Complex Modulus The Zimm Theory

Suppose a force, F, is exerted by a bead on the Newtonian solvent at the origin. This force sets the surrounding solvent in motion away from the origin at a point r the solvent velocity, calculated from the Stokes equation, reaches the steady-state value 

Both the scaling with co and the proportionality constant, V3, are confirmed by experimental data (see Fig. 3-13). The lines in Fig. 3-13 are proportional to G and G — computed in the nondraining limit. The agreement with data for a polystyrene of high molecular weight (M = 860,000) in theta solvents is excellent. In addition to its agreement with experimental data, the predictions of Zimm theory are supported by molecular dynamics simulations (Pierleoni and Ryckaert 1991 DUnweg and Kremer 1991). 

In a good solvent, where there are excluded-volume effects, G and G can be fit to the Zimm theory simply by adjusting h downward, for finite Ns (Ferry 1980). Thus, as the solvent quality improves, the relaxation spectrum becomes more Rouse-like (since 

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