Inverted forces in counterion condensation theory

J. Ray and G. S. Manning, in Physical Chemistry of Polyelectrolytes, T. Radeva, Ed., Marcel Dekker, New York, 2001, pp. 111-133. Inverted Forces in Counterion Condensation Theory. 

A recent attempt to extend the scope of counterion condensation theory to the calculation of counterion-polyion, coion-polyion, and polyion-polyion pair potentials retains structural idealization but may nonetheless be capable of generating useful new information about the real molecular structure of polyelectrolyte solutions [57-59], The validity of the first and second stages of the theory, as discussed above, has been heavily documented, including the physical reality of the condensed layer and the onset of condensation at a critical charge density [55,56,60,61], In contrast, the inverted forces predicted by our extended theory have yet to be confirmed by experiment or simulation. We will argue, however, that their presence is at least suggested by current experimental knowledge. 

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