Semidilute solutions screening length

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... 

On length scales larger than the correlation length, the excluded volume interactions are screened by the overlapping chains. The semidilute solution on these length scales behaves as a melt of chains made of correlation blobs and the polymer conformation is a random walk of correlation blobs ... 

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

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... 

In semidilute solutions, hydrodynamic interactions are not screened on scales smaller than the correlation length Each mode involves... 

A more refined scaling model, developed recently in [93], introduces the concept of a screening length rg < td to specify the PE star behavior in the salt-dominated regime. According to [125], rg governs the screening of the electrostatic interactions in a semidilute PE solution with added salt. A smaller value of with re-... 

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. 

Now let US discuss the mechanical properties of semidilute solutions and g< ls in connection with scaling constructions (Candau et al., 1979, 1982). The clastic properties of. semidilute solutions are controlled by two parameters the screening length i corresponding to the mean distance between cross-links (sec Subsection 3.1.1) auid the cross-link lifetime T,. Any solution exhibits its elasticity only over intervals shorter than Tr (see Section 3.5). Hence, semidilute solutions can not show mechanical elasticity since mechanical mea.siirements require much more time than T,. 

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. 

For semidilute polyelectrolyte solutions, the effeaive charge on a chain section inside the electrostatic screening length is equal to (see eqn [139])... 

The hydrodynamic interactions between sections of a chain in semidilute solutions are screened on the length scales larger than the correlation length 323339.124 jjjg correlation... 

Combining all the information collected so far, for the single chain pair distribution function in a semidilute solution we can predict an overall shape as indicated in Fig. 3.8. For the presentation we choose a plot of 4nr g r) versus r. The curve is a composite of different functions in four ranges, with cross-overs at the persistence length Ips, the thermic correlation length and the screening length Up to r we find the properties of the expanded chain, which... 

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