Diffusion coefficient for diffusion of time-varying surface concentration by the film-roll method

Abstract

This research on the sublimation diffusion of disperse dye in print paste to polyethylene terephthalate film was performed at 170–190°C for various times using a film-roll method. It was found that the second layer surface concentrations obtained from the concentration–distance curves were proportional to the square root of time. To determine the diffusion coefficient for the diffusion of the time-varying surface concentrations, the solution of the diffusion equation for the boundary condition of the surface concentration varying with the square root of time was deduced by applying the Laplace transform. Assuming that the time taken for a dye in paste to pass through the first layer is the delay time and the second layer surface is the starting point for diffusion, the diffusion coefficient and the delay time were determined by the proportional constant obtained from the plot of the second layer surface concentrations against the square root of the total time and by the total amount which is the amount that has passed through the second layer surface and is a primary function of time. The diffusion coefficients for the total time were similar to those for the diffusion time excluding the delay time, and their reliability was identified by Arrhenius plots. The activation energy for the diffusion coefficients obtained from the equation deduced by the complementary error function in this study was similar to that for the diffusion coefficients obtained by the complementary error function in three recent studies by about 27 kcal · mol⁻¹.