In this paper we use the polymer adsorption theory of Scheutjens and Fleer to describe polymer brushes at spherical and cylindrical surfaces that are immersed in a low molecular weight solvent. We analyze the volume fraction profiles of such brushes, focusing our attention on spherical brushes in athermal solvents. These are shown to generally consist of two parts: a power law-like part and a part that is consistent with a parabolic potential energy profile of the polymer segments. Depending on the curvature of the surface, one of these two parts is more important, or may even dominate completely. We especially consider the distribution of the free end segments and the possible existence of a "dead zone" for these segments. Such a dead zone is actually found and is seen to follow a scaling law in the case of large curvatures. Furthermore, the effect of diminishing the solvent quality is considered for both the total volume fraction profile and the distribution of the end segments.

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Self-consistent-field (SCF) calculations are presented of a planar grafted polymer layer that interacts either with free polymer chains or with another grafted layer. Three different systems are studied. The first is a grafted polymer layer immersed in a polymer solution. The interaction between grafted and free polymer can significantly influence the grafted polymer volume fraction profile. For grafted chains that are strongly stretched the lattice calculations are compared with the theory of Zhulina, Borisov, and Brombacher (Macromolecules 1991, 24, 4679). Good agreement is found when the free chain length is far smaller than the grafted chain length. The scaling behavior of the penetration of free polymer into the grafted layer is also studied for this system. In the second type of system the interaction between two grafted layers in the absence of free polymer is considered. The lattice calculations agree well with the theory of Zhulina et al. In the third system free polymer is present between the interacting grafted layers. If this free polymer has a small chain length, its main effect on the interaction free energy is the compression of the free grafted layers, and only repulsion is found. However, for larger chain lengths a depletion attraction between the grafted layers appears.

We present Gibbs ensemble Monte Carlo simulations of monomer-solvent and polymer-solvent mixtures with soft interaction potentials, that are used in dissipative particle dynamics simulations. From the simulated phase behavior of the monomer-solvent mixtures one can derive an effective Flory-Huggins -parameter as a function of the particle interaction potential. We show that this -parameter agrees very well with the free energy difference between a monomer surrounded by solvent particles, and a solvent particle surrounded by solvent particles. We develop a new ''identity change'' Monte Carlo move to equilibrate the polymer-solvent mixtures. In this move a polymer chain from one box is exchanged with an equal number of solvent particles from the other box. At realistic densities this new move offers a large computational advantage over the convential insertion method for a polymer chain using a configurational bias Monte Carlo algorithm. The new algorithm is demonstrated for polymer-solvent mixtures with a chain length of up to 150 segments. Significant differences are found between the simulated polymer-solvent phase behavior and results predicted by mean-field theory. Finally, we fit a master-equation to the simulated binodal curves at different chain lengths. This function is used to make a quantitative comparison between the simulations and experimental data for the phase equilibrium of the polystyrene-methylcyclohexane system.

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