Regular structures

The wave function T i oo ( = 11 / = 0, w = 0) corresponds to a spherical electronic distribution around the nucleus and is an example of an s orbital. Solutions of other wave functions may be described in terms of p and d orbitals, atomic radii Half the closest distance of approach of atoms in the structure of the elements. This is easily defined for regular structures, e.g. close-packed metals, but is less easy to define in elements with irregular structures, e.g. As. The values may differ between allo-tropes (e.g. C-C 1 -54 A in diamond and 1 -42 A in planes of graphite). Atomic radii are very different from ionic and covalent radii. 

For a fluid, with no underlying regular structure, the mecin squared displacement gradually increases with time (Figure 6.9). For a solid, however, the mean squared displacement typically oscillates about a mean value. Flowever, if there is diffusion within a solid then tliis can be detected from the mean squared displacement and may be restricted to fewer than three dimensions. For example. Figure 6.10 shows the mean squared displacement calculated for Li+ ions in Li3N at 400 K [Wolf et al. 1984]. This material contains layers of LiiN mobility of the Li" " ions is much greater within these planes than perpendicular to them. 

Figure 7.10 shows the 60-MHz spectra of poly (methyl methacrylate) prepared with different catalysts so that predominately isotactic, syndiotactic, and atactic products are formed. The three spectra in Fig. 7.10 are identified in terms of this predominant character. It is apparent that the spectra are quite different, especially in the range of 5 values between about 1 and 2 ppm. Since the atactic polymer has the least regular structure, we concentrate on the other two to make the assignment of the spectral features to the various protons. 

If a polymer molecule has a sufficiently regular structure it may be capable of some degree of crystallisation. The factors affecting regularity will be discussed in the next chapter but it may be said that crystallisation is limited to certain linear or slightly branched polymers with a high structural regularity. Well-known examples of crystalline polymers are polyethylene, acetal resins and polytetrafluoroethylene. 

If a rubbery polymer of regular structure (e.g. natural rubber) is stretched, the chain segments will be aligned and crystallisation is induced by orientation. This crystallisation causes a pronounced stiffening in natural rubber on extension. The crystalline structures are metastable and on retraction of the sample they disappear. 

The ability of a material to crystallise is determined by the regularity of its molecular structure. A regular structure is potentially capable of crystallinity whilst an irregular structure will tend to give amorphous polymers. Structural irregularities can occur in the following ways ... 

The regular structure of the alternating copolymer with its absence of side chains enables the polymer to crystallise with close molecular packing and with interchain attraction augmented by the carbonyl groups. As a result these polymers exhibit the following characteristics ... 

It will be seen that the molecule has an extremely regular structure and that questions of tacticity do not arise. The polymer is thus capable of crystallisation. 

Although the polymer has a regular structure, it is amorphous, the natural polymer being transparent and oreuige in colour. 

The commercial polymer was said to have a number average molecular weight of 250000-350000. Because of its regular structure (Figure 19.4 it is capable of crystallisation. 

All of the commercial polymers are linear and although most have regular structures they are all, at least for practical intents and purposes, amorphous. The high in-chain aromaticity leads to high values of the Tg, the Amoco product Udel having a of about 190°C whilst the ICI polymer has an even higher value of about 230°C. The Amoco materials have a condary transition at -100°C and that of the ICI polymer is -70°C. Typical M values are about 23 000. 

The polymer has a regular structure and is therefore crystallisable. Three crystalline forms are known ... 

Fig. 3. The regular structure of a procyanidin-type condensed tannin showing characteristic 4,8 interflavonoid bonds linking the flavonoid units.

Guyot et al. [87] studied the influence of regular structures on thermal degradation of PVC in an inert... 

At r = 0.5 (Fig. 9b), the most interesting and novel morphology can be observed. This morphology can be described as follows. The P4VP cores of the microspheres form a regular structure, and a P4VP bilayer surrounds each microsphere with a honeycomb-like structure, similar to a cell wall, as the number of the microsphere surrounded by the P4VP wall ( T) was 1.08. Similar structures have been observed for ABC triblock copolymers [39]. Our honeycomb-like novel structure, however, is different from that of the ABC triblock co-... 

Crystalline non-polar polymers and amorphous solvents Most polymers of regular structure will crystallise if cooled below a certain temperature, i.e. the melting point T. This is in accordance with the thermodynamic law that a process will only occur if there is a decrease in Gibbs free energy (-AF) in going from one state to another. Such a decrease occurs on crystallisation as the molecules pack regularly. 

Calculation of dependence of o on the conducting filler concentration is a very complicated multifactor problem, as the result depends primarily on the shape of the filler particles and their distribution in a polymer matrix. According to the nature of distribution of the constituents, the composites can be divided into matrix, statistical and structurized systems [25], In matrix systems, one of the phases is continuous for any filler concentration. In statistical systems, constituents are spread at random and do not form regular structures. In structurized systems, constituents form chainlike, flat or three-dimensional structures. 

Thus, the polymers have a regular structure and can attain high molecular weights under controlled reaction conditions. 

These polymers could not be crystallized, despite their apparent stereoregularity, probably because of the sterically-hindered character of the chains. It was proposed by Farina and Bressan62 that the chain growth was stereoregulated by the optically active anion of the ion-paired chain carrier. Further studies63 showed that the first portion of the polymer produced in a given reaction always possessed a less regular structure than later portions, unless the reaction was started in the presence of previously prepared polymer. This observation was interpreted as evidence for the pre-... 

The interest in this area may be seen to stem from the biological area where the phenomenon is well known and accounts for the regularity in the structure of natural proteins and polynucleotides. Such polymers are efficiently synthesized by enzymes which arc capable of organizing monomer units within regularly structured molecular-scale spaces and exploiting weak forces such as hydrogen bonds and Van der Waal forces to control the polymerization process.. 

The presence in these copolymers of hetero-substituted monomeric units randomly dispersed along the phosphazene skeleton brings about the extreme difficulty of the polymeric chains to be packed in regular structures. They lose, therefore, the original stereo-regularity of the parent phosphazene homopolymers (microcrystalline materials), and show only amorphous structures, with sharp decrease in the values of the Tg (collapsed up to about -90 °C) and with the onset of remarkable elastomeric properties [399,409,457]. 

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