| Polymer foams are used extensively in a variety of applications. A firm understanding of bubble nucleation is vital to predict foam properties based on process conditions. However, a number of theoretical and experimental challenges have thus far limited progress in this area. The use of a scaling theory is proposed to connect nucleation behavior to well understood bulk phase behavior of polystyrene-CO2 systems, which can be predicted by equations of state, such as the Sanchez--Lacombe or Statistical Associating Fluid Theory equation of state. Scaling theory of nucleation asserts that when the reversible work of critical nucleus formation is properly normalized and plotted against the normalized degree of supersaturation, the resulting scaling curve is insensitive to temperature and the materials being used. Once the form of the scaling function is known, it can be used to predict the nucleation barrier knowing only the initial foaming conditions and calculating only bulk thermodynamic values. Using an extension of diffuse interface theory, the slope of the scaling curve near saturation was determined. This initial slope constrains the scaling function for better predictions of the reversible work. The accuracy of the scaling theory was examined by comparison to experiments. The scaled free energy barriers determined from experiments are consistent with the scaling function so constructed, and the theoretical results qualitatively agree with those found previously. |
