The massive field theory approach in fixed space dimensions d<4 is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls, and for the mixed case of one inert and one repulsive wall. The well-known correspondence between the field theoretical phi4 O(n) -vector model in the limit n-->0 and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. In order to make the theory UV finite in renormalization-group sense in 3

Based on a dipole model for the mutual magnetic interactions among the magnetizable micro-particles in magneto-sensitive elastomers we develop a mean field approach to describe the arrangement of these particles into elongated micro-structures. If these micro-structures are oriented parallel to an external magnetic field the present approach provides an efficient calculation of the behavior of such samples, which is a result of the interplay between micro-structure and shape effects. Accordingly, we are able to draw comprehensive phase diagrams for the resultant deformation and predict for very oblate samples a discontinuous shape change in the presence of a homogeneous external field.

We present a numerical self-consistent field (SCF) method which describes freely jointed chains of spherical monomers applied to densely grafted polymer brushes. We discuss both the Flory-Huggins model and the Carnahan-Starling equation of state and show the latter being preferable within our model at polymer volume fractions above 10%. We compare the results of our numerical method with data from molecular dynamics (MD) simulations [G.-L. He, H. Merlitz, J.-U. Sommer, and C.-X. Wu, Macromolecules 40, 6721 (2007)] and analytical SCF calculations [P. M. Biesheuvel, W. M. de Vos, and V. M. Amoskov, Macromolecules 41, 6254 (2008)] and obtain close agreement between the density profiles up to high grafting densities. In contrast to prior numerical and analytical studies of densely grafted polymer brushes our method provides detailed information about chain configurations including fluctuation, depletion, and packing effects. Using our model we could study the recently discovered instability of densely grafted polymer brushes with respect to slight variations of individual chain lengths, driven by fluctuation effects [H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. Sommer, Macromolecules 41, 5070 (2008)]. The obtained results are in very close agreement with corresponding MD simulations.

Using a numerical quasi off-lattice self-consistent field method which describes heterogeneous chains of spherical monomers we study the case of a densely grafted polymer brush with a fraction of free chain ends being replaced by a modified end-group differing in size and solvent selectivity. We can confirm the observation from molecular dynamics simulations that upon changing the solvent conditions, a switching in location of end-groups which are bigger than monomers from a state "exposed" to the solvent (on the top of the brush) to a "hidden" state (inside the brush) takes place. Our numerical method allows a detailed study of the switching effect as a function of the relevant parameters, such as grafting density, chain length, size of end-groups and their volume fraction. We find that the switching effect is enhanced for long chains, low fractions of modified chains, and big end-groups. We consider the case of low fraction of modified chains in more detail using a test chain method. Here, we explore the optimal grafting density as a function of the size of the end-groups, where the switching is most sensitive. These values can be in the experimental range for end-groups which are at least 3-4 times bigger than the monomers. The end-groups can be realized by attaching nano-particles to the last monomer of a brush-chain.