Polyelectrolyte solutions in solvents of extremely high dielectric constant

The physics of polyelectrolyte solutions are of great importance in understanding various processes in nature but they pose a challenge due to their complex behavior. For strong electrolytes discussed here the fraction of the condensed counterions depends on the charge density of polyion, i.e., 1-1/z$\lambda $ where z is the valence of the counterions, and $\lambda $ is the reduced coupling constant defined by .$\lambda =l_{B} /a$Here $a$ is the distance between ions on the polyion and $l_{B}$ is the Bjerrum length $l_{B} =\frac{e^{2}}{4\pi \varepsilon_{0} \varepsilon kT}$ where $e$ is the elementary charge, $\varepsilon $ the dielectric constant of the solvent, $k$~the Boltzmann constant and $T$ absolute temperature. The Bjerrum length is the distance between charged species (counterions, co-ions or charged monomers) when the electrostatic energy between them is equal to the thermal energy k$T$. We exploit the strong temperature dependence of dielectric constant of N-methylformamide to vary the Bjerrum length in a solution of polyelectrolytes (sodium polystyrene sulfonate) and to thus investigate the dynamic properties of salt-free solutions over a broad temperature range, from $+$54 to --58$^{o}$C. Fast and slow diffusion processes are observed. The ratio of diffusion coefficients, $D_{s}$/$D_{f}$ , increases and the ratio of amplitudes $A_{s}$/$A_{f}$ decreases, both by a factor of about two in this temperature range corresponding to the expected temperature variation of the Bjerrum length.