Thermal Analysis of Polymeric Materials

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The noncrystalline region in a semicrystalline polymer, measured by crystallinity, is itself a typical polymer-specific defect. It is also called an amorphous, or threedimensional crystal defect. As shown schematically in Fig. 5.87, the chain molecules are connected to the neighboring crystals, permitting to assign the defect to the surrounding crystals. The strain within the molecules bridging the crystals keeps the amorphous regions from crystallizing and broadens the glass transition with a shift to

Fig. 5.87

higher temperatures. The rigid amorphous fraction, described in Sect. 6.1, has most likely its origin at the interface of the amorphous defect with the crystal. In crystals of small and rigid macromolecules such amorphous defects are also found in grain boundaries, but only in semicrystalline, flexible polymers do these defects become truly three-dimensional and take on a nanophase dimension, as suggested already in the 1960s along with many other polymer-specific defects, redrawn in Fig. 2.98.

Figure 5.88 is an illustration of two-dimensional defects in the form of surfaces and grain boundaries. They either terminate a crystal or separate it from the threedimensional defects. In polymer crystals, these surfaces and grain boundaries are rarely clean terminations of single-crystalline domains, as one would expect from the unit cell descriptions in Sect. 5.1. The surfaces may contain folds or chain ends and may be traversed by tie molecules to other crystals and cilia and loose loops that enter the amorphous areas, as is illustrated in Figs. 5.87 and 2.98. The properties of a polycrystalline sample are largely determined by the cohesion achieved across such surfaces and the mechanical properties of the interlamellar material, the amorphous defects.

One-dimensional or line-defects are added to the list of defects in Fig. 5.86. They are commonly known as dislocations and are prominently involved in deformation mechanisms of metals and salts. In polymers, they have a more restricted function.

which connects the ends of a Burgers circuit that would meet in an ideal crystal. In the screw dislocation a slip of one cube has occurred in the Burgers circuit, giving rise to a spiral. The line defect is shown on the left of Fig. 5.90. In this case the dislocation vector is at right angles to the Burgers vector. One can visualize the edge dislocation as an extra layer of motifs that terminates, causing a strained region within the crystal along the direction of the dislocation vector.

In crystals of small molecules and rigid macromolecules the dislocations are primarily involved in deformation mechanisms, as is illustrated in Fig. 5.91. For the edge dislocation, a glide can occur only parallel to the Burgers vector in the glide

Fig. 5.91

plane S, defined by d and b. The screw dislocation, in contrast, can glide in any plane

parallel to the dislocation vector d. In trying to transfer this deformation mechanism to flexible macromolecules, one finds that many dislocations are sessile, i.e., they do not move. If we assume that the heavy lines in Fig. 5.91 represent the covalent backbone bonds, the glide of the edge dislocation would have to involve breakage of bonds, which does not happen in flexible macromolecules. Glide planes in polymers must thus be parallel to the chain direction. Before bonds break, flexible macromolecules will be able to slip, involving point defects rather than dislocations, as will be discussed below. The glide of the screw dislocation would be possible, but macromolecules have often screw dislocations of such large Burgers vectors, that a glide does not occur. Furthermore, the motion of a single dislocation produces a deformation of a magnitude of only one Burgers vector, so that a continuous generation of new dislocations is necessary for larger deformations. Such sources exist within crystals of small molecules and rigid macromolecules and produce continuous streams of defects on application of small stresses. They need, however,

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crystal domains of micrometer in size. In crystals of flexible polymers such dimensions rarely available making the generation of new dislocations unlikely (see Sect. 5.2).

Screw dislocations are also of help in developing crystal thickness by providing a continuous, indestructible secondary nucleus (see Sect. 3.5). In chain-folded crystals of flexible, linear macromolecules, crystal growth in direction of the chain axis is limited by the chain folds. The screw dislocations, however, can provide a mechanism for continuous growth in the chain direction via screw dislocations with a Burgers vector of the enormous length of the thickness of the lamellar crystal instead of the unit cell dimension. The example on the right of Fig. 5.92 has screw dislocations with leftas well as right-handed rotations when looking along the dislocation vector. The terrace, close to the center of the figure, is caused by two screw dislocations of

Fig. 5.92

opposite handedness, generated in close proximity. Whenever the layers of the two screw dislocations meet, a new terrace layer is generated (see also Fig. 3.72). The screw dislocations with large Burgers vectors can be generated by reentrant crystal growth faces or a tear or slip of a lamella.

Edge dislocations with their extra planes of motifs as seen in Fig. 5.90 can be made visible on magnification by double diffraction, illustrated by the optical analog of Fig. 5.93. Two lamellae are represented by the parallel lines, with each line representing the projection of a growth plane of Fig. 5.54. At the point of the missing portion of the extra growth plane, the rotation angle changes and a new fringe is created, as described in more detail in Appendix 17. The additional fluctuations in the fringes in Fig. 5.93 are due to minor variations in line separation of the drawing.

A similar picture is created when two superimposed polymer crystals are viewed in the electron microscope, as shown in Fig. 5.94. The changes in rotation angle and

522 5 Structure and Properties of Materials

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Fig. 5.93

Fig. 5.94

separation of the planes of motifs in the interior of the crystal cause the more complicated patterns. By following the Moiré lines, one discovers the three terminating fringes, caused by three dislocations.

Some more insight in plastic deformation can be gained by molecular dynamics (MD) simulation of a crystal that was enclosed on three sides in a rigid box of too

524 5 Structure and Properties of Materials

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axes, as it is also introduced in Sect. 5.2. Details on the MD simulations are given in Sects. 1.3 and 2.1 and in the figures given in Sect. 5.3.4. Note that the initial crystal was monoclinic, so that the chain axes are parallel to the b-axes, which are the z axes in Fig. 5.95 (the a-axis is x, and the c-axis is the diagonal of the crystal).

Point defects cannot be seen directly in crystals of flexible macromolecules, but have been deduced from calculations and models. The defect in Fig. 5.96 in the third chain from the left consists of a sequence of gauche, trans, and gauche conformations and is called a 2g1 kink (see also Fig. 5.86). This disruption of the crystal is small, but it will be shown to assist in the motion of chains in annealing and deformation, as well as contribute to the change in heat capacity beyond the vibrational contributions.

5.3.4 Supercomputer Simulation of Crystal Defects

Major progress in the understanding of point defects in polymers listed in Fig. 5.86 became possible when sufficiently large segments of crystal could be simulated on supercomputers for a time sufficiently long to show the approach to equilibrium in what one might consider super-slow motion to bridge the enormous jump from the atomic to the macroscopic time scale [32,33] (see Sects. 1.3.4 and 5.3.5). Figure 5.97 details a 180o twist in a polyethylene crystal. The bottom-portions of seven chains of a simulation are shown, as in Fig. 1.47. At time zero the twist is centered in the

Fig. 5.97

middle chain and forces the bottom portion of the chain to be out of register with the other chains. The twist has the extremely short life time of 2 ps and quickly diffuses to the nearest crystal surface, as seen by the complete turning of the marked chain end between steps d and e. If such twists are to cause large-scale motion, as are involved in deformation, there must be a continuous source of new twists.

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A point defect that does not lead to a full rotation of the chain by 180o is a single gauche conformation as illustrated in Fig. 1.37 which is equivalent to a single bond being rotated by 120o and accommodating the distortion of the chain by a twist in either direction away from the all-trans chain. The tracking of such simple gauche defects at high temperature is shown in Fig. 5.98. A defect is marked by a heavy line for the time of its existence which is defined by a bond with a rotation angle of more than 90o away from the stable trans conformation. From Fig. 5.98, one can deduce

Fig. 5.98

more or less random appearances of defects, an extremely short life time, and a tendency to cluster in kinks (see Fig. 5.96). Changing the temperature, crystal size, and restrictions changes the life times of the defects, their concentration, and also their distribution (see also Fig. 1.48).

The results of many MD simulations are summarized in Fig. 5.99. The rate of attainment of defects is computed for the whole chain, so that for every bond in the crystal of polyethylene one expects at room temperature, 300 K, about 1010 brief excursions to a gauche conformation in every second! The polymer crystals have thus much more mobility and disorder than is conveyed by the drawings of the crystal structures in Sect. 5.1. The short life times connected with the high rate of formation and destruction gives the concentrations plotted in Fig. 5.100 (see also the simulations of Figs. 2.14 and 2.15). At room temperature, the concentration is only a fraction of one percent, in agreement with the infrared data shown in the figure and the increase of heat capacity beyond the vibrational contributions (see Fig. 2.65). Close to melting, the gauche concentration reaches about 2% of all bonds.

The details of the mechanism of formation of a kink can be deduced from Fig. 5.101, where one chain that develops a kink has been drawn in a sequence of snapshots, spaced 0.1 ps apart. The perspective is as before in Figs. 1.47 and 5.97.

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Fig. 5.99

Fig. 5.100

By inspection, one can see that the kink is the result of the collision of a transverse (A), torsional (B), and longitudinal vibration (C) between 0.5 and 1.1 ps (see also Fig. 1.47). After formation, this particular kink defect had a life time of about 2 ps.

The mechanism of twisting of a single chain is illustrated in Fig. 5.102. One can see a very gradual twist starts at about 1.5 ps, and is completed after 2.3 ps. After this