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Journal of Applied Mathematics and Computational Mechanics

The wetting layers For long-range wall-particle potentials

Artur Barasiński, A. Drzewiński

Published Jan 1, 2007• 0 citations
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Abstract

The complete wetting in 2D Ising strips subject to identical surface fields decaying as h1z −p is studied by means of the density-matrix renormalization-group technique. Using different criteria the thickness of a layer is determined along some isotherms above the wetting temperature. It is found that magnetization profiles are characterized by wide interfacial regime.

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The complete wetting in 2D Ising strips subject to identical surface fields decaying as h1z −p is studied by means of the density-matrix renormalization-group technique. Using different criteria the thickness of a layer is determined along some isotherms above the wetting temperature. It is found that magnetization profiles are characterized by wide interfacial regime.
We obtain an exact solution of the d = 2 infinite Ising strip with surface fields of opposite signs , . Earlier predictions by Parry et al are confirmed of the crucial importance of wetting for a system confined between two parallel walls that exert competitive surface fields. The transition of the magnetization profile m(z) from the partial wetting regime below the critical wetting temperature at a single wall with a surface field , to the soft-mode single phase in the temperature range , where is the critical temperature of the bulk system, is described in detail. A scaling ansatz is verified for the singular part of the surface excess free energy, and for the profile, . The modification of the magnetization profile near one wall, due to wetting, is studied. Near the (-) wall at the profile is found to be a linear function of the scaled distance but its slope is different than for the case of perfect asymmetry system hence these two cases belong to the different universality regime.
The excess adsorption Gamma in two-dimensional Ising strips (infinityxL), subject to identical boundary fields at both one-dimensional surfaces decaying in the orthogonal direction j as -h1j(-p), is studied for various values of p and along various thermodynamic paths below the bulk critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete-wetting and critical-adsorption regimes, occurring in semi-infinite systems, is strongly influenced by confinement effects. Along isotherms T=const the asymptotic power-law dependences on the external bulk field, which characterize these two regimes, are pre-empted by capillary condensation. Along the pseudo-first-order phase-coexistence line of the strips, which varies with temperature, we find a broad crossover regime in which both the thickness of the wetting film and Gamma increase as functions of the reduced temperature tau but do not follow any power law. Above the wetting temperature the order-parameter profiles are not slablike but exhibit wide interfacial variations and pronounced tails.
Using the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large l as slow as l(-delta) with delta<2, where l is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Svrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases delta=2 and delta=49 with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.
We consider an Ising model confined in an $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ geometry with identical surface fields at the boundaries. According to the Kelvin equation the bulk coexistence field scales as 1/L1/L1/L for large L;L;L; thermodynamics and scaling arguments predict higher-order corrections of the type 1/L2{1/L}^{2}1/L2 and 1/L5/3{1/L}^{5/3}1/L5/3 at partial and complete wetting, respectively. Our numerical results, obtained by density-matrix renormalization techniques for systems of widths up to L=144,L=144,L=144, are in agreement with a 1/L2{1/L}^{2}1/L2 correction in the partially wet regime. However, at complete wetting we find a large range of surface fields and temperatures with a correction to scaling of type 1/L4/3.{1/L}^{4/3}.1/L4/3. We show that this term is generated by a thin wetting layer whose free energy is dominated by the contacts with the wall. For LLL sufficiently large we expect a crossover to a 1/L5/3{1/L}^{5/3}1/L5/3 correction as predicted by the theory for a thick wetting layer. This crossover is indeed found in a solid-on-solid model, which provides a simplified description of the wetting layer and allows the study of much larger systems than those available in a density-matrix renormalization calculation.
Using the quasi-exact density-matrix renormalization-group method we calculate the solvation forces in two-dimensional Ising films of thickness L subject to identical algebraically decaying boundary fields with various decay exponents p. At the bulk critical point the solvation force acquires a universal contribution which is long-ranged in L due to the critical fluctuations, a phenomenon known as the critical Casimir effect. For p = 2, 3 and 50, we study the scaling behaviour of the solvation force along the pseudo-phase coexistence and along the critical and sub-critical isotherms.