Collective dynamics of polymer solutions

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Abstract
We present a field-theoretic treatment of polymer solution dynamics. The method involves the construction of a Martin–Siggia–Rose generating functional for flexible polymer chains dissolved in a low molecular weight solvent. This formalism is shown to be particularly convenient for investigating the dynamics of collective field variables, such as polymer concentration or elastic stress. Moreover, it provides an extension to nonequilibrium phenomena of Edwards’ conjugate field approach to the static properties of semidilute polymer solutions. The theory is amenable to conventional field-theoretic approximation methods. We explicitly investigate a Gaussian approximation, which gives concentration correlation and response functions identical to those obtained from the dynamical random phase approximation. However, the method also demonstrates screening of hydrodynamic disturbances, the crossover to macroscopic hydrodynamics, and provides information on elastic stress dynamics. We expect that the advantages of the present formalism will become most apparent far from equilibrium, such as in the description of flow-induced fluctuations and phase separation of polymer solutions.