Field-theoretic simulations of random copolymers with structural rigidity

Abstract

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 comparable 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.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

“…There may also be promise in recently-reported meth-ods for using modular assembly 96 or automation 61,62,93 to realize sequence on larger macromonomer length scales. 97 Phase behavior is a function of and a sequence parameter ( = −1 is alternating, = 0 is random, → 1 is increasingly blocky), ranging from homogeneous (H), aligned mesophase separation (AM), and random mesophase separation (RM); these regions change with molecular stiffness. 97,98 Adapted from Mao, et al Soft Matter, 2017, 13, 2760-2772. https://doi.org/10.1039/C7SM00164A.…”

“…Related single-chain in mean field (SCMF) simulations have demonstrated the importance of addressing these limitations for copolymers, [121][122][123] for example showing that semiflexible random copolymers exhibit non-trivial phase behavior due to how molecular packing and monomer-level structure relate to monomer sequence (Figure 3a). 97,98,124 There is evidence that detailed models, that specifically resolve monomer length-scales, are indeed a crucial aspect for studying sequence-defined polymers. Particle-based computational models have demonstrated sequence-specific effects in compatibilization, 125 where highly non-regular sequences decrease the interfacial tension between two species beyond regular blocky or alternating sequences.…”

Sequence and entropy-based control of complex coacervates

“…In particular, the continuum of behaviors between block and random co-polymers has been probed in terms of equilibrium properties (e.g., phase behavior 18 , 19 , compatibilization 20 ) using coarse-grained modeling and theory. These works consider portions of a vast sequence parameter space, using monomer sequence correlations (i.e., blockiness) 18 , 19 , sophisticated machine learning methods 20 , or sequence gradients 21 . These situations focus on short-range dispersive interactions, where monomers interact primarily with their immediate neighbors.…”

Self-assembly in densely grafted macromolecules with amphiphilic monomer units: diagram of states

“…The mixing degree hZi was determined as the product of the local relative content of A and B groups averaged over space. 53 In our calculations Z is measured as follows:…”

“…Thus, it could be helpful for the detection of the A-B segregation with an increase in A-B incompatibility. 53 The mixing degree hZi (averaged over time) for the different energy parameters e AB and e BB and bin size D = 2s was calculated along the nine rays shown in Fig. 2 and the results are presented in Fig.…”