Equilibrium melting temperature, polymer

Each crystallizable polymer exhibits a characteristic equilibrium melting temperature, at which the crystalline and amorphous states are in equilibrium. Above this temperature crystallites melt. Below this temperature a molten polymer begins to crystallize. 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

Temperature has a complex effect on crystallization rate. Initially, as the temperature falls below the equilibrium melting temperature, the crystallization rate increases because nucleation is favored. However, as the temperature continues to fall, the polymer s viscosity increases, which hampers crystallization. As a rule of thumb, a polymer crystallizes fastest at a temperature approximately mid-way between its glass transition temperature and its equilibrium melting temperature. 

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 The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Measurements by many researchers have shown that PTFE s equilibrium melting temperature is 327°C. ° Once it is heated above its melting temperature, its initial properties are irrecoverable. Compaction of PTFE powder and heating above 327°C results in a partially crystalline solid polymer composed of large crystals with a coexisting noncrystalline phase. Crystal size and perfection depend on die crystallization conditions slow cooling results in larger, more perfect crystals. On this point, we present detailed information from electron microscopy, corroborated by measurements of X-ray line breadth. 

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 ... 

The equilibrium melting temperature, T°m, can be obtained from data for crystals of finite thickness using the Thompson-Gibbs equation. The melting point of crystalline polymers with a well-defined crystal thickness (/c) can be measured and the data extrapolated to 41 = 0 using the Thompson Gibbs equation (Gedde 1995) ... 

True thermodynamic equilibrium refers to the phase in their most stable state, and for the crystalline polymer phase the most stable conformation is the fully extended one. The equilibrium melting temperature, T , corresponds to the melting of perfect crystals of infinite size with fully extended chains. The value of for a polymer is unique. Since the crystalline samples of polymers are made up of crystals of finite size in which the chains are folded and not fully extended, the experimentally determined melting temperature, is always lower than There is a strong dependence of T on the thickness of the crystalline lamella, / always increases with /. 

Table 2.2 Equilibrium Melting Temperatures Enthalpies and Entropies of Melting for Some Polymers...

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 Tm(o)- and Hf(max)-values of PK copolymer Three extrapolation methods are, according to Cheng [5], available to determine the equilibrium melting temperature tTm(o)-value] of a polymer ... 

All isotactic vinyl polymers can be arranged in four ways in the usual crystals. Polypropylene has as stable conformation a 2 3/1 helix that consists of successive tg(—) or tg rotational isomeric states (left-handed or right-handed helices). In addition, it was possible for the helices to have the —CHj groups point up or down , relative to the crystallographic c-axis. In the ideal, monoclinic crystal form I (P2j /c) all four types of helices occur only at specific, symmetry-related positions The equilibrium melting temperature and entropy are 460.7 K and 15.1 J/(K mol), respectively. 

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). 

In addition to the ambiguities inherent to the physical concept, the determination of thermodynamic quantities such as the latent heat and the volume change at the transition is often hampered by the fact that the crystalline state of chain molecules is quite complex. The polymer crystals are usually polycrystalline and coexist with the disordered amorphous domain. An accurate estimation of the equilibrium melting temperature defined for a perfectly aligned crystal requires great effort [5,18,19]. At the melting temperature, equilibrium usually exists between the liquid and somewhat imperfect crystalline phases. 

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

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