Speaker
Description
The non-equilibrium dynamics of inhomogeneous polymer systems undergoing processes that change the number of polymers is an essential component of many biological systems, such as solvent exchange with an external reservoir or the binding of small molecules to a polymer backbone. Our previous theories were formulated in the canonical ensemble, fixing the number of polymers and limiting our ability to describe grand canonical systems (with variable polymer number) without ad hoc modifications to the dynamical equations. To overcome this limitation, we construct a manifestly grand-canonical theory in the Fock space formalism of quantum field theory. We introduce polymer creation and annihilation operators that act to create or destroy polymer chains in a given configuration, obeying bosonic commutation relations. The microscopic dynamics of interacting polymer systems are reformulated as an operator theory capable of naturally describing processes that change polymer number. We introduce bosonic coherent states to convert the operator theory to a field theoretic representation in terms of a complex single chain propagator. In the saddle-point approximation, we obtain a Smoluchowski equation describing the mean-field dynamics of the propagator. The power of this formalism is that chemical reactions between polymer species can be easily constructed in the operator theory, and we can systematically derive the corresponding terms in the mean-field Smoluchowski equation, which is the central equation of the theory. We demonstrate the formalism by showing that a pair of spatially localized reactions that create and destroy chains on the system boundary can be used to model the exchange of chains with an external reservoir, leading to boundary conditions that we had previously imposed ad hoc in our canonical theory. The power and flexibility of this theory to describe the dynamics of interacting grand canonical polymer systems makes this a promising approach for quantitative modeling of biological systems.
| Keyword-1 | Polymer physics |
|---|---|
| Keyword-2 | Self-consistent field theory |