A Frozen Tube Model of Melting Point Depression of Solvents in Entangled Polymer Systems

The entanglement model, which was proposed previously on the melting point depression of a crystalline low molecular weight diluent in an un-cross-linked amorphous polymer, was modified so as to be consistent with a frozen tube model. In the latter model, the crystallization of the diluent occurs within the entangled polymer chains, which act as a confining frozen and hard tube involving an unfrozen solvent within. The new model accounts reasonably for the experimental observations and provides estimates of the diluent crystal size, frozen tube size, and other well-defined parameters for the un-cross-linked systems. The calculation based on the new model for two different cases of lightly cross-linked and un-cross-linked rubber mixtures can explain well the crystal sizes determined by X-ray and NMR measurements for some relevant concentrations.