Primitive chain network model for block copolymers

A coarse-grained molecular simulation for block copolymers in the entangled state is proposed as an extension of the primitive chain network model. Polymers are represented as a sequence of segments between consecutive entanglements, the latter being modeled as sliplinks with other chains. Each sliplink connects two chains only, i.e., entanglements are taken as ‘binary’. The resulting 3D structure is a network of primitive chains, which makes our model different from other sliplink single-chain models, where the link to other chains is ‘virtual’. The 3D nature of our simulation makes it similar to, though considerably more coarse grained than, conventional molecular dynamics simulations. Because of the 3D space assignment of the polymers, monomeric density fields can be defined, and interactions due to different chemistry of the monomers can be accounted for, similarly to density field calculations. Polymer motion is described both by the 3D motion of sliplinks, and by the 1D transport of monomers along the primitive chain, while network topological rearrangement occurs due to chain-end hooking and unhooking processes. Each kinetic equation accounts for elastic forces along the chains, field forces arising from density gradients, and thermal random forces. In this paper, the primitive chain network model was modified (i) in the procedure of network rearrangement to account for the different chemistries in the copolymer, and (ii) in some details of the kinetic equations whenever the boundary between blocks is involved. We report results for diblock copolymers where for simplicity all relevant properties of the two monomers are the same, except for the interactions. Simulations reasonably reproduce the micro-phase formation process and the phase diagram for well entangled copolymers with a low calculation cost.