Calculation of membrane pressure for a sol of spherical particles

Abstract

Electronic computation has been used to obtain the Poisson-Boltzmann distribution of counter ions between an outer spherical surface, radius R 0, where the potential gradient is zero, and an inner concentric surface, radius R, representing a uniformly charged spherical particle. Here c 0 is the concentration of the counter ions at the outer surface, and c m is their mean concentration in the volume between the two surfaces. The results of the computations are given in a plot of c 0 c m against ln R R 0 . For given values of R and R 0, c 0 at first increases linearly with the number of counter ions per particle, but ultimately approaches a limit. Values of the membrane potential, p 0, are calculated from the equation P 0 = NkT( c 0 + C)/1000 for 1% and 0.1% sols of particles 10 −6 cm. in radius.