Molecular-Based Theory for Electron-Transfer Reorganization Energy in Solvent Mixtures

Abstract

Using statistical-field techniques, we develop a molecular-based dipolar self-consistent-field theory (DSCFT) for charge solvation in liquid mixtures under equilibrium and nonequilibrium conditions, and apply it to compute the solvent reorganization energy of electron-transfer reactions. In addition to the nonequilibrium orientational polarization, the reorganization energy in liquid mixtures is also determined by the out-of-equilibrium solvent composition around the reacting species due to preferential solvation. Using molecular parameters that are readily available, the DSCFT naturally accounts for the dielectric saturation effect and the spatially varying solvent composition in the vicinity of the reacting species. We identify three general categories of binary solvent mixtures, classified by the relative optical and static dielectric permittivities of the solvent components. Each category of mixture is shown to produce a characteristic local solvent composition profile in the vicinity of the reacting species, which gives rise to the distinctive composition dependence of the reorganization energy that cannot be predicted using the dielectric permittivities of the homogeneous solvent mixtures.

110th Anniversary: Theory of Activity Coefficients for Lithium Salts in Aqueous and Nonaqueous Solvents and in Solvent Mixtures

“…Wang and co-workers developed a theory to predict the extent of preferential solvation by accounting for permanent and induced dipole-ion interactions. The Supporting Information outlines this theory for calculating the volume fraction of solvent at the surface of an isolated ion, , in a solvent with bulk volume fraction of . , …”

“…The Supporting Information outlines this theory for calculating the volume fraction of solvent at the surface of an isolated ion, φ * , in a solvent with bulk volume fraction of φ . 21,22 Figure 4 shows the volume fraction, calculated with the use of the theory outlined in the Supporting Information (lines), of solvent at the surface of a Li + ion in a mixture of solvents and as a function of volume fraction of in the bulk for two water/alcohol mixtures: water/ethanol (EtOH) and water/ methanol (MeOH), and for two common lithium-ion-battery solvents: ethylene carbonate (EC)/dimethyl carbonate (DMC) and EC/ethyl methyl carbonate (EMC). As the fraction of solvent in the bulk increases, the fraction at the ion's surface also increases but the relation is not linear.…”

“…To determine an effective ion diameter in a solvent mixture, we use results from Wang and co-workers who presented a dipolar self-consistent-field theory (DSCFT) that relates the bulk solvent composition to that of the local solvent environment around a solvated ion. (21,22) We first summarize pertinent thermodynamic variables. Next, we briefly review the MSA theory for electrolyte solutions.…”

“…In solvent mixtures, experimental and theoretical research has long ago shown that polarizable solvents and those with strong specific interactions preferentially solvate ions. − As a result of preferential solvation, activity coefficients of salts in a solvent mixture are not simple averages of pertinent single-solvent electrolyte properties. ,,− Authors often interpolate properties from those of single-solvent electrolytes using arbitrary mixing rules or equations with multiple adjustable parameters. ,,− …”

“…A major advantage of BiMSA is that for practical results, BiMSA requires only the solvated diameter of each ion as an adjustable parameter. To determine an effective ion diameter in a solvent mixture, we use results from Wang and co-workers who presented a dipolar self-consistent-field theory (DSCFT) that relates the bulk solvent composition to that of the local solvent environment around a solvated ion. , …”