The influence of the addition of small quantities of anisotropic layered silicates on the ordering of block copolymers is studied by a combination of linear viscoelasticity and small angle neutron scattering. Specifically, we examine the influence of varying the lateral dimensions of thermodynamically roughly equivalent layered silicates on the development of cylindrical and spherical microdomain order in a blend of a matched diblock and triblock copolymer. The kinetics for the development of spheres arranged on a bcc lattice from an initial disordered state are dramatically accelerated by the two larger layered silicates with equivalent diameters of similar to1 and 10 mum, while the incorporation of an organically modified laponite, with an equivalent diameter of similar to 30 nm, has no influence on these kinetics. On the other hand, the addition of layered silicates, irrespective of layer dimensions, has no influence on the development of cylindrical ordered microdomains and the epitaxial transformation of shear-aligned cylindrical microdomains to spherical microdomains.