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.

Revisiting Dynamic Processes and Relaxation Mechanisms in a Heterocyclic Glass-Former: Direct Observation of a Transient State

“…where ε 0 is the vacuum permittivity, q is the charge on an ion, μ is the dipole moment of an organic molecule, and |r qμ | is the center of mass distance between the charge and the molecular dipole. 59 These possible angular fluctuations correspond to small displacement of atoms S1, S2, C1, and C2, which do not exceed 0.03, 0.03, 0.10, and 0.09 Å, respectively (Figure 6e). Consequently, one can expect a well-ordered structure of the complex salt PdCl 2 (MeBzS 2 ) in its crystal phase with relatively small thermal ellipsoids.…”

“…Their preferred occurrence can be ascribed, among others, to charge–dipole interactions. Namely, ions are the source of the local electric field, and any polar objects (i.e., possessing a permanent electric dipole moment) are subject to torque when placed in an external electric field. , The torque makes the dipoles align parallel with the field so that the potential energy is minimized and the attractive Coulomb interactions with ionic species are the most effective. Eq.…”

“…Eq. 15 defines the standard Coulomb energy describing the charge–dipole interaction U q μ false( bold-italicr false) = − 1 4 π ε 0 q false( bold-italicr bold-italicq bold-italicμ · bold-italicμ false) | r q μ | 3 where ε 0 is the vacuum permittivity, q is the charge on an ion, μ is the dipole moment of an organic molecule, and | r q μ | is the center of mass distance between the charge and the molecular dipole . Interaction between Pd 2+ and lone pairs of S atoms from MeBzS 2 is ineffective for conformers M1 and M2 because of the considerable angle between vectors r qu and μ .…”

“…15 defines the standard Coulomb energy describing the charge–dipole interaction where ε 0 is the vacuum permittivity, q is the charge on an ion, μ is the dipole moment of an organic molecule, and | r q μ | is the center of mass distance between the charge and the molecular dipole. 59 Interaction between Pd 2+ and lone pairs of S atoms from MeBzS 2 is ineffective for conformers M1 and M2 because of the considerable angle between vectors r qu and μ . Maximizing the Coulomb energy (in terms of its absolute value) requires transforming MeBzS 2 to the strained intermediate conformer T1* (or T2*), characterized by the highest dipole moment value and almost collinear alignment of vectors r qu and μ .…”

Using Implicit-Solvent Potentials to Extract Water Contributions to Enthalpy–Entropy Compensation in Biomolecular Associations

“…Equations and highlight the surprising result that electrostatic assembly in water at room temperature is primarily entropy-driven. The origin of this entropic driving force can be understood as arising from the increased orientational freedom of water molecules upon pairing of two oppositely charged ions, , as illustrated in Figure A. This entropic contribution due to water reorganization in electrostatic interactions has been invoked to successfully explain the predominantly entropy-driven nature in polyelectrolyte complex coacervation systems .…”