The estimation of cell density in isotropic microcellular polymeric foams using the critical bubble lattice

Abstract

In this study, models for estimating the cell density of isotropic polymeric foams using the surface cell density were developed. The basic morphological unit cell for these models is a gas-filled pentagonal dodecahedral cell cavity. The critical bubble lattice model was introduced to associate the packing structure of the pentagonal dodecahedral cells with a face-centered cubic (FCC) packing structure, and the cell density was estimated. This model was then used to investigate the effect of nonperfect cell cross-sections as found in the micrographs of cell densities of foams. Two cases were examined: first, the ideal case of a perfect cross-section, and second, the actual case of a nonperfect cross-section. The plots of cell density versus surface cell density from recently published data show the effect of a nonperfect cross-section on the estimation of cell density within an FCC lattice with perfect and nonperfect cell cross-sections. The percentage average absolute deviation (AAD) showed that the nonperfect cell cross-sectional model reliably predicts the cell density of isotropic low-density foam with an AAD of 39.2%. The perfect cell cross-sectional model reliably predicts the cell density of isotropic high-density foam with an AAD of 57.2%. These new models are more reliable than the conventional model, which give AADs 59.4% for low-density foams and 62.4% for high-density foams. Furthermore, the isotropic foam index was introduced as a parameter to indicate the isotropic foam behavior.