Polyethylene equilibrium melting

Fig. 8. Superheating of polyethylene extended chain crystals. Curves 1) at 421.7 K, 2) at 419.2, 3) at 417.7 K, 4) at416.7K, 5) at 414.7 K. The equilibrium melting temperature is 414.6 K. Drawn after Ref.40). "w is the weight fraction molten, obtained by isothermal calorimetry...

Fig. 9. Melting kinetics and crystallization kinetics of polymeric selenium (right) and polyethylene (left). The equilibrium melting temperatures are 494.2 and 414. 6K. The dotted curve indicates that on crystallization of the macromolecule from small molecules Sc2 there is no molecular nucle-ation necessary as in the melt crystallization (see also ref. 43 for a more detailed discussion of Se crystallization and melting). Drawn after Ref. 4,)...

Thermal analysis data on lamellar crystals of polyethylene over a wide range of thicknesses are plotted in Fig. 2.90. The Gibbs-Thomson equation is a good mathematical description of the observed straight line and can be used to calculate the equilibrium melting temperature by setting C = (t ° = 414.2 K). Also, the ratio of the surface free energy to the heat of fusion can be obtained from the equation. 

Polyethylene data are shown in Fig. 2.23. At the equilibrium melting temperature of 416.4 K, the heat of fusion and entropy of fusion are indicated as a step increase. The free enthalpy shows only a change in slopes, characteristic of a first-order transition. Actual measurements are available to 600 K. The further data are extrapolated. This summary allows a close connection between quantitative DSC measurement and the derivation of thermodynamic data for the limiting phases, as well as a connection to the molecular motion. In Chaps. 5 to 7 it will be shown that this information is basic to undertake the final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems. 

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. 

There are obvious difficulties in obtaining T by either of these extrapolative methods. Therefore, caution must be used in accepting, and using, the values so obtained. Equilibrium melting temperatures listed in Tables 11.1 and 11.3 have been obtained by one or the other of these methods, except for the theoretical value for linear polyethylene. 

Fig. 5. A graph showing the variation of the fold length (1) with supercooling (AT) for polyethylene crystallized from a variety of solvents and from the melt. In the case of solvent crystallization, supercooling is taken with respect to the so-called equilibrium dissolution temperature. For the melt-crystallized data set the equilibrium melting temperature is used. The remarkable coincidence between the curves, despite the wide range of absolute temperatures to which each supercooling corresponds, is strong evidence in favor of the kinetic origin of crystal thickness selection. Solvents xylene, hexyl acetate, 0 ethyl esters, O dodecanol, V dodecane, A octane, x tetradecanol, + hexadecane, melt crystallized. Reprinted from Ref. 44. Copsright (1985), with permission from Kluwer Academic Publishers.

An experimental phase diagram of polyethylene dissolved in 1,2,4,5-tetrachlorobenzene (TCB) is shown in Figure 16b (132). Both polymer and low molar mass solvent have similar equilibrium melting temperatures. On the left-hand side of the phase diagram, the liquidus line follows equation 47, the right-hand side does not follow equation 46. Again, this indicates the usual nonequilibrium state of polymer crystals. Besides too low melting temperatures, low... 

There is still considerable controversy over equilibrium melting point values for polyethylene (414 cf. 419 K) and poly(ethylene oxide) (342 cf. 348 K), which appears to be associated with various melting point theories and crystal structures used in their derivation. 

Wunderlich, B., Czomyj, G., Study of equilibrium melting of polyethylene. Macromolecules 1977, 10 906-913. 

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