We investigate the phase behavior of athermal polymer-nanoparticle blends near a substrate. We apply a recent fluids density functional theory of Tripathi and Chapman to a simple model of the blend as a mixture of hard spheres and freely jointed hard chains, near a hard wall. We find that there is a first-order phase transition in which the nanoparticles expel the polymer from the surface to form a monolayer. The nanoparticle transition density depends on the length of the polymer and the overall bulk density of the system. The effect is due both to packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy. The simplicity of the system allows us to understand the so-called "entropic-push" observed in experiments.

We investigate the role of surface roughness on solvation forces and solvation free energies. Roughness is introduced by dividing a surface into an array of square tiles that are then randomly displaced in the direction perpendicular to the wall. The integrated wall strength of these tiled surfaces is independent of the surface roughness and hence this class of rough walls is ideally suited for isolating roughness effects. We use grand canonical Monte Carlo simulations of a Lennard-Jones fluid confined in a slit pore with rough walls to generate the solvation interactions as a function of roughness, tile size, and surface area. The simulation data are compared to a simple superposition approximation of smooth wall solvation interactions (obtained from simulation or density functional theory), based on a distribution of wall separations. We find that this approximation provides a surprisingly accurate route to the solvation interaction of rough surfaces. In general, increased roughness leads to a reduction of oscillations in the solvation forces and surface free energies. However, nonmonotonic behavior of the oscillation amplitude with roughness can be observed for finite surfaces. The washing out of the oscillations found for large surface roughness produces a solvation force that exhibits a broad repulsive peak with separation. The broad repulsion is a consequence of the resistance to squeezing out fluid from the smallest gaps between two opposing rough surfaces. It is as much a reflection of packing effects as are the solvation oscillations for perfectly smooth pores. In addition, we present results for patterned and undulating surfaces produced by an analogous modification of the one-body external field for smooth walls. Finally, we discuss the implications of our results for a number of experimental systems including self-assembled monolayers, microporous materials, protein solutions, and DNA crystals.

This paper summarizes our efforts to develop fast algorithms for density functional theory (DFT) calculations of inhomogeneous fluids. Our goal is to apply DFTs to a variety of problems in nanotechnology and biology. To this end we have developed DFT codes to treat both atomic fluid models and polymeric fluids. We have developed both three-dimensional real space and Fourier space algorithms. The former rely on a matrix-based Newton’s method while the latter couple fast Fourier transforms with a matrix-free Newton’s method. Efficient computation of phase diagrams and investigation of multiple solutions is facilitated with phase transition tracking algorithms and arclength continuation algorithms. We have explored the performance that can be obtained by application of massively parallel computing, and have begun application of the codes to a variety of two-and three-dimensional systems. In this paper, we summarize our algorithm development work as well as briefly discuss a few applications including adsorption and transport in ion channel proteins, capillary condensation in disordered porous media and confinement effects in a diblock copolymer fluid.

We use polymer reference interaction site model ͑PRISM͒-based density functional theory ͑DFT͒ to study the structures and morphologies of block copolymer thin films. The polymers are modeled as freely jointed chains, allowing numerical solution of the nonlinear DFT equations. The use of PRISM with DFT allows the inclusion of compressibility and local packing effects due to the finite size of the monomers. We also employ a pseudo-arclength continuation algorithm to locate phase transitions and new morphologies. We study symmetric diblock copolymers confined between two parallel surfaces which both attract one component of the diblock, for two different values of AB segregation strength and for various surface interactions. The predicted equilibrium morphologies are in good qualitative agreement with previous self-consistent field calculations and are consistent with experiment. We are able to resolve the detailed packing structure near the surfaces. We find that packing effects enhance the stability of the perpendicular morphologies.

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