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A lattice model for a symmetrical copolymer "bottle brush" molecule, wheretwo types (A,B) of flexible side chains are grafted with one chain end to arigid backbone, is studied by a variant of the pruned-enriched Rosenbluthmethod (PERM), allowing for simultaneous growth of all side chains in the MonteCarlo sampling. Choosing repulsive binary interactions between unlike monomersand varying the solvent quality, it is found that phase separation into an$A$-rich part of the cylindrical molecule and a $B$-rich part can occur onlylocally. Long range order (in the direction of the backbone) does not occur,and hence the transition from the randomly mixed state of the bottle brush tothe phase separated structure is strongly rounded, in contrast to correspondingmean field predictions. This lack of a phase transition can be understood froman analogy with spin models in one space dimension. We predict that the rangeof microphase separation along the bottle brush backbone can be controlled onthe nanoscale by varying the solvent quality.Comment: 5 pages, 7 figures. Edited for typo

Intramolecular phase separation of copolymer “bottle brushes”: No sharp phase transition but a tunable length scale