Self-consistent field theory for loop-containing polymers: A general algorithm for path-determination

Abstract

An algorithm was developed for self-consistent field theory (SCFT) simulations of loop-containing polymers (LCPs), where the total number of independent loops (fundamental cycles in the polymer structure) is characterized by the “cycle rank.” Although various multi-ring and cage-like polymers have been reported, there is no explicit SCFT scheme for LCPs with multiple loops. An LCP was cut to open its fundamental cycles to form a pseudo-tree-like polymer. Conventional SCFT calculations for pseudo-tree-like polymers require extra spatial constraints on the pseudo-free endpoints generated by opening the fundamental cycle, which increases the computational cost. A reduction in the computational cost was observed, and the algorithm was applied to microphase-separated structures of small LCPs.