Quantitative predictions for structured polymeric melts

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Quantitative simulation methods will be developed and applied to structured polymeric melts, in particular, those involving block copolymers. This is only possible because all models and experiments reduce to a standard Gaussian-chain model (GCM) at high molecular weights. The profound implication of this universality is that even simple models can be quantitatively matched to experiments by mapping both onto the GCM. Block copolymer are much like ordinary polymers, except that they consist of chemically distinct sections (or blocks). The tendency for the distinct blocks to separate tempered by their connectivity causes a liquid (or melt) of these molecules to self-assemble into structures with nanometer-sized domains. The ability to combine components with different characteristics into well-defined nanostructures provides a powerful way of controlling material properties. Furthermore, the ordered nanostructures have many applications in the emerging field of nanotechnology. The GCM treats polymers as thin elastic threads interacting by contact forces, the strength of which is control by a Flory-Huggins chi parameter. The key to mapping other models or experiments onto the GCM is knowing how to calibrate chi, which is something that we have made great progress on over the past few years. Although the GCM underpins most theoretical calculations on block copolymers, it is impractical to simulate directly and thus one needs other approaches. One strategy is to use particle-based lattice models, where the simulation is made efficient by restricting the polymers to a lattice. Although the lattice is artificial, quantitative predictions are still possible due to universality. In the past, these simulations have been limited to low molecular-weight polymers, but we have now developed a lattice model that can be mapped onto high molecular-weight polymers. It will be used to develop quantitative predictions of diblock copolymer melts and of binary homopolymer blends for the purpose of calibrating the chi parameter in experimental systems. Another strategy is field-theoretic simulations (FTS), where the particle-based GCM is transformed into a mathematically equivalent field-based model, which can then be simulated. This approach has been plagued by computational challenges and a so-called ultraviolet divergence, but we have overcome these obstacles to generate a highly efficient FTS algorithm capable of simulating systems that are too complicated for traditional particle-based models. FTS will be used to investigate ternary blends of diblock copolymers with their parent homopolymers, which are well known for producing bicontinuous microemulsions. FTS will also be applied to complicated bottlebrush block copolymers, which are gaining huge attention due to their fast dynamics and large domains.