Highly charged polyelectrolytes

Olvera de la Cruz, M., Belloni, L., Delsanti, M., Dalbiez, J.P., Spalla, O. and Drifford, M. (1995) Precipitation of highly charged polyelectrolyte solutions in the presence of multivalent salts. J. Chem. Phys., 103, 5781-5791. 

H. Schiessel and P. Pincus (1998) Counterion-condensation-induced collapse of highly charged polyelectrolytes. Macromolecules 31, pp. 7953-7959... 

Manning s condensation theory ( 1 ) describes the behavior of small ions around a long, highly charged polyelectrolyte by postulating that there are two populations of counter-ions, one normal, and one "condensed". If we have counter-ions with valence z, the fraction, Fm, of these ions in the condensed population is... 

Tanahatoe JJ, Kuil ME. Dynamic light scattering of a flexible highly charged polyelectrolyte in the dilute concentration regime. Macromolecules 1997 30 6102-6106. 

Essafi W, Lafuma F, Williams CE. Structural evidence of charge renormalization in semi-dilute solutions of highly charged polyelectrolytes. Eur Phys J B 1999 9 261-266. 

The solubility of flexible highly charged polyelectrolytes in the presence of multivalent counterions depends on the affinity between counterions and charged groups of the polyelectrolyte. Two extreme cases can be encountered in the first one the precipitation is induced by the complexation of the polyelectrolyte with the multivalent ions, whereas in the second one the electrostatic attraction is the principal driving force for phase separation. 

Yibnaztiirk S, Deligdz H, Yihnazoglu M, Damyan H, Oksuzomer F, K09 SN, Durmu A, Gtirkaynak A (2010) Self-assembly of highly charged polyelectrolyte complexes with superior proton conductivity and methanol barrier properties for fuel cells. J Power Sources... 

In water at 25° C, the last formula simplifies to k = 0.304/ nm when / is expressed in mole per liter (M). When I =1.0 M, for example, c is about 0.3 nm, and when I = 0.001 M, k is about 10 nm. The largest experimentally obtainable values of K are in the range of tens to hundreds of nanometers, values characteristic of dilute, essentially salt-free polyelectrolyte solutions. For these extreme cases, I is dominated by the bulk concentration of counterions dissociated as the polymer dissolves. How this concentration can be estimated is discussed later for highly charged polyelectrolytes, not all dissociated counterions contribute to I. 

The Debye-Hiickel approximation strictly limits the OSF analysis to f [Pg.6028]

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