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We quantified the Manning free (uncondensed) counterions fraction $\theta$for dilute solutions of rod-like polyions - 150bp DNA fragments, in very lowsalt $<0.05$mM. Conductivity measurements of aqueous DNA solutions in theconcentration range $0.015\leq c \leq 8$~mM (bp) were complemented byfluorescence correlation spectroscopy (FCS) measurements of the DNA polyiondiffusion coefficient $D_p(c)$. We observed a crossover in the normalizedconductivity $\sigma(c)/c$ which nearly halved across $c=0.05-1$ mM range,while $D_p(c)$ remained rather constant, as we established by FCS. Analyzingthese data we extracted $\theta(c)=0.30 - 0.45$, and taking the Manningasymmetry field effect on polyelectrolyte conductivity into account we got$\theta(c)=0.40-0.60$. We relate the $\theta(c)$ variation to gradual DNAdenaturation occuring, in the very low salt environment, with the decrease inDNA concentration itself. The extremes of the experimental $\theta(c)$ rangeoccur towards the highest, above 1 mM and the lowest, below 0.05 mM, DNAconcentrations, and correspond to the theoretical $\theta$ values for dsDNA andssDNA, respectively. Therefore, we confirmed Manning condensation andconductivity models to be valuable in description of dilute solutions ofrod-like polyions.

Manning free counterions fraction for a rod-like polyion - short DNA fragments in very low salt