Counterion condensation
Encyclopedia
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
,
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-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).
theory (Manning 1969), which assumes that counterions
Counterion
A counterion is the ion that accompanies an ionic species in order to maintain electric neutrality. In table salt the sodium cation is the counterion for the chlorine anion and vice versa.In a charged transition metal complex, a simple A counterion is the ion that accompanies an ionic species in...
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
,where
represents the Bjerrum lengthBjerrum length
The Bjerrum length is the separation at which the electrostatic interaction between twoelementary charges is comparable in magnitude to the thermal energy scale,...
and
the distance between neighboring charged monomersMonomer
A monomer is an atom or a small molecule that may bind chemically to other monomers to form a polymer; the term "monomeric protein" may also be used to describe one of the proteins making up a multiprotein complex...
.
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
Chondroitin sulfate
Chondroitin sulfate is a sulfated glycosaminoglycan composed of a chain of alternating sugars . It is usually found attached to proteins as part of a proteoglycan. A chondroitin chain can have over 100 individual sugars, each of which can be sulfated in variable positions and quantities...
(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-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).