Application of an equation derived from the solution of diffusion equation with constant surface concentration to the film-roll method

Abstract

In this study, an equation to obtain reliable diffusion coefficients for the sublimation diffusion of disperse dye in paste into polyethylene terephthalate film using the film-roll method was derived from the solution of the diffusion equation with the constant surface concentration. The constant surface concentration in the equation, where the total amount of dye passed through the first-layer surface is a linear function of the square root of time, was obtained by the steady-state straight line for a sufficiently long heat treatment time. The diffusion coefficients were obtained by the constant surface concentration and the slope of the linear regression line for the plot of the total amount against the square root of time. Their reliability was proved by the good linearity of linear regression for the Arrhenius plot. The activation energy for the diffusion coefficients obtained by this equation was similar to that obtained by another equation derived from the solution with the time-varying second-layer surface concentration. The diffusion coefficients for data containing $\left(0\text{,}0\right)$ in the plot of the total amount against the square root of time were judged to be more reliable than those for data not containing $\left(0\text{,}0\right)$ .