Crystalline polymers crystallization

Mesoscopic non-equilibrium thermodynamics provides a description of activated processes. In the case considered here, when crystallization proceeds by the formation of spherical clusters, the process can be characterized by a coordinate y, which may represent for instance the number of monomers in a cluster, its radius or even a global-order parameter indicating the degree of crystallinity. Polymer crystallization can be viewed as a diffusion process through the free energy barrier that separates the melted phase from the crystalline phase. From mesoscopic non-equilibrium thermodynamics we can analyze the kinetic of the process. Before proceeding to discuss this point, we will illustrate how the theory applies to the study of general activated processes. 

In general, however, identification of the crystal cell is only part of the problem of characterizing the structure of crystalline polymers. Crystals are never perfect and the units cells do not infinitely duplicate through space even when they are grown very carefully from dilute solution using low molecular mass materials. As with the organic crystals considered in Chapter 3, a variety of defects can be observed and are associated with chain ends, kinks in the chain and jogs (defects where the chains do not lie exactly parallel). The presence of molecular (point) defects in polymer crystals is indicated by an expansion of the unit cell as has been shown by comparison of branched and linear chain polyethylene. The c parameter remains constant, but the a and b directions are expanded for the branched polymer crystals. Both methyl and... 

Surfaces give information on material morphology only in seldom cases (e.g., crystalline polymers crystallized from solution or melt). But specially prepared surfaces can yield information on the internal morphology of the material, for instance, brittle fracture surfaces or selectively etched... 

A nnmber of techniques are appropriate to investigate the hierarchy of structnres formed by crystalline polymers. Crystallized polymer chains form crystal structures with lattices built up by translation of unit cells, just like crystals formed by low molar mass compounds. The space group symmetry depends on the polymer under consideration and also the conditions of the sample. For example, polyethylene usually forms a structure belonging to the orthorhombic crystal system, but at high pressures it is possible to obtain a hexagonal structure. Because it can adopt more than one crystal structure, polyethylene is said to be polymorphic. The best way to determine the crystal structure of a polymer is to perform wide-angle x-ray scattering (WAXS) experiments. WAXS on oriented polymers also provides information on the orientation of crystalline stems (chains). 

Seguela R (2007) Plasticity of semi-crystalline polymer Crystal slip versus melting-recrystallization, e-Polymers 032 1-20. 

The positive deviation from linearity of the crystalline melting point has been explained using classical theories [312]. The higher melting point crystalline polymer crystallizes faster until depletion results in inclusion of the lower melting polymer. The resultant effect is a melting point versus composition with a positive deviation, because the lower melting polymer will be included into the crystalline phase at a lower concentration relative to the composition of the blend. 

In order to reach a crystalline state, polymers must have sufficient freedom of motion. Polymer crystals nearly always consist of many strands with a parallel packing. Simply putting strands in parallel does not ensure that they will have the freedom of movement necessary to then find the low-energy con-former. The researcher can check this by examining the cross-sectional profile of the polymer (viewed end on). If the profile is roughly circular, it is likely that the chain will be able to change conformation as necessary. 

For crystalline polymers, the bulk modulus can be obtained from band-structure calculations. Molecular mechanics calculations can also be used, provided that the crystal structure was optimized with the same method. 

No polymer is ever 100% crystalline at best, patches of crystallinity are present in an otherwise amorphous matrix. In some ways, the presence of these domains of crystallinity is equivalent to cross-links, since different chains loop in and out of the same crystal. Although there are similarities in the mechanical behavior of chemically cross-linked and partially crystalline polymers, a significant difference is that the former are irreversibly bonded while the latter are reversible through changes of temperature. Materials in which chemical cross-linking is responsible for the mechanical properties are called thermosetting those in which this kind of physical cross-linking operates, thermoplastic. 

The loop formed by the chain as it emerges from the crystal, turns around, and reenters the crystal may be regarded as amorphous polymer, but is insufficient to account for the total amorphous content of most crystalline polymers. 

In order to carry out an experimental study of the kinetics of crystallization, it is first necessary to be able to measure the fraction d of polymer crystallized. While this is necessary, it is not sufficient we must also be able to follow changes in the fraction of crystallinity with time. So far in this chapter we have said nothing about the experimental aspects of determining 6. We shall now briefly rectify this situation by citing some of the methods for determining 6. It must be remembered that not all of these techniques will be suitable for kinetic studies. 

Tensile Properties. Tensile properties of nylon-6 and nylon-6,6 yams shown in Table 1 are a function of polymer molecular weight, fiber spinning speed, quenching rate, and draw ratio. The degree of crystallinity and crystal and amorphous orientation obtained by modifying elements of the melt-spinning process have been related to the tenacity of nylon fiber (23,27). 

Polymer crystals most commonly take the form of folded-chain lamellae. Figure 3 sketches single polymer crystals grown from dilute solution and illustrates two possible modes of chain re-entry. Similar stmctures exist in bulk-crystallized polymers, although the lamellae are usually thicker. Individual lamellae are held together by tie molecules that pass irregularly between lamellae. This explains why it is difficult to obtain a completely crystalline polymer. Tie molecules and material in the folds at the lamellae surfaces cannot readily fit into a lattice. 

A crystalline or semicrystalline state in polymers can be induced by thermal changes from a melt or from a glass, by strain, by organic vapors, or by Hquid solvents (40). Polymer crystallization can also be induced by compressed (or supercritical) gases, such as CO2 (41). The plasticization of a polymer by CO2 can increase the polymer segmental motions so that crystallization is kinetically possible. Because the amount of gas (or fluid) sorbed into the polymer is a dkect function of the pressure, the rate and extent of crystallization may be controUed by controlling the supercritical fluid pressure. As a result of this abiHty to induce crystallization, a history effect may be introduced into polymers. This can be an important consideration for polymer processing and gas permeation membranes. 

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Compared with most other crystalline polymers the permeability of P4MP1 is rather high. This is no doubt due to the ability of gas molecules to pass through the open crystal structure with the large molecular spacing. 

Crystalline polymers primarily of interest as fibres, including some grades which may be considered as liquid crystal polymers. 

Structurally the difference between PEN and PET is in the double (naphthenic) ring of the former compared to the single (benzene) ring of the latter. This leads to a stiffer chain so that both and are higher for PEN than for PET (Tg is 124°C for PEN, 75°C for PET is 270-273°C for PEN and 256-265°C for PET). Although PEN crystallises at a slower rate than PET, crystallization is (as with PET) enhanced by biaxial orientation and the barrier properties are much superior to PET with up to a fivefold enhancement in some cases. (As with many crystalline polymers the maximum rate of crystallisation occurs at temperatures about midway between Tg and in the case of both PEN and PET). At the present time PEN is significantly more expensive than PET partly due to the economies of scale and partly due to the fact that the transesterification route used with PEN is inherently more expensive than the direct acid routes now used with PET. This has led to the availability of copolymers and of blends which have intermediate properties. 

Figure 25.24. Difference in behaviour between liquid crystal polymers and conventional crystalline polymers in the melt at rest, during shear and when cooled after shearing...

Addition of a plasticizer decreases the Tg of the polymer and, in partially crystalline polymers, also influences both crystallization and melting. The amount of plasticizer affects its effectiveness. Thus, while the Tg of the polymer is strongly depressed by small plasticizer additions, the increase in the plasticizer content leads to lower decrease in To and in several systems two T values can be found [36J. Therefore, the increase in the plasticizer content in polymers does not show a monotonic decrease in Tg. 

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