Nonlocality and Short-Range Wetting Phenomena

Abstract

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition. [2] are complementary approaches to the theory of confined fluids. Mean-field, non-local density functionals give an accurate description of structural properties but are unable to account correctly for long-wavelength interfacial fluctuations. To understand these it is usually necessary to employ mesoscopic interfacial Hamiltonians based on a collective coordinate l(x), measuring the local interfacial thickness. These models are essentially local in character containing a surface energy term proportional to the stiffness Σ of the unbinding interface and a binding potential function W (l). In more refined theories the stiffness also contains a position dependent term [3], Σ(l), which, it is has been argued, may drive the wetting transition first-order [4]. Despite progress over the last few years there are a number of outstanding problems particularly for wetting with short-ranged forces. In addition, recent studies of fluids in wedge-like geometries have uncovered hidden connections or wedge covariance relations between observables at planar wetting and wedge filling transitions [5], which have yet to understood at a deeper level. In this paper we argue that analogous to developments in density functional methods the general theory of short-ranged three-dimensional wetting should be formulated in terms of a non-local (NL) interfacial Hamiltonian. The model we propose directly allows for bulk-like correlations arising from tube-like fluctuations Consider a Landau-Ginzburg-Wilson Hamiltonian based on a continuum order-parameter (magnetization) m(r) in a semi-infinite geometry with bounding surface described by a single-valued height function ψ(x) where x = (x, y) is the parallel displacement vector. Denoting the surface magnetization by m 1 (x) we write (1) where ds ψ = 1 + (∇ψ) 2 dx is the wall area element whilst φ(m) and φ 1 (m 1 ) are suitable bulk and surface potentials [9]. The bulk Hamiltonian is isotropic so the interfacial tension and stiffness are the same. Following FJ we identify the interfacial modelwhere m Ξ (r) is the profile which minimises Eq. (1) subject to a given interfacial configuration. FJ determined m Ξ (r) perturbatively in terms of local planar constrained profiles [3]. He...

Capillary wave spectrum at adsorbed liquid films

“…The simplest classical version, (7), is recovered if γ FJ = 0. For flat substrates the Hamiltonian of Fisher and Jin is recovered as the low-q limit of the nonlocal functional form proposed by Parry et al, 34 but the latter includes a q dependence in γ (q,ξ IS ). Therefore, the first difference between the two theoretical assumptions would appear as the curvature terms in the expansion γ LV (q) + γ (q,ξ IS ) ≈ γ 0 + γ FJ e −λξ IS + (κ + κ(ξ IS ))q 2 + · · ·.…”

“…(15) and (16), in terms of γ LV (q) and γ (q,ξ IS ), are more general than the top lines in the same equations, given in terms of the local function of ξ (x,y) and its derivatives. Strictly nonlocal interfacial Hamiltonians, as proposed by Parry and 085401-4 coworkers, 34 include double integrals over the surface, like (18) where a kernel function K(|R 1 − R 2 |) links the functional dependence at two points of the interface, with a generic function S(ξ ). The expansion of (16).…”

Fluctuation Forces and Wetting Layers in Colloid-Polymer Mixtures

“…For liquid interfaces, where surface tension dominates, the situation is more complex. From a theoretical point of view, the influence of capillary fluctuations on wetting phenomena has attracted much attention as it could lead to nonuniversal wetting behavior with critical exponents depending explicitly on temperature [7,8]. Experimentally, the observation of this entropic repulsion in typical liquid layers is challenging, but some observations have shown that a correct description of adsorption isotherms of molecularly thin films could be achieved if one takes the entropic interaction into account [9][10][11][12].…”

“…Further, for the Ising universality class, the wetting parameter ! k B T= 4 2 takes the value 0:8 close to bulk criticality [2,8]. Using results of renormalization group (RG) theory for complete wetting [27,28], which incorporates thermal fluctuation effects, we derive that the mean-squared width of the confined interface depends linearly on the wetting layer thickness [29],…”

Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA

“…In the wetting context, a long-standing problem, regarding the order of the transition in three-dimensional systems, has been recently solved [23]. The original renormalizationgroup calculations led to the prediction of non-universal results in blatant disagreement with computational studies [24] and experiments [25], both of which yield a meanfield-like second-order phase transition.…”