Fluctuation Effects in Semiflexible Diblock Copolymers

We present a simulation study of the equilibrium thermodynamic behavior of semiflexible diblock copolymer melts. Using discretized wormlike chains and field-theoretic Monte Carlo, we find that concentration fluctuations play a critical role in controlling phase transitions of semiflexible diblock copolymers. Polymer flexibility and aspect ratio control the order− disorder transition Flory−Huggins parameter χODTN. For polymers with low aspect ratios, fluctuations strongly elevate the phase transition χODTN at finite molecular weights. For high aspect-ratio polymers, chain semiflexibility decreases the phase transition χODTN. We find that the simulated phase behavior agrees well with our recently developed fluctuation theory based on wormlike chain configurations and a one-loop treatment of concentration fluctuations. C composed of incompatible chemical blocks self-assemble into microstructures with mesoscale domain sizes ranging from a few angstroms to many nanometers. Such microstructures endow such polymeric materials with ideal mechanical, interfacial, and transport properties. Furthermore, copolymer self-assembly can be used as an informative model for the structural organization of biomolecules. For several decades, numerous experimental and theoretical works have established our foundational understanding of polymeric self-assembly. In the theoretical study of the phase behavior of copolymers, polymer field theory has been the primary theoretical framework, and the majority of the work implementing polymer field theory uses the Gaussian chain model and mean-field theory. The Gaussian chain model assumes polymer configurations exhibit random walk statistics. Mean-field theory assumes that the chemical monomers interact through spatially averaged density fields, neglecting the impact of correlated concentration fluctuations. A classical example of a copolymer is the diblock copolymer, which consists of two covalently bonded segments with chemically different monomers (i.e., ...-A-A-A-B-B-B-...). Experiments map out the phase diagram of diblock copolymers at different A-segment fraction fA and interaction strength between A and B monomers, controlled by the Flory−Huggins parameter χ. The coarse-grained model assuming Gaussian chain configurations and mean-field interactions is able to qualitatively predict the phase diagram of diblock copolymer melts. However, experiments observe an elevated order− disorder transition χODT over the mean-field predictions. Such quantitative discrepancy is partially corrected by incorporating finite molecular weight effects with concentration fluctuations. Molecular simulations and experiments show agreement with the fluctuation-corrected theories at relatively high molecular weights. However, nonuniversal phase behavior at low molecular weights is also noted by recent experiments. One source of nonuniversality is the finite polymer flexibility at low molecular weights. Recently, we developed a theory that accounts for polymer semiflexibility and fluctuation effects using the wormlike chain model. We show that phase transitions of semiflexible diblock copolymers with finite aspect ratios strongly deviate from the Gaussian chain theory at molecular weights lower than N ≈ 100. Such nontrivial strong deviations show that the incorporation of density fluctuations is critical in studying phase transitions of semiflexible copolymers. In this work, we aim to leverage field-theoretic Monte Carlo simulations to study the phase behavior of semiflexible copolymers in the presence of density fluctuations. This work Received: August 21, 2017 Accepted: December 13, 2017 Letter pubs.acs.org/macroletters Cite This: ACS Macro Lett. 2018, 7, 59−64 © XXXX American Chemical Society 59 DOI: 10.1021/acsmacrolett.7b00638 ACS Macro Lett. 2018, 7, 59−64 provides a concrete assessment of the impact of concentration fluctuations on copolymer phase behavior as the molecular weight is reduced. The technological trend for copolymer materials is to assemble into morphologies with smaller domain sizes (i.e., nanometer length scales), making our predictions crucial for practical applications of copolymer assembly. We consider a diblock copolymer melt consisting of np polymers. Each polymer has Aand B-type segments, with Asegment fraction fA. The total energy of the system is the sum of polymer conformation energy and monomer interaction energy β β β = + E E E poly int (1) where β = 1/(kBT) and kB is the Boltzmann constant. To capture polymer semiflexibility, we model each chain as a wormlike chain whose conformational energy is proportional to the square of the chain curvature