Connecting Thermodynamics of Alkali Ion Exchange on the Quartz (101) Surface with Density Functional Theory Calculations

Abstract

Periodic plane-wave density functional theory (DFT) calculations were performed on the α-quartz (SiO₂) (101) surface to model exchange of adsorbed Li⁺ and either Na⁺, K⁺, or Rb⁺ in inner- and outer-sphere adsorbed, and aqueous configurations, which are charge-balanced with 2 Cl^-. SiO^- or SiOH groups represented the adsorption surface sites. The SiO^- models included 58 H₂O and 2 H₃O⁺ molecules to approximate an aqueous environment, whereas the SiOH models had 59 H₂O and 1 H₃O⁺ molecules. The goal of this work is to calculate the heats of exchange for these alkali ions and to compare the results with those measured by flow microcalorimetry to ascertain the most probable mechanisms for these cations exchanging on the α-quartz (101) surface. Energy minimizations of each alkali ion adsorbed as outer-sphere complexes on SiOH surface sites, and as inner- and outer-sphere complexes on SiO^- surface sites, were used to determine the energy of exchange (ΔE_ex) with Li⁺ for comparison with experimentally determined ΔH_ex values. Here, we present a novel method for calculating ΔE_ex using the difference in energies of geometry-optimized end member models. The aqueous and surface structures produced are similar to those observed experimentally. Although the trend for the calculated ΔE_ex values is consistent with those from the heats of exchange measured experimentally, the magnitude of our modeled ΔE_ex results is significantly larger than select experimental data from the literature [Peng, L. Zeta-Potentials and Enthalpy Changes in the Process of Electrostatic Self-Assembly of Cations on Silica Surface. Powder Technol. 2009, 193(1), 46-49]; we discuss the reasons for this discrepancy herein. The relative energy differences of the various configurations modeled have implications for the measurements of the surface charge via potentiometric titrations due to the more active role of alkali cations in quartz surface chemistry that have been previously considered as inert background electrolytes.