Ultrasonic study of the kinetics of counterion site binding in aqueous solutions of polyelectrolytes

The excess ultrasonic absorption due to counterion binding has been studied as a function of frequency for a series of polysalts in the range 1-150 MHz. All the relaxation spectra can be represented by a relaxation equation with two relaxation terms. The relaxation frequencies appear concentration independent and the relaxation amplitudes seem proportional to concentration. The low frequency relaxation process appears to depend mainly on the nature of the counterion while the high frequency relaxation process seems to be mostly dependent on the nature of the polyion. These results are quite similar to those obtained in ultrasonic studies of ion-pairing in solutions of divalent sulfates. The kinetic model used for the quantitative analysis of these results has been modified for polysalts through introducing the concept of"counterion condensation". In this modified model the excess absorption is assigned to the perturbation by the ultrasonic waves of the equilibria between the three states of hydration of ths complex formed by a counterion and that part of the polyion where it is bound. Analytical expressions of the relaxation amplitudes have been derived using classical procedures for this modified kinetic model. In the case of cobalt-polyphosphate (Co-PP), the ultrasonic data together with the results of NMR measurements on either Co(2+) or Co-PP have been used for the evaluation of the volume changes, the rate constants and the fractions of counterions in the three states of hydration involved in the binding equilibria. The volume changes obtained in this manner depend only slightly on the method of calculation and appear to be consistent with volume changes for outer-sphere and inner-sphere complex formation. These results are discussed.