Using a real space implementation of the self-consistent field theory for the polymeric system, we explore microphases of ABC linear triblock copolymers. For the sake of numerical tractability, the calculation is carried out in a two-dimensional (2D) space. Seven microphases are found to be stable for the ABC triblock copolymer in 2D, which include lamellae, hexagonal lattice, core-shell hexagonal lattice, tetragonal lattice, lamellae with beads inside, lamellae with beads at the interface, and hexagonal phase with beads at the interface. By systematically varying the composition, triangle phase diagrams are constructed for four classes of typical triblock polymers in terms of the relative strengths of the interaction energies between different species. In general, when both volume fractions and interaction energies of the three species are comparable, lamellar phases are found to be the most stable. While one of the volume fractions is large, core-shell hexagonal or tetragonal phases can be formed, depending on which of the blocks dominates. Furthermore, more complex morphologies, such as lamellae with beads inside, lamellae with beads at the interface, and hexagonal phases with beads at the interface compete for stability with lamellae structures, as the interaction energies between distinct blocks become asymmetric. Our study provides guidance for the design of microstructures in complex block copolymers.

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Microphases and triangle phase diagrams of ABC star triblock copolymers are investigated on the basis of a real-space implementation of the self-consistent field theory (SCFT) for polymers. For the sake of numerical tractability, the calculations are carried out in two dimensions (2D). Nine stable microphases are uncovered, including hexagonal lattice, core−shell hexagonal lattice, lamellae, and lamellae with beads at the interface as well as a variety of complex morphologies that are absent in linear ABC triblocks, such as a “three-color” hexagonal honeycomb phase, knitting pattern, octagon−octagon−tetragon phase, lamellar phase with alternating beads, and decagon−hexagon−tetragon phase. We have found that when the volume fractions of the three species are comparable the star architecture of the polymer chain is a strong topological constraint that regulates the geometry of the microphases formed. However, when at least one of the volume fractions of the three species is low, the influence of the star architecture on the morphology is not significant. Our calculations reasonably agree with previous theoretical and experimental results and can be used to guide the design of novel microstructures involving star triblock copolymers.

A generic Fourier-space approach to solve the self-consistent field theory of block copolymers is developed. This approach is based on the fact that, for any computational box with periodic boundary conditions, all spatially varying functions are spanned by the Fourier series determined by the size and shape of the box. The method reproduces all known diblock copolymer phases. The application of this method to a model "frustrated" triblock copolymer leads to a phase diagram with a number of new phases. Furthermore, the capability of the method to reproduce experimentally observed structures is demonstrated using the knitting pattern of triblock copolymers.

The kinetics and chain length distributions occurring in living free-radical polymerizations are simulated using a hybrid Monte Carlo algorithm. The new algorithm is much faster than the conventional one because the activation/deactivation exchange reactions, which are CPU intensive, are treated by a biased-sampling method with an analytical expression for the exchange equilibrium, while the reactions of chain propagation, irreversible chain termination, etc. are treated by exact stochastic Monte Carlo simulation. Two models of living radical polymerizations, i.e., the polymerization initiated by alkoxyamines and the nitroxide radical, 2,2,6,6-tetramethyl-1-piperidinyloxy, mediated radical polymerization, are simulated to study the effects of experimental variables, such as the concentration ratio of stable free radicals to initiators, initiation rate constants, etc., on the kinetics and molecular weight distributions. A comparison between simulated and analytical results in the literature is made. Taking thermal initiation into consideration, the algorithm reproduces the experimental results very well. Therefore, its feasibility and usefulness in studying living free-radical polymerization are demonstrated.