Quenched and annealed disorder in randomly grafted copolymer melts.

A model of randomly grafted AB copolymer melts is constructed in which flexible B polymer grafts are statistically attached at three possible sites along flexible A polymer backbones. An incompressible melt of such molecules is examined theoretically at equilibrium for two situations: (1) the grafting is irreversible so that the chemical disorder associated with the statistical placement of the grafts is quenched, and (2) the grafting is reversible so that the disorder is annealed. Because of the simplicity of the model, we are able to exactly carry out the two types of disorder averages, yielding effective field theories for the quenched and annealed cases. These field theories are investigated in the mean-field approximation, but without further invoking the usual weak-amplitude random phase approximation. Our results clarify the conditions for which quenched and annealed averages can be interchanged.

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