Prepare a polymeric foam article having a thermoplastic polymer matrix defining multiple cells therein, wherein the polymeric foam article has the following characteristics: (a) the thermoplastic polymer matrix contains dispersed within it nano-sized nucleating additive particles that have at least two orthogonal dimensions that are less than 30 nanometers in length; (b) possesses at least one of the following two characteristics: (i) has an effective nucleation site density of at least 3×1014 sites per cubic centimeter of pre-foamed material; and (ii) has an average cell size of 300 nanometers or less; and (c) has a porosity percentage of more than 50 percent by rapidly expanding at a foaming temperature a foamable polymer composition containing the nucleating additive and a blowing agent containing at least one of carbon dioxide, nitrogen and argon.