The influence of surfaces on vapor pressures

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Abstract
An analysis of internal particle equilibrium in J. Chem. Phys. 81, 2489 (1984) is generalized by means of Lagrange’s method of undetermined multipliers to show that a one-component crystalline particle of fixed size and shape is at equilibrium at constant temperature and pressure when the chemical potentials of molecular species, μi, μj, ..., and of vacancies μvi, μvj, ..., for sites i, j,... of different characteristic bond environments fit the relation μi−μvi=μj−μvj =⋅⋅⋅ . The chemical potential differences between molecular species and vacancies is shown to be the chemical potential for the component. The influence of surfaces on vapor pressures is predicted by setting the chemical potential of the component in the particle equal to that of its vapor. The predicted effects of surfaces are larger than those of classical theory but are in reasonable agreement with measurements for liquid drops.