Thermodynamic upper bounds for polymer foam cell densities are predicted using 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, indicating that low temperatures and high blowing agent content should be used to achieve high cell densities. The inhomogeneous bubble structure reveals deviations from the expected homogeneous Sanchez-Lacombe equation of state, consistent with some experimental results. A generalized Sanchez -Lacombe equation of state is discussed in the context of its suitability as a simple alternative to the Simha-Somcynsky equation of state. (C) 2012 Elsevier Ltd. All rights reserved.