Erin Lennon, Chemical Engineering, University of California, Santa Barbara, Engr. II, Room 3357, UCSB, Santa Barbara, CA 93106-5080, Kirill Katsov, Materials Research Laboratory, University of California, Santa Barbara, Engr. II, Room 3357, UCSB, Santa Barbara, CA 93106-5080, and Glenn H. Fredrickson, Chemical Engineering and Materials, University of California, Santa Barbara, Engr. II, Room 3357, UCSB, Santa Barbara, CA 93106-5080.
Free energy calculations are well-established in particle based simulations, but similar tools have yet to be fully developed for systems described by continuous fields discretized on a spatial lattice. These field-based systems are of particular importance when studying macromolecules and their self-assembly. For example, the functionality of polymeric materials is strongly correlated with their mesoscale equilibrium structure. The study of systems on this scale is often intractable by traditional particle based MD and MC simulations. Previous work has shown how field theoretic simulations can be used to appropriately investigate these systems in the mean-field limit (for a review, see [1]); however, progress beyond this approximation is limited by a lack of techniques for determining the free energy of field-based systems. In this work, we present a novel application of traditional thermodynamic integration methods to discretized field theoretic models. Using this to determine the absolute free energy of a diblock copolymer system, we qualitatively study the effect of polymer size on the order-disorder transition. [1] G.H. Fredrickson, The Equilibrium Theory of Inhomogenous Polymers (Clarendon Press, 2005).