Polyethylene equilibrium melting data

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. 

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.

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... 

Figure 1.12 Molar mass dependence of the equilibrium melting point of oligo- and polyethylene. Drawn after data collected by Boyd and Phillips (1993).

The equilibrium melting point is indeed very difficult to determine. When crystallized at elevated pressures (500 K and 435 MPa), polyethylene forms so-called extended-chain crystals. These extraordinarily thick crystals melt at temperatures very near the equilibrium melting point. Cormier and Wunderlich (1966) determined the dissolution temperatures for such samples in a variety of solvents and, by fitting eq. (8.23) to the experimental data, the interaction parameter values listed in Table 8.2 were obtained. 

Calculate the molar entropy of fusion for linear polyethylene from the following data equilibrium enthalpy of fusion Ah° = 293 J and the equilibrium melting point TJ, = 415-418 K (different values have been reported). 

The thermoplastic melt viscosity can also be determined by TMA, using the Du Pont parallel plate rheometer accessory. Viscosity range of lO -lO8 poise can be measured with shear rates of 10°-10"5 sec-1. Viscosity data of polyethylene made by this method are shown in Figure 11.13 (29). Approximately 15 min are required to reach temperature equilibrium for a 60 mg sample. 

With these three simple equations, all equilibrium calorimetry can be described, so that measurement of heat capacity and latent heat allows a full thermal characterisation. Figure 4.2 illustrates a typical diagram of the thermal properties of crystalline polyethylene and its melt. The data were obtained by extrapolation of measurements of heat capacities on... 

Fig. 16. (a) Phase diagram of poly(ethylene oxide) 3,500/100,000 mol-wt mixtures at different concentrations. The open circles represent the calculation of and, calculated by using the Flory-Huggins equations 46 and 47, respectively. The filled symbols represent the experimental data, (b) Phase diagram of polyethylene dissolved in 1,2,4,5-tetrachlorobenzene (TCB). The experimental data were obtained by melting after crystallization. The macromolecular crystals, 2, were not at equilibrium, but melted considerably lower than (see Table 1). 

In the third paragraph we shall discuss the results of some Monte-Carlo calculations related to the structure of "liquid" polyethylene preliminary evidence will be given that bundles of chains are not present at equilibrium in the melt of polyeth lene and their existence is not required to explain the X-ray diffraction data with its characteristic 4.5 X halo. 

Figure 5.9 shows the creep and recoverable compliances of a metallocene, linear, low-density polyethylene at 150 °C [36]. This polymer has a polydispersity index (Af, /M ) of about two. The data shown start in the transition from the plateau to the terminal zones, and the last few points are in the terminal zone, which corresponds here to steady flow. Note that the experiment had to be continued for about 2.5 hours to reach steady state, where J t) = /° +tlr)g and /j (f) = /°. (/r is the recoverable compliance defined in Eq. 4.26.) It is of interest to compare the creep compliance of an entangled polymer melt with that of a cross-linked elastomer. The latter cannot flow, so at long times /(t) approaches a constant value, the equilibrium compliance, /°. 

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