Polymer crystal

Amorphous polymers with irregular bulky groups are seldom crystallizable, and unless special techniques are used even ordered polymers are seldom 100% crystalline. The combination of amorphous and crystalline structures varies with the structure of the polymer and the precise conditions that have been imposed on the material. For instance, rapid cooling often decreases the amount of crystallinity because there is not sufficient time to allow the long chains to organize themselves into more ordered structures. The reason linear ordered polymers fail to be almost totally crystalline is largely kinetic, resulting from an inability of 

FIGURE 2.14 Schematic two-dimensional representation of a modified micelle model of the crystalline-amorphous structure of polymers. 

FIGURE 2.15 Structure of a spherulite from the bulk, (b) A slice of a simple spherulite. As further growth occurs, filling in, branch points, etc. occur as shown in (a). The contour lines are simply the hairpin turning points for the folded chains. 

Many polymers form more complex single crystals when crystalhzed from dilute solution including hollow pyramids that often collapse on drying. As the polymer concentration increases, other structures occur, including twins, spirals, and multilayer dendritic structures with the main structure being spherulites. 

FIGURE 2.16 Spherulite structure showing the molecular-level lamellar chain-folded platelets and tie and frayed chain arrangements (a), and a more complete model of two sets of three lamellar chain-folded platelets formed from polyethylene (PE) (b). Each platelet contains about 850 ethylene units as shown here. 

Many bulk polymers that are crystallized from a melt are semicrystalline and form a spherulite structure. As implied by the name, each spherulite may grow to be roughly spherical in shape one of them, as foimd in natural rubber, is shown in the transmission 

Transmission electron micrograph showing the spheruhte structure in a natural rubber specimen. (Photograph supphed by P. J. Phillips. First published in R. Bartnikas and R. M. Eichhorn, Engineering Dielectrics, Vol. IIA, Electrical Properties of Solid Insulating Materials Molecular Structure and Electrical Behavior, 1983. Copyright ASTM, 1916 Race Street, Philadelphia, PA. Reprinted with permission.) 

Spherulites are considered to be the polymer analogue of grains in polycrystalline metals and ceramics. Flowever, as discussed earher, each spheruhte is really composed of many different lamellar crystals and, in addition, some amorphous material. Polyethylene, polypropylene, poly(vinyl chloride), polytetrafluoroethylene, and nylon form a spherulitic structure when they crystalhze from a melt. 

FigMra 14.13 Schematic representation of the detailed structure of a spheruhte. 

The obvious questions to ask concerning crystallinity in polymers are why and how do polymer molecules crystallize The answer to the question why is given by consideration of the thermodynamics of the crystallization 

As with all applications of thermodynamics, it can only be strictly applied to processes which occur qu i-statically, that is very slowly. Polymers are often cooled rapidly from the melt, particularly when they are being processed industrially. In this situation crystallization is controlled by kinetics and the rate at which the crystals nucleate and grow becomes important. With many crystallizable polymers it is possible to cool the melt so rapidly that crystallization is completely absent and an 

Single crystals of many materials occur naturally (e.g. quartz and diamond). For other materials such as metals and semi-conductors the growth of single crystals from the melt is now a routine matter. With polymers it is only recently that true single crystals have been prepared. This can only be done by using the process of solid-state polymerization outlined in Section 2.11. The most perfect crystals are obtained with certain substituted diacetylene monomers which polymerize topochemi-cally to give polymer crystals which can be 100% crystalline and are of macroscopic dimensions. 

When the crystal structure of a molecular compound is analysed both the relative positions of the atoms on the molecular repeat units and the arrangement of these segments in the unit cell must be determined. This three-dimensional structure is normally determined using X-ray diffraction, involving measurement of the positions and intensities of all the X-ray maxima from a single crystal sample. Computer-controlled, four-circle diffractometers are now available which allow the relative positions of all the atoms in crystals with quite complex structures to be determined as a matter of routine in a period of a few days, but such machines required good, relatively large crystals. 

The angle / is related to hi and the radius of the film, r, through the simple geometrical construction shown in Fig. 4.3(b). This leads to the relation 

The negative expansivity in the direction of the chain axis in crystalline lattices has been found for many polymers. There is only a small variation in values for various polymer crystals which points towards a universal mechanism independent of their chemical structure. The aL values of various polymer crystals have been tabulated in Table 8.1. Polyethylene crystals were first and extensively investigated by various workers over an extended range of temperature. Lifshitz [53] predicted the negative thermal expansion of the chain-like structures in the 1950s. He showed that the excitement of bending waves in such structures with the dispersion relationship W must lead to negative 

Lacks and Rutledge [46] carried out simulation for isotactic polypropylene (IPP) using the Sorensen, Lian, Kesner and Boyd (SLKB ) force field for the temperature range 0-350 K. They observed that although the 

The negative expansivity along the chain direction (a[j) seems to be a universal phenomenon with planar zigzag chains as it is exhibited by a variety of polymers of different chemical compositions, i.e. PE [37,38,60], ethylene tetrafluoroethylene alternating copolymer [61], PET [36], nylon 6 [39, 40], poly (vinyl alcohol) [62] and poly diacetylene 

A number of studies have been carried out on the helical chain structure. Two crystals i.e. polyoxymethylene (POM) and poly(4-methylpentene 1) (P4MP1) have been extensively studied by Choy and Nakafuku [64] and White et al [42], respectively. Choy and Nakafuku 

In general, polyimides have relatively high glass transition temperatures. 

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Snetivy D and Vancso G J 1994 Atomic force microscopy of polymer crystals 7. Chain packing, disorder and imaging of methyl groups in oriented isotactic polypropylene Po/yme/ 35 461... 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

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. 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

Polymer crystals form by the chain folding back and forth on itself, with crystal growth occurring by the deposition of successive layers of these folded chains at the crystal edge. The resulting crystal, therefore, takes on a platelike structure, the thickness of which corresponds to the distance between folds. 

Whenever a phase is characterized by at least one linear dimension which is small, the properties of the surface begin to make significant contributions to the observed behavior. We shall examine the structure of polymer crystals in more detail in Sec. 4.7, but for now the following summary of generalizations about these crystals will be helpful ... 

Polymers crystallize in the form of thin plates or lamellae. The thickness of each of these lamellae is on the order of 10 nm. 

Figure 4.4 Idealized representation of a polymer crystal as a cylinder of radius r and thickness 1. Note the folded nature of polymer chains in crystal.

The fundamental equilibrium relationships we have discussed in the last sections are undoubtedly satisfied to the extent possible in polymer crystallization, but this possibility is limited by kinetic considerations. To make sense of the latter, both the mechanisms for crystallization and experimental rates of crystallization need to be examined. 

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. 

Figure 4.8a shows how this quantity varies with time for polyethylene crystallized at a series of different temperatures. Several aspects of these curves are typical of all polymer crystallizations and deserve comment ... 

The greater the undercooling, the more rapidly the polymer crystallizes. This is due to the increased probability of nucleation the more supercooled the liquid becomes. Although the data in Fig. 4.8 are not extensive enough to show it, this trend does not continue without limit. As the crystallization temperature is lowered still further, the rate passes through a maximum and then drops off as Tg is approached. This eventual decrease in rate is due to decreasing chain mobility which offsets the nucleation effect. 

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. 

Melting temperatures of as-polymerized powders are high, ie, 198—205°C as measured by differential thermal analysis (dta) or hot-stage microscopy (76). Two peaks are usually observed in dta curves a small lower temperature peak and the main melting peak. The small peak seems to be related to polymer crystallized by precipitation rather than during polymerization. 

Fig. 22.5. A chain-folded polymer crystal. The structure is like that of a badly woven carpet. The unit cell shown below, is relatively simple and is much smaller than the polymer chain.

The repeat length in the triclinic polymer crystals (75.3 nm) is significantly less than for PBT (86.3 nm) and PET (99.5 nm). This has been claimed to make the crystal more spring-like in the long axis resulting in enhanced resilience and wear resistance in carpet fibres to a level approaching that of polyamide fibres. 

Whenever the polymer crystal assumes a loosely packed hexagonal structure at high pressure, the ECC structure is found to be realized. Hikosaka [165] then proposed the sliding diffusion of a polymer chain as dominant transport process. Molecular dynamics simulations will be helpful for the understanding of this shding diffusion. Folding phenomena of chains are also studied intensively by Monte Carlo methods and generalizations [166,167]. 

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