Counter ion condensation

The phenomenon of counterion condensation is generally described by Manning's theory (Manning 1969), in which it is assumed that counterions can condense on polyelectrolytes until the charge density between adjacent monomer charges along the polyion chain has fallen below a certain critical value. In the model, the real polyion chain is replaced by an idealized line charge, the polyion being represented by a uniformly charged thread with a radius of zero, an infinite length and a finite charge density, and it is assumed that the condensed counterion layer is in physical equilibrium with the ionic one Atmosphere surrounding the polyion is. The uncondensed mobile ions in the ion atmosphere are treated in the Debye-Hückel approximation . The phenomenon of counter ion condensation occurs when the dimensionless Coulomb coupling strength

${\displaystyle \Gamma ={\frac {\lambda _{\mathrm {B} }}{l_{\mathrm {Ladung} }}}>1}$ is

where stands for Bjerrum's length and is the distance between adjacent charged monomers . ${\displaystyle \lambda _{\mathrm {B} }}$ ${\displaystyle l_{\mathrm {Ladung} }}$

In this case, the Coulomb interactions dominate over the thermal interactions, and counterion condensation is preferred. This phenomenon is relevant for many standard polyelectrolytes since the distance between adjacent monomer charges is typically between 2 and 3 Å and is in water. ${\displaystyle \lambda _{\mathrm {B} }\approx 7\,\mathrm {\AA} }$

Manning theory states that the proportion of counterions within the Manning radius condenses around the rod charge. In the Limes of infinite dilution, the manning radius diverges. ${\displaystyle 1-1/\Gamma }$ ${\displaystyle R_{M}}$

Mannan's theory of a charged rod neglects the molecular details of real polyion chains, such as local solvation effects or atomic partial charge distributions

criticism

The counterion condensation originally only describes the behavior of a charged rod. It competes here with the Poisson-Boltzmann equation , which gives less artificial results than the counter-ion condensation theories.

literature

• Korinna Krohne: Topologically controlled interpolyelectrolyte complexes made of rigid polyelectrolytes: influence of polycation, solvent and proton equilibrium . Dissertation 2011. ( d-nb.info ).
• Steffen Traser: Counterion activity in new rod-shaped and flexible, branched polyelectrolytes of variable charge density . Dissertation 2005. Technical University, Darmstadt 2005 ( tu-darmstadt.de [PDF]).
• Martin Franz: The effective charge of a polyelectrolyte as a function of the polymer concentration and ionic strength . Dissertation 2014. Mainz University Library, Mainz 2014 ( uni-mainz.de [PDF]).

Individual evidence

1. ↑ Gerald S. Manning: Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties . In: The Journal of Chemical Physics . tape 51 , no. 3 , August 1, 1969, p. 924-933 , doi : 10.1063 / 1.1672157 .
2. ^ Per Lyngs Hansen, Rudi Podgornik, V. Adrian Parsegian: Osmotic properties of DNA: Critical evaluation of counterion condensation theory . In: Physical Review E . tape 64 , no. 2 , July 23, 2001, ISSN  1063-651X , doi : 10.1103 / physreve.64.021907 .
3. ↑ D. Stierter: Evaluation of the counterion condensation theory of polyelectrolytes . In: Biophysical Journal . 69, No. 2, August 1995, ISSN  0006-3495 , pp. 380-388. doi : 10.1016 / S0006-3495 (95) 79910-6 . PMID 8527651 . PMC 1236262 (free full text).