Polyelectrolytes counterion condensation

Nucleic Acids are Polyelectrolytes Counterion Condensation 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... 

Manning, G. S. (1969). Limiting laws and counterion condensation in polyelectrolyte solutions. 1. Colligative properties. Journal of Chemical Physics, 51, 924-33. 

Satoh, M., Komiyama, J. lijima, T. (1984). Counterion condensation in polyelectrolyte solutions a theoretical prediction of the dependences on the ionic strength and degree of polymerization. Macromolecules, 18, 1195-2000. 

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. 

Counterions are necessary to ensure electroneutrality in polyelectrolyte solutions. Therefore, it can be energetically advantageous if a fraction of counterions are situated in the vicinity, or at the surface, of the polyion in order to reduce the charge of the polyion. To answer the question under which conditions this occurs, the concept of the counterion condensation has been introduced by Fuoss, Katchalsky and Lifson [98],Alexandrowicz and Katchalsky [99] or Oosawa [100] and subsequently theoretically developed by Manning [101-108]. 

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

Phase II describes saturated counterion condensation [47]. The polyelectrolyte charge is nearly compensated by the counterions [47]. The uncondensed counterions are dispersed in a self-similar fashion throughout the cylindrical region [47]. In fact, the number of counterions bounded between radius r and, say, 2r is independent of r [47]. 

The Manning counterion condensation line model provides insights into the mean-square number fluctuations of the condensed counterions, ((A0)2), where 0 is the number of condensed counterions per polyion charge [50], Denote by 0O the value of 0 for which the total polyelectrolyte free energy G per charge is a minimum, that is, (0G/00)e=e vanishes. Expanding G in powers of 0 0O to quadratic order leads to [50]... 

G. S. Manning, Biophys. Chem., 7, 95 (1977). Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. 4. Approach to Limit and Extraordinary Stability of Charge Fraction. 

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. 

Rare earth element complexation by PAA and HA is fast (5). However, most of the initial interactions are labile or weak stronger interactions take over as the metal reside longer on the polyelectrolyte. Weak and strong interactions are indicated by both ion exchange and ligand exchange dissociation experiments. It is difficult to infer site binding versus counterion condensation from these methods, and such a distinction must await methods that probe more directly the molecular character of the different interactions. 

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