Opposing Surface Fields Research Articles

Wetting and emergence of long-range couplings in arrays of fluid cells.

Critical wetting is of crucial importance for the phase behavior of a simple fluid or Ising magnet confined between walls that exert opposing surface fields so that one wall favors liquid (spin up), while the other favors gas (spin down). We show that arrays of boxes filled with fluid and linked by channels with appropriately chosen opposing walls can exhibit long-range cooperative effects on a length scale far exceeding the bulk correlation length. We give the theoretical foundations of these long-range couplings by using a lattice gas (Ising model) description of a system.

Anisotropic interfacial tension, contact angles, and line tensions: a graphics-processing-unit-based Monte Carlo study of the Ising model.

As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest-neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin-film geometry L(x)×L(y)×L(z) with periodic boundary conditions along the z axis and two free L(x)×L(y) surfaces at which opposing surface fields ±H(1) act, under conditions of partial wetting, a single planar interface inclined under a contact angle θ<π/2 relative to the yz plane is stabilized. In the y direction, a generalization of the antiperiodic boundary condition is used that maintains the translational invariance in the y direction despite the inhomogeneity of the magnetization distribution in this system. This geometry allows a simultaneous study of the angle-dependent interface tension, the contact angle, and the line tension (which depends on the contact angle, and on temperature). All these quantities are extracted from suitable thermodynamic integration procedures. In order to keep finite-size effects as well as statistical errors small enough, rather large lattice sizes (of the order of 46 million sites) were found to be necessary, and the availability of very efficient code implementation of graphics processing units was crucial for the feasibility of this study.

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.

Interfaces in Driven Ising Models: Shear Enhances Confinement

We use a phase-separated driven two-dimensional Ising lattice gas to study fluid interfaces exposed to shear flow parallel to the interface. The interface is stabilized by two parallel walls with opposing surface fields, and a driving field parallel to the walls is applied which (i) either acts locally at the walls or (ii) varies linearly with distance across the strip. Using computer simulations with Kawasaki dynamics, we find that the system reaches a steady state in which the magnetization profile is the same as that in equilibrium, but with a rescaled length implying a reduction of the interfacial width. An analogous effect was recently observed in sheared phase-separated colloidal dispersions. Pair correlation functions along the interface decay more rapidly with distance under drive than in equilibrium and for cases of weak drive, can be rescaled to the equilibrium result.

Density functional theory study of the nematic–isotropic transition in an hybrid cell

We have employed the density functional theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyze the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropiclike to nematiclike states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interfacelike states which allow us to continuously transform the nematiclike phase to the isotropiclike phase without undergoing a sharp phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematiclike state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematiclike state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematiclike states.

Cumulant ratios and their scaling functions for ising systems in a strip geometry

We calculate the fourth-order cumulant ratio (proposed by Binder) for the two-dimensional Ising model in the strip geometry Lxinfinity. The density-matrix renormalization-group method enables us to consider typical open boundary conditions up to L=200. Universal scaling functions of the cumulant ratio are determined for strips with parallel as well as opposing surface fields. Their asymptotic properties are also examined.

Pseudo-Casimir effect in nematic liquid crystals in frustrating geometries

We study theoretically the fluctuation-induced structural force in nematic systems frustrated by external fields. We focus on the uniform director structure in the hybrid-aligned film characterized by opposing surface fields and in the Freedericksz cell where frustration arises from competing bulk and surface fields. We find that frustration gives rise to several interesting features of the interaction, including a crossover from attraction at small distances to repulsion at large distances. The fluctuation-induced interaction is enhanced substantially by frustration, the enhancement being progressively stronger on approaching the transition from uniform to distorted structure. At the structural transition the interaction diverges and we show that the pretransitional singularity is universal.

Phase coexistence in confined Ising systems: a density matrix renormalization approach

Using a density matrix renormalization approach we have calculated the phase diagram of a two-dimensional Ising model confined between two infinite walls, with opposing surface fields and a bulk field which grows linearly as a function of the distance from the walls and models the effect of gravity on a confined fluid. In the absence of gravity, two-phase coexistence is restricted to temperatures below the wetting temperature as pointed out by Parry and Evans [A.O. Parry, R. Evans, Phys. Rev. Lett. 64, (1990) 439]. We find that the competing effects of gravity and surface fields restore the `ordinary' finite size scaling to the bulk critical point, in agreement with previous mean-field results. We have calculated the exponents related to the shift toward the critical point in the limit L→∞, where L is the distance between the walls and we have found good agreement with previous scaling assumptions. Magnetization profiles calculated from a solid-on-solid Hamiltonian agree well with density matrix renormalization results for temperatures not too close to the bulk critical temperature.

Interfacial Structural Changes and Singularities in Nonplanar Geometries

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics.

Critical point shift in a fluid confined between opposing walls

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$ geometry with opposing surface fields at the walls are studied by density matrix renormalization techniques. In particular we focus on the effect of gravity on the system, which is modeled by a bulk field whose strength varies linearly with the distance from the walls. It is well known that in the absence of gravity phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores phase coexistence up to the bulk critical temperature, in agreement with previous mean field results. A detailed study of the scaling to the critical point, as $L \to \infty$, is performed. The temperature shift scales as $1/L^{y_T}$, while the gravitational constant scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic exponents respectively. For weak surface fields and $L$ not too large, we also observe a regime where the gravitational constant scales as $1/L^{1+y_H - \Delta_1 y_T}$ ($\Delta_1$ is the surface gap exponent) with a crossover, for sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$.

Phase properties of nematics confined by competing walls

The consequences of confinement on the isotropic-nematic (IN) transition are investigated for a slab geometry with walls that compete in molecular alignment. We employ the Landau-de Gennes free energy with symmetrically opposing wall fields that favor random parallel and homeotropic orientations, respectively, at each wall, and describe the phase diagram with the use of the associated nonlinear dynamical-system phase portraits. The differences in phase behavior with respect to the bulk, or with the system confined by identical walls, are important: Depending on the wall separation L and the strength of the walls' field μ s , the IN transition is either unaffected and its temperature T IN remains fixed, or, the transition disappears altogether. We find: (i) when μ s < μ s w (where μ s w is the wall field value for the wetting transition of the semi-infinite system) the transition occurs for all wall separations, and (ii) when μ s > μ s w there is no transition for all wall separations above a given value L qw ( μ s ). The boundary L qw ( μ s ) between these two regions is identified as a shifted wetting transition in which IN phase coexistence is transformed into an interface-like state, and it is of the 1st order, tricritical and critical when μ s w < μ s < μ s tc , μ s = μ s tc and μ s > μ s tc , respectively. For temperatures in the neighborhood of T IN , L qw ( μ s ) is continued as a locus of shifted prewetting transitions. This behavior is equivalent, but manifests differently, to that already known for a magnetic slab under symmetrically opposing surface fields and vanishing surface coupling enhancement.

Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.

Novel phase behaviour of a confined fluid or Ising magnet

The phase behaviour of a simple fluid or Ising magnet (at temperatures above its roughening transition) confined between parallel walls that exert opposing surface fields h 2 = - h 1 is found to be markedly different from that which arises for h 2 = h 1. Whereas critical wetting plays little role for confinement by identical walls, it is of crucial importance for opposing surface fields. Analysis of a Landau functional and other mean-field treatments show that if h 1 is such that critical wetting occurs at a single wall ( L = ∞) at a transition temperature T w , then phase coexistence, for finite wall separation L, is restricted to temperatures T < T c , L, where the critical temperature T c, L lies below T w . In the temperature range T c, b > T > T w there is a single soft mode phase that is characterized, for zero bulk field and large L, by a +- interface located at the centre of the slit, a transverse correlation length ξ ∼≈ e L and a solvation force that is repulsive. For large h 1, T w can lie arbitrarily far below the bulk critical temperature T c, b . Scaling arguments, whose validity we have confirmed in two dimensions by comparison with exact solutions for interfacial Hamiltonians, predict that such behaviour persists beyond mean-field for systems with short-ranged forces. They also predict similar phase behaviour for long-ranged forces, but with ξ ξ ∼ increasing algebraically with L in the soft mode phase. The solvation force t̃f s changes from repulsive to attractive (at large L) as the temperature is reduced below T w , i.e. the sign of t̃f s reflects wetting characteristics.

Long-ranged surface perturbations for confined fluids.

When a fluid, or magnet, is confined between parallel walls that exert opposing surface fields ${\mathit{h}}_{2}$=-${\mathit{h}}_{1}$ the order-parameter (magnetization) profile near one wall can be modified severely by the presence of the other. For sufficiently low dimensions (d3) the surface-layer perturbation and the force between the walls decay algebraically with wall separation L for all temperatures ${\mathit{T}}_{\mathit{c},}$b\ensuremath{\ge}T\ensuremath{\ge}${\mathit{T}}_{\mathit{w}}$. Near ${\mathit{T}}_{\mathit{w}}$, the temperature of a critical wetting transition, the perturbation can be longer ranged than at the bulk critical temperature ${\mathit{T}}_{\mathit{c},}$b. The predictions of a scaling theory are supported, for d=2, by results obtained from interfacial Hamiltonians and from Monte Carlo simulations of the Ising strip.