Equilibrium melting temperature, of polymer crystals

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Figure 1 also shows that plasticized polyvinyl chloride begins to flow at a lower temperature. This is to be expected in view of the fact that equilibrium melting temperature of polymer crystals is depressed by monomeric diluents. A statistical thermodynamic treatment by Flory (13), showed that this effect depends on the nature of the polymer, concentration of the diluent, and the degree of polymer-diluent interaction in the following manner ... 

Determination of the equilibrium melting temperature of polymer crystals linear and nonlinear Hofiman-Weeks extrapolations. Macromolecules, 31, 8219-8229. 

Thermodynamic Equilibrium Melting Temperature of Polymer Crystals... 

Lovell R, Mitchell GR, Windle A (1979) Wide-angle X-ray scattering study of structural parameters in non-crystalline polymers. Faraday Discuss Chcm Soc 68 46-57 Maraud H, Xu JN, Srinivas S (1998) Determination of the equilibrium melting temperature of polymer crystals Linear and nonlinear Hoffinan-Weeks extrapolatimis. Macromolecules... 

The thermodynamic equilibrium melting point of polymer crystals can be measured by means of DSC and small-angle X-ray diffraction. The following procedure is recommended for the measurement of the equilibrium melting temperature of a polymer crystal,... 

Polymer crystallization and melting are typically first-order phase transitions between the amorphous phase and the crystalline phase. When these two phases are in thermodynamic equilibrium, two phase transitions are thermodynamically reversible under a certain temperature. This temperature is referred to the equilibrium melting point of polymer crystallization. The free energy changes of amorphous phase and crystalline phase under various temperatures are depicted in Fig. 4.1, illustrating the definition of the equilibrium melting point 7. ... 

There are thus two specific places where the dilution directly influences AG (v2) the In V2 term and AG (V2). The latter can be approximated by AG = AH iTm — r)/ Tn,. Tm is now the equilibrium melting temperature of the crystallizing polymer in the mixture. There is also the distinct possibility, which cannot be ruled out, that either, or both, of the interfacial free energies, cTen mid cTun, depend on composition. 

The values of the equilibrium melting temperature T, determined from Eq. (3), decrease in a continuous way with increasing PMMA content (Fig, 6). The depression observed for the equilibrium melting temperature of pure PEO, AT = T° - T j (where T° refers to pure PEO) has then been related to the volume fraction of the non-crystallizing polymer according to the equation derived by Nishi and Wang for compatible binary blends ... 

The melting enthalpy of perfect polymeric crystals can be measured by DSC. When crystalline polymers absorb a small amount of the solvent, the equilibrium melting temperature of the pure polymeric crystals is depressed from to... 

If the network structure is such that the crystallization of the cross-linked units is not restricted, AH and A5 can be taken to be independent of the fraction of units cross-linked. Under these conditions, A5 is identified with the entropy of fusion of the pure non-cross-linked polymer, and the ratio of A5 to AH is identified with the equilibrium melting temperature of the pure polymer. If, however, steric requirements are such that cross-linked units are excluded from the crystalline regions, an alteration will occur in these quantities. The presence of cross-linked units in the molten phase and not in the crystalline phase results in an increase in A 5 (when compared with the non-cross-linked polymer) of an amount Rp per mole of chain units. The melting temperature must accordingly be depressed for this reason, as long as AH is unaffected by the presence of cross-links. 

Semicrystalline polymers show a more complicated DMA picture. It was indicated in Fig. 6.4 that the glass transition results only in a partial softening because of the high level of cross-linking due to the crystals. Only above the melting temperature is the fully liquid state reached. A typical torsion pendulum result, obtained with an instrument similar to that in the sketch of Fig. 6.18, is shown in Fig. 6.24 for linear polyethylenes of different crystallinity. Three regions of maxima in G and tan S can be found below the equilibrium melting temperature of 414.6 K. Customarily these relaxations are called a, p, and y. A detailed interpretation of such DMA data has been... 

---