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

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.

19 pages, 5 figures, to appear in Physical Review E

References in corpus (2)

• Hard-Sphere Fluids in Contact with Curved Substrates
• Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces

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• Many-body correlations from integral geometry
• Generalization of the Wall Theorem to Out-of-equilibrium Conditions
• Bending and Gaussian rigidities of confined soft spheres from second-order virial series
• Reexamination of Tolman's law and the Gibbs adsorption equation for curved interfaces