Concentration dependence in dye diffusion

Abstract

The adherence of the diffusion of (cationic) dyes in polyacrylonitrile fibers to Fick's law with a constant diffusion coefficient is discussed at the hand of diverse experiments. More specifically, an attempt is made to account for apparently abnormal radial color intensity distributions. There is no evidence for polymer plasticization by the dye. The (linear axial) thermal expansion, glass transition temperature, disorienting shrinkage temperature, and other properties are not appreciably affected by saturating the fiber with dye. The evidence from both sorption and penetration measurements indicate concentration-independent diffusion from a limited number of specific (sulfonate) surface sites. The behavior appears to be so simple that saturation values can be measured from the sorption curves. It is shown that, for diluents with the molecular properties of dyes, a free volume model of dye diffusion predicts the absence of plasticization effects in dyeing systems in general. Replacement of the concentration in the diffusion equation by an activity function, θ/(1 − θ), where θ is the fraction of sites occupied by dye, suggested for the analogous case of anionic dyes on nylon is considered and shown not to be justified on a thermodynamic basis. A similar function can be derived on reasonable kinetic grounds, but is not borne out by the detailed results.