  Solid-state nanofoaming experiments are conducted on two PMMA grades of
markedly different molecular weight using CO$_2$ as the blowing agent. The
sensitivity of porosity to foaming time and foaming temperature is measured.
Also, the microstructure of the PMMA nanofoams is characterised in terms of
cell size and cell nucleation density. A one dimensional numerical model is
developed to predict the growth of spherical, gas-filled voids during the
solid-state foaming process. Diffusion of CO$_2$ within the PMMA matrix is
sufficiently rapid for the concentration of CO$_2$ to remain almost uniform
spatially. The foaming model makes use of experimentally calibrated
constitutive laws for the uniaxial stress versus strain response of the PMMA
grades as a function of strain rate and temperature, and the effect of
dissolved CO$_2$ is accounted for by a shift in the glass transition
temperature of the PMMA. The maximum achievable porosity is interpreted in
terms of cell wall tearing and comparisons are made between the predictions of
the model and nanofoaming measurements; it is deduced that the failure strain
of the cell walls is sensitive to cell wall thickness.
