Counterion condensation

The counterion condensation phenomenon is commonly described by Manning’s theory (Manning 1969), which assumes that counterions can condense onto the polyions until the charged density between neighboring monomer charges along the polyion chain is reduced below a certain critical value. In the model the real polyion chain is replaced by an idealized line charge, where the polyion is represented by a uniformly charged thread of zero radius, infinite length and finite charge density, and the condensed counterion layer is assumed to be in physical equilibrium with the ionic atmosphere surrounding the polyion. The uncondensed mobile ions in the ionic atmosphere are treated within the Debye–Hückel (DH) approximation. The phenomenon of counterion condensation now takes place when the dimensionless Coulomb coupling strength

Γ = λ_B / l_charge > 1,

where λ_B represents the Bjerrum length and l_charge the distance between neighboring charged monomers. In this case the Coulomb interactions dominate over the thermal interactions and counterion condensation is favored. For many standard polyelectrolytes, this phenomenon is relevant, since the distance between neighboring monomer charges typically ranges between 2 and 3 Å and $\lambda_B \approx$ 7 Å in water.

In the case of the chondroitin sulfate (CS) systems, which is a major biopolyelectrolyte controlling the frictional-compressive properties of articular cartilage, the Coulomb coupling strength $\Gamma \approx$ 1.4, which implies that according to Manning's theory counterion condensation should take place. However, since Manning’s theory does not take into account the molecular details of real polyion chains, like e.g. local solvation effects or atomic partial charge distributions, CS systems are a borderline case and should be considered more carefully (Bathe 2005). Field-theoretic investigations (Baeurle 2009) have recently demonstrated that the phenomenon of counterion condensation disappears in the limit of infinite dilution in solutions of low concentration of added salt, which is in opposition with the predictions of Manning’s theory but in conformity with Ostwald’s principle. By contrast at physiological salt concentration, the phenomenon has been found to play a predominant role in determining the frictional-compressive properties of articular cartilage (Baeurle 2009).

References

• Manning, G.S. (1969). "Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties". J. Chem. Phys. 51 (3): 924. doi:10.1063/1.1672157. http://jcp.aip.org/jcpsa6/v51/i3/p924_s1?isAuthorized=no. 

• Bathe, M.; Rutledge, G.C.; Grodzinsky, A.J.; Tidor, B. (2005). "A Coarse-Grained Molecular Model for Glycosaminoglycans: Application to Chondroitin, Chondroitin Sulfate, and Hyaluronic Acid". Biophys. J. 88 (6): 3870–87. doi:10.1529/biophysj.104.058800. PMC 1305620. PMID 15805173. http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B94RW-4TT2KH4-K&_user=616165&_coverDate=06%2F30%2F2005&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=0943848e801f071d539a78fbcd86baf7. 

• Baeurle, S.A.; Kiselev, M.G.; Makarova, E.S.; Nogovitsin, E.A. (2009). "Effect of the counterion behavior on the frictional–compressive properties of chondroitin sulfate solutions". Polymer 50 (7): 1805. doi:10.1016/j.polymer.2009.01.066. http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TXW-4VK6NCM-1&_user=616165&_coverDate=03%2F20%2F2009&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_rerunOrigin=scholar.google&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=1f9ec2e3787d41f62c1f90b3d7406e11. 

External links

• Nano- and Bio-Polymer Theory Group