Macrophase and microphase separation in random comb copolymers

We introduce and analyze three models for comb copolymer melts that allow for randomness in the placement and number of teeth. In the first model the polymers are constructed using a two-parameter Markov process, which links dispersity in the number of teeth with correlations in their placement. In the other two models these two effects are separated so that the dispersity is allowed to vary while tooth-tooth correlations remain fixed. In one such model the tooth placement is uncorrelated, while in the second it is perfectly correlated. The behavior of these models is studied as a function of the dispersity in the number of teeth and the average number of teeth. The results pinpoint the factors that control micro- versus macrophase separation and thereby yield guidelines for controlling the phase behavior of comb copolymer melts.