Thermal Analysis of Polymeric Materials

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The amorphous macromolecules are entangled random coils (see Sects. 1.3). At low temperature these are frozen to glassy solids. Above the glass transition temperature they are viscous liquids (see Sects. 2.5 and 5.6). Corner A of Fig. 5.42 gives a schematic representation of the amorphous macroconformation of a polymer in the solid (glassy) or liquid state.

Fig. 5.42

To identify the macroconformation of an equilibrium crystal, one must first find the helix of lowest energy and then pack such helices densely, side-by-side as described in Sect. 5.1.8. Such crystals are of an extended-chain macroconformation, as illustrated schematically at corner C of Fig. 5.42. Two problems prevent the common occurrence of extended-chain crystals. First, unlike in short, small molecules, macromolecules are not all of the same length. They could, thus, not produce a smooth, low-energy surface with their chain ends. Second, flexible molecules in the melt or in solution are not sufficiently extended to immediately go to the equilibrium crystal. To produce the extended-chain macroconformation, a substantial reduction of its entropy is necessary, producing a barrier of positive free enthalpy of extension ( G = T S, see the discussion of entropy elasticity in Sect. 5.6.5). The ultimate compensation of the entropy of extension can occur only after the packing of the molecule into the crystal is achieved and all heat of

crystallization has been absorbed ( Hcryst = Tm Scryst). If the major disentanglement and close packing do not occur in close succession, i.e., are decoupled processes, the

nonequilibrium path to the crystal leads to arrested, metastable states.

A path with a lower positive free-enthalpy barrier to crystallization than to the extended-chain crystals involves a folded-chain macroconformation and leads to the chain-folding principle. Crystallization occurs first with shorter, chain-folded segments of the molecules, as shown schematically at B of Fig. 5.42 (A B). From

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the most mobile amorphous state with separated macromolecules, the dilute solution, rather perfect lamellar crystals have been grown as is illustrated in Sect. 5.4. The path A C, in contrast, is not possible for flexible macromolecules. After the initial folding, extended-chain crystals result only, if there is sufficient mobility in the folded-chain crystal to permit annealing with chain extension, as is documented in Sect. 5.7. The mobility is linked to a sliding diffusion within the crystal [10]. Frequently, such mobility is found in conformationally disordered mesophases (condis crystals, see Sects. 2.5 and 5.5). Another path to extended chain crystals is crystallization during polymerization. In this case the mobile monomer goes directly to the polymer crystals, i.e., the randomly coiled amorphous phase is bypassed. Examples of crystallization during polymerization can be found in Fig. 5.77, below for polydiynes, Fig. 3.104 and 3.105 for poly(oxymethylene), and Figs. 3.86 and 3.16–22 for lithium polyphosphate. On crystallization from the most mobile state, the gas phase, rather perfect extended-chain single-crystals have been grown. A typical example is Se, which can easily be grown into large, equilibrium crystals [11]. For the crystal structure of Se see Fig. 5.20.

The corners A, B, and C in Fig. 5.42 form the three limiting molecular macroconformations. All three were described in the 1930s [12 and 13], but applied only in the 1960s and 1970s, following the fundamental work of Keller (UK), Fischer (Germany), Geil and Till (USA), and Kobayashi (Japan) [14–18].

A fringed-micellar structure was proposed in 1930 for the structures of colloids and gels [19]. By adding the possibility of chain-folded crystals, as illustrated in the center of Fig. 5.42, all three limiting macroconformations are combined. Semicrystalline polymers, thus, are a system consisting of folded-chain crystals, intercrystalline amorphous, and possibly extended-chain subsystems (see Fig. 2.80). The latter are expected particularly in fibers drawn to large extension. Most samples have a macroconformation somewhere within the triangle of Fig. 5.42.

The dimensions of the crystal and amorphous subsystems vary from nanometers to micrometers, i.e., polymeric materials are nanophaseor microphase-separated and have only a partial crystallinity. If we treat homopolymers as one-component systems, the phase rule of Sect. 2.5.7 does not permit equilibrium between two phases, except at the transition temperature. Partially crystalline homopolymers are, thus, not in equilibrium. The properties of semicrystalline polymers are critically influenced by the interactions between the amorphous and crystalline domains, as is seen in the formation of rigid amorphous fractions, discussed in Sect. 6.1.3 and 6.3.4.

5.2.3 Fold Length

The lamellar thickness of the crystal, and with it the fold length of the macroconformation, is a function of the crystallization conditions. Figure 5.43 illustrates the temperature dependence of the lamellar thickness on the example of polyethylene crystallized from various solvents. The curves in the figure shift proportionally with the temperatures of dissolution of equilibrium crystals and reveal that the supercooling of the solution is the main factor determining the fold length. On approaching the longer fold lengths at higher crystallization temperatures, the crystallization rate slows and finally it becomes impossible to wait for crystallization.

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The fact that the lamellar thickness is not mainly a function of temperature, but of the degree of supercooling, expressed by Tm Tc, can also be deduced from Fig. 5.45 which shows the results of crystallization of polyethylene from dilute solution at increasing pressure. The crystallization temperatures were chosen at about equal supercoolings, but increasing temperatures. On going from atmospheric pressure to 500 MPa, the crystallization temperature was increased from 360 K to 445 K. The

Fig. 5.45

increase in thickness on crystallization under higher pressures under these conditions is small and approximately proportional to 1/T, in contrast to the atmospheric-pressure data of Fig. 5.43.

Crystallization of polyethylene from the melt under elevated pressure of more than 300 MPa leads to crystals that are initially folded, but extend increasingly faster with temperature because of the existence of a hexagonal mesophase, discussed in Sect. 5.5 and shown also in Sect. 5.7. In Fig. 5.46 one can see that at higher temperature the subsequent thickening at 500 MPa increases quickly at higher temperature, reaching practically full extension at about 500 K. The data in Fig. 5.47 illustrate lesser rates of thickening at atmospheric pressure. In all cases the annealing of polyethylene to greater thickness is a process which accelerates with temperature, in contrast to the initial crystallization rate, which decreases as one approaches the melting temperature (see Sect. 3.6).

The question of the length of a flexible macromolecule before it folds on crystallization was first measured on oligo-urethanes:

HO (CH2 )4[O CO NH (CH2 )6NH CO O (CH2 )4]xOH

Figure 5.48 documents that the short-chain oligomers crystallize fully extended. As the chain length increases to the fold-length of the polyurethanes, the molecules fold,

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Fig. 5.46

Fig. 5.47

as expected from the larger entropy of chain extension. For paraffins the limit of

growth in the extended-chain form has been reported to be 37 nm (C294H590, molar mass 4,100) [20]. When rather sharp, low-molar-mass fractions of poly(oxyethylene)

molecules became available, it was found that, depending on supercooling, molecules could grow as extended chain, once, and multiply folded crystals. Figure 5.49 displays the data for 10,000 and 25,000 molar masses. The high-molar-mass sample

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Fig. 5.48

Fig. 5.49

has a fold length which changes continuously with supercooling, while the low-molar- mass sample shows the step-wise change due to integral folding, with the hightemperature crystallization leading to once-folded molecules.

Theories about the details of the fold-length dependence of lamellar crystals have gone through many steps, but are not fully resolved at present. References to some

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of the more detailed discussions are listed in the general references to this section. A theory of polymer crystallization must explain not only the fold length, but also the rejection of different molecular masses on crystallization, the reasons for the larger supercooling than even necessary for chain folding, the increases and decreases of the initial fold length on annealing at the crystallization temperature, the attainment of integral folds for molar masses, and the regularity of folds (see also Sect. 3.6).

5.2.4 Lamellar Crystals

In the following figures the morphology of folded-chain single-crystals is shown with a series of electron and optical micrographs [21]. The regular hexagonal lamellae of poly(oxymethylene) in Fig. 5.50 permits the easy recognition of trigonal crystal symmetry and an assignment of the Miller indices for the crystal structure indicated in Fig. 5.12. The folds are aligned in the {001} lamellar surfaces. The (CH2 O )x chains have 2*9/5 helices with bond rotations of 102o, close to a continuous succession of gauche conformations.

Fig. 5.50

Figures 5.51 and 5.52 show the special features of polyethylene grown from dilute solution. The two folded-chain lamellae in Fig. 5.51 can easily be recognized as orthorhombic crystals. The fast-growing faces on crystallization, causing the lamellar morphology, are of type {110}. These are the active growth faces where new folded chains are added on crystallization. The top and bottom faces should then be {001}. The crystals in Fig. 5.52 display additional {100} faces. These develop often on crystallization at higher temperature and are prominent on crystallization from the melt. Also, one can see that the lamellae develop growth spirals, defects that permit thickening along c. Otherwise the fold surfaces preclude growth in direction [001] (see Sects. 3.6 and 5.3). Some special features are the pleats in the crystals, which are

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Fig. 5.51

Fig. 5.52

roughly parallel to the a- and b-axes. The optical micrographs in Fig. 5.53 reveal the origin of the pleats. They indicate that, while floating in solution, the crystals are not actually flat, but are tent-like, as is actually seen in the upper optical micrograph for a crystal of the type seen in Fig. 5.52. The floating crystal displays sloping lamellar surfaces of indices {312} for the faces leading to the {110} growth faces, and {201} adjacent to {100}. The pleats are produced on collapse of the tent. The two bottom