Polyelectrolyte solutions, phase boundary

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. 

The present review deals mainly with two examples of polyelectrolyte phase behavior as discussed above. As an example for an H-type precipitation, the solution properties of polyvinylpyridinium chains are monitored as function of added inert salt. Here, we focus on the determination of the effective charge density and of the solvent quality parameter which are supposed to play a central role for the understanding of polyelectrolyte solution without specific counterion interactions. The second system under investigation comprises the interaction of polyacrylic acid with alkaline earth cations which exhibit very specific interactions, thus representing an example for type L-precipitation. Here the coil dimensions close to the phase boundary are compared to those close to type H-precipitation with inert added salt. 

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+ ... 

Unfortunately, a fundamental difference between a gel (resin) and a linear polyelectrolyte precludes this possibility. In resins and gels there is a well-defined physical boundary, each phase being essentially electrically neutral. However, in the case of a simple linear polyelectrolyte solution there is no discernible boundary, and the two phases, polymer and liquid, are not uncharged a sizeable charge on the macromolecule is compensated by the presence of oppositely charged counterions in the liquid phase. 

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... 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

Addition of low molecular weight salts into mixtures of oppositely charged polyelectrolytes has a pronounced influence on the behavior of water-soluble nonstoichiometric IPECs. In particular, this manifests itself in a shift of the boundary between the regions A and B, that is, Z, to lower values. The low molecular weight salts induce conformational transformations of particles of nonstoichiometric IPECs, (i.e., a coil-globule transition) followed by phase separation of the solution and macroscopic precipitation of a stoichiometric IPEC [31, 34]. 

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