Relative nucleation rates for fluid bubbles of nanometre dimensions in polymer matrices are calculated using both classical nucleation theory and self-consistent field theory. An identical model is used for both calculations showing that classical nucleation theory predictions are off by many orders of magnitude. The main cause of the failure of classical nucleation theory can be traced to its representation of a bubble surface as a flat interface. For nanoscopic bubbles, the curvature of the bubble surface is comparable to the size of the polymer molecules. Polymers on the outside of a curved bubble surface can explore more conformations than can polymers next to a flat interface. This reduces the free energy of the curved interface which leads to a significantly smaller barrier energy to nucleation and thus a much higher nucleation rate. Also, there is a reduction of unfavorable energetic contacts between polymer and fluid molecules in the vicinity of a curved interface. Polymers on the outside of a curved interface are less likely to find a portion of themselves in the interior of the unfavorable fluid bubble. A secondary cause of the failure of classical nucleation theory is due to the collapse of the bulk region inside the bubble. As the radius of a bubble is reduced, eventually the diffuse walls collide causing increased mixing of polymer and fluid molecules everywhere. This causes a reduction of internal energy associated with the interface, leading to smaller nucleation barrier energies and, again, a reduced barrier energy to nucleation.

Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to clas sical nucleation theory or activation barrier kinetic arguments. Maximum pos sible cell density predictions are also made subject to constraining the systems to have maximal possible internal interface and to have well formed bubbles (no deviation from bulk conditions on the interior of the bubble). This last condi tion is found to be the most restrictive on possible cell densities. Comparison is made with classical nucleation theory and it is found that the surface tension is not an important independent consideration for predicting conditions consistent with high cell density polymeric foams or achieving the smallest possible bub ble sizes. Instead, the volume free energy density, often labelled as a pressure difference, is the dominant factor for both cell densities and cell sizes.

Thermodynamic upper bounds for polymer foam cell densities are predicted us ing compressible self-consistent field theory. It is found that the incompressible limit always gives the highest, and therefore ultimate, upper bound. Qualitative comparisons between the compressible and incompressible cases agree, indicat ing that low temperatures and high blowing agent content should be used to achieve high cell densities. The inhomogeneous bubble structure reveals devia tions from the expected homogeneous Sanchez-Lacombe equation of state, con sistent with some experimental results. A generalized Sanchez-Lacombe equa tion of state is discussed in the context of its suitability as a simple alternative to the Simha-Somcynsky equation of state.