Symmetrical disorder

Low and high are relative to the guest species, meta-bromonitrobenzene shows the transition at about 60°C, while meta-dinitrobenzene shows transition of this sort at about 95°C. Description is somewhat simplified here. The ordered guest molecules shown on the picture still have some 10-15 % of disordering over two different orientations. This, however, is qualitatively different from the symmetric disordering around the threefold axis. 

Fig. 8. Simple model of order-disorder or displacive ferroelectric phase transition. Left, ferroelectricity by relative displacement of the anion and cation sublattices (a) displacive model, where r — 0 in the HTP and the atoms are translated by r/0 in the LTP. The order parameter is r. (b) Order-disorder model in the high-temperature phase, the ions are symmetrically disordered with equal probabilities p+ — p — 1/2 over two positions r — +rQ. In the low-temperature phase, the occupancies of the sites become unequal with probabilities p p +. The order parameter is the difference Ap — p+—p. The spontaneous polarization Psocr and PsccAp for the displacive model and order-disorder model, respectively. Right, ferroelectricity by alignment of molecular dipoles (c) displacive model in the HTP, all the molecules are aligned with a = 0 in the LTP, the molecules are rotated around the center of inversion with angles +a/0, the order parameter is a. (d) Order-disorder model. The spontaneous polarization Ppx ct and PsccAp for the displacive model and order-disorder model, respectively.

A solid is said to be stoichiometric if the ratio of the quantities of the two elements A and B remains constant and equal to its theoretical value in the perfect crystal. The ratio between the number of sites of A and the number of sites of B also remains constant. These two constants mean that we must have at least two types of defects occurring simultaneously. This set of two defects present simultaneously is known as a disorder. We can see from the list of defects set out above that there are six classes of disorders with two defects, which are classified into two groups symmetrical disorders and anti-symmetrical disorders. In practice, we find only four types of disorders with two defects. 

The solid being stoichiometric, the ratio of the number of atoms (B/A) must remain constant. In addition, as the ratio of sites (B sites/A sites) should also remain constant, we must thus have the simultaneous presence of at least two types of defects. This whole of two defects found simultaneously is called a disorder. We can see, according to the list of defects described earlier, that theoretically there exist six classes of disorders with two defects. Among these classes, we can distinguish two groups the symmetrical disorders, which utilize the two sub-lattices of A and B, and the asymmetrical disorders, which utilize only one of the two sublattices of A or B. In fact, in practice, only four types of disorders are known. Two are symmetrical Schotlky disorder and antistructure disorder. The other two disorders are asymmetrical Frenkel disorder and S. A. disorder. 

In order to address the possible influence of positional disorder, we have chosen to analyze the way basic operations such as translations and rotations affect the properties calculated for highly symmetric configurations. This approach could provide guidelines to prevent the loss of significant optical coupling between the ground state and the lowest excited state, and hence the quenching of luminescence in the solid state. 

Another example of rr-delocalized radical is cyclopentadienyl 43, which was reported by Sitzmann et al. to be rendered persistent and crystalline by derivatization with /io-propyl groups as in radical 44 (Fig. 7.19). ° "° An interesting feature in the X-ray structure of 44 is that the /io-propyl groups adopt a paddlewheel-like conformation, also showing disorder in the crystal. The bond distances show that the radical is not Dsh symmetric, but that it is slightly distorted (C1-C2 = 1.412 A, C2-C3 = 1.401 A). Radical 44 also packs in a columnar motif with rings eclipsing each other... 

Guillain-Barre syndrome is a transient neurologic disorder involving inflammatory demyelination of the peripheral nerves. The syndrome is characterized by progressive symmetric weakness of the legs and arms with loss of reflexes. Occasionally sensory abnormalities and paralysis of respiratory muscles will occur.16... 

The term plastic crystal is not used if the rotation of the particles is hindered, i.e. if the molecules or ions perform rotational vibrations (librations) about their centers of gravity with large amplitudes this may include the occurrence of several preferred orientations. Instead, such crystals are said to have orientational disorder. Such crystals are annoying during crystal structure analysis by X-ray diffraction because the atoms can hardly be located. This situation is frequent among ions like BF4, PFg or N(CH3)J. To circumvent difficulties during structure determination, experienced chemists avoid such ions and prefer heavier, less symmetrical or more bulky ions. 

It is generally assumed that the disorder can be represented by a symmetric Gaussian-type pair distribution function and that the thermal vibration will be harmonic in nature. 

Fig. 18 Phase space of PI-fc-PS-fc-PEO in vicinity of ODT. Filled and open circles-. ordered and disordered states, respectively, within experimental temperature range 100 < T/° C< 225. Outlined areas compositions with two- and three-domain lamellae (identified by sketches) shaded regions three network phases, core-shell double gyroid (Q230), orthorhombic (O70), and alternating gyroid (Q214). Overlap of latter two phase boundaries indicates high- and low-temperature occurrence, respectively, of each phase. Dashed line condition tfin = 0peo associated with symmetric PI-fc-PS-fc-PEO molecules. From [75]. Copyright 2004 American Chemical Society...

Fig. 21 Schematic summary of thermodynamic phase behaviour for neat, composition-ally symmetric PI-fc-PS-fc-PDMS (ISD) and PS-fc-PI-fc-PDMS (SID) terpolymers. Heating PI-fc-PS-fc-PDMS or decreasing molecular weight causes transition from three-domain lamellae to hexagonally packed two-domain cylindrical morphologies, followed by disordering. PS-fc-PI-fc-PDMS disorders directly from three-domain lamellar state. From [88], Copyright 2002 American Chemical Society...

Fig. 59 Phase diagram for blend consisting of two symmetric PS-6-PI block copolymers of different molecular weights in parameter space of temperature and fraction of higher molecular weight copolymer, . disordered state lamella A PS cylinder. From [179]. Copyright 2001 American Chemical Society... 

Fig. 67 Schematic of phase behaviour for blend of novolac epoxy resin with nearly symmetric poly(methyl acrylate-co-glycidylmelhacrylate)-0-polyisoprene. Ordered L can be swollen with up to about 30% of resin before macroscopic phase separation occurs, producing heterogeneous morphologies containing various amounts of L, C, worm-like micelles and pristine epoxy. At lower concentrations, disordered worm-like micelles transform into vesicles in dilute limit. According to [201]. Copyright 2003 Wiley...

Adrenoleukodystrophy is an X-linked dysmyelinative disorder caused by mutations in the ABCD1 gene, which encodes the peroxisomal integral membrane ALD protein, a member of the ATP binding cassette transporter family. These mutations result in impaired clearance of plasma very-long-chain fatty acids. Affected males may present with symmetrical distal axonal polyneuropathy, adrenocortical insufficiency or CNS demyelination, while occasional heterozygous women demonstrate deficits suggestive of multiple sclerosis [56]. Manipulation of dietary fatty acid intake has some minimal therapeutic effect, while bone marrow transplantation has diminished deficits in a few patients. (See in Ch. 41.)... 

Rheumatoid arthritis (RA) is a chronic and usually progressive inflammatory disorder of unknown etiology characterized by polyarticular symmetric joint involvement and systemic manifestations. 

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