First-order interface localization-delocalization transition in thin Ising films using Wang-Landau sampling

Interfacial segregation of interacting vacancies and their role on the wetting critical properties of the Blume-Emery-Griffiths model

We study the wetting critical behavior of the three-state (s=±1,0) Blume-Emery-Griffiths model using numerical simulations. This model provides a suitable scenario for the study of the role of vacancies on the wetting behavior of a thin magnetic film. To this aim we study a system confined between parallel walls with competitive short-range surface magnetic fields (h_{L}=-|h_{1}|). We locate relevant critical curves for different values of the biquadratic interaction and use a thermodynamic integration method to calculate the surface tension as well as the interfacial excess energy and determine the wetting transition. Furthermore, we also calculate the local position of the interface along the film and its fluctuations (capillary waves), which are a measure of the interface width. To characterize the role played by vacancies on the interfacial behavior we evaluate the excess density of vacancies, i.e., the density difference between a system with and without interface. We also show that the temperature dependence of both the local position of the interface and its width can be rationalized in term of a finite-size scaling description, and we propose and successfully test the same scaling behavior for the average position of the center of mass of the vacancies and its fluctuations. This shows that the excess of vacancies can be associated to the presence of the interface that causes the observed segregation. This segregation phenomena is also evidenced by explicitly evaluating the interfacial free energy.

Probing interface localization-delocalization transitions by colloids

Interface localization-delocalization transitions (ILDT) occur in two-phase fluids confined in a slit with competing preferences of the walls for the two fluid phases. At low temperatures the interface between the two phases is localized at one of the walls. Upon increasing temperature it unbinds. Although intensively studied theoretically and computationally, such transitions have not yet been observed experimentally due to severe challenges in resolving fine details of the fluid structure. Here, using mean field theory and Monte Carlo simulations of the Ising model, we propose to detect these ILDT by using colloids. We show that the finite-size and fluctuation induced force acting on a colloid confined in such a system experiences a vivid change if, upon lowering the temperature, the interface localizes at one of the walls. This change can serve as a more easily accessible experimental indicator of the transition.

Nonadditive interactions and phase transitions in strongly confined colloidal systems

The behaviour of colloids can be controlled effectively by tuning the solvent-mediated interactions among them. An extensively studied example is the temperature-induced aggregation of suspended colloids close to the consolute point of their binary solvent. Here, using mean field theory and Monte Carlo simulations, we study the behaviour of colloids confined to a narrow slit containing a nearly-critical binary liquid mixture. We found that the effective interactions in this system are highly non-additive. In particular, the effective interactions among the colloids can be a few times stronger than the corresponding sum of the effective pair potentials. Inter alia, this non-additivity manifests itself in the phase behaviour of confined colloids, which depends sensitively on the slit width and temperature. In addition, we demonstrate the possibility of a first-order bridging transition between colloids confined to a slit and suspended in a phase-separated fluid well below the critical point of the solvent and at its critical composition in the bulk. This transition is accompanied by a remarkably large hysteresis loop, in which the force between the colloids varies by two orders of magnitude.

Influence of nonuniform surface magnetic fields in wetting transitions in a confined two-dimensional Ising ferromagnet

Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls where competitive surface fields act. In our finite samples of size L×M, the walls are separated by a distance L, M being the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the form H(1),δH(1),H(1),δH(1),..., where the parameter -1≤δ≤1 allows us to control the nonuniformity of the fields. By performing Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of an interface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, such an interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transition that takes place in the thermodynamic limit. By exactly working out the ground state (T=0), we found that besides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for δ<-1/3 and large fields (H(1)>3), H(1)(tr)/J=3, δ(tr)=-1/3,T=0, being a triple point where three phases coexist. By means of Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures; e.g., we examined in detail the case T=0.7×T(cb). Furthermore, we also recorded phase diagrams for fixed values of δ, i.e., plots of the critical field at the wetting transition (H(1w)) versus T showing, on the one hand, that the exact results of Abraham [Abraham, Phys. Rev. Lett. 44, 1165 (1980)] for δ=1 are recovered, and on the other hand, that extrapolations to T→0 are consistent with our exact results. Based on our numerical results we conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the case of nonuniform fields. In fact, by considering a nonuniform surface field of some period λ, with λ<<M, e.g., [H(1)(x,λ)>0], one can obtain the effective field H(eff) at a λ coarse-grained level given by H(eff)=1/λ∑(x=1)(λ)H(1)(x,λ). Then we conjectured that the exact solution for the phase diagram is now given by H(eff)/J=F(T), where F(T) is a function of the temperature T that straightforwardly follows from Abraham's solution. The conjecture was exhaustively tested by means of computer simulations. Furthermore, it is found that for δ≠1 the nonwet phase becomes enlarged, at the expense of the wet one, i.e., a phenomenon that we call "surface nonuniformity-induced nonwetting," similar to the already known case of "roughness-induced nonwetting."

Wetting transition in the two-dimensional Blume-Capel model: a Monte Carlo study

The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of L×M lattices where competing boundary fields ±H_{1} act on the first or last row of the L rows in the strip, respectively. We show that using the appropriate anisotropic version of finite-size scaling, critical wetting in d=2 is equivalent to a "bulk" critical phenomenon with exponents α=-1, β=0, and γ=3. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength H_{1c}(T) where critical wetting occurs goes to zero when the bulk second-order transition is approached, while H_{1c}(T) stays nonzero in the region where in the bulk a first-order transition from the ordered phase, with nonzero spontaneous magnetization, to the disordered phase occurs. Interfaces between coexisting phases then show interfacial enrichment of a layer of the disordered phase which exhibits in the second-order case a finite thickness only. A tentative discussion of the scaling behavior of the wetting phase diagram near the tricritical point is also given.

Phase transitions in thin films with competing surface fields and gradients

As a generic model for phase equilibria under confinement in a thin-film geometry in the presence of a gradient in the field conjugate to the order parameter, an Ising-lattice gas system is studied by both Monte Carlo simulations and a phenomenological theory. Choosing an L×L×D geometry with L≫D and periodic boundary conditions in the x,y directions, we place competing surface fields on the two L×L surfaces. In addition, a field gradient g is present in the z direction across the film, in competition with the surface fields. At temperatures T exceeding the critical temperature of the interface localization-delocalization transition, one finds a phase coexistence between oppositely oriented domains, aligned parallel to the surface fields and separated by an interface in the center of the film, for small enough g. For a weak gradient, a second-order transition to a monodomain state occurs, but it becomes first order if g exceeds a tricritical threshold. For sufficiently large gradients, another domain state becomes stabilized with domains oriented antiparallel to the surface fields.

Heterogeneous nucleation at a wall near a wetting transition: a Monte Carlo test of the classical theory

While for a slightly supersaturated vapor the free energy barrier ΔF(hom)(*), which needs to be overcome in a homogeneous nucleation event, may be extremely large, nucleation is typically much easier at the walls of the container in which the vapor is located. While no nucleation barrier exists if the walls are wet, for incomplete wetting of the walls, described via a nonzero contact angle Θ, classical theory predicts that nucleation happens through sphere-cap-shaped droplets attracted to the wall, and their formation energy is ΔF(het)(*) = ΔF(hom)(*)f(Θ), with f(Θ) = (1-cosΘ)(2)(2+cosΘ)/4. This prediction is tested through simulations for the simple cubic lattice gas model with nearest-neighbor interactions. The attractive wall is described in terms of a local 'surface field', leading to a critical wetting transition. The variation of the contact angle with the strength of the surface field is determined by using thermodynamic integration methods to obtain the wall free energies which enter Young's equation. Obtaining the chemical potential as a function of the density for a system with periodic boundary conditions (and no walls), the droplet free energy of a spherical droplet in the bulk is obtained for a wide range of droplet radii. Similarly, ΔF(het)(*) is obtained for a system with two parallel walls. We find that the classical theory is fairly accurate if a line tension correction for the contact angle is taken into account.

Performances of Wang-Landau algorithms for continuous systems

The relative performances of different implementations of the Wang-Landau method are assessed on two classes of systems with continuous degrees of freedom, namely, two polypeptides and two atomic Lennard-Jones clusters. Parallel tempering Monte Carlo simulations serve as a reference, and we pay particular attention to the variations of the multiplicative factor f during the course of the simulation. For the systems studied, the Wang-Landau method is found to be of comparable accuracy as parallel tempering, but has significant difficulties in reproducing low-temperature transitions exhibited by the Lennard-Jones clusters at low temperature. Using a complementary order parameter and calculating a two-dimensional joint density of states significantly improves the situation, especially for the notoriously difficult LJ(38) system. However, while parallel tempering easily converges for LJ(31), we have not been able to get data of comparable accuracy with Wang-Landau multicanonical sampling.

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.

Forces between chemically structured substrates mediated by critical fluids

We consider binary liquid mixtures close to their critical points confined by two parallel, geometrically flat, and chemically structured substrates. Universal order parameter profiles are calculated within mean field theory for periodic patterns of stripes with alternating preferences for the two species of the mixture and with different relative positions of the two substrates. From the order parameter profiles the effective forces between the two plates are derived. The tuning of Casimir amplitudes is discussed.

Phase transitions in nanosystems caused by interface motion: the Ising bipyramid with competing surface fields

The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/-H(s) is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bipyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L --> infinity) at the temperature Tf(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a susceptibility that diverges with a Curie-Weiss power law, when the transition is approached from either side. A Landau theory with size-dependent critical amplitudes is proposed to explain these observations, and confirmed by finite size scaling analysis of the simulation results. The extension of these results to other nanosystems (gas-liquid systems, binary mixtures, etc.) is briefly discussed.