Thermodynamics of Block Polymers – Monte Carlo Simulations and Self-Consistent Field Theory Study

Block polymers self-assemble at mesoscopic length scales to form a wide variety of ordered structures that are instrumental for several emerging technologies such as nanostructured membranes and photonic crystals. Their equilibrium structure depends on numerous molecular parameters: chemistry, length, sequence, and the number of blocks bonded together to form a polymer molecule. Usually, the existence of these ordered structures is not known a priori and many past discoveries are the result of immense experimental effort. However, synthesizing every possible block polymer in such a high-dimensional parameter space is expensive and time-consuming. Therefore, efficient computational methods are key to discovering new materials.

In this poster presentation, we discuss our results for two different class of block polymers: AB diblocks and ABA′C tetrablocks. Our first study focusses on “short” diblock copolymers, motivated by the ever growing demand in microelectronics industry for ordered structures with characteristic dimensions as small as possible. We implemented an efficient lattice-based Monte Carlo simulation tool to predict nanostuctures and their associated properties in linear AB diblocks. In this study, we resolved long-standing artifacts in lattice simulations, namely, commensurability and finite-size effects. This enabled us to accurately determine the characteristics dimensions of a lamellar structure as well as the fluctuation-driven weakly first-order transition in symmetric diblocks.

In order to study multiblock polymers, i.e., ABA′C tetrablocks, we use a field-theoretic simulation method called self-consistent field theory (SCFT). The SCFT framework involves highly non-linear partial differential equations, which are solved using a pseudospectral algorithm employing efficient Fast Fourier Transform, and Anderson-mixing iteration scheme. The SCFT solver begins with a guess structure, solves the governing equations iteratively, and outputs a defect-free ordered structure. The convergence of the iteration procedure depends strongly on the guess structure. We developed a robust, physically-informed approach to generate guess structures that is required to initiate the SCFT iterator, and a efficient method to converge the solutions to stress-free crystals. We used this approach to perform SCFT simulations for different sphere-forming structures in ABA′C tetrablock terpolymers and predicted the most promising range of experimental parameters for discovering new phases. Our experimental colleagues synthesized these polymers, and together we discovered nine nanostructures, including the complex Frank-Kasper σ and A15 phases. In order to accelerate the discovery of block polymer materials, we have shared our SCFT tool online (http://pscf.cems.umn.edu) for public download.