Entanglements in Lamellar Phases of Diblock Copolymers

Using molecular dynamics (MD) simulations in conjunction with topological analysis algorithms, we investigate the changes, if any, in entanglement lengths of flexible polymers in ordered lamellar phases of diblock copolymers. Our analysis reveals a reduction in the average entanglement spacing of the polymers with increasing degree of segregation between the blocks. Furthermore, the results of the topological analysis algorithms indicate an inhomogeneous distribution of entanglement junctions arising from the segregated morphology of the block copolymer. To understand such trends, we invoke the packing arguments proposed by Kavassalis and Noolandi in combination with the framework of polymer self-consistent-field theory (SCFT) and Monte Carlo simulations. Such an analysis reveals qualitatively similar characteristics as our MD results for both the average entanglement spacing and the inhomogeneities in entanglements. Together, our results provide evidence for the changes in entanglement features arising from compositional inhomogeneities and suggest that the ideas embodied in packing arguments may provide a simple means to semiquantitatively characterize such modifications.