Elucidation of the pH-Dependent Electric Double Layer Structure at the Positively Charged Amorphous Alumina/Water Interface Using Heterodyne-Detected Vibrational Sum-Frequency Generation

Abstract

Alumina is one of the most abundant oxides in nature. Hence, the molecular-level elucidation of the alumina/water interface is important not only for a fundamental understanding of the oxide surface, but also for applications of oxide-related materials in extensive research fields. In the present study, the water structure in the electrical double layer (EDL) at the alumina–water interface is investigated through the interface-selective vibrational spectra (χ⁽²⁾) in the OH stretch region, measured with heterodyne-detected vibrational sum-frequency generation spectroscopy. The imaginary part of χ⁽²⁾ (Imχ⁽²⁾) spectra is collected while salt concentrations are varied (0.01–5.0 M) in the acidic and neutral pH range (pH 2.0–8.0), where the alumina surface is positively charged. The spectral additivity of the Imχ⁽²⁾ spectra enables the decomposition of the spectra into the contributions of the diffuse layer (DL) and Stern layer (SL) to discuss them separately. The surface charge density at each pH is evaluated from the salt-concentration dependence of the amplitude of the DL spectra using the modified Gouy–Chapman theory, providing a single pK _a value of ∼3.7 ± 0.2 due to the Al₂OH₂ ⁺/Al₂OH equilibrium at the alumina surface. Moreover, it is found that the spectra of the DL and SL are very similar to each other, indicating that the water in the SL is bulk-like water with highly concentrated salt, without specific interaction with the alumina surface. This implies that the water structure of the EDL at the alumina/water interface is much simpler than that at the silica/water interface, where the water molecule has specific interactions with the silica surface. These findings reveal that the alumina/water interface provides another distinct prototype of the EDL structure at oxide/water interfaces.

1. Introduction

Oxides, such as silica (SiO₂) and alumina (Al₂O₃), are the most abundant materials in nature, and they have been attracting extensive attention because they are crucially important in various fields of fundamental and applied science/technology. − Because oxide surfaces are charged when in contact with water, the electric double layer (EDL) is generally formed at oxide/water interfaces. Therefore, molecular-level elucidation of the EDL structure at the interface is essential not only for a fundamental understanding of the oxide surface, but also for the application of oxide-related materials. Many experimental studies have been carried out to elucidate the properties of the EDL at the oxide/liquid interfaces, − and different theoretical models were also proposed to explain the structure of the EDL. − Nevertheless, the understanding obtained from these studies is still limited due to the complexity of the interfaces.

Former applications of vibrational sum-frequency generation (VSFG) spectroscopy have proven that this technique is a powerful tool for investigating oxide surfaces and interfaces. − For instance, the adsorption of organic molecules on the oxide surface was studied by several groups using the VSFG technique. − The pH dependence and salt dependence of the water structure at oxide/water interfaces were also investigated extensively. The VSFG studies have shown that the SFG intensity of water at the oxide/water interface decreases with the increase in salt concentration. − A common understanding is that this SFG intensity decrease by excess salt is due to the screening of the electric field arising from the charged oxide surface, which results in the shrinkage of the diffuse layer (DL) of the EDL and the decrease in the net orientation of water molecules. It has been reported that the dynamics of water molecules at the oxide/water interface were also changed by the addition of salt. ,

Recently, heterodyne-detected (HD-) VSFG spectroscopy has been applied to study the silica/water interfaces. ,− Using this advanced VSFG technique, the spectra of second-order nonlinear susceptibility (χ⁽²⁾) are experimentally obtainable. The conventional VSFG only provides the square of χ⁽²⁾ (|χ⁽²⁾|²) spectra, where the sign information on χ⁽²⁾ is lost, and different spectral components interfere with each other. In the χ⁽²⁾ spectra obtained with HD-VSFG, in contrast, the total spectrum is a simple sum of different spectral components with sign information, and hence, they are readily separated. This linear additive nature of the spectral components in the χ⁽²⁾ spectra enables us to perform spectral decomposition to interpret the spectra unambiguously. In fact, we succeeded in separating the interfacial water spectra at the negatively charged silica/water interface into the spectra of the compact Stern layer (SL) and diffuse Gouy–Chapman layer (DL) based on the quantitative analysis of the salt concentration dependence of the χ⁽²⁾ spectra in a wide pH range from 2.0 to 12.0. The separated salt-dependent DL contribution allowed us to evaluate the surface charge density and to determine the pK _a value using the modified Gouy–Chapman (MGC) theory. Furthermore, the pH-dependent SL spectra clearly showed that three distinct SL water structures appear depending on pH, owing to the specific interaction between the silica surface and interfacial water.

The alumina surface is another important oxide surface. The OH group orientation and surface charge state of the crystalline alumina/water interface were elucidated by the salt-induced changes of the χ⁽²⁾ spectra by the Shen group. − They showed that the alumina surface is positively charged in acidic solutions (pH < 5.0) and negatively charged in basic solutions (pH > 9.0). Several other groups have studied crystalline alumina/water interfaces in various contexts, such as water structure, − ion adsorption, ,, and ice nucleation, using the conventional VSFG technique. Yet, the EDL structure of the alumina/water interface is not well understood. Importantly, the alumina/water interface enables us to investigate the EDL of the positively charged oxide/water interface, which may be essentially different from the negatively charged silica/water interface studied by HD-VSFG previously.

In the present study, we investigate positively charged amorphous alumina/water interfaces to elucidate their EDL structure, taking full advantage of HD-VSFG. The Imχ⁽²⁾ spectra (imaginary part of χ⁽²⁾ spectra) in the OH stretch region (2900–3800 cm^–1) are collected at various salt concentrations in the pH range of 2.0–8.0, where the alumina/water interface serves as a prototypical system of the positively charged oxide/water interface. The salt dependence of Imχ⁽²⁾ spectra indicates that the measured spectra can be separated into the DL and SL components, and the pH dependence of the DL component enables us to evaluate the surface charge density at each pH and hence determine a pK _a value of the alumina/water interface. Furthermore, the pH dependence of the SL spectrum is clarified, revealing the essential nature of the SL water structure at the positively charged alumina/water interface, which is water with highly concentrated salt without specific interaction with the alumina surface, having a net “H-down orientation” (pointing its hydrogen atoms away from the alumina surface).

2. Results

2.1. Salt-Concentration-Dependent Imχ⁽²⁾ Spectra of Alumina/H₂O Interface in the pH Range from pH 2.0 to pH 8.0

To measure Imχ⁽²⁾ spectra by HD-VSFG, alumina films with a thickness of ca. 20 nm were prepared on silica substrate using the atomic layer deposition (ALD) technique, as shown in Figure . The completion of the chemical reaction used in the ALD process was verified by Imχ⁽²⁾ spectra in the CH stretch region (see Section S1). As discussed previously, the phase shift of SFG signals from a thin film on a silica substrate with a thickness lower than 50 nm is negligible. Thus, the ALD-prepared alumina thin films provide a system suitable for investigating the positively charged alumina/water interface.

1.

Scheme of the experiment. (A) Preparation procedure of the Al₂O₃ thin film sample. (B) Sample part of the setup for the HD-VSFG measurements.

Figure shows the Imχ⁽²⁾ spectra of the alumina/water (H₂O) interface measured with various salt concentrations (0.01–5.0 M) at different pH values (pH 2.0–8.0). (The corresponding real part and modulus square of the χ⁽²⁾ spectra are shown in Section S2) The Imχ⁽²⁾ spectra shown in Figure are Fresnel-factor and reflectivity corrected (see Section S3). In this pH range, the ALD-prepared Al₂O₃ thin film on a silica substrate can maintain stability for long-term HD-VSFG measurements. In fact, the alumina thin film is stable at pH 8 or lower but unstable at pH values higher than 9.0 (see Section S1 for details).

2.

$\mathrm{Im}{\chi }^{(2)}$ spectra at the alumina/water interface with bulk NaCl concentrations from 0.01 to 5.0 M at various pH: (A) 2.0 ± 0.1, (B) 3.0 ± 0.1, (C) 4.0 ± 0.2, (D) 5.0 ± 0.2, (E) 6.0 ± 0.2, and (F) 8.0 ± 0.3. The $\mathrm{Im}{\chi }^{(2)}$ spectra shown have been corrected by the reflectivity of LO and Fresnel factors at the alumina/water interfaces.

As shown in Figure A,B, the Imχ⁽²⁾ spectra at pH 2.0 and pH 3.0 in the diluted NaCl solutions (0.01 M) show a large negative OH band peaked at ∼3200 cm^–1 with a shoulder around ∼3450 cm^–1. The negative sign of the OH bands indicates that the interfacial water molecules have an “H-down” orientation (pointing H away from the alumina surface) at the interface. The negative amplitude of the OH bands decreases as the NaCl concentration increases from 0.01 to 2.0 M. This salt-induced decrease in the SFG signal is attributable to the shrinkage of DL, ,, i.e., reduction of the net orientation of “H-down” water molecules, with the screening of the electric field generated by the positive charge at the alumina surfaces. As already discussed in previous studies, the alumina surface is abundant in positive charge under acidic pH conditions, − which is consistent with the Imχ⁽²⁾ spectra indicating the H-down orientation of interfacial water. As the NaCl concentration increases from 2.0 to 5.0 M, the negative amplitude of the OH band around ∼3200 cm^–1 further decreases, while the amplitude decrease around 3450 cm^–1 is less pronounced. At 5.0 M, the Imχ⁽²⁾ spectra at pH 2.0 and pH 3.0 exhibit a negative OH band peaked at ∼3450 cm^–1.

Figure C,D shows the Imχ ⁽²⁾ spectra at pH 4.0 and 5.0, respectively. Although the amplitudes of the negative Imχ ⁽²⁾ band are smaller than those at pH 2.0 and 3.0, they exhibit similar amplitude decreases in the OH bands peaked at ∼3200 cm^–1 and ∼3450 cm^–1 with the increase of the NaCl concentration (from 0.01 to 2.0 M). The decreasing trend is more significant for the amplitude around ∼3200 cm^–1 compared to that around ∼3450 cm^–1. In addition, a shoulder peak at around 3650 cm^–1 is observed at these pH levels, and it does not exhibit noticeable changes with the change in the salt concentration. At the concentration of 5.0 M, the $\mathrm{Im}{\chi }^{(2)}$ spectra show two negative OH bands peaked at ∼3450 cm^–1 and 3650 cm^–1.

Figure E,F shows the Imχ⁽²⁾ spectra at pH 6.0 and 8.0, respectively. The Imχ⁽²⁾ spectra at these two pH levels display the OH band peaked at around ∼3450 cm^–1 and ∼3650 cm^–1 with a much smaller negative amplitude compared to the OH band at the lower pH levels. These Imχ⁽²⁾ spectra show a small but recognizable decrease in amplitude with the addition of excess salt. This observation indicates that the positive charge still exists on the alumina surface at pH 6.0 and 8.0, although the charge density is low.

2.2. Separation of Imχ⁽²⁾ Spectra into the Spectra of DL and SL

For the EDL structure of the charged interface, the Stern model has been widely adopted. ,,,, In this model, a layer of compactly adsorbed ions is formed at the vicinity of the surface (Stern layer, SL), while in the region outside of the SL, the electronic potential and ionic concentration gradually decrease toward the bulk (diffuse layer, DL). In our previous work on the negatively charged silica/water interface, the quantitative analysis of the Imχ⁽²⁾ spectra provided a clear molecular-level picture that is very consistent with the Stern model. In this section, we discuss the Imχ⁽²⁾ spectra of the positively charged alumina–water interface and its relevance to the Stern model, focusing on the spectra taken at pH 2.0.

Figure A shows the Imχ⁽²⁾ spectra of the alumina/H₂O interface at pH 2.0 (which are the same as those in Figure A), and Figure B shows their normalized spectra. As already mentioned in the previous section, the amplitude of the negative OH band largely decreases with the addition of excess salt due to the screening of the electric field arising from the positive charge at the alumina surface. Importantly, the magnitude of the amplitude decrease becomes much smaller at high salt concentrations of >2.0 M, but the OH band remains with substantial amplitude. Because the contribution of the DL water is sufficiently suppressed at such high salt concentrations, the resultant Imχ⁽²⁾ signal can be attributed to the contribution of the SL. In other words, the salt-dependent Imχ⁽²⁾ change of the alumina/H₂O interface at pH 2.0 can be understood based on the Stern model. Interestingly, the normalized Imχ⁽²⁾ spectra (Figure B) indicate that the spectral shape exhibits only a small, gradual change, while the amplitude of the DL component drastically decreases with the addition of excess salt. This implies that the difference between the DL-dominant Imχ⁽²⁾ spectrum (0.01 M) and SL-dominant Imχ⁽²⁾ spectrum (>2.0 M) is minor, i.e., only the change in the relative amplitude of the 3200 cm^–1 and 3450 cm^–1 peaks.

3.

(A) The spectra, (B) the normalized $\mathrm{Im}{\chi }^{(2)}$ spectra, and the separated (C) SL and (D) DL spectra at the alumina/H₂O interface at pH 2.0. (E) The $\mathrm{Im}{\chi }^{(2)}$ spectra, (F) the normalized $\mathrm{Im}{\chi }^{(2)}$ spectra, and the separated (G) SL and (H) DL spectra at the alumina/HOD (H₂O:D₂O = 1:4) interface at pD 2.0. All the spectra in (B) and (F) were normalized to the amplitudes at 3335 cm^–1 and at the peak frequency, respectively.

The singular value decomposition (SVD) analysis , shows that the spectral changes observed by changing the salt concentration from 0.01 to 5.0 M are well reproduced with only two major components, which can be explained by the amplitude changes and the spectral shift induced by the increase in salt concentration (see Section S4). This indicates that the difference in the Imχ⁽²⁾ spectra between SL and DL can be explained solely by the difference in the salt concentration between the two layers.

Because the OH band of the H₂O spectra often exhibits complexity due to the intra/intermolecular vibrational couplings, we also measured the Imχ⁽²⁾ spectra using isotopically diluted water (20% H₂O in D₂O), in which the vibrational couplings are greatly suppressed and hence the interpretation can be simplified. Figure E shows Imχ⁽²⁾ spectra at the alumina/isotopically diluted water interface (the alumina/HOD interface) at pD 2.0, and Figure F shows their normalized spectra. The Imχ⁽²⁾ spectrum at the alumina/HOD interface with the lowest salt concentration (0.01 M, red line in Figure E) shows an OH band with a single peak at ∼3450 cm^–1, which is markedly different from the double-peaked OH band (peaked at ∼3200 cm^–1 and ∼3450 cm^–1, red line in Figure A) in the spectra at the alumina/H₂O interface. This implies that the double-peak feature of the OH band at the alumina/H₂O interface originates from vibrational coupling, which exists in H₂O but is absent in HOD. Remarkably, the normalized Imχ⁽²⁾ spectra in Figure F show that the single-peaked OH band at the alumina/HOD interface does not exhibit recognizable spectral change with the addition of salt up to 2.0 M. This means that the Imχ⁽²⁾ spectra of SL and DL at the alumina/HOD interface are indistinguishable up to 2.0 M because the DL contribution largely decreases with the addition of excess salt. The OH band in the normalized Imχ⁽²⁾ spectra at the alumina/HOD interface also shows significant spectral shifts at a concentration higher than 2.0 M: the peak of the OH band shifts from ∼3450 cm^–1 to ∼3500 cm^–1 at the highest concentration of 5.0 M (pink dashed lines in Figure F). Because the DL contribution is sufficiently suppressed at such a high salt concentration, this spectral change indicates that the SL water structure starts changing when the NaCl concentration exceeds 2.0 M.

A simulation based on the modified Gouy–Chapman (MGC) theory shows that the screening effect on the electric field by the excess salt is almost saturated, and the electronic potential at Z = 1.0 nm is nearly zero at the concentration of 2.0 M (Figure S5A). , In other words, the theory indicates that the DL sufficiently shrinks at this high salt concentration, and hence the resultant spectra can be attributed to the SL. In fact, MGC theory also indicates that the electric potential sharply decreases in the vicinity of the interface (<1 nm), and the magnitude of the potential decrease is not very sensitive to the salt concentration (Figure S5A), which fits well with the concept of SL. Furthermore, the salt-concentration-dependent Imχ⁽²⁾, particularly those at the alumina/HOD interface, show that the spectral shape exhibits no change in the salt concentration range from 0.01 to 2.0 M, while DL contribution substantially changes, implying that the SL spectrum does not change in this range of salt concentration. Therefore, it is reasonable to regard the Imχ⁽²⁾ spectrum at 2.0 M NaCl as the spectrum of the SL $(\mathrm{Im}{\chi }_{\mathrm{SL}}^{(2)})$ , which does not change in the salt concentration range of 0.01–2.0 M (Figure C,G), as in the case of the silica/water interface. Consequently, we can attribute the difference spectrum from the $\mathrm{Im}{\chi }^{(2)}$ spectrum with 2.0 M salt $(\mathrm{Dif}\_\mathrm{Im}{\chi }^{(2)}=\mathrm{Im}{\chi }^{(2)}-\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)})$ to the spectrum of the DL (Figure D,H) although $\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)}$ might still contain a very small contribution from DL.

The very surprising finding for the alumina–water interface is the very minor change in the spectral shape with the addition of excess salt. In fact, for the alumina/H₂O interface, the spectral shapes of the SL spectrum (2.0 M spectrum), and DL spectra $(\mathrm{Dif}\_\mathrm{Im}{\chi }^{(2)})$ only show a small difference in the relative amplitude between the 3200 cm^–1 and 3450 cm^–1 OH bands (Figure C,D). As for the alumina/HOD interface, the spectral shapes of the SL spectrum (2.0 M spectrum) and DL spectra $(\mathrm{Dif}\_\mathrm{Im}{\chi }^{(2)})$ are indistinguishable (Figure G,H). These results mean that the water structure in SL is very similar to that in DL at the alumina–water interface, at least from the viewpoint of the water structure. In other words, the Imχ⁽²⁾ spectra do not provide any indication of the specific interaction between water and alumina surface at pH 2.0, although the alumina surface has substantial positive charges. Regarding the relative amplitude change between the 3200 cm^–1 and 3450 cm^–1 peaks of the OH band at the alumina/H₂O interface, this change is considered to arise from the change in the vibrational coupling of H₂O induced by the change in salt concentrations. Because the relative amplitude of the double peaks due to the vibrational coupling in H₂O is very sensitive to the salt concentration, we consider that the salt-concentration-dependent spectral change up to 2.0 M can be recognized only for the alumina/H₂O interface.

2.3. Analysis of pH-Dependence of the DL Spectra and the pK _a Value of the Aluminum Surface

To obtain a quantitative understanding of the EDL structure at the alumina/water interface, we evaluate the surface potential as well as related parameters, such as the surface charge density and pK _a values, by analyzing the Imχ⁽²⁾ spectra of the DL. As discussed in the previous section, the total Imχ ⁽²⁾ signal observed from the alumina/water interface is expressed as $\mathrm{Im}{\chi }_{\mathrm{total}}^{(2)}=\mathrm{Im}{\chi }_{\mathrm{DL}}^{(2)}+\mathrm{Im}{\chi }_{\mathrm{SL}}^{(2)}$ , where $\mathrm{Im}{\chi }_{\mathrm{DL}}^{(2)}$ and $\mathrm{Im}{\chi }_{\mathrm{SL}}^{(2)}$ are the contributions of the DL and the SL, respectively (The sketch of the EDL structure is shown in Figure A). Between the two terms, $\mathrm{Im}{\chi }_{\mathrm{DL}}^{(2)}$ is directly related to the surface potential at the SL plane ${\varphi }_{\mathrm{S}}$ , by assuming the charge-induced orientation of the DL water is proportional to the static electric field (E ₀) arising from the charge at the interface. Then, we obtained the following equation:

$${\chi }_{\mathrm{total}}^{(2)}={\chi }_{\mathrm{DL}}^{(2)}+{\chi }_{\mathrm{SL}}^{(2)}={\varphi }_{\mathrm{S}}{\chi }_{\mathrm{DL},\mathrm{N}}^{(2)}+{\chi }_{\mathrm{SL}}^{(2)}$$ 1

Here, ${\chi }_{\mathrm{DL},\mathrm{N}}^{(2)}$ is the normalized ${\chi }_{\mathrm{DL}}^{(2)}$ contribution per unit potential, which is also called ${\chi }^{(3)}$ contribution in literature. ,,,,,

4.

(A) Scheme for EDL structure at alumina/water interface. (B) Concentration $(C_0)$ dependence of integrated amplitude $A_{\mathrm{D}\mathrm{L}}(C_0)$ at various pH values. $C_0$ is NaCl concentration in the bulk solution. The dashed lines are fitted curves using eq (). The data points are the average of at least two data sets, and the error bars indicate deviations from the average. (C) pH dependence of the surface charge density ${\sigma }_0$ at the alumina/water interface. The dashed red line is the fitted curve using eq ().

To quantify the experimental $\mathrm{Im}{\chi }^{(2)}$ spectra shown in Figure , we integrate the amplitude of the OH band in the frequency range from 2900 to 3800 cm^–1, $(A(C_0)={\int }_{2900{\mathrm{cm}}^{-1}}^{3800{\mathrm{cm}}^{-1}}\mathrm{Im}{\chi }^{(2)}\mathrm{d}\omega )$ . Then we obtain,

$$\mathrm{A}(C_0)=A_{\mathrm{DL}}(C_0)+A_{\mathrm{SL}}(C_0)={\varphi }_{\mathrm{S}}{A}_{\mathrm{DL},\mathrm{N}}(C_0)+A_{\mathrm{SL}}(C_0)$$ 2

where C ₀ is the NaCl concentration in the bulk solution, A _DL (C ₀ ) represents the magnitude of the contribution from the DL, and $A_{\mathrm{SL}}(C_0)$ is that from the SL (note that the small salt-induced spectral shift in the ImX ⁽²⁾ spectra does not contribute to the integrated amplitude). As we explained in the previous section, it can be considered that the SL does not change in the salt concentration range of 0.01–2.0 M. Therefore, $A_{\mathrm{SL}}(C_0)$ can be treated as the constant offset up to 2.0 M salt concentration, assuming A(2.0 M) as A _SL. Then, we can rewrite eq () as follows,

$$A_{\mathrm{DL}}(C_0)=A(C_0)-A(2.0\mathrm{M})={\varphi }_{\mathrm{S}}(C_0)A_{\mathrm{DL},\mathrm{N}}({\mathrm{C}}_0\le 2\mathrm{M})$$ 3

This expression is the same as the one used for the silica/water interface in our previous work. ,

Figure B shows the salt-concentration dependence of the A _DL(C₀) values at various pH levels. These curves show a drastic decrease in the low-concentration region, and the decrease becomes smaller in the higher-concentration region. These curves can be fitted with salt-dependent ${\varphi }_{\mathrm{S}}(C_0)$ that is calculated using MGC theory. In this calculation, the surface charge density (σ₀) is treated as a fitting parameter to reproduce the A _DL(C₀) curves at different pH levels, with the thickness of the Stern layer of 1.0 nm, i.e., ϕ_s = ϕ (1.0 nm) (see Section S5). The best fits of the salt-concentration-dependent A _DL(C₀) curves at different pH levels are shown with the dotted curves in Figure B, which accurately reproduce the A _DL(C₀) curves obtained experimentally.

The ${\sigma }_0$ values obtained from the salt-concentration-dependent A _DL(C₀) curves at different pH levels are plotted in Figure C. As seen in this figure, the ${\sigma }_0$ value exhibits a drastic change in the pH region between pH 3.0 and 4.0, implying that the positive surface charge density noticeably changes only in this pH region. In other words, the $\mathrm{Im}{\chi }_{\mathrm{DL}}^{(2)}$ spectra obtained in this study indicate a single pK _a value at around this pH value for the protonation of the molecular sites at the alumina/water interface.

The pH dependence of ${\sigma }_0$ can be represented by the following equation based on the pH titration equilibrium:

$${\sigma }_0(\mathrm{pH})=\frac{D_{\mathrm{M}}}{1+{10}^{\mathrm{p}{K}_a}{[{\mathrm{H}}^{+}]}_{\mathrm{s}}}+D_0$$ 4

$${[{\mathrm{H}}^{+}]}_{\mathrm{s}}={10}^{-\mathrm{pH}}\exp (-\frac{e{\varphi }_0}{k_{b}T})$$ 5

Here, ${[{\mathrm{H}}^{+}]}_s$ is the H⁺ concentration at the interface, D_M is the surface density of the positively charged groups, ${\varphi }_0$ is the surface potential, e is the elemental charge, and D ₀ is the surface density of the positively charged molecular groups at pH 8.0. The curve fitting of the ${\sigma }_0$ values with eq () provides a pK _a value of 3.7 ± 0.2. The best fit is shown with a dashed line in Figure C. We note that a similar drastic change in SFG intensity around 3200 cm^–1 and 3400 cm^–1 was also observed at pH ∼ 4.0 in the studies of the crystalline alumina surfaces. −

2.4. Analysis of pH-Dependence of the SL Spectra and the SL Water Structure

In this section, we analyze the SL spectrum and its pH dependence. In section , we discussed the salt-concentration-dependent Imχ⁽²⁾ spectral shape at pH 2.0 and concluded that the Imχ⁽²⁾ spectrum at 2.0 M NaCl (Im ${\chi }_{2\mathrm{M}}^{(2)}$ spectrum) can be considered the spectrum of SL. Furthermore, at pH 2.0, where the alumina surface is positively charged, the SL water structure can be considered, basically, as water with highly concentrated salt without any noticeable specific interaction with the alumina surface, as represented by the double-peaked OH band for H₂O. When we examine the Imχ⁽²⁾ spectra at higher pH levels , e.g., pH 6.0 and 8.0 (Figure E,F), we notice that another band at 3650 cm^–1 appears, which is not observed in the Imχ⁽²⁾ spectra at low pH levels, such as pH 2.0. Consequently, the pH-dependent Imχ⁽²⁾ spectra of SL can be analyzed with these two spectral components, i.e., the band showing double peaks at 3200 cm^–1 and 3450 cm^–1, and the band peaked at 3650 cm^–1.

In order to analyze the pH-dependent changes in the SL spectrum more quantitatively, global fitting analysis was performed for the SL spectra (Im ${\chi }_{2\mathrm{M}}^{(2)}$ spectra) at different pH values using three Gaussian functions,

$$\mathrm{Im}{\chi }^{(2)}(\omega )=\sum _{\mathrm{n}}^3{A}_{\mathrm{n}}{e}^{-\frac{1}{2}{(\frac{\omega -{\omega }_{\mathrm{n}}}{{\tau }_{\mathrm{n}}})}^2}$$ 6

where $A_{\mathrm{n}}$ , ${\omega }_{\mathrm{n}}$ , ${\tau }_{\mathrm{n}}$ are the amplitude, center frequency, and spectral width of each Gaussian, respectively. Figure shows the observed $\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)}$ spectra as well as the best fits obtained from the fitting. As seen, the results of the global fitting show that $\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)}$ spectra can be well fit with the three Gaussians peaked at ∼3200 cm^–1, ∼3450 cm^–1, and ∼3650 cm^–1 (see Section S6). Note that the two Gaussians peaked at ∼3200 cm^–1 and ∼3450 cm^–1 represent the double-peaked band.

5.

(A) $\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)}$ spectra at different pH values and the best fits using eq ( ). (B) pH dependence of the area intensities of the two spectral components in the SL spectra at the alumina/water interface (black squares: A ₁ + A ₂ = A ₃₂₀₀ + A ₃₄₅₀; red dots: A ₃ = A ₃₆₅₀). The dashed lines are eye guides. The data points in (B) are the average of at least two data sets, and the error bars indicate deviations from the average.

As seen in Figure S6-1, the $\mathrm{Im}{\chi }_{2\mathrm{M}}^{(2)}$ spectrum at pH 2.0 (red line in Figure A) can be fit predominantly with two negative Gaussians peaked at ∼3200 cm^–1 and ∼3450 cm^–1 with comparable amplitudes. As the pH value increases to pH 8.0 (black line in Figure A), the relative amplitude of these two components (A ₁/A ₂ = A ₃₂₀₀/A ₃₄₅₀) substantially decreases. Because the estimated density of aluminol OH oscillators (4–13 OH/nm²) − is lower than the density of the OH oscillators of water molecules (25 OH/nm²), this double-peaked OH band at ∼3200 cm^–1 and ∼3450 cm^–1 is predominantly assignable to the hydrogen-bonded OH of the SL water molecules, although the OH stretch of the surface OH groups may contribute to some extent. The change in the relative amplitude of the two peaks is considered to arise from a pH-dependent change in the OH stretching frequency and the resultant change in the vibrational coupling. The plot of the amplitude ratio ((A ₁/A ₂) at different pH (Figure S6-2) shows that the most drastic change occurs at the pK _a (3.7 ± 0.2) of the alumina surface determined in this study. Thus, this spectral change highly likely reflects the change in equilibrium at the alumina surface and the resultant change in the surface charge density.

The third spectral component peaked at 3650 cm^–1 is significant at high pH values (> 4.0). Because the frequency is high, this component is attributable to the OH stretch of the weakly hydrogen-bonded OH groups. A high-frequency band at ∼3700 cm^–1 was reported in a homodyne VSFG study of the crystalline alumina(0001)/water interface, and this band was assigned to the OH stretch of the surface Al₂OH groups. We calculate ${|{\chi }^{(2)}|}^2$ spectra using the Imχ⁽²⁾ and Reχ⁽²⁾ spectra obtained in the present study and found that the 3650 cm^–1 peak in the Imχ⁽²⁾ spectra appears at ∼3680 cm^–1 in the ${|{\chi }^{(2)}|}^2$ spectra (Figure S2–2) due to the interference with the real part of χ⁽²⁾ (Reχ⁽²⁾), confirming that the origin is the same. The Imχ⁽²⁾ spectra measured in this study clearly show that this high-frequency OH band has a negative sign, indicating a H-down orientation (OH orienting toward the bulk). Therefore, the sign information on this band obtained with the present HD-VSFG measurements supports the assignment of this band to the OH stretch of the surface OH groups (Al₂OH) as it should have an H-down orientation. A former study reported that the apparent peak frequency of the high-frequency band of the amorphous alumina surface is lower than 3600 cm^–1. This may be attributable to the different preparation procedures of the amorphous alumina films, such as the annealing process at 550 °C in the present study.

The amplitude of the double-peaked OH band (A ₁ + A ₂ = A ₃₂₀₀ + A ₃₄₅₀) and that of the 3650 cm^–1 OH band (A ₃ = A ₃₆₅₀) at different pH values are plotted in Figure B. Interestingly, A ₁ + A ₂ representing hydrogen-bonded OH in SL, only gradually decreases as the pH value increases from 2.0 to 8.0. This is in sharp contrast to the amplitude of hydrogen-bonded OH in DL, which sharply changes at pK _a, reflecting the drastic change in the surface charge, as discussed in the previous section. This suggests that the oriented water molecules in SL are not solely governed by the electric field due to the surface charge. In contrast, A ₃ shows a sharp rise between pH 3.0 and 4.0, which accords with the pK _a value (3.7 ± 0.2) evaluated from the analysis of DL water spectra. This indicates that the 3650 cm^–1 OH band arises from the OH species increasing as the alumina surface becomes neutral, which further supports the assignment of this band to the OH stretch of the Al₂OH groups at the alumina surface. Nevertheless, we note that the A ₃ value is not zero even at pH 2, implying that some Al₂OH groups may have a lower pK _a. ,

3. Discussion

The present study provides the $\mathrm{Im}{\chi }^{(2)}$ spectra for the entire OH stretch frequency range of 2900–3800 cm^–1 in the pH range from pH 2.0 to 8.0, with systematically changing salt concentration. The thorough measurements enable us to separate the spectra of DL and SL at each pH, allowing us to obtain a molecular-level understanding of the EDL structure at the positively charged alumina/water interface.

The analysis of the pH dependence of the DL water contribution indicates a single pK _a value (pK _a = 3.7 ± 0.2) in the pH range from pH 2.0 to 8.0 (Figure C). It is known that the alumina surface can be positively charged, neutral, or negatively charged, depending on pH, and hence exhibits bipolar pH dependence, showing multiple pK _a values. The pK _a in the low pH region determined in this study is ascribed to the equilibrium between positively charged and neutral species at the alumina surface. Previously, several possible acid–base equilibria were proposed for the low pK _a, e.g., Al₂OH₂ ⁺/Al₂OH, Al₂OH⁺/Al₂O, Al₃OH⁺/Al₃O. Among them, the contribution of the Al₂OH₂ ⁺/Al₂OH has been believed to be predominant under acidic pH conditions. , This assignment is consistent with the observation of the 3650 cm^–1 OH band observed above pH 4.0, which is assignable to the OH stretch of the Al₂OH groups. Thus, following the former studies, we assign the acid–base pair showing pK _a at 3.7 predominantly to Al₂OH₂ ⁺/Al₂OH. (Accordingly, the acid–base pair giving a higher pK _a value is considered to be Al₂OH/Al₂O^–.) It is noteworthy that in the Imχ⁽²⁾ spectra at neutral pHs (pH 6.0 and pH 8.0) collected in this study, the amplitude of the OH band still shows a small but noticeable decrease with the addition of excess salt. This observation indicates the presence of the DL contribution at these pHs. In other words, the alumina surface is slightly positively charged, even at pH 8.0. This likely suggests the existence of other surface OH species, such as Al₂OH⁺ or Al₃OH⁺ at neutral pH. Nevertheless, the small salt-induced change in Imχ⁽²⁾ spectra at pH 8.0, i.e., small DL contribution, indicates that the positive charge density in the neutral pH region is very small (<5%) compared to pH 2.0 and 3.0. Thus, we do not consider that these minor surface species noticeably affect the SL water spectrum.

The salt-concentration dependence of the Imχ⁽²⁾ spectra indicates that the spectrum with 2.0 M salt can be considered the spectrum of SL. Remarkably, it is found that the SL spectrum at the alumina/water interface is indistinguishable from the DL spectrum, except for the difference in the amplitude. In this regard, the SL water of the positively charged alumina–water interface is very different from that at the negatively charged silica/water interface. As reported in our previous paper, the SL water spectra of the silica/water interface indicate specific interactions between the interfacial water and the silica surface. For instance, the SL water at the silica/water interface shows a negative OH band (H-down) around 3150 cm^–1 due to the interaction with SiOH under acidic conditions, whereas the SL water shows a positive OH band (H-up) around 3100 cm^–1, which arises from the interaction with the SiO^– group under basic conditions. This demonstrates that the SiOH and SiO^– surface groups can act as strong hydrogen bond donors and acceptors, respectively, inducing a substantial red-shift of the OH stretch frequency of the SL water, regardless of the up/down orientation. In sharp contrast, the SL spectra of the alumina/water interface show bulk-like spectra that look essentially the same as those of DL. This implies that the hydrogen bonding between the SL water and alumina surface moieties is similar to the hydrogen bonding between water molecules, at least when we use NaCl as the salt. The SL spectra obtained in this study show no evidence to indicate a specific interaction between SL water and the alumina surface. Because the aluminol groups are considered to act as hydrogen-bond donors, it implies that the surface aluminol groups (Al₂OH₂ ⁺/Al₂OH) are not as good hydrogen-bond donors as the SiOH at the silica interface but are moderate hydrogen bond donors, even though they are positively charged under acidic conditions.

The present study shows that the alumina/water interface fits into the concept of the Stern model, in which the EDL consists of the SL and DL, as in the case of the silica/water interface investigated in our previous study. Furthermore, it is found that the salt-concentration dependence of the DL contribution to the observed Imχ⁽²⁾ spectra can be quantitatively described by simple MGC theory up to 2.0 M, also at the alumina/water interface. On the other hand, the SL water structures are remarkably different between the two interfaces: at the silica/water interface, the SL water has specific interactions with SiOH, SiO^–, and Si–O–Si sites, whereas the SL water at the alumina/water interface resembles water with highly concentrated salt, without specific interaction with the alumina surface. In this sense, the water structure of the EDL at the alumina/water interface is simpler, and it fits well with the concept of the MGC theory that does not include any specific interactions and only considers the ion size to represent the ion–ion interaction. This implies that the roles of nonelectrostatic interactions are insignificant in describing the EDL at the alumina/water interface up to 2 M salt in the pH range of 2.0–8.0, at least when NaCl is employed as the salt. A more complex model, including ion-surface interaction, may be needed when other salts that show specific adsorption are employed or for understanding the change in the Imχ⁽²⁾ spectra observed at very high salt concentrations (>2.0 M).

The schematics of the EDL at the alumina–water interface at various salt concentrations and pH levels are depicted in Figure . Under acidic conditions, the alumina surface is abundant with positively charged surface species, Al₂OH₂ ⁺ groups, and water molecules taking an “H-down” orientation due to the electric field created by the positive charge at the alumina surface. In the H-down orientation, SL water is considered to donate hydrogen bonds toward DL water and neighboring SL water molecules while accepting hydrogen bonds from the surface Al₂OH₂ ⁺ groups. The addition of excess salt suppresses the DL water with the screening effect. The DL is considered sufficiently suppressed at 2.0 M salt concentration, and hence the Imχ⁽²⁾ spectrum at this salt concentration can be regarded as the spectrum of SL. The SL spectrum at acidic pH shows a double-peaked spectral feature similar to the DL spectrum, indicating that the SL water structure is very similar to the DL water (bulk-like water) and that the difference between SL and DL is essentially a difference in salt concentration. The spectral change observed at higher salt concentration is considered to arise from the change of the SL water structure owing to a further increase in the salt concentration in SL. In fact, the SVD analysis shows that the spectral change observed in the whole salt concentration range (0.01 M – 5.0 M) only shows two major components, which can be explained in terms of the bulk-like water band and its concentration-dependent spectral shift.

6.

Schematic of the salt- and pH-dependent EDL structures at the alumina/water interface. SL: Stern layer; DL: diffuse layer.

Under neutral pH conditions, the alumina surface is abundant with neutral surface species, i.e., Al₂OH groups. Nevertheless, a small number of positive charges due to minor surface species induce the “H-down” orientation of SL and DL water molecules. Consequently, the addition of salt still induces a small decrease in the amplitude of the Imχ⁽²⁾ spectra, reflecting the shrinkage of the DL water contribution. The SL spectrum at neutral pH shows a high-frequency OH band at 3650 cm^–1, which is attributable to the OH stretch of the charge-neutral Al₂OH surface species.

The amorphous alumina interface studied in this study provides another prototypical EDL structure at the positively charged oxide/water interface, which interacts moderately without specific interactions with interfacial water molecules. This interface differs significantly from the negatively charged silica/water interface, where the oxide surface and interfacial water exhibit strong specific interactions.

4. Conclusion

In the present study, Imχ⁽²⁾ spectra in the whole OH stretch region of 2900–3800 cm^–1 were collected at the amorphous alumina/water interface at various pH levels, ranging from pH 2.0 to 8.0, while varying the salt concentration from 0.01 to 5.0 M. Our results provide a comprehensive molecular-level picture of how the EDL changes at the positively charged interface by separating multiple spectral components, which is made possible by the additivity of spectral components in the Imχ⁽²⁾ spectra. Quantitative analysis of the Imχ⁽²⁾ spectra based on MGC theory provides information on the pH-dependent surface charge density ${\sigma }_0$ and the acid dissociation constant $\mathrm{p}{K}_{\mathrm{a}}$ of 3.7 ± 0.2. The DL and SL water spectra can be understood as the bulk-like water spectrum with the salt-concentration-dependent spectral shift. These results indicate no specific interaction between SL water and the alumina surface.

The present study once again demonstrates the strength and capabilities of the HD-VSFG technique in investigating complex charged buried interfaces. The measurements and analysis performed in the present study, as well as those in our previous study for the silica/water interface, provide a versatile spectroscopic protocol for elucidating the EDL structure and quantifying surface properties, e.g., the charge density at the positively and negatively charged solid/electrolyte interfaces. These findings are fundamentally important because detecting and controlling molecular behaviors at the charged surfaces/interfaces is of general importance in biomembranes, catalysis, sensors, and electrochemistry.

Glossary

Abbreviations

HD-VSFG

heterodyne-detected vibrational sum-frequency generation

SVD

singular value decomposition

EDL

electrical double layer

MGC theory

modified Gouy–Chapman theory

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c18656.

• S1: experimental details; S2: Reχ⁽²⁾ spectra and |χ⁽²⁾|² spectra of the alumina/water interface; S3: correction of reflection coefficient and Fresnel factor; S4: SVD analysis; S5: fitting method using MGC theory; and S6: fitting results of the SL spectra (PDF)

The manuscript was written with contributions from all authors. All authors have given approval to the final version of the manuscript.

This work was supported by JSPS KAKENHI (Grant No. 23H00292) and the Excellent Discipline Cultivation Project by JHUN (Grant No. 2023XKZ044).

The authors declare no competing financial interest.