Pattern formation and glassy phase in the $\phi^4$ theory with screened electrostatic repulsion

TL;DR

This paper investigates the phase behavior of a system with competing short-range attraction and long-range screened electrostatic repulsion, revealing complex phases including coexistence, lamellar, and glassy states, with implications for charged colloids.

Contribution

It provides an analytical study of the phase diagram of a model with competing interactions, linking observed colloidal cluster phases to an underlying equilibrium lamellar phase.

Findings

Identification of phase coexistence, lamellar, and glassy phases.

Evidence suggesting colloidal cluster phases are related to hidden lamellar phases.

Use of self-consistent Hartree and replica methods to analyze the system.

Abstract

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.