Nondraining chain limit

Fixed points A and B are version. of free draining of the chain while C and D relate to a nondraining chain. The fixed points with u = 0 correspond to the 0 state, while u = 7T e/2 correspond to the self-avoiding limit (the maximum good solvent). 

Within this limit, called the nondraining chain, the hydrodynamic radius is proportional to the root mean-squared radius of gyration ... 

Still another indication of the upper limit given earlier may. be found from another combination of sedimentation and viscosity data. By combining Eqs. (4), (53), (66), (68), and (69) we easily find for nondraining flexible chains ... 

Barrett [1984] has further proposed TP expressions for and an, formulated within the Kirkwood-Riseman hydrodynamic theory in the nondraining limit and using approximate formulas, based on numerical simulation, for the requisite statistical averages, (/f >and Rf/), where Ry refers to the distance between the ith andyth chain segments ... 

The translational diffusion coefficient D of a polymer coil can be found from the time-dependent correlation function of scattered intensity measured in dynamic light-scattering experiments. Using the Stokes-Einstein equation, the translational diffusion coefficient D can be related to the apparent hydro-dynamic radius (the radius of equivalent hard sphere). In the limit of nondraining for the solvent coil formed by infinitely long chain, the hydrodynamic radius is given by... 

In the limit of N—both l h and 1 , scale with the degree of polymerization in the same way as the gyration radius of the Gaussian or swollen coil N"a. Remarkably, for finite-length semiflexible chains, the nondraining condition does not strictly apply. As a result, deviation in the observable N dependence of the gyration radius and those of the hydrodynamic radii... 

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