Crystal structures, polymers unit cells

Table 6.1 Crystal structure and unit cell dimensions for some common semi-crystalline polymers...

A very recent and exciting example of a 3-D coordination polymers can found in the work of Ferey et al,25 on the use of trinuclear chromium clusters in combination with benzene-1,4-dicarboxylic acid. This reaction yields porous structures with unit cells volumes of up to 700 000 A3, i.e. similar to that of a small protein In the absence of single crystals for structure determination, the structures were solved by the ingenious use of Monte Carlo simulations with simulated annealing. 

Macromolecular crystallinity differs in three important ways from low-molecular weight molecular crystallinity polymers never crystallize completely, the unit cells are always smaller than the macromolecule, i.e. the crystal lattice is formed by the subunits rather than by the whole molecule and a long polymer chain can thread through different crystallites. Complete crystallization is impeded because of the structural polydispersity and the topological constraints resulting from the fact that... 

The unit cell dimensions calculated by these procedures for polyethylene are a = 0.740 nm, b = 0.493 nm and c = 0.254 nm and the density is (8.6 kg/m. Figure 8.3 shows the ab plane. The c-axis is parallel to the chain axis and its length of 0.254 nm is equal to the distance between alternate carbon atoms. This structure for polyethylene is identical with that determined for crystals of pure n-paraffins such as C32H66 - low molecular analogs of polyethylene. X-ray structures have been determined for many crystalline polymers. Miller [5] has published an extensive compilation of polymer unit cell data. 

Monomer B5A exhibits two enantiotropic smectic mesomorphic phases (Se66Sb75I). The S phase does not crystallize even when cooled down to -20 "C. In this study, we will concentrate on the photopolymerization of B5A at room temperature (Sg phase) and the detailed structural characterization of the resulting polymeric network (subsequently called PB5A-RT). The synthesis and structural characterization for monomer B5A will be presented in a separate paper and only summarized results are presented here for comparison with its polymer. Monomer B5A in the smectic E phase has an orthorhombic structure with unit cell dimensions, a=6.609 A, b=7.704 A and c=51.92 A. It adopts a tilted molecular bilayer structure within the unit cell in the c direction. Within each smectic layer the molecules are tilted, making an angle of about SO with the smectic layer normal (or c direction). 

Figure 4.10 Crystal structure of polyethylene (a) unit cell shown in relation to chains and (b) view of unit cell perpendicular to the chain axis. [Reprinted from C. W. Bunn, Fibers from Synthetic Polymers, R. Hill (Ed.), Elsevier, Amsterdam, 1953.]...

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. 

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.

Amorphous stereotactic polymers can crystallise, in which condition neighbouring chains are parallel. Because of the unavoidable chain entanglement in the amorphous state, only modest alignment of amorphous polymer chains is usually feasible, and moreover complete crystallisation is impossible under most circumstances, and thus many polymers are semi-crystalline. It is this feature, semicrystallinity, which distinguished polymers most sharply from other kinds of materials. Crystallisation can be from solution or from the melt, to form spherulites, or alternatively (as in a rubber or in high-strength fibres) it can be induced by mechanical means. This last is another crucial difference between polymers and other materials. Unit cells in crystals are much smaller than polymer chain lengths, which leads to a unique structural feature which is further discussed below. 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

Vc crystalline Va, amorphous). The densities of the pure crystalline (pc) and pure amorphous (pa) polymer must be known at the temperature and pressure used to measure p. The value of pc can be obtained from the unit cell dimensions when the crystal structure is known. The value of pa can be obtained directly for polymers that can be quenched without crystallization, polyfethylene terephtha-late) is one example. However, for most semi-crystalline polymers the value of pa is extrapolated from the variation of the specific volume of the melt with temperature [16,63]. 

This polymer crystallizes in three polymorphs. The threefold helical structure packs in a trigonal unit-cell with a = 14.3 A (1.43 nm) and c = 28.7 A (2.87 nm). The 8-fold helical structure occurs in a tetragonal unit-cell with a = 13.8 A (1.38 nm) and c = 78.2 A (7.82 nm). Axial periodicity in both cases is similar [h = 9.6 A (960 pm) and 9.8 A (980 pm), respectively], but the helix twist-angle is different (120 and 45°, respectively). Distribution of the charged side-groups in these helices was discussed. An orthorhombic form, with a twofold helical structure, has a repeat of 18.6 A (1.86 nm). 

Experiments at high pressure have shown that the P-T phase diagram of butadiene is comparatively simple. The crystal phase I is separated from the liquid phase by an orientationally disordered phase II stable in a narrow range of pressure and temperature. The strucmre of phase I is not known, but the analyses of the infrared and Raman spectra have suggested a monoclinic structure with two molecules per unit cell as the most likely [428]. At room temperature, butadiene is stable in the liquid phase at pressures up to 0.7 GPa. At this pressure a reaction starts as revealed by the growth of new infrared bands (see the upper panel of Fig. 25). After several days a product is recovered, and the infrared spectrum identifies it as 4-vinylcyclohexene. No traces of the other dimers can be detected, and only traces of a polymer are present. If we increase the pressure to 1 GPa, the dimerization rate increases but the amount of polymer... 

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