The Crystallinity Dependence of Heat Capacities

Several steps are necessary before heat capacity can be linked to its various molecular origins. First, one finds that linear macromolecules do not normally crystallize completely, they are semicrystaUine. The restriction to partial crystallization is caused by kinetic hindrance to full extension of the molecular chains which, in the amorphous phase, are randomly coiled and entangled. Furthermore, in cases where the molecular structure is not sufficiently regular, the crystallinity may be further reduced, or even completely absent so that the molecules remain amorphous at all temperatures. 

The first step in the analysis must thus be to establish the crystallinity dependence of the heat capacity. In Fig. 2.44 the heat capacity of polyethylene, the most analyzed polymer, is plotted as a function of crystallinity at 250 K, close to the glass transition temperature (T = 237 K). The fact that polyethylene, [(CH2-)xl, is semicrystalline implies that the sample is metastable, i.e., it is not in equilibrium. Thermodynamics 

One way to establish the weight-fraction crystallinity, w, is from density measurements (dilatomeury, see Sect. 4.1). The equation is listed at the bottom of Fig. 2.44 and its derivation is displayed in Fig. 5.80. A similar equation for the volume-fraction crystallinity, v, is given in the discussion of crystallization in Sect 3.6.5 (Fig. 3.84). Plotting the measured heat capacities of samples with different crystallinity, often results in a linear relationship. The plot allows the extrapolation to crystallinity zero (to find the heat capacity of the amorphous sample) and to crystallinity 1.0 (to find the heat capacity of the completely crystalline sample) even if these limiting cases are not experimentally available. 

As the temperature is raised, the crystallinity dependence of the heat capacity becomes less it is only a few percent between 50 to 200 K. In this temperature range, heat capacity is largely independent of physical structure. Glass and crystal 

Crystallinity Dependence of the Heat Capacity of Polyethylene at High and Low Temperatures 

---

The temperature range from 1° K to 30° K was remeasured and discussed in detail by Tucker and Reese (1967). They used in their discussion data by Isaacs and Garland (19 ) Dainton, Evans, Hoare, and Meilia (1962) Sodiava (1 0) and Reese andTucker (1965). F. III.9 illustrates the dependence of the heat capadty on crystallinity in this low temperature region. The heat capacity s ms to depend lin rly on crystallinity. The difference between completely crystalline and amca -phous heat capacity is largest at about 5° K, decr sii on either e. At about 5Q° K the crystallinity dependence of heat capacity disappears. 

---