Entropic Origin of Ionic Interactions in Polar Solvents

Abstract

Implicit solvent models that reduce solvent degrees of freedom into effective interaction potentials are widely used in the study of soft materials and biophysical systems. For electrolyte and polyelectrolyte solutions, coarse-graining the solvent degrees of freedom into an effective dielectric constant embeds entropic contributions into the temperature dependence of the dielectric constant. Properly accounting for this electrostatic entropy is essential to discern whether a free energy change is enthalpically or entropically driven. We address the entropic origin of electrostatic interactions in a dipolar solvent and provide a clarified physical picture of the solvent dielectric response. We calculate the potential of mean force (PMF) between two oppositely charged ions in a dipolar solvent using molecular dynamics and dipolar self-consistent field theory. We find with both techniques that the PMF is dominated by the entropy gain from the dipole release, owing to the diminished orientational polarization of the solvent. We also find that the relative contribution of the entropy to the free energy change is nonmonotonic with temperature. We expect that our conclusions are applicable to a broad range of problems involving ionic interactions in polar solvents.

Figure 1

PMFs for various dipole moments calculated from (a) DSCFT and (b) molecular dynamics simulation with σ = 3 Å, T = 300 K, q₁ = −q₂ = e, v = 30 ų. The insets of both panels show PMFs for larger dipole moments. For reference, μ̅ = 1.85D corresponds to the gas-phase dipole moment of water.

Figure 2

PMFs decomposed into their energetic and entropic contributions with solvent dipoles of (a, b) μ̅ = 0 D and (c, d) μ̅ = 1 D. The PMFs are calculated from DSCFT in (a) and (c) and MD simulation in (b) and (d). Other parameters are the same as in Figure 1.

Figure 3

Ratio of PMF due to entropy for σ = 3 Å, q₁ = −q₂ = e and various calculated via (a) DSCFT and (b) molecular dynamics.

Figure 4

Free energy, internal energy, and entropy change from infinite separation to r = 5σ vs for σ = 3 Å and q₁ = −q₂ = e. Calculations were done using DSCFT.

Figure 5

Solvent polarization at the midplane of the ions for both theory (top row) and simulation (bottom row). Spatial positions are in units of σ. The ions are at separations of r = 5σ, 3σ, and 1σ going from left to right. Both ions have size σ = 3 Å and charges q₁ = −q₂ = e.

Figure 6

Normalized excess polarization versus the ion separation for various dipole moments μ̅, near the energy/entropy crossover, with σ = 3 Å and q₁ = −q₂ = e. Here, the excess polarization is normalized by the infinite separation excess polarization for μ̅ = 1.0 D. Calculations were done using (a) DSCFT and (b) simulation.