Calculating Water Diffusion Rates in Hygroscopic Polymers during Desiccant Drying
Calculate water diffusion in hygroscopic polymers using Crank's spherical solution with Arrhenius-derived diffusivity to establish minimum hopper drying times.
Dual-Mode Sorption
Meaning
Mathematical models of gas penetrant concentration in glassy polymers divide the total population of dissolved molecules into two distinct populations that occupy different molecular environments. This division defines dual-mode sorption, which describes how gas molecules dissolved in a glassy plastic exist partly in a mobile dissolved state and partly trapped within microvoids. It establishes the limits of gas barrier performance in extruded packaging films.
The model applies only below the glass transition temperature of the polymer.
Transport Mechanism
Dissolution of gas follows a linear relationship at low pressures while the filling of microvoids follows a non-linear path. Under dual-mode sorption, gas molecules migrate freely or remain trapped.
Polymer Structure
Glassy matrices contain unrelaxed free volume created during rapid cooling below the glass transition temperature during film extrusion. These unrelaxed spaces act as microvoids that capture penetrant molecules and slow down their diffusion. In semi-crystalline polymers, the crystalline regions remain impermeable, which forces the gas to navigate the amorphous regions where these microvoids exist.
Processing Consequence
Molders and film extruders find that rapid quenching increases the concentration of unrelaxed free volume, which alters the gas permeability of the final part. If the cooling rate of the polymer melt varies, the barrier properties of the moulded containers fluctuate during subsequent shelf life. This variability increases costs for packaging manufacturers who must maintain consistent gas retention.