Melting of Lamellar Crystals

Most macromolecular, lamellar crystals are only about 10 nm thick (see Sect. 5.2), i.e., their surface area is about 200 m g. For any reasonable specific surface free energy, such a large surface will lead to a sizeable metastability, overshadowing most 

Gg = Gibbs energies (g a Perg of bulk samp e) me, mg = masses 

6 = surface free energy 9 = crystal density t = lamellar thickness 

The amorphous part of the usually semicrystalline polymer and the melt produced on fusion are assumed to be coales(id to a single, amorphous system or subsystem with the free enthalpy G. If this were not so, additional amorphous subsystems would have to be introduce, and, if these subsystems are small, their surface effects would have to be considered via their area and the specific surface free energies. This leads, again, to experimental problems that are difficult to resolve. 

The whole sample, consisting of crystals and melt, is enclosed in the sample holder of the calorimeter (see Sects. 4.2-4.4), making it the overall closed system, isolated from the surroundings. As melting progresses, mass is transferred in Fig. 2.82 from the left to the right. On crystallization, the mass transport goes in the opposite direction. The heat transport across the open boundary is minimal since it is assumed that the calorimeter remains at constant temperature. 

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Experimental Data for the Melting of Lamellar Crystals of Polyethylene... 

Employing a dilatometric technique, Booth and coworkers determined the melt behavior of fractionated PPO as a function of crystallization temperature and by this technique found the thermodynamic melting point for PPO to be near 82° (Fig. 31), surprisingly 100° C lower than that of POM. These authors also detected three dilatometric transitions for partially isotactic material. The first below 60° was ascribed to the melting of lamellar crystals of limited thickness arising from the isotactic sequence. The other two transitions which depended on Tf- were attributed to the melting of lamellae with thicknesses determined by primary nudeation. 

The DSC trace also gives information on the range of lamellar crystal perfection, since the thinnest, lowest molecular weight, lamellae melt some 30 °C below the final melting point. If a rapidly cooled polyethylene is subsequently annealed in this temperature range, the lamellae will thicken by a process of partial melting and recrystallisation, and the shape of the DSC trace will change. 

In the case of PHA copolymers, crystallinity and lamellar crystal sizes play a decisive role in their enzymatic degradation process in analogy with P(3HB) homopolymer. The enz3nnatic erosion rates of melt-crystallized PHA copolymer films inaeased with a decrease in the crystallinity (see Figure 16(a)), and the degradation rates of crystalline regions inaeased with a decrease in the thickness of lamellar crystals (Figure 16(b)). 

With this description of open and closed systems, melting and reorganization of lamellar crystals is treated next as an example of the irreversible thermodynamics of defectpolymer crystals and their melting [24]. The added variable for the description of lamellae is the shape of the crystal. A more general treatment of internal variables is given in Sect 2.4.4, and the detailed time-dependence of the processes is discussed in Sects. 2.4.5 and 2.4.6. 

Figure 4.8. Zero-entropy-production melting temperatures of lamellar crystals of...

Figure 4.9. Decrease of melting temperature of lamellar crystals of polyethylene when heating with increasing rates. The right figure is a typical electron micrograph of a lamella of such polyethylene. DSC data from Ref. [20].

The thickness of lamellar crystals normally exhibits a broad distribution, so their melting points also cover a broad temperature range, which is often called the melting range. Note that the melting range usually occurs far below the equilibrium melting point. 

The linear growth rate acmally reflects a net competition result between the growth and the melting upon thermal fluctuations at the lateral surface of lamellar crystals, as given by (Ren et al. 2010)... 

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