UC Santa Barbara

I demonstrate how to conduct efficient field theoretic simulations (FTS) and self-consistent field theory (SCFT) calculations for a variety of polymer models, including comb-like and bottlebrush diblock copolymers, binary blends of heterobonding telechelic homopolymers, and end-linking star polymers in solution. I develop field theory models in both the auxiliary field (AF) framework and coherent states (CS) framework, which are well suited to unreactive and reversibly-bonding polymers, respectively. Numerical methods for both types of models are developed and compared for SCFT calculations, and also for FTS of AF models. I demonstrate that depending on whether the system is on average disordered or inhomogeneous affects which choice of algorithm performs best. Additionally, the CS representation can conduct simulations more efficiently than AF for SCFT, but is disadvantaged for FTS.

I apply these numerical methods to study trends in phase behavior of both reactive and unreactive polymers. I examine the effect of architecture, including side-chain length and grafting density, on the stability of Frank-Kasper sphere phases for comb-like and bottlebrush diblock copolymers. I show that the effect of architecture is related to conformational asymmetry in linear polymers, and a universal phase diagram that combines all these effects into a single parameter.

I then shift my focus to reactive polymers, where I use the CS models and algorithms to simultaneously compute phase stability and reaction equilibrium in self-assembled blends of reactive homopolymers. Although these blends produce wide distributions of products, they can be well approximated with simple blends of unreactive block copolymers and homopolymers. Exotic trends in phase behavior, such as reentrance are also observed, but are explained via the temperature dependence of the reaction equilibrium and phase segregation strength.

Finally, I apply the CS approach to polymer networks formed from star polymers. The mean field analysis of this model is consistent with classical Flory-Stockmayer theory and predicts that spinodal decomposition can only occur after the system has undergone gelation. Including fluctuation effects accounts for loop and ring formation, which is not accounted for in Flory-Stockmayer theory and creates strong corrections to the mean field picture for dilute polymers.