ELECTROKINETIC PHENOMENA
VIII. Surface Conductance of Cellulose and the Theory of Smoluchowski* BY HAROLD A. ABRAMSON
In a recent series of papers dealing with the properties of the cellulosewater interface, Briggsl and Bull and Gortner2 have described excellent methods for the measurement of surface conductance. They have, in addition, published most extensive and interesting reports of the effect of electrolytes on the specific surface conductance, ( K , - K ) , of cellulose diaphragms. Briggs pointed out that electrolytes produced, in general, a continuous increase in the surface conductance but a decrease in the [-potential after a primary small increase. This was apparently completely contrary to the predictions of Smoluchowski8 who postulated a concurrent increase of ( K , - K ) and [. It is the purpose of this communication to reconsider certain data of the authors mentioned above in the light of Smoluchowski's theory and that of Gouy4and of Debye and H U ~ k e l .It ~ will be shown that the general changes of (K. - K ) and 5 are not inconsistent with the theory of Smoluchowski if the thickness of the double layer is considered, but that the theory is incomplete.
Theoretical Consider with Smoluchowskis a cylindrical glass capillary having the property of surface conduction where the radius of the capillary is large compared with, d, the thickness of the double layer. The ratio of the current carried by the surface phase to that of the bulk is,
where{=-
E P
(KJ;
S
=
circumference of capillary; D = dielectric constant;
Q = cross-section; 7 = coefficient of viscosity of the liquid; K = specific conductance of the liquid in bulk; E = streaming potential; P = the pressure difference; K~ = specific conductance of the liquid in the capillary; units are c.g.5. electrostatic. Briggs developed a method for determining the specific conductance of the bulk liquid in cellulose diaphragms so that he- could replace I./I by its equivalent ( K ~- K ) / K , yielding
I n order to compare ( K , - K ) and [ when the concentration of electrolyte is changed, it is necessary to sort out the constants. I n a given cellulose dia'From the Department of Biological Chemistry, College bf Physicians and Surgeons, Columbia University, New York.
2142
HAROLD A. ABRAMSON
phragm with small changes in concentration of salt [ S / Q v ( D / 4 ~ ) 2 can ] be taken as approximately constant, but and d are variables. The theory of Smoluchowski as here considered postulates that
