On the Calculation of Diffusion Coefficients from Sorption Data

The general equation of diffusion in which the diffusion coefficient D(c) is given by D0(1+αc+βc2+···), where α, β··· are small, can be solved by the method of successive approximation: The solution has the form c(ξ)=c0(1−Φ(ξ))+c02αψ(ξ)+c03[α2χ1(ξ)+βχ2(ξ)]+···,where Φ(ξ) is the error function and ψ(ξ), χ1(ξ)··· may be computed by numerical integrations. On the other hand, one knows from the sorption experiments the quantities defined by Kc0=2D0½∫0∞ c(ξ)dξ as a function of c0. Thus, by the above solution one may obtain a set of linear equations, from which the constants D0, α, β··· can be found with a reasonable amount of labor. For practical purposes it would be necessary to tabulate the functions ψ(ξ), χ1(ξ), ···, because they are needed for all the problems of this kind.