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

Abstract

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

Ordering kinetics of a conserved binary mixture with a nematic liquid crystal component

“…The systems involving liquid crystals are investigated via simulation [47,53,31,45,11] and the phase diagram indicating where transitions between the nematic and isotropic phases of the liquid crystal occur is analyzed [47,53,40]. Recently, applications of models for similar systems include polymer-dispersed liquid crystals [44,1,34,48,19,21,22,39,29], diblock copolymers [32,46], and other cases of problems involving phase separation [5,27,33,38,6,41,42,61].…”

Self-assembly in rod/coil block copolymers: Degenerate behavior under nonconfinement

“…Thus, the ordered morphologies of the copolymers depend on two molecular parameters: f rod (the volume fraction of the rod block C) and χ AC N (the interaction between A and C components). The calculations are preformed in N L = 60 3 to N L = 80 3 lattices to make sure that the emergence of self-assembled structures is not constrained by system size. Figure 1 shows the phase diagram constructed by f rod versus χ AC N. In addition to micelles, centrosymmetric lamellae (CSLM), lamellae, perforated lamellae, strips and gyroid, noncentrosymmetric lamellae (NCSLM) and wavy lamellae are observed.…”

“…The self-assembly of coil/rod block copolymers has attracted special attention in recent years due to their rich mesoscopic structures and their tunable physical properties [1][2][3][4]. Various morphologies including lamellae, strips, cylinders, vesicles, perforated lamellae, arrowhead, wavy lamellae, zigzag lamellae, and so on have been observed, as summarized in several recent reviews [5][6][7].…”

The study of the structure factor of a wormlike chain in an orientational external field

“…21,40,[45][46][47][48] The first term in Eq. (2) represents the bending energy of the wormlike chain 44 and the second term is the external field which describes the interaction between particles in the system.…”