Making use of results pertaining to Painlevé III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limi...

We present a new theory of rodlike polyelectrolyte solutions. It is found that at low densities, and below teInperature T~i, the counterions associate with the polyions forIning clusters consisting of one polyion and n counterions. The distribution of du8ters sizes is Gaussian, leading to strong logarithmic corrections to the liIniting laws obtained by Manning. In the Inathelnatical limit of in...

According to a theorem of Jordan and Manning (cf [26; 13.10]), if G is a primitive permutation group of degree n =qp + k with q small and p a prime and if G contains an element of order p and degree qp but does not contain the alternating group An, then k is bounded in terms of q. In [24] we shall show that the bound can be improved in some special cases. On the other hand, if q = 4 then the Ma...

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in the presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick, an...