Wetting of van der Waals solid films on self-affine rough surfaces

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In this work we investigate the influence of random self-affine substrate roughness on the solid layer thickness under conditions of triple-point wetting of adsorbed van der Waals films. Our calculations show that a significant solid film thickness ${\ensuremath{\lambda}}_{s}$ can be reached (in the nanometer range) for substrate roughness parameters $w/\ensuremath{\xi}l~0.05$ and/or $H\ensuremath{\approx}1$ with w the rms roughness amplitude, \ensuremath{\xi} the lateral roughness correlation length, and H the roughness exponent $(0l~Hl~1).$ Independent of substrate-particle and particle-particle interactions, with increasing roughness exponent H and/or decreasing ratio $w/\ensuremath{\xi}$ the solid film thickness ${\ensuremath{\lambda}}_{s}$ increases since the substrate surface becomes smoother. Finally, the solid layer thickness is shown to be sensitive to growth details of the substrate roughness as described in many cases in terms of dynamic scaling theory.