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

Molecular weight effects on interfacial properties of linear and ring polymer melts: A molecular dynamics study

Using molecular dynamics simulations, we study and compare the pressure, P, and the surface tension, γ, of linear chains and of ring polymers at the hard walls confining both melts into a slit. We examine the dependence of P and γ on the length (i.e., molecular weight) N of the macromolecules. For linear chains, we find that both pressure and surface tension are inversely proportional to the chain length, P(N)-P(N→∞)∝N^-1,γ(N)-γ(N→∞)∝N^-1, irrespective of whether the confining planes attract or repel the monomers. In contrast, for melts comprised of cyclic (ring) polymers, neither the pressure nor the surface tension is found to depend on molecular weight N for both kinds of wall-monomer interactions. While other structural properties as, e.g., the probability distributions of trains and loops at impenetrable walls appear quantitatively indistinguishable, we observe an amazing dissimilarity in the probability to find a chain end or a tagged monomer of a ring at a given distance from the wall in both kinds of polymeric melts. In particular, we demonstrate that the conformational equivalence of linear chains in a confined melt to a single chain under conditions of critical adsorption to a planar surface, established two decades ago, does also hold for ring polymers in a melt of linear chains. This analogy does not hold, however, for linear and ring chains in a confined melt of ring chains.

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.

Scaling properties of fluid adsorption near the base of a cylinder

We consider the adsorption of fluid at the foot of a cylinder that protrudes from a flat substrate made of the same material. Provided the contact angle θ is small enough, a drop of liquid condenses near the base, the size of which can be determined using simple macroscopic arguments. The adsorption in this geometry shows scaling behavior related to a number of different interfacial phase transitions and, for systems with short-ranged forces, shows a remarkable property; for small θ, the height of the drop (measured from the base) and the width (measured from the cylinder axis) are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films (at planar walls). The only difference is that the bulk correlation length is replaced by the radius of the cylinder. By taking into account the correct singular behavior of the line tension we show that this geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.

Direct calculation of interfacial tensions from computer simulation: results for freely jointed tangent hard sphere chains

We develop a methodology for the calculation of surface free energies based on the probability distribution of a wandering interface. Using a simple extension of the NpT sampling, we allow the interface area to randomly probe the available space and evaluate the surface free energy from histogram analysis and the corresponding average. The method is suitable for studying systems with either continuous or discontinuous potentials, as it does not require explicit evaluation of the virial. The proposed algorithm is compared with known results for the surface tension of Lennard-Jones and square well fluids, as well as for the interface tension of a bead-spring polymer model, and good agreement is found. We also calculate the interfacial tensions of freely jointed tangent hard sphere chains on athermal walls for a wide range of chain lengths and densities. The results are compared with three different theoretical approaches: scaled particle theory (SPT), Yu-Wu density functional theory, and an analytical approximation based on the latter approach. Whereas SPT only yields qualitative results, the last two approaches are found to yield very good agreement with simulations.