Modeling of oxygen scavenging polymers and composites
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Polymers films and membranes with immobile and irreversible reactive sites can provide significant barrier properties for packaging materials. There is a need to develop mathematical models to understand the behavior of these reactive materials and to confidently extrapolate experimental data. Due to mechanical and optical requirements, barrier films may consist of composites, such as polymer blends and multilayer films with alternating reactive and inert layers. The reactive term that consumes the mobile species in the governing transport equations for such materials is a function of both the mobile species and the immobilized reactive sites, leading to non-linear partial differential equations that typically have to be solved numerically. Composite structures add to the complexity of the model. For the polymer blend, a multiscale model was developed, incorporating the reactive details within the particle into the bulk transport equation. For the multilayer film, initial conditions and diffusion coefficients were assigned independently for reactive or inert layers. The models developed for the three configurations were solved numerically over a wide parameter space. Three regimes were identified, namely early times characterized by an initial flux plateau, and intermediate regime, and long times, characterized by the time lag. Asymptotic analysis of the homogeneous model was used to develop analytical predictions for the three regimes, obviating the need to numerically solve the model’s non-linear equations. These predictions were generalized to polymer blends. For multilayer films, predictions for early and long times were developed. Results for polymer blends and multilayer composites were compared and discussions of the most suitable configuration for different scenarios were presented. The reactive barrier configurations studied require the knowledge of parameters such as reaction rates and coefficients of diffusion and solubility of the reactive polymer. Model and predictive equations have been developed to describe the transient mass uptake in reactive homogeneous films, enabling the extraction of these parameters from sorption experiments.