Counterion condensation determination

This property of P, derived within the framework of PB theory, can in turn be used to define the condensed fraction [4], It provides a suitable way to quantify counterion condensation beyond the scope of PB theory, and it is exact in the salt-free PB limit. From here on this method will be referred to as the inflection point criterion. This criterion has the advantages of (1) not fixing by definition the amount of condensed counterions (fe and RM can be determined independently of each other), (2) reproducing the salt-free PB limit, namely P(RM) = 1 l/ , and (3) quantifying the breakdown... 

NMR spectroscopy is a most effective and significant method for observing the structure and dynamics of polymer complexes both in solution and in the solid state. The widest application of NMR spectroscopy is in the field of structure determination. The identification of certain atoms or groups in a molecule as well as their position relative to each other can be obtained by one-, two-, and three-dimensional NMR. Information about the local dynamics, molecular and supramolecular organization, and the counterion condensation can be obtained. The counterion condensation and polyelectrolyte complexation between TEAC in poly(acrylic acid) was studied by Ni using C NMR. 

Prediction from Counterion Condensation Alone. Katchalsl s theory does not consider counterion condensation. The question then is how important is the counterion condensation in determining the salt partitioning Can the counterion condensation alone account for all the non-ideality of the Donnan equilibrium To examine this problem, we will calculate the salt absorption by only considering the counterion condensation from both linear and nonlinear counterion condensation theories and compare the predictions with experimental results. 

The above equation elucidates that the longer the chain length, then the lower is the elastic force. In other words, a compression of the corona is the easier possible the longer the stabilizing chain. If the stabilizer is a long polyelectrolyte chain, the osmotic force (Posm) is determined mainly by counterion condensation and can be expressed in the form of the following equation (54) ... 

Manning determined values of fc and Ap for a line charge model with counterion condensation (18). Above fc. 

The properties of polyelectrolyte solutions depend strongly on the interactions between the polymers and the surrounding counterions. Manning s theory of counterion condensation predicts that a certain quantity of counterions condenses onto a polymer, whose charge density exceeds a critical value [44]. This leads to an effective decrease in the polymer charge. The macroscopic properties of the polyelectrolyte are not determined by its bare charge but by an effective charge. In particular, the flexibility and hydrophobicity of the polyelectrolyte chain, the... 

The high proportion of counterionic condensation in PE-dmg aqueous dispersions determines many of the particular properties of these systems such as the effects of addition of electrolytes and non-electrolytes, the kinetic of drug release under different conditions, the raise of compatibihty of low solubility drugs, the improvement of chemical stability and the rheological behavior. 

The degree of counterion condensation k at infinite dilution in water is determined from experimental data for the osmotic coefficient at infinite dilution (as... 

M. O. Fenley, W. K. Olson, and G. S. Manning, Macromolecules, 33, 1899 (2001). Dependence of Counterion Binding on DNA Shape as Determined by Counterion Condensation Theory. 

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