A field theoretic approach for simulating assemblies of interacting polymers is discussed. By applying a Hubbard-Statonovich transformation to a molecularly informed coarse-grained polymer model, auxiliary fluctuating fields are introduced to decouple segmental interactions, and particle degrees of freedom are integrated out. The resulting theory has several advantages for simulating polymeric systems, including access to mesoscale phenomena without simulating the atomic/molecular scale. The theory is commonly employed in mean-field appoximation (SCFT), which is exact for asymptotically long polymer chains in the melt state. However, for intermediate-molecular-weight melts, for solvated or charged polymers, or for systems close to critical phase transitions, the mean-field approximation is qualitatively inadequate. We discuss a stochastic computational method based on complex Langevin (CL) sampling to directly simulate the fully fluctuating field theory without critical inefficiencies of the sign problem.<br/><br/>Side effects of incorporating fluctuations into the common polymer models include the loss of direct access to free energies, and the presence of UV divergences which make many observables non-finite as spatial discretization is refined toward the continuum limit. Both of these issues have long prevented the use of CL for quantifying fluctuation corrections to phase diagrams. In this talk we describe two advances that in tandem allow computation of fluctuation corrected phase diagrams: a UV regularization procedure, and Helmholtz free energies with fluctuation corrections computed using thermodynamic integration. We note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures.

Progress in fully fluctuating field theoretic simulations of polymers

251st National Meeting (2016)

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