Effect of surface roughness on bulk-disorder–induced wetting

Abstract

PACS. 68.45Gd -Wetting. PACS. 05.70Fh -Phase transitions: general aspects. PACS. 82.65Dp -Thermodynamics of surfaces and interfaces.Abstract. -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. . 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 ∆ −ψ , 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].

First-order wetting of rough substrates and quantum unbinding

“…In summary, our RG picture demonstrates first-order wetting in 2D with sufficiently rough substrates exerting short range forces on the interface. This is consistent with earlier numerical work suggestive of discontinuous transitions [8,16]. The threshold for first-order wetting is precisely identified as ζ w = 1/2 in the case of ordered bulk.…”

“…Numerical results in ref. [16] support this conclusion, giving evidence of first-order wetting for sufficiently large ζ w and finite disorder. Similar arguments apply to long range forces in SF and, for ζ w > ζ * , in MF regime.…”

“…Consistently with our expectation, numerical results for short range forces in ref. [16] support continuous wetting in Kardar's class for ζ w sufficiently lower than 2/3, even with finite bulk disorder.…”

“…(6), we performed transfer matrix calculations for a model on square lattice with both wall and interface represented by directed paths, as described in ref. [16]. Fig.1 reports numerical results for the probability distribution of h. Data are taken just below the depinning temperature for ζ w = 2/3 (τ (2/3) = 1).…”

3D wedge filling and 2D random-bond wetting

“…Recent studies of filling transitions for fluids in 3D wedges [1,2] have revealed the much stronger influence of interfacial fluctuations compared with wetting at flat and rough substrates [3][4][5][6][7]. Encouragingly effective Hamiltonian predictions for the critical exponents at continuous (critical) wedge filling with short-ranged forces have been confirmed in large scale Ising model simulation studies [8].…”