Influence of variable draining and excluded volume on hydrodynamic radius within Kirkwood–Riseman model: Dynamical renormalization group description to order ε2

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Abstract
The renormalization group method is employed in conjunction with the Kirkwood–Riseman and two-parameter models to study the double crossover dependence of the hydrodynamic radius of flexible polymers on both hydrodynamic and excluded volume interactions. An exact second order in ε crossover analysis is derived for the limiting cases of Gaussian and self-avoiding chains and for free-draining and nondraining chains. Our calculations show that the excluded volume and hydrodynamic interactions act competitively to affect the dynamical measures of the molecular dimensions, so that an increase in the excluded volume interaction produces a decrease in the strength of the effective hydrodynamic interaction. This coupling of the hydrodynamic and excluded volume interactions can provide an explanation of why dynamical measures of polymer dimensions are often found to scale with lower exponents than equilibrium measures, and methods are described for experimentally testing such an explanation.