# Cotracking of Na+ and Br− Adsorption through Surface-Induced Quadrupolar Relaxation (SIQR): An Alternative to Zeta Potential Measurements for High Ionic Strengths (>0.1 M) and Nondispersed Liquid–Solid Mixtures

Zlanseu Ruth Tan, Cécile Pagnoux, Vincent Sarou-Kanian, Sandra Ory, Michaël Deschamps

► To cite this version:

Zlanseu Ruth Tan, Cécile Pagnoux, Vincent Sarou-Kanian, Sandra Ory, Michaël Deschamps. Cotracking of Na+ and Br− Adsorption through Surface-Induced Quadrupolar Relaxation (SIQR): An Alternative to Zeta Potential Measurements for High Ionic Strengths (>0.1 M) and Nondispersed Liquid–Solid Mixtures. Journal of Physical Chemistry A, 2025, 129 (40), pp.9412-9422. 10.1021/acs.jpca.5c02542 . hal-05305660

HAL Id: hal-05305660

https://univ-orleans.hal.science/hal-05305660v1

Submitted on 9 Oct 2025

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Cotracking of Na⁺ and Br⁻ Adsorption through Surface-Induced Quadrupolar Relaxation (SIQR): An Alternative to Zeta Potential Measurements for High Ionic Strengths (>0.1 M) and Nondispersed Liquid–Solid Mixtures

Zlanseu Ruth Tan, Cécile Pagnoux, Vincent Sarou-Kanian,* Sandra Ory, and Michaël Deschamps*

<figure><img src="image_2.png" /></figure>

Cite This: J. Phys. Chem. A 2025, 129, 9412–9422

<figure><img src="image_3.png" /></figure>

Read Online

## ACCESS

<figure><img src="image_4.png" /></figure>

Metrics & More

<figure><img src="image_5.png" /></figure>

Article Recommendations

<figure><img src="image_6.png" /></figure>

Supporting Information

**ABSTRACT:** We compare traditional zeta potential measurements with a surface-induced quadrupolar relaxation-based approach to characterize the surface electric properties of oxides in aqueous media, particularly at high ionic strengths and solid contents where classical methods fail. Three oxide materials (two TiO₂ and one α-alumina) were tested in 1 M NaBr aqueous solutions. Zeta potential measurements are expected to yield reliable isoelectric points (IEP) at moderate solid contents and up to 0.1 M ionic strengths. In contrast, NMR relaxation rate measurements, exploiting surface-induced quadrupolar relaxation (SIQR) of ⁸¹Br and ²³Na, successfully provided IEP even at 1 M ionic strength and high solid content, although they are usually much more challenging under conditions suitable for conventional zeta potential measurements. Our NMR results correlated well with zeta potential trends at lower concentrations. Notably, TiO₂_325 showed only acidic surface behavior, likely due to surface carbonate and/or phosphate groups. Surface acidity constants derived from NMR data allowed IEP estimation consistent with the literature values. This demonstrates that NMR relaxation rate measurements provide a robust alternative to zeta potential experiments under conditions where the latter are unreliable

<figure><img src="image_7.png" /></figure>

## INTRODUCTION

To characterize the surface electric properties of metallic oxides in aqueous media, researchers often refer to electrokinetic techniques.¹⁻⁵ This generally results in the determination of the zeta potential (ζ), which is defined as the average potential at the shear plane, according to the electric double layer theory.⁶ The zeta potential is of great interest for many scientific fields, since it is, for instance, a good predictor of the surface net charge (σ₀) of materials in solution⁶⁻⁸ and generally governs the affinity between charged or polar species and particles in solid/liquid mixtures.⁷,⁹⁻¹¹ For ionic ligands, positive or negative ζ involves the predominant adsorption of, respectively, negative and positive counterions in the Stern layer.¹² The sign and magnitude of the zeta potential (and thus σ₀) are influenced by a number of parameters, the main one being pH.¹¹ In the specific case of metallic oxides, the effects of pH on σ₀ are associated with the protonation or deprotonation of surface hydroxyl groups (≡M–OH) and/or the physical trapping of ions at the surface.⁴,¹³⁻¹⁸ The ionization of ≡M–OH can be illustrated by the following acid–base equilibria:¹⁸,¹⁹

$$≡M - OH + H^{+} \rightarrow ≡M - OH_{2}^{+} Ka_{1} \quad (1)$$

$$≡M - O^{-} + H^{+} \rightarrow ≡M - OH Ka_{2} \quad (2)$$

where ≡M–OH₂⁺ and ≡M–O⁻ are the positive and negative surface sites, respectively. Kaᵢ (i = 1 or 2) represents the acidity constant (pKaᵢ = –logKaᵢ) of the iᵗʰ surface acid–base reaction. For known pKaᵢ, the isoelectric point can be estimated according to Equation 3:²⁰

$$IEP = \frac{1}{2}(pKa_{1} + pKa_{2}) \quad (3)$$

This quantity refers to the configuration where there are as much positive as negative ionized groups (such as ≡M–OH₂⁺ and ≡M–O⁻). The IEP induces the cancellation of ζ, when the latter is measured as a function of pH.¹⁶ In real polycrystalline samples without facet controls, surface oxygens are likely inequivalent, leading to an ensemble of pKaᵢ values.²¹,²²

Despite the popularity of ζ-based techniques, many limitations remain. The determination of ζ is, first, subject to

Received: April 14, 2025

Revised: August 27, 2025

Accepted: September 2, 2025

Published: September 15, 2025

<figure><img src="image_8.png" /></figure>
several assumptions as a value theoretically deduced from experimental quantities such as electrophoretic mobility, streaming or sedimentation potentials, electro-osmosis flow, or electrokinetic sonic amplitude (ESA).<sup>23-25</sup> It also provides a global overview of the surface net charge, without distinguishing the intrinsic contributions of positive and negative surface charges. Moreover, zeta potential measurements remain practically challenging for samples with both high ionic strength (>0.01 M)<sup>2,26</sup> and high solid content.<sup>27</sup> These two latter limitations motivated the present investigations.

Our objective is to determine whether SIQR effects yield results consistent with zeta potential measurements under conditions of high ionic strength and solid content, where ESA measurements become less reliable, and to demonstrate the value of adopting a relaxometry-based approach. On the one hand, the zeta potential was measured on colloidal suspensions made of 3 wt % solid content and 0.1 and 1 M ionic strengths. The larger ionic strengths (i.e., >0.01 M) require the removal of the contribution of the background electrolyte.<sup>9,11,28</sup> On the other hand, the NMR samples are compact slurries at salt concentrations ranging between 0.1 and 1 M.

NMR probes local structures at atomic resolution, as well as dynamics at different length scales,<sup>29-33</sup> which makes it a suitable tool to differentiate ions according to their location and dynamics in solid/liquid mixtures. In NMR, the longitudinal relaxation rate ($R_1 = 1/T_1$) characterizes the return to equilibrium of the magnetization and is known to be sensitive to solid/liquid interface phenomena (i.e., the SIQR effect), as shown in a large number of studies in which the effects of surface charges, ionic strengths, or solid contents on ion binding properties were examined.<sup>31,34-41</sup> NMR relaxation is governed by stochastic fluctuations of spin interactions due to atomic motions. The latter is related to correlation times ($\tau_c$) characterizing these motions in the medium.<sup>29,42-44</sup> For the <sup>23</sup>Na and <sup>81</sup>Br nuclei ($S = 3/2$), relaxation is dominated by the interaction between the nuclear electric quadrupolar moment and the electric field gradient (EFG) at the nucleus.<sup>34,35,43,45,46</sup> The quadrupolar relaxation is most efficient when the correlation function of the EFG fluctuations is characterized by a correlation time $\tau_c$ close to the inverse of the Larmor frequency $\frac{1}{\omega_0}$. At a Larmor frequency close to 100 MHz, for example, dynamics of the order of nanoseconds will contribute the most to longitudinal relaxation.<sup>47</sup> In water, the longitudinal relaxation of quadrupolar spin-bearing ions stems from the fast, subnanosecond motion of water molecules in the first solvation shell, which affects the electronic cloud symmetry and creates fluctuating EFG at the nucleus. In oxide/aqueous solution mixtures, the magnitude of the EFG is generally greater at solid/liquid interfaces due to the surface electric charges and the loss of symmetry in the environment.<sup>36,48-50</sup> Moreover, the fluctuation of this EFG at the appropriate frequency ($\sim \frac{1}{\tau_c}$) is ensured by the slowdown of ion dynamics in the vicinity of oxide particles.<sup>16</sup> The consequence is a relaxation that becomes much faster for the nuclear spins of counterions compared to those in the bulk, i.e., the SIQR effect.<sup>34</sup> Moreover, the SIQR effect is expected to broaden the line widths of quadrupolar nuclei (in our study <sup>23</sup>Na, <sup>81</sup>Br, and <sup>35</sup>Cl in Maki's study).<sup>39,51</sup>

Comparing the SIQR effects on cations and anions is expected to provide new insights into the relative proportions of positive ($\equiv M-OH_2^+$) and negative ($\equiv M-O^-$) surface

charges. This strategy was explored on three different oxides, namely, two titanium dioxides (TiO<sub>2</sub>, P25 and TiO<sub>2</sub>, 325) and one alpha-alumina sample (AKP-30). The electrolytes were sodium bromide (NaBr) aqueous solutions used to study <sup>23</sup>Na and <sup>81</sup>Br NMR relaxation as a function of pH.

## MATERIALS AND METHODS

**Materials and Reagents.** To implement our comparative study between zeta potential measurements and NMR SIQR effects, three model materials were chosen, namely, two titanium dioxide (TiO<sub>2</sub>, Sigma-Aldrich) and one alpha alumina (α-Al<sub>2</sub>O<sub>3</sub>, Sumitomo Chemical Company, Japan). Each of them was used as provided, without further purification. The first TiO<sub>2</sub> sample (Degussa P25), very popular in the literature for its high photocatalytic activity,<sup>52-55</sup> is a mixture of anatase and rutile polymorphs, to the extent of 70–85% and 15–30%, respectively. The second TiO<sub>2</sub> is a commercial-grade, pure 325-mesh anatase powder (99.6%), which is very little described in the literature to the best of our knowledge. Thereafter, the former will be designated TiO<sub>2</sub>-P25 and the later TiO<sub>2</sub>-325. Regarding the last material, it is a high-purity (>99.99%) α-Al<sub>2</sub>O<sub>3</sub> referenced as AKP-30 (or AKP30) by the supplier and extensively used in the field of colloids and ceramics.<sup>2-4,56,57</sup> Table 1 summarizes the main features of each

<table><caption>**Table 1.** Densities, Specific Area, Grain Sizes, and Surface Hydroxyl Group Densities for TiO<sub>2</sub>-P25, TiO<sub>2</sub>-325, and AKP-30<sup>a</sup></caption><thead><tr><th>Samples</th><th>Density (g/cm<sup>3</sup>)</th><th>Specific area (m<sup>2</sup>/g)</th><th>Grain size range (nm)</th><th>Surface -OH density (σ<sub>OH</sub>) (/nm<sup>2</sup>)</th></tr></thead><tbody><tr><td>TiO<sub>2</sub>-P25</td><td>4.26</td><td>50-57</td><td>25-51</td><td>4.9</td></tr><tr><td>TiO<sub>2</sub>-325</td><td>3.90</td><td>14</td><td>70-240</td><td>-</td></tr><tr><td>AKP-30</td><td>3.98</td><td>7</td><td>87-814</td><td>5.3</td></tr></tbody></table>

<sup>a</sup>The densities are those provided by the suppliers. The specific areas were determined by Brunauer–Emmett–Teller analyses, and the range of grain sizes was determined from the analysis of scanning electron microscopy images. The last column represents the density of surface hydroxyl groups derived from thermogravimetric analyses.

material. While the densities and densities of surface hydroxyl groups are very similar, one can notice significant changes in the specific areas and the grain sizes. TiO<sub>2</sub>-P25, which has the smallest grain sizes, has a specific area about four and eight times larger than TiO<sub>2</sub>-325 and AKP-30, respectively. The grain sizes were estimated from scanning electron microscopy (SEM) images prior to the study (Supporting Information, Section A). Since we did not perform laser granulometry experiments to assess the average grain size, we provide instead size ranges obtained from SEM images. The specific areas were determined by Brunauer–Emmett–Teller (BET) analyses and found to be consistent with the literature for TiO<sub>2</sub>-P25<sup>58</sup> and AKP-30.<sup>3</sup> Lastly, the densities of surface hydroxyl groups were derived from thermogravimetric (TGA) analyses (Supporting Information, Section B).

**Sample Preparation for NMR Experiments.** For each oxide, two sets of samples were prepared for the NMR SIQR experiments. The first set contained samples with variable ionic strengths at a constant pH value, and the second set consisted of samples with variable pH at a constant ionic strength.

To prepare the variable ionic strength samples, appropriate amounts of NaBr (Sigma-Aldrich) were first dissolved in ultrapure water (Milli-Q) to obtain solutions with concen-
trations ranging from 0.1 to 1 M. For the variable pH samples, an aqueous NaBr solution at the optimum concentration was prepared using the optimized ionic strength obtained from the preliminary study. From this primary solution, we derived a set of acid-base solutions by adding gradual amounts of HBr or NaOH (1 M, Sigma-Aldrich) to obtain solutions with pH₀ values ranging from 2.3 to 12.4. We neglected the influence of the added volumes used to adjust the pH on the ionic strength, assuming that the ionic strengths remained unchanged after pH adjustment.

For the remaining steps, the procedure is the same for both the variable ionic strengths and the variable pH of oxide/NaBr mixtures. The NaBr solutions (either variable ionic strengths or variable pH) were mixed with each oxide up to a 3 wt % solid content. The mixtures were kept under stirring at 500 rpm for a minimum of one h to allow equilibration. The initial pH₀ and the final pH of the mixtures after equilibration (pHₘₘ) were measured using a SevenCompact S210 Mettler Toledo pH meter. Prior to the measurement, the pH meter was calibrated with commercial-grade solutions of pH 4.01, 7.00, and 9.21. After equilibration, each mixture was filtered with a nylon membrane filter of 0.45 µm diameter (Merck, France), and the supernatants were separated from the sediments. The latter were weighed and transferred into a 10 mm NMR quartz tube. The quartz tubes containing the sediments were then centrifuged at 4000 rpm for 6 min (G-force of 2254 RCF) with an EBA 270 centrifuge (Hettich, Germany) to properly pack the samples. It was assumed that the pH values in the sediments were the same as those measured in the prefiltration mixtures (i.e., pHₘₘ). Through a straightforward calculation procedure detailed in Supporting Information, Section C, we estimated the solid contents to reach 41, 72, and 86 wt % in the sediments involving TiO₂_P25, TiO₂_325, and AKP-30, respectively.

**Zeta Potential Measurements.** Zeta potentials as a function of pH were measured for TiO₂_P25, TiO₂_325, and AKP-30 using an ESA analyzer (AcoustoSizer II S flow-through system, Colloidal Dynamics). The oxide powders were first dispersed into reverse osmosis water at 3 wt % solid content, and appropriate amounts of NaBr were added to achieve ionic strengths of either 0.1 or 1 M. The mixtures were ultrasonicated (Vibra-Cell ultrasonic disintegrator VC 600, Sonic & Materials, USA) to deagglomerate the powders. The corresponding NaBr aqueous solution was used as the background electrolyte. Two suspensions were prepared for each oxide to cover the pH range from 3 to 11. A pH sensor, included in the measuring equipment, automatically monitored acid-base titrations. The acidic and basic pH levels were adjusted with 1 M aqueous solutions of HBr and NaOH during titration. The natural pH (without the addition of any acid or base) of TiO₂_P25, TiO₂_325, and AKP-30 in 0.1 M NaBr aqueous solutions was 5.1, 6.3, and 7.7, respectively.

The electroacoustic method used by the AcoustoSizer apparatus to estimate the zeta potential has already been described in previous works.3,4,7,59 Briefly, a high-frequency alternating electric field (1 MHz) is applied to the colloidal suspension, which causes particle displacement due to their nonzero net charge and generates an acoustic wave at the same frequency. As the oscillating motion of particles takes place at the shear plane of the electric double layer, the resulting ESA signal is directly related to the zeta potential. The ESA is derived from an electric signal measured by a piezoelectric transducer integrated into AcoustoSizer. This quantity is

proportional to the mobility of particles, which is itself related to the zeta potential through O'Brien's formula.24 The final relationship between the ESA signal and the zeta potential is written as

$$ \zeta = \frac{\text{ESA} \times \eta}{\varepsilon \times \phi \times \Delta\rho \times C} \times G(\alpha) \quad (4) $$

where η is the medium viscosity, ε is the solvent dielectric constant, φ is the solid volumetric fraction, and Δρ is the difference in density between the solid and liquid. According to O'Brien,24 G(α) is a complex corrective term that depends on the angular frequency, particle radius and density, viscosity, and dielectric constant of the solvent.

The total ESA signal is a vector sum of the signals from the suspended particles and the electrolyte ions.26 In the literature, zeta potentials are usually measured at ionic strengths lower than or equal to 0.01 M and low solid content (<volume fraction around 2%).3,4 In such a configuration, the background electrolyte signal and the particle-particle interactions are negligible, so the ESA signal is considered to reflect only the electrical properties of the isolated suspended particles.26,60 A background correction to the total signal has been derived to remove the ESA signal from the electrolyte (ionic strength >0.01 M),2,26 and another correction can compensate for the overlapping of the electric double layers in high solid content systems.27 The background correction option is implemented in AcoustoSizer and was used for our zeta potential measurements at 0.1 and 1 M. The following zeta potential measurements were performed on 3 wt % solid content samples to limit the effects of electric double layer overlapping on the global ESA response. Concerning the contribution of the electrolyte, the signal used for the background correction must be measured on the electrolyte alone. Ionic strengths of 0.1 and 1 M were chosen, instead of 0.01 M, to highlight the challenges related to zeta potential measurements in high ionic strength systems.

**NMR Relaxation.** NMR relaxation experiments were conducted using a Bruker Avance III 400 MHz (9.4 T) spectrometer equipped with a 10 mm ¹H/X double-resonance probe for liquid samples. At this magnetic field, the corresponding Larmor frequencies for ²³Na and ⁸¹Br were 105.9 and 108.4 MHz, respectively. Since the two nuclei have close Larmor frequencies, they can typically be observed with the same NMR probehead (usually tunable to the commonly observed ¹³C nucleus), and their longitudinal relaxation exhibits similar dependencies on the correlation times of the fluctuating interactions. The longitudinal relaxation rates of ²³Na and ⁸¹Br in the oxide/NaBr mixtures (sediments) were determined using the standard inversion-recovery pulse sequence. Although quadrupolar relaxation is usually biexponential30,31,43,44,47 in this case, only one relaxation rate was observed. The experiments consisted of 32 spectra with variable relaxation delays (t) ranging from 1 µs to 500 ms for ²³Na and 1 µs to 20 ms for ⁸¹Br. The recycle delays were set to at least 5 × T₁ for all experiments to ensure complete recovery of the magnetization between experiments. The optimal length of the π/2 pulses was 40 µs in both mixtures and pure NaBr electrolytes, regardless of the oxide, the pH, and the nucleus, confirming that these pulses excite all transitions and are not selective for the central transition. The magnetization curves were fitted using the following monoexponential function:
<figure><img src="image_9.png" /><figcaption>Figure 1. Evolution of the noncorrected zeta potential curves as a function of pH for colloidal suspensions of TiO₂_P25 (circles), TiO₂_325 (triangles), and AKP-30 (squares) at 0.1 M ionic strength. The open symbols refer to samples with the same materials at 1 M. The solid content was 3 wt % for each oxide.</figcaption></figure>

$$ \frac{M_z}{M_0} = 1 - 2I_{\text{eff}} \exp(-t/T_{1,\text{mix}}) \quad (5) $$

where $R_{1,mix} = 1/T_{1,mix}$ is the relaxation rate of the spin in the mixtures. $R_{1,mix}$ is optimized during the fitting procedure. $I_{\text{eff}}$ is the factor that indicates the efficiency of the magnetization inversion by the $\pi$ pulse in the inversion-recovery sequence. The factor $I_{\text{eff}}$ is of great importance in the measurement of quadrupolar nuclei relaxation rates.³⁹ If $I_{\text{eff}}$ is lower than one ($I_{\text{eff}} < 1$), part of the magnetization undergoes relaxation during the RF pulse. The smaller $I_{\text{eff}}$ the larger the portion of the magnetization that relaxes under RF irradiation. The fit was performed using the Python `curve_fit` function, and errors on the fitted $T_1$ values were systematically lower than 1%. For fast-relaxing spins such as $^{81}$Br, long pulse durations such as those used in this work (40 µs) can be challenging, as $T_1$ values may approach the same order of magnitude. A single $T_1$ measurement was performed for each sample, and while performing repeated measurements would be beneficial for estimating the true experimental error.

## RESULTS AND DISCUSSION

Figure 1 compares the noncorrected zeta potential curves as a function of pH for colloidal suspensions with TiO₂_P25, TiO₂_325, and AKP-30 at 0.1 and 1 M. For the same oxide, the curve trends are drastically modified when the concentration increases from 0.1 to 1 M. For TiO₂_P25 and AKP-30, for example, the curves that showed IEP at pH = 6.54 and 8.41 at 0.1M, no longer display them at 1 M, as the entire curves remain completely in the negative potential region over the entire pH range. In the case of TiO₂_325, the general trend remains the same, with more negative zeta values at 1 M.

This result highlights the challenge related to zeta potential measurement at high ionic strength and the necessity of background corrections. The latter was attempted for TiO₂_P25, and the result is reported below (Figure 2). After the background correction, we obtained IEP values of 7.05 and 4.53 for samples at 0.1 and 1 M, respectively. The gap between IEP at 0.1 and 1 M is however quite large, which reveals the strong influence of the ionic strength on the ESA signal. Background correction tests were also carried out on the other two materials. However, concerns have been reported regarding the reliability of measurements at high ionic strengths.⁶¹ Therefore, we limit our interpretation to the

<figure><img src="image_10.png" /><figcaption>Figure 2. Evolution of the corrected zeta potential curves as a function of pH in a colloidal suspension of TiO₂_P25 (full symbols: 0.1 M and open symbols: 1 M ionic strengths).</figcaption></figure>

corrected zeta potential curves of oxides in 0.1 M ionic strength media.

Figure 3 shows the evolution of the corrected zeta potential as a function of pH for samples with TiO₂_P25, TiO₂_325,

<figure><img src="image_11.png" /><figcaption>Figure 3. Evolution of the corrected zeta potential as a function of pH in samples made of TiO₂_325 (squares), TiO₂_P25 (circles), and AKP-30 (triangles). Oxides were dispersed in a 0.1 M aqueous solution of NaBr, with a solid content of 3 wt %. The measurement was performed by acoustophoresis, with acid/base pH adjusted with 1 M aqueous HBr and NaOH, respectively.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 4. $^{23}$Na relaxation (a) and inversion efficiency factor (b) as a function of ionic strength in systems involving $TiO_2\_325$ (squares), $TiO_2\_P25$ (circles), and AKP-30 (triangles). The pH ranges were 9.1–9.7 for $TiO_2\_P25$, 5.8–6.4 for $TiO_2\_325$, and 10.1–10.41 for AKP-30. The full lines are guides to the eyes, while the dotted line refers to the $^{23}$Na relaxation rates recorded in pure NaBr solutions at the corresponding ionic strengths.</figcaption></figure>

and AKP-30. This corresponds to colloidal suspensions with an ionic strength of 0.1 M and a solid content of 3 wt %. The uncertainty in measurements is about 3%. Over the entire pH range, each oxide exhibits a unique signature in terms of electric properties. The profiles of $TiO_2\_P25$ and AKP-30 indicate IEP at pH 7.05 and 8.80, respectively, while the $TiO_2\_325$ sample shows consistently negative zeta potentials across the entire pH range (no apparent IEP). For $TiO_2\_P25$ and AKP-30, the positive surface net charge density ($\sigma_0$) below IEP implies a predominant adsorption of $Br^-$ ions at solid/liquid interfaces, whereas the adsorption of $Na^+$ prevails above ($\sigma_0 < 0$). The decrease of $\zeta$ with basification suggests a transition from the equilibrium between $\equiv M-OH_2^+$ / $\equiv M-OH$ to the equilibrium between $\equiv M-OH/\equiv M-O^-$ which becomes predominant beyond the IEP. This assumption is in good agreement with the TGA and IR analyses showing the presence of surface $\equiv M-OH$ groups and the absence of surface impurities (see Supporting Information Sections C and D). The IEP at 7.05 for $TiO_2\_P25$ is quite close to the values reported in the literature,⁵,⁵⁸⁻⁶³ although those have been measured at 0.01 M ionic strength. The lowest zeta potential of -27.5 mV at pH = 10.1 and the highest of 50.4 mV at pH = 3 reveal an almost amphoteric behavior for $TiO_2\_P25$.⁶⁴,⁶⁵ AKP-30 rather exhibits a basic behavior,¹⁶ namely that only a weak portion of surface positive sites at acidic pH is converted into surface negative sites beyond its IEP. This IEP at pH = 8.8 is consistent with the literature, again for measurements conducted with the sample at 0.01 M ionic strength.⁴ Regarding $TiO_2\_325$, the negative trend of the zeta potential curve is characteristic of purely acidic oxides such as $SiO_2$, whose IEPs are shifted to pH values lower than 4.¹⁶,⁶⁶,⁶⁷ In the literature, such trends are very common for anatase-type⁶⁸,⁶⁹ or chemically modified $TiO_2$.⁶³,⁷⁰

This behavior can be explained by the presence of acidic groups on the $TiO_2\_325$ surface, i.e., surface groups that do not undergo protonation even at the lowest pH used here.¹⁶,⁷¹,⁷² The absence of mass loss in the temperature region associated with surface hydroxyl desorption (as seen in the TGA analysis, Supporting Information, Section B) seems to confirm the absence of $M-OH$ groups observed in the other samples. Infrared spectroscopy, ¹H and ³¹P NMR

confirmed the presence of phosphate and/or organic groups (C=O, P=O, and P-O) on the $TiO_2\_325$ surface (Supporting Information, Section D). The presence of phosphate groups could justify the purely acidic behavior of $TiO_2\_325$ due to their intrinsic acidic features. Moreover, concerning the contribution of C=O groups, Kosmulski et al. have shown that the presence of carbonate ($-CO_3^{2-}$) induces a shift in the IEP of metal oxides to low pH.⁷³ Finally, acidic oxides adsorb alkali ions according to the sequence $Cs^+ > Rb^+ > K^+ > Na^+ > Li^+$, due to their ability to disrupt the structure of water in their vicinity.⁵ Such behavior has been highlighted for $TiO_2\_325$ in our previous work,³⁹ which strengthens the current assumptions.

In terms of magnitude, the oxides' zeta potential follows the sequence AKP-30 > $TiO_2\_P25$ in the range of positive surface charges and $TiO_2\_325 > TiO_2\_P25$ > AKP-30 in the negative charge regions. Therefore, one expects the strength of interactions between the charged particles and the counterions ($Br^-$ below and $Na^+$ above the IEP) to follow the same hierarchy at a given pH.

To interpret the NMR relaxation results in mixtures, fast exchange was considered between the fraction $\alpha$ of the spin population, which is adsorbed at the surface of oxide particles during the measurement, and the remainder in the bulk. This assumption is based on the simulation of magnetization curves, which are reproduced with a single exponential component (Figures S6 and S7). Slow exchange is expected to give rise to two distinct exponential components in the inversion-recovery curve. In the two-site fast exchange model, the observed relaxation rate ($R_{1,2,mix} = \frac{1}{T_{1,2,mix}}$) is defined as the average of the intrinsic relaxation rates in each considered site ($R_{1,2,surf} = \frac{1}{T_{1,2,surf}}$ and $R_{1,2,bulk} = \frac{1}{T_{1,2,bulk}}$), weighted by their respective populations (i.e., $\alpha$ and $1-\alpha$).

This results in the following expression:³³,³⁴

$$R_{1,2,mix} = R_{1,2,bulk} + \alpha(R_{1,2,surf} - R_{1,2,bulk}) \quad (6)$$

In this equation, $R_{1,2,surf}$ and $\alpha$ are the unknown quantities. $R_{1,2,bulk}$ represents the relaxation of $^{23}$Na and $^{81}$Br in aqueous NaBr solutions at 1 M and variable pH. Indexes 1 and 2 refer
to longitudinal and transverse relaxation, respectively. According to Equation 6, R<sub>1,2,mix</sub> depends on both α and the relaxation rate of adsorbed species R<sub>1,surf</sub> which are difficult to separate. Variations of R<sub>1,2,mix</sub> can therefore be related to either variation of α<sub>2</sub>R<sub>1,2,surf</sub> or both.

**Figure 4a** represents the evolution of <sup>23</sup>Na longitudinal relaxation rates as a function of ionic strength, at pH ranging from [9.1 to 9.7] for TiO<sub>2</sub>_P25, [5.8 to 6.4] for TiO<sub>2</sub>_325, and [10.1 to 10.41] for AKP-30. The slight pH variations over the concentration ranges were disregarded in the interpretation. In the pure electrolyte systems (dashed line), the relaxation rates remain weak (R<sub>1,bulk Na</sub> ~19 s<sup>-1</sup>) and almost unchanged over the entire concentration range.

This is a typical behavior of quadrupolar nuclei relaxing in
aqueous solutions.³⁸ This relaxation is induced by the
fluctuations of the EFG, resulting from motions occurring in
the water solvation shell, which is not affected by moderate
changes in the electrolyte concentration.⁵¹,⁷⁴

Regarding the oxide/NaBr mixtures, the relaxation rates increase at lower concentrations, which is also an expected result based on the works of Gossuin et al.<sup>38</sup> and Kirkpatrick and coworkers.<sup>34</sup> Considering the fast exchange assumption, one could explain this behavior by the decrease of the population of spins from the bulk electrolyte in favor of those adsorbed on the surface of oxide particles. As R<sub>1,mix</sub> is a weighted average value of R<sub>1,liq</sub> and R<sub>1,surf</sub> (Equation 6), the weight of the latter becomes increasingly large, so that it dominates the overall relaxation phenomena. Based on these results, one could consider the concentration range below 0.5 M as the optimal one to study surface relaxation effects, as, in this concentration range, the SIQR effect is going to be stronger. However, as shown in Figure 4b, reducing the ionic strength in mixtures results in a decrease in the inversion efficiency factor. This also leads to reduced signal-to-noise ratios and longer experimental times (not shown). The maximal I<sub>eff</sub> values are 0.7, 0.82, and 0.83 at 1 M, and the lowest are 0.5, 0.62, and 0.7 at 0.1 M for TiO<sub>2</sub>_P25, TiO<sub>2</sub>_325, and AKP-30, respectively. Although these values are lower than one, they remain large enough to measure R<sub>1,mix</sub> in a precise manner (Supporting Information, Section E). A similar approach for <sup>81</sup>Br in the region of positive surface charge (pH 2.7) is limited by fast signal relaxation during the RF pulses. If we consider <sup>81</sup>Br relaxation in TiO<sub>2</sub>_P25/NaBr mixtures (Figure 5), one can see that the R<sub>1,mix</sub> results are scattered under 0.5 M, and the highest value is greater than 12000 s<sup>-1</sup> at 0.1 M (i.e., T<sub>1,mix</sub> ≈ 80 µs). In such conditions,

<figure><img src="image_13.png" /><figcaption>**Figure 5.** <sup>81</sup>Br relaxation (black full circles) and inversion efficiency factor (blue open circles) as a function of ionic strength in samples with TiO<sub>2</sub>_P25 at a pH range of 2.71–2.92.</figcaption></figure>

T<sub>1,mix</sub> is only twice as long as the π/2 pulse length (40 μs). Moreover, among the samples in this series, only the one at 1 M ionic strength exhibits an inversion efficiency (I<sub>eff</sub>) greater than 0.5. At lower ionic strengths, I<sub>eff</sub> becomes smaller, with the lowest value around 0.3 for the 0.1 M sample. Thus, it becomes obvious that working at a low ionic strength is not the best strategy for the NMR relaxometry method developed in the current work. Moreover, lower NaBr concentrations will also lead to lower signal-to-noise ratios and longer experimental times. We therefore chose 1 M as the optimal ionic strength and preferred R<sub>1,mix</sub> measurements to R<sub>2,mix</sub> as the 180° refocusing pulses are unlikely to work in our systems. Our oxides are not mutually compared at this step, as our samples are not in the same conditions of pH and solid content.

Based on the above discussion, the optimal ionic strength
used for NMR relaxometry at variable pH is set to 1 M.

**Figure 6** presents all NMR spectra recorded at each pH. All spectra exhibit a single peak at around zero ppm, with no apparent distinction between signals from adsorbed spins and those in the bulk electrolyte. Such behavior supports the fast exchange hypothesis between these two spin populations.<sup>34</sup> For TiO<sub>2</sub>_P25 and AKP-30, the spectra of <sup>81</sup>Br broaden as the medium acidifies, while those of <sup>23</sup>Na evolve in the opposite direction. Regarding TiO<sub>2</sub>_325, the trend for <sup>23</sup>Na is similar to what was observed for TiO<sub>2</sub>_P25 and AKP-30, whereas no significant change over the whole pH range is observed in the corresponding <sup>81</sup>Br NMR spectra. Similar effects have already been observed by Maki and coworkers for <sup>23</sup>Na and <sup>35</sup>Cl in mixtures made of α-Al<sub>2</sub>O<sub>3</sub> (ζ < 0 at pH ≈<5.1 and ζ < 0 above) and SiO<sub>2</sub> (ζ < 0 at pH = 2–11) dispersed in aqueous solutions of sodium chloride (NaCl, 0.1M).<sup>36</sup> According to the authors, these behaviors are governed by the electrostatic interactions between oxide particles (α-Al<sub>2</sub>O<sub>3</sub> and SiO<sub>2</sub>) and counterions (Cl<sup>-</sup> or Na<sup>+</sup>) in aqueous media. In the region of positive surface charge (pH ≈<5.1 for α-Al<sub>2</sub>O<sub>3</sub> and pH ≈<2 for SiO<sub>2</sub>), the particles predominantly attract Cl<sup>-</sup>, and the NMR lines of quadrupolar <sup>35</sup>Cl ions are broadened by the SIQR effect. In the case of <sup>35</sup>Cl, they observed negligible changes in the line widths for SiO<sub>2</sub> slurries, as observed in our TiO<sub>2</sub>_325. On the other hand, negative surface charges lead to the adsorption of Na<sup>+</sup> ions and a broadening of their peaks, as seen in all three samples as the pH increases.

The broadening of the NMR line (∝1/T<sup>*</sup><sub>2,mix</sub>) is the earliest evidence of the SIQR effect, as the contribution of the quadrupolar relaxation to the line width of the NMR signal is proportional to the transverse quadrupolar relaxation rate.<sup>75</sup> The line widths as a function of pH are presented in *Supporting Information* for the two TiO<sub>2</sub> samples (Figure S9). However, as field inhomogeneity also affects the line widths and may depend on many uncontrollable factors, and refocusing of fast relaxation magnetization is difficult, longitudinal relaxation rate measurements were preferred in the end. As <sup>81</sup>Br possesses a stronger quadrupolar coupling constant (eQ = 13.35 fm<sup>2</sup>) compared to <sup>23</sup>Na (eQ = 10. 40 fm<sup>2</sup>), we systematically observed broader lines. In the same chemical environment, <sup>81</sup>Br is more likely to undergo stronger SIQR effects, shorter relaxation times, and much broader spectra.

**Figure 7** shows the evolution of <sup>23</sup>Na and <sup>81</sup>Br relaxation rates as a function of pH. The dashed line represents the longitudinal relaxation rates in pure aqueous solutions (at variable pH), while the solid lines correspond to those in
<figure><img src="image_14.png" /><figcaption>**Figure 6.** $^{23}$Na (top) and $^{81}$Br (bottom) signal evolution as a function of pH in solid/liquid mixtures involving (a) TiO$_{2}$ P25, (b) TiO$_{2}$ 325, and (c) AKP-30. The liquid phase consisted of a 1 M aqueous NaBr solution.</figcaption></figure>

mixtures composed of TiO$_{2}$ P25, TiO$_{2}$ 325, and AKP-30. For mixtures involving TiO$_{2}$ P25 and AKP-30, the SIQR effect concerns $^{23}$Na for pH values greater than 6 and 8, respectively, while $^{81}$Br displays an increasing SIQR at pH values below these thresholds. Compared to the zeta potentials (Figure 3), these regions correspond to particles that are negatively and positively charged, respectively. This supports the hypothesis of electrostatic interactions between particles and counterions, as mentioned in Maki's works$^{36}$ and implied in the previous section to explain the evolution of the spectra. The SIQR of $^{23}$Na increases with the basification of the medium due to two main factors. On one hand, higher pH values lead to the ionization of a greater proportion of surface hydroxyls (i.e., more adsorption sites $\equiv M-O^-$ for $Na^+$ ions), and the instantaneous fraction of adsorbed $^{23}$Na becomes larger, resulting in greater overall SIQR effects. Conversely, acidification of the medium creates more positively charged adsorption sites ($M-OH_{2}^{+}$) for $Br^-$ ions. On the other hand,

the magnitude of the EFG is likely to increase with surface charge density.$^{36}$ Since surface ionization intensifies with changes in pH, there is strong evidence to expect surface-induced EFG to increase for adsorbed counterions, causing the relaxation rate $R_{1,surf}$ while adsorbed to also become larger (see Equation 6). Interestingly, the SIQR effect of $^{23}$Na$^+$ and $^{81}$Br$^-$ in positive and negative surface charge pH regions is almost undetectable (i.e., their relaxation rates are close to those in the pure electrolyte), indicating that they are repelled by the surfaces and that very few negative or positive charges, respectively, are present on the surface in these pH ranges.

Regarding TiO$_{2}$ 325, the trend of the $^{23}$Na SIQR curve is similar to those of TiO$_{2}$ P25 and AKP-30, indicating an increase in the density of negative charges on the surface, while no $^{81}$Br SIQR effect is detected over the investigated pH range, indicating that $Br^-$ ions never adsorb on the TiO$_{2}$ 325 surface and no positive charges are created even at our lowest pH values. This evolution is consistent with the acidic nature of TiO$_{2}$ 325 and is supported by our zeta potential measure-
<figure><img src="image_15.png" /><figcaption>**Figure 7.** Evolution of $^{23}$Na (a) and $^{81}$Br (b) longitudinal relaxation rates ($R_1 = 1/T_1$) as a function of pH in mixtures involving $TiO_2\_325$ (squares), $TiO_2\_P25$ (circles), and AKP-30 (triangles). The full colored lines are best fits obtained with the modified Henderson-Hasselbalch equation with one $pK_a$ value, and the black line corresponds to the fit with two $pK_a$ values for $TiO_2\_325$. The dotted lines represent the relaxation rates in the bulk electrolytes.</figcaption></figure>

<table><caption>**Table 2.** Optimization Parameters (a, b, and $pK_a$) Used for pH-Dependent SIQR Curves Fitted with the Modified Henderson-Hasselbalch Equation<sup>a</sup></caption><thead><tr><th>Nuclei</th><th>Parameters</th><th>TiO<sub>2</sub>_P25</th><th>TiO<sub>2</sub>_325</th><th>pH &lt; 8.03</th><th>pH &gt; 8.03</th><th>AKP-30</th></tr></thead><tbody><tr><td rowspan="3"><sup>81</sup>Br</td><td>a<sub>1</sub></td><td>3436 ± 204</td><td>164 ± 58</td><td rowspan="3">22.3</td><td rowspan="3">89.6</td><td>3906 ± 81</td></tr><tr><td>b<sub>1</sub></td><td>322 ± 98</td><td>16 ± 10.2</td><td>570 ± 47</td></tr><tr><td>pKa<sub>1</sub></td><td>4.2 ± 0.1</td><td>3.0 ± 0.52</td><td>7.0 ± 0.1</td></tr><tr><td rowspan="3"><sup>23</sup>Na</td><td>a<sub>2</sub></td><td>5.6 ± 2.7</td><td>22.7 ± 11</td><td rowspan="3">89.6</td><td rowspan="3">122.6</td><td>8.2 ± 3.2</td></tr><tr><td>b<sub>2</sub></td><td>92 ± 4</td><td>104 ± 14</td><td>47 ± 4</td></tr><tr><td>pKa<sub>2</sub></td><td>7.4 ± 0.2</td><td>5.5 ± 0.4</td><td>9.1 ± 0.3</td></tr><tr><td>IEP<sub>NMR</sub></td><td></td><td>5.8 ± 0.3</td><td>-</td><td></td><td></td><td>8.1 ± 0.4</td></tr><tr><td>IEP<sub>zeta</sub></td><td></td><td>7.05</td><td>-</td><td></td><td></td><td>8.8</td></tr></tbody></table>

<sup>a</sup>The IEPs calculated from these $pK_a$ values (IEPNMR) for $TiO_2\_P25$ and AKP-30 are compared to those from the zeta potential obtained in 0.1M colloidal suspensions (IEP<sub>zeta</sub>).

ments. These acidic surface groups $\equiv$M-OH cannot be converted into $\equiv$M-OH<sub>2</sub><sup>+</sup>; no Br<sup>-</sup> counterions will get close enough to the surface to experience SIQR. This is expected if the surface presents a significant proportion of phosphate groups, which will hardly become positively charged over this pH range.

Based on our interpretation of SIQR effects, $TiO_2\_325$ is the oxide with the highest affinity for $Na^+$ ions, followed by $TiO_2\_P25$ and AKP-30. On the other hand, $TiO_2\_P25$'s affinity for Br<sup>-</sup> ions is the strongest in the region of positive surface charges, followed by AKP-30 and $TiO_2\_325$. This hierarchy is again consistent with the order displayed in the zeta potential curves (Figure 3) in the two regions. As expected, the oxide with the highest net surface charge is the oxide with the strongest SIQR.

The acid/base properties of surface groups ($pK_a$) and the isoelectric points (IEPs) are often used to characterize the physicochemical properties of oxide surfaces. Assuming a single average value, the $pK_a$ and IEP were determined from the modified Henderson-Hasselbalch equation:

$$pH = pKa + \log\left(\frac{\Delta R_1 - a}{b - \Delta R_1}\right) \quad (7)$$

In this equation, the SIQR effect is noted $\Delta R_1 = R_{1,mix} - R_{1,bulk}$, a represents the value of $\Delta R_1$ at maximum surface protonation, and b represents the value of $\Delta R_1$ when the

surface is completely deprotonated. In its original form, the Henderson-Hasselbalch equation was written to relate the pH of a weak acid to the acidity constant ($K_a$) and the ratio of the activities of the acid and its conjugate base (i.e., $[base]/[acid]$) in the medium.<sup>76</sup> It was first adapted to express the dependence of NMR chemical shifts on pH,<sup>77,78</sup> before being extended to account for changes in the relaxation rates. Equation 7 is inspired by the one written by Pollard et al.<sup>79</sup> to describe the pH dependence of surface relaxivity. In practice, Equation 7 was used to simulate our SIQR curves as a function of pH (Figure 7). Overall, the modified Henderson-Hasselbalch equation provides a good description of the SIQR effect for both $^{23}$Na and $^{81}$Br in $TiO_2\_P25$ ($R^2 = 0.988$ and 0.977, respectively) and AKP-30 ($R^2 = 0.93$ and 0.975, respectively) with a single $pK_a$ value for each curve. For $TiO_2\_325$, both $^{23}$Na and $^{81}$Br fits with single $pK_a$ values are of poorer quality, with $R^2 = 0.837$ and $R^2 = 0.767$, respectively. Concerning $^{81}$Br relaxation, as no significant SIQR effect is detected, we assumed that the surface was hardly ever protonated. Referring to the FT-IR spectra (Supporting Information, Section C) and the detection of $^1$H and $^{31}$P NMR signals for $TiO_2\_325$, its $^{23}$Na SIQR curve was simulated assuming that the surface groups were negatively charged weak diacids (one $pK_a$ for each acidity), a behavior consistent with a mix of carbonate and/or phosphate moieties. This led to a much better fit with $pKa_1 =$
5.7 and pKa₂ = 9.3 (Figure 7), supporting the key role of multiple groups with distinct pKa in TiO₂_325's behavior.

Table 2 presents the optimized parameters from the modified Henderson–Hasselbalch equation. Regarding TiO₂_P25 and AKP-30, IEP values of 5.8 and 8.1, respectively, have been estimated (Equation 3), compared to 7.1 and 8.8 from zeta potential experiments, respectively. These values are of the same order of magnitude, although they were not obtained under the same conditions. As a reminder, the SIQR experiments were carried out on compact slurry-like samples with an ionic strength of 1 M, while the zeta potential measurements mentioned are those obtained on colloidal samples at 0.1 M ionic strength. Moreover, the solid contents were 41, 72, and 86 wt % for TiO₂ P25, TiO₂_325, and AKP-30, respectively, compared to 3 wt % for the zeta potential measurements. The analysis of the SIQR effect offers an alternative to zeta potential measurements for large solid contents and high ionic strengths, where the latter is usually less reliable. On the other hand, SIQR experiments require high ionic strengths to avoid limitations related to sensitivity and problems with magnetization inversion or saturation and perform better in media with relatively large solid content to ensure the SIQR affects enough ions. The small deviation between the IEP<sub>NMR</sub> and the IEP<sub>zeta</sub> can be attributed to either the influence of solid content or the ionic strength, as shown in our work (IEP of TiO₂_P25 going from 7.1 to 4.5 for samples with 0.1 and 1 M NaBr solutions) and previous studies stating that large solid content or higher ionic strengths can modify pKa values<sup>76</sup> and therefore IEP.<sup>4</sup>

## ■ CONCLUSION

In this work, we developed a straightforward relaxometry-based approach to probe the surface electric properties of oxides in aqueous environments, particularly under conditions where conventional zeta potential measurements become unreliable—namely, at high ionic strengths (≥0.1 M) and in dense, noncolloidal suspensions (up to 86 wt %). We demonstrated that under these conditions, zeta potential curves are significantly distorted and require background correction. For example, in 1 M suspensions of TiO₂_P25, zeta potential curves were drastically altered, with no discernible isoelectric points (IEPs). A single background correction for this system shifted the IEP from 7.05 (observed at 0.1 M and 3 wt %) to 4.53. In contrast, background corrections failed for TiO₂_325 and AKP-30 under the same conditions.

Remarkably, the relaxometry-based protocol remained effective in these challenging regimes. By correlating pH-dependent surface-induced quadrupolar relaxation effects (SIQR) with zeta potentials, we gained new insights into the surface charge distribution of the oxides. Specifically, we exploited the selective sensitivity of <sup>81</sup>Br and <sup>23</sup>Na nuclei to detect positive and negative surface charges, respectively, providing information complementary to that obtained from traditional zeta potential measurements. This approach enabled a qualitative description of the net surface charge for TiO₂_P25, TiO₂_325, and AKP-30 as a function of pH (provided R<sub>1,surf</sub> changes with pH), specifically in compact and highly concentrated suspensions, which are impractical conditions for zeta measurements and are commonly encountered in many areas of chemistry.

Furthermore, modeling the relaxation behavior using a modified Henderson–Hasselbalch equation allowed us to estimate the IEP for TiO₂_P25 and AKP-30 in dense sludges

(41 and 86 wt %) at 1 M ionic strength, yielding values of 5.8 and 8.1, respectively. These values are consistent with the IEP obtained from dilute (0.1 M) colloidal suspensions, reinforcing the validity of the SIQR-based method. In the case of TiO₂_325, its exclusively acidic behavior was attributed to different surface groups, including phosphate and carbonyl moieties.

Despite its advantages, the SIQR approach faces certain limitations. Fast relaxation during RF pulsing can impact measurement accuracy and must be considered during protocol optimization. Additionally, manual sample preparation introduces variability, unlike fully automated techniques such as acoustophoresis. Therefore, future developments should focus on automating the method to enhance its reproducibility and minimize sources of error.

The ability to characterize surface properties in highly concentrated electrolytes and dense solid suspensions holds relevance for fields such as heterogeneous catalysis, electro-chemistry, electrochemical energy storage, colloid and interface science, environmental chemistry, and materials synthesis, where interfacial phenomena critically influence reactivity, stability, and functional performance.

## ■ ASSOCIATED CONTENT

### SI Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.5c02542.

Scanning electronic microscopy images (Section A); thermogravimetric analysis (Section B); solid content determination procedure (Section C); Fourier-transformed infrared spectroscopy spectra (Section D); magnetization evolution curves (Section E) for TiO₂_P25, TiO₂_325, and AKP-30 (PDF)

## ■ AUTHOR INFORMATION

### Corresponding Authors

Michaël Deschamps – CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans F-45071, France; Réseau sur le Stockage Electrochimique de l'Energie (RS2E), CNRS FR3459, Amiens 80039, France; ○ orcid.org/0000-0001-8309-3932; Email: michael.deschamps@univ-orleans.fr

Vincent Sarou-Kanian – CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans F-45071, France; ○ orcid.org/0000-0001-9611-8377; Email: vincent.sarou-kanian@cnrs-orleans.fr

### Authors

Zlanseu Ruth Tan – CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans F-45071, France

Cécile Pagnoux – IRCER, Centre Européen de la Céramique, Université de Limoges, Limoges 87068, France

Sandra Ory – CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans F-45071, France

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jpca.5c02542

### Notes

The authors declare no competing financial interest.

## ■ ACKNOWLEDGMENTS

We are indebted to the Centre-Val de Loire region (France) and the CEMHTI laboratory (Conditions Extrêmes et
Matériaux: Haute Température et Irradiation) for the financial support that made this work possible. Our thanks also go to Dr. María Concepción Ovín Ania for the very constructive discussions about surface acidity. This project has received funding from the European Union's Horizon Europe research and innovation programme under grant number No. 101103873.

## REFERENCES

(1) Gu, Y.; Li, D. The ζ-Potential of Glass Surface in Contact with Aqueous Solutions. *J. Colloid Interface Sci.* **2000**, *226* (2), 328–339.

(2) Oja, T.; Petersen, G.; Cannon, D. *Post-processing equipment*. JP 4,497,207 B2, 1995.

(3) Garcia-Perez, P.; Pagnoux, C.; Rossignol, F.; Baumard, J.-F. Heteroconagulation between SiO₂ Nanoparticles and Al₂O₃ Submicron Particles; Influence of the Background Electrolyte. *Colloids Surf.*, A **2006**, *281* (1–3), 58–66.

(4) Pagnoux, C.; Serantoni, M.; Laucournet, R.; Chartier, T.; Baumard, J.-F. Influence of the Temperature on the Stability of Aqueous Alumina Suspensions. *J. Eur. Ceram. Soc.* **1999**, *19* (11), 1935–1948.

(5) Abendroth, R. P. Behavior of a Pyrogenic Silica in Simple Electrolytes. *J. Colloid Interface Sci.* **1970**, *34* (4), 591–596.

(6) Ellmer, K. Electrical Properties. In *Transparent Conductive Zinc Oxide*; Springer, 2008, Vol. 104, pp 35–78. DOI: .

(7) Al-Tahan, R.; Mayet, R.; Duport, P.; Tessier-Doyen, N.; Aimable, A.; Gasgnier, G.; Pagnoux, C. Characterization of Kaolinite Aqueous Suspensions by Acoustophoresis: Influence of Crystallinity and of the Ratio between Basal and Lateral Surface of Grains. *Colloids Surf*, A **2022**, *649*, 129473.

(8) Selvamani, V. Stability Studies on Nanomaterials Used in Drugs. In *Characterization and Biology of Nanomaterials for Drug Delivery*; Elsevier, 2019; pp. 425–444, DOI: .

(9) Kosmulski, M. Confirmation of the Differentiating Effect of Small Cations in the Shift of the Isoelectric Point of Oxides at High Ionic Strengths. *Langmuir* **2002**, *18* (3), 785–787.

(10) Das, M. R.; Borah, J. M.; Kunz, W.; Ninham, B. W.; Mahiuddin, S. Ion Specificity of the Zeta Potential of α-Alumina, and of the Adsorption of p-Hydroxybenzoate at the α-Alumina-Water Interface. *J. Colloid Interface Sci.* **2010**, *344* (2), 482–491.

(11) Johnson, S. B.; Scales, P. J.; Healy, T. W. The Binding of Monovalent Electrolyte Ions on α-Alumina. I. Electroacoustic Studies at High Electrolyte Concentrations. *Langmuir* **1999**, *15* (8), 2836–2843.

(12) Guinard, L. *Colloids: A Review of Current Knowledge with a View to Application to Phenomena of Transportation Within PWR*; Électricité de France (EDF), 1996.

(13) Davis, J. A.; James, R. O.; Leckie, J. O. Surface Ionization and Complexation at the Oxide/Water Interface. *J. Colloid Interface Sci.* **1978**, *63* (3), 480–499.

(14) Davis, J. A.; Kent, D. B. Surface Complexation Modeling In Aqueous Geochemistry. *Mineral-Water Int. Geochem.* **2018**, *23*, 177–260.

(15) Huang, J.; Wu, Z.; Chen, L.; Sun, Y. Surface Complexation Modeling of Adsorption of Cd(II) on Graphene Oxides. *J. Mol. Liq.* **2015**, *209*, 753–758.

(16) Jolivet, J.-P.; Henry, M.; Livage, J. *De La Solution à l'oxyde: Condensation Des Cations En Solution Aqueuse*; Les Ulis: EDP Sciences, 1994.

(17) Thomas, F.; Rakotonarivo, E.; Bottero, J.-Y. La Charge de Surface Des Solides Divisés: Origine, Mesure et Modélisation./The Surface Charge of Divided Solids: Origin, Measurement and Modeling. *Sci. Géologiques. Bulletin* **1993**, *46* (1), 217–227.

(18) Venema, P. *Charging And Ion Adsorption Behaviour Of Different Iron (Hydr)oxides*, Ph.D. thesis; Wageningen Agricultural University, 1997.

(19) Hiemstra, T.; Yong, H.; Van Riemsdijk, W. H. Interfacial Charging Phenomena of Aluminum (Hydr)Oxides. *Langmuir* **1999**, *15* (18), 5942–5955.

(20) Levene, P. A.; Simms, H. S. Calculation of Isoelectric Points. *J. Biol. Chem.* **1923**, *55* (4), 801–813.

(21) Contescu, C.; Popa, V. T.; Miller, J. B.; Ko, E. I.; Schwarz, J. A. Proton Affinity Distributions of TiO₂-SiO₂ and ZrO₂-SiO₂ Mixed Oxides and Their Relationship to Catalyst Activities for 1-Butene Isomerization. *J. Catal.* **1995**, *157*, 244–258.

(22) Contescu, C.; Jagiello, J.; Schwarz, J. A. Heterogeneity of Proton Binding Sites at the Oxide/Solution Interface. *Langmuir* **1993**, *9* (7), 1754–1765.

(23) Mohammadi-Jam, S.; Waters, K. E.; Greenwood, R. W. A Review of Zeta Potential Measurements Using Electroacoustics. *Adv. Colloid Interface Sci.* **2022**, *309*, 102778.

(24) O'Brien, R. W. Electro-Acoustic Effects in a Dilute Suspension of Spherical Particles. *J. Fluid Mech.* **1988**, *190*, 71–86.

(25) O'Brien, R. W.; Jones, A.; Rowlands, W. N. A New Formula for the Dynamic Mobility in a Concentrated Colloid. *Colloids Surf.*, A **2003**, *218* (1–3), 89–101.

(26) Desai, F. N.; Hammad, H. R.; Hayes, K. F. Background Electrolyte Correction for Electrokinetic Sonic Amplitude Measurements. *Langmuir* **1993**, *9* (11), 2888–2894.

(27) Long, R. P.; Ross, S. The Effects of the Overlap of Double Layers on Electrophoretic Mobilities of Polydisperse Suspensions. *J. Colloid Interface Sci.* **1968**, *26* (4), 434–445.

(28) Kosmulski, M.; Rosenholm, J. B. Electroacoustic Study of Adsorption of Ions on Anatase and Zirconia from Very Concentrated Electrolytes. *J. Phys. Chem.* **1996**, *100* (28), 11681–11687.

(29) Huynh, T. V.; Messinger, R. J.; Sarou-Kanian, V.; Fayon, F.; Bouchet, R.; Deschamps, M. Restricted Lithium Ion Dynamics in PEO-Based Block Copolymer Electrolytes Measured by High-Field Nuclear Magnetic Resonance Relaxation. *J. Chem. Phys.* **2017**, *147*, 134902.

(30) Meersmann, T.; Deschamps, M.; Bodenhausen, G. Probing Aerogels by Multiple Quantum Filtered ¹³¹Xe NMR Spectroscopy. *J. Am. Chem. Soc.* **2001**, *123* (5), 941–945.

(31) Korb, J. P. Relaxation Magnétique Nucléaire Multi-Échelles Des Liquides Dans Les Milieux Poreux. C. R. Phys. **2010**, *11* (2), 192–203.

(32) Porion, P.; Warmont, F.; Faugère, A. M.; Rollet, A. L.; Dubois, E.; Marry, V.; Michot, L. J.; Delville, A. ¹³³Cs Nuclear Magnetic Resonance Relaxometry as a Probe of the Mobility of Cesium Cations Confined within Dense Clay Sediments. *J. Phys. Chem. C* **2015**, *119* (27), 15360–15372.

(33) Kim, Y.; Kirkpatrick, R. J. NMR T₁ Relaxation Study of ¹³³Cs and ²³Na Adsorbed on Illite. *Am. Mineral.* **1998**, *83*, 661–665.

(34) Yu, P.; Kirkpatrick, J. ³⁵Cl NMR Relaxation Study of Cement Hydrate Suspensions. Cem. Concr. Res. **2001**, *31* (10), 1479–1485.

(35) Maki, H.; Yoshida, K.; Nariai, H.; Mizuhata, M. Multinuclear NMR Studies on the Effect of Electrostatic and Hydrophobic Interactions on Bindings to Counterions to Weakly Acidic and Basic Polyelectrolytes. *Colloids Surf.*, A **2015**, *471*, 1–10.

(36) Maki, H.; Tachibana, T.; Jung Eun, S.; Mizuhata, M. Estimation of Solid-Liquid Interfacial Potential Enabled by Quantitative Analysis and Relaxation Observation of Quadrupolar NMR. *Colloids Surf*, A **2020**, *604*, 125286.

(37) Donati, I.; Asaro, F.; Paoletti, S. Experimental Evidence of Counterion Affinity in Alginates: The Case of Nongelling Ion Mg²⁺. *J. Phys. Chem. B* **2009**, *113* (39), 12877–12886.

(38) Gossuin, Y.; Colet, J.-M.; Roch, A.; Muller, R. N.; Gillis, P. Cesium Adsorption in Hydrated Iron Oxide Particles Suspensions: An NMR Study. *J. Magn. Reson.* **2002**, *157* (1), 132–136.

(39) Tan, Z. R.; Pagnoux, C.; Sarou-Kanian, V.; Deschamps, M. Surface-Induced Quadrupolar Relaxation (SIQR): Probing Adsorption of Monovalent Ions (NH₄⁺, NO₃⁻, Li⁺, Na⁺, Rb⁺, Cs⁺, Br⁻) on Anatase Titanium Dioxide in Aqueous Media by NMR. *J. Phys. Chem. C* **2023**, *127* (39), 19717–19727.
(40) Janc, T.; Korb, J.-P.; Lukšič, M.; Vlachy, V.; Bryant, R. G.; Mériguet, G.; Malikova, N.; Rollet, A.-L. Multiscale Water Dynamics on Protein Surfaces: Protein-Specific Response to Surface Ions. *J. Phys. Chem. B* **2021**, *125* (31), 8673–8681.

(41) Ward-Williams, J.; Korb, J.-P.; Rozing, L.; Sederman, A. J.; Mantle, M. D.; Gladden, L. F. Characterizing Solid–Liquid Interactions in a Mesoporous Catalyst Support Using Variable-Temperature Fast Field Cycling NMR. *J. Phys. Chem. C* **2021**, *125* (16), 8767–8778.

(42) Carper, W. R.; Wahlbeck, P. G.; Dölle, A. ¹³C NMR Relaxation Rates: Separation of Dipolar and Chemical Shift Anisotropy Effects. *J. Phys. Chem. A* **2004**, *108* (29), 6096–6099.

(43) Wimperis, S. Relaxation of Quadrupolar Nuclei Measured via Multiple-Quantum Filtration. *Encycl. Nucl. Magn. Reson.* **2011**, *31* (3), 1–8.

(44) Deschamps, M.; Burghardt, I.; Derouet, C.; Bodenhausen, G.; Belkić, D. Nuclear Magnetic Resonance Study of Xenon-131 Interacting with Surfaces: Effective Liouvillian and Spectral Analysis. *J. Chem. Phys.* **2000**, *113* (4), 1630–1640.

(45) James, T. L.; Noggle, J. H. Sodium-23 Nuclear Magnetic Resonance Studies of Sodium Aminocarboxylic Acid Complexes. *J. Am. Chem. Soc.* **1969**, *91* (13), 3424–3428.

(46) Man, P. P. Quadrupolar Interactions. In *NMR of Quadrupolar Nuclei in Solid Materials*; Wiley, 2012, pp 1. DOI:.

(47) Huynh, T. V.; Messinger, R. J.; Sarou-Kanian, V.; Fayon, F.; Bouchet, R.; Deschamps, M. Restricted Lithium Ion Dynamics in PEO-Based Block Copolymer Electrolytes Measured by High-Field Nuclear Magnetic Resonance Relaxation. *J. Chem. Phys.* **2017**, *147* (13), 134902.

(48) Lodge, K. W.; Scholl, C. A. Calculation of Electric Field Gradients in Metals. *J. Phys. F: Met. Phys.* **1974**, *4* (11), 2073–2083.

(49) Korecki, J.; Gradmann, U. In-Situ Conversion Electron Mössbauer Spectroscopy on Fe(110)-Surfaces and Thin Films. *Hyperfine Interact.* **1986**, *28* (1–4), 931–934.

(50) Korecki, J.; Karas, W. Electric Field Gradients near the Fe(110) Surface. *J. Magn. Magn. Mater.* **1990**, *92* (1), L11–L13.

(51) Deverell, C.; Frost, D. J.; Richards, R. E. Quadrupole Relaxation in Solutions of Electrolytes. *Mol. Phys.* **1965**, *9* (6), S65–S77.

(52) Konecoglu, G.; Safak, T.; Kalpakli, Y.; Akgun, M. Photocatalytic Degradation of Textile Dye CI Basic Yellow 28 Wastewater by Degussa P25 Based TiO₂. *Adv. Environ. Res.* **2015**, *4* (1), 25–38.

(53) Ohtani, B.; Prieto-Mahaney, O. O.; Li, D.; Abe, R. What Is Degussa (Evonik) P25? Crystalline Composition Analysis, Reconstruction from Isolated Pure Particles and Photocatalytic Activity Test. *J. Photochem. Photobiol.*, **A** *2010*, *216* (2–3), 179–182.

(54) Hurum, D. C.; Agrios, A. G.; Gray, K. A.; Rajh, T.; Thurnauer, M. C. Explaining the Enhanced Photocatalytic Activity of Degussa P25 Mixed-Phase TiO₂ Using EPR. *J. Phys. Chem. B* **2003**, *107* (19), 4545–4549.

(55) Jensen, H.; Joensen, K. D.; Jorgensen, J.-E.; Pedersen, J. S.; Søgaard, G. Characterization of Nanosized Partly Crystalline Photocatalysts. *J. Nanopart. Res.* **2004**, *6* (5), 519–526.

(56) Na Nakorn, P.; Jinawath, S.; Wada, S. Mechanical Strength and Thermal Conductivity of High Purity Al₂O₃ Ceramics Using AKP-30 Powder. *J. Sci. Res. Chula. Univ.* **2005**, *30*, 77–85.

(57) Han, K. R.; Lim, C. S.; Hong, M.; Jang, J. W.; Hong, K. S. Preparation Method of Submicrometer-Sized α-Alumina by Surface Modification of γ-Alumina with Alumina Sol. *J. Am. Ceram. Soc.* **2000**, *83* (4), 750–754.

(58) Wu, C.-Y.; Tu, K.-J.; Deng, J.-P.; Lo, Y.-S.; Wu, C.-H. Markedly Enhanced Surface Hydroxyl Groups of TiO₂ Nanoparticles with Superior Water-Dispersibility for Photocatalysis. *Materials* **2017**, *10* (5), 566.

(59) Pagnoux, C.; Chartier, T.; de F. Granja, M.; Doreau, F.; Ferreira, J. M.; Baumard, J. F. Aqueous Suspensions for Tape-Casting Based on Acrylic Binders. *J. Eur. Ceram. Soc.* **1998**, *18* (3), 241–247.

(60) Johnson, S. B.; Russell, A. S.; Scales, P. J. Volume Fraction Effects in Shear Rheology and Electroacoustic Studies of Concent-

trated Alumina and Kaolin Suspensions. *Colloids Surf, A* **1998**, *141* (1), 119–130.

(61) Kosmulski, M.; Granqvist, B.; Rosenholm, J. B. Numerical Values of the Electrokinetic Potentials of Anatase at High Concentration of NaI. *J. Colloid Interface Sci.* **2006**, *301* (1), 310–314.

(62) Loosli, F.; Le Coustumer, P.; Stoll, S. Impact of Alginate Concentration on the Stability of Agglomerates Made of TiO₂ Engineered Nanoparticles: Water Hardness and pH Effects. *J. Nanopart. Res.* **2015**, *17* (1), 44.

(63) Alvarado, E. D.; Juárez, M. G. P.; Perez, C. P.; Perez, E.; Gonzalez, J. A. Improvement in the Dispersion of TiO₂ Particles inside Chitosan-Methyl Cellulose Films by the Use of Silane Coupling Agent. *J. Mex Chem. Soc.* **2019**, *63* (2), 154–168.

(64) Matter, F.; Luna, A. L.; Niederberger, M. From Colloidal Dispersions to Aerogels: How to Master Nanoparticle Gelation. *Nano Today* **2020**, *30*, 100827.

(65) Orwat, K.; Bernard, P.; Migdal-Mikuli, A. Obtaining and Investigating Amphoteric Properties of Aluminum Oxide in a Hands-On Laboratory Experiment for High School Students. *J. Chem. Educ.* **2016**, *93* (5), 906–909.

(66) Xu, P.; Wang, H.; Tong, R.; Du, Q.; Zhong, W. Preparation and Morphology of SiO₂/PMMA Nanohybrids by Microemulsion Polymerization. *Colloid Polym. Sci.* **2006**, *284* (7), 755–762.

(67) Liu, L.; Guo, Z.; Huang, Z.; Zhuang, J.; Yang, W. Size-Selective Separation of DNA Fragments by Using Lysine-Functionalized Silica Particles. *Sci. Rep.* **2016**, *6* (1), 22029.

(68) Skocaj, M.; Filipic, M.; Petkovic, J.; Novak, S. Titanium Dioxide in Our Everyday Life: Is It Safe? *Radiol. Oncol.* **2011**, *45* (4), 227.

(69) Solymos, K.; Ágoston, Á.; Gyulavári, T.; Szalma, L.; Todea, M.; Kukovecz, Á.; Kónya, Z.; Pap, Z. Environmental Impacts on the Photocatalytic Activities of Anatase and Rutile. *Catalysts* **2025**, *15* (2), 190.

(70) Miyauchi, M.; Ikezawa, A.; Tobimatsu, H.; Irie, H.; Hashimoto, K. Zeta Potential and Photocatalytic Activity of Nitrogen Doped TiO₂ Thin Films. *Phys. Chem. Chem. Phys.* **2004**, *6* (4), 865.

(71) Dumont, F.; Van Tan, D.; Watillon, A. Study of Ferric Oxide Hydrosols from Electrophoresis, Coagulation, and Peptization Measurements. *J. Colloid Interface Sci.* **1976**, *55* (3), 678–687.

(72) Tadros, T. F.; Lyklema, J. Adsorption of Potential-Determining Ions at the Silica-Aqueous Electrolyte Interface and the Role of Some Cations. *J. Electroanal. Chem.* **1968**, *17* (3–4), 267–275.

(73) Kosmulski, M.; Próchniak, P.; Rosenholm, J. B. Letter: The IEP of Carbonate-Free Neodymium(III) Oxide. *J. Dispersion Sci. Technol.* **2009**, *30* (5), 589–591.

(74) Wehrli, F. W. Spin-lattice relaxation of some less common weakly quadrupolar nuclei. *J. Magn. Reson.* **1978**, *30* (2), 193–209.

(75) Levitt, M. H. Spin Dynamics - Basics of Nuclear Magnetic Resonance; 2nd Ed.; Wiley: Chichester, UK, 2008; p. 752.

(76) Samuelsen, L.; Holm, R.; Lathuile, A.; Schönbeck, C. Buffer Solutions in Drug Formulation and Processing: How pKa Values Depend on Temperature, Pressure and Ionic Strength. *Int. J. Pharm.* **2019**, *560*, 357–364.

(77) Chang, C.; Muccio, D. D.; Pierre, T. S. Determination of the Tacticity and Analysis of the pH Titration of Poly(Acrylic Acid) by Proton and Carbon-13 NMR. *Macromolecules* **1985**, *18* (11), 2154–2157.

(78) Forman-Kay, J. D.; Clore, G. M.; Gronenborn, A. M. Relationship between Electrostatics and Redox Function in Human Thioredoxin: Characterization of pH Titration Shifts Using Two-Dimensional Homo- and Heteronuclear NMR. *Biochemistry* **1992**, *31* (13), 3442–3452.

(79) Pollard, A. C.; de la Cerda, J.; Schuler, F. W.; Pollard, T. R.; Kotrottsou, A.; Pisaneschi, F.; Pagel, M. D. Radiometal-Based PET/MRI Contrast Agents for Sensing Tumor Extracellular pH. *Biosensors* **2022**, *12* (2), 134.