Migration of antioxidants from polylactic acid films, a parameter estimation approach: Part I - A model including convective mass transfer coefficient

Abstract

A two-step solution based on the boundary conditions of Crank's equations for mass transfer in a film was developed. Three driving factors, the diffusion (D), partition (K_p,f) and convective mass transfer coefficients (h), govern the sorption and/or desorption kinetics of migrants from polymer films. These three parameters were simultaneously estimated. They provide in-depth insight into the physics of a migration process. The first step was used to find the combination of D, K_p,f and h that minimized the sums of squared errors (SSE) between the predicted and actual results. In step 2, an ordinary least square (OLS) estimation was performed by using the proposed analytical solution containing D, K_p,f and h. Three selected migration studies of PLA/antioxidant-based films were used to demonstrate the use of this two-step solution. Additional parameter estimation approaches such as sequential and bootstrap were also performed to acquire a better knowledge about the kinetics of migration. The proposed model successfully provided the initial guesses for D, K_p,f and h. The h value was determined without performing a specific experiment for it. By determining h together with D, under or overestimation issues pertaining to a migration process can be avoided since these two parameters are correlated.

Keywords: Convective mass transfer coefficient; Diffusion coefficient; Ordinary least square estimation; Partition coefficient.