Foams and methods of forming foams of chain extended/branched copolymers of vinylidene substituted aromatic monomers

A method of forming a foam comprising:

• a) heating a foaming composition comprising one or more copolymers having nucleophilic groups prepared from of one or more vinylidene aromatic monomers and one or more unsaturated compounds containing the nucleophilic groups, the one or more copolymers having nucleophilic groups have on average about 0.02 to less than 0.25 percent by weight of nucleophilic groups pendant from the one or more copolymers having nucleophilic groups;
• one or more copolymers having electrophilic groups prepared from one or more vinylidene aromatic monomers and one or more unsaturated compounds having the electrophilic groups, wherein the one or more copolymers having electrophilic groups are present in an amount of 0.1 to about 0.5 percent by weight of the foaming composition;
• and one or more blowing agents, to a temperature sufficient to melt and react the one or more copolymers having nucleophilic groups and the one or more copolymers having electrophilic groups to form a branched and/or chain extended and un-crosslinked copolymers;
• and
• b) extruding the foaming composition from a higher pressure to a lower pressure to form an extruded foam comprised of the branched and/or chain extended and un-crosslinked copolymers;
• and wherein the branched and/or chain extended and un-crosslinked copolymers are soluble in methylene chloride at 23° C. and exhibit a polydispersity of 2.5 or greater.