On the possibility of extending the Nore-Frenkel generalized law of correspondent states to non-isotropic patchy interactions

TL;DR

This paper explores extending the generalized law of corresponding states (GLCS) to non-isotropic patchy interactions in colloidal and protein systems, focusing on short-range, small-angular amplitude interactions near the critical point.

Contribution

It proposes that the GLCS can be generalized to certain non-spherical, patchy interactions under specific conditions near the critical point.

Findings

GLCS can be extended to patchy interactions with small angular amplitude.

Thermodynamic properties depend mainly on the second virial coefficient near the critical point.

The approach applies when particles form only one bond per patch.

Abstract

Colloidal systems (and protein solutions) are often characterized by attractive interactions whose range is much smaller than the particle size. When this is the case and the interaction is spherical, systems obey a generalized law of correspondent states (GLCS), first proposed by Noro and Frenkel [ J.Chem.Phys. 113, 2941 (2000) ]. The thermodynamic properties become insensitive to the details of the potential, depending only on the value of the second virial coefficient B_2 and the density $\rho$. The GLCS does not generically hold for the case of non-spherical potentials. In this Letter we suggest that when particles interact via short-ranged small-angular amplitude patchy interactions (so that the condition of only one bond per patch is fulfilled) it is still possible to generalize the GLCS close to the liquid-gas critical point. Keywords: Colloids, Second Virial Coefficient, Proteins interactions, Short-ranged attractive attractions.