An analysis of the cylindical brush of an isolated comb copolymer molecule consisting of a semiflexible backbone and flexible side chains is presented. Using the Alexander-de Gennes approximation, we calculate the free energy of both straight and bent cylindrical brush and the brush persistence length λ, and show that λ scales as a function of the side chain length M as λ ∝ M 2. The discrepancy between the asymptotic scaling behavior and recent computer simulation results is also discussed.

We report the results of a Monte Carlo simulation study of isolated comb copolymer cylindrical brushes. The conformational characteristics of molecules consisting of a flexible backbone densely grafted with side chains strongly depend on the rigidity of the side chains, which is exemplified by using both fully flexible and totally rigid side chains. The short length scale fluctuations of the backbone are not affected by the presence of rigid rod side chains, whereas flexible side chains induce local stretching of the backbone. However, at the large length scale, the persistence length λ of the cylindrical brush is considerably larger for rigid rod side chains than for flexible side chains. Moreover, for rigid side chains the ratio between the persistence length λ and the diameter D of the brush increases approximately linearly as a function of the rod length L, thus supporting the possibility of lyotropic behavior. In contrast to this, in the case of flexible side chains, λ/D is approximately independent of the side chain length M.

A quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength B (Mikhailov 2002 Nucl. Fusion 42 L23) has been obtained by an integrated physics optimization comprising MHD and neoclassical theory. For a configuration with six periods and aspect ratio approximately 12, a main result is the attainability of an essentially MHD-stable high-β (β ≈ 0.085) plasma with low neoclassical transport, approximately vanishing bootstrap current in the long-mean-free-path regime and excellent α-particle confinement.

Self-organized structure formation in the melt of hairy-rod polymers is analyzed theoretically. It is shown that the interplay between unfavorable repulsive rod-coil interactions and stretching of the side chains is responsible for the appearance of three different microphases: one lamellar and two hexagonal. The first-order phase transitions between these are considered in detail. If the side chains are long enough for the elastic stretching free energy to dominate the repulsive interactions, hexagonally ordered domains of hairy-rod cylindrical brushes are formed. The lamellar phase is shown to be stable for shorter side chains and occupies an important part of the phase diagram. In the intermediate side chain length regime another hexagonally ordered structure appears, characterized by cylindrical micelles with an elongated cross section, containing several hairy-rod polymers.