Towards maximal cell density predictions for polymeric foams

Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to classical nucleation theory or activation barrier kinetic arguments. Maximum possible 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 condition 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 bubble sizes. Instead, the volume free energy density, often labelled as a pressure difference, is the dominant factor for both cell densities and cell sizes.