Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization

Using field-theoretic techniques, we study the solvation of salt ions in liquid mixtures, accounting for the permanent and induced dipole moments, as well as the molecular volume of the species. With no adjustable parameters, we predict solvation energies in both single-component liquids and binary liquid mixtures that are in excellent agreement with experimental data. Our study shows that the solvation energy of an ion is largely determined by the local response of the permanent and induced dipoles, as well as the local solvent composition in the case of mixtures, and does not simply correlate with the bulk dielectric constant. In particular, we show that, in a binary mixture, it is possible for the component with the lower bulk dielectric constant but larger molecular polarizability to be enriched near the ion.

Figure 1

The solvation free energy $\Delta G$ of monovalent ions (${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, ${\mathrm{Cs}}^{+}$, ${\mathrm{Et}}_4{\mathrm{N}}^{+}$, ${\mathrm{Me}}_4{\mathrm{N}}^{+}$, ${\mathrm{Br}}^{-}$, ${\mathrm{I}}^{-}$, ${\mathrm{ClO}}_4^{-}$, and ${\mathrm{Cl}}^{-}$) and divalent (inset) ions (${\mathrm{Ca}}^{2+}$, ${\mathrm{Zn}}^{2+}$, ${\mathrm{Cd}}^{2+}$, ${\mathrm{Pb}}^{2+}$, and ${\mathrm{Cu}}^{2+}$) with different effective ionic radius $a$ [38, 39] in MeOH. (a) Filled squares represent experimental data [9, 30, 31, 32]. (b) The solid red curves represent $\Delta G$ calculated by the DSCFT. (c) The dashed green curves represent the standard Born energy $\Delta G_{\mathrm{st}}$ with the experimental value of the bulk dielectric constant.

Figure 2

(a) Composition profile of MeCN and MeOH as a function of the radial distance $r$ from a ${\mathrm{Ag}}^{+}$ ion. (b) The transfer free energy $\Delta G^{*}$ as a function of the volume fraction of MeCN. Square points, experimental data [33]; solid purple line, $\Delta G^{*}$ calculated by the DSCFT; and dashed green line, result implied by the Born expression and linear mixing rule for the bulk dielectric constant.

Figure 3

(a) Composition profile of chloroform and ethyl acetate as a function of the radial distance $r$ from a ${\mathrm{Na}}^{+}$ ion. (b) Profile for the local dielectric function. The bulk composition for the mixture is ${\varphi }_{\mathrm{Chl}}=0.026$ and ${\varphi }_{\mathrm{EthA}}=0.974$.