Paracrystalline disorder

Being composed of linear chains of a highly crystalline polysaccharide, linked by 1 — 4, D-anhydroglucopyranose bonds that are hydrolyzed with relative ease, cellulose has long been the subject of partial acid hydrolysis to mixtures of hydrocolloid particles [65]. Hydrolysis of the disordered (paracrystalline) regions of cellulose liberates highly crystalline particles with dimensions in the 50 to 100 pm range. When dissolved in a suitable cellulose solvent, these par-... 

Nelson, D.G.A., Featherstone, J.D.B., Duncan, J.E and Cuttress, T.W. 1982 Paracrystalline disorder of biologieal and synthetic carbonate-substituted apatites. Journal of Denial Research 61 1274-1281. 

It is worth to be noted that these definitions of first- and second-order distortions according to Warren-Averbach are model-free. From a linear or a quadratic increase of peak breadths it can neither be concluded in reverse that strain broadening, nor that paracrystalline disorder were detected. 

Figure 8.21. Features of a ID correlation function, yi (x/L) for perfect and disordered topologies. L is the number-average distance of the domains from each other (i.e., long period). Dotted Perfect lattice. Dashed and solid lines Paracrystalline stacks with increasing disorder. a = — v/j / (1 — v/j) with 0 < v/j < 0.5 is a measure of the linear volume crystallinity in the material, which is either or 1 —...

Although the lipid bilayer structure is quite stable, its individual phospholipid and sterol molecules have some freedom of motion (Fig. 11-15). The structure and flexibility of the lipid bilayer depend on temperature and on the kinds of lipids present. At relatively low temperatures, the lipids in a bilayer form a semisolid gel phase, in which all types of motion of individual lipid molecules are strongly constrained the bilayer is paracrystalline (Fig. ll-15a). At relatively high temperatures, individual hydrocarbon chains of fatty acids are in constant motion produced by rotation about the carbon-carbon bonds of the long acyl side chains. In this liquid-disordered state, or fluid state (Fig. 11—15b), the interior of the bilayer is more fluid than solid and the bilayer is like a sea of constantly moving lipid. At intermediate temperatures, the lipids exist in a liquid-ordered state there is less thermal motion in the acyl chains of the lipid bilayer, but lateral movement in the plane of the bilayer still takes place. These differences in bilayer state are easily observed in liposomes composed of a single lipid,... 

The spread of the reflections around the reciprocal lattice points due to the finite particle dimensions and to cumulative lattice disorders of the "ideally paracrystalline" type is calculated according to the formula given by Hosemann and Wilke (7). They showed that for a one-dimensional crystal the integral breadth (8) varies with the Miller index (h) of the reflection and can be approximated by the expression... 

The effects of paracrystalline type disorder in the z direction can be approximated by decreasing the value of p with increasing Z (7). 

Methods for estimating lattice distortion generally require two or more orders of a particular reflection to be present, and most polymers have only one order available. A method for estimating both crystallinity and lattice disorder, which does not need higher orders of a reflection, and indeed takes into account the whole of the diffraction trace, is that due to Buland (27). This method has been applied to many different fibres by Sotton and his colleagues, who have discussed their results both here (28) and elsewhere (12). The major problem with Ruland s method is that an arbitrary separation of the crystalline scatter from the non-crystalline scatter must be made other restrictions are that the method cannot be used to measure crystallite size and cannot give any indication of the presence of paracrystalline or intermediate-phase material. 

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

Paracrystalline disorder will cause electron localization, but there is no reason for the corresponding characteristic length to be equal to L. It will therefore be interesting to compare Lp in particular to the average conjugation lengths inferred from resonance Raman scattering studies (see Section III). 

In these polymers, data are often of poorer quality than is PA, so, for instance, analysis in terms of paracrystallinity has rarely been performed. Disorder in the translational position of the chains along their axis may exist, especially in PPV [47]. The unit cell invariably contains more independent atoms than in PA, so that a larger number of simplifying assumptions are required it is difficult, for instance, to determine experimentally from diffraction data the geometry of the conjugated cycle that these chains contain. 

At this step, then, the differences between the effects of surface chemistry and secondary molecular motions as dictated by morphological order can be observed on thrombogenesis. In the case of the sterically ordered substrate, in conjunction with the subsurface cationic array, the sorbed pro-tein(s) can assume a paracrystalline state, and subsequently be subjected to further pertubations. However, in the case of the disordered substrate, the sorbed proteins can not assume a paracrystalline state and, therefore, will not, per se, be subjected to any further conformational changes. 

Isotactic polypropylene crystallizes below 350 K on quick cooling from the melt increasingly as condis glass This conformationally disordered polypropylene had first been described as bdng smectic mesomorphic or paracrystalline ... 

A consideration of the paracrystalline distortions, primarily the limited lateral correlations of axial chain coordinates ( chain shift disorder ), is found in the paper by Kawaguchi and Petermann [174]. According to the analysis of their electron diffraction patterns of flow-oriented PPP films, the diffraction on the third and higher layer lines is essentially single-chain diffraction. Although indications for an off-meridional position of the (002) reflection are found in some patterns, the authors favour the orthorhombic unit cell. 

Mesophase reveals intermediate order between amorphous and crystaUine phases. In the first studies it was labelled as smectic (Natta Corradini, 1960) or paracrystalline (Miller, 1960). Further studies revealed that mesophase is made up of bundles of parallel chains, which maintain typical for all polymorphic forms of polypropylene three-fold helical conformation. Bundles are terminated in the direction of the chain axis by helix reversals or other conformational defects (Androsch et al., 2010). In the bundles long range ordering maintains only along the chain axes, whereas in lateral packing a large amount of disorder is present (Natta Corradini, 1960). The mesophase is formed by quenching of the molten polypropylene (Miller, 1960 Wyckoff, 1962) or by deformation of the crystalline structure (Saraf Porter, 1988 Qiu, 2007). As for the fibres, the mesophase was observed in fibres taken at low take-up velocity (Spruiell White, 1975 Jinan et al., 1989, Bond Spruiell, 2001) in fibres intensively cooled in water with addition of ice or in the mixture of dry ice... 

Because of the presence of structural disorder, the X-ray diffraction patterns of mesophases show a large amount of diffuse scattering and need a special care for a quantitative evaluation. Paracrystalline distortions of the lattice [59,60] usually affect the shape and the width of the diffraction peaks to a large extent. The analysis of disorder necessarily implies a multidisciplinary approach, in order to unravel the complicated nature of disorder in disordered crystalline materials [61]. 

In the most crude approach, Eq. 18 may be used to evaluate the diffraction intensity of model structures containing specific kinds of disorder. The terms of summation rapidly fade away for large distances between interfering atoms. In some cases it may be convenient to multiply each term in the sums of Eq. 18 by paracrystalline disorder factors which reduce the interference between each couple of atoms according to the following equation [152,162] ... 

As shown in Fig. 4, the X-ray diffraction patterns of nylon 6 fibers in the P form (Fig. 4A) present only two equatorial reflections (Fig. 4B) and several meridional reflections (up to the 7-th order. Fig. 4C) [163]. This indicates a pseudo-hexagonal unit cell with a(= b) = 4.80 A and a mean periodicity along the chain axis equal to c = 8.35 A. The substantial absence of diffraction off the equator and off the meridian indicates that a high degree of conformational disorder is present. From the meridional profile reported in Fig. 4C it is apparent that the half-height widths of the meridional reflections increase with increasing diffraction order, indicating paracrystalline distortions of the lattice parameter c. 

The results of these analyses have indicated that the mesomorphic form of iPP is characterized by small bundles of parallel chains in ordered 3/1 helical conformation with disorder in the lateral packing [262]. The relative heights of neighboring chains within each bundle are mainly correlated. The local correlations are near to those which characterize the crystal structure of monoclinic a form [262,263]. Any correlation about the relative position of atoms is lost at distances higher then 30-40 A [262]. Since the lateral order is maintained at very short range, it was proposed that the term paracrystalline could be used for description of this form, if the paracrystalline distortion is intended to mean that a correlation exists within small nuclei of chains and fades away at longer interchain distances [262]... 

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