Dynamic screening length

I his comparison shows that the dynamic screening length in semidilute solutions and the hydrodynamic radius Rn in dilute ones have the same homology in reference to the contour length. 

Under -conditions the situation is more complex. On one side the excluded volume interactions are canceled and E,(c) is only related to the screening length of the hydrodynamic interactions. In addition, there is a finite probability for the occurrence of self-entanglements which are separated by the average distance E,i(c) = ( (c)/)1/2. As a consequence the single chain dynamics as typical for dilute -conditions will be restricted to length scales r < (c) [155,156],... 

In scenario (c) corresponding to semidilute solutions, polyelectrolyte chains interpenetrate. Under these circumstances, there are three kinds of screening. The electrostatic interaction, excluded volume interaction, and the hydro-dynamic interaction between any two segments of a labeled polyelectrolyte chain are all screened by interpenetrating chains. Each of these three interactions is associated with a screening length, namely, and These screening... 

In semidilute solutions, both statics and dynamics are similar to dilute solutions on length scales shorter than the screening length. For short distances from a given monomer (r < ). essentially all other monomers... 

On length scales larger than the screening length the dynamics are many-chain-like, with both excluded volume and hydrodynamic interactions... 

The properties of crosslinked gels are considered in detail in section 3.5. Here w e note the analogy of the dynamic properties of concentration fluctuations in semidilute and concentrated solutions with the screening length and in polymer networks with the same distance between entanglements. 

Scaling relations for quantities that are time independent, for example, the osmotic pressure 7t, the mean-square end-to-end distance (R ), and the screen length are known as static scaling relations. Those for time-dependent quantities, such as the translational diffusion coefficient, are called dynamic scaling relations. 

FIGURE 12.13 Residual Difference between Actual and Model Predicted Exposed Screen Length using Analytical Flow Model Coupled with Dynamic Bubble Point Model. 

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