Counterion condensation effect

P. J. Heath and J. M. Schurr, Macromolecules, 25,4149 (1992). Counterion Condensation. Effects of Site Binding, Fluctuations in Nearest-Neighbors Interactions, and Bending. 

The effect is more than just a matter of pH. As shown in Fig. XV-14, phospholipid monolayers can be expanded at low pH values by the presence of phosphotungstate ions [123], which disrupt the stmctival order in the lipid film [124]. Uranyl ions, by contrast, contract the low-pH expanded phase presumably because of a type of counterion condensation [123]. These effects caution against using these ions as stains in electron microscopy. Clearly the nature of the counterion is very important. It is dramatically so with fatty acids that form an insoluble salt with the ion here quite low concentrations (10 M) of divalent ions lead to the formation of the metal salt unless the pH is quite low. Such films are much more condensed than the fatty-acid monolayers themselves [125-127]. 

Manning s theory does not take the local effective dielectric constant into consideration, but simply uses the a value of bulk water for the calculation of E,. However, since counterion condensation is supposed to take place on the surface of polyions. Manning s 2, should be modified to E, by replacing a with aeff. The modified parameters E, is compared with E, in Table 1, which leads to the conclusion that the linear charge density parameter calculated with the bulk dielectric constant considerably underestimates the correct one corresponding to the interfacial dielectric constant. 

As discussed extensively in this chapter, most of the surprising properties of polyelectrolyte dynamics are due to the coupling of counterion dynamics with polymer dynamics. But, there is no adequate understanding of how much of the counterions are mobile and how much are effectively condensed on polymer chain backbone. Theoretical attempts [77, 78] on counterion condensation need to be extended to concentrated poly electrolyte solutions. 

Deeper insight into the consequences of counterion condensation is gained by an effective monomer-monomer and counterion-counterion potential, respectively. The idea is to reduce the multicomponent system (macromolecules + counterions) to effective one-component systems (macromolecules or counterions, respectively). We define the simplified model in such a way that the effective potential between the counterions or monomers, respectively, of the new system yields exactly the same correlation function (gcc, gmm) as found in the multicomponent case at the same density. Starting from the correlation function gcc -respectively gmm-of the multi-component model we calculate an effective direct correlation function cefy via the one-component Ornstein-Zernike equation. An effective potential is then obtained from the RLWC closures of the one- and multicomponent models [24]. For low and moderate densities the effective potential is well approximated by... 

Study on the rapid transport of a polymer in dextran solutions, first observed by Preston et al., is extended into two directions. They arc (1) enhancement effect on the transport rate of polyvinylpyrrolidone (PVP) by the addition of a simple salt, and (2) extension to the transport of linear polyelectrolytes. The enhancement effect was observed on the structured flow as well as on the transport rate. The enhancement effect was correlated with the densities of the solutions in the lower compartment of the diffusion cell. The correlation was improved when the rate was corrected for the differences in viscosities. We have found that effects of charges on the polymers favor the rapid transport of polyacrylates (PA) and sodium hyaluronate. Counterion condensation was manifested in the transport rate of PA. Transport rates of several salts of PA in the absence of added salt increased linearly with their partial specific volumes in water. 

Theoretical considerations of the coulombic interactions of dissolved biopolymers have produced a complete picture of the distributions of counter and coions under the influence of the electrostatic charge on the macroion(56,57). The counterion condensation theory of Manning(56) has stimulated a great deal of activity in the study of dissolved macroions, especially because it provides a group of limiting laws describing the contribution of electrostatic effects to the thermodynamic and transport properties of polyelectrolyte solutions. Data... 

Counterion condensation theory, however, does not provide a detailed picture of the distribution of the condensed Ions. Recent research using the Poisson-Boltzmann approach has shown that for cylindrical macroions exceeding the critical linear charge density the fraction of the counterions described by Manning theory to be condensed remain within a finite radius of the macroion even at infinite polyion dilution, whereas the remaining counterions will be infinitely dispersed in the same limit. This approach also shows that the concentration of counterions near the surface of the macroion is remarkably high, one molar or more, even at infinite dilution of the macromolecule. In this concentrated ionic milieu specific chemical effects related to the chemical identities of the counterions and the charged sites of the macroion may occur. 

Apart from the phenomenon of a negative osmotic coefficient the remarks which have been made on monovalent measurements also apply here. The actual p is smaller than the PB prediction, only this effect is much more pronounced in the multivalent systems. This overestimation of p is again accompanied by an underestimation of counterion condensation see for instance Figure 9. The osmotic coefficient converges to the PB result upon dilution, but already at intermediate densities it is surprisingly well described by the Manning limit l/2 w. Notice finally that contrary to Figure 12 the curves for different valences intersect. The reason for this is the way in which Eq. 40 depends on valence. 

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