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- Counterion_condensation abstract "The counterion condensation phenomenon is commonly described by Manning’stheory (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, infinitelength 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 , where represents the Bjerrum length and 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 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 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-theoreticinvestigations (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).".
- Counterion_condensation wikiPageExternalLink p924_s1?isAuthorized=no.
- Counterion_condensation wikiPageExternalLink 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.
- Counterion_condensation wikiPageExternalLink 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.
- Counterion_condensation wikiPageID "27657824".
- Counterion_condensation wikiPageRevisionID "596148141".
- Counterion_condensation hasPhotoCollection Counterion_condensation.
- Counterion_condensation subject Category:Polyelectrolytes.
- Counterion_condensation subject Category:Salts.
- Counterion_condensation type Abstraction100002137.
- Counterion_condensation type Chemical114806838.
- Counterion_condensation type Compound114818238.
- Counterion_condensation type Electrolyte114847929.
- Counterion_condensation type Material114580897.
- Counterion_condensation type Matter100020827.
- Counterion_condensation type Mixture114586258.
- Counterion_condensation type Part113809207.
- Counterion_condensation type PhysicalEntity100001930.
- Counterion_condensation type Polyelectrolyte114590441.
- Counterion_condensation type Polyelectrolytes.
- Counterion_condensation type Relation100031921.
- Counterion_condensation type Salt115010703.
- Counterion_condensation type Salts.
- Counterion_condensation type Solution114589223.
- Counterion_condensation type Substance100019613.
- Counterion_condensation comment "The counterion condensation phenomenon is commonly described by Manning’stheory (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.".
- Counterion_condensation label "Counterion condensation".
- Counterion_condensation sameAs m.0c3zdzg.
- Counterion_condensation sameAs Q5176986.
- Counterion_condensation sameAs Q5176986.
- Counterion_condensation sameAs Counterion_condensation.
- Counterion_condensation wasDerivedFrom Counterion_condensation?oldid=596148141.
- Counterion_condensation isPrimaryTopicOf Counterion_condensation.