Effect of surface roughness on bulk-disorder–induced wetting

– Transfer-matrix results in 2D show that wetting of a rough, self-affine wall induced by bulk bond disorder turns discontinuous as soon as the wall roughness exponent ζW exceeds ζ0 = 2/3, the spatial anisotropy index of interface fluctuations in the bulk. For ζW < 2/3 critical wetting is recovered, in the same universality class as for the flat-wall case. These and related findings suggest a free-energy structure such to imply first-order wetting also without disorder, or in 3D, whenever ζW exceeds the appropriate ζ0. The same thresholds should apply also with van der Waals forces, in cases when ζ0 implies a strong-fluctuation regime. Disorder induced critical wetting [1]-[3] is a remarkable phenomenon in the physics of interfaces in random media [2], [4], [5]. Even at temperature T = 0, under the effect of quenched bulk impurities, an interface can undergo depinning from an attractive (smooth) wall [1]. An example is offered by the 2D Ising model on semi-infinite lattice. At T = 0, with suitable boundary conditions, the interface can be localized on a line of weak ferromagnetic bonds along the edge (wall). If the bulk couplings are disordered, upon reducing wall attraction depinning eventually occurs. This ill-condensed matter version of critical wetting in 2D belongs to a different universality class as similar transitions controlled by thermal fluctuations alone. Indeed, the mean wall-interface distance h diverges as ∆ , where ψ = 2 [1] and ∆ measures the deviation from critical edge attraction conditions. ψ = 1 holds for the thermal case without disorder [6]. An as yet unanswered question concerns the possible effect of additional, geometrical surface disorder on this type of wetting. Rough substrate walls with self-affine geometry, are produced in experiments [7], [8] and adsorption phenomena have been already observed on them [8]. On the other hand, interface depinning belongs to a more general class of disorder-induced delocalization phenomena of fluctuating manifolds from extended defects [9]. () Present address: Instituut-Lorentz, Rijks Universiteit Leiden, 2300 RA Leiden, The Netherlands. c © Les Editions de Physique 634 EUROPHYSICS LETTERS In the present letter we show that a self-affine roughness of the attractive wall can indeed have dramatic effects on the wetting induced by bulk disorder. By extensive calculations in 2D and by a study of the interfacial free energy, we show that wetting turns first-order as soon as the wall roughness exceeds that of the interface in the bulk. If, on the contrary, the wall is smoother than the bulk interface, critical wetting persists, in the same universality class as with flat wall. For first-order wetting due to roughness our results allow to draw a general scenario, encompassing also cases in 3D, with ordered bulk or long-range substrate forces. The possibility for geometrical surface disorder to drive wetting first-order has been recently envisaged by some of us for pure systems and in the context of hierarchical models [10]. A key issue here is to assess whether and up to what extent this disorder, which is correlated in the case of self-affine roughness, can determine modifications when acting simultaneously with uncorrelated bulk randomness. Here wetting of a rough boundary is studied by means o the model illustrated in fig. 1. To each bond b of a square lattice, a random energy b is independently assigned from a uniform distribution in (0, 1). The interface configurations are directed paths with one end in the origin O and t steps (t measures also the longitudinal distance). At T = 0 the only interface configuration is that minimizing the total energy of a path P , given by