Hydrodynamic screening length

Fig. 65. Concentration dependence of the hydrodynamic screening length (c). The solid line represents the result of the simultaneous fit, the dashed line in correlation length (c) related to the transition from single to many chain behavior. (Reprinted with permission from [40]. Copyright 1984 American Chemical Society, Washington)...

The Dependencies of Radius of Gyration Rg, Static Correlation Length Hydrodynamic Screening Length Viscosity r, Self-Translational Diffusion Coefficient D, Cooperative Diffusion Coefficient Dc, Coupled Diffusion Coefficient Df, and Electrophoretic Mobility p on c and N for Various Regimes of Polyelectrolyte and Salt Concentrations... 

In view of the dependence of l on c as given in Table I, the hydrodynamic screening length has the following concentration dependence... 

In dilute solutions, Dc = D. In the Rouse regime, Dc depends on both static and hydrodynamic screening lengths and... 

The hydrodynamic screening length in semidilute solutions is expected to be proportional to the static correlation length ... 

The hydrodynamic screening length can neither be much larger nor... 

Increasing polymer concentration affects chain scission in several ways, as it increases the bulk viscoelasticity, the stress transmission efficiency, tq, and the hydrodynamic screening. The hydrodynamic screening means the hydrodynamic interactions become negligible between chain segments whose spatial distance apart is larger than a certain value (termed hydrodynamic screen length). In both... 

In concentrated solutions, with the increase of the polymer concentration, the screen effect of hydrodynamic interactions is enhanced due to the interpenetration of polymer chains. We can assume that the hydrodynamic screening length is close to the screening length of volume exclusion of monomers as given by... 

As usual, the osmotic diffusion coefficient is linked to the bulk osmotic modulus and to the effective mobility per monomer p = p x K/C. The quantity p can be measured through the sedimentation coefficient S = p(1- vp). Comb ing the experimental results for K and S, we obtain >c = 1.13 X 10"° X in agreement with the result presented above. This result confirms that the hydrodynamic screening length is proportional to that of the concentration fluctuations. Actually the scaling law is well verified (see Fig. 6) where is the diffusion coefficient of the isolated polymer chain, is only a function of CIC, ... 

A. Bennett, P. J. Daivis, R. Shanks, and R. Knott. Concentration dependence for static and hydrodynamic screening lengths for three different polymers in a variety of solvents. Polymer, 45 (2004), 8531-8540. 

The scaling result for the cooperative diffusion constant finds a simple interpretation in terms of blobs. The hydrodynamic screening length X is of the order of the blob size As far as hydrodynamic... 

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