Morphology diagrams forA₂Bcopolymer melts: real-space self-consistent field theory

Abstract

The standard Gaussian model for block copolymermelts M W Matsen -Stability of the fcc structure in block copolymer systems Makiko Nonomura -SCFT simulation and SANS study on spatial distribution of solvents in microphase separation induced by a differentiating non-solvent in a semi-dilute solution of an ultra-high-molecular-weight block copolymer K Ando, T Yamanaka, S Okamoto et al. Abstract. Morphology diagrams for A2B copolymer melts are constructed using real-space self-consistent field theory (SCFT). In particular, the effect of architectural asymmetry on the morphology diagram is studied. It is shown that asymmetry in the lengths of A arms in the A2B copolymer melts aids in the microphase separation. As a result, the disorder-order transition boundaries for the A2B copolymer melts are shown to shift downward in terms of χN, χ and N being the Flory's chi parameter and the total number of the Kuhn segments,respectively, in comparison with the A2B copolymers containing symmetric A arms. Furthermore, perforated lamellar (PL) and a micelle-like (M) microphase segregated morphologies are found to compete with the classical morphologies namely, lamellar, cylinders, spheres and gyroid. The PL morphology is found to be stable for A2B copolymers containing asymmetric A arms and M is found to be metastable for the parameter range explored in this work. IntroductionMicrophase separation in block copolymer melts [1,2,3,4,5,6,7] has motivated the scientific community over the last couple of decades. Delicate balance[3] of chain conformational entropy and repulsive interaction energy between unlike monomers allows block copolymers to readily self-assemble into a number of ordered morphologies. Typical morphologies [3,8,9] include lamellar, cylinder, sphere, gyroid and Fddd network phases, which have been proven to be equilibrium states.Experimentally, the balance of the energy and entropy can be tuned by a number of molecular characteristics such as molecular weight [3], chain architecture [10,11], conformational asymmetry [12,13], polydispersity [14,15,16,17,18] and temperature. A number of studies [1,2,3,4,5,6,7] have been done to elucidate the effects of molecular weight, polydispersity, conformational asymmetry and temperature on the mircophase separation in linear di-block copolymer melts. However, the effects of chain architecture are not that well established. On the computational side, this is primarily due to a large parameter space for the simulations and resulting large number of morphologies, which need to be compared in terms of their free-energy

Effect of Macromolecular Architecture on the Morphology of Polystyrene–Polyisoprene Block Copolymers

“…30 Quantitative comparison of our experimental results to Figure 2 in ref 42 and Figure 5 in ref 32 shows discrepancies. A similar real-space SCFT study 33 for conformationally symmetric nonlinear block copolymers shows the same. In particular, for an estimated value of χN = 54 for the PSPI 2 molecules studied by us, all of these studies predict a lamellar morphology (even for Φ PS = 74%), while experimentally, a gyroid morphology is found.…”

“…For a reduced value of χN = 30, used in our SCFT calculations, an excellent agreement with these studies is observed, and the sample is found to be close to the cylinder−gyroid boundary. Similarly, the PS 2 PI sample at χN = 30 and Φ PS = 70% is predicted 32,33,42 to be close to the sphere−cylinder boundary. Our SCFT calculations incorporating conformational asymmetry as presented in Figure 11 show elongated spheres, which confirm qualitative agreement with these previous studies.…”

“…Note that the effects of conformational asymmetry have been largely ignored in the previous SCFT studies − , on nonlinear block copolymers. It is very well-known that conformational asymmetry − plays a significant role in affecting the disorder–order and order–order transition boundaries in the case of linear block copolymer melts.…”

“…The theory has been used recently to construct morphology diagrams for different kinds of miktoarm star copolymers. 32,33 Here, we only present a brief description of the numerical algorithms and relevant details related to comparison of the theory with the experiments.…”

“…Numerical self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. , In particular, the SCFT for the branched block copolymer melts is detailed in refs and . The theory has been used recently to construct morphology diagrams for different kinds of miktoarm star copolymers. , Here, we only present a brief description of the numerical algorithms and relevant details related to comparison of the theory with the experiments.…”