Polyelectrolyte solutions, phase boundary concentration

In order to calculate the phase boundary concentrations for stiff polyelectrolyte solutions, we express the total intermolecular interaction u for the polyion as the sum of the hard-core interaction u0 and the electrostatic interaction wel, and assume Eq. (1) for u0 and the following for wd ... 

In concluding this section, we should touch upon phase boundary concentration data for poly(p-benzamide) dimethylacetamide + 4% LiCl [89], poly(p-phenylene terephthalamide) (PPTA Kevlar)-sulfuric acid [90], and (hydroxy-propyl)cellulose-dichloroacetic acid solutions [91]. Although not included in Figs. 7 and 8, they show appreciable downward deviations from the prediction by the scaled particle theory for the wormlike hard spherocylinder. Arpin and Strazielle [30] found a negative concentration dependence of the reduced viscosity for PPTA in dilute Solution of sulfuric acid, as often reported on polyelectrolyte systems. Therefore, the deviation of the Ci data for PPTA in sulfuric acid from the scaled particle theory may be attributed to the electrostatic interaction. For the other two systems too, the low C] values may be due to the protonation of the polymer, because the solvents of these systems are very polar. 

Though the phase boundary is not necessarily observable, the remarkable salt concentration (Cs/mol/dm3) dependence of the ion binding equilibria in polyion systems implies the phase separation nature of the polyelectrolyte solutions. A straightforward proof for this property can be gained by the careful examination of the acid dissociation equilibria of weak acidic polyelectrolytes, (HA) , and the conjugate acids of weak basic polyelectrolytes, (BH+) , respectively, expressed as the repeated functionalities of HA and BH+ ... 

For the effective temperature r (f/M), the correlation length f becomes on the order of the size of a bead Db at polymer concentration cb z. At higher polymer concentrations, the system crosses over into the concentrated polyelectrolyte solution (regime IV). However, if the value of the parameter [r[is larger than (f/ ) the system will phase separate into a concentrated polymer solution and a solution of necklaces. The left boundary of the two-phase region is... 

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