Polymer layered silicate nanocomposites may be formed by annealing layered silicate particles with a polymer melt. Polymer molecules leave the bulk melt and intercalate between the silicate layers, producing a structure in which polymers are confined on the nanometer scale by the silicate layers. We report here molecular dynamics simulations of this formation process, which is modeled by the flow of polymer from a bulk melt into a slit whose walls are maintained at constant pressure and whose surfaces are decorated by grafted short hydrocarbon chains. The results are compared with x-ray diffraction studies of the intercalation of high molecular weight polymers into organically modified silicates, and with a previous simulation of the flow of polymer molecules from a bulk melt into a slit of fixed dimension.