Polyelectrolyte-counterion interaction

In addition to the article by Jones et al. in ref. 1, several other reviews of polymer relaxation in dilute solution have appeared, filling a long-existing need. Cohen-Addadhas briefly reviewed n.m.r. in concentrated polymer solutions where entanglements lead to non-zero dipole-dipole coupling. Weill et alP have surveyed the application of n.m.r. to counterion-polyelectrolyte interactions. 

Polyelectrolyte complexes formed by polyion pairing are of special interest, including protein-polyelectrolyte interactions such as protein-DNA complexes. A special case of polyelectrolyte complexes are polyelectrolyte multilayers (PEM) on surfaces formed by ion pairing, van der Waals interactions and counterion release of oppositely charged polyelectrolytes [2, 3]. 

Hayakawa K, Kwak JCT. Study of surfactant—polyelectrolyte interactions. 2. Effect of multivalent counterions on the binding of dodecyltrimethylammonium ions by sodium dextran sulfate and sodium poly(styrenesulfonate) in aqueous solution. J Phys Chem 1983 87 506-509. 

Like-charged polyelectrolytes can attract and condense into compact ordered states via counterion-mediated interactions. Recent examples include DNA toroids and F-actin bundles. Condensed divalent ions within F-actin... 

P. Mills, C. F. Anderson, and M. T. Record Jr., J. Phys. Chem., 89, 3984 (1985). Monte Carlo Studies of Counterion-DNA Interactions. Comparison of the Radial Distribution of Counterions with Predictions of Other Polyelectrolyte Theories. 

An interaction between the metabolites and the polyelectrolytes was investigated by titrating solid free controls at pH 5 and 8, respectively. Results that differ significantly from the values obtained from back-titrating the counterionic polyelectrolyte could be observed in the alkaline controls. Therefore, the following experiments were carried out at lower pH values. Some data were obtained from alkaline controls that did not contain any metabolites. 

Benegas, J.C., Paoletti, S., Van Den Hoop, M.A.G.T. Affinity interactions in counterion-polyelectrolyte systems competition between different counterions. Macromol. Theor. Simul. 8(1), 61-64 (1999)... 

Alexander-Katz, A., Leibler, L. Controlling polyelectrolyte equilibria and structure via counterion-solvent interactions. Soft Matter 5, 2198 (2009). doi 10.1039/b814653e... 

The parameter n reflects the measure of deviation of the system from the behavior of the monomeric acid where n = 1, i.e., it characterizes the degree of interaction between the neighboring functional groups of the macroion. The value of n depends on the structure of the polyelectrolyte and the nature of the counterion pK = pK0 — log (1 — a)/a is the negative decadic logarithm of the effective dissociation constant of the carboxylic CP depending on a. 

High sorption capacities with respect to protein macromolecules are observed when highly permeable macro- and heteroreticular polyelectrolytes (biosorbents) are used. In buffer solutions a typical picture of interaction between ions with opposite charges fixed on CP and counterions in solution is observed. As shown in Fig. 13, in the acid range proteins are not bonded by carboxylic CP because the ionization of their ionogenic groups is suppressed. The amount of bound protein decreases at high pH values of the solution because dipolar ions proteins are transformed into polyanions and electrostatic repulsion is operative. The sorption maximum is either near the isoelectric point of the protein or depends on the ratio of the pi of the protein to the pKa=0 5 of the carboxylic polyelectrolyte [63]. It should be noted that this picture may be profoundly affected by the mechanism of interaction between CP and dipolar ions similar to that describedby Eq. (3.7). 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolyte chains is known to occur when the charge density along the chain exceeds the critical value [40]. Our work indicates the existence of a critical value for the separation distance between chains, where the interchain interaction changes drastically, most likely due to the transition in the binding mode of the counterions (see Fig. 13). Many peculiar forms of behavior, which are often interpreted by the cluster formation or the interchain organization of polyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes... 

Of the preponderance of small ions, the colligative properties of polyelectrolytes in ionising solvents measure counterion activities rather than Molecular weight. In the presence of added salt, however, correct Molecular weights of polyelectrolytes can be measured by membrane osmometry, since the small ions can move across the membrane. The second virial coefficient differs from that previously defined, since it is determined by both ionic and non-ionic polymer-solvent interactions. 

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... 

Assuming that the total charge Q of a polyelectrolyte chain is uniformly distributed on the chain backbone so that each segment carries a charge of ezp where e is the electronic charge and by integrating over the positions of counterions, salt ions, and solvent molecules, the potential interaction V between any two segments i and j separated by a distance R,y is taken to be [48]... 

Mg has been studied in a polyelectrolyte system where the counterion is a phosphazene-bound sulphonate group. In this case the finite but low conductivity is due to Mg migration. A large increase in conductivity is noted when a bicyclic ligand, crypt [2.1.1.], is introduced (Hancock and Martell, 1988). Apparently, the cation-anion and cation-polymer interactions are reduced by complex formation, resulting in a more mobile cation, despite its larger effective radius. 

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