Debye-Hueckel-Bjerrum theory for charged colloids

TL;DR

This paper extends the Debye-Hueckel-Bjerrum theory to describe the thermodynamics of highly asymmetric charged colloids, accounting for cluster formation and predicting no phase transition, aligning with experimental and simulation data.

Contribution

It introduces a new theoretical framework for charged colloids that includes cluster formation and provides thermodynamic predictions consistent with observations.

Findings

No evidence of phase transition in the model.

Cluster-density distribution and pressure are derived.

Results agree with experimental and Monte Carlo data.

Abstract

We formulate an extension of the Debye-Hueckel-Bjerrum theory [M. E. Fisher and Y. Levin, Phys. Rev. Lett. 71, 3826 (1993)] to the fluid state of a highly asymmetric charged colloid. Allowing for the formation of clusters consisting of one polyion and n condensed counterions, the total Helmholtz free energy of the colloidal suspension is constructed. The thermodynamic properties, such as the cluster-density distribution and the pressure, are obtained by the minimization of the free energy under the constraints of fixed number of polyions and counterions. In agreement with the current experimental and Monte Carlo results, no evidence of any phase transition is encountered.