Several model fluids in contact with planar, spherical, and cylindrical walls are investigated for small number densities within density functional theory. The dependence of the solid-fluid interfacial tension on the curvature of spherical and cylindrical walls is examined and compared with the corresponding expression derived within the framework of morphometric thermodynamics. Particular attention is paid to the implications of the choice of the interface location, which underlies the definition of the interfacial tension. We find that morphometric thermodynamics is never exact for the considered systems and that its quality as an approximation depends sensitively on the choice of the interface location.
Within the Poisson-Boltzmann approach, electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance C on the surface charge density σ and the ionic strength I are examined as a function of the wall curvature. The surface charge density has a strong effect on the capacitance for small curvatures, whereas for large curvatures the behavior becomes independent of σ. An expansion for small curvatures gives rise to capacitance coefficients which depend only on a single parameter, allowing for a convenient analysis. The universal behavior at large curvatures can be captured by an analytic expression.
Density functional theory is used to describe electrolyte solutions in contact with electrodes of planar or spherical shape. For the electrolyte solutions, we consider the so-called civilized model, in which all species present are treated on equal footing. This allows us to discuss the features of the electric double layer in terms of the differential capacitance. The model provides insight into the microscopic structure of the electric double layer, which goes beyond the mesoscopic approach studied in Paper I. This enables us to judge the relevance of microscopic details, such as the radii of the particles forming the electrolyte solutions or the dipolar character of the solvent particles, and to compare the predictions of various models. Similar to Paper I, a general behavior is observed for small radii of the electrode in that in this limit the results become independent of the surface charge density and of the particle radii. However, for large electrode radii, non-trivial behaviors are observed. Especially the particle radii and the surface charge density strongly influence the capacitance. From the comparison with the Poisson-Boltzmann approach, it becomes apparent that the shape of the electrode determines whether the microscopic details of the full civilized model have to be taken into account or whether already simpler models yield acceptable predictions.
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