Practical compatibility between self-consistent field theory and dissipative particle dynamics

Abstract

Self-consistent field theory (SCFT) and dissipative particle dynamics (DPD) simulations for the predicted microphase-separated structures of block copolymers (BCPs) are effective methods to reproduce behaviors at a scale larger than the Kuhn length. For linear chains, polymer-level correspondence at larger than the Kuhn length scale is maintained by their definition. For nonlinear polymer architectures, practical compatibility is expected to be governed by their natures originating from their architectures. Although the relation χ ≅ 0.306 Δa between the Flory–Huggins interaction parameter (χ) and segregation strength (Δa) for the mean structure at equilibrium is empirically accepted with a qualitative agreement for the large limit of polymerization-degree N, we need to verify the practicality of this relation in a chain of finite sizes and/or non-linear architectures for the recent advances of topology-controlled synthesis technology. We clarified the difference between the DPD and the conventional SCFT and the required improvements for a problem of the domain spacing D of the lamellar structures of symmetric AB-type BCPs of branched/star chains. For the four-arm star structure with H-shaped bonded star, SCFT should consider the particle-based H-shaped chains like DPD. Although the D values of SCFT agreed with that of DPD at the linear melts, the H-shaped bonded star melt presented a small discrepancy in the values of D; the discrepancy significantly decreased from the conventional SCFT for star chains with the point junction without considering H-shape. These understandings allow the prediction of D for BCPs synthesized with arbitrary topologies.