Diffusion of dyes in polyester fibers. II. Diffusion coefficients from the radial distribution curves

The computational method of a concentration-dependent diffusion coefficient D(C) of dyes in fibers has been presented. This method is based on concentration profiles determined with the microphotometric technique and the numerical solution of Fick's second law of diffusion for the cylindrical system. Exploiting the grid method and data of experimental concentration profiles, diffusion coefficients of disperse dye Synthene Scarlet P3GL in the anionically modified polyester fiber have been calculated. The results have been compared with those obtained by the Boltzmann–Matano method. It was stated that (1) in the investigated polymer–dye system the relation between D and C is of the form D(C) = D₀ exp(δC); (2) the allowance for the cylindrical symmetry of the fiber leads to the lower values D(C) in the total concentration range than those obtained by the Boltzmann–Matano method; and (3) values of D₀ calculated with both methods are coincident.