Effective interactions in polydisperse systems of penetrable macroions

Abstract

A coarse-graining approach based on the linear response theory is applied to deduce general expressions for the effective pair potentials in a multi-component system of soft macroions. Within the underlying approximations, the effective pair potentials can be written as simple convolutions between the intrinsic macroion charge distributions and a Yukawa-like potential which effectively contains the averaged contributions from the small ions. Two different charge distributions are assigned to the soft macroions: a Gaussian-like diffuse distribution and a uniform charge distribution inside the particle cores. The resulting effective pair potentials are then used in an effective model based on the hyppernetted chain approximation to investigate the structural properties of a two-component system of oppositely charged particles as a function of the various system parameters. It is found that the condensation of counterions is much stronger in the case of particles with a Gaussian charge distribution, leading to much weaker electrostatic interactions and less structured pair correlations in comparison with the system of uniformly charged macroions.

Keywords:

• coarse-graining
• microgels
• charged colloids
• statistical mechanics

Acknowledgements

It is a pleasure and a great honour to dedicate this work to Prof. Jean-Pierre Hansen, whose enormous contributions to the theory of liquids – and in particular of systems of charged particles – have dramatically improved our knowledge about these systems.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Throughout this paper, we adopt the convention that the mesoscopic components are denoted by Greek indices.

2. We adopt here for calculational convenience an asymmetric definition of the structure factor with respect to indices exchange. This plays however no role in what follows, since the response function ${\widehat{\chi }}_{ij}\left(\mathbf{k}\right)=-\beta {\rho }_i{S}_{ij}\left(\mathbf{k}\right)$ does recover exchange symmetry between indices i and j.

Additional information

Funding

This work was partially supported by the Conselho Nacional de Pesquisa (CNPq) [grant number 236575/2012-0].