This journal is © The Royal Society of Chemistry 2017 Soft Matter Cite this: DOI: 10.1039/c7sm00164a Field-theoretic simulations of random copolymers with structural rigidity† Shifan Mao,‡ a Quinn MacPherson,‡ b Jian Qin a and Andrew J. Spakowitz * acdef Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales com- parable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density–density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density–density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies. Introduction Statistical random copolymers are multiblock copolymers consis- ting of monomers with fixed but random chemical identities. The microphase segregation of random copolymers is important in a variety of applications such as polymer electrolyte membranes, 1–3 styrene-butadiene rubbers, 4 surface modification, 5,6 and polymer mixing. 7 Recent studies show that incorporating sequence stochas- ticity can enhance stability of assembled microstructures. 8–12 The self-assembly of random copolymers is also relevant in a range of biological phenomena, including protein folding and chromatin organization. 13–17 Most previous and current studies of block copolymers are based on mean-field formulations of flexible polymers. 18–23 When the polymer chains are flexible such that phase-segregation domains correspond to many Kuhn steps, a mean-field treatment based on random-walk statistics is a reasonable approximation. However, this approach suffers from several shortcomings for understanding the phase beha- vior of random copolymers. Phase segregation of random copolymers often occurs on length scales comparable to a monomer unit. Therefore, struc- tural rigidity of the monomer segments significantly influences the local microstructure. With small length scales of microphase segregation, concentration fluctuations become significant near the order–disorder transition (ODT), 24,25 rendering the mean-field approximation inaccurate. Due to chemical-sequence random- ness, the local chemical environment surrounding a random copolymer chain has more variation than a polymer chain in a regular block copolymer melt. As a result, the free-energy landscape for microphase segregation from the melt phase is very rugged, resulting in frustration that can dramatically influence the phase behavior. In studying the thermodynamics of random copolymers, incorporating both chain rigidity and density fluctuations is critical. Previous studies considering chain rigidity effects are limited to systems of homopolymers and diblock copolymers using mean-field approximations. For example, wormlike chains with Maier–Saupe type interactions are used to study transitions to a nematic liquid-crystalline phase. 26–28 Semiflexible diblock copolymers are studied based on the wormlike chain model, a Department of Chemical Engineering, Stanford University, Stanford, CA, 94305, USA. E-mail: ajspakow@stanford.edu b Department of Physics, Stanford University, Stanford, CA, 94305, USA c Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA d Department of Materials Science and Engineering, Stanford University, Stanford, CA, 94305, USA e Biophysics Program, Stanford University, Stanford, CA, 94305, USA f Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA † Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sm00164a ‡ These two authors contributed equally to this work. Received 22nd January 2017, Accepted 10th March 2017 DOI: 10.1039/c7sm00164a rsc.li/soft-matter-journal Soft Matter PAPER Published on 13 March 2017. Downloaded by Stanford University on 24/03/2017 19:43:30. View Article Online View Journal