The free energy cost of confining a star polymer where f flexible polymer chains containing N monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance D apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens–Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with N, f and D, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.

We present a self-consistent field theoretical study of the microstructure of concave cylindrical brushes as a function of the cylinder radius, grafting density, grafted chain length, and the solvent quality. We show that the results for the radial monomer density profile and the distribution of the free ends are in good agreement with the corresponding molecular dynamics results. Part of the investigation is focused on the conformational behavior of a free macromolecule in a cylindrical brush. A central result is the observed non-monotonous variation of the size of a free chain in a brush-coated tube when the tube radius is systematically changed. An interpretation of this behavior which differs qualitatively from that of a polymer in cylindric confinement is suggested in terms of scaling theory and rationalized by considering the overlap between the free polymer and the grafted chains as a function of the tube radius.