Counterion Activity of Highly Charged Strong Polyelectrolytes

Abstract

Comprehensive counterion activity studies have revealed clear influence of the polyelectrolyte concentration and chain length on the polyion-counterion interaction, neither of which is evident from the existing theoretical models. The counterion activity coefficient (f a) increases below the overlap concentration c* as calculated from Odijk's scaling approach. At dilutions where the Debye length (lD) exceeds the contour length (L), this increase is more pronounced. It is concluded that these changes in the ionic interactions are primarily responsible for the strong increase of the equivalent conductivity (Λ) below c*. The findings are not restricted to oligomers but apply to all chain lengths of polyelectrolytes at concentrations less than c*. The correlation of fa and Λ with both c* and the ratio lD/L leads to a general description of polyelectrolyte behavior. Experiments were performed above and below c* and over the range 0.1 e lD/L e 10 using a series of poly(vinylbenzyltrialkylammonium) model polyelectrolytes with contour lengths over a range 7 nm e L e 102 nm and characterized by a charge density parameter ) 2.85.

Collapse of polyelectrolyte brushes: Scaling theory and simulations

“…The main finding was that the leading term indeed is the standard Debye-Hückel term for a simple salt solution with correction terms due to polymer connectivity, which shows that neglecting the polymer connectivity can be interpreted as a zeroth-order approximation. On the other hand, the activity coefficient of polyelectrolyte solutions has been determined experimentally both in the high-concentration [35] and in the low-concentration range [36], and the basic features do not differ qualitatively from the simple-salt case. We therefore argue that the leading Debye-Hückel term (as employed by us) in conjunction with the second viral term should give a qualitatively correct phenomenological description of the polyelectrolyte solution free energy.…”

Transport properties of some cationic polysaccharides

“…These interactions are strongly sensitive to some parameters such as the chain length, the charge density, the polyelectrolyte concentration, the counterion type, the ionic strength, the solvent polarity, etc. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Perhaps the most significant parameter affecting the solution properties of a polyelectrolyte is the linear charge density whose importance has been promoted by Manning in his counterion condensation theory [24,25].…”

Polyelectrolyte Complex Nanoparticles of Poly(ethyleneimine) and Poly(acrylic acid): Preparation and Applications

“…As an explanation of the increasing PEC particle size with increasing c PEL , we assume an influence of the Debye length, which is a measure of electrostatic reach. As was pointed out by Wandrey [31], not only increasing salt but also PEL concentration decreases the Debye length of a PEL system. Hence, based on the model of aggregation of primary PEC to secondary PEC particles due to short range dispersive interactions, we suggest that increasing c PEL results in the reduced electrostatic repulsion between like charged primary PEC particles and thus in their elevated dispersive attraction.…”