On the nature of screening in Voorn-Overbeek type theories

TL;DR

This paper investigates the screening length in Voorn-Overbeek theories using a Legendre transform approach, revealing a more general form that differs from the classical Debye length and applies to non-ideal entropy cases.

Contribution

It introduces a generalized screening length formula for Voorn-Overbeek theories based on Legendre transforms, extending beyond ideal entropy assumptions.

Findings

Derived a new expression for screening length in non-ideal systems.

Showed the generalized screening length differs from Debye length in certain regimes.

Reduced to Debye length in limiting cases.

Abstract

By using the recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek type theories, that remains valid also in the cases where the entropy is not given by the ideal gas form as in the Debye-Huckel theory. The screening length consistent with the non-electrostatic terms in the free energy Ansatz for the Flory-Huggins and Voorn-Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some limiting cases.