(605a) Modeling of Oxygen Scavenging Polymer Blends

Oxygen scavenging polymers (OSPs) can be incorporated into thin plastic films to make high performance oxygen barriers used as packaging materials for a variety of items, from food and drugs to consumer electronics. Ideal materials will have both good mechanical properties and barrier properties. Scavenging polymers, such as polybutadiene, typically have poor mechanical properties, and thus are usually employed as blends with polymers such as poly(ethylene terephthalate) and polystyrene. Anticipated increase in the barrier properties of these polymer blends would make complete experimental characterization impractical due to the long time scales involved; a viable barrier material should prevent significant oxygen flux for months or perhaps even years. Therefore, modeling is a key component for understanding these materials and confidently extrapolating limited experimental data for product design purposes.

A multiscale mathematical model describing the transport of oxygen in a blend of OSP particles within an inert polymer matrix is presented. At the particle scale, the reactive consumption of oxygen in each particle is assumed to progress as a moving front, resulting in an oxidized shell around a shrinking reactive core. The rate of reduction of the reactive core radius takes into account the oxygen diffusivity, the rate of oxygen consumption and the scavenging capacity of the polymer. The model assumes that the particles are monodisperse, spherical, small compared to the film thickness, in large enough numbers and uniformly distributed so that the volume average of the particle-scale reaction and transport appears as oxygen consumption in a film scale reaction-diffusion equation coupled to an evolution equation of the average size of the unreacted, shrinking core. The resulting system of non-linear partial differential equations is solved numerically over a wide parameter space, utilizing polymer properties and design parameters relevant to packaging applications.

The transient flux of oxygen through the film and the cumulative oxygen permeate, the kill time and the time lag for the polymer blend are calculated. Three regimes for the oxygen flux are observed. For early times most reactive sites are still present, and an initial flux plateau is observed. For intermediate times, a moving reaction front is found to travel across the film. Finally, for long times when most reactive sites are consumed, the transient flux approaches its steady value. The cumulative oxygen flux, kill time and time lag are presented as functions of OSP loadings, film thickness, oxygen diffusivity and reaction rate. Analytic design equations characterizing the three regimes are developed and presented.