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The Preparation of Bipolar Ion-exchange Membranes 435 consequence in that it provides a simple method for obtaining accurately the zero shear viscosity. Straight line extrapolation of the raw viscosity data, obtained from a low shear viscometer of the type described above, provides (i?ap/c)o directly. Finally, plotting the zero shear reduced viscosity against the concentration results in the zero shear intrinsic viscosity, Mo. On the other hand, making measurements over a fairly wide range of shear rates leads to a curved viscosity-shear plot which involves considerable uncertainty in extrapolation. In a previous paper,2 it was shown that a modified Katchalsky equation could be used to give the zero shear value accurately, but it is now possible to dispense with this somewhat indirect approach and merely extrapolate the data obtained over a restricted range of low shear rates.An attempt to fit the shear data to an equation proposed recently by Bueche8 is shown in Fig. 4. The agreement is quite good for shear rates up to about 12,000 sec.-1 beyond which point the Bueche curve falls steadily below the experimental points. Inasmuch as his theoretical equation (number 8, ref. 7) was derived by dropping terms which become important only at large shear rates, it appears that the Bueche equation, when modified to incorporate some of these terms, may fit the data quite well even up to about 20,000 sec.-1. The equation needs to take into account the ultimate asymptotic levelling-off of the viscosity at very high gradients.Furthermore, because the gradient enters to the one-half power in the equation at low shear rates, it implies a virtually infinite slope of the viscosityshear curve at the ordinate, which, of course, is not realized experimentally. Nevertheless, the Bueche equation is perhaps the most successful theoretical relation proposed to date connecting the viscosity and the rate of shear.Any new theoretical equation designed to express the shear dependence of viscosity should be able to account for the following experimental facts. The viscosity reaches an asymptotic limit at some finite value of the gradient. The difference between the initial and final values of the intrinsic viscosity is proportional to the square of the zero shear intrinsic viscosity, for various molecular weight fractions of a given polymer. The limiting slope of the viscosity-shear plot close to the origin is finite and proportional to the square of the zero shear viscosity.Acknowledgments.-This work was carried out under the sponsorship of the Federal Facilities Corporation, Office of Synthetic Rubber, in connection with the Government Synthetic Rubber Program. The author is much indebted to Hugh E. Diem of these laboratories who kindly supplied the Alfin polyisoprene, and to Mrs. Marilyn E. Gordon for her assistance with the experimental work. It is a pleasure to acknowledge also helpful discussions with R. A. Harrington of the Physical Research Department.

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