Crystals of Macromolecules

Since the macromolecules are so large, the positional and the orientational contributions to the entropy of fusion are negligible. By dividing the molecule into mobile beads (given in parentheses) the conformational entropy of fusion per mobile bead can be estimated to be  

Combining the results of all presented data, a number of valuable conclusions can be drawn about polymers from their melting characteristics. Furthermore, this experience helps to predict the melting properties from information about the chemical structure. Adding this information about melting to the predictions possible from the heat-capacity analysis (see Sect. 2.3 and Appendix 1), a rather complete profile can be developed for the thermal properties of a given chemical structure. 

The series of five polymers with particularly low entropies of melting in Fig. 5.124 show crystals that are disordered, most likely to condis crystals (see Sect. 2.5), as shown aljove for PTFE. Of special interest is the difference between cis- and trans-1,4-polybutadiene. Their entropies are shown in Fig. 2.113. 

Once these empirical rules have been established, it is possible to link the melting temperatures of polymers to chain flexibility, interactions (cohesive energy densities), internal heats of fusion, and the possible presence of mesophases (see Fig. 2.103). Such analyses are of importance for the design of new polymers and of changes in existing polymers when there is a need to alter thermal stabiUty. 

Mesophases are intermediate phases between rigid, fully ordered crystals and the mobile melt, as explained in the introductory discussion of phases in Sect. 2.5, and summarized in Figs. 2.103 and 2.107. The quantitative analysis of melting in Sect. 5.4 shows that with a suitable molecular stracture, three types of disorder and motion can be introduced on fusion (1) positional disorder and translational motion, (2) orientational disorder and motion, and (3) conformational disorder and motion [43]. In case not all the possible disorders and motions for a given molecule are achieved, an intermediate phase, a mesophase results. These mesophases are the topic of this section. Both structure and motion must be characterized for a full description of mesophases. 

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The latest results of a controlled crystallization of macromolecules are the polymer fibrids which are a completely new modification of synthetic polymers as far as the micro- and macro-structure is concerned. They exist of small fibers having a length of up to some millimeters, which are highly oriented, and which have a macro-morphology similar to that of cellulose pulp. 

Garman, E. F (1991). Modern methods for rapid X-ray diffraction data collection from crystals of macromolecules. In Methods in Molecular Biology, vol. 56, Crystallographic Methods and Protocols, Jones, C., MuUoy B. and Sanderson, M. R., eds. Humana Press. 

Alexander McPherson and Paul J. Shlichta have suggested using insoluble minerals as heterogeneous nuclei for the crystallization of macromolecules. They obtained excellent protein crystals, which could be cleaved from the mineral nucleus and used for X-ray diffraction studies. The mineral is introduced into a supersaturated solution of the material to be crystallized. As supersaturation increases, nucleation occurs on a specific face of the mineral nucleus, and a crystal begins to grow. The orientation and periodicity of the molecules on the nucleus surface promote an oriented overgrowth that has a similar periodicity. 

The perplexing difficulties that arise in the crystallization of macromolecules, in comparison with conventional small molecules, stem from the greater complexity, lability, and dynamic properties of proteins and nucleic acids. The description offered above of labile and metastable regions of supersaturation are still applicable to macromolecules, but it must now be borne in mind that as conditions are adjusted to transport the solution away from equilibrium by alteration of its physical and chemical properties, the very nature of the solute molecules is changing as well. As temperature, pH, pressure, or solvation are changed, so may be the conformation, charge state, or size of the solute macromolecules. 

Crystals of macromolecules, like those shown in Figure 3.1, are like crystals of all other kinds. They are precisely ordered three-dimensional arrays of molecules that may be characterized by a concise set of determinants that exactly define the disposition and periodicity of the fundamental units of which they are composed. The set of parameters is comprised of three elements. These define the symmetry properties, the repetitive and periodic features, and the distribution of atoms in the repeating unit. The properties may be separated and understood by considering how a crystal can be developed as a three-dimensional form from a basic building block (the asymmetric unit), by the application of symmetry (the space group), and translation (the unit cell, or lattice). As illustrated in Figure 3.2, this can be accomplished in four stages. 

McPherson, A. 1985. Crystallization of macromolecules general principles. Meth. Enzymol. 114 112-120. 

Simultaneous polymerization emd crystallization is another approach to memroscopic, defect-free single crystals of macromolecules (59). Recent examples include a preparative method for mixed metal coordination polymers (60), emd M. Hemack emd coworkers have reacted hemipotphyreizine (6 with iron (II) acetate in nitrobenzene to obtain single crystals of em oxygen-bridg polymer with iron in a -i- 4 oxidation state. 

As remarked in note (3) of Table 2.1 crystals of macromolecules cannot contain an inversion centre, a mirror or a glide plane. The diffraction pattern from a protein crystal can, however, contain an inversion centre (otherwise known as a centre of symmetry and a mirror plane. The symmetry symbols given here are for those symmetry elements seen therefore for macromolecular crystals and their diffraction patterns. 

Matsushige K, Takemura T (1980) Crystallization of macromolecules under high pressure. J. Crystal Growth 48 343... 

K. A. Mauritz, E. Baer, A. J. Hopfinger, The Epitaxial Crystallization of Macromolecules,... 

Let us point out that according to Wunderlich [2], plastic crystals may also be considered as mesophases. They are characterized by positional order but orientational disorder of the structural motif. Molecules of plastic crystals are generally close to spherical so that there is no high-energy barrier to their reorientation. Of course, the condition of a spherical shape of the molecules may not be fulfilled by the macromolecular chains of linear synthetic polymers, which generally crystallize in extended chains or helical conformations [2]. However, there is at least one case of crystals of macromolecules presenting orientational disorder of the structural motif as in plastic crystals. 

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