Noro-Frenkel scaling in short-range square well: A Potential Energy Landscape study

TL;DR

This study investigates the potential energy landscape of particles with short-range square-well interactions, revealing how thermodynamics scale with attraction range and enabling counting of floppy modes.

Contribution

It provides an exact evaluation of basin free energy, separating vibrational and floppy components, and explains the thermodynamic equivalence based on the second virial coefficient.

Findings

Partition function depends on ^{ u_0}

Thermodynamics are equivalent for systems with same second virial coefficient

Able to count floppy modes and their entropy

Abstract

We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth $-u_0$), as a function of the range of attraction $\Delta$ to provide thermodynamic insights of the Noro and Frenkel [ M.G. Noro and D. Frenkel, J.Chem.Phys. {\bf 113}, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a {\it vibrational} ($\Delta$-dependent) and a {\it floppy} ($\Delta$-independent) component. We also show that the partition function is a function of $\Delta e^{\beta u_o}$, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).