Dynamics of wetting transitions: A time-dependent Ginzburg-Landau treatment

Tricritical wetting in the two-dimensional Ising magnet due to the presence of localized non-magnetic impurities

Fixed vacancies (non-magnetic impurities) are placed along the centre of Ising strips in order to study the wetting behaviour in this confined system, by means of numerical simulations analysed with the aid of finite size scaling and thermodynamic integration methods. By considering strips of size L × M (L << M) where short-range competitive surface fields (H(s)) act along the M-direction, we observe localization-delocalization transitions of the interface between magnetic domains of different orientation (driven by the corresponding surface fields), which are the precursors of the wetting transitions that occur in the thermodynamic limit. By placing vacancies or equivalently non-magnetic impurities along the centre of the sample, we found that for low vacancy densities the wetting transitions are of second order, while by increasing the concentration of vacancies the transitions become of first order. Second- and first-order lines meet in tricritical wetting points (H(tric)(SW), T(tric)(W)), where H(tric)(SW) and T(Tric)(W) are the magnitude of the surface field and the temperature, respectively. In the phase diagram, tricritical points shift from the high temperature and weak surface field regime at large vacancy densities to the T --> 0, H(tric)(SW) --> 1 limit for low vacancy densities. By comparing the locations of the tricritical points with those corresponding to the case of mobile impurities, we conclude that in order to observe similar effects, in the latter the required density of impurities is much smaller (e.g. by a factor 3-5). Furthermore, a proper density of non magnetic impurities placed along the centre of a strip can effectively pin rather flat magnetic interfaces for suitable values of the competing surface fields and temperature.

First-order and tricritical wetting transitions in the two-dimensional Ising model caused by interfacial pinning at a defect line

We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples.

Kinetics of phase separation in thin films: lattice versus continuum models for solid binary mixtures

A description of phase separation kinetics for solid binary (A,B) mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size l(t) in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov t;{13} law with time t after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatment is reliable also at temperatures far below criticality, where the correlation length in the bulk is only of the order of a lattice spacing, and steep concentration variations may occur near the walls, invalidating the gradient square approximation. A further merit is that the relation to the interaction parameters in the bulk and at the walls is always transparent, and the correct free energy at low temperatures is consistent with the time evolution by construction.

Dynamics of condensation of wetting layer in time-dependent Ginzburg–Landau model

The dynamics of liquid condensation on a substrate or within a capillary is studied when the wetting film grows via interface-limited growth. We use a phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with long-range substrate potential. Using an order parameter, which does not directly represent the density, we can derive an analytic formula for the interfacial growth velocity that is directly related to the substrate potential. Using this analytic expression the growth of wetting film is shown to conform to a power-law-type growth, which is due to the presence of a long-range dispersion force.

Cell dynamics simulation of droplet and bridge formation within striped nanocapillaries

The kinetics of droplet and bridge formation within striped nanocapillaries is studied when the wetting film grows via interface-limited growth. The phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with thermal noise is used and numerically solved using the cell dynamics method. The model is two-dimensional and consists of undersaturated vapor confined within a nanocapillary made of two infinitely wide flat substrates. The surface of the substrate is chemically heterogeneous with a single stripe of lyophilic domain that exerts long-range attractive potential to the vapor molecule. The dynamics of nucleation and subsequent growth of droplet and bridge can be simulated and visualized. In particular, the evolution of the morphology from droplet or bump to bridge is clearly identified. The crucial role played by the substrate potential on the morphology of bridge of nanoscopic size is clarified. Nearly temperature-independent evolution of capillary condensation is predicted when the interface-limited growth dominates. In addition, it is shown that the dynamics of capillary condensation follows the scenario of capillary condensation proposed by Everett and Haynes three decades ago.

Dynamical behavior of three-dimensional confined Ising systems with short- and long-range competing surface fields

The dynamical behavior of ferromagnetic Ising films confined in a DxLxL geometry (D<<L,1< or =i< or =D) is studied by means of Monte Carlo simulations when either short- or long-range competing magnetic fields H(i) of equal strength but opposite sign are applied at opposite walls, given by the LxL surfaces. It is well known that, for appropriate choices of the control parameters, these systems exhibit wetting phase transitions that occur in the limit of infinite film thickness at the critical curve Tw(hw) , where hw=H(i=1) is the magnitude of the surface field at the wall. Results of the dynamical approach to equilibrium, at criticality and for the complete wetting regime, obtained by starting the systems from different (far-from equilibrium) initial conditions, are presented and discussed. We determine quite accurately a wetting critical point [Tw=0.8982(57),hw=0.555] for the case of short-range fields, by measuring the detachment of the wetting layer from a wall, which for this type of field obeys a logarithmic dependence on time. For retarded van der Waals forces we obtained [Tw=0.8982,hw=0.449(1)] for the critical point. The scaling behavior of the average position of the interface is also studied for the complete wetting regime at T=0.8982 and in the presence of a bulk magnetic field H=1 . The numerical results are in full agreement with the theoretical expectations for the cases of short-range and long-range (both retarded and nonretarded van der Waals forces) fields, where logarithmic and power-law divergences are found, respectively.