Critical Casimir forces and anomalous wetting

We present a review of critical Casimir forces in connection with successive experiments on wetting near the critical point of helium mixtures.     

Complete wetting in the three-dimensional transverse Ising model

We consider a three-dimensional Ising model in a transverse magnetic fieldh and a bulk fieldH. An interface is introduced by an appropriate choice of boundary conditions. At the point (H=0,h=0) spin configurations corresponding to different positions of the interface are degenerate. By studying the phase diagram near this multiphase point using quantum mechanical perturbation theory, we show that the quantum fluctuations, controlled byh, split the multiphase degeneracy giving rise to an infinite sequence of layering transitions.     

Critical Casimir effect in dilute He–He mixture films

Recently, we have found that ⁴He films thin near the lambda point. Based on our measurements, the thinning appears to be caused by the confinement of superfluid order parameter fluctuations in the films. The phenomenon of the thinning is believed to be analogous to the Casimir effect in electromagnetism where the confinement of electromagnetic fluctuations causes the vacuum layer that separates two metal plates to thin. In this paper, we report the result of an experiment extending our previous study to ³He–⁴He mixture films. Thinning is found near the new lambda points and the characteristics of the thinning are similar to that found in pure ⁴He films.     

Critical Casimir effects in 2D Ising model with curved defect lines

This work is aimed at studying the influence of critical Casimir effects on energetic properties of curved defect lines in the frame of 2D Ising model. Two types of defect curves were investigated. We start with a simple task of globule formation from four-defect line. It was proved that an exothermic reaction of collapse occurs and the dependence of energy release on temperature was observed. Critical Casimir energy of extensive line of constant curvature was also examined. It was shown that its critical Casimir energy is proportional to curvature that leads to the tendency to radius decreasing under Casimir forces. The results obtained can be applied to proteins folding problem in polarized liquid.     

Critical wetting in the square Ising model with a boundary field

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH ₁ acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.Alexander von Humboldt-Fellow     

Critical Casimir force in 4He films: confirmation of finite-size scaling

We present new capacitance measurements of critical Casimir force-induced thinning of 4He films near the superfluid transition, focused on the region below Tlambda where the effect is the greatest. 4He films of 238, 285, and 340 A thickness are adsorbed on atomically smooth, N-doped silicon substrates. The Casimir force scaling function theta, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum theta=-1.30+/-0.03 at x=td1/nu=-9.7+/-0.8 A1/nu. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to 2.13 K of the Goldstone or surface fluctuation force, which makes the superfluid film approximately 2 A thinner than the normal film.     

Phase coexistence in binary mixtures in thin films with symmetric walls: model calculations for two- and three-dimensional Ising lattices

Binary mixtures (A, B) that undergo phase separation in the bulk are considered in thin film geometry, assuming that one of the components is preferentially attracted to one of the walls. We discuss the average profile of the order parameter {volume fraction φ(z) of one of the components} in the z-direction (perpendicular to the surfaces), paying attention to the lateral inhomogeneity of the thin film when the average volume fraction corresponds to a state inside the coexistence curve. We consider the situation where due to (short range) surface forces a second-order wetting transition would occur in semi-infinite geometry: in the thin film geometry, this transition is rounded off and its only remnant is a smooth increase of the adsorbed mass in the surface-enriched layer in the transition region. Monte Carlo calculations for nearest neighbor Ising square and simple cubic lattices are used to derive typical concentration profiles. In the two-dimensional case, also the kinetics of domain formation after the quench from a disordered state is considered, and it is shown that the typical concentration oscillations perpendicular to the wall (“surface directed spinodal decomposition”) do not occur, due to strong lateral fluctuations of the local position of the interface between the enrichment layer at the surface and the neighboring depleted region. Finally, also phase-separated states in thin films with competing walls (where one surface prefers A and the other prefers B) are briefly treated, and experimental applications are discussed.     

Critical absorption in binary liquid systems

The refractive index of coexisting phases in two binary liquid systems, viz., perfluorodekalineheptane (PFD-H) and acetic anhydride-pentane (AA-P), in the vicinity of the critical consolution temperature of the system T _c was measured. It was shown that it is possible to observe (using the refractometry method, if the instrument is updated appropriately) critical absorption phenomena; a surface layer enriched by perfluorodekaline (in the PFD-H system) and by pentane (in the AA-P system) occurs at the liquid-vapor interface near the critical consolute point under T > T _c .     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Critical properties of the three-dimensional Ising model with quenched disorder

The static critical properties of the three-dimensional Ising model with quenched disorder are studied by the Monte-Carlo (MC) method on a simple cubic lattice, in which the quenched disorder is distributed as nonmagnetic impurities by the canonical manner. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.0; 0.95; 0.9; 0.8; 0.7; 0.6. The systems of non-linear sizes L×L×L, L=20-60 are researched. On the basis of the finite-size scaling (FSS) theory, the static critical exponents of specific heat α, susceptibility γ, magnetization β, and an exponent of the correlation radius in a studied interval of concentrations p are calculated. It is shown that the three-dimensional Ising model with quenched disorder has two regimes of the critical behavior universality in a dependence on nonmagnetic impurities.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Off-critical Casimir effect in Ising slabs with symmetric boundary conditions in d=3

Extended de Gennes-Fisher (EdGF) local-functional method has been applied to the thermodynamic Casimir effect away from the critical point for systems in the Ising universality class confined between parallel plane plates with symmetric boundary conditions [denoted (ab)=(++)]. Results on the universal scaling functions of the Casimir force W++(y) (y is a temperature-dependent scaling variable) and Gibbs adsorption G[over ](y) are presented in spatial dimension d=3. Also, the mean-field form of the universal scaling function of the Gibbs adsorption G[over ](y) is derived within the local functional theory. Asymptotic behavior of W++(y) for large values of the scaling variable y is analyzed in general dimension d.     

Critical exponents for a three-dimensional impure Ising model in the five-loop approximation

The renormalization-group functions governing the critical behavior of the three-dimensional weakly-disordered Ising model are calculated in the five-loop approximation. The random fixed point location and critical exponents for impure Ising systems are estimated by means of the Padé-Borel-Leroy resummation of the renormalization-group expansions derived. The asymptotic critical exponents are found to be γ=1.325 ± 0.003, η=0.025 ± 0.01, ν= 0.671 ± 0.005, α=?0.0125 ± 0.008, β=0.344 ± 0.006, while for the correction-to-scaling exponent, a less accurate estimate ω=0.32 ± 0.06 is obtained.     

Critical casimir effect and wetting by helium mixtures

We have measured the contact angle of the interface of phase-separated 3He-4He mixtures against a sapphire window. We have found that this angle is finite and does not tend to zero when the temperature approaches T(t), the temperature of the tricritical point. On the contrary, it increases with temperature. This behavior is a remarkable exception to what is generally observed near critical points, i.e., "critical point wetting." We propose that it is a consequence of the "critical Casimir effect" which leads to an effective attraction of the 3He-4He interface by the sapphire near T(t).     

Thermodynamic Casimir effect in 4He films near Tlambda: Monte Carlo results

The universal finite-size scaling function of the critical Casimir force for the three dimensional XY universality class with Dirichlet boundary conditions is determined using Monte Carlo simulations. The results are in excellent agreement with recent experiments on 4He Films at the superfluid transition and with available theoretical predictions.     

Critical Casimir Forces in Colloidal Suspensions

Some time ago, Fisher and de Gennes pointed out that long-ranged correlations in a fluid close to its critical point T _c cause distinct effective forces between immersed colloidal particles which can even lead to flocculation [C. R. Acad. Sc. Paris B 287:207 (1978)]. Here we calculate such forces between pairs of spherical particles as function of both relevant thermodynamic variables, i.e., the reduced temperature t=(T–T _c )/T _c and the field h conjugate to the order parameter. This provides the basis for specific predictions concerning the phase behavior of a suspension of colloidal particles in a near-critical solvent.