A method for making a flat polymer foam having a core layer of nano-sized open, interconnected cells that includes saturating a solid-state polymer with a supercritical fluid, allowing the gas to desorb for at least 35 minutes, and then heating the gas-saturated solid polymer for at least 3 minutes while constraining the foam in the thickness dimension. Any skin layer formed on the exterior may be removed via polishing, thus creating a foam with an open structure from side to side. The foam can be used as a battery separator.