# Electrostatics of Patchy Surfaces

## TL;DR

This paper reviews the electrostatic interactions of heterogeneously charged surfaces, emphasizing experimental and theoretical insights into their stability, ionic environment, and interactions, highlighting new physical parameters like patch size and charge correlations.

## Contribution

It provides a comprehensive review of recent studies on heterogeneously charged surfaces, focusing on electrostatics and introducing key parameters affecting their behavior.

## Key findings

- Long-range attraction between neutral patchy surfaces observed.
- Patch size and charge correlations significantly influence surface interactions.
- Heterogeneous charge distributions require new physical parameters for accurate modeling.

## Abstract

In the study of colloidal, biological and electrochemical systems, it is customary to treat surfaces, macromolecules and electrodes as homogeneously charged. This simplified approach is proven successful in most cases, but fails to describe a wide range of heterogeneously charged surfaces commonly used in experiments. For example, recent experiments have revealed a long-range attraction between overall neutral surfaces, locally charged in a mosaic-like structure of positively and negatively charged domains ("patches"). Here we review experimental and theoretical studies addressing the stability of heterogeneously charged surfaces, their ionic strength in solution, and the interaction between two such surfaces. We focus on electrostatics, and highlight the important new physical parameters appearing in the heterogeneous case, such as the largest patch size and inter-surface charge correlations