Hydrodynamics of polymer solutions via two-parameter scaling

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Abstract
We discuss the temperature and concentration regimes for the hydrodynamic properties of linear polymer solutions. New regimes are reported in addition to the known regimes for the static conformations of the coils. The new regimes appear because of the existence of a second length scale, the tube diameter, which is not proportional to the screening length. In the theta regime, the polymer volume fraction where entanglement becomes important is φe≈(a1/b)3/2 N -3/4, where a1, b, and N are the tube diameter in the melt, the Kuhn length, and the number of Kuhn segments in the chain, respectively. Except for very large N, φe is larger than the overlap concentration φ*. In the good solvent region, φ* and φe have the same scaling for their dependence on N, but have different temperature dependences. The results are summarized on a diagram in the temperature-concentration plane

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