On the Frequency Dependence of the Viscosity of High Polymer Solutions

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Abstract
The ultrasonic shear waves technique introduced by Mason offers the possibility of measuring the viscosity of a liquid in laminar flow at ultrasonic frequencies. A dilute high polymer solution exhibits, besides the usual shear viscosity, a shear elasticity as well for rather low frequencies (of the order of 105). A theory is given for infinitely dilute solutions using as a model for the chain molecule an elastic sphere. This model, which the author has used previously for the theory of flow birefringence, represents the limiting case of complete impermeability. The theory is compared with experimental results of Baker, Mason, and Heiss and of Rouse on polystyrene. The theory gives a good picture of the phenomena as a whole and is particularly successful in describing the apparently anomalous temperature dependence of the elasticity coefficient of polystyrene solutions at high frequencies. The interest of combining results on flow birefringence and on high frequency viscosity measurements is emphasized, as well as the possibilities of the latter technique for determining the molecular elasticity and internal viscosity as a function of frequency. On the basis of preliminary results for a sample of polystyrene of molecular weight 130,000, the tentative conclusion is given that the elastic sphere model will not have a quantitative significance for chains of such a low molecular weight and that it might be necessary to take into account the effect of permeation.

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