Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers

摘要

This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behaviornof AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is thencombination of the mean-field approach together with a statistical weight that describes the configurationalnproperties of a polymer chain. In recent years, this approach has been extensively used for structural predictionnof block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain modelnhas played an important role in the description of polymer systems, covering the semiflexible-to-rod crossovernof the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties tondescribe. Although the idea of developing a self-consistent field theory for wormlike chains could be tracednback to early development in polymer physics, the solution of such a theory has been limited due to technicalndifficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation ofnthe phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paperndescribes a computational algorithm that combines a number of numerical tricks, which can be used for suchna calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain systemnand reported by us, where the ratio between the total length and the persistence length of a constituent polymer isnsuggested as another tuning parameter for the microphase-separated structures; all detailed technical issues arencarefully addressed in the current paper.