Bubble nucleation in polymeric liquids. II. theoretical considerations

Abstract

A theory based on classical nucleation theory is developed for bubble nucleation in polymer solutions. The theory requires information on solubility, diffusivity, concentration, surface tension, temperature, and degree of supersaturation. The effects of supersaturation and of the presence of large molecules in a liquid mixture on the free energy of bubble formation are included in the theoretical development. A semiempirical equation for the determination of bubble nucleation rate is developed, with the aid of experimental results reported in part I of this series. Using the experimental data, computer simulations of bubble nucleation in polymer solutions are performed. The consumptions of the volatile component in a liquid mixture, due to bubble nucleation and subsequent growth, and the variation of bubble nucleation rate during the expansion process are included in the simulation of the bubble nucleation process.

Evolution of cellular morphologies and crystalline structures in high-expansion isotactic polypropylene/cellulose nanofiber nanocomposite foams

“…49 Specically, the formation of large numbers of smaller-sized crystals in the composites, because of the heterogeneous nucleating effect of CNF, would generate more bubble nucleation sites and greatly expedite the cell nucleation. [50][51][52] Similarly, the CNF itself could also act as a cell nucleating agent and again enhance the bubble nucleation power. On the other hand, the presence of CNF in the PP matrix improved its melt strength and led to restricted cell growth and reduced cell coalescence.…”

Assisted heterogeneous multinucleation and bubble growth in semicrystalline ethylene-vinyl acetate copolymer/expanded graphite nanocomposite foams: Control of morphology and viscoelastic properties

“…Among the polymer foaming community, the discrepancy between the classical theory and experimental results is sometimes attributed to the intervening heterogeneous nucleation provided by filler solid surface and has led to the classical theory modifications by incorporating certain aspects specific to the polymer foaming process [9,[32][33][34]. Nanoparticles have been validated that undoubtedly serve with heterogeneous nucleation sites and their influence on the cell density has been qualitatively represented by the classical nucleation theory [32,34]. In heterogeneous nucleation process, the highest nucleation efficiency can be achieved only if the nucleation on the nucleant surface is energetically favored comparing with its homogeneous counterpart and the nucleant is well dispersed in the polymer matrix.…”

A numerical model for combustion of bubbling thermoplastic materials in microgravity

“…The nucleation rate per unit volume J is related linearly to the number of molecules per unit volume of the metastable (liquid) phase M and a frequency factor B, and exponentially to the free energy change F cr required to form the critical bubble [33], [34]:…”