Equilibrium melting temperature, of polymer

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 The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...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 simple method based on Equation 10.13, however, is not commonly used because 100% pure crystalline samples for most polymers are not available. One alternative approach is to use the fusion enthalpy, the latent heat of melting, of chemical repeated units (A Hu) to replace A/fioo in the calculations. AHu can be calculated using the I dory relationship for the depression of the equilibrium melting temperature of a homopolymer due to the presence of low molecular mass diluents. The AHu values of some polymers are available in literature. 

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 ... 

We have seen that the experimental determination of the melting temperature of pol3nneric systems, suitable for use in thermodynamic analysis, possesses several inherent difficulties concerned with both concept and technique. Some of the main problems have been pointed out in this paper and the procedures by which they could be overcome has been indicated. Hence there are obvious difficulties in determining the equilibrium melting temperature from polymer data, even admitting the extrapolative procedure. A more detailed discussion of this aspect of the problem will be taken up in a subsequent publication (32). 

T, solid-liquid equilibrium melting temperature of the solvent in the polymer solution... 

Figure 7.14 contrasts the liquidus line of a polyethylene with a molar mass of 25,000 Da with those of its oligomers. A paraffin C9H20, for example, would cause a value of x = 200 in Eq. (13) of Fig. 7.6, and has an equilibrium melting temperature of 219.6 K. Such low melting temperature is srill far below any reasonable concentration of paraffin, v in the phase diagram, and the eutectic point lies on the ordinate at Vj 1.0 or Vj 0. The melting curve of the polymer, however, is considerably broadened due to the dissolution of the polymer into the hquid paraffin. 

Hobbs SY (1996) The development of flow instabilities during the injection molding of multicomponent resins. Polym Eng Sci 36 1489-1494 Hoffman JD, Weeks JJ (1962) Melting process and the equilibrium melting temperature of polychlorotrifluoroethylene. J Res Natl Bur Stand 66 A 13-28 Holman IP (1976) Heat transfer, 4th edn. McGraw-FIill, New York... 

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,... 

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... 

The equilibrium melting temperature of the pure polymer of infinite chain length, T, is identified with the ratio AH /AS,i. The fact that fe is independent of A e is a consequence of approximations made in calculating A5f. Physically significant values of occur only when V2D is less than unity. 

Calculations based on Eq. (2.35) for the exponential molecular weight distribution indicate that the equilibrium melting temperatures of the poly(ethylene oxides), and presumably other polymers as well, are sensitive to the width of the distribution. Significant changes in the equilibrium melting temperature can occur. For example. 

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. 

---