Ionic Reactions in Two Dimensions with Disorder

TL;DR

This paper investigates how disorder affects ion pairing and reaction kinetics in a two-dimensional Coulomb gas, revealing non-universal critical behavior and anomalous decay exponents.

Contribution

It demonstrates that disorder induces non-universality in the Kosterlitz-Thouless transition and causes anomalous, variable decay kinetics in ion reactions.

Findings

Disorder shifts the critical temperature of the KT transition.

Ion pairing kinetics become anomalous with a variable decay exponent.

Strong disorder can eliminate the phase transition altogether.

Abstract

We analyze the dynamics of the ion-dipole pairing reaction in the two-dimensional Coulomb gas in the presence of disorder. Sufficiently singular disorder forces the critical temperature of the Kosterlitz-Thouless-Berezinskii fixed point to be non-universal. This disorder leads to anomalous ion pairing kinetics with a continuously variable decay exponent. Sufficiently strong disorder eliminates the transition altogether. For ions that are chemically reactive, anomalous kinetics with a continuously variable decay exponent also occurs in the high-temperature regime. The Coulomb interaction inhibits reactant segregation, and so the ionic $A^+ +B^- \to \emptyset$ reaction behaves like the nonionic $A + A \to \emptyset$ reaction.