New insight into isothermal frontal polymerization models: Wiener's method to determine the diffusion coefficients for high molecular-weight poly(methyl methacrylate) with neat methyl methacrylate

We used Wiener's method (a laser sheet deflection technique abbreviated LLD) to determine how well LLD (laser line deflection) could detect different diffusive layers within a glassy polymer system of poly(methyl methacrylate) with its own monomer of methyl methacrylate. LLD showed distinct boundaries that defined the layers that existed within the swelling/diffusing system, i.e. pure polymer, penetrated polymer, and swollen layer as identified and defined by Ueberreiter in the 1960s. Analysis of the LLD images showed that for early times within the diffusion that the layers between the pure, unpenetrated polymer and the pure monomer possessed a continuous refractive-index gradient, and thus, these layers formed one continuous layer, the “swollen layer”. The width of this swollen layer widened over time, and its widening was halted by the appearance of a second swollen layer formed from the pure polymer underneath the first swollen layer. Using the boundary positions of the swollen layer over time, we determined the solvent penetration velocity and the induction period, and we used these two parameters to calculate the average mutual diffusion coefficient (D¯). In addition, we studied the diffusion at three different temperatures to determine if the diffusion coefficients had a measurable temperature dependence. This paper also discusses how LLD relates to other techniques that have been used to monitor glassy polymer diffusion.