Determination of kinetic parameters for reactive dyeing from concentration profiles. I Theory and calculation method.

Abstract

The reaction/diffusion behavior of active species of reactive dyes in cellulose was assumed to be described by a diffusion equation accompanied by the pseudofirst-order chemical reaction with cellulose and water in cellulose. Applying the diffusion equation to the reactive dyeing system of cellulose, a method of least mean squares for finding the fittest values of the constant diffusion coefficient, D, the rate constants, kc and kw, of the reaction with cellulose and water in cellulose, the surface concentration, Co, of the active species of a reactive dye from the concentration profiles of the active and fixed species, which were obtained by using the cylindrical film roll method, was presented. The initial value of D was estimated by the diffusion from the neutral dyebath, that of Co by the extrapolation of the profile of active species to the surface and that of kc, was calculated from the surface concentration of fixed and active species. Using these initial values and minimizing the variance defined by the weighted residual sum of squares between the experimental and theoretical concentrations for each layer, the fittest values of parameters were calculated. There are some strong interactions between parameters, especially between D and kw or Co and kc, depending on the value of kc and time. The value of kw is difficult to be determined due to the insensibility to the concentration profiles and the interaction with D. A method for testing the validity of model with the variance was also presented.