-Frequency Vibrational Spectroscopy on Water Interfaces: Polar Orientation of Water Molecules at Interfaces. Chem. Rev. 2006, 106, 1140−1154. (4) Shultz, Mary Jane Sum Frequency Generation: An Introduction Plus Recent Developments and Current Issues. In Advances in MultiPhoton Processes and Spectroscopy; Lin, S. H., Villaeys, A. A., Fujimura, Y., Eds.; World Scientific: Singapore, Japan, 2008; Vol. 18, pp 133− 200. (5) Chang, R. K.; Ducuing, J.; Bloembergen, N. Relative Phase Measurement between Fundamental and Second Harmonic Light. Phys. Rev. Lett. 1965, 15, 6−8. (6) Kemnitz, K.; Bhattacharyya, K.; Hicks, J. M.; Pinto, G. R.; Eisenthal, K. B.; Heinz, T. F. The Phase of Second-Harmonic Light Generated at an Interface and Its Relation to Absolute Molecular Orientation. Chem. Phys. Lett. 1986, 131, 285−290. (7) Ji, N.; Ostroverkhov, V.; Chen, C.-Y.; Shen, Y.-R. Phase-Sensitive Sum-Frequency Vibrational Spectroscopy and Its Application to Studies of Interfacial Alkyl Chains. J. Am. Chem. Soc. 2007, 129, 10056−10057. (8) Stiopkin, I. V.; Jayathilake, H. D.; Bordenyuk, A. N.; Benderskii, A. V. Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy. J. Am. Chem. Soc. 2008, 130, 2271−2275. (9) Yamaguchi, Shoichi; Tahara, Tahei Heterodyne-Detected Electronic Sum Frequency Generation: Up Versus Down Alignment of Interfacial Molecules. J. Chem. Phys. 2008, 129, 101102/1−101102/ 4. (10) Covert, P. A.; Fitzgerald, W. R.; Hore, D. K. Simultaneous Measurement of Magnitude and Phase in Interferometric SumFrequency Vibrational Spectroscopy. J. Chem. Phys. 2012, 137, 014201/1−014201/6. (11) Hua, W.; Chen, X.; Allen, H. C. Phase-Sensitive Sum Frequency Revealing Accommodation of Bicabonate Ions, and Charge Separation of Sodium and Carbonate Ions within the Air/Water Interface. J. Phys. Chem. A 2011, 115, 6233−6238. (12) deBeer, A. G. F.; Samson, J.-S.; Hua, W.; Huang, Z.; Chen, X.; Allen, H. C.; Roke, S. Direct Comparison of Phase-Sensitive Vibrational Sum Frequency Generation with Maximum Entropy

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EXPERIMENTAL METHODS The visible excitation is 532 nm, and the infrared is generated by an OPG-OPA described elsewhere.28 Z-cut, α-quartz surfaces oriented +x are used for reference and calibration. A cw-HeNe beam inserted along with the visible excitation provides the tracker beam. Interferometer operation on the zeroth-order fringe is ensured via white-light interference during setup alignment. Optimum stability requires the interferometer to operate at −90° (the midpoint of the tracker interferogram, a positive slope with a change in combiner position) with respect to balance in the linear Mach−Zehnder interferometer. The SF interferogram is shifted to −90° from balance via vis-BS translation while under active control. Operation at −90° is chosen to support the sine function in eq 2, distinguishing positive from negative Δ. The OTS spectrum is dependent on predeposition surface treatment as well as water content in fabrication.20 (Details are given in the Supporting Information.) The investigated surface was fabricated according to the procedure of Messmer and coworkers.20

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followed, and using the interferometer to measure the phase from a low-intensity response (PDF)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b00792. Information on generating the real and imaginary spectra from the experimental intensity and phase spectra, description of the resulting phase and amplitude from superposition of multiple waves, the silanizing procedure 1948

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The Journal of Physical Chemistry Letters Method: Case Study of Water. J. Chem. Phys. 2011, 135, 224701/1− 224701/9. (13) Nihonyanagi, S.; Yamaguchi, S.; Tahara, T. Direct Evidence for Orientational Flip-Flop of Water Molecules at Charged Interfaces: A Heterodyne-Detected Vibrational Sum Frequency Study. J. Chem. Phys. 2009, 130, 204704/1−204704/5. (14) Jena, K. C.; Hore, D. K. Variation of Ionic Strength Reveals the Interfacial Water Structure at a Charged Mineral Surface. J. Phys. Chem. C 2009, 113, 15364−15372. (15) Vanselous, H.; Petersen, P. B. Extending the Capabilities of Heterodyne-Detected Sum-Frequency Generation Spectroscopy: Probing Any Interface in Any Polarization Combination. J. Phys. Chem. C 2016, 120, 8175−8184. (16) Inoue, K.-i.; Ishiyama, T.; Nihonyanagi, S.; Yamaguchi, S.; Morita, A.; Tahara, T. Efficient Spectral Diffusion at the Air/Water Interface Revealed by Femtosecond Time-Resolved HeterodyneDetected Vibrational Sum Frequency Generation Spectroscopy. J. Phys. Chem. Lett. 2016, 7, 1811−1815. (17) Ye, S.; Nihonyanagi, S.; Uosaki, K. Sum Frequency Generation (SFG) Study of the pH-Dependent Water Structure on a Fused Quartz Surface Modified by an Octadecyltrichlorosilane (Ots) Monolayer. Phys. Chem. Chem. Phys. 2001, 3, 3463−3469. (18) Ge, A.; Peng, Q.; Qiao, L.; Yepuri, N. R.; Darwish, T. A.; Matsusaki, M.; Akashi, M.; Ye, S. Molecular Orientation of Organic Thin Films on Dielectric Solid Substrates: A Phase-Sensitive Vibrational SFG Study. Phys. Chem. Chem. Phys. 2015, 17, 18072− 18078. (19) Ghalgaoui, A.; Shimizu, R.; Hosseinpour, S.; Á lvarez-Asencio, R.; McKee, C.; Johnson, C. M.; Rutland, M. W. Monolayer Study by Vsfs: In Situ Response to Compression and Shear in a Contact. Langmuir 2014, 30, 3075−3085. (20) Liu, Y.; Wolf, L. K.; Messmer, M. C. A Study of Alkyl Chain Conformational Changes in Self-Assembled N-Octadecyltrichlorosilane Monolayers on Fused Silica Surfaces. Langmuir 2001, 17, 4329− 4335. (21) Lambert, A. G.; Neivandt, D. J.; Maloney, R. A.; Davies, P. B. A Protocol for the Reproducible Silanization of Mica Validated by Sum Frequency Spectroscopy and Atomic Force Microscopy. Langmuir 2000, 16, 8377−8382. (22) Wei, X.; Hong, S.-C.; Lvovsky, A. I.; Held, H.; Shen, Y. R. Evaluation of Surface Vs Bulk Contributions in Sum-Frequency Vibrational Spectroscopy Using Refection and Transmission Geometries. J. Phys. Chem. B 2000, 104, 3349−3354. (23) Covert, P. A.; Hore, D. K. Assessing the Gold Standard: The Complex Vibrational Nonlinear Susceptibility of Metals. J. Phys. Chem. C 2015, 119, 271−276. (24) Fu, L.; Chen, S.-L.; Wang, H.-F. Validation of Spectra and Phase in Sub-1 cm−1 Resolution Sum-Frequency Generation Vibrational Spectroscopy through Internal Heterodyne Phase-Resolved Measurement. J. Phys. Chem. B 2016, 120, 1579−1589. (25) Shen, Y. R. Optical Second Harmonic Generation at Interfaces. Annu. Rev. Phys. Chem. 1989, 40, 327−350. (26) Walter, S. R.; Youn, J.; Emery, J. D.; Kewalramani, S.; Hennek, J. W.; Bedzyk, M. J.; Facchetti, A.; Marks, T. J.; Geiger, F. M. In-Situ Probe of Gate Dielectric-Semiconductor Interfacial Order in Organic Transistors: Origin and Control of Large Performance Sensitivities. J. Am. Chem. Soc. 2012, 134, 11726−11733. (27) de Beer, A. G. F.; Chen, Y.; Scheu, R.; Conboy, J. C.; Roke, S. Analysis of Complex Spectra Using Fourier Filtering. J. Phys. Chem. C 2013, 117, 26582−26587. (28) Wang, C.-y.; Groenzin, H.; Shultz, M. J. Molecular Species on Nano-Particle Anatase Tio2 Film Detected by Sum Frequency Generation: Trace Hydrocarbons and Hydroxyl Groups. Langmuir 2003, 19, 7330−7334.

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