SynopsisThe theoretical equations which described the concentration profile of immobilized species of reactive dyes in the substrate were derived from the diffusion equation with the chemical reaction of first-order or pseudofirst-order. The theoretical profiles in the substrate described by the equations were discussed. The larger the diffusion coefficient D of active species and the smaller the reaction rate constant h , the deeper is the penetration of the immobilized and active species of reactive dyes into the substrate. The method of estimating D and k from the diffusion profiles of both species obtained by means of the method of the cylindrical cellophane film roll was described.The diffusion coefficients of the hydrolyzed species of C.I. Reactive Orange 1 and Red 1 were nearly constant in all the pH values examined. The concentration profiles of both the species of Orange 1 at pH 8.8 were identical with the theoretical ones; while the profiles of immobilized species of Red 1 at pH 10 and of Orange 1 a t pH 12 agreed with the theoretical ones and those of active species did not because of the hydrolysis. The diffusion coefficients of active species of these dyes a t these pH ranges were smaller than those of the hydrolyzed species.

SynopsisTheoretical equations that describe the concentration profiles of immobilized and active species for reactive dyes were derived from the diffusion equation accompanied by the reaction with cellulose and water in the substrate. The diffusion coefficient D and the rate constant of the reaction with cellulose, kcell, and that with water in cellulose, k,, were estimated by using the theoretical equations and the cylindrical film roll method. The theory predicted that the apparent diffusion coefficients decreased with the hydrolysis of active species in cellulose. Results from diffusion experiments with C.I. Reactive Yellow 4 and Orange 1 show that the ratio P of k , to kcell for Orange 1 increased with increase in pH to about pH 13 and that the P for Yellow 4 was smaller than unity. Using an alternative experiment to diffusion, P of Orange 1 was measured to be 1.0-1.5, and that of Yellow 4 was smaller than unity at pH 11.6 at 3OOC. It was therefore concluded that the D of active species was constant to a highly alkaline region and that the decrease in the apparent diffusion coefficient of Orange 1 was mainly due to the hydrolysis of active species in cellulose.

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