Analysis of bubble coalescence and determination of the bubble radius for long-chain branched poly(ethylene terephthalate) melt foaming with a pressure balanced bubble-growth model

A pressure balanced bubble-growth (PBB) model was proposed to analyze bubble coalescence and determine the bubble radius for the melt foaming of long-chain branched poly(ethylene terephthalate) (LCB-PET). The key for the PBB model calculation was to determine the bubble inner pressure composed of additional pressure induced by interface tension, and molecular stress, that is, the biaxial tensile stress of the polymer cell wall calculated with the molecular stress function model. LCB-PET was generated by reactive extrusion, and the molecular structure and viscoelasticity were well characterized. Batch melt-foaming experiments with CO2 were conducted for the LCB-PET. The critical coalescence radius curve was calculated with the PBB model to dynamically describe the bubble coalescence and evaluate the melt foamability. The PBB model was also used to determine the bubble size of LCB-PET foam. Both the evaluation of the melt-foamability and the determination of the bubble radius agreed well the experimental results.