Thermoplastic polymer compositions, films, containers, laminates and fibers can comprise a modified polymer. The said modified polymer having a moiety comprising a half-ester reaction product of cyclodextrin and metal and/or organic group covalently bonded to some portion of the half-acid moieties. The cyclodextrin compound, grafted to the polymer structure, can scavenge impurities, permeants, or other undesirable volatile contaminants. The cooperation between the modified polymer's carboxylic acidic groups, basic groups and grafted cyclodextrin can provide active barrier properties to a film, web, fiber or other polymer structure. A permeant or a contaminant can be complexed or trapped within the polymer and held within the film, web or fiber preventing the permeant from passing into the interior of a container, or the contaminant can be scavenged from the enclosed headspace or surrounding environment.