AbstractThe statistical mechanical methods developed in Parts I and II in this series permit the postulation of a thermodynamic criterion for the molecular fractionation which occurs during crystallization. Using this criterion we define a “local equilibrium” melting temperature as that temperature at which a polymer molecule (considered as a small thermodynamic system) has the same free energy when crystallized into the lowest possible free energy conformation on a given crystal surface (or surfaces) as it does in a completely molten state but still in contact with the same surfaces. This temperature will be a function not only of molecular length but also of the nature of the crystal surfaces to which it is exposed. Lowest “local equilibrium” melting temperatures occur on large flat crystal surfaces (secondary nucleation sites), higher temperatures result from the intersection of two crystal surfaces (tertiary nucleation sites). A number of such potential tertiary nucleation sites have been investigated and the resulting temperatures satisfactorily cover the range over which molecular fractionation has been o