Divalent Ion-Specific Outcomes on Stern Layer Structure and Total Surface Potential at the Silica : Water Interface

1 Divalent Ion-Specific Outcomes on Stern Layer Structure and Total Surface Potential at the Silica:Water Interface Emily Ma and Franz M. Geiger* Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60660, United States ABSTRACT. The second-order nonlinear susceptibility, c(2), in the Stern layer, and the total interfacial potential drop, F(0)tot, across the oxide:water interface are estimated from SHG amplitude and phase measurements for divalent cations (Mg2+, Ca2+, Sr2+, Ba2+) at the silica:water interface at pH 5.8 and various ionic strengths. We find that interfacial structure and total potential depend strongly on ion valency. We observe statistically significant differences between the experimentally determined χ(2) value for NaCl and that of the alkali earth series, but smaller differences between ions of the same valency in that series. These differences are particularly pronounced at intermediate salt concentrations, which we attribute to the influence of hydration structure in the Stern layer. Furthermore, we corroborate the differences by examining the effects of anion substitution (SO42for Cl-). Finally, we identify that hysteresis in measuring the reversibility of ion adsorption and desorption at fused silica in forward and reverse titrations manifests itself both in Stern layer structure and in total interfacial potential for some of the salts, most notable CaCl2 and MgSO4, but less so for BaCl2 and NaCl.

strength of 100 mM, after which we return the ionic strength in a stepwise fashion to the starting condition of ultrapure water at 2 µM. Using the procedure described, the phase drift during the duration of the experiment is negligible (<1°).
C. Data Fitting, Phase Referencing Procedure, and Point Estimates of and χ (2) . We utilize our previously published methods to extract the parameters needed for calculating the second order nonlinear susceptibility and surface potential. The generated interference patterns are fit to a sinusoidal function: Here, " is the signal intensity offset, the SHG amplitude, A, corresponds to the SHG signal, Esig, f is the periodicity of our spectrometer, x is the position on the translational stage, and the SHG phase, &$' , is obtained from #$% . Both A and #$% are obtained by fitting eqn. 1 to the SHG interference fringes. The #$% obtained at 2 µM pH 5.7 is set to 60 o ± 1 o , which is the previously determined phase difference between that ionic solution condition and the one obtained for 500 mM NaCl at pH 2.5, 20 the measured point of zero charge (PZC) of silica, 1,2,27,28 where the Coulombic contribution to the total interfacial potential is zero. The SHG phase, &$' , at 2 µM and pH 5.7 is then +60 o ± 1 o .
The non-resonant SHG amplitude and phase obtained from eqn. 1 yields the total secondorder nonlinear susceptibility in our HD-SHG spectrometer according to: 20 &$' × $( !"# ∝ %)% (+) = (+) − Φ(0) %)% -.%/0 (1) 9cos= 23,526 > $( $%,'$( + 1.5 C Here, (+) is the second-order nonlinear susceptibility of the interface, which is given by the sum of the second-order nonlinear susceptibilities of the interfacial species (in order of abundance, these are interfacial water molecules, then the surface silanol groups, and then the anions and cations adsorbed to the protonated and deprotonated surface silanol groups, respectively, vide Ma and Geiger 6 infra). The third-order contribution in eqn. 2 is multiplied into the total interfacial potential, F(0)tot, which includes all electrostatic contributions (Coulomb, dipole, and multipolar potentials, vide infra). The third-order term is dominated by the third-order contribution from the water molecules in the EDL, which is given by -.%/0 (1) (9.6 ± 1.9 × 10 7++ m + V 7+ from off-resonant SHG experiments at the air/water interface or 10.3 × 10 7++ m + V 7+ estimated from the third-order molecular hyperpolarizability obtained through quantum mechanical calculations). 29 For silica substrates, the C/R ratio is 3.6 × 10 7++ + 7D in our spectrometer. 20 Interfacial water is an ideal species to probe with nonlinear optics. Even though the nonresonant 2 nd -order hyperpolarizability of water, a (2) , is modest, 37 it is by far the majority species in most aqueous interfacial systems and often aligned in the Stern layer. How an array of water molecules is aligned in the Stern layer is encoded in the second-order susceptibility, a fundamental structural property of matter in noncentrosymmetric environments. 15 It is a measure of how the electrons are distributed in a non-centrosymmetric medium (the interface) and given by the number Ni of a given interfacial species i multiplied by the orientational average of the hyperpolarizability, ai (2) . 17 (SiOgroups) on silica at circumneutral pH reported from XPS measurements. 43 Ma and Geiger 8 Our current HD-SHG measurements reveal a nonmonotonic trend in the recorded SHG amplitude for the aqueous NaCl solution, as recently reported. 11,19 In contrast, the divalent chloride salts show a less pronounced, weakly non-monotonic trend with increasing ionic strength in the SHG amplitude.
In our previous work, 21 we determined a phase shift (Δ &$' ) of 29.7 ± 0.7° for the pristine fused silica/water interface for hemispheres that were first exposed to ultrapure water (2 μΜ) at B. Estimated Trends in F(0) tot and χ (2) Across the Cations. Our recent report shows a possible method of separating the second-and third-order contributions to the SHG signal and therefore estimating interfacial structure and potential using eqn. 2, 20 resulting in eqns. 3 and 4. We now use this method to determine how the second order nonlinear susceptibility (χ (2) ) and the total surface potential, F(0)tot, depend on the chemical identity of the adsorbed ions and their concentrations. Fig. 2A shows a large difference in χ (2) between NaCl and all the divalent cations, but no statistically significant difference in the χ (2) values among the divalent chloride salts. Fig. 2B reveals differences in χ (2) when sulfate is introduced as an anion (for both Na and the Mg salts).
The F(0)tot point estimates reveal a statistically significantly larger difference among the alkali earth chlorides we surveyed (bottom halves of Fig. 2). These differences do not follow the ionic radius of each cation species, which matches findings from previous work, including from calorimetric measurements. 44-46 Ca 2+ appears to have the largest field screening effect in the cation series, with F(0)tot reaching close to 0 V at 100 mM ionic strength. The larger ions, strontium and barium, come next, while the smallest (and hardest) ion, magnesium, lowers F(0)tot the least relative to NaCl.
Eqn. 4 shows that χ (2) is a linear combination of the contributions from the individual interfacial constituents. 21, 23 These are, in our case, the interfacial water molecules, then the surface silanol groups, and then the anions and cations adsorbed to the protonated and deprotonated surface silanol groups, respectively. The χ (2) value from the interfacial water and surface silanol groups should be close to the one obtained at the lowest ionic strength (ultrapure water, 2 µM ionic strength, pH 5.8) condition. We therefore subtract this χ (2) value from the data shown in Fig. 2 and obtain, at least to leading order, the χ (2) values of the ions bound to the interfacial SiOand SiOH2 + sites (Fig. 3). The results indicate non-monotonic behavior and a maximum in χ (2) around 0.1 mM ionic strength for most of the salts we surveyed. We also find a change in the sign of χ (2) at an ionic strength around 1 mM for the divalent chloride salts we studied (Fig. 3A), and to a lesser extent in the sulfates (Fig. 3B). This observation would be expected in case of a flip in the net orientation of the radiating dipoles that produce the SHG response based on trends documented in previous studies. 47-49 We therefore find experimental evidence for a significant change in interfacial structure with increasing surface coverage for some of the ions we surveyed, consistent with reports by others for mica:water 50-53 and silica:water 47-49, 54 interfaces. Previous studies of divalent cations, specifically magnesium and calcium, by Gibbs and co-workers, 55, 56 have shown that low concentrations of these salts (0.033mM) attenuate the vibrational sum frequency generation (SFG)-resonant water signal in comparison to NaCl at similar concentrations albeit at a higher pH than the conditions studied here. The resonant vibrational SFG experiments attributed these trends to displacement of the hydration layer above the silica surface by ions retaining their centrosymmetric hydration shell. 55 These trends were attributed to close association of Ca 2+ to the interface, 55, 57-62 a finding that would be consistent with the non-resonant c (2) estimates reported here (as well as the largest reduction in interfacial potential by CaCl2 relative to NaCl).
These results are in some ways surprising. Previous studies that have explored hydration structure and the point of zero charge of silica indicate that cation identity has an outsize effect on the electrostatics over structure at the interface. 63 Likewise, previous x-ray reflectivity studies have revealed that hydration shell structures play a role in trends of interfacial potential.  ions at the interface relative to M + ions with a positive lyotropic effect on heats of adsorption for increasing ionic radius. 44 In these experiments, the observed trends in ΔHads were strongly correlated with hydration properties for the monovalent ions, but did not hold as strongly for the divalent cations. Adsorption phenomena and changes in that behavior for various alkali earth cations were instead attributed to bare ionic radius and ionic potential (or charge/radius ratio). 44 Our findings may corroborate this scenario given differences between cation species in our experiments decrease with increasing surface coverage. Studies of the muscovite/water interface have also demonstrated that divalent ions with larger electron density such as Sr 2+ can adsorb in both fully and partially hydrated states. 52, 66 Different adsorption mechanisms for counterion species with larger electron may explain the larger magnitude surface potential for Sr 2+ and Ba 2+ at 100mM, in spite of similar χ (2) values in comparison to Ca 2+ and Mg 2+ at higher surface coverages.
With the observed trends in χ (2) among all divalent ions, we compare our findings to previous studies that have examined the effects of increasing ion size on the overall hyperpolarizability in different molecular systems. From our experimental measurements, we find relatively small changes in the second order nonlinear susceptibility between the divalent halide salts. This outcome is surprising given the precedent for relatively large changes in the hydration structure at the interface. 45, 55 Simulations have shown, for example, a highly ordered first solvation shell for divalent cations such as Mg 2+ vs a fairly labile hydration structure for Na + . 67 Furthermore, Na + is predicted to form direct contact ion pairs with silanol groups, whereas Mg 2+ is proposed to not bind directly to silanol groups at the surface, but rather form a hydrogen bonded complex through its tightly bonded hydration sphere. 67 Other MD simulations have shown Ca(OH) + can form at the silica surface upon deprotonation of one of the water molecules in the hydration shell of the Ca 2+ cation. 68 Previous theoretical studies of model complexes have indicated that hyperpolarizabilities generally increase with ionic radius, 69, 70 but our experiments show little changes between ions to such extent. These studies have also found a threefold increase in the hyperpolarizability in these complexes between substitution of Ca 2+ with Na + . However, when examining the normalized (+) values, Ca 2+ and Mg 2+ represent the smallest change in comparison to Na + observed in these experiments. 68 These are also the hardest cations in the series we studied.

C. Chloride vs Sulfate.
We applied the same analysis to anion identity to corroborate whether cation behavior did indeed play the largest role at the interface. While positively charged experiments (pH 5.8), previous experiments have shown a small number of SiOH + groups present even at neutral pH conditions. 71 In titrations of Na2SO4 and MgSO4, we observe changes in both and Φ " (Fig. 2B) and χ (2) (Fig. 3B) indicating that the presence of sulfate anions may have outsize effects on interactions at the interface, where the establish the largest negative potential at ionic strengths < 1mM. 72,73 Sulfates have been postulated to lead to silica dissolution through salting out effects that become especially pronounced at high temperatures. 26 In spite of silica's overall negative charge at circumneutral pH, 45, 71 we observe a reduction in χ (2) and Φ " with the addition of Na2SO4 which demonstrates that the anion species likely plays a role in the electrical double layer 72 even though the "standard" electrical double layer model (e.g. Gouy-Chapman-Stern theory) predicts Na + should be the predominant surface-bound species. 47, 74, 75 We observe the opposite trend for the 2:2 salt MgSO4 which could indicate that sulfate ions have a notable influence on the magnesium ion coverage. We postulate that these may play a role in the changes in overall structure that facilitate salting out effects (i.e. sulfate-silicic acid structures that form) at higher concentrations. 26 We also note that the Φ " point estimates for chloride and sulfate anions are invariant between each shared cation species at ionic strengths > 1 mM, which may indicate little change to hydration structure in the diffuse layer at higher concentrations.

D. Hysteresis and Manifestation in
and χ (2) . Another aspect we explore in this study is the dependence of adsorption and desorption reversibility on the cation identity. We perform reverse Among all salts studied ( Fig. 4 and S8-12) we observe the largest difference in χ (2) values for CaCl2 (Fig. 4A), for which the χ (2) point estimates are ~1.5 times larger in magnitude for the reverse titration in the lower concentration regime. The magnitude of the potential, on the other hand, is smaller for the reverse titration, again in the lower concentration regime. We observe these effects are less pronounced for BaCl2 and SrCl2 (Fig. 4A and S10). The MgSO4 reversibility manifests itself largely in the surface potential (Fig. 4C), while NaCl shows only very minor differences in interfacial structure and surface potential (Fig. 4D). Taken together, we find clear ion-specific outcomes on the structural and electrostatic hysteresis of our system for several of the salts we studied.
These results can be viewed in light of previous studies that have shown hysteresis in mineral oxide systems depends strongly on water structure as well as surface charge density. 46 Previous calculations of energies of adsorption indicate Ca 2+ likely forms a tighter contact ion pair with the silica surface disrupting the hydration structure at the surface than ions with a larger hydration shell, such as Ba 2+ . 54 These findings may demonstrate why larger hysteretic effects present for the CaCl2 salts compared to the other divalent cations. Surprisingly, we observe the least amount of hysteresis when using NaCl, at least under our present experimental conditions. A previous study we performed on a faster timescale, where the salt concentration was immediately jumped from ultrapure water to 100mM NaCl and vice versa, however, did demonstrate pathdependent effects. 19 The differences between these two outcomes highlight the importance of characterizing each step in surface-specific experiments involving fused silica, water, and salts. Conclusions and Outlook. Divalent cations at the silica/water interface probed with non-resonant HD-SHG spectroscopy measurements reveal that interfacial structure and total potential depend strongly on ion valency. When purely evaluating cation identity, we observe significant differences between the experimentally determined χ (2) value for NaCl and alkali earth cations, but smaller differences between ions of the same valency in that series. These differences are amplified at intermediate salt concentrations, which we attribute to the influence of hydration structure in the Stern layer, which is the origin of χ (2) . Furthermore, we corroborate the differences we report by examining the effects of anion substitution. Finally, we identify that hysteresis in measuring the reversibility of ion adsorption and desorption at fused silica under the stated conditions of our experiments manifests itself both in Stern layer structure, c (2) , and in total interfacial potential, Our estimates of c (2) are directly comparable to atomistic simulations of interfacial structure at aqueous interfaces that readily produce the second-order nonlinear susceptibility for  (2) , ion specific effects were not pursued in that study.

Ma and Geiger 15
Our c (2) estimates should be similarly informative for identifying those structural arrangements in the production runs of atomistic simulations that recapitulate the experimental c (2) values at oxide:water interfaces at a given pH (or surface charge), ion identity, and ionic strength.
Likewise, we expect that the estimates of the F(0)tot drop across the oxide:water interface we report here for the various salts we surveyed provides an experimental benchmark for mean field and/or atomistic models that include dipolar and multipolar contributions to the popular Gouy-Chapman-Stern theory, 83 the "standard model". Ionizing surface potential measurements published in 2021 by Allen and coworkers show that the surface potential ("c potential", 84 no relation to c (2) reported here) of the (nominally uncharged) pure air:water interface is as low as ~ -500 mV, 85 and that it is slightly less negative (~ -400 mV) at the air:electrolyte (1 M NaCl and 1M Na2SO4) interface.
Dipolar arrays of interfacial water molecules are thought to be the main contributors to this potential. [86][87][88] Multipolar contributions may also be important. 85 continuum, despite large differences in reported er. [97][98][99][100][101][102][103][104][105] The experimentally determined F(0)tot estimates obtained here include all the contributions to the potential and should thus be an Ma and Geiger 16 appropriate experimental benchmark to which theory must conform. It will also be informative to determine how ion-specific effects manifests themselves on other oxides, such as hematite, 106,107 which is an area we are actively pursuing.

V. Associated Content
Supporting Information: optical fringe data, c (2) and F(0)tot point estimates for forward and reverse titrations, for all salts studied. Figure Captions:   Figure 1. SHG amplitude A) and C) and phase B) and D) recorded for NaCl (dark green), MgCl2, CaCl2, SrCl2, and BaCl2 (light to dark blue), and Na2SO4 (orange), MgCl2 (blue), and MgSO4 (red), all at the ionic strengths indicated, and pH 5.8. Standard deviation between replicate measurements indicated by colored shading between point estimates.