Plasticization effects on bubble growth during polymer foaming

During polymer foaming with physical blowing agents, plasticization affects the melt viscosity, gas diffusivity in the melt, and the gas-melt interfacial tension. In this paper, we propose a model for plasticization during bubble growth, and estimate its effects under typical foaming conditions. The theoretical model incorporates well-established mixture theories into a recent model for diffusion-induced bubble growth. These include the free-volume theories for the viscosity and diffusivity in polymer-blowing agent mixtures and the density gradient theory for the interfacial tension. The viscoelasticity of the melt is represented by an Oldroyd-B constitutive equation. We study the radial growth of a single bubble in an infinite expanse of melt, using parameter values based on experiments on polystyrene-CO2 systems. Our results show that even at relatively low gas concentrations, plasticization increases the blowing-agent diffusivity markedly and thus boosts the rate of bubble growth. In contrast, the reduction in melt viscosity and interfacial tension has little effect on bubble growth. Though not intended as quantitative guidelines for process design, these results are expected to apply qualitatively to typical foaming conditions and common polymer-blowing agent combinations.