On dynamic scaling theories of individual polymers in solution

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Abstract
Dynamical scaling relations are derived for the diffusion coefficient, viscosity, and the dynamic structure factor for polymer chains at infinite dilution. The derivation begins with the full diffusion equation with unaveraged hydrodynamic interaction for the dynamical motion of a continuous chain in solution. The scaling relations emerge from asymptotic dimensional analysis for very long chains. The dependence on all dimensional variables is retained, and previous scaling results are recovered. The use of interdimensional scaling enables the derivation of the dynamical exponents which are found to involve the static ones in the fashion assumed by de Gennes.