High frequency dielectric dispersion of polyelectrolyte solutions and its relation to counterion condensation

摘要

The dielectric properties of polyelectrolyte solutions are studied in terms of counterion condensation by measurements of the dielectric response ofpH buffered Na polyacrylate solutions.pH values are selected to allow variation of the charge density parameter xgr; in the range between 0.5ndash;2.8, that is, across xgr;=1, the theoretical critical level for counterion condensation. The dielectric increment of the high frequency dispersion, Dgr;egr;2, is found to have nonzero values only above the counterion condensation threshold and is therefore linked to the occurrence of counterion condensation. Above the condensation threshold Dgr;egr;2(ape;6) and its corresponding polarizability agr;par;2(ape;6times;10minus;16cm3) are found to be approximately constant with increasing xgr;. This result is predicted by Manningrsquo;s polarizability model for condensed counterions which results in a good fit to the experimental data when the average length of the polyion segments parallel to the external field,Ls, is set to 284 Aring;. This value ofLsis also shown to be in relatively close agreement with the value calculated for the length of a rigid subunit in Mandelrsquo;s polyion model, obtained using the relaxation time of the high frequency dispersion. The lengthLs, which is larger than the persistence length, is estimated to be of the order of magnitude of the correlation length between segments.