Quantifying the Effect of Multivalent Ions in Polyelectrolyte Solutions

We apply a recently developed scaling approach utilizing the concentration dependence of the specific viscosity of polymer solutions to quantify the properties of carboxymethyl cellulose and polystyrene sulfonate solutions with mono- and divalent counterions. This approach is based on the relationship between the correlation blob size ξ=lg^ν/B and the number of repeat units per blob, g, with projection length l. The B-parameters are acquired for each value of the exponent ν using the dependence of g on the repeat unit concentration c, g~c^1/(1-3ν), and the specific viscosity in the unentangled regime, η_sp=N_w/g, where N_w is the weight-average degree of polymerization. This analysis indicates that, for polyelectrolytes with divalent counterions, the excluded volume is halved and the Kuhn length is increased by less than 10%. We also use the B-parameters to estimate the fraction f ^* of free counterions outside the electrostatic blobs and find that for both mono- and divalent systems, f ^*<12%. Combined, these effects promote a reduction in chain stretching, a larger number of repeat units per correlation blob, and a broader unentangled concentration regime in solutions with divalent ions.