Thursday, April 25, 2013

1304.6557 (Edgar M. Blokhuis et al.)

Density Functional Theory of a Curved Liquid-Vapour Interface:
Evaluation of the rigidity constants

Edgar M. Blokhuis, Alan E. van Giessen
It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k_bar in its description. New formulas for k and k_bar in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k_bar are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k_bar corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 kT and that k_bar is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R^2 replaces the rigidity constants and we determine the (universal) proportionality constants.
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