Paweł Bryk

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.

Depletion potentials near geometrically structured substrates

Using the recently developed so-called White Bear version of Rosenfelds Fundamental Measure Theory we calculate the depletion potentials between a hard-sphere colloidal particle in a solvent of small hard spheres and simple models of geometrically structured substrates: a right-angled wedge or edge. In the wedge geometry, there is a strong attraction beyond the corresponding one near a planar wall that significantly influences the structure of colloidal suspensions in wedges. In accordance with an experimental study, for the edge geometry we find a free-energy barrier of the order of several kBT which repels a big colloidal particle from the edge.

Hard-sphere fluids in contact with curved substrates

The properties of a hard-sphere fluid in contact with hard-spherical and cylindrical walls are studied. Rosenfelds density functional theory (DFT) is applied to determine the density profile and surface tension gamma for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to gamma which is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution, we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of gamma.

Short chains at solid surfaces: Wetting transition from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the wetting transition changes with the change of the chain length and with the relative strength of the fluid-solid interaction. End segments adsorb preferentially in the first adsorbed layer whereas the concentration of the middle segments is enhanced in the second layer. We observe that the wetting temperature rescaled by the bulk critical temperature decreases with an increase of the chain length. For longer chains this temperature reaches a plateau. For the surface critical temperature an inverse effect is observed, i.e., the surface critical temperature increases with the chain length and then attains a plateau. These findings may serve as a quick estimate of the wetting and surface critical temperatures for fluids of longer chain lengths.

Wetting at curved substrates: Non-analytic behavior of interfacial properties

We argue that for complete wetting at a curved substrate (wall) the wall-fluid surface tension is non-analytic in Ri−1, the curvature of the wall, and that the density profile of the fluid near the wall acquires a contribution proportional to the gas-liquid surface tension ×Ri−1 plus higher-order contributions which are non-analytic in Ri−1. These predictions are confirmed by results of density functional calculations for the square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder where complete wetting by gas (drying) occurs. The implications of our results for the solvation of big solvophobic particles are discussed.

Density functional theory for inhomogeneous associating chain fluids

We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.

Capillary condensation of short-chain molecules

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.

Bulk and interfacial properties of binary polymer mixtures

A microscopic density functional theory is used to investigate a binary mixture of polymers, built of freely jointed tangent hard spheres. The difference in the chain length and in the segment diameter of polymers gives rise to a demixing transition. We evaluate the bulk fluid phase equilibria (binodal) and the limit of stability of a mixed state (spinodal) for selected systems, and analyze the decay of the critical packing fraction, critical mole fraction, and critical pressure with an increase of the chain length. The bulk results are subsequently used in the calculations of the density profiles across the fluid-fluid interface. The obtained profiles are smooth and do not exhibit any oscillations on the length scale of the segment diameter. Upon approaching the critical point the interfacial tension vanishes as (Deltarho)3, where Deltarho is the difference between bulk densities of one component in bulk phases rich and poor in that species. This indicates that the microscopic density functional theory applied here is of a mean-field type.

Depletion interaction of two spheres —Full density functional theory vs. morphometric results

Morphological thermodynamics is employed to calculate the depletion potential between two big hard spheres in a solvent of small spheres. Thereby, the potential is characterized solely by the geometric properties of the solvent-accessible surface of the two-sphere configuration in the depletion region. Comparison with explicit density functional theory calculations using accurate functionals of the fundamental measure type shows good agreement.