Macromolecules in the Crystalline State

In most cases, however, polymers crystallize neither completely nor perfectly. Instead, they give semicrystalline materials, containing crystalline regions separated by adjacent amorphous phases. Moreover, the ordered crystalline regions may be disturbed to some extent by lattice defects. The crystalline regions thus embedded in an amorphous matrix typically extend over average distances of 10-40 nm. The fraction of crystalline material is termed the degree of crystallinity. This is an important parameter of semicrystalline materials. 

The fringed micelle picture is not particularly suitable for describing synthetic polymers crystallized from solution or melt. However, the fibrils of many nat- 

The shape of macromolecules within a folded lamella is not the same for all polymers. In crystalline polyethylene, for example, the chains assume a planar zigzag conformation, but in some other polymers like polypropylene and polyoxymethylene the chains prefer a helical shape, as in proteins. The helix might have three, four, or five monomer units per turn, i.e., the helices are three-, four-, or five-fold (Fig. 1.12) 

Finally, it should be mentioned that polymers can exhibit polymorphism, i.e., they can crystallize in different types of lattices. The different crystal forms generally differ in their physical properties, e.g., crystallite melting point and density. 

Crystalline polymers exhibit the following basic properties They are opaque as long as the size of the crystallites or spherulites, respectively, lies above the wavelength of light. Their solubility is restricted to few organic solvents at elevated temperature. The following crystalline polymers have attained technical importance as thermoplastic materials polyethylene, polypropylene, aliphatic polyamides, aliphatic/aromatic polyamides, aliphatic/aromatic polyesters, poly-oxymethylene, polytetrafluoroethylene, poly(phenylene sulfide), poly(arylene ether ketone)s. 

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P. Corradini. Observation of different conformations of a macromolecule in the crystalline state , J. Polym. Sci., Polym. Symp. 51, 1 (1975). 

The impossibility of transferring these solid-state structures into a fluid state was also an apparent argument against inorganic macromolecules. The existence of inorganic macromolecules in the crystalline state is also difficult to prove decisively, since a transformation from a molecular to an ionic lattice can occur with temperature. Germanium telluride, for example, is present in an arsenic-type structure below 670 K, whereas above 670 K, it exists as a rock-salt structure. The former is a molecule lattice, the latter an ion lattice. The same substance could, therefore, be defined as macromolecular or nonmacromolecular according to its state. 

On the basis of the general concepts of the energy state of amorphous and crystalline structures, we might assume that the stability of a polymer is directly dependent on the degree of its crystallinily. However, we must consider the fact that the high degree of lability of the macromolecules in the crystalline state at increased temperatures can promote a more intensive development of the decomposition processes [60]. 

Figure 6 Different helical conformations adopted by macromolecules in the crystalline state. The molecular helices are shown for PE, isotactic polypropylene, syndiotactic polypropylene, and polyethylene oxide from left to right, respectively. The type of the helix is denoted by the number of monomers per integer number of turns shown in subscript.

Studies are in progress of the molecular dynamics of macromolecules in the crystalline state. The work on polyethylene, poly(oxymethylene), and certain biopolymers has recently been reviewed. ... 

A X-ray crystallographic method for detecting the transient accumulation of intermediates in enzyme catalysis, protein folding, ligand-binding interactions, and other processes involving macromolecules. The approach is premised on the well documented retention of substantial reactivity of biological macromolecules, even in the crystalline state. 

The problem is further complicated for vinyl polymers with their problems of stereoisomerism. The first descriptions of the conformational state of isotactic polypropylene in solution go back 25 years (178, 179, 192, 193). Corradini, Allegra, and Ganis proposed a model, still essentially valid today, according to which macromolecules possess a local helical structure analogous to that observed in the crystalline state. The helix segments are rather short, only a few monomer units, after which an inversion of the helix sense occurs, with simultaneous alteration of its direction (Figure 15). As a whole this disordered con-... 

Fig. 1. Side view (above) and end view (below) of the macromolecule of isotactic poly[l-(l-naphthyl)ethane-l,2-diyl] in the crystalline state. The helix symbol is s(2 4/1). The chain axis is shown by the dashed line, and c is the chain identity period. Hydrogen atoms are omitted. [From P. Corradini and P. Ganis. Nuovo Cimento, Suppl. 15, 96 (I960)].

Probably the most convincing evidence that crystalline structures can safely be used to draw conclusions about molecular function is the observation that many macromolecules are still functional in the crystalline state. For example, substrates added to suspensions of crystalline enzymes are converted to product, albeit at reduced rates, suggesting that the enzyme s catalytic and binding sites are intact. The lower rates of catalysis can be accounted for by the reduced accessibility of active sites within the crystal, in comparison to solution. 

Finally, high-resolution NMR has proved to be a technique of extraordinary power in the examination of the detailed structure of biological macromolecules, principally proteins and nucleic acids. It usefully complements their study in the crystalline state by X-ray diffraction, and while it cannot be said precisely to rival X-ray it also is capable of supplying many hundreds of structural parameters. In addition, NMR can provide many insights that X-ray cannot, including kinetic information. 

Isotactic poly(x-olcfin)s crystallise in a helical conformation, and, in the case of polypropylene, with three units per turn [4,5], Isotactic polypropylene has a melting point of 175°C and does not dissolve in boiling n-heptane [6,7], Note that, depending upon the configuration of the tertiary carbon atom of the polymer main chains, the poly(x-olefin) helices will be characterised by right-handedness or left-handedness. It should be mentioned that the helical structure of the poly(x-olcfin) chain per se is sufficient for the appearance of chirality of such a macromolecule [8], Figure 3.3 presents the helical conformation of chains of isotactic poly(a-olefin)s in the crystalline state (with three units per turn - the case of polypropylene) [5],... 

As discussed earlier, solid polymers can be distinguished into amorphous and the semicrystalline categories. Amorphous solid polymers are either in the glassy state, or - with chain cross linking - in the rubbery state. The usual model of the macromolecule in the amorphous state is the "random coil". Also in polymer melts the "random coil" is the usual model. The fact, however, that melts of semi-crystalline molecules, although very viscous, show rapid crystallisation when cooled, might be an indication that the conformation of a polymer molecule in such a melt is more nearly an irregularly folded molecule than it is a completely random coil. 

As with the corresponding macromolecules, the nucleosides and nucleotides are generally hydrated in the crystalline state about 45% of their crystal structures re-... 

As outlined in Chapters 23 and 24, water molecules are only loosely bound by hydrogen bonding at the peripheral atoms of the proteins and nucleic acids. Consequently, they are even more mobile than the atoms of the macromolecules to which they are coordinated. As we know from H2O/D2O exchange experiments, some water of hydration molecules are fully and easily replaced even in the crystalline state. The rate of dissociation must be diffusion-controlled and therefore at least in the ns time range. 

Although interesting within the framework of polymer physics and material science this would not be sufficient to attract so many workers from areas outside of conventional polymer research. Additional interest arouse because of the unusual structure of the polymers obtained via solid-state polymerization of diacetylenes and because of the mechanistic features related to its formation. Polydiacetylenes exhibit a fully conjugated and planar backbone in the crystalline state and are thus considered the prototype study object as far as the nature and physical behavior of polyconjugated macromolecules are concerned Theoretical discussions of the electronic structure of these polymers (2) lead to a description in terms of a wide band one-dimensional semiconductor... 

In order to form a crystal, molecules must aggregate in an orderly manner. This implies that intermolecular interactions have occurred in specific ways. It therefore follows that the crystal structure per se contains information on preferred modes of binding between the molecules in the crystalline state. In this Chapter we show how information on the most likely stereochemistries of interactions between functional groups in different molecules can be extracted from the three-dimensional coordinates of atoms listed in reports of crystal structure determinations. Three-dimensional structural data on binding stereochemistry may also be obtained from X-ray diffraction studies of the binding of small molecules to crystalline proteins and other macromolecules. These two types of information can be used, for example, to predict how drugs will interact with their biological receptors. 

Matsumoto, A., Katayama, K., Odani, T., Oka, K., Tashiro, K., Saragai, S. and Nakamoto, S. (2000) Feature of y-radiation polymerization of muconic acid derivative in the crystalline state. Macromolecules, 33, 7786-7792. 

Because most macromolecules exert their biological action in an aqueous solution, one may ask whether the molecular structure of a macromolecule in the crystal is a fair representation of the protein structure in solution. Since enzymes can be fully active in the crystalline state the answer is obviously that it is. 

Macromolecules exist in a variety of conformational forms that range from randomly coiled chains to more spatially ordered structures. Of particular interest are the polymers that adopt helical symmetry. Helical conformation is a result of an orderly repeated unit with internal rotational angles along the polymer backbone. In the crystalline state, polyoxyethylene exists in a helical conformation that contains seven chemical units (-CH2CH2-O-) and two turns in a backbone identity period of 19.3 A (7-9). 

The analysis of the amide I band to obtain the estimation of protein secondary structure content in terms of percentage helix, j3 strand, and reverse turn that was developed by Williams has proved very successful and has now been used by numerous workers.In this method the amide I region is analyzed as a linear combination of the spectra of the reference proteins whose structures are known. As noted above the Raman spectra of globular proteins in the crystal and in solution are almost identical, reflecting the compact nature of the macromolecules. Thus one may use the fraction of each type of secondary structure determined in the crystalline state by the X-ray diffraction studies for proteins in solution. If there are n reference proteins with the Raman spectrum of each of them represented as normalized intensity measurements at p different wave numbers, then this information is related by the following matrix equation ... 

Molecules are dynamic, undergoing vibrations and rotations continually. Therefore the static picture of molecular structure provided by MM is not realistic. Flexibility and motion are clearly important to the biological functioning of biomacromolecules. These molecules are not static structures, but exhibit a variety of complex motions both in solution and in the crystalline state. Energy minimization concerns only the potential energy term of the total energy and so it treats the biomacromolecule as a static entity. The dynamic properties of the atoms in a macromolecule or the momentum of the atoms in space requires the description of the kinetic term. The momentum (p) is related to the force exerted on the atom (Ft) and the potential energy (V) by... 

Figure 4-11. Dissolution of a macromolecule occurring in the crystalline state in the form of a helix. Only a few kinks are required to produce the macroconformation of a coil, with the helix microconformation being largely retained.

The precipitation of the eutectics from solutions upon cooling occurs when the free energy of the solute molecules in the crystalline state becomes less than that of the molecules in solution. Therefore, a change in the tanperature of precipitation of the eutectics indicates a change in the chanical potentials of the components of the solutions in the presence of protein molecules. On concentration of the solution, this may occur in the hydrate shells of the protein molecules. Since for the organic solute molecules close to the macromolecules not only do the molecules of the solvent but also the structural elanents of the protein molecules form the medium, it is most probable that the observed phenomenon of a rise in the temperature of freezing is based on the interaction of the molecules of the organic additive with the biopolymer. 

High-resolution NMR in the solid state of matter has been developed fairly recently. Since this technique can detect the local structure of molecules via chemical shift and magnetic relaxation, it has been possible to obtain detailed information on chain conformation as well as chain dynamics of macromolecules not only in the crystalline state but also in the non-crystalline, glassy or rubbery state. This chapter gives a brief description of the basic principles of solid-state high-resolution NMR as well as its recent application to crystalline polymers. 

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