Polyelectrolytes, association with counterions

The nature of counterions in the vicinity of a flexible polyelectrolyte chain recently was investigated by taking into accounting the various competing factors between the free energy associated with electrostatic interactions... 

The fifth term describes the free energy of a polyelectrolyte chain associated with M dipoles and N-M charges. The chain is in aqueous solution of N-M counterions and salt ions [48]. This free energy is obtained from the Edwards Hamiltonian [49]... 

The number of counterions associated with the tetrahedral junction was less than sensitive not only to parameters that define the junction region, but also to the interbranch angle between 90° and 109.5° [74] The number of associated counterions is substantially larger in the four-way junction than other junction geometries and constructs studied [74]. As salt concentration is increased, the stability of the junction is enhanced over a linear polyelectrolyte molecule of identical length as the junction [74], For junctions with symmetrical branches, the counterions associated with the junction in excess of that of a linear construct increases with the length of the branches and then saturates [74],... 

It should be stressed that such condensation of counterion by polyion is determined just by the structural parameter that defines charge density along the length of the macromolecule. It is not influenced by external condition, such as Cp or the addition of salt. The fact that the colligative properties of salt and polyelectrolyte are found to be additive [32,33] when salt is added to the polyelectrolyte provides insight with respect to the uniqueness of ( )p and y,. Such behavior is attributable to the inaccessibility of the polyion, the condensed Na" " ions and the solvent associated with the polyion domain, to the measurements being carried out. Their presence as a separate phase, however, is not detectable by the counterion activity measurement in the absence of simple salt. 

With regard to counterion binding, some similarities are also observed between ionomer nonaqueous solution and polyelectrolyte aqueous solution. This is the short-range effect due to partial desolvation associated with coun-... 

Insoluble polyelectrolyte complex may be formed when dissolved acidic and basic polyelectrolyte polymers are brought into intimate contact (131). Complex formation is generally agreed to be driven by the increase in entropy associated with the loss of small counterions into the bulk of the solution (132). Polyelectrolyte complex from concentrated solutions of strongly acidic and basic homopolymers has been shown to form sufficiently rapidly to produce a 20-30 nm thick membrane at the solution interface, as was found through reaction of dissolved poly(vinylbenzyl trimethylammonium chloride) with sodium poly (styrene sulfonate) (132). 

Counterion condensation onto polyelectrolytes has heen operationally defined as association such that the total fraction of polyion sites compensated for with counterion remains invariant over a wide range of X values. If the interaction of Na+ with polyelectrolytes is properly described as "counterion condensation", then a plot of f° j (X + l) vs. X should he linear with slope Note that this would indicate that the fraction of sodium ions dissociated from the polyelectrolyte is constant and independent of the concentrations of polyelectrolyte and of simple salt. It is clear that is the fraction of the condensed or hound Na+ ions which are originally on the polyelectrolyte and (l-r) is the charge fraction of the polyelegtrolyte. 

We have shown that surfactants associate with oppositely charged polyelectrolytes preadsorbed onto surfaces having the same charge as the surfactant. The association is, just like in bulk solution, a cooperative process driven by the hydrophobic interaction between the surfactant side chains and made more favorable by the presence of polyelectrolytes acting as counterions to the surfactant aggregates. It is possible to define a critical association... 

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