A process for making a block copolymer compatibilizer comprises reacting an acrylic and/or vinyl monomer that has functional groups with one or more vinyl monomers in the presence of a free radical initiator and a stable free radical to form a reaction product that includes residual unreacted acrylic and/or vinyl monomer, and reacting one or more vinyl monomers with the reaction product to form a second block that incorporates the residual unreacted acrylic monomer. The block copolymer is used to compatibilize a clay nanocomposite material with a thermoplastic or thermoset resin. The block copolymer can be used with existing, commercially-available clays, or the block copolymer can be formed with a polar block that is miscible in a polar dispersion medium for use as a intercalate in producing a clay nanocomposite material.