Low- and high-frequency relaxations in linear polyelectrolyte solutions with different counter-ion species

Abstract

We have studied the low- and high-frequency relaxations in polystyrene sulfonate solutions with different counter-ion species [X +=H +, Li +, Na +, K +, (C 4H 9) 4N +], from the frequency-domain electric birefringence (FEB) and the dielectric relaxation spectroscopies. The high-frequency (HF) relaxation frequency f H is proportional to the free intrinsic mobility, μ 0, of the counter-ion, whereas the low-frequency (LF) relaxation frequency f L is not proportional to μ 0. These different dependencies of f L and f H on the counter-ion species, support the notion that the LF relaxation arises from the fluctuation of counter-ions tightly bound in the vicinity of a poly-ion, in the direction parallel to the poly-ion long axis, and that the HF relaxation arises from the motion of counter-ions loosely bound away from the poly-ion in the direction perpendicular to the poly-ion axis.