On the bulk modulus of the cell model of charged macromolecules suspensions

TL;DR

This paper theoretically investigates the bulk modulus of suspensions of charged macro-ions using a cell model and local density functional theory, establishing conditions for positive compressibility and repulsive interactions.

Contribution

It provides a general theoretical framework linking bulk modulus positivity with effective pair potentials in charged macro-ion suspensions.

Findings

Bulk modulus positivity conditions are derived.

Several existing models satisfy the positivity condition.

The theory rules out the existence of a critical point.

Abstract

We study theoretically the bulk modulus (inverse of the compressibility) of a suspension of charged objects (macro-ions), making use of a cell model to account for the finite density of macro-ions. The diffuse layer of charged micro-species around a macro-ion is described by a generic local density functional theory. Within this general framework, we obtain the condition for a positive bulk modulus, which is fulfilled by several proposals made in the literature and rules out the possibility of a critical point. We show that a sufficient condition for a positive compressibility also ensures that the same theory produces repulsive effective pair potentials.