Application of a density functional theory

Stefan Sokolowski

Department for the Modeling of Physico-Chemical Processes, Maria Curie-Sklodowska University, 20-031 Lublin, Poland

A microscopic density functional theory is used to investigate thermodynamic and structural properties of nonuniform chain-particle fluids. Two systems are considered: (a) a binary mixture of mixture of polymers, built of freely jointed tangent hard spheres, and (b) adsorption of short chains built of segments interacting via attractive-repulsive forces on an attractive wall. In the first case we study how 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 (Δρ3), where Δρ 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. In the case of adsorption of a single-component fluid containing chain particles we analyze the structure of the adsorbed fluid and investigate how the wetting transition changes with the change of the chain length and with relative strength of the fluid-solid interaction. Our calculations have indicated that end segments adsorb preferentially in the first adsorbed layer whereas the concentration of the middle segments is enhanced in the second layer. We have observed 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.