Acidic and Electrosurface Properties of Binary TiO2-SiO2 Xerogels Using EPR of pH-Sensitive Nitroxides

The binary xerogels TiO2-SiO2 are widely used as catalysts and their carriers in organic synthesis. Characterization and adjustment of the electrostatic properties of the surface and the local acidity inside the pores, are necessary for the further development of TiO2-SiO2 xerogels applications. This research investigates acid–base equilibria in the pores, and the surface electrostatic potential (SEP) of binary TiO2-SiO2 xerogels, by the EPR of stable pH-sensitive nitroxide radicals. These radicals are small enough to penetrate directly into the pores, and to be adsorbed onto the surface of the material under study. This makes it possible to obtain valuable information on the acidic and electrosurface properties of the studied system. The highest negative surface electrical charge associated with surface electrical potential (SEP) was equal to −196 ± 6 mV. It was induced by the surface of the sample with a 7% TiO2 content. The local acidity inside the pores of this sample was found to be higher, by approximately 1.49 pH units, as compared to that in the external bulk solution.


Introduction
The binary SiO 2 -TiO 2 xerogels have been applied in a variety of fields of science and technology. These materials are widely used in optical waveguides and sensors [1], hydrophilic coatings, selective sorbents for purification of air [2,3], and aqueous media [4] made from organic and inorganic compounds [5][6][7], and in self-purifying materials, based on glass [8] or cotton [9]. They have been successfully applied as carriers of catalysts in the Fischer-Tropsch process [10] and various oxidation reactions [11], as well as a matrix for the immobilization of the biomacromolecules and components of drug delivery systems [12]. Cu(II)-containing TiO 2 -SiO 2 xerogels were investigated and found to be efficient photocatalysts [13]. Polyfunctional heterogeneous systems, based on Cu(II)-containing titanium dioxide, were proven to consist of various self-organized copper-containing structures, which are catalytically active in the reactions of hydroxyarene oxidation [14][15][16][17].
At present, the sol-gel technology is widely used as a method of synthesis, based on the reactions that were developed by Nikolaon and Teichner in 1976, to obtain silica aerogels [18]. These are the reactions of the hydrolysis and gelation of alkoxides or other reactive compounds in an alcohol solution, with the addition of acids and alkalis as catalysts.
It was found that in different processes utilizing these xerogels, the acidity of the solutions contacting with them plays an important role; however, the pH values of the

Xerogels Characterization
The morphology of the oxide xerogels was examined by SEM. Figure 1 shows the SEM micrographs of the samples TiO2 (7%)-SiO2. The images demonstrate porous structure synthesis samples.   The complex-shaped band corresponded to asymmetric stretching vibrations and the average intensity band at 798 cm −1 to symmetric stretching vibrations of SiO 4 tetrahedra. The absorption band with a maximum at 945 cm −1 demonstrated symmetric stretching vibrations of nonbridging Si-O-bonds. An intense band at 435 cm -1 corresponded to the bending vibrations of polyhedra. The absorption bands of stretching vibrations of surface hydroxyl groups and water appeared to be in the range of 3700-3000 cm -1 . A broadband of average intensity in the region of 1626 cm −1 corresponded to the bending vibrations of water [29]. The ratios of the intensities of the absorption bands of Ti-O-Si and Si-O-Si groups at 950 cm -1 and 1079 cm -1 , respectively, for binary oxide xerogels as a function  Table 1. These data demonstrated that the number of Ti-O-Si groups decreased with increasing titanium oxide fraction of the binary system. Annealing at 850 • C (Figure 2b) caused dehydroxylation of the SiO 2 sample, as evidenced by the absence of absorption bands at 3700-3000 cm −1 , and the non-bridging Si−O−bonds in the spectra. Similarly, in titanium dioxide, due to calcination, the absorption bands of the Ti−OH groups (1126, 1095, and 1036 cm −1 ) were also not found. In the spectra of binary xerogels and TiO 2 , water absorption bands (3700-3000 cm −1 , 1625 cm −1 ) were present, which was the result of sorption from the atmosphere, due to the hygroscopicity of the samples.

Rotational Motion of Spin Probes in Individual Oxides and Binary Oxide Xerogels
The acid-base characteristics of water in the micropores of inorganic oxides and ionexchange resins, are known to differ from those in the external solution [30]. To measure the pH loc inside the pores of the samples, the pH-sensitive spin-probe technique was used [24]. We evaluated the SEP of individual and binary oxide xerogels, and its effect on the acidity of the solution inside the pores in the samples.
At a pH ext below 10, the experimental EPR spectra of NR in the TiO 2 -SiO 2 and SiO 2 samples represented a superposition of isotropic and anisotropic signals (Figure 3), indicating the coexistence of two forms of NR, with different molecular mobilities. The isotropic signal ( Figure 3, highlighted in magenta) corresponds to the fast-motioned NR molecules that are located in a diffusion layer inside the pores [31]. The signals produced by the NR molecules allow information on the acidity of the solution inside the pores of oxide materials to be obtained [30,32]. The anisotropic signal ( Figure 3, highlighted in blue and green) was generated by the NR molecules that were adsorbed onto the surface. This signal provides information on SEP [33].  . Experimental (black curve) and simulated (red curve) EPR spectra of the NR on the surface of the TiO2 (7%)-SiO2 binary system at pHext = 5.58. The simulated EPR spectrum of the NR is a superposition of three signals, namely, fast-motioned NR (magenta curve), slow-motioned NR in the protonated (blue curve), and non-protonated forms (green curve).

EPR Titration of NR in the Individual and Binary Intrinsic Oxides
EPR titration curves of the NR in external aqueous solution, as well as in SiO2 and binary TiO2-SiO2 xerogels, are shown in Figure 4. For NR in external aqueous solution, the isotropic hyperfine splitting constant (HFS) was plotted vs. the pHext. The fraction of the slow-motion component of NR inside the pores was determined via EPR spectra sim- . Experimental (black curve) and simulated (red curve) EPR spectra of the NR on the surface of the TiO 2 (7%)-SiO 2 binary system at pH ext = 5.58. The simulated EPR spectrum of the NR is a superposition of three signals, namely, fast-motioned NR (magenta curve), slow-motioned NR in the protonated (blue curve), and non-protonated forms (green curve). At a pH ext value greater than 10, only the isotropic EPR signal characteristic of fastmotioned NR, which was located inside the pores of the oxide xerogels, was recorded.
The NR that was adsorbed on the TiO 2 surface only gave isotropic spectra for all the pH ext values.

EPR Titration of NR in the Individual and Binary Intrinsic Oxides
EPR titration curves of the NR in external aqueous solution, as well as in SiO 2 and binary TiO 2 -SiO 2 xerogels, are shown in Figure 4. For NR in external aqueous solution, the isotropic hyperfine splitting constant (HFS) was plotted vs. the pH ext . The fraction of the slow-motion component of NR inside the pores was determined via EPR spectra simulation, and was used as a pH-dependent parameter for the investigation of SiO 2 and binary TiO 2 -SiO 2 xerogels.  For the binary TiO2 (7%)-SiO2 samples, the EPR titration curves of the NR showed a greater shift to the right (to the higher pHext values) from the calibration curve, as compared to the curve for the individual SiO2, indicating the stronger negative charge of the pores surface at high values of pHext. The existence of a plateau in the pHext range of 2.5-3.5 indicated the formation of new acidic centers with a higher acidity than that of the silanol groups in the individual SiO2. As a result of the deprotonation of these groups at higher pHext values, the surface acquired a negative charge (SEP). This charge caused a decrease in the acidity of the remaining silanol groups, shifting the plateau in the upper part of the titration curve further upwards (to the higher pHext region). Remarkably, the titration of the TiO2 (50%)-SiO2 sample showed a much lower shift of the titration curve to the right (the surface became charged negatively). We noted that a buildup of the titanium dioxide content in the samples led to an increase in the dissociation constant of the silanol groups, since the upper plateau on the titration curve for NR in the TiO2 (7%)-SiO2 sample was positioned above that for pristine SiO2. We assumed that for the TiO2 (50%)-SiO2 sample, the titration of silanol groups would take place at the pHext values above the sensitivity range of the NR used. Therefore, we did not observe the characteristic plateau on the titration curve for this sample. Interestingly, the EPR titration curve of the NR was shifted higher to the right for a binary system with a 7% mol of TiO2 content. The IR spectroscopy data (Table 1), which indicated the maximum amount of the mixed phase for this sample, allowed us to conclude that an increase in the negative surface charge for this sample is associated precisely with the formation of a mixed Ti-O-Si phase.
The plateau in the titration curves of the NR in binary oxides in the pHext value range from 2.5 to 4.5, corresponds to the deprotonation of either the silanol groups of the silica located near titanium atoms or new functional groups arising in the mixed Ti-O-Si phase. The upper part of the titration curve for the SiO 2 sample was found to be shifted to the right (to the higher pH ext values), relatively to the EPR titration curves of the NR in external aqueous solution (the black curve), which indicated a negative charge of the silicon dioxide surface in a neutral and weakly acidic solution (at pH ext > 3-4) [30,33]. As the value of pH ext decreased, the EPR titration curve for this oxide came closer to the calibration curve and intersected it, thus shifting to the left, relatively to that at a pH ext less than three. It is known that the hydroxylated silica surface has point of zero charges (PZC) at pH ext values between two and three, and becomes charged positively at the lesser value pH ext [34].
The horizontal plateaus in the titration curves of the NR inside SiO 2 , and the TiO 2 -SiO 2 binary xerogels obtained by simulating the anisotropic spectra, reflected the invariance of the fraction of the non-protonated form of the NR, f, with a change in pH ext . These plateaus were explained by the ionization of the silicon dioxide silanol groups [33]. The pKa values of functional groups can be measured by projecting any pH-sensitive parameter of an EPR spectrum of the NR inside the material corresponding to a horizontal plateau on the calibration curve, and then to the pH ext axis [33]. In our case, the pH-sensitive parameter was f (Figure 4).
For the binary TiO 2 (7%)-SiO 2 samples, the EPR titration curves of the NR showed a greater shift to the right (to the higher pH ext values) from the calibration curve, as compared to the curve for the individual SiO 2 , indicating the stronger negative charge of the pores Gels 2021, 7, 119 6 of 13 surface at high values of pH ext . The existence of a plateau in the pH ext range of 2.5-3.5 indicated the formation of new acidic centers with a higher acidity than that of the silanol groups in the individual SiO 2 . As a result of the deprotonation of these groups at higher pH ext values, the surface acquired a negative charge (SEP). This charge caused a decrease in the acidity of the remaining silanol groups, shifting the plateau in the upper part of the titration curve further upwards (to the higher pH ext region). Remarkably, the titration of the TiO 2 (50%)-SiO 2 sample showed a much lower shift of the titration curve to the right (the surface became charged negatively). We noted that a buildup of the titanium dioxide content in the samples led to an increase in the dissociation constant of the silanol groups, since the upper plateau on the titration curve for NR in the TiO 2 (7%)-SiO 2 sample was positioned above that for pristine SiO 2 . We assumed that for the TiO 2 (50%)-SiO 2 sample, the titration of silanol groups would take place at the pH ext values above the sensitivity range of the NR used. Therefore, we did not observe the characteristic plateau on the titration curve for this sample. Interestingly, the EPR titration curve of the NR was shifted higher to the right for a binary system with a 7% mol of TiO 2 content. The IR spectroscopy data (Table 1), which indicated the maximum amount of the mixed phase for this sample, allowed us to conclude that an increase in the negative surface charge for this sample is associated precisely with the formation of a mixed Ti-O-Si phase.
The plateau in the titration curves of the NR in binary oxides in the pH ext value range from 2.5 to 4.5, corresponds to the deprotonation of either the silanol groups of the silica located near titanium atoms or new functional groups arising in the mixed Ti-O-Si phase. It proved the presence of the mixed Ti-O-Si phase, along with the individual phases of SiO 2 and TiO 2 in the binary TiO 2 -SiO 2 xerogels, by the NMR method, and it was noted that the functional groups that were associated with the mixed-phase showed higher acidity than the silanol ones [35]. These groups, with similar values of pKa, were revealed in the study of binary ZrO 2 -SiO 2 oxide xerogels, which indicated that they (groups) belonged to a mixed phase [36].

EPR Titration of NR in the Individual and Binary Annealed Oxides
The annealing of SiO 2 samples at 850 • C led to the formation of multiple acidic centers on the sample surface, and resulted in the shift of the titration curve to the right at a pH ext value range of 4-5.5. At the higher pH ext values, these centers were ionized, providing the negative SEP, which in turn decreased the acidity of the remaining silanol groups. As a result, further ionization of these silanol groups occurs at the higher pH ext values, with the titration curve plateau shifting upwards. We observed that the shift of the titration curve for the NR in the annealed sample at pH ext > 8, was found to be lesser than that for the sample before annealing. This effect was due to the partial decomposition of acidic silanol groups, which led to a decrease in the total negative charge of the surface (SEP) at alkaline pH ext .
Specifically, the increase in the pKa value of silanol functional groups, after annealing at 850 • C, was attributed to the fact that upon completion of the titration in the annealed sample, SEP became greater (in absolute value) than that for the unannealed one ( Figure 5, green curve). Within the pH ext range from four to seven, the curve is positioned at the right, relatively to the red curve. Hence, the dissociation of silanol groups (removal of the positively charged hydrogen H + ions) in these samples was impeded not only by the bond strength in the acid group Si-O-H, but also by the increased negative charge of the entire matrix of the sample. An increase in the negative charge of the silicon oxide surface after calcination can be associated with the formation of both siloxane groups on the silicon oxide surface and Lewis acid sites. This is due to the detachment of silanol groups during heat treatment.
right, relatively to the red curve. Hence, the dissociation of silanol groups (removal of the positively charged hydrogen Н + ions) in these samples was impeded not only by the bond strength in the acid group Si-O-H, but also by the increased negative charge of the entire matrix of the sample. An increase in the negative charge of the silicon oxide surface after calcination can be associated with the formation of both siloxane groups on the silicon oxide surface and Lewis acid sites. This is due to the detachment of silanol groups during heat treatment. In contrast, annealing of the binary TiO2-SiO2 samples at 850 °C did not lead to a decrease in the total number of ionized groups at alkaline pHext values ( Figure 6). Thus, the TiO2 additive increased the thermal stability of the silanol groups. However, strongly acidic groups present only in binary oxides, and providing a plateau in the titration curve at pH 2-4 completely disappeared from the sample surface. Acidic centers that are similar to those observed in the annealed SiO2 were formed, instead of exhibiting on the titration curve plateau at the pHext value of 2.5-4.5. The dissociation constants of the functional groups before and after calcination were found to be equal to 1.90 ± 0.08 and 2.90 ± 0.08, respectively. In contrast, annealing of the binary TiO 2 -SiO 2 samples at 850 • C did not lead to a decrease in the total number of ionized groups at alkaline pH ext values ( Figure 6). Thus, the TiO 2 additive increased the thermal stability of the silanol groups. However, strongly acidic groups present only in binary oxides, and providing a plateau in the titration curve at pH 2-4 completely disappeared from the sample surface. Acidic centers that are similar to those observed in the annealed SiO 2 were formed, instead of exhibiting on the titration curve plateau at the pH ext value of 2.5-4.5. The dissociation constants of the functional groups before and after calcination were found to be equal to 1.90 ± 0.08 and 2.90 ± 0.08, respectively.
A broad singlet in the EPR spectra of the NR appeared only for the annealed TiO 2 (50%)-SiO 2 sample. This occurred due to the presence of coal that formed as a result of burning the organic fraction of the precursors retained in the sample pores [29]. A broad singlet in the EPR spectra of the NR appeared only for the annealed TiO2 (50%)-SiO2 sample. This occurred due to the presence of coal that formed as a result of burning the organic fraction of the precursors retained in the sample pores [29].

Effect of Incorporation of Cu(II) Ions into the Binary Oxides on EPR Titration of NR for Cu(II)-Containing Binary Xerogels
The incorporation of Cu(II) into TiO 2 -SiO 2 samples allowed partial compensation for the negative charge, with a pronounced shift of the titration curve to the left, as shown in Figure 7. The dissociation constants of the functional groups (pKa values) of different oxide xerogels, and the highest SEP of their surface (in absolute value), are shown in Table 2. The decrease in the pKa can be associated with the decline in the negative charge of the sample matrix. It facilitated the dissociation of the silanol groups, and, as a result, the plateau in the titration curve was shifted down to the lower pH ext values.
A broad singlet in the EPR spectra of the NR appeared only for the annealed TiO2 (50%)-SiO2 sample. This occurred due to the presence of coal that formed as a result of burning the organic fraction of the precursors retained in the sample pores [29].

Effect of Incorporation of Cu(II) Ions into the Binary Oxides on EPR Titration of NR for Cu(II)-Containing Binary Xerogels
The incorporation of Cu(II) into TiO2-SiO2 samples allowed partial compensation for the negative charge, with a pronounced shift of the titration curve to the left, as shown in Figure 7. The dissociation constants of the functional groups (рКa values) of different oxide xerogels, and the highest SEP of their surface (in absolute value), are shown in Table  2. The decrease in the рКa can be associated with the decline in the negative charge of the sample matrix. It facilitated the dissociation of the silanol groups, and, as a result, the plateau in the titration curve was shifted down to the lower pHext values.   As was mentioned above, no signal in the EPR spectrum for immobilized NR was observed in the TiO 2 samples. However, titration of the fast-motioned NR molecules near the TiO 2 and SiO 2 surfaces led to similar a,% vs. pH ext dependences ( Figure 8) (a is the pH-sensitive parameter, characterizing the hyperfine coupling constant, HFS constant).
The EPR titration curves for the dissolved NR near the surface of the SiO 2 samples were significantly shifted to the right, relatively to the titration curve for the NR in the bulk aqueous solution. The shift is more noticeable at a pH ext less than 4.5, which can be ascribed to an increased acidity of the solution inside the samples' pores, compared to the pH ext [30], due to the surface charge (close to zero) of pH ext (Figure 4). The highest shift of the EPR titration curves for the NR to the right, relatively to that in the bulk aqueous solution, was observed in the TiO 2 (7%)-SiO 2 sample (Figures 4 and 8). The surface charge affects the acid-base equilibrium of the NR in a solution inside the pores.
TiO2 (7%)-SiO2-Cu(II) 5.30 -1.97 −115 As was mentioned above, no signal in the EPR spectrum for immobilized NR was observed in the TiO2 samples. However, titration of the fast-motioned NR molecules near the TiO2 and SiO2 surfaces led to similar a,% vs. pHext dependences (Figure 8) (a is the pHsensitive parameter, characterizing the hyperfine coupling constant, HFS constant). The EPR titration curves for the dissolved NR near the surface of the SiO2 samples were significantly shifted to the right, relatively to the titration curve for the NR in the bulk aqueous solution. The shift is more noticeable at a pHext less than 4.5, which can be ascribed to an increased acidity of the solution inside the samples' pores, compared to the pHext [30], due to the surface charge (close to zero) of pHext (Figure 4). The highest shift of the EPR titration curves for the NR to the right, relatively to that in the bulk aqueous solution, was observed in the TiO2 (7%)-SiO2 sample (Figures 4 and 8). The surface charge affects the acid-base equilibrium of the NR in a solution inside the pores.
The differences between pHext and pHloc in the oxide xerogels are shown in Table 3. The differences between pH ext and pH loc in the oxide xerogels are shown in Table 3.

Conclusions
CW X-band EPR spectroscopy of a pH-sensitive nitroxide radical, used as a freemotioned or adsorbed spin probe, was applied to study acid-base equilibria in the pores and surfaces of TiO 2 -SiO 2 binary xerogels that were prepared by a sol-gel technique in the wet ammonia vapors atmosphere. The results showed that the variation in the composition of binary xerogels led to a change in both the electrosurface and acidic properties of the materials studied.
The new acidic centers, with a higher acidity than silanol groups, were formed in the binary system TiO 2 (7%)-SiO 2 . Moreover, these samples showed a higher content of acidic groups on the surface, hence, the higher negative surface electrical potential compared to the pure silica samples (−196 to −204 mV vs. −137 to −159 mV). The local acidity inside the sample's pores was found to increase by approximately 1.49 pH units, as compared to the bulk external solution. The annealing of pure silicon oxide at 850 • C decreased the number of silanol groups on the surface and increased the value of the dissociation constant of these groups. While the calcination of the TiO 2 (7%)-SiO 2 sample did not affect a decrease in the number of silanol groups, the breakdown of strongly acidic groups in the substituted oxide was observed.

Synthesis of Binary TiO 2 -SiO 2 Xerogels
The synthesis of the samples was carried out by the sol-gel technique, according to the protocol previously described in [29], using titanium and silicon alkoxides as precursors. The hydrolysis of the samples was performed in presence of wet ammonia vapors.
Samples with 7% and 50% TiO 2 were obtained by mixing TBT and TEOS in ratios of 1:9 and 6:4, respectively. The synthesis was carried out in porcelain dishes with a round bottom, 60 mm in diameter and 30 mL in volume. To synthesize the SiO 2 and TiO 2 individual oxides, 10 mL of TBT or TEOS were subjected to hydrolysis. The dish was placed into a 3 L desiccator containing a beaker with 100 mL of 10% aqueous ammonia and stored until hydrolysis was complete. After hydrolysis, the samples were dried for 48 h at room temperature, then kept in a drying oven at 90 • C for 24 h. Some samples were calcined annealed in a quartz reactor at a temperature of 850 • C (heating rate 10 • C/min) in air flow with a rate of 0.075 m 3 /h for an hour.
The TiO 2 (7%)-SiO 2 -Cu (II) samples were obtained by dissolving 0.01 g of CuCl 2 × 2H 2 O in the appropriate TEOS/TBT mixture with a subsequent treatment, according to the protocol above.
Compact FT-IR spectrometer: ALPHA II (manufacturer: Bruker Optics) was used for FT-IR measurements in the wavenumber range from 4000 to 400 cm −1 . Scanning electron microscope (SEM) images were obtained by using a Carl Zeiss EVO LS 10 device (manufacturer: Carl Zeiss NTS, Jena, Germany).

EPR-Based Spin Probe Method for Measuring Acid-Base and Electrosurface Properties
Potentiometric titration of powdered individual and binary oxides in the range of pH ext from 1 to 10 was carried out by a conventional batch multi-sample technique [30,37]. Titration was carried out at 293 K with 0.1 N solutions of acid (HCl) and alkali (NaOH).
The samples were kept in the NR solution with a concentration of 1 × 10 −4 M for 2 h to establish dynamic equilibrium between the external bulk solution and the solution inside solid phase. Thereafter, pH values of the equilibrium pH ext were measured by a 3-in-1 combination pH electrode and a Mettler Toledo FP20 pH meter (Mettler-Toledo, Columbus, OH, USA) with the specified accuracy of ±0.01 pH. The ±0.01 pH error was significantly less than typical errors of ±0.05 pH units arising from the analysis of EPR titration curves and, therefore, were neglected. After the residual powder was filtered off and compressed between filter papers to remove excess liquid, the sample was placed inside the quartz EPR tube (i.d. = 3.5 mm), and EPR spectra were recorded immediately thereafter. Sealing of the samples inside the quartz tube prevented water evaporation from the pores. Detailed descriptions of EPR titration experiments and analysis of EPR spectra can be found in [26,31,38].
All EPR spectra were recorded at room temperature (≈293 K) using the X-band CW Bruker Elexys E-500 EPR spectrometer. Aqueous solutions of NR were positioned into open-end quartz capillaries with i.d. = 0.50 mm and o.d. = 0.70 mm (VitroCom Inc., Mountain Lakes, NJ, USA), the ends of the capillary were sealed with Critoseal ® (Leica Microsystems Inc., Buffalo Grove, IL), and placed in a standard quartz tube (i.d. = 3.5 mm). The tube was consequently inserted into an EPR resonator.
All EPR titrations were carried out in a solution of I = 0.1 M. Errors of the individual measurements for NR in the bulk aqueous phase were ±0.002 mT while for NR confined inside xerogels those values were ±0.004 mT. To record the EPR spectra, the optimal conditions of microwave power and amplitude of modulation of the magnetic field were chosen.

Titration Curves Plotting
Further processing of the experimental spectra was carried out using J. Freed's software [39] and Microcal OriginPro 2015. The experimental hyperfine coupling constant (HFS) characterized by parameter a,% was plotted against pH ext .
The electrosurface properties were obtained from the analysis of the anisotropic signal of the NR EPR spectra. The change in the fraction of the non-protonated form (f ) of the NR adsorbed on the surface of the solid-phase material was monitored in the range of pH ext from 1 to 10, as follows: f = n R /(n R + n RH2++ ) where n R and n RH2++ are the fractions of slow-motioned radical molecules in the nonprotonated form and the protonated form, respectively.

SEP Calculation
In the case of the pH-sensitive probe adsorbed on the surface of the material under study, Khramtsov et al. in [24] established a relationship between the surface potential and the ionization constant of pH-sensitive NR, as follows: where ∆pK a el is the shift in pK a of the NR in the sample induced by an electric potential; e is an electron charge; ϕ-electrostatic potential, mV; k is the Boltzmann constant; T is the temperature, K.