Analytic formulae for the design of reactive polymer blend barrier materials

Reactive particles that scavenge an undesirable permeate can be incorporated into thin plastic films to make high performance composite barriers used as packaging materials. A multiscale model is presented with analytic solutions to the resulting equations to describe blends of non-spherical particles in the limiting cases of fast and slow reaction rates. These analytic design formulae include predictions for the permeate flux, time lag and kill time. In particular a quasi-steady permeate flux is quantified, which is observed at early times when most reactive sites are still available. This flux can lead to significant leakage of the mobile species well before the time lag, and it is proposed as a critical figure of merit for the design of reactive barrier materials. The equation for the quasi-steady flux is valid for reactive particles of any shape and requires only knowledge of average area to volume ratio for the particles within the blend in the limit of fast reactions. The time lag is also shown to be valid for any polymer blends, irrespective of particle geometry, aspect ratio or reaction mechanism within the particle. The ranges of validity of the design formulae are found to be broad based on comparisons with numerical solutions of the model.