TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The cell walls are formed of partially reduced graphene oxide sheets, and/or reduced graphene oxide sheets. The cell wall has an average height of 100-5000 times greater than the average cell wall thickness. The interconnected and ordered open cells comprise cells with an edge connectivity of 3. In the process the only graphene material in the dispersion that is freeze cast to form the graphene-based foam is partially reduced graphene oxide sheets, and/or reduced graphene oxide sheets. The freeze castable medium provides for anisotropic frozen particles during freeze casting. The dispersion comprises graphene sheets, partially reduced graphene oxide sheets, and/or reduced graphene oxide sheets which are present at 0.5-7 mg/ml. Preferred Process: The resulting graphene foam is annealed.    TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The composition is in the form of a polymer composition comprising the graphene-based foam. The polymer composition is a polymer hydrogel. EXAMPLE - 5 g Of graphite powder was placed in an 80 degrees C solution of 7.5 ml of concentrated sulfuric acid, 2.5 g of potassium persulfate and 2.5 g of phosphorus pentoxide. The resultant dark blue mixture was cooled to room temperature for 6 hours, then carefully diluted with distilled water, filtered, and washed until the pH of the filtrate was close to 7. The peroxidized product was dried in 50 degrees C oven overnight, and placed into 115 ml of cold (0 degrees C) concentrated sulfuric acid. 15 g Of potassium permanganate was added gradually under stirring and the temperature of the mixture was kept below 20 degrees C. The mixture was then stirred at 35 degrees C for 2 hours. 230 ml Of water was added into the mixture, then after 15 minutes 700 ml of water and 30% of 12.5 ml of hydrogen peroxide were added to terminate the reaction. The mixture was then washed with 1:10 hydrochloric acid solution. Then the sample was subjected to 5 minutes of centrifugation at 3000 rpm. The sediment was collected, dispersed in water and centrifuged. The process was repeated 2-3 times, until no sediment was found. The graphite oxide dispersion was then subjected to dialysis to completely remove metal ions and acids to obtain graphene oxide which was further sonicated in water. The obtained 1.5 ml of graphene oxide solution was mixed with 15 mg of ascorbic acid in a 4 ml cylindrical glass vial, which was then placed in boiling water bath for 30 minutes to obtain partially reduced graphene oxide dispersion. The vial was then immersed in a dry ice bath to freeze for 0.5 hours. After thawing at room temperature, the vial was placed in boiling water bath to further reduce graphene oxide for 8 hours. The obtained gel was then sequentially subjected to dialysis in water (to remove soluble species), freezing drying and thermal annealing at 200 degrees C in air for 2 hours to obtain the graphene-based foam.