Renormalization group study of Rouse–Zimm model of polymer dynamics through second order in ε

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Abstract
Gell–Mann–Low style renormalization group methods are employed in conjunction with dimensional regularizations and ε expansions to study the bead‐spring model of polymers with excluded volume in dilute solutions. Perturbation calculations are carried out through order ε2 for the translational diffusion coefficient D (ε=4−d, d being the spatial dimension) both with and without the use of the preaveraging approximation. Polymer excluded volume interactions are systematically incorporated into the Rouse–Zimm model by using the well‐known two parameter model along with the ε expansion. The nondraining limit hydrodynamic interaction fixed point is found to be unaffected by preaveraging through order ε2 and is identical to that obtained previously from the order ε2 preaveraged Kirkwood–Riseman formalism. Our work indicates that the nonpreaveraged renormalization group perturbation expansions appear more well behaved (controllable) in the Rouse–Zimm model than in the Kirkwood–Riseman rigid body model.