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

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Abstract
The dielectric properties of polyelectrolytesolutions are studied in terms of counterion condensation by measurements of the dielectric response of pH buffered Na polyacrylate solutions.pH values are selected to allow variation of the charge density parameter ξ in the range between 0.5–2.8, that is, across ξ=1, the theoretical critical level for counterion condensation. The dielectric increment of the high frequency dispersion, Δε2, 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 Δε2 (≊6) and its corresponding polarizability α∥2 (≊6×10− 1 6 cm3) are found to be approximately constant with increasing ξ. This result is predicted by Manning’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, L s , is set to 284 Å. This value of L s is also shown to be in relatively close agreement with the value calculated for the length of a rigid subunit in Mandel’s polyion model, obtained using the relaxation time of the high frequency dispersion. The length L s , which is larger than the persistence length, is estimated to be of the order of magnitude of the correlation length between segments.