The model of Colby et al. predicts the specific conductance (\(\Lambda\)) of a polyelectrolyte solution without added salt to be: \[ \Lambda = f\left[\lambda_C + f\frac{N_A^2 c \xi^2 e^2 \ln(\xi/D)}{3\pi\eta_s}\right] \]
\(D\) is the chain's cross-sectional diameter, \(\eta_s\) is the viscosity of the solvent, \(f\) is the fraction of monomers with a dissociated counterion, and \(e\) is the electrostatic unit of charge. \(\lambda_C\), the limiting ionic mobility of the counterion, is known from the conductivity of simple electrolyte solutions. The correlation length \(\xi\) can be measured by SAXS or SANS.
This spreadsheet calculates the fraction of free counterions for a given electrical conductivity and polymer concentration: Download the Excel spreadsheet.Reference: Colby, R. H.; Boris, D. C.; Krause, W. E.; Tan, J. S. Polyelectrolyte conductivity. Journal of Polymer Science, Part B: Polymer Physics 1997, 35, 2951–2960. DOI.