Polyelectrolyte Gaussian

It decreases with the solvent quality and crosses over to the radius of a Gaussian polyelectrolyte for T (f-ls/b)1/3. In the pearl-necklace structure most of the polymer mass and charge belongs to the pearls but the size of the chain is dominated by the stretched strands. 

Theoretical treatment of the viscosity-concentration relationship for polyelectrolyte solutions would involve both the cumbersome statistics of highly elongated chains beyond the range of usefulness of the Gaussian approximation and the even more difficult problem of their electrostatic interactions when highly charged. There appears to be little hope for a satisfactory solution of this problem from theory. Fuoss has shown, however, that experimental data may be handled satisfactorily through the use of the empirical relation ... 

For a polyelectrolyte chain that has non-Gaussian statistics, exact analytical expression for B is not feasible. To get some insight, we notice that the static structure factor has the limiting behavior. 

Note that. In a sense, the polyelectrolyte behaves now as If it were an "ideal" (Gaussian) chain with a relatively small number of Kuhn lengths. This coil size Is determined by the local stiffness, but not by long-range excluded volume. Should q Increase even furher (approaching L), then the wormlike chain would be better described by a slightly curved rod (as expressed by (5.2.21)) than by a random-flight chain. 

At length scales larger than the electrostatic interactions are screened by the other chains and counterions and the statistics of a chain is Gaussian with effective bond lengths of the order of the correlation length Thus, the chain size R in the semidilute salt-free polyelectrolyte solution is R - A /2c->/4 [26,29],... 

The term weak adsorption implies that the entropic free energy of a chain is comparable to its electrostatic attraction energy to the interface. The chain is assumed to be Gaussian and its conformations are only weakly perturbed by interactions with the surface. This is the most severe approximation of the current model. We also assume that the polyelectrolyte-density profile is built up near the adsorbing surface without disturbing the electrostatic potential and ionic distribution near the interface prescribed by the Poisson-Boltzmann theory. A more general... 

The authors also showed evidence in the study reported in Reference [66] that aggregates seen upon dissolution in water were already present in the dry polyelectrolyte powder and represented a minor mass fraction of the entire population which, before dissolving, evolve in time from initially spherically symmetric Gaussian mass distributions into structures resembling random coils containing multiple chains. 

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