Electrostatic Attraction between Overall Neutral Surfaces

TL;DR

This paper analytically demonstrates that overall neutral surfaces with charged patches can exhibit long-range electrostatic attraction in ionic solutions, with the strength and range depending on patch size and charge density.

Contribution

It provides a theoretical calculation of osmotic pressure between neutral surfaces with charged patches, extending beyond linear theories and matching experimental observations.

Findings

Attraction occurs at large separations for patchy neutral surfaces.

Larger patches and higher charge densities strengthen the attraction.

Crossover separation inversely depends on patch charge density squared and screening length.

Abstract

Two overall neutral surfaces with positive and negative charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-H\"uckel theory, yields an {\it overall attraction} at large inter-surface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch charge-density and to the Debye screening length.