Wetting of Rough Walls

Quenched geometric disorder of a wall delimiting a spectator phase can have dramatic effects on the nature of critical wetting transitions. We consider self-affine walls in 2D with roughness exponent _W. Transfer matrix results for directed interfacial models with short-range interactions suggest that wetting turns first-order as soon as _W exceeds ₀, the anisotropy index of interface fluctuations in the bulk. Discontinuous interface depinning is best identified by a peculiar two-peak structure in the statistical distributions of wall–interface contacts obtained by sampling over disorder. On the other hand, for _W<₀ wetting remains continuous, most plausibly in the same universality class as with flat walls. This occurs both with ordered (₀ = 1/2) and with bond-disordered (₀ = 2/3) bulk. A precise location of the thresholds at _W = ₀ can be argued on the basis of an analysis of different terms in the interfacial free energy. This analysis elucidates the peculiar role played by the intrinsic interfacial roughness and suggests extensions of the results to 3D and to long-range substrate forces.