The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?

TL;DR

This paper demonstrates that a hard-sphere liquid near a curved wall exhibits a non-zero bending rigidity, challenging the Hadwiger theorem and supporting the Helfrich expansion for surface free energy.

Contribution

It shows that the bending rigidity for a hard-sphere fluid near a curved wall is non-zero, contradicting the Hadwiger theorem and favoring the Helfrich model.

Findings

Bending rigidity is non-zero for the fluid near a curved wall.

The bending rigidity is smaller than Gaussian curvature constant.

It changes sign with fluid volume fraction.

Abstract

In the context of Rosenfeld's Fundamental Measure Theory, we show that the bending rigidity is not equal to zero for a hard-sphere fluid in contact with a curved hard wall. The implication is that the Hadwiger Theorem does not hold in this case and the surface free energy is given by the Helfrich expansion instead. The value obtained for the bending rigidity is (1) an order of magnitude smaller than the bending constant associated with Gaussian curvature, (2) changes sign as a function of the fluid volume fraction, (3) is independent of the choice for the location of the hard wall.