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Density functional theory for random sequential adsorption

We treat the non-equilibrium process of random sequential adsorption of hard particles onto a solid substrate by means of a geometry-based density functional theory. As a prerequisite we solve the zero-dimensional case exactly and use it to construct density functionals in higher dimensions, permitting the treatment of adsorption onto arbitrary spatially inhomogeneous substrates. As applications we study the influence of a hard boundary of the adsorption region in the one-dimensional car-parking problem and for colloidal deposition on a two-dimensional solid substrate. Comparing to our computer simulation results, we find that the respective density functionals correctly predict the oscillatory density profiles near the boundary, with amplitudes that are considerably smaller than in the corresponding equilibrium models.