A unified picture of roto-translational dynamics in aqueous polyatomic ions

TL;DR

This paper develops a unified theoretical and computational framework to describe the coupled rotational and translational dynamics of polyatomic ions in aqueous solutions, revealing deviations from classical hydrodynamic laws.

Contribution

It introduces a self-consistent mode-coupling theory for polyatomic ions, integrating rotational and translational motions, and compares it with existing dielectric friction models.

Findings

Nitrate ions exhibit higher rotational diffusivity than sulfate and acetate.

All studied ions defy classical size-dependent hydrodynamic laws.

Theoretical models reveal the coupling between rotational and translational dynamics.

Abstract

Mode-coupling theory provides a unified description of the rotational and translational dynamics of polyatomic ions. These molecular ions are distinct from usual models of ion diffusion, such as K+ , Cl- etc., and also different from rotational dynamics of dipolar molecules often modeled in dielectric continuum models as point dipoles. Both these approaches are untenable for polyatomic ions. Here rotational and translational dynamics are so strongly coupled that one obtains a more coherent description by treating them together. We carry out theoretical and computational studies of a series of well-known polyatomic ions, namely sulfate, nitrate and acetate ions. All the three ions exhibit different rotational diffusivity, with that of nitrate ion being considerably larger than the other two. They all defy the hydrodynamic laws of size dependence. Study of the local structure around the ions provides valuable insight into the origin of these differences. We carry out a detailed study of the rotational diffusion of these ions by extensive computer simulation and using the theoretical approaches of the dielectric friction developed by Fatuzzo-Mason (FM) and Nee-Zwanzig (NZ), and subsequently generalized by Alavi and Waldeck. We develop a self-consistent mode-coupling theory (SC-MCT) formalism that helps elucidating the role of coupling between translational and rotational motion of these ions. In fact, these two motions self-consistently determine the value of each other. The RISM-based MCT suggests an interesting relation between the torque-torque and the force-force time correlation function with the proportionality constant being determined by the geometry and the charge distribution of the polyatomic molecule.We point out several parallelism between the theories of translational and rotation friction calculations of ions in dipolar liquids.