Antisymmetric Surface Fields Research Articles

Critical and Tricritical Wetting in the Two-Dimensional Blume–Capel model

The two-dimensional Blume–Capel model with free surfaces where a surface field $$H_1$$ acts and the “crystal field” (controlling the density of the vacancies) takes a value $$D _s$$ different from the value $$D$$ in the bulk, is studied by Monte Carlo methods. Using a recently developed finite size scaling method that studies thin films in a $$L \times M$$ geometry with antisymmetric surface fields $$(H_L=-H_1)$$ and keeps a generalized aspect ratio $$c = L^2/M$$ constant, surface phase diagrams are computed for several typical choices of the parameters. It is shown that both second order and first order wetting transitions occur, separated by tricritical wetting behavior. The special role of vacancies near the surface is investigated in detail.

Interplay Between Wetting and Phase Behavior in Binary Polymer Films and Wedges: Monte Carlo Simulations and Mean Field Calculations

Confining a binary mixture, one can profoundly alter its miscibility behavior. The qualitative features of miscibility in confined geometry are ratheruniversal and shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. The interplay between wetting and miscibility of a symmetric polymer mixture via large-scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self–consistent field calculations is studied. The film surfaces interact with the monomers via short ranged potentials, and the wetting transition of the semi–infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young’s equation. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi–infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. The dependence of the phase diagram on the film thickness Δ for antisymmetric surface fields is investigated. Upon decreasing the film thickness, the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness Δtri, there remains only a single critical point at the symmetric composition. This corresponds to a second-order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film thickness, Δtri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analog of the wetting transition of a planar surface, the latter is related to the filling behavior of a single wedge. Evidence for a second-order interface localization/delocalization transition in an antisymmetric double wedge is presented, and its unconventional critical behavior is related to the predictions of Parry et al. (Phys. Rev. Lett. 83:5535 (1999)) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.

The interplay between wetting and phase behaviour in binary polymer films and wedges:Monte Carlo simulations and mean field calculations

By confining a binary mixture, one can profoundly alter its miscibility behaviour. Thequalitative features of miscibility in confined geometry are rather universal and are sharedby polymer mixtures as well as small molecules, but the unmixing transition in the bulkand the wetting transition are typically well separated in polymer blends. We study theinterplay between wetting and miscibility of a symmetric polymer mixture via largescale Monte Carlo simulations in the framework of the bond fluctuation modeland via numerical self-consistent field calculations. The film surfaces interactwith the monomers via short-ranged potentials, and the wetting transition of thesemi-infinite system is of first order. It can be accurately located in the simulationsby measuring the surface and interface tensions and using Young’s equation.If both surfaces in a film attract the same component, capillary condensation occurs andthe critical point is close to the critical point of the bulk. If surfaces attract differentcomponents, an interface localization/delocalization occurs which gives rise to phasediagrams with two critical points in the vicinity of the pre-wetting critical point of thesemi-infinite system. The crossover between these two types of phase diagrams as afunction of the surface field asymmetry is studied.We investigate the dependence of the phase diagram on the film widthΔ for antisymmetric surface fields. Upon decreasing the film width the two critical pointsapproach the symmetry axis of the phase diagram, and below a certain width,Δtri, there remains only a single critical point at symmetric composition. Thiscorresponds to a second order interface localization/delocalization transitioneven though the wetting transition is of first order. At a specific film width,Δtri, tricritical behaviour is found.The behaviour of antisymmetric films is compared with the phase behaviour in anantisymmetric double wedge. While the former is the analogy of the wetting transition of aplanar surface, the latter is the analogy of the filling behaviour of a single wedge. Wepresent evidence for a second order interface localization/delocalization transition in anantisymmetric double wedge and relate its unconventional critical behaviour to thepredictions of Parry et al (1999 Phys. Rev. Lett. 83 5535) for wedge filling. The criticalbehaviour differs from the Ising universality class and is characterized by strong anisotropicfluctuations. We present evidence that the transition in large double wedges can be ofsecond order although there is a first order wetting transition on a planar substrate.

Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields.

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4</=L</=320, 30</=L(y)</=1000), in an attempt to clarify finite size effects on the wedge filling transition in this "double-wedge" geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T<T(f)(H(s)), however, this interface is bound either to the wedge where the two surfaces with field -H(s) meet (then the total magnetization m of the system is positive) or to the opposite wedge (then m<0). The distance l(0) of the interface midpoint from the wedges is studied as T-->T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.

Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling

Using Monte Carlo simulations and finite-size scaling methods we study "wetting" in Ising systems in a LxLxL(y) pore with quadratic cross section. Antisymmetric surface fields H(s) act on the free LxL(y) surfaces of the opposing wedges, and periodic boundary conditions are applied along the y direction. In the limit L--> infinity, L(y)/L(3)=const, the system exhibits a new type of phase transition, which is the analog of the "filling transition" that occurs in a single wedge. It is characterized by critical exponents alpha=3/4, beta=0, and gamma=5/4 for the specific heat, order parameter, and susceptibility, respectively.

Interplay between wetting and miscibility in thin binary polymer films

Abstract We study the interplay between wetting and miscibility of a symmetric AB polymer mixture via Monte Carlo simulations and numerical self-consistent field calculations. The crossover between capillary condensation in films with symmetric surface fields and interface localization/delocalization transition in films with antisymmetric boundaries is studied. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually; however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. We study the dependence of the phase diagram on the film thickness Δ for antisymmetric surface fields. Upon decreasing the film thickness the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness Δ tri , there remains only a single critical point at symmetric composition. This corresponds to a second order interface localization/delocalization transition. At Δ tri tricritical behaviour is found and the rich crossover behaviour is investigated by Monte Carlo simulations.

Phase diagram of polymer blends in confined geometry

Abstract Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding smei-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surfaces fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. Only below a triple point there is a single two phase coexistence region. The crossover between these qualitatively different limiting behaviors occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. The dependence of the phase behavior for antisymmetric boundaries is studied as a function of the film thickness and the strength of the surface interactions. Upon reducing the film thickness or decreasing the strength of the surface interactions we can change the order of the interface localization/delocalization transition from first to second. The role of fluctuations is explored via Monte Carlo simulations of a coarse grained lattice model. Close to the (prewetting) critical points we observe 2D Ising critical behavior. At lower temperatures capillary waves of the AB interface lead to a pronounced dependence of the effective interface potential on the lateral system size.

PHASE EQUILIBRIA IN THIN POLYMER FILMS

Within self-consistent field theory and Monte Carlo simulations the phase behavior of a symmetrical binary AB polymer blend confined into a thin film is studied. The film surfaces interact with the monomers via short ranged potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. Only below a triple point there is a single two-phase coexistence region. The crossover between these qualitatively different limiting behaviors occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. The dependence of the phase behavior for antisymmetric boundaries is studied as a function of the film thickness and the strength of the surface interactions. Upon reducing the film thickness or decreasing the strength of the surface interactions we can change the order of the interface localization/delocalization transition from first to second. The role of fluctuations is explored via Monte Carlo simulations of a coarse grained lattice model. Close to the (prewetting) critical points we observe 2D Ising critical behavior. Also, there is a rich crossover behavior between Ising critical, tricritical and mean field behavior. At lower temperatures capillary waves of the AB interface lead to a pronounced dependence of the effective interface potential on the lateral system size.