Partially Annealed Disorder and Collapse of Like-Charged Macroions

TL;DR

This paper explores how partially annealed charge disorder on macroion surfaces affects electrostatic interactions, revealing that it can lead to reduced repulsion or even collapse of like-charged macroions due to disorder-induced attraction.

Contribution

It develops a formalism for partially annealed disorder and demonstrates its effects on macroion interactions, including charge renormalization and disorder-driven collapse transitions.

Findings

Partial annealing reduces inter-plate repulsion.

Disorder induces long-range attraction at strong coupling.

System can undergo collapse due to disorder variance exceeding a threshold.

Abstract

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.