Counterions multivalent salt

These results show that the solubility of polyelectrolytes in the presence of multivalent salt, especially at high salt concentration, depends on the relative affinity between charged groups of the polyelectrolyte and counterions. With organic multivalent cations, as spermidine and spermine, where... 

The full self-consistent calculation is necessary if the chain changes its conformation significantly as the experimental conditions are varied. As an example, the polymer chain collects most of the counterions when it undergoes coil-to-globule transition (Kundagrami and Muthukumar 2010) as seen in experiments (Loh et al. 2008). The polyelectrolyte chain is essentially uncharged in its collapsed state. The role of multivalent counterions and salt... 

This short discussion shows that despite significant progress in the analytical theories, there are still many unsolved issues. The situation gets even more complicated if one allows for added salt and/or multivalent counterions [58] or varies the Manning ratio in the system. 

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. 

Qualitatively, the phase diagram fits very well to the phase diagram known for single-chain polyelectrolytes, the phase boundaries are only slightly shifted. In principle, the parameter space for polyelectrol ffes has far more dimensions, such as the solvent quality parameter, the valency of monomers or counterions, and additional salt concentration in the system. Especially for multivalent counterions, one can expect an even more complex picture, since correlation effects are known to play an important role even for single chains. 

It can be shown that the addition of trace amounts of Z-ions to the solution leads to a rapid substitution of monovalent counterion in the star corona by Z-ions. This is due to their stronger attraction to the oppositely charged PE star polymer. Since a smaller number of Z-ions is needed to ensure the electroneutrality of the star interior, an increase in (i.e., in relative amount of Z-ions in the bulk of the solution) leads to a rapid decrease in the osmotic pressure inside the corona and, consequently, to a de-swelling of the PE star. This effect, of replacing monovalent counterions by multivalent ones is most pronounced at low salt concentrations (in the osmotic regime), where ... 

Thus, the replacement of monovalent counterions by multivalent ones (at constant and high bulk concentration of monovalent salt co-ions), results in a contraction of the star macroion by a factor of Rz i/Rz —... 

A different effect occurs with the use of polycarboxy-lates in combination with zeolites. Small amounts of polycarboxylates or phosphonates can retard the precipitation of sparingly soluble calcium salts such as CaCOs (the threshold effect ). As they behave as anionic polyelectrolytes, they bind cations (counterion condensation), and multivalent cations are strongly preferred. Whereas the pure calcium salt of the polymer is almost insoluble in water, mixed Ca/Na salts are soluble, i.e. only overstoichiometric amounts of calcium ions can cause precipitation. Polycarboxylates are also able to disperse many solids in aqueous solutions. Both dispersion and the threshold effect result from the adsorption of the polymer on to the surfaces of soil and CaCOs particles, respectively. 

The coagulants (typically multivalent counterions) commonly used are the salts of aluminium and iron and salts or the bases of calcium and magnesium. The transition from stabilized to destabilized emulsions on changing the temperature is very sharp at the critical flocculation temperature (CFT) when nonionic surfactants are used. Generally, aqueous dispersions destabilize upon increasing temperature, while non-aqueous dispersions destabilize with decreasing temperature. 

Alginates have interesting ion-exchange properties most monovalent counterions (except Ag ) form soluble alginate salts, whereas divalent and multivalent cations (except Mg " ) form gels or precipitates. The affinity was found to follow the order [60-63] ... 

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