The diffusion of colloidal electrolytes and other charged colloids

Abstract

Measurements of the diffusion of colloidal substances have frequently been used as a method for determining their particle size. The well-known Stokes-Einstein equation has generally been considered to give the relationship between the quantities. The influence of electrical forces in making the Stokes-Einstein equation inapplicable seems to have been almost generally neglected. Thus a considerable amount of work has been done on the diffusion of dyes and conclusions drawn using this equation about the particle size which, as shown in this paper, are quite unjustified. From such work a theory of dyeing with cotton substantive dyes has been built up. Freundlich in his text book points out that since dyes are electrolytes, the Nernst relation between the diffusion constant and the mobilities of the two ions composing the electrolyte, 1/D = 1/2RT (1/U + 1/V), (1) must be taken into account. He then adds, “We can, however, conclude from these measurements at what size of particle, at what value of diffusion constant therefore, a dissolved substance begins to behave like a colloid.” He does not, however, point out that this equation only applies to uni-univalent electrolytes. When the extended equation for multivalent electrolytes is used, then, as will be shown later, one cannot conclude even qualitatively what the particle size is. With the exception of Svedberg and Tiselius, who take the electrical forces into consideration in the case of sedimentation equilibrium, previous writers seem for the most part to have entirely neglected the matter. Thus the question is not dealt with at all in the 60 pages devoted to diffusion in von Hahn’s “Dispersoidanalyse.” Freundlich ( loc. cit. ) goes so far as to say, “Perhaps no method is more fruitful for the investigation of lyophilic sols than the measurement of diffusion . . . the only difficulty is that the measurements are tedious.” But, as we will explain, the electrical forces may also play a part in the diffusion of charged colloids not usually considered as “colloidal electrolytes” and give rise to unexpectedly high diffusion velocities. Since the time of Thomas Graham, low diffusion has been considered a characteristic of a colloid, and the possibility of a substance of several thousand “particle weight” having a diffusion coefficient of the same order as that of, for example, copper sulphate does not seem to have been realised. In this respect the recent striking experiments of Bruins on the diffusion of starch and gum arabic, as well as measurements of diffusion coefficients of dyes by one of us (C. R.), are of consideable interest.