A polymeric foam has a thermoplastic polymer matrix defining multiple cells, the foam characterized by: (a) the polymer matrix having greater than 50 weight-percent copolymer containing at least two different monomers at least one of which is a methacrylate monomer, each monomer having a solubility parameter lower than 20 (megaPascals)0.5 and a chemical composition where twice the mass fraction of oxygen plus the mass fraction of nitrogen, fluorine and silicon is greater than 0.2; wherein the monomers comprise at least 90 weight-percent of all monomers in the copolymer; (b) at least one of the following: (i) a nucleation site density of at least 3×1014 effective nucleation sites per cubic centimeter of foamable polymer composition; (ii) an average cell size of 300 nanometer or less; (c) a porosity percentage greater than 30%; (d) an absence of nano-sized nucleating additive; and (e) a thickness of at least one millimeter.