Self-Assembly of Asymmetrically Interacting ABC Star Triblock Copolymer Melts

Abstract

The phase behavior of asymmetrically interacting ABC star triblock copolymer melts is investigated by the self-consistent field theory (SCFT). Motivated by the experimental systems, in this study, we focus on the systems in which the Flory-Huggins interaction parameters satisfy χAC > χ BC ≈ χAB. Using various initialization strategies, a large number of periodic structures have been obtained in our calculations. A fourth-order pseudospectral algorithm combined with Anderson mixing method is used to compute the free energy of candidate structures carefully. The stability has been analyzed in detail by splitting the free energy into internal and entropic parts. A complete and complex triangular phase diagram is presented for a model with χAC > χBC = χAB in which 15 ordered phases, including two- and three-dimensional structures, have been predicted to be stable from the SCFT calculations. Generally speaking, with the asymmetrical interactions, the hierarchical structures tend to be formed near the B-rich corner of the triangular phase diagram. This work broadens the previous theoretical results from equal interaction systems to unequal interaction systems. The predicted phase behavior is in good agreement with experimental observations and previous theoretical results.

On the morphological behavior of ABC miktoarm stars containing poly(cis 1,4‐isoprene), poly(styrene), and poly(2‐vinylpyridine)

“…The free energies of the resulting structures were compared to determine a morphology with the lowest free energy. ABC terpolymers have been studied extensively using the SCFT . A brief description of the SCFT model and the parameters used for ISV‐ x is presented below.…”

“…These terpolymers have been synthesized and characterized since 2000 to understand the influence of the composition of the components on the morphology . A complete triangular phase diagram was constructed for ISV by Yushu et al based on their numerous studies, and, in general, a number of theoretical studies focused on different aspects of the microphase separation in ABC miktoarms . By changing the length of one of the arms, typically V, while keeping the other two arms (I and S) fixed, represented as ISV‐ x , where x is the volume ratio of V over I, it has been shown that, as x increases from 0.2 to 0.4 to 0.7 to 1.2 to 1.9 to 3 and then to 10, the morphology transitions from spheres sandwiched by lamellae to a [12.6.4] tiling, a [6.6.6], a [8.8.4], a [12.6.4] tiling, an alternating lamellae (ALT.…”

“…LAM) and, finally, to cylinders in lamellae, respectively . Modeling attempts have been made to simulate these morphological transitions . Assuming symmetric interactions between the three pairs, a detailed triangular phase diagram has been constructed based on the self‐consistent field theory (SCFT) calculations .…”

“…However, it was noted that there were discrepancies between the simulated and experimentally observed morphologies, which were attributed mainly to the asymmetric interactions between the three different pairs. In other studies, two interaction parameters (χ IS and χ SV ) are assumed to be equal but less than χ IV , that is, χ IS ≈ χ SV < χ IV . Using this simplified model, it was possible to mimic some ISV‐ x morphologies observed in the experiments.…”

A finite element method of the self-consistent field theory on general curved surfaces

“…Theoretically, the self-consistent field theory (SCFT) [10] proposes a successful framework in the study of the self-assembling of block copolymers. It has predicted a variety of ordered bulk phases that have been observed in experiments, e.g., lamella, hexagonal cylinder, sphere and gyroid phases of diblock copolymers [11], and many intricate ordered phases of triblock copolymers [12]. Mathematically, the SCFT model is a very complicated variational problem, possessing many unsatisfactory features, such as saddle-point, nonlinearity, multi-solutions, and multi-parameters.…”