On the experimental determination of the repulsive component of the potential from high pressure measurements: what is special about twelve?

TL;DR

This paper reviews high-pressure measurements to understand the repulsive part of intermolecular potentials, highlighting a common behavior where the scaling exponent gamma approaches 4, implying a potential with n~12 for many molecular systems.

Contribution

It provides an overview of the thermodynamical scaling of liquids and polymers, emphasizing the significance of gamma=4 and its relation to a universal repulsive potential exponent n~12.

Findings

Gamma approaches 4 in high-pressure regimes dominated by repulsive interactions.

Gamma relates to the potential exponent n via gamma = n/3, suggesting n~12.

Many molecular systems can be described by a potential U(r)~ r^{12}.

Abstract

In this paper we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent gamma, and argue that it exhibits the limiting behavior gamma=4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r)= r^n, gamma has been found to be related to the exponent n via the relation gamma = n/3. Therefore, this limiting behavior for gamma would suggest that a large number of molecular systems may be described by a common repulsive potential U(r)~ r^n with n~12.