Ion Exchange Thermodynamics at the Rutile–Water Interface: Flow Microcalorimetric Measurements and Surface Complexation Modeling of Na–K–Rb–Cl–NO₃ Adsorption

Abstract

Flow microcalorimetry was used to investigate the energetics associated with Rb, K, Na, Cl, and NO exchange at the rutile-water interface. Heats of exchange reflected differences in bulk hydration/dehydration enthalpies (Na > K > Rb, and Cl > NO) such that exchanging Na or Cl from the surface was exothermic, reflecting their greater bulk hydration enthalpies. Exchange heats were measured at pH 2, 3.25, 5.8, and 11 and exhibited considerable differences as well as pH dependence. These trends were rationalized with the aid of a molecularly constrained surface complexation model (SCM) that incorporated the inner-sphere binding observed for the cations on the rutile (110) surface. Explicitly accounting for the inner-sphere binding configuration differences between Rb, K, and Na, as well as accompanying differences in negative surface charge development, resulted in much better agreement with measured exchange ratios than by considering bulk hydration enthalpies alone. The observation that calculated exchange ratios agreed with those measured experimentally lends additional credence to the SCM. Consequently, flow microcalorimetry and surface complexation modeling are a useful complement of techniques for probing the energetics associated with ion exchange and adsorption processes and should also serve to help validate molecular simulations of interfacial energetics.

Adsorption Study of Al3+, Cr3+, and Mn2+ onto Quartz and Corundum using Flow Microcalorimetry, Quartz Crystal Microbalance, and Density Functional Theory

“…It has been suggested recently that most cations undergo a partial dehydration before adsorbing onto a mineral surface − through inner-sphere binding mode. Furthermore, the relationship between cation dehydration and the heats of cation interactions was established ,, for alkali and alkaline earth, and other multivalent cations (Cd 2+ , Co 2+ , Zn 2+ , Eu 3+ ). In particular, Hawkins et al and Allen et al demonstrated that the endothermic heats measured during cation adsorption were primarily a function of the bulk dehydration enthalpy.…”

“…Furthermore, the relationship between cation dehydration and the heats of cation interactions was established ,, for alkali and alkaline earth, and other multivalent cations (Cd 2+ , Co 2+ , Zn 2+ , Eu 3+ ). In particular, Hawkins et al and Allen et al demonstrated that the endothermic heats measured during cation adsorption were primarily a function of the bulk dehydration enthalpy. As such, it is a reasonable assertion that the endothermic heats measured for both Mn 2+ and Al 3+ adsorption could also be a function of a partial dehydration step as seen in eq . where >S is a representative surface functional group, Me is a metal cation, and n corresponds to the charge on the cation.…”

“…Experiments were performed using custom-designed flow microcalorimeters fabricated in the Kabengi laboratories at Georgia State University. The instrument design and experimental procedures have been thoroughly discussed in previous works. − To obtain the heats of cation adsorption ( Q ads in mJ/mg), a known mass (∼30.0–35.0 mg) of either Al 2 O 3 or SiO 2 powder was packed into the sample holder and equilibrated with the NaNO 3 solution until a thermal baseline was established at 20 ± 0.1 °C. The input solution was then switched to a M n + (NO 3 ) n solution, and the calorimetric signal for the M n + reaction with the surface was recorded (denoted [Na/M n + ]).…”

Assessment of Modeling Uncertainties Using a Multistart Optimization Tool for Surface Complexation Equilibrium Parameters (MUSE)

“…The model was built with custom-made Mathematica notebooks, versions of which have been previously used to simulate the rutile, − magnetite, ferrihydrite, and goethite interfaces. They have also been extended to fit adsorption data to 290 °C. , The multistart optimization routine was integrated in the original SCM model to optimize multiple parameters using as criteria the mean squared error (MSE) and Model Selection Criterion (MSC), with larger MSC values indicating a better fit. , Both MSE and MSC depend on the experimental data, specifically the amount and variability of available data, and number of fitting parameters for the latter; thus, they are used to compare different fits for a single data set.…”

Surface Complexation Modeling Approach for Aluminum-Substituted Ferrihydrites

“…Surface complexation models (SCMs) have been successfully applied to describe and predict surface protonation and ion sorption at a host of interfaces, primarily metal oxides, − but also clay minerals, and ionic solids such as carbonates. , Although most SCMs mimic interfacial reactions fairly well, the parameters used in early models were not based on specific molecular-level data for the systems studied. Consequently, one experimental data set could be modeled by several different yet plausible sets of parameter values .…”