Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum

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Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, and Tahei Tahara J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04043 • Publication Date (Web): 03 Jun 2019 Downloaded from http://pubs.acs.org on June 7, 2019

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The Journal of Physical Chemistry

Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces Lin Wang1,2, Satoshi Nihonyanagi,3,4* Ken-ichi Inoue,1 Kei Nishikawa,5 Akihiro Morita1,2*, Shen Ye1,2 and Tahei Tahara3,4 1. Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, JAPAN 2. Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, JAPAN 3. Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, 351-0198, JAPAN 4. Ultrafast Spectroscopy Research Team, RIKEN Center for Advanced Photonics (RAP), RIKEN, 2-1 Hirosawa, Wako, 351-0198, JAPAN 5. Rechargeable Battery Materials Group, Center for Green Research on Energy and Environmental Materials, National Institute for Material Sciences, Tsukuba 305-0044, JAPAN AUTHOR INFORMATION Corresponding Author E-mail: [email protected], [email protected]

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Abstract: Vibrational sum frequency generation (VSFG) spectroscopy is a powerful tool for selective probing of interfaces based on second-order nonlinear optics. The line shapes of observed VSFG spectra are governed by second-order nonlinear susceptibility as well as Fresnel factors for constituent light fields. Hence, determination of the second-order nonlinear susceptibility requires exact knowledge about the Fresnel factors for the light fields. However, the latter has been less examined than the former for interpretation of VSFG spectra to date and is sometimes hard to be calculated due to a lack of optical constants, especially in the infrared regions. The present work employs ATR-IR measurements and model fitting to determine the complex refractive indices of organic solvents and clarifies the effect of the Fresnel factor on the line shape analysis of VSFG spectra. As an example, we determine the complex refractive indices of organic carbonates, which are typical solvents for lithium-ion battery, in the C=O and C-H stretch vibration regions, and then examined the effect of frequency-dependent Fresnel factor on the VSFG spectra of electrode/carbonate as well as air/carbonate interfaces by model calculations. The Fresnel factor in the C=O stretch region has considerable dispersion due to the large extinction coefficient, which strongly influences the line shape of VSFG spectra at LiCoO2/carbonates interfaces, especially for SPS polarization combination. On the contrary, the frequency-dependent Fresnel factor in the C-H stretch region little affects the line shape of the band. The present systematic study of Fresnel factor revealed that the effect of Fresnel factor on the VSFG line shape becomes significant when (i) the frequency dependence of complex refractive index is large in the range of the band and (ii) non-resonant amplitude of nonlinear susceptibility is considerable relative to the resonant amplitude.


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1. Introduction Vibrational sum frequency generation (VSFG) spectroscopy is a particularly useful technique of interface characterization because it possesses intrinsic interface-selectivity of second-order nonlinear optical process, which is forbidden in the media with centro-symmetry under the dipole approximation.1-2 This feature makes VSFG intrinsically interface-selective because the symmetry is necessarily broken at interfaces. VSFG using visible and infrared (IR) lights has been extensively utilized for studying vibrational spectra of various liquid interfaces, in particular aqueous interfaces.3-12 VSFG is applicable to buried interfaces, such as solid-liquid ones, as long as they are accessible by lights. The observed VSFG spectra offer rich information on molecules at interfaces. The validity of VSFG measurements and interpretations has been extensively discussed in the past two decades.13-17 The intensity of VSFG is proportional to the square of product of secondorder nonlinear susceptibility 𝜒(2)(𝜔𝑆𝐹,𝜔𝑣𝑖𝑠,𝜔𝐼𝑅) and Fresnel factors 𝐿 of SFG, visible and IR lights,1 𝑆𝐹𝐺

𝐼

(𝜔𝑆𝐹) ∝

|∑ ∑ 𝑝

|

2

𝐿𝑝𝑝(𝜔𝑆𝐹)𝜒(2) 𝑝𝑞𝑟(𝜔𝑆𝐹,𝜔𝑣𝑖𝑠,𝜔𝐼𝑅)𝐿𝑞𝑞(𝜔𝑣𝑖𝑠)𝐿𝑟𝑟(𝜔𝐼𝑅) 𝐼𝑣𝑖𝑠𝐼𝐼𝑅,

𝑞,𝑟

(1)

where 𝑝, 𝑞, 𝑟 = 𝑋, 𝑌, 𝑍 are the space-fixed coordinates. 𝜒(2) consists of vibrationally resonant (2) term 𝜒(2) res and non-resonant one 𝜒nonres, and the former accounts for the IR frequency dependence

of the VSFG response as it involves the resonance effect of IR light with vibrational states. For the purpose of interface analysis, the 𝜔𝐼𝑅-dependence of 𝜒(2) is most important, as it carries information about interfacial molecules. Hence, in interpreting the line shapes of VSFG spectra, the Fresnel factors were usually estimated under the assumption that they were constants in the frequency range in question. However, one should also consider the fact that the Fresnel factors may involve the frequency dependence as well. 16, 18-19 Since the Fresnel factor primarily reflects


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the refractive indices of the media, highly dispersive media result in frequency-dependent Fresnel factors. Thus, in order to extract pure 𝜒(2)(𝜔𝐼𝑅) spectra from the observed VSFG intensity, it is important to answer the following questions: (a) How does the frequency dependence of Fresnel factors influence the band shape of VSFG spectra? (b) In what case that the frequency dependence of refractive index can be ignored? These are the questions we address in this paper. In fact, for aqueous interfaces, it has been reported that VSFG spectra of prism/metal thin film/water interfaces are heavily affected by the frequency dependence of Fresnel factor.16 However, frequency dependence of Fresnel factors for non-aqueous liquids have been little examined to date, mainly because the frequency-dependent refractive indices of most organic solvents in the IR region are not available in literature. Previous VSFG studies of electrode/organic solvent interfaces ignored the frequency dependence of refractive indices of solvents.20-23 Thus, precise data of frequency-dependent refractive indices are indispensable to further examine the effect of the Fresnel factors. The frequency-dependent refractive index in the IR region is derived from the extinction coefficient of IR absorption spectrum, which corresponds to the imaginary part of complex refractive index. The IR absorption spectrum can be measured in either transmission or reflection geometry. For the transmission geometry, the precise knowledge about an optical path length is required to convert an observed absorption spectrum to the corresponding extinction coefficient spectrum. Therefore, the transmission geometry is hard to be applied to the measurement of strong absorption bands, such as C=O stretch of carbonates, since the absorption is easily saturated with any thickness of spacer and it is difficult to control the small optical path length. Since we are mainly interested in vibrational bands of large extinction coefficients, the reflection


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geometry is more suitable for the purpose. It is free from the determination of optical path length and easy to be implemented with any organic solvents. Therefore, in this work, we evaluate the complex refractive index from the measurement of attenuated total internal reflection (ATR-) IR spectra.24-27 This method is widely applicable to determine the complex, frequency-dependent refractive index in any vibrational region of strong absorption. In the present work, we discuss the VSFG analysis of organic carbonates, such as propylene carbonate (PC), ethylene carbonate (EC), and dimethyl carbonate (DMC). They are widely used in modern rechargeable batteries, and their interfaces with redox-active materials have received wide attentions for industrial applications. For example, the structure of lithium cobalt oxide (LiCoO2)/organic carbonate solution interfaces has been intensively studied using in-situ Fourier-transformed IR spectroscopy28-31 and VSFG spectroscopy.20-21 These organic solvents have vibrational bands of C=O and C-H stretching. We first determined the complex refractive indices of the organic carbonates by analyzing the ATR-IR spectra. Then using the obtained refractive indices, we generally examined the effect of frequency-dependent Fresnel factor on the VSFG spectra of carbonates interfaces in the C=O and C-H stretch regions, with modeling different patterns of 𝜒(2)(𝜔) spectra with varying ratios of resonant and non-resonant terms. The present general argument allows for answering the two questions (a) and (b) mentioned above, and suggests that reconsideration is needed for the analysis of previous VSFG spectra of organic carbonate interfaces.

2. Methods In this section, we describe how we determine complex refractive indices of PC, EC and mixture of EC+DMC using ATR-IR spectra. The theory and fitting procedure are common for


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different systems. Therefore, we discuss the C=O stretching region of PC as an example to explain the determination of the complex refractive index. The details of ATR-IR experiment are described in Sec. 2.1. Using the model fitting of the ATR-IR spectra, the complex refractive index is determined as shown in Sec. 2.2.

2.1. ATR-IR measurements ATR-IR spectra of PC, EC/ 1 M LiClO4, and EC+DMC/ 0.5 M LiClO4 were measured by using FT/IR-6300 (JASCO) with the resolution of 4 cm-1. PC ( ≧ 98 %, Wako), EC ( ≧ 98 %, Wako), DMC ( ≧98 %, Kanto Chemical) and LiClO4 (98 %, Kishida Chemical) were used as received. EC+DMC/ 0.5 M LiClO4 was prepared by mixing 1:1 volume ratio of EC/1 M LiClO4 and DMC. The geometry of ATR measurement is illustrated in Figure 1. Diamond and ZnSe were used as ATR crystal. The incident angle 𝜃𝑖 was 45°. The polarization of the incident IR was controlled with a wire grid polarizer (S. T. JAPAN). In the polarizer angle dependence measurements, the maximum and minimum reflectivity correspond to the reflectivity of s-polarized and p-polarized IR, respectively. The results of the reflectance spectra are displayed in Figure 2 (a), which are analyzed to derive the complex refractive index in the next subsection.


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Figure 1. Light geometry of reflection and transmission. 𝑘𝐼, 𝑘𝑅 and 𝑘𝑇 are wave vectors of the incident, reflected and transmitted lights, respectively. 𝑛𝑖 and 𝑛𝑗 are complex refractive indices of substrate and PC liquid, respectively. Note that 𝑘𝑇 becomes imaginary in the ATR setting.

2.2. Analysis of ATR spectra Here we summarize the analysis procedure to derive the complex refractive index spectra. The ATR experiment in the geometry of Figure 1 is treated with the two-layer model. The amplitude ratios of reflected to incident light in the p- and s-polarizations are respectively given by32 r𝑝𝑖𝑗 =

r𝑠𝑖𝑗 =

𝑛𝑗cos𝜃𝑖 ― 𝑛𝑖cos𝜃𝑗 𝑛𝑗cos𝜃𝑖 + 𝑛𝑖cos𝜃𝑗 𝑛𝑖cos𝜃𝑖 ― 𝑛𝑗cos𝜃𝑗 𝑛𝑖cos𝜃𝑖 + 𝑛𝑗cos𝜃𝑗

,

(2)

,

(3)

where 𝑛𝑖 and 𝑛𝑗 denote the complex refractive indices of substrate and liquid PC, respectively. The incident angle 𝜃𝑖 and the transmitted angle 𝜃𝑗 are related by the Snell’s law, 𝑛𝑖sin𝜃𝑖 = 𝑛𝑗sin𝜃𝑗 .

(4)

Thus cos𝜃𝑗 is calculated from Eq. (4) by


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𝑛2𝑖 cos𝜃𝑗 = 1 ― 2sin2𝜃𝑖 . 𝑛𝑗

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(5)

The refractive index of the substrate 𝑛𝑖 is real, and their values are 2.38 and 2.41 for diamond and ZnSe, respectively. Therefore, the critical angles are estimated to be 36.6° and 36.1° for the two substrates with assuming 𝑛𝑗 ≃ 1.42 for PC liquid, and thus the present incident angle 𝜃𝑖 = 45° satisfies the condition of total reflection in either case of substrate. In the total reflection condition, the intensity ratios of reflected light |𝑟𝑝𝑖𝑗|2 and |𝑟𝑠𝑖𝑗|2, where 𝑟𝑝𝑖𝑗 and 𝑟𝑠𝑖𝑗 are defined in Eqs. (2) and (3), are unity when 𝑛𝑗 is real. However, |𝑟𝑝𝑖𝑗|2 and |𝑟𝑠𝑖𝑗|2 become less than unity when the refractive index of the liquid 𝑛𝑗 is complex, 𝑛𝑗 = 𝜂𝑗 + 𝑖𝜅𝑗, where 𝜂𝑗 is the real refractive index and 𝜅𝑗 is the extinction coefficient. The reduced intensity ratios of the reflected light are a consequence of the absorption of the evanescent light. In the C=O stretching region of liquid PC, the ATR spectra of absorption are experimentally measured in both s- and p-polarizations using either of the two substrates. Therefore, the observed spectra with different polarizations and substrates allow for determining the refractive index 𝜂𝑗(𝜔) and 𝜅𝑗(𝜔) of liquid PC at the same time by the least square fitting. We represent the complex refractive index of liquid PC in the C=O stretching region with a set of Lorentz functions as 𝑙max

𝑛𝑗(𝜔) = 𝜂𝑗(𝜔) + 𝑖𝜅𝑗(𝜔) =

𝑛0𝑗

+

𝐴𝑙

∑𝜔 ― 𝜔 ― 𝑖Γ ,

𝑙=1

𝑙

𝑙

(6)

where 𝑛0𝑗 = 1.42 is the non-resonant refractive index, taken from experimental refractive index of PC in visible regions.33 It should be noted that the true value of 𝑛0𝑗 in IR region might be smaller than that in visible region, according to Cauchy's equation.34 Thus, we also implemented 𝑛0𝑗 = 1.36 in the fitting procedure and found that the results of extinction coefficients with two


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𝑛0𝑗 values differ little (within 10%) from each other. In this case, the use of 𝑛0𝑗 = 1.42 hardly influences the extinction coefficient and the following further discussion of frequency-dependent Fresnel factor. 𝑙max is the number of Lorentz functions to be used. We employed 𝑙max = 2, since the experimental spectra obviously deviate from a single Lorentz function. The fitting results were actually little improved using a larger number of 𝑙max. 𝐴𝑙,𝜔𝑙 and Γ𝑙 in Eq. (6) are the parameters of amplitude, peak frequency and bandwidth of each Lorentz function, which are determined by the least square fitting. The detailed fitting procedure is given in Supporting Information (SI). The present fitting curves for PC were obtained with the parameters listed in Table 1. We note that the formula of Eq. (6) warrants the Kramers-Kronig relation. PC in C=O stretch region (𝑛0𝑗 = 1.42, 𝑙𝑚𝑎𝑥 = 2) 𝑙

𝐴𝑙

𝜔𝑙(cm ―1)

Γ𝑙(cm ―1)

1

3.436

1790

7.998

2

4.936

1807

14.22

Table 1: The fitting results of PC in C=O stretch region.

The calculated and experimental intensity ratios of reflected light, together with the fitting results of refractive index, are shown in Figure 2. The results indicate that the extinction coefficient 𝜅(𝜔) is as large as 0.5 at the maximum of the C=O stretching band. This value of the extinction coefficient is in agreement with that of the C=O band of a molecular thin film on a solid substrate which was determined by IR ellipsometry.35


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Figure 2: (a) Calculated (solid) and experimental (dotted) intensity ratios of reflected light in the ATR experiments using diamond (Red: p-polarized. Blue: s-polarized) and ZnSe (Green: ppolarized. Pink: s-polarized). (b) Fitted results of real refractive index (𝜂𝑗) and extinction coefficient (𝜅𝑗) of PC in C=O stretching region.

The refractive indices of EC solution and EC+DMC mixed solution are also examined using the same procedure as described above. The results also indicate that the extinction coefficient is quite large in the C=O stretching region. The detailed results are given in SI.

3. Results and Discussion In the preceding section, we determined the spectrum of 𝑛(𝜔𝐼𝑅) = 𝜂(𝜔𝐼𝑅) + 𝑖𝜅(𝜔𝐼𝑅) of liquid PC in the C=O stretching region, which exhibits significant frequency dependence. In this section, we elucidate the consequences of the frequency-dependent 𝑛(𝜔𝐼𝑅) on the Fresnel factor and interpretation of VSFG spectra. The C=O band of liquid PC offers an excellent example to examine the influence since its frequency dependence of 𝑛(𝜔𝐼𝑅) is quite remarkable. In what follows, we examine LiCoO2/PC and vapor/PC interfaces in the C=O stretch region in Secs. 3.1


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and 3.2, respectively. In addition, the influence on the LiCoO2/PC interface in the C-H stretch region is discussed in Sec. 3.3 for comparison. In each case we first introduce relevant model systems of 𝜒(2)(𝜔) to represent possible general situations, and discuss how the VSFG spectra are influenced by the complex Fresnel factors. Then the results of above discussion are compared with experimental VSFG spectra to interpret the experiment.

3.1. LiCoO2/PC interface Prior VSFG studies of LiCoO2/PC interface20-21 adopted the internal reflection geometry, where visible and IR lights are input through a LiCoO2 thin film electrode deposited on a transparent substrate (CaF2) and internally reflected sum frequency light is detected. This geometry does not propagate the IR light through solution phase, and thus this approach is free from the IR absorption due to the bulk solution. The internal reflection geometry is beneficial for investigating electrochemical solid/liquid interfaces on condition that the electrode of interest is transparent. The system of VSFG measurement is depicted in Figure 3.15-16, 36-37 The media 1, 2 and 3 refer to CaF2, LiCoO2, and carbonates, respectively, with their refractive indices 𝑛1, 𝑛2 and 𝑛3. Besides the three media, the system in Figure 3 involves two interfaces; CaF2/LiCoO2 interface is referred to “interface I” and LiCoO2/carbonate liquid to “interface II”. Accordingly, the geometry of VSFG measurement in Figure 3 is regarded as five-layer model consisting of the media 1, 2, 3 and interfaces I, II. In Figure 3, 𝜃1 and 𝜃2 are the angles of incidence in the media 1 and 2, respectively, while 𝜃3 is the angle of refraction in the medium 3.


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Figure 3. Schematic of a solid / thin film electrode / liquid interface.

The VSFG intensity measured in homodyne detection (𝐼𝑆𝐹𝐺 eff ) is proportional to the modulus square of the sum of contributions from the two interfaces: 𝐼𝑆𝐹𝐺 eff, 𝑆𝑆𝑃

II II II ∝ |𝐿I𝑌𝑌(𝜔𝑆𝐹)𝐿I𝑌𝑌(𝜔𝑣𝑖𝑠)𝐿I𝑍𝑍(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃1,𝐼𝑅 𝜒(2) 𝑌𝑌𝑍,I + 𝐿𝑌𝑌(𝜔𝑆𝐹)𝐿𝑌𝑌(𝜔𝑣𝑖𝑠)𝐿𝑍𝑍(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃 2 (2) 2,𝐼𝑅 𝜒𝑌𝑌𝑍,II ,

|

𝐼𝑆𝐹𝐺 eff, 𝑆𝑃𝑆

(7)

II II II ∝ |𝐿I𝑌𝑌(𝜔𝑆𝐹)𝐿I𝑍𝑍(𝜔𝑣𝑖𝑠)𝐿I𝑌𝑌(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃1,𝑣𝑖𝑠 𝜒(2) 𝑌𝑍𝑌,I + 𝐿𝑌𝑌(𝜔𝑆𝐹)𝐿𝑍𝑍(𝜔𝑣𝑖𝑠)𝐿𝑌𝑌(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃 2 (2) 2,𝑣𝑖𝑠 𝜒𝑌𝑍𝑌,II .

|

(8)

The subscript SSP in Eq. (7) represents the polarization combination in which the polarization of SFG, visible and IR lights are s-, s- and p-polarized, respectively. In the same manner, SPS in Eq. (8) denotes that the SFG, visible and IR lights are s-, p- and s-polarized, respectively. 𝜒(2) 𝑝𝑞𝑟, I/II (p,q,r=X~Z) is the second-order nonlinear susceptibility for the interface I/II. 𝐿I/II 𝑝𝑝 (p=Y, Z) are


12

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the Fresnel factors to relate electric fields of the incident/emitted lights in medium 1 and those at the interface I/II. The Fresnel factors take account of multiple reflections inside the thin film, and are expressed by the following equations,15-16 𝐿I𝑌𝑌(𝜔)

𝐿I𝑍𝑍(𝜔)

𝐿II𝑌𝑌(𝜔)

=

=

=

𝑡𝑠12

(1 + 𝑟𝑠23𝑒2𝑖𝛽),

(9)

1 + 𝑟𝑠12𝑟𝑠23𝑒2𝑖𝛽 𝑡𝑝12

𝑛1𝑛2

1 + 𝑟𝑝12𝑟𝑝23𝑒

(1 + 𝑟𝑝23𝑒2𝑖𝛽) 2𝑖𝛽

𝑡𝑠12𝑒𝑖∆

𝑛′I

2

,

(1 + 𝑟𝑠23),

(11)

1 + 𝑟𝑠12𝑟𝑠23𝑒2𝑖𝛽

𝐿II𝑍𝑍(𝜔) =

𝑡𝑝12𝑒𝑖∆ 1 + 𝑟𝑝12𝑟𝑝23𝑒

(10)

𝑛1𝑛2

(1 + 𝑟𝑝23) 2𝑖𝛽

𝑛′II

2

,

(12)

where 𝛽=

2𝜋𝑛2𝑑 cos 𝜃2

∆𝑆𝐹𝐺 =

∆𝑣𝑖𝑠 =

2𝜋𝑛2,𝑣𝑖𝑠𝑑 𝜆𝑣𝑖𝑠cos 𝜃2,𝑣𝑖𝑠 ∆𝐼𝑅 =

―

𝜆

,

2𝜋𝑛2,𝑆𝐹𝐺𝑑 𝜆𝑆𝐹𝐺cos 𝜃2,𝑆𝐹𝐺

(13)

,

(14)

2𝜋𝑛1,𝑣𝑖𝑠𝑑

2𝜋𝑛2,𝐼𝑅𝑑 𝜆𝐼𝑅cos 𝜃2,𝐼𝑅

𝜆𝑣𝑖𝑠 ―

(tan 𝜃2,𝑣𝑖𝑠 + tan 𝜃2,𝑆𝐹𝐺)sin 𝜃1,𝑣𝑖𝑠 ,

2𝜋𝑛1,𝐼𝑅𝑑 𝜆𝐼𝑅

(tan 𝜃2,𝐼𝑅 + tan 𝜃2,𝑆𝐹𝐺)sin 𝜃1,𝐼𝑅 .

(15)

(16)

Here,  denotes the wavelength. 𝑟𝑝𝑖𝑗 and 𝑟𝑠𝑖𝑗 are the amplitude ratios of reflected to incident light in p- and s-polarizations in Eqs. (2) and (3). 𝑡𝑝𝑖𝑗 and 𝑡𝑠𝑖𝑗 are the amplitude ratios of transmitted to incident light in p- and s-polarizations, respectively, given as follows: 𝑡𝑝𝑖𝑗 =

2𝑛𝑖cos 𝜃𝑖 𝑛𝑗cos 𝜃𝑖 + 𝑛𝑖cos 𝜃𝑗

,

(17)


13


𝑡𝑠𝑖𝑗 =

2𝑛𝑖cos 𝜃𝑖 𝑛𝑖cos 𝜃𝑖 + 𝑛𝑗cos 𝜃𝑗

Page 14 of 29

.

(18)

Eqs. (10) and (12) include 𝑛′I and 𝑛′II, the refractive indices of the interfaces I and II, respectively. They were estimated by 𝑛′I = (𝑛1 + 𝑛2)/2 and 𝑛′II = (𝑛2 + 𝑛3)/2. We note that the values of 𝑛′I and 𝑛′II are not directly measureable quantities, and include some ambiguities.38 Here we also examined two other models of interface refractive indices: 1)𝑛′I = 𝑛22 + 𝑛23 + 4

.

2(𝑛2―2 + 𝑛3―2 + 1)

39-40

𝑛21 + 𝑛22 + 4

, 𝑛′II =

2(𝑛1―2 + 𝑛2―2 + 1)

and 2) 𝑛′I = 𝑛2, 𝑛′II = 𝑛2. We found that the lineshapes of calculated

frequency-dependent Fresnel factors are quite similar to each other. Thus, we confirmed that the following argument is not sensitive to the assumed values of 𝑛′I and 𝑛′II. In the following model calculations, 𝑛1 is set to be real constant (𝑛1,SFG = 1.432, 𝑛1,vis = 1.431, 𝑛1,IR = 1.39)41 and 𝑛2 to be complex constant (𝑛2,SFG = 2.05 + 0.3i, 𝑛2,vis = 2.07 + 0.25i, 𝑛2,IR = 2.07 + 0.1i).42 𝑛3 of liquid PC is constant in the visible region (𝑛3,SFG = 𝑛3,vis = 1.42)33 but is the frequency-dependent in the IR region (𝑛3,IR(ω) = 𝜂3,IR(ω) + 𝑖𝜅3,IR(ω)) as determined in Sec 2.2. We used the incident angles 𝜃1,𝐼𝑅 = 50o and 𝜃1,𝑣𝑖𝑠 = 70o, following the experimental condition in Ref 20. The thickness of the medium 2 (d) was fixed at 50 nm. In order to evaluate the effect of frequency dependence of 𝑛3,IR(ω) on VSFG spectra, we simulate the VSFG intensity spectrum at LiCoO2/PC interface by employing some model (2) formulas for 𝜒(2) in Eqs. (7) and (8). 𝜒(2) I is assumed to be non-resonant, while 𝜒II involves the

vibrational resonance. Accordingly, we assume to take the following simple model formula, (2) 𝜒(2) I = 𝜒nonres,I ,

(2) (2) (2) 𝜒(2) II = 𝜒nonres,II + 𝜒res,II = 𝜒nonres,II +

(19) 𝐴𝑚 𝜔𝑚 ― 𝜔 ― 𝑖Γ𝑚

.

(20)


14

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This simple model of 𝜒(2) is sufficiently useful to delineate qualitative influence of the complex Fresnel factors in the following discussion. The role of the non-resonant term will be particularly examined. Here we vary the amplitudes of 𝜒nonres, I, 𝜒nonres, II and 𝐴𝑚 with the other parameters fixed, and investigate four models of 𝜒(2) spectra (Model-1~4) as shown in Table 2. Model-1 represents the situation that the resonant part of 𝜒(2) II is dominant, while Model-4 represents the situation that the non-resonant parts of 𝜒(2) and 𝜒(2) I II are dominant. Model-2 and Model-3 interpolate the two extreme situations. The VSFG intensity spectrum of each model system is calculated by Eqs. (7)~(20) with the complex refractive index in Sec. 2.2.

Table 2: Parameters of each model system 1~4 in Eqs. (19) and (20) for LiCoO2/PC interface. 𝜒nonres,I, 𝜒nonres,II and 𝐴𝑚 are in arbitrary unit, 𝜔𝑚 and 𝛤𝑚 are in cm ―1

Model-1 2 3 4

𝜒nonres,I 0.0 0.2 0.4 0.6

𝜒nonres,II 0.0 0.2 0.4 0.6

𝐴𝑚 12.0 8.0 4.0 0.0

𝜔𝑚 1800 1800 1800 1800

Γ𝑚 12 12 12 12

Figures 4 (a1~a4) and (b1~b4) show the calculated band shapes for the model systems of LiCoO2/PC interface under the SSP and SPS polarization combinations, respectively. In order to clarify the influences of the frequency dependence of 𝑛3(𝜔IR) of PC, the control results of the same model systems with assuming that the refractive index of PC is a real constant (𝑛3,IR = 1.42) are also shown with dashed lines.


15


Page 16 of 29

Figure 4. Calculated VSFG intensity spectra by using Model-1~4 under SSP (a1~a4) and SPS (b1~b4) polarization combinations at LiCoO2/PC interface. The description of Model-1~4 are listed in Table 2. The calculated results with complex 𝑛3,IR(𝜔) are shown by solid lines, while those with a real constant 𝑛3,IR by dashed lines. Panel (c) shows the experimental VSFG intensity at LiCoO2/PC interface.20 Adapted with permission from Ref. 20. Copyright (2009) American Chemical Society. (2) In Model-1 (Panels (a1, b1)) where 𝜒(2) amplitude, the calculated VSFG res, II dominates the 𝜒

intensities with the frequency-dependent 𝑛3,IR(ω) (solid lines) and the constant 𝑛3,IR (dashed lines) are almost the same for both SSP and SPS, which indicates that the frequency dependence of 𝑛3,IR(ω) can be neglected in Model-1 when analyzing the VSFG spectra. However, as (2) relative contributions of 𝜒(2) nonres,I and 𝜒nonres,II terms increase from Model-1 to Model-4,

differences in the spectral shapes emerge between two values of the refractive index. In the extreme case of Model-4 where 𝜒(2) is dominated by 𝜒nonres,I and 𝜒nonres,II, the difference is quite conspicuous. Both the SSP and SPS spectra calculated with the real constant 𝑛3,IR in (a4) and (b4) are constant, while the spectra with the complex 𝑛3,IR(ω) show apparent spectral structure,


16

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which obviously originates from the frequency dependence of the Fresnel factors. These results reveal that the frequency dependence of 𝑛3,IR(ω) particularly affects the band shape of the VSFG spectra when the non-resonant components of 𝜒(2) is relatively significant as compared to resonant components. Since the band shape is determined by the product of the (frequencydependent) Fresnel factor and 𝜒(2) amplitude in Eqs. (7) and (8), the large nonresonant 𝜒(2) background magnifies the effect of frequency-dependent Fresnel factor on the band shape of the spectra. In such situation, neglecting the frequency dependence of Fresnel factor will cause large error in analyzing the band shape of 𝜒(2) spectra. In the experimental spectra of LiCoO2/PC interface20 illustrated in Figure 4 (c), both SSP and SPS VSFG bands show significant background intensity outside the vibrational band, particularly the SPS spectrum, indicating large non-resonant 𝜒(2) amplitude due to the LiCoO2 substrate. We find that the experimental SPS line shape of the C=O band (blue line) is analogous to that of Model-4 in Figure 4 (b4). Similar results are also found in the LiCoO2/EC and LiCoO2/EC+DMC interfaces (see SI for detailed results).21 The present analysis strongly suggests that the SPS band is severely affected by the complex refractive index of liquid PC in the C=O stretching region. For SSP polarization, the frequency-dependent Fresnel factor also should affect the band shape when the non-resonant component of 𝜒(2) is dominant, as suggested in Figure 4 (a4). However, the experimental band shape of SSP spectrum in Panel (c) (red line) is obviously distinct from either in Panels (a1~a4). This discrepancy indicates that the resonant component of 𝜒(2) also plays an important role to determine the band shape of the SSP spectrum. We note that previous analysis of polarization and orientation did not consider the frequencydependence of refractive index due to lack of the optical constants in the infrared region.

20

The

analysis of polarization dependence and orientation angle has to be performed with the pure 𝜒(2)


17


Page 18 of 29

spectra after calibrating the frequency-dependent complex refractive index in the C=O stretching region. Although we tried to correct the effect of Fresnel factor by fitting the intensity spectra (~

|𝜒(2)|2) using equations (7) and (8), we could not obtain a unique fitting result mainly because of the lack of phase information. Thus, to extract the true 𝜒(2) spectra of VSFG by correcting the frequency-dependent Fresnel factor, one needs complex 𝜒(2) spectra by heterodyne detection rather than the intensity spectra, because the phase information is crucial.

3.2 Vapor/PC interface

Figure 5. Schematic of a vapor/liquid interface. In the previous section, we argued that the frequency dependence of complex refractive index affects the line shape of VSFG spectra when the non-resonant amplitude of 𝜒(2) is significant. In this section we deal with another situation, vapor/liquid interface, where the non-resonant amplitude of 𝜒(2) is often less significant.

Here we analyze the effect of complex refractive


18

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index on VSFG spectra at the vapor/liquid interface for comparison in the similar manner with Sec. 3.1. The beam geometry of vapor/liquid interface is shown in Figure 5. In this case, 𝑛1 for the vapor phase is set to be unity (𝑛1,𝑆𝐹𝐺 = 𝑛1,𝑣𝑖𝑠 = 𝑛1,𝐼𝑅 = 1), while 𝑛2,IR(𝜔) = 𝜂2,IR(𝜔) + 𝑖𝜅2,IR(𝜔) of liquid PC has the frequency dependence. The intensity of SFG spectra in SSP and SPS polarizations are given by 2

(2) 𝐼𝑆𝐹𝐺 eff, 𝑆𝑆𝑃 ∝ |𝐿𝑌𝑌(𝜔𝑆𝐹)𝐿𝑌𝑌(𝜔𝑣𝑖𝑠)𝐿𝑍𝑍(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃1,𝐼𝑅 𝜒𝑌𝑌𝑍| ,

(21)

2

(22)

(2) 𝐼𝑆𝐹𝐺 eff, 𝑆𝑃𝑆 ∝ |𝐿𝑌𝑌(𝜔𝑆𝐹)𝐿𝑍𝑍(𝜔𝑣𝑖𝑠)𝐿𝑌𝑌(𝜔𝐼𝑅)𝑠𝑖𝑛𝜃1,𝑣𝑖𝑠 𝜒𝑌𝑍𝑌| .

The Fresnel factors of vapor/liquid interface are given by 𝐿𝑌𝑌(𝜔) = 𝑡𝑠12, (23) 𝐿𝑍𝑍(𝜔) = (1 +

)

𝑟𝑝12

2

( ) 𝑛1

𝑛′𝑖𝑛𝑡

.

(24)

The refractive index of interface (𝑛′) is evaluated by 𝑛′𝑖𝑛𝑡 = (𝑛1 + 𝑛2)/2. The incident angles are set to be 𝜃1,𝐼𝑅 = 50o and 𝜃1,𝑣𝑖𝑠 = 70o, following the experimental condition in Ref 43. (2) 𝜒(2)(𝜔) consists of vibrational resonant part 𝜒(2) res (𝜔) and non-resonant part 𝜒nonres. Following

the previous section, we assume the following form: (2) (2) 𝜒(2) = 𝜒(2) nonres + 𝜒res = 𝜒nonres +

𝐴𝑚 𝜔𝑚 ― 𝜔 ― 𝑖Γ𝑚

.

(25)

We examine the effect of the frequnecy dependence of 𝑛2,IR(𝜔) of liquid PC on the VSFG band shape in the analogous manner with that in Sec. 3.1. Four models are employed in Table 3. Table 3: Parameters of each model system 1~4 in Eq. (25) for vapor/PC interface. 𝜒nonres and 𝐴𝑚 are in arbitrary unit, 𝜔𝑚 and 𝛤𝑚 are in cm ―1 Model-1

𝜒nonres 0.0

𝐴𝑚 12.0

𝜔𝑚 1800

Γ𝑚 12


19


2 3 4

0.4 0.8 1.2

8.0 4.0 0.0

1800 1800 1800

Page 20 of 29

12 12 12

The calculated VSFG intensity spectra of vapor/PC interface are shown in Figure 6, with assuming Models 1~4 in SSP (a1~a4) and SPS (b1~b4) polarizations, together with the calculation results assuming the refractive index to be a real constant 𝑛2,IR = 1.42 (dashed lines). The results for vapor/PC interface show qualitatively similar trend to that for LiCoO2/PC (2) interface shown in Sec. 3.1. With a relatively large 𝜒(2) spectrum (a1 and res amplitude in the 𝜒

b1), the frequency dependence of Fresnel factor can be neglected in the VSFG spectra, while the effect of Fresnel factor becomes significant with the relatively large 𝜒(2) nonres component (a4 and b4). In Model-4 where 𝜒(2) is dominated by 𝜒(2) nonres, the band structure of both SSP and SPS entirely originates from the frequency dependence of Fresnel factor.

Figure 6: Calculated VSFG intensity spectra by using Model-1~4 under SSP (a1~a4) and SPS (b1~b4) polarization combinations at vapor/liquid PC interface. The descriptions of Model-1~4 are listed in Table 3. The calculated results with complex 𝑛2,IR(𝜔) are shown by solid lines,


20

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while those with a real constant 𝑛2,IR by dashed lines. Panel (c) shows the experimental VSFG intensity at PC vapor-liquid interface.43 Reprinted with permission from Ref. 43. Copyright (2016) American Chemical Society.

In the experimental VSFG study of vapor/PC interface,43 as illustrated in Figure 6 (c), the SSP spectrum shows a large resonant band in the C=O stretching region while the non-resonant background is found to be relatively small. Similar behaviors are also found in vapor/EC interface

44

(see SI for detailed information). This situation is close to Model-1, and thus the

spectral structure of the C=O band is dominated by the vibrational resonant component of 𝜒(2). For the SPS spectrum, the peak intensity is much smaller than that of the SSP spectrum. This different intensity is attributed to a smaller 𝜒(2) 𝑟𝑒𝑠 amplitude in the SPS spectrum. The analysis of the SPS spectrum is harder than that of the SSP in extracting the information of 𝜒(2) spectrum at the vapor/PC interface.

3.3. SFG spectra of LiCoO2/PC interface in the CH stretch region


21


Page 22 of 29

Figure 7: Calculated VSFG intensity spectra by using Model-1~4 under SSP (a1~a4) and SPS (b1~b4) polarization combinations at PC/LiCoO2 interface in C-H stretch region. The parameters of Model-1~4 are the same as Table 2 in Sec. 3.1, except that 𝜔𝑚 is shifted to 2900 cm-1. Other notations are same with Figure 4.

In this section, we show the effect of Fresnel factor in the C-H stretch region. Although SFG experiment in this region has not been reported yet, we found that it is most promising. The ATR-IR spectra and fitting results of PC in the C-H stretch region are shown in SI. The results show that the maximum value of extinction coefficient of PC in C-H stretch region is 0.02, indicating that the C-H stretch modes have much smaller extinction coefficients than the C=O band (~0.5). By using the obtained refractive index, four model systems are used to examine the effect of Fresnel factor in the C-H stretch region. The parameters of Model-1~4 are the same as Table 2 in Sec. 3.1, except that 𝜔𝑚 is shifted to 2900 cm-1. The calculation results are shown in


22

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Figure 7. For all models, the calculated results using real constant 𝑛3,IR are nearly identical with that using complex 𝑛3,IR(ω). As evident from the simulation result with model-4 (without 𝜒(2) res (𝜔 )), frequency dependence of Fresnel factor in the C-H stretch region is negligibly small. Therefore, the line-shape of VSFG spectrum is free from the influence of Fresnel factor, irrespective of the relative magnitude of 𝜒(2) nonres. Thus, vibrational features in VSFG spectra in the C-H stretch region can be safely attributed to 𝜒(2) res (𝜔) and hence analysis of VSFG spectra in the C-H stretch region would be more reliable than that in the C=O stretch region for interfaces with a large non-resonant background such as LiCoO2 and other electrodes.

4. Conclusion In the present study, we employed ATR-IR measurements and model fitting to determine complex refractive indices of organic solvents and evaluated the complex, frequency-dependent Fresnel factors of the various liquid interfaces. As an example, we determined refractive indices of various liquid carbonates. The extinction coefficient of the C=O stretch band of carbonates is as large as 0.5 at maximum, which results in significant frequency dependence of the complex Fresnel factors. On the other hand, the extinction coefficient in C-H stretch region is much smaller, 0.02 at maximum for liquid PC. The influences of the complex Fresnel factors on the line shape analysis of VSFG spectra are fully examined at solid/liquid and vapor/liquid interfaces. We found that the complex Fresnel factors in the C=O band remarkably distorts the line shape when the non-resonant amplitude of 𝜒(2) is relatively substantial. Such typical example is found in the VSFG spectra of LiCoO2/carbonate interfaces, particularly for the SPS polarization. It is important to consider the


23


Page 24 of 29

complex Fresnel factor to properly interpret the VSFG spectra of C=O stretch mode. On the other hand, the C=O stretch region of vapor/liquid interface of organic carbonates is less influenced by the complex Fresnel factor, because the non-resonant 𝜒(2) background is relatively small. The line shape of the C-H stretching band is virtually not influenced by the frequencydependent Fresnel factor, since the dispersion of the Fresnel factor is quite small in that range. To summarize the present analysis, we conclude that the Fresnel factor strongly influences the line shape of VSFG spectra when both the extinction coefficient of detected species and nonresonant 𝜒(2) amplitude in VSFG spectra are substantial. Therefore, one must take the effect of complex Fresnel factors into account in interpreting the VSFG spectra in such cases. In contrast, when the non-resonant contribution is not significant (e.g. vapor/liquid PC interface) or the extinction coefficient of liquid is small (e.g. C-H stretch region of PC), the frequency dependence of the Fresnel factor barely influences the line shape of VSFG spectra. These findings offer a useful criterion for properly interpreting observed line shapes of VSFG spectra whether the frequency-dependent Fresnel factor plays a significant role to extract the vibrational structure of susceptibility. In order to extract pure 𝜒(2) spectra and analyze the molecular orientation at LiCoO2/carbonate interfaces, the heterodyne detections, together with molecular dynamics simulations, are in progress.

ASSOCIATED CONTENT Supporting Information. The detailed fitting procedure of complex refractive index, ATR-IR spectra and complex refractive indices of EC and EC+DMC solutions, simulated VSFG spectra of the LiCoO2/EC and LiCoO2/EC+DMC interfaces in the C=O stretch region, simulated VSFG spectra of vapor/EC


24

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interface in the C=O stretch region, ATR-IR spectra and complex refractive indices of PC in C-H stretch region. These results are available for free of charge. AUTHOR INFORMATION Corresponding Author E-mail: [email protected], [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT This work was financially supported by JST PRESTO and Grant-in-Aid for Scientific Research (18H05265), JSPS. SN acknowledges PRESTO advisors for their continuous encouragements and supports. ABBREVIATIONS VSFG, vibrational sum frequency generation; LiCoO2, lithium cobalt oxide; PC, propylene carbonate; EC, ethylene carbonate; DMC, dimethyl carbonate. REFERENCES (1) Shen, Y. R. The Principles of Nonlinear Optics. John Wiley & Sons, Inc.: New York, 1984. (2) Shen, Y. R. Surface-Properties Probed by 2nd-Harmonic and Sum-Frequency Generation. Nature 1989, 337, 519-525. (3) Richmond, G. L. Molecular Bonding and Interactions at Aqueous Surfaces as Probed by Vibrational Sum Frequency Spectroscopy. Chem. Rev. 2002, 102, 2693-2724. (4) Nihonyanagi, S.; Ye, S.; Uosaki, K.; Dreesen, L.; Humbert, C.; Thiry, P.; Peremans, A. Potential-Dependent Structure of the Interfacial Water on the Gold Electrode. Surf. Sci. 2004, 573, 11-16. (5) 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. (6) Gopalakrishnan, S.; Liu, D. F.; Allen, H. C.; Kuo, M.; Shultz, M. J. Vibrational Spectroscopic Studies of Aqueous Interfaces: Salts, Acids, Bases, and Nanodrops. Chem. Rev. 2006, 106, 1155-1175. (7) Noguchi, H.; Okada, T.; Uosaki, K. Molecular Structure at Electrode/Electrolyte Solution Interfaces Related to Electrocatalysis. Faraday Discuss. 2009, 140, 125-137.


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(8) Shen, Y. R. Phase-Sensitive Sum-Frequency Spectroscopy. Ann. Rev. Phys. Chem. 2013, 64, 129-150. (9) Nihonyanagi, S.; Mondal, J. A.; Yamaguchi, S.; Tahara, T. Structure and Dynamics of Interfacial Water Studied by Heterodyne-Detected Vibrational Sum-Frequency Generation. Ann. Rev. Phys. Chem. 2013, 64, 579-603. (10) Johnson, C. M.; Baldelli, S. Vibrational Sum Frequency Spectroscopy Studies of the Influence of Solutes and Phospholipids at Vapor/Water Interfaces Relevant to Biological and Environmental Systems. Chem. Rev. 2014, 114, 8416-8446. (11) Ishiyama, T.; Imamura, T.; Morita, A. Theoretical Studies of Structures and Vibrational Sum Frequency Generation Spectra at Aqueous Interfaces. Chem. Rev. 2014, 114, 84478470. (12) Nihonyanagi, S.; Yamaguchi, S.; Tahara, T. Ultrafast Dynamics at Water Interfaces Studied by Vibrational Sum Frequency Generation Spectroscopy. Chem. Rev. 2017, 117, 1066510693. (13) 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 Reflection and Transmission Geometries. J. Phys. Chem. B 2000, 104, 3349-3354. (14) Tian, C. S.; Shen, Y. R. Sum-Frequency Vibrational Spectroscopic Studies of Water/Vapor Interfaces. Chem. Phys. Lett. 2009, 470, 1-6. (15) Tong, Y.; Zhao, Y.; Li, N.; Osawa, M.; Davies, P. B.; Ye, S. Interference Effects in the Sum Frequency Generation Spectra of Thin Organic Films. I. Theoretical Modeling and Simulation. J. Chem. Phys. 2010, 133, 034704. (16) Backus, E. H. G.; Garcia-Araez, N.; Bonn, M.; Bakker, H. J. On the Role of Fresnel Factors in Sum-Frequency Generation Spectroscopy of Metal–Water and Metal-Oxide–Water Interfaces. J. Phys. Chem. C 2012, 116, 23351-23361. (17) Kundu, A.; Tanaka, S.; Ishiyama, T.; Ahmed, M.; Inoue, K.; Nihonyanagi, S.; Sawai, H.; Yamaguchi, S.; Morita, A.; Tahara, T. Bend Vibration of Surface Water Investigated by Heterodyne-Detected Sum Frequency Generation and Theoretical Study: Dominant Role of Quadrupole. J Phys Chem Lett 2016, 7, 2597-601. (18) Urashima, S.-h.; Myalitsin, A.; Nihonyanagi, S.; Tahara, T. The Topmost Water Structure at a Charged Silica/Aqueous Interface Revealed by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy. J. Phys. Chem. Lett. 2018, 9, 4109-4114. (19) Ramsay, M.; Beutier, C.; McGarvey, G. B.; Hore, D. K. Adsorption of Heptane–Toluene Binary Mixtures on a Hydrophobic Polymer Surface. J. Chem. Phys. 2019, 150, 014702. (20) Liu, H.; Tong, Y.; Kuwata, N.; Osawa, M.; Kawamura, J.; Ye, S. Adsorption of Propylene Carbonate (PC) on the LiCoO2 Surface Investigated by Nonlinear Vibrational Spectroscopy. J. Phys. Chem. C 2009, 113, 20531-20534. (21) Yu, L.; Liu, H.; Wang, Y.; Kuwata, N.; Osawa, M.; Kawamura, J.; Ye, S. Preferential Adsorption of Solvents on the Cathode Surface of Lithium Ion Batteries. Angew. Chem. Int. Ed. 2013, 52, 5753-5756. (22) Nicolau, B. G.; Garcı́a-Rey, N.; Dryzhakov, B.; Dlott, D. D. Interfacial Processes of a Model Lithium Ion Battery Anode Observed, in Situ, with Vibrational Sum-Frequency Generation Spectroscopy. J. Phys. Chem. C 2015, 119, 10227-10233. (23) Peng, Q.; Liu, H.; Ye, S. Adsorption of Organic Carbonate Solvents on a Carbon Surface Probed by Sum Frequency Generation (SFG) Vibrational Spectroscopy. J.Electroanal. Chem. 2017, 800, 134-143.


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Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum

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