Elucidation of the pH-Dependent Electric Double Layer Structure at the Silica/Water Interface Using Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy

Abstract

The silica/water interface is one of the most abundant charged interfaces in natural environments, and the elucidation of the water structure at the silica/water interface is essential. In the present study, we measured the interface-selective vibrational (χ⁽²⁾) spectra in the OH stretch region of the silica/water interface in a wide pH range of pH 2.0–12.0 while changing the salt concentration by heterodyne-detected vibrational sum-frequency generation spectroscopy. With the help of singular value decomposition analysis, it is shown that the imaginary part of the χ⁽²⁾ (Imχ⁽²⁾) spectra can be decomposed into the spectra of the diffuse Gouy–Chapman layer (DL) and the compact Stern layer (SL), which enables us to quantitatively analyze the spectra of DL and SL separately. The salt-concentration dependence of the DL spectra at different pH values is analyzed using the modified Gouy–Chapman theory, and the pH-dependent surface charge density and the pK_a value (4.8 ± 0.2) of the silica/water interface are evaluated. Furthermore, it is found that the pH-dependent change of the SL spectra is quantitatively explained by three spectral components that represent the three characteristic water species appearing in different pH regions in SL. The quantitative understanding obtained from the analysis of each spectral component in the Imχ⁽²⁾ spectra provides a clear molecular-level picture of the electric double layer at the silica/water interface.

1. Introduction

The silica/water interface has attracted much attention and has been a subject of intensive studies because of its importance in many fundamental and applied research fields. From the fundamental viewpoint, the silica/water interface has been regarded as a prototypical model system for studying mineral/water interfaces as well as charged solid/water interfaces because of its abundance in the natural environment.¹ The silica/water interface is also involved in many applications, such as heterogeneous catalysis,² drug delivery,^3,4 and ion-sensitive sensors.⁵ Therefore, molecular-level elucidation of the properties of the silica/water interface is essential for both a fundamental understanding of the silica surface and the application of silica-related materials.

The silica/water interface consists of water molecules, ions in the aqueous phase, and silica surface species such as silanol (SiOH) and bridge oxygen (Si–O–Si). Since the SiOH groups at the silica surface are deprotonated (SiO^–) under most pH conditions (>pH 2.0), the silica interface is usually negatively charged when in contact with water.^6,7 Consequently, the negatively charged silica surface attracts countercations in the aqueous phase, and an electrical double layer (EDL) is formed at the silica/water interface. For an interface with a low charge density and a dilute solution, the EDL structure can be well described by the Gouy–Chapman theory.^8,9 At the silica/water interface, however, the ion concentration can become high in the vicinity of the silica surface due to its high charge density (∼0.87 e/nm²),⁹ making the assumptions of Gouy–Chapman theory invalid. Thus, the EDL is described by the Stern model, which consists of a compact Stern layer (SL) and a diffuse Gouy–Chapman layer (DL).^10,11 The elucidation of the structure and property of SL and DL is indispensable for a comprehensive understanding of EDL.

Many experimental^7,9,12−29 and theoretical studies^11,30−32 have been carried out to understand the properties of EDL at the charged surface. In addition to the conventional electrochemical scanning and electrocapillarity experiments,¹³ many spectroscopic methods, such as X-ray absorption spectroscopy,¹⁴ ambient pressure X-ray photoelectron spectroscopy,¹⁵ second harmonic generation (SHG),^9,16−18 vibrational sum-frequency generation (VSFG) spectroscopy,¹⁹⁻²⁹ have been applied to gain molecular insights into the charged interface. Among these spectroscopic methods, VSFG spectroscopy is particularly useful because it can probe molecules within the EDL.²⁴⁻²⁸ Several VSFG studies have shown that the SFG intensity at the silica/water interface decreases with the increase of the ionic strength, reflecting the decrease of net orientation of water molecules in DL due to the screening of the electric field that arises from the charge at the interface.^24,33,34 However, the molecular structures in SL and DL at the silica/water interface are still elusive because the conventional VSFG measurements can only provide the SFG intensity information, which is proportional to the modulus square of the molecular response, that is, the square of the second-order nonlinear susceptibility (). Therefore, the sign of the nonlinear susceptibility (χ⁽²⁾) is lost, and the obtained vibrational spectrum is distorted due to the interference between different spectral components, including the non-resonant background. These drawbacks make it difficult to derive proper information about the silica/water interface from the VSFG spectra, even with the assistance of theory and computation.

To avoid the difficulties brought by the square nature of the conventional SFG intensity spectra, heterodyne-detected (HD-) VSFG techniques were developed to directly measure χ⁽²⁾ spectra.³⁵⁻⁴⁰ The χ⁽²⁾ spectra obtained by HD-VSFG spectroscopy are linear to the nonlinear susceptibility. In particular, the imaginary part of the χ⁽²⁾ spectrum (Imχ⁽²⁾) exhibits vibrational resonances with absorptive line shapes and is directly compared to the infrared and Raman spectra. Furthermore, spectral decomposition is readily achieved by model fitting³⁷ or simple subtractions,⁴⁰ making interpretation of the data straightforward. HD-VSFG spectroscopy has been applied for studying various aqueous interfaces, including buried interfaces such as the SiO₂/water interfaces.^37,39,40 In a pioneering study, Shen and co-workers observed three OH bands in the Imχ⁽²⁾ spectrum at the quartz (0001)/water interface and discussed the interfacial water structures.³⁷ Later, our group measured the Imχ⁽²⁾ spectra of the silica/water interface using H₂O and isotopically diluted water (HOD-D₂O) at pH 12.1, pH 7.2, and pH 2.1 and showed that the spectra at the silica/H₂O interface are significantly affected by the vibrational coupling.³⁹ We discussed the water structure at the silica/H₂O interface, as well as its pH-dependent change, based on the spectra at the silica/HOD-D₂O interface that are free from the vibrational coupling. However, a full picture of the EDL structure at the silica/water interface is still unclear because these early studies were performed with a low ion concentration, and hence they did not separately discuss SL and DL.

Several groups tried to decompose the VSFG () spectra at the silica/water interface into the spectra of the SL and DL, using various means such as theoretical modeling,⁴¹ DFT-based molecular dynamics simulations,⁴² and the maximum entropy method (MEM).⁴³ Nevertheless, such separation is sensitive to the choice of model and the parameters used in the analysis. Obviously, the model-independent analysis and spectral decomposition are desired for a solid discussion of the EDL structure. Our group measured the Imχ⁽²⁾ spectra of the silica/water interface at pH 12.0 while systematically changing the salt (NaCl) concentration and demonstrated that the Imχ⁽²⁾ spectra can be decomposed into two spectral components that are attributed to the SL and DL using simple spectral subtraction.⁴⁰ This study has led us to obtain molecular-level pictures of the EDL at the silica/water interface in a wide pH range based on spectral decomposition of the salt concentration-dependent Imχ⁽²⁾ spectra.

The present study aims to obtain molecular insights into the silica/water interface at various pH (2.0–12.0), based on the Imχ⁽²⁾ spectra in the OH stretch region measured at each pH with various salt concentrations (0.01 to 5.0 M). To realize model-independent spectral decomposition in the wide pH range, we use singular value decomposition (SVD) analysis. SVD is a mathematical method to find the number of independent spectral components, and it has widely been used for the analysis of various types of spectra.⁴⁴⁻⁴⁶ The spectral decomposition based on SVD enables us to obtain clear molecular pictures of the water structures at the silica/water interface at various pHs, with the minimum assumption of the EDL model. It is found that the Imχ⁽²⁾ spectra measured at various salt concentrations are decomposed into spectral components of water in SL and DL at all pHs. The pH dependence of the DL spectra enables us to estimate the surface charge density at each pH and pK_a value of the silica/water interface using the modified Gouy–Chapman (MGC) theory. Furthermore, the pH-dependent change of the SL spectrum allows us to clarify the change of the water structure in the vicinity of the silica surface, which is caused by the deprotonation/protonation of the silanol/silanolate groups.

2. Methods

2.1. Materials

The silica substrates used in this study were fused silica windows with a diameter of 20 mm and thickness of 3 mm (IR grade, Pier optics). Before the experiments, each silica substrate was soaked in concentrated sulfuric acid (Nacalai Tesque, Inc., >99.5%) for at least 12 h to remove the organic contaminants. After being taken out of sulfuric acid, the silica substrate was washed with deionized water and cleaned by O₂ plasma for at least 10 min. Then, the silica substrate was half-coated with a 0.8 nm titanium buffer layer and 150 nm gold film using an electron beam evaporator (vide infra). Before HD-VSFG measurements, the silica substrate was cleaned again by O₂ plasma for at least 10 min before assembling it with the sample cell. The pH of each solution was adjusted by adding an adequate amount of HCl (Nacalai Tesque, Inc., 35% in H₂O) or NaOH (Nacalai Tesque, Inc., >99.5%) solutions into the solution. The salt-concentration dependence was examined using NaCl (Merck, 99.99%) as the salt. The pH values of the NaCl solutions were measured by a pH meter (Horiba LAQUAtwin pH-22) before and after HD-VSFG experiments.

The data discussed in the main text were obtained from a single silica window. The observed spectra somewhat depend on the silica windows used (see Section 3.2.2 and Supporting Information for the details). However, the essential arguments and conclusions are the same, free from this sample dependence.

2.2. HD-VSFG Measurements

We used an HD-VSFG setup that was newly constructed based on a diode-pumped Yb:KGW regenerative amplifier system (PHAROS SP-1.5, Light Conversion) operated at a repetition rate of 100 kHz. Its output (6 W) centered at ∼1030 nm was divided into two parts. One-third of the output (∼2 W) was used for generating narrowband NIR pulses (ω₁). After passing two bandpass filters, we obtained the ω₁ pulses with a center frequency of 1028.8 nm and a 25 cm^–1 bandwidth in full width at half-maximum (FWHM). Two-third of the output (∼4 W) was directed into an optical parametric amplifier (OPA: ORPHEUS One, Light Conversion) to generate tunable IR pulses (ω₂). Since the FWHM of ω₂ was limited to ∼125 cm^–1, eight spectra were measured with different center ω₂ and merged to obtain the Imχ⁽²⁾ spectra in the entire OH stretch region (2900–3800 cm^–1). The average power of the ω₂ beam was 40–80 mW, depending on the center ω₂ wavenumber.

The ω₁ and ω₂ pulses were first focused on a gold mirror to generate the SFG signal that was used as the local oscillator (LO) SFG. (see Figure S1 for the optical configuration). Then, these three beams (ω_1, ω_2, and LO) were refocused to the buried silica/water interface by a concave mirror (r = 300 mm). A silica substrate was placed on top of a 1 mL aqueous solution in a Teflon cell. A 3 mm thick UV-grade silica plate was placed in the optical path of the LO before the sample cell to provide LO with a proper time delay. In addition, a 0.2 mm thick UV-grade silica plate was placed in the path of the ω₁ beam before the sample cell to compensate for the time delay between ω₁ and ω₂ caused by the sample silica substrate. The silica substrate was continuously moved in a range of y = ±0.2 mm horizontally (perpendicular to the incident plane of the ω₁ and ω₂ beams) during the measurements to avoid the accumulation of heat due to laser irradiation. The SFG signal generated at the silica/water interface and LO reflected at the silica/water interface were introduced into a polychromator (HRS-300-MS, Teledyne Princeton Instruments) and detected by a CCD (BLAZE-400HR-20, Teledyne Princeton Instruments). The SFG, ω₁,_, and ω₂ beams were s-, s-, and p-polarized, respectively (SSP polarization combination).

The raw spectra of the silica/water interface were normalized by the spectrum of the silica/Au film interface (used as “the temporary standard”) that was obtained from the gold-coated half part of the sample silica substrate. The phase of the χ⁽²⁾ spectrum at this silica/Au film interface was calibrated using the χ⁽²⁾ spectra of the silica/air interface (“the true standard”), which was obtained from another half of the sample silica substrate with half-filled D₂O in the sample cell before introducing the solution for the measurement. The χ⁽²⁾ spectra shown in the present paper have been corrected for the complex conjugate of the reflectivity of LO and Fresnel factors at the silica/water interfaces, which vary with the salt concentration (see Section S2 in the Supporting Information for details).

3. Results

3.1. Salt-Concentration-Dependent Imχ⁽²⁾ Spectra in a Wide pH Range and Spectral Decomposition

3.1.1. Salt-Concentration-Dependent Imχ⁽²⁾ Spectra in the pH Range of pH 2.0–12.0

Figure 1 shows the Imχ⁽²⁾ spectra of the silica/water interface at various pH measured with the NaCl concentration ranging from 0.01 to 5.0 M. As shown in Figure 1A, the Imχ⁽²⁾ spectra at pH 12.0 with diluted solutions (0.01 M) show a positive OH band peaked at ∼3200 cm^–1 with a shoulder at ∼3450 cm^–1 and a small negative OH band at 3650 cm^–1. The amplitude of the OH bands decreases gradually as the salt concentration increases from 0.01 to 5.0 M. As already discussed in previous studies,^24,47−49 this salt-induced decrease of the SFG signal is primarily attributed to the decrease of net orientation of the water molecules having “H-up” orientation (orienting H toward the silica surface) in DL. Although the phase of the SFG signal arising from DL is noticeably shifted at a very low NaCl concentration due to a large DL thickness, the phase shift is already not significant with a salt concentration at 0.01 M.^21,40,50 After the drastic amplitude decrease, the Imχ⁽²⁾ spectra show a positive band around ∼3150 cm^–1, a small negative band around ∼3500 cm^–1, and a small positive band around ∼3600 cm^–1 at the high salt concentration of ≥2.0 M. These spectral changes observed at pH 12.0 are consistent with our previous report.⁴⁰

Figure 1.

Imχ⁽²⁾ spectra of the silica/water interface with bulk NaCl concentrations from 0.01 to 5.0 M at various pH: (A) 12.0 ± 0.1, (B) 10.0 ± 0.1, (C) 7.5 ± 0.3, (D) 6.0 ± 0.2, (E) 4.0 ± 0.1, and (F) 2.0 ± 0.1. The Imχ⁽²⁾ spectra shown have been corrected by the complex conjugate of the reflectivity of LO and Fresnel factors at the silica/water interfaces.

Figure 1B–D shows the Imχ⁽²⁾ spectra at pH 10.0, pH 7.5, and pH 6.0. The observed salt-concentration-dependent Imχ⁽²⁾ spectra are similar to those observed at pH 12.0: the spectra show two positive OH bands peaked at ∼3200 and ∼3450 cm^–1 with a small negative OH band at ∼3650 cm^–1, and the amplitudes of the positive 3200 and 3450 cm^–1 bands decrease with the increases of the salt concentration. Nevertheless, several distinct features are recognized with the change in pH. First, in the dilute solutions, for example, 0.01 M, the relative amplitude of the 3200 cm^–1 OH band to the 3450 cm^–1 band decreases as the pH decreases. Second, in the spectra at high NaCl concentrations of ≥2.0 M, the amplitude of the positive signal below the 3150 cm^–1 band drastically decreases with lowering pH, and it almost vanishes at pH 6.0. On the other hand, the amplitude of the positive signal around 3600 cm^–1 increases.

Figure 1E,F shows Imχ⁽²⁾ spectra at pH 4.0 and 2.0, respectively. They show much smaller amplitudes and different spectral shapes compared to the spectra at higher pH. In the dilute solution (0.01 M), the Imχ⁽²⁾ spectra at pH 2.0 and 4.0 show one negative OH band at ∼3050 cm^–1 and a broad positive OH band at ∼3450 cm^–1. These spectra accord well with the spectrum of the silica/water interface at pH 2.0 reported in our previous study.³⁹ The salt-induced spectral changes are also much smaller in magnitude at low pH than those observed at higher pH, although the amplitudes of the positive OH bands decrease in a similar way. In our previous study,⁵¹ we assumed that EDL does not exist at pH 2.0 based on the prior zeta potential measurements. However, the salt concentration-dependent spectral change at pH 2.0 observed in this study clearly indicates the decrease of the “H-up” water signal from EDL water, indicating that negative charges still exist at the silica surface at pH 2.0.

In our previous study of the silica/water interface at pH 12.0,⁴⁰ we concluded that the Imχ⁽²⁾ spectral change up to 2.0 M NaCl is solely attributable to the decrease of the DL contribution due to the screening of the electric field by the counterion (Na⁺), whereas the spectral change at higher salt concentrations (e.g., 5.0 M) arises from the salt-induced change of the SL. This conclusion was consistent with earlier conventional VSFG studies that concluded that the DL contribution is sufficiently suppressed with 2.0 M NaCl.^24,27,34,52 The Imχ⁽²⁾ spectra shown in Figure 1 indicate that this argument is valid for all pH examined in this study because the spectra measured with 5.0 M NaCl exhibit further changes in addition to the gradual spectral change observed up to 2.0 M. For instance, at pH 4.0 and 2.0, the spectral change between 1.0 and 2.0 M is already very small, but the difference between 2.0 and 5.0 M becomes substantial. This spectral change observed between 2.0 and 5.0 M cannot be explained by the decrease in the DL contribution. Therefore, we analyze and discuss the salt-concentration dependence of the Imχ⁽²⁾ spectra for the spectra measured with the NaCl concentration up to 2.0 M to avoid complications arising from too high salt concentration, such as the salt-induced change of SL, hereafter.

3.1.2. SVD Analysis and Separation of DL and SL Spectral Components

To obtain more quantitative information from the Imχ⁽²⁾ spectra, we performed SVD analysis for the salt concentration-dependent Imχ⁽²⁾ spectra measured at each pH. In this section, we describe the procedure and results of our analysis, using the Imχ⁽²⁾ spectra measured at pH 10.0 as an example. (See Section S3 in the Supporting Information for details of all the SVD analyses.)

Figure 2A shows the singular values obtained by the SVD analysis of the Imχ⁽²⁾ spectra at pH 10.0 (black dots). As seen, the singular values quickly become small, and only the first three values are significant. In fact, the spectra reconstructed using the first three components perfectly reproduce the experimental Imχ⁽²⁾ spectra at all the NaCl concentrations up to 2.0 M, as shown in Figure 2B (broken lines). We also calculated the Imχ⁽²⁾ spectra only with the first two components, but some deviation from the experimental spectra is noticeable, particularly at high NaCl concentrations at 2.0 M (Figure S5-2 in the Supporting Information). This result demonstrates that the salt concentration-dependent Imχ⁽²⁾ spectra at pH 10.0 can be represented by linear combinations of independent spectral components, and at least three spectral components are necessary to reproduce the spectra in a wide NaCl concentration range of 0.01–2.0 M.

Figure 2.

SVD analysis of the Imχ⁽²⁾ spectra at the silica/water interface. (A) Singular values obtained from the SVD analysis of the Imχ⁽²⁾ spectra at pH 10.0 ± 0.1. The dashed line is the indicator for <2% of the largest singular value, which can be regarded as noise. (B) Imχ⁽²⁾ spectra and the reconstructed Imχ⁽²⁾ spectra using three major components. (The reconstructed spectra are shown with broken lines.) (C) Singular values obtained from the SVD analysis of Dif_Imχ⁽²⁾ spectra at pH 10.0 ± 0.1. The dashed line is the indicator for <2% of the largest singular value, which can be regarded as noise. (D) Dif_Imχ⁽²⁾ spectra and reconstructed Dif_Imχ⁽²⁾ spectra using two major components. (The reconstructed spectra are shown with broken lines.) (E) Imχ⁽²⁾ spectra of the silica/water interface measured with 2.0 M NaCl. (F) The normalized Dif_Imχ⁽²⁾ spectra measured with different salt concentrations. (G) The bulk vibrational spectra ( of aqueous NaCl solutions measured with different NaCl concentrations.

With the increase of the NaCl concentration, the amplitude of the positive OH band monotonically decreases. This observation is explained by the shrinkage of the DL due to the screening of the electric field by the counterion Na⁺. Since it is considered that the DL contribution is suppressed almost completely with 2.0 M NaCl, the decreased Imχ⁽²⁾ spectral component is attributable to the spectrum in DL (Imχ_DL⁽²⁾), whereas the Imχ⁽²⁾ spectrum measured at 2.0 M NaCl is considered to be the spectrum of SL (Imχ_SL,2.0M) at 2.0 M NaCl, although Imχ_2.0M⁽²⁾ might still contain a very small amount of the DL contribution.

We subtract the Imχ_2.0M⁽²⁾ spectrum from the Imχ⁽²⁾ spectra measured with various NaCl concentrations (Dif_Imχ⁽²⁾ = Imχ⁽²⁾ – Imχ_2.0M). The obtained Dif_Imχ⁽²⁾ spectra at pH 10.0 are shown in Figure 2D. These spectra show two OH bands peaked at 3200 and 3450 cm^–1, and the amplitudes of these two bands decrease with increasing the NaCl concentration. We also performed the SVD analysis of the Dif_Imχ⁽²⁾ and found that the third singular value becomes negligibly small (Figure 2C), implying that the Dif_Imχ⁽²⁾ spectra can be reproduced only with two spectral components (the broken lines in Figure 2D). We also calculated the Dif_Imχ⁽²⁾ spectra only with the first component, but some deviations from the experimental spectra are noticeable (Figure S6-2 in the Supporting Information). This result indicates that the subtraction of the Imχ_2.0M⁽²⁾ spectrum removes one spectral component from the Imχ⁽²⁾ spectra. Since the Imχ_2.0M spectrum can be regarded as the SL spectrum at 2.0 M (Imχ_2.0M⁽²⁾ ≈ Imχ_SL,2.0M), this means that the component identical to the SL spectrum at 2.0 M (Imχ_SL,2.0M⁽²⁾) commonly exists unchanged in all the Imχ⁽²⁾ spectra measured with different NaCl concentrations.

The Dif_Imχ⁽²⁾ spectra, which are obtained with the subtraction of the Imχ_2.0M⁽²⁾ spectrum, are shown in Figure 2F after amplitude normalization at 3300 cm^–1. The SVD analysis indicates that there are two spectral components in the Dif_Imχ⁽²⁾ spectra. The origin of one component is obvious, that is, the DL water spectrum. The question is the origin of the second spectral component. To clarify it, we estimate the corresponding bulk water spectra with the square root of the product of the IR and Raman spectra of bulk water, that is, , because the VSFG optical process can be decomposed into the IR and Raman transitions. The calculated I_bulk spectra are shown in Figure 2G, and the original IR and Raman spectra are given in Figure S7-1 in the Supporting Information. The salt concentration-dependent Dif_Imχ⁽²⁾ spectra (Figure 2F) and the I_bulk spectra (Figure 2G) exhibit very similar spectral changes: the amplitude of the 3200 cm^–1 band relative to the 3450 cm^–1 band gradually decreases as the NaCl concentration increases from 0.01 to 2.0 M. In fact, the SVD analysis shows that the I_bulk spectra are reproduced with two independent spectral components, as in the case of Dif_Imχ⁽²⁾ (see Section S4 in the Supporting Information for the details). Since it is known that the spectra of the water in DL are similar to the spectra of bulk water,^40,41,43 this similarity strongly indicates that the second component of the Dif_Imχ⁽²⁾ spectra is the component required to reproduce the salt-induced change of the DL water spectrum. In other words, the Dif_Imχ⁽²⁾ spectra are solely attributed to the DL water spectra, which exhibit significant amplitude decrease accompanied with a slight spectral change with the increase of the salt concentration. This result also implies that the SL spectrum at 2.0 M (Imχ_2.0M ≈ Imχ_SL,2.0M⁽²⁾) exists as the unchanged spectra of SL (Imχ_SL) in all Imχ⁽²⁾ spectra in the salt concentration range from 0.01 to 2.0 M. It means that, surprisingly, the SL formed at low NaCl concentration (0.01 M) is unchanged up to the salt concentration as high as 2.0 M.

The analysis using SVD clarifies that we can decompose salt-concentration-dependent Imχ⁽²⁾ spectra at pH 10.0 into two spectral components: (1) the spectrum of the water in DL (Imχ_DL⁽²⁾) that exhibits NaCl-concentration-dependent spectral change and becomes smaller and finally negligible with the addition of NaCl, and (2) the spectrum of the water in SL (Imχ_SL) that exists in all the Imχ⁽²⁾ spectra and unchanged with the change in NaCl concentration from 0.01 to 2.0 M.

3.1.3. Separated DL and SL Spectra at Different pH Values

We perform SVD analysis for the salt concentration-dependent Imχ⁽²⁾ spectra measured at all pH from 2.0 to 12.0 and found that the spectra at other pH can also be analyzed in the same way as the case of pH 10.0 (see Figures S4–S6, and S7-3 in the Supporting Information): at each pH, the Imχ_2.0M⁽²⁾ spectrum can be considered to be the unchanged Imχ_SL spectrum that is included in all the spectra measured with NaCl concentrations from 0.01 to 2.0 M, whereas Dif_Imχ⁽²⁾ spectra are attributed to the Imχ_DL⁽²⁾ spectra that exhibit spectra similar to the corresponding bulk water spectra. This means that the Imχ⁽²⁾ spectra at all pHs examined (pH 2.0–12.0) are represented as the sum of the Imχ_SL and Imχ_DL⁽²⁾ spectra

1

We stress that formula 1 is derived from the model-free spectral decomposition of the Imχ⁽²⁾ spectra using the SVD without assumption of the Stern model. In other words, the present HD-VSFG study provides direct spectroscopic evidence that the EDL structure at the silica/water interface is well described by the Stern model in a wide pH range from 2.0 to 12.0. The separated Imχ_DL⁽²⁾ spectra and Imχ_SL spectra at pH 12.0, pH 7.5, and pH 2.0 are shown in Figure 3, along with the schematic of the Stern model of EDL.

Figure 3.

Separated SL spectra and DL spectra at the silica/water interface and the Stern model of EDL. SL spectra at pH 12.0 (A), 7.5 (B), and 2.0 (C); DL spectra with 0.01 M NaCl solution at pH 12.0 (D), 7.5 (E), and 2.0 (F). (G) Scheme of the Stern model of the EDL structure. SL: compact Stern layer; DL: diffuse Gouy–Chapman layer; Z_SL: thickness of the Stern layer; ϕ₀: potential at the silica surface (surface potential); ϕ_S: potential at the edge of the Stern layer (Stern potential).

As shown in Figure 3A–C, the Imχ_SL⁽²⁾ spectra significantly change as pH changes. This reveals that the water structure in the Stern layer substantially changes with pH, reflecting the change of the negative charge density due to the protonation/deprotonation at the silica surface. In contrast, as shown in Figure 3D–F, the Imχ_DL spectra exhibit similar positive OH bands centered at ∼3300 cm^–1. They are assigned to bulk-like water molecules having H-up orientation (toward the silica surface) in DL, which is induced by the electric field due to the negative charge at the silica surface.^40,41,43 Observation of the H-up water in DL at all pH directly indicates that the silica surface is negatively charged in the pH range of pH 2.0–12.0. The amplitude of the Imχ_DL⁽²⁾ spectra does not show a significant change when pH changes from 12.0 to 7.5, whereas it decreases to about half from pH 7.5 to 2.0. It indicates that the negative charge, and hence the protonation state of the silica surface, substantially changes in this pH region (vide infra).

In the following sections, we separately analyze the pH-dependent changes of the Imχ_DL⁽²⁾ and Imχ_SL spectra to evaluate the pK_a value of the silica surface and pH-dependent water structure in the Stern layer, respectively.

3.2. Analysis of DL Spectra and the pK_a Value of the Silica Surface

In this section, we analyze the DL spectra (Imχ_DL⁽²⁾ = Dif_Imχ⁽²⁾) to estimate the charge density σ₀ at different pHs and the pK_a value of the protonation/deprotonation equilibrium of the silica surface.

3.2.1. Estimation of Surface Charge Density

The amplitude of Imχ_DL⁽²⁾ represents the amount of the oriented water in DL, which is determined by the electric field due to the negative charge at the silica surface. To estimate the charge density σ₀ at the silica surface from the Imχ⁽²⁾ spectra, we first evaluate the Imχ_DL amplitude at a NaCl concentration C₀ by integrating the Dif_Imχ⁽²⁾ spectra in the frequency range of 2900–3800 cm^–1

2

Then, we use as a measure of the magnitude of the spectral response from DL. Figure 4A shows calculated for the NaCl concentration of 0.01–2.0 M at different pHs. As seen in this figure, decreases as the NaCl concentration increases, reflecting the shrinkage of DL. It is known that the amplitude of the spectral response from DL is proportional to the integration of the electric field (E(Z) = −dϕ/dZ) over the DL^9,23,40,53

3

Here, Z_SL is the thickness of the Stern layer, ϕ_S is the Stern potential (the potential at the border between SL and DL), Δk_Z is the inverse of coherence length,^23,53,54Z is the distance from the silica surface, and χ_DL,N⁽²⁾ is the χ_DL amplitude per unit ϕ_S. This χ_DL,N⁽²⁾ is often represented as χ_B and is treated as “third-order” nonlinear susceptibility^{9,21,24,25,48} because this component arises under the existence of three electric fields, that is, the electric fields of incident ω₁ and ω₂ light, and a static electric field generated by the surface charge. Nevertheless, it was recently shown theoretically that the VSFG signal from DL predominantly arises from the second-order optical process, originating from hyperpolarizability (β_ijk), and that the role of the static electric field is to make water molecules oriented in DL.^41,49 To emphasize this point, we represent this spectral component as χ_DL,N⁽²⁾ in this paper, although it is equivalent to χ_B that arises from the orientation of the molecules. Note that the most right-hand side expression of formula 3 is obtained by neglecting e^iΔk_ZZ in DL, which is valid for the C₀ ≥ 0.01 M used in this study.^23,53,54

Figure 4.

Analysis of the Imχ⁽²⁾ signal from the diffuse Gouy–Chapman layer (DL) at the silica/water interface. (A) NaCl-concentration dependence of at different pH. The dashed lines are the best fits using Z_SL = 0.7 nm. (B) Distance dependence of the potential ϕ(Z) calculated by the MGC theory for the surface charge density of σ₀ = 1.0 e/nm² = 0.16 C/m². (C) Salt-concentration dependence of the surface potential ϕ₀ and the Stern potential ϕ_S (Z_SL = 0.2, 0.5, and 0.7 nm) calculated by the MGC theory. (D) Salt-concentration dependence of the Stern potential ϕ_S calculated by the MGC theory for the surface charge density of σ₀ = 0.1, 0.5, and 1.0 e/nm² (corresponds to 0.016, 0.08, and 0.16 C/m², respectively). (E) pH dependence of the surface charge density σ₀ estimated from the experimental Imχ_DL⁽²⁾ spectra. The black solid line is the best fit to eq 5 for the range between pH 2.0 and pH 10.0. The dashed black line is extended from the solid black line for an eye guide.

It is worth mentioning that formula 3 is slightly different from the formula in the literature:^9,21,55 The integration along the Z axis starts not from 0 (or 0+) but Z_SL, and Imχ_DL⁽²⁾ is proportional not to the surface potential ϕ₀ but to the Stern potential ϕ_S. By using ϕ_S, formula 3 can adequately treat the Stern layer as a layer having a finite thickness, being consistent with the Stern model. The difference between ϕ₀ and ϕ_S is the potential decrease in the Stern layer. (Similar treatments can also be found in recent literature.^43,56,57) Formula 3 is equivalent to the following formula that we can use for analyzing the Imχ_DL spectra measured in this study

4

where A_DL,N is the A_DL at the unit ϕ_S. The formula 4 enables us to estimate the salt-concentration dependence of the Stern potential ϕ_S from the Imχ_DL⁽²⁾ spectral amplitudes obtained experimentally.

We use the modified GC (MGC) theory to relate ϕ_S with the surface potential ϕ₀ and surface charge density σ₀ (see Section S5 in the Supporting Information for the details). As an example, Figure 4B depicts the distance dependence of the potential, ϕ(Z), which is calculated with the MGC theory for σ₀ = 1.0 e/nm². In this calculation, we assume that hydrated ions have an ionic diameter (a) of 0.7 nm, according to the previous studies.^23,40 As shown in this figure, the potential ϕ(Z) in the EDL of a 0.01 M NaCl solution decreases from −192 to −40 mV as the distance Z increases from 0 to 3.0 nm. Furthermore, as the NaCl concentration increases from 0.01 to 2.0 M, ϕ(Z) exhibits more and more sharp drops as Z increases due to the screening effect of the counterion. At all the NaCl concentrations, however, ϕ(Z) exhibits the largest decrease in the distance range of Z = 0–0.7 nm. The magnitude of this large potential decrease in the vicinity of the silica surface is insensitive to the NaCl concentration.

The salt-concentration dependence of the surface potential ϕ₀ = ϕ(Z = 0 nm) calculated with the MGC theory is plotted in Figure 4C (blue line). The calculated ϕ₀ decreases as the NaCl concentration increases. However, it does not approach zero even at a NaCl concentration as high as 2.0 M and exhibits an offset. This offset potential comes from the potential drop within the Stern layer, that is, ϕ₀ – ϕ_S, which remains even when the electric field in DL is completely suppressed by the screening effect of the highly concentrated counterions. In other words, we can calculate the Stern potential ϕ_S by subtracting this offset from the surface potential ϕ₀. We calculated the Stern potential by assuming several thicknesses of SL (Z_SL) and found that ϕ_S shows no offset when we set Z_SL at 0.7 nm (Figure 4C, red line). Therefore, we can obtain ϕ_S from ϕ₀ by subtracting the value using Z_SL = 0.7 nm.

The salt-concentration dependence of is calculated for different σ₀ values and shown in Figure 4D. As we can expect from formula 4, the calculated curves show excellent similarity to the curves that are experimentally obtained at each pH (Figure 4A). This agreement assures that the MGC theory adequately describes the NaCl-concentration dependence of Imχ_DL⁽²⁾ from 0.01 to 2.0 M and that the Z_SL value we adopted is adequate. The calculated curves change with the change of the σ₀ value used, whereas the experimental curves change with the change of pH. It means that we can estimate the surface charge density σ₀ at each pH by searching for the σ₀ value that can best reproduce the curve determined experimentally. The σ₀ values at different pHs estimated in this way are plotted in Figure 4E, and the best fits to the curves are shown in Figure 4A (broken lines).

3.2.2. Estimation of the Silica Surface pK_a Value

The estimated σ₀ values directly reflect the surface density of the SiO^– group because the SiO^– group is the only source of the negative charge at the silica surface. As seen in Figure 4E, the pH dependence of the σ₀ value exhibits a significant increase only in the pH region between pH 4.0 and 6.0, implying that the SiO^– density substantially increases in this pH region. In other words, the Imχ_DL⁽²⁾ spectra obtained in this study indicate a single pK_a value for the deprotonation of the SiOH site at the silica/water interface. The pH dependence of σ₀ can be represented by the following equation based on the SiO^–/SiOH equilibrium⁵⁸

5

Here, is the H⁺ concentration at the interface, D_M is the site density of the SiOH groups (which are deprotonated by the pH titration), e is the elemental charge, and D₀ is the density of the negatively charged SiO^– site at pH 2.0. Figure 4E also shows that the σ₀ value estimated at pH 12.0 is substantially smaller than the value estimated at pH 10.0, which cannot be explained simply with the SiO^–/SiOH equilibrium because it is very unlikely that the SiO^– site is more protonated at the higher pH. (This deviation will be discussed in Section 4.2.) Therefore, a fitting of the σ₀ values with formula 5 is made only for the pH range of pH 2.0–10.0, and pK_a = 4.8 ± 0.2 is obtained. (The best fit is shown in Figure 4E with the black solid line). We also collected the Imχ_DL⁽²⁾ spectra at the silica/water interface using different silica substrates (Figure S9A in the Supporting Information). It was found that the obtained spectra somewhat deviated, indicating that the SiO^–/SiOH site density (and hence the surface charge density σ₀) is substantially dependent on substrate. However, the pH dependence of the Imχ_DL amplitude exhibits a significant change only in a single, similar pH range, regardless of the difference in the substrates. This indicates that each silica substrate has only a single pK_a value in the pH range examined in this study, although the SiO^–/SiOH site density is noticeably varied.⁵⁹⁻⁶¹

3.3. Analysis of SL Spectra and pH-Dependent SL Water Structure

In this section, we analyze the SL spectra (Imχ_SL⁽²⁾) obtained at different pHs to elucidate the SL water structure and its change with the change of pH. We apply SVD analysis to the pH-dependent Imχ_SL spectra and obtain a molecular-level picture of the water structure in SL that changes with the change of the charge density at the silica surface.

3.3.1. SL Spectra at Different pH and Spectral Decomposition

Figure 5A shows Imχ⁽²⁾ spectra of SL (Imχ_SL⁽²⁾:Imχ⁽²⁾ spectra with 2.0 M NaCl) at the silica/water interface obtained in the pH range of 2.0–12.0. As shown, the Imχ_SL spectrum drastically changes with the change of pH: At pH 12.0, the spectrum shows a positive broad band peaked at ∼3200 cm^–1. As pH lowers to pH 6.0, the amplitude of the positive band decreases while exhibiting a redshift. At the low pH of pH 4.0 and 2.0, a negative OH band peaked at ∼3150 cm^–1 appears in the low-frequency region, and a positive band appears at ∼3550 cm^–1 in the high-frequency region. The amplitudes of these positive and negative OH bands increase as the pH decreases from pH 4.0 to 2.0.

Figure 5.

SVD analysis of the Imχ⁽²⁾ spectra from the compact Stern layer (SL) at the silica/water interface. (A) SL water spectra (Imχ_SL⁽²⁾ = Imχ_2.0M) at various pH. The reconstructed spectra are also shown with broken lines. (B) Singular values obtained by the SVD analysis of the Imχ_SL⁽²⁾ spectra. Imχ_SL,low represents the Imχ_SL⁽²⁾ spectra in the low pH region (pH 6.0, 4.0, and 2.0). Imχ_SL,high represents the Imχ_SL⁽²⁾ spectra in the high pH region (pH 12.0, pH 10.0, and pH 7.5). The dashed line is the indicator for <2% of the largest singular value, which can be regarded as noise. (C) Difference Imχ_SL spectra (Dif_Imχ_SL⁽²⁾) at various pH. The reconstructed spectra are also shown with broken lines. (D) Singular values obtained by the SVD analysis of Dif_Imχ_SL. Dif_Imχ_SL,low⁽²⁾ represents the Dif_Imχ_SL spectra in the low pH region (pH 6.0, 4.0, and 2.0). Dif_Imχ_SL,high⁽²⁾ represents the Dif_Imχ_SL spectra in the high pH region (pH 12.0, 10.0, and 7.5). The dashed line is the indicator for <2% of the largest singular value, which can be regarded as noise.

To elucidate the molecular origin of the above-described spectral change, we performed the SVD analysis of the pH-dependent Imχ_SL⁽²⁾ and obtained singular values (Figure 5B). The analysis shows three significant singular values. The spectra reconstructed with the three major singular values reproduce Imχ_SL spectra very well in the pH range of pH 2.0–12.0 (broken lines in Figure 5A), indicating that the pH-dependent Imχ_SL⁽²⁾ spectra can be represented as the sum of three independent spectral components. We also perform the SVD analysis of the Imχ_SL spectra in the high pH region (pH 7.5–pH 12.0; Imχ_SL,high⁽²⁾) and low pH region (pH 2.0–pH 6.0; Imχ_SL,low) separately, and found that they have only two significant components (Figure 5B). This result implies that the Imχ_SL,high⁽²⁾ and Imχ_SL,low spectra contain two spectral components, but one of them does not appear in the other. Furthermore, the Imχ_SL⁽²⁾ spectra in the neutral pH region (pH 6.0 and pH 7.5; Imχ_SL,neutral) exhibit a completely different spectral feature from Imχ_SL⁽²⁾ at the high and low pH regions. Thus, we can consider that the Imχ_SL,neutral is the component that is present in all pH-dependent Imχ_SL⁽²⁾ spectra and that the Imχ_SL,high and Imχ_SL,low⁽²⁾ spectra are the sum of the Imχ_SL,neutral and another spectral component. To verify this idea, the difference Imχ_SL⁽²⁾ spectra (Dif_Imχ_SL) are calculated by subtracting Imχ_SL,neutral⁽²⁾ from the Imχ_SL spectra at each pH

6

Here, we adopt the average of the Imχ_SL⁽²⁾ spectra at pH 6.0 and 7.5 as Imχ_SL,neutral. The calculated Dif_Imχ_SL⁽²⁾ spectra are shown in Figure 5C. As expected, the SVD analysis of Dif_Imχ_SL spectra in all pH ranges from pH 2.0 to 12.0 only show two significant singular values, as shown with red squares in Figure 5D. (The Dif_Imχ_SL⁽²⁾ spectra reconstructed with the two components are also shown in Figure 5B with broken lines.) This reduction of the significant singular values for Dif_Imχ_SL implies that the subtraction of Imχ_SL,neutral⁽²⁾ erases the third spectral component. In other words, the Imχ_SL,neutral is the constant/unchanged component that is present in the Imχ_SL⁽²⁾ spectra at all pHs.

As shown in Figure 5C, the spectral feature of the Dif_Imχ_SL⁽²⁾ at high pH (pH 12.0 and pH 10.0) is very similar to each other, while that at low pH (pH 4.0 and pH 2.0) is also very similar to each other. This similarity can be more readily seen after amplitude normalization (Figure S10). In fact, the SVD analyses of the Dif_Imχ_SL spectra at the low pH (Dif_Imχ_SL,low⁽²⁾) and the high pH (Dif_Imχ_SL,high) show only a single significant singular value, indicating that each of Dif_Imχ_SL,high⁽²⁾ and Dif_Imχ_SL,low contain, essentially, only a single spectral component. Therefore, these spectral components have clear physical meanings: Imχ_SL⁽²⁾ spectra specific to the high and low pH regions, which we name Imχ_SL,SpBasic and Imχ_SL,SpAcidic⁽²⁾, respectively.

Consequently, the SVD analysis reveals that the Imχ_SL⁽²⁾ spectra in the pH range of pH 2.0–12.0 can be separated into the following three spectral components: the spectral component that appears only at high pH (Imχ_SL,SpBasic), the spectral component that appears only at low pH (Imχ_SL,SpAcidic⁽²⁾), and the spectral component that appears at all pH without change (Imχ_SL,SpNeutral).

3.3.2. pH-Dependent Water Structure in SL

The spectra of the three spectral components in the Imχ⁽²⁾ spectra of SL (Imχ_SL,SpBasic⁽²⁾, Imχ_SL,SpNeutral, and Imχ_SL,SpAcidic⁽²⁾) are shown in Figure 6A. They represent different water species that appear at different pH in SL of the silica/water interface. In this figure, the Imχ⁽²⁾ spectra of DL (Imχ_DL) are also shown for comparison, which is calculated by averaging the Imχ_DL⁽²⁾ spectra measured with 0.01 M NaCl at pH 2.0–12.0. The Imχ_SL,SpBasic spectrum (red line in Figure 6A), which appears only at high pH, shows a major positive OH band peaked at ∼3150 cm^–1 and a smaller negative OH band around 3500 cm^–1. The low-frequency positive OH band indicates H-up (orienting H toward the silica surface) OH groups that are strongly hydrogen-bonded. The negative OH band in the intermediate frequency region indicates the presence of H-down (orienting H away from the silica surface) OH groups that are hydrogen-bonded with medium strength. The absence of the isotopic dilution effect in the Imχ_SL⁽²⁾ spectrum at pH 12.0 reported in our previous paper indicates that the spectrum at high pH mainly arises from water molecules that are asymmetrically hydrogen bonded.⁴⁰ Therefore, the Imχ_SL,SpBasic spectrum is attributed to the water molecule, which has an OH group that is strongly hydrogen-bonded to the SiO^– groups at the silica surface with H-up orientation and has another OH group that is hydrogen-bonded to other neighboring water molecules with H-down orientation. This picture is consistent with the water structure in SL at the high pH proposed in our previous paper.⁴⁰

Figure 6.

Spectral components of the Imχ⁽²⁾ spectra at the silica/water interface in a pH range from 2.0 to 12.0. (A) Spectra of four spectral components in the Imχ⁽²⁾ spectra (Imχ_DL⁽²⁾, Imχ_SL,SpBasic, Imχ_SL,SpNeutral⁽²⁾, and Imχ_SL,SpAcidic.) The spectra of the Imχ_DL⁽²⁾ component were calculated by averaging the Imχ_DL spectra measured with 0.01 M NaCl at pH 2.0–12.0. (B) pH-dependence of the integrated amplitude of each spectral component. The broken line is an eye guide. (C) Schematic of pH-dependent water structure at the silica/water interface. SL: compact Stern layer; DL: diffuse Gouy–Chapman layer.

The Imχ_SL,SpNeutral⁽²⁾ spectrum (green line in Figure 6A) shows a broad positive OH band peaked at ∼3400 cm^–1. This component appears at all pH range from pH 2.0 to 12.0 with a constant amplitude. The positive sign of this band indicates that the corresponding OH group has the H-up orientation by the interaction with the silica surface. The Si–O–Si bridge site is present at the silica surface, irrespective of the difference in pH as well as deprotonation/protonation of the SiOH/SiO^– site, and its O atom can interact with the OH of water molecules with hydrogen bonding. In our previous HD-VSFG study on the silica/water interface at pH 12.0, we assigned a small positive band at 3600 cm^–1 to the water OH interacting with the Si–O–Si bridge site.⁴⁰ However, the rigorous SVD analysis in this study shows that the small spectral feature at ∼3600 cm^–1 appears as a result of overlap with the Imχ_SL,SpBasic spectral component and that the true spectrum due to the OH group interacting with the Si–O–Si bridge site exhibits a much broader positive band. Nevertheless, this water species is considered minor in SL at the silica/water interface because the amplitude of the Imχ_SL,SpNeutral⁽²⁾ spectrum is small compared to the other two spectral components.

The Imχ_SL,SpAcidic⁽²⁾ spectrum (blue line in Figure 6A), which appears only at low pH, shows a major negative OH band peaked at ∼3200 cm^–1 and a smaller positive OH band peaked at ∼3650 cm^–1. The low-frequency negative OH band indicates strongly hydrogen-bonded OH groups with H-down orientation. The peak frequency of this negative OH band is slightly higher than the frequency of the positive OH band in the Imχ_SL,SpBasic that is assigned to the OH group interacting with the SiO^– site. It implies that the hydrogen bonding of the H-down OH in SL at low pH is slightly weaker than that of the water OH interacting with the SiO^– site. This negative OH band is attributable to the H-down water OH that accepts hydrogen bonding from the SiOH site and/or the OH of the SiOH site itself because these OHs highly likely exhibit a low-frequency negative band due to the strong hydrogen bonding. It is noted that Tuladhar et al. recently reported a DFT-based molecular dynamics simulation that suggested that the negative OH band observed at pH 2.0 are contributed 76% by water and 24% by silanol.⁶² The Imχ_SL,SpAcidic⁽²⁾ spectrum also exhibits a minor positive OH band in the high-frequency region around 3650 cm^–1. This positive band is assignable to the OH groups that are weakly interacting with a surface site that can form weak hydrogen bonding only at low pH. This pH-dependent weak hydrogen-bonding site is considered to be the O atom of the pH-dependent SiOH site rather than the O atom of the pH-independent siloxane bridges (Si–O–Si).⁶³

4. Discussion

4.1. Structure of EDL at the Silica/Water Interface

Based on the results of the experiments and analyses described in Section 3, we first discuss the structure of EDL at the silica/water interface. The water spectrum of DL (Imχ_DL⁽²⁾) (black line in Figure 6A) shows a major OH band similar to the bulk water spectra and exhibits a doublet feature (peaked at ∼3200 and ∼3450 cm^–1). The spectral similarity to the bulk water indicates that the hydrogen-bonding structure of water in DL is not significantly changed by the electric field/Coulomb forces arising from the charge at the silica surface. This experimental observation is consistent with the prediction of theoretical studies.^41,42 Our previous HD-VSFG study revealed that the doublet feature of the band disappears with isotopic dilution.³⁹ Therefore, it arises from the vibrational coupling such as Fermi resonance but not from different water structures, although the two peaks were sometimes called “ice-like” and “liquid-like” bands in the literature.^20,37,64

The water spectra of SL (Imχ_SL⁽²⁾) at different pH are independent from the NaCl concentration in the range from 0.01 to 2.0 M at each pH, and they can be decomposed into three spectral components, that is, Imχ_SL,SpBasic, Imχ_SL,SpAcidic⁽²⁾, and Imχ_SL,SpNeutral which are shown with red, blue, and green lines in Figure 6A, respectively. In some conventional VSFG studies, the bands peaked at 3200 and 3400 cm^–1 were assigned to water in DL and SL, respectively,^24,27,48 but the present HD-VSFG study clearly shows both Imχ_DL⁽²⁾ and Imχ_SL have substantial amplitude around 3200 cm^–1. Furthermore, the SVD analysis of pH-dependent Imχ_SL⁽²⁾ indicates that there is contribution from Imχ_SL,SpNeutral at all pHs, although the amplitudes of Imχ_SL⁽²⁾ at ∼3400 cm^–1 at high and low pH regions are small because of the cancellation of different spectral components.

The Imχ_SL⁽²⁾ spectra and their three spectral components are very different from the Imχ_DL spectrum (Figures 3 and 6). This demonstrates that the direct interaction between the silica surface and the water molecules in SL is much stronger than the effect of the electric field/Coulomb forces on the water in DL. Two strong interactions with the silica surface are possible for water in SL: hydrogen bonding (10–35 kJ/mol)^65,66 and charge–dipole interactions (3–18 kJ/mol).^67,68 In particular, under basic pH conditions where the silica surface is abundant with SiO^– sites, both interactions with negatively charged SiO^– sites can induce the orientation of one OH of the water molecule toward the silica surface in SL, giving rise to the Imχ_SL,SpBasic⁽²⁾ component in the Imχ_SL spectra. On the other hand, under acidic pH conditions, the silica surface is abundant with SiOH sites, and the neutral SiOH acts as the hydrogen-bond donor to induce the OH orientation of water molecules away from the silica surface in SL, as indicated by the Imχ_SL,SpAcidic⁽²⁾ component (Figure 6).

4.2. Surface Charge and pK_a of the Silica Surface

The analysis described in Section 3.2 shows that a significant increase in the surface charge density occurs only at around pH 5.0 (Figure 4E). In the past, several homodyne SHG studies reported multiple pK_a values for the protonation/deprotonation equilibrium at the silica surface based on the two- or three-step increases of the SHG intensity observed with varying pH.^9,25,28 In these SHG studies, the SHG intensity was directly related to the surface potential ϕ₀ under the assumption of the simple GC theory, without separating the contribution from SL and DL. This way of estimating the pK_a value seems unreliable because of the co-existence of the χ_SL⁽²⁾ and χ_DL contributions in total intensity. Indeed, the first (lower) pK_a indicated by the SHG studies is roughly consistent with the pK_a determined from the separated Imχ_DL⁽²⁾ contribution in the present study, whereas the apparent second (higher) pK_a suggested by the SHG data seems to correspond to the changes in the Imχ_SL contribution observed in our data. Because the relationship between the charge density σ₀ and Imχ_SL⁽²⁾ is not clear at the moment, it can be said that, only after separating the Imχ_SL contribution, we can safely evaluate the pH dependence of the charge density σ₀ and the pK_a value of the silica surface from the pH-dependent Imχ_DL⁽²⁾ signal.

We note that the pH dependences of the Imχ_DL⁽²⁾ amplitude of different substrates also show no noticeable increase in the high pH region, indicating a single pK_a value around pH 5.0 (Figure S9A), although the Imχ_DL amplitude itself exhibits some deviations. Similar behaviors of the zeta potential (ϕ_ζ), which increases significantly around pH 5.0 and saturates between pH 6.0 and pH 9.0, have been reported for silica particles.⁶⁹⁻⁷³ The zeta potential ϕ_ζ is known as the potential at the shear plane of DL, which is proportional to the Stern potential ϕ_S (ϕ_ζ ∝ ϕ_S).⁷⁴⁻⁷⁶ This similarity between pH dependences of ϕ_ζ and Imχ_DL⁽²⁾ also validates our analysis of the Imχ_DL spectra and the pK_a value obtained. Thus, we emphasize the importance of separately discussing the DL and SL spectra as well as their pH dependences to obtain a proper/accurate understanding.

The separate discussion of pH-dependent change of the Imχ_DL⁽²⁾ and Imχ_SL also helps us to think about the arguments made in other previous studies. As seen in Figure S11A in the Supporting Information, the integrated intensity exhibits a decrease-then-increase pH dependence with C₀ ≥ 0.1 M. Such a dependence originates from the sign-flip of the Imχ⁽²⁾ amplitude (Figure S11B). In previous conventional homodyne-detected VSFG studies, the sign-flip of the DL component was claimed to explain the decrease-then-increase pH dependence of the VSFG intensity ().^48,56 However, the silica surface is negatively charged from pH 2.0 to pH 12.0, as shown by the positive Imχ_DL⁽²⁾ amplitudes in the present study (Figures S6 and S11C) and the zeta potential reported.⁶⁹⁻⁷³ Thus, it is clear that the sign-flip of Imχ⁽²⁾ solely originates from the sign-flip of Imχ_SL (Figure S11D) rather than the charge reversal of the silica surface during the pH titration. The Imχ_DL⁽²⁾ always appears with a positive sign in the NaCl concentration range of 0.01–2.0 M at all pHs, revealing that no charge reversal occurs with the addition of NaCl. These results also clearly negate the charge reversal of the silica surface at different NaCl concentrations, which was proposed in a simulation study.⁵⁷

The pH dependence of the Imχ_SL⁽²⁾ spectra described in Section 3.3 also brought new insights into the pH-dependent spectra of the water in the vicinity of the silica surface. As shown in Figure 5A, the Imχ_SL spectra show significant change only for the low-frequency OH bands (∼3200 cm^–1), which reflect strong hydrogen bonding with the silica surface. The sign inversion of the total Imχ_SL⁽²⁾ amplitude at around pH 5.0 (Figure S11D) is mainly caused by the sign flipping of this low-frequency OH band. This result strongly indicates that the sign of the Imχ_SL spectrum is not simply determined by the charge and potential at the silica surface. Therefore, it is safe to say that the sign inversion of the net Imχ_SL⁽²⁾ amplitude at around pH 5.0 occurs as the result of the balance between the hydrogen bonding and charge–dipole interactions in SL rather than the reversal of the charge or potential within the SL.

4.3. pH-Dependence of Water Structures in DL and SL

Finally, we discuss the pH-dependent water structure in DL and SL. The absolute amplitudes of Imχ_DL⁽²⁾ and the three spectral components of Imχ_SL (Imχ_SL,SpAcidic⁽²⁾, Imχ_SL,SpNeutral, and Imχ_SL,SpBasic⁽²⁾) are plotted against pH in Figure 6B, which are obtained by integrating the absolute spectral amplitude in the frequency range of 2900–3800 cm^–1 at each pH. This plot represents how the population of the corresponding water species changes in DL and SL, depending on pH.

The Imχ⁽²⁾ spectrum of the silica/water interface at pH 2.0 is dominated by the contribution of Imχ_SL,SpAcidic⁽²⁾. As the pH increases from pH 2.0 to 6.0, the amplitude of the Imχ_SL,SpAcidic decreases, whereas the amplitude of Imχ_DL⁽²⁾ increases. The change of these amplitudes is both attributed to the deprotonation of the SiOH site: the decreases of the Imχ_SL,SpAcidic amplitude reflect the decrease of the surface SiOH density that causes the decrease of the water species that accepts hydrogen-bonding from the OH of SiOH, while the increases of the Imχ_DL⁽²⁾ amplitude arise from the increase of the surface SiO^– density due to the deprotonation of the SiOH, which generates a stronger electric field and hence induces more oriented water in DL.

Interestingly, the amplitudes of Imχ_SL,SpAcidic⁽²⁾ and Imχ_SL,SpBasic are both practically zero, and the contribution of the small Imχ_SL,SpNeutral⁽²⁾ component dominates Imχ_DL in the neutral pH region (pH 6.0 to 7.5), although the pH-dependent amplitude of Imχ_DL⁽²⁾ indicates that the surface charge density is almost saturated at neutral pH. It means that the water in SL has the least net orientation at the neutral pH region, even though the silica surface is negatively charged. This surprising result indicates that the water structure in SL changes collectively rather than each water molecule separately interacting with the surface sites (SiO^– or SiOH), particularly in the neutral pH region.

As the pH increases from pH 7.5 to pH 12.0, the amplitude of Imχ_SL,SpBasic⁽²⁾ increases. The growth of the Imχ_SL,SpBasic amplitude indicates the orientational ordering of the SL water is enhanced in the basic pH region as pH becomes higher. This Imχ_SL,SpBasic⁽²⁾ spectrum corresponds to the water molecules forming strong hydrogen bonding under the high electric field at the charged surface.¹³ It is intriguing that the water ordering in SL is greatly enhanced, although the DL water contribution (Imχ_DL) shows a small decrease at pH 12.0. Such a small decrease in the Imχ_DL⁽²⁾ amplitude is also observed for other silica substrates (Figure S9A). The reason for this observation is not clear at the moment, but it seems that it arises from a phenomenon beyond the MGC theory, such as an increase in the number of Na⁺ in SL and/or a change in the thickness of SL (Z_SL). Such changes would cause a decrease in the Stern potential ϕ_S and the Imχ_DL contribution at pH 12.0, leading to a noticeable decrease in the estimated σ₀ value at this pH (Figure 4E).

As mentioned earlier, the amplitude of Imχ_DL⁽²⁾ exhibits substantial substrate dependence (Figure S9A), whereas the amplitude of Imχ_SL shows almost no noticeable variation (Figure S9B). The Stern layer spectral components obtained from the SVD analysis of different silica substrates (Figure S10C) also show no noticeable variations. These observations support that the amplitude of Imχ_SL⁽²⁾ does not simply reflect the potential of the silica surface that is proportional to the Imχ_DL amplitude but is determined by the multiple properties and interactions appearing in SL.

The molecular picture of water structure in EDL and its pH-dependent changes obtained in this study are illustrated in Figure 6C.

While we were preparing the manuscript of this paper, a combined HD-SHG and conventional VSFG study on the silica/water interface was reported by the Gibbs group and the Geiger group.⁷⁷ In their paper, the Imχ⁽²⁾ spectra at different pH were calculated from homodyne VSFG spectra using the MEM analysis, referring to the Imχ⁽²⁾ spectra reported by our group³⁹ for a phase reference. Then, using the measured zeta potential ϕ_ζ and the Imχ_DL⁽²⁾ spectral shape reported in literature,³⁹ they estimated the Imχ_DL spectral contributions at different pH and calculated the Imχ_SL⁽²⁾ spectra by subtracting the estimated Imχ_DL at each pH. The pH dependences of the Imχ_DL⁽²⁾ and Imχ_SL spectra in their paper fairly accord with the pH dependences obtained in the present study, in particular at high pH and low pH. The basically consistent results obtained with very different approaches assure the validity of these two approaches and the obtained results. Yet, they did not decompose the SL water spectra into the spectra of each SL water species and did not quantitatively discuss the pH-dependent change of their populations. We emphasize that, in the present work, the Imχ⁽²⁾ spectra were directly obtained from the HD-VSFG measurements, and the Imχ_DL⁽²⁾ and Imχ_SL spectra were obtained by the model-free separation using SVD analysis. Therefore, these spectra are free from any assumptions and theoretical models. We stress that this model-free approach allowed us to decompose the Imχ_SL⁽²⁾ spectra into three spectral components and provide detailed, solid information about EDL at the silica/water interface, highlighting the advantage of the direct HD-VSFG measurements.

5. Summary

In this study, we measured the Imχ⁽²⁾ spectra of the buried silica/water interface in a wide pH range (pH 2.0–pH 12.0) with changing the salt concentration (0.01–5.0 M). Taking full advantage of the Imχ⁽²⁾ spectra, we analyzed the obtained spectra using SVD to elucidate the structure of EDL at the silica/water interface. It was found that the Imχ⁽²⁾ spectra can be decomposed into the spectra of DL and SL (Imχ_DL⁽²⁾ and Imχ_SL), demonstrating that the EDL is well described by the Stern model. Furthermore, this spectral decomposition enabled us to quantitatively analyze the water in different parts of the EDL. The positive Imχ_DL⁽²⁾ spectra at all pHs ranging from pH 2.0 to 12.0 indicate that the silica/water interface is negatively charged in the entire pH range investigated. Quantitative analysis of the pH- and salt-dependences of the amplitude of Imχ_DL provides only one single pK_a value of pK_a = 4.8 ± 0.2 with the use of the MGC theory. It was also found that the SL is fully formed at a low salt concentration (0.01 M), and the SL is unchanged up to the salt concentration as high as 2.0 M at all pH examined. The pH-dependent change of Imχ_SL⁽²⁾ is quantitatively explained with the pH-dependent change of the amplitude of the three spectral components (Imχ_SL,SpAcidic, Imχ_SL,SpBasic⁽²⁾, and Imχ_SL,SpNeutral) that represent three different types of water species in SL adjacent to the silica surface. The three water species show distinctive OH orientations and pH-dependent populations, originating from the competition/balance between hydrogen bonding and charge–dipole interaction. These clear molecular pictures of the EDL at the silica/water interface were obtainable only with Imχ⁽²⁾ spectra that are linear to the second-order nonlinear molecular response, which affords the additivity of multiple spectral components and allows us to rigorously use SVD analysis. The present study not only provides a clear molecular picture of EDL at the silica/water interface but also demonstrates the importance and strength of HD-VSFG in investigating various interfaces, including buried interfaces.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.2c11344.

• Optical configuration of the HD-VSFG setup, correction of the χ⁽²⁾ spectra for the Fresnel factor and reflectivity, singular value decomposition (SVD) analysis, salt-concentration dependence of the bulk water spectra and the SVD analysis, modified Gouy–Chapman (MGC) theory, substrate dependence of the DL and SL spectra, normalized difference SL spectra at high pH and low pH, and pH dependence of the integrated intensity and integrated Imχ⁽²⁾ amplitude (PDF)

Author Present Address

^§ Institute of Interdisciplinary Research & School of Optoelectronic Materials and Technology, Jianghan University, Wuhan 430056, China

Author Present Address

^∥ Tokyo University of Science, Kagurazaka, Shinjuku, Tokyo, 162-8601, Japan.

Author Contributions

The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.

The authors declare no competing financial interest.