AbstractThe crystallization of highly oriented homopolymer melts (or glasses) is modeled. It is shown that in such cases heat flow controls the kinetics and microstructure of the transforming material. The situation is modeled similarly to the growth of a thermal dendrite, with the inclusion of large and variable concentrations of defects in the fibrillar crystals. Expressions relating the undercooling, growth velocity, filament tip radius, and defect concentration to a normalized tensile force are derived. Example predictions for the case of isotactic polystyrene are given.