Polymers in good solvent solution with overlap

Bringing the (corrected) experimental values of 3EGl and the theoretical values A, in eqns (15.3.59), we can determine the values of the interaction parameters z from a linear expansion in z. The result is reproduced in Table 15.8. Although the swellings X, are different, the interaction parameters z, must be equal. This is what we verify (but really at the price of the readjustment mentioned above ). 

POLYMERS IN GOOD SOLVENT SOLUTION WITH OVERLAP 

Until recently (1970), the experimental effort has mostly been profitable in the field of dilute solutions, in the limit of zero concentration in this limit, the basic quantities Rq and A2 are measured. 

This situation changed not long ago polymer solutions with overlap have aroused new interest. The use of neutron scattering and the technique of labelled molecules has contributed to this change. Furthermore, a decisive step was taken when it became obvious that experiments on solutions with overlap are easily interpretable in terms of the concentration p and of the basic quantities Rg and A2 (which are defined for p - 0). In other words, it is necessary to account for swelling effects, which remain important 

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POLYMERS IN GOOD SOLVENT. SOLUTION WITH OVERLAP... 

When soluble polymers are attached by one end to a surface, the thickness of the resulting layer, L, depends on the surface density of chains a as well as n and the excluded volume v/l3 (de Gennes, 1980). At low densities risolated chains extend 1/2 into the solution, creating a layer with the density profile shown in Fig. 26a and a thickness of L = n1/2f for ideal chains and L n3/sl in good solvents. When 1 the coils overlap and the interactions will cause the chains to expand away from the surface into the bulk. The configurations of the individual molecules and the density profile within the layer (Fig. 26b) differ markedly from the dilute situation. When cl2 1 the molecules become fully stretched. 

In this chapter, polymers are represented by means of the standard continuous model, described in Chapter 10. To calculate their properties in good solvent, we shall use the renormalization techniques described in Chapter 12. The principles and methods which serve to determine the properties of isolated polymers or of a small number of polymers (dilute solutions) also apply quite naturally to the study of polymer ensembles (solution with overlap) which we consider in the second part of the present chapter. In this way, we obtain all kinds of results which can be compared to experimental data. 

In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

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