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	~~I am 32 years old~~ and ~~my name~~ is ~~Isidro Rymill~~. ~~I life~~ in ~~Saint-Medard-En-Jalles~~ (~~France~~).<br><br>~~Here~~ is ~~my blog post~~: [http://www.~~supershootergames~~.com/~~profile~~/~~motalbot Cannondale mountain bike sizing~~.]		{{Orphan\|date=September 2013}}

			The '''counterion condensation''' phenomenon is commonly described by Manning’s
			theory (Manning 1969), which assumes that [[counterion]]s 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 equation\|Debye–Hückel]] (DH) approximation. The
			phenomenon of counterion condensation now takes place when the dimensionless
			Coulomb coupling strength
			:<math>\Gamma = \lambda_B/l_{charge} > 1</math>,
			where <math>\lambda_B</math> represents the [[Bjerrum length]] and
			<math>l_{charge}</math> the distance between neighboring charged [[monomer]]s.
			In this case the [[The Coulomb potential\|Coulomb interactions]] dominate over
			the thermal interactions and counterion condensation is favored. For many standard
			[[polyelelctrolyte\|polyelectrolytes]], this phenomenon is relevant, since the
			distance between neighboring monomer charges typically ranges between 2 and 3 Å and
			<math>\lambda_B \approx</math> 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 <math>\Gamma \approx</math>
			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 ==
			* {{cite journal
			\|doi = 10.1063/1.1672157
			\|url = http://jcp.aip.org/jcpsa6/v51/i3/p924_s1?isAuthorized=no
			\|last = Manning
			\|first = G.S.
			\|title = Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties
			\|journal = J. Chem. Phys.
			\|volume =51
			\|pages = 924
			\|year = 1969
			\|issue = 3}}

			* {{cite journal
			\|url = 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
			\|last = Bathe
			\|first = M.
			\|coauthors = Rutledge, G.C.; Grodzinsky, A.J.; Tidor, B.
			\|title = A Coarse-Grained Molecular Model for Glycosaminoglycans: Application to Chondroitin, Chondroitin Sulfate, and Hyaluronic Acid
			\|journal = Biophys. J.
			\|volume = 88
			\|issue = 6
			\|pages = 3870–87
			\|year = 2005
			\|pmid = 15805173
			\|pmc = 1305620
			\|doi = 10.1529/biophysj.104.058800}}

			* {{cite journal
			\|url = 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
			\|last = Baeurle
			\|first = S.A.
			\|coauthors = Kiselev, M.G.; Makarova, E.S.; Nogovitsin, E.A.
			\|title = Effect of the counterion behavior on the frictional–compressive properties of chondroitin sulfate solutions
			\|journal = Polymer
			\|volume = 50
			\|pages = 1805
			\|year = 2009
			\|doi = 10.1016/j.polymer.2009.01.066
			\|issue = 7}}

			[[Category:Polyelectrolytes]]
			[[Category:Salts]]


			{{Chemistry-stub}}

en>Crookesmoor: /* Flood Estimation Handbook */

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I am 32 years old and my name is Isidro Rymill. I life in Saint-Medard-En-Jalles (France).<br><br>Here is my blog post: [http://www.supershootergames.com/profile/motalbot Cannondale mountain bike sizing.]

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