A composite material comprising an EVOH matrix polymer in an amount of about 40% to about 99.95% by weight of the composite material, and about 0.05% to about 60% by weight exfoliated platelets of a phyllosilicate material, said platelets derived from an intercalate formed by contacting a phyllosilicate, having a water content of at least about 4% by weight, with a non-EVOH intercalant to form an intercalating composition, thereby achieving sorption of the intercalant between adjacent spaced layers of the phyllosilicate to expand the spacing between a predominance of the adjacent phyllosilicate platelets to at least about 10 .ANG., when measured after sorption of the intercalant, and thereafter exfoliating the intercalate into a predominance of single platelets.