Asymmetrical disorder

In an asymmetrical disorder, the two defects that make it up pertain to the same sub-lattice of A or of B. In practice, we find only two families of anti-S5mmetrical disorders Frenkel disorder and so-called AS disorder. 

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. 

The Frenkel disorder is the simultaneous presence of vacancies and atoms in interstitial positions of the same element, for exattple, Va and A . This is an asymmetrical disorder one will thus have two possible Frenkel disorders for a binary sohd the disorder on the A atoms and the disorder on the B atoms. As we will see in section 2.5.2.2.2, the well and the source of the Frenkel disorder are purely local its formation does not require displacement of atoms with long distance. The defects that constitute the disorder can be ionized or not, respecting the electric neutrality. It is for the atom of smaller volume that the Frenkel disorder is most probable because it is easiest to place it in an interstitial position. We will quote, as an example, the Frenkel disorder on silver in silver halides. 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

First, we would like to eonsider a simple hard sphere model in a hard sphere matrix, similar to the one studied in Refs. 20, 21, 39. However, our foeus is on a very asymmetric hard sphere mixture adsorbed in a disordered matrix. Moreover, having assumed a large asymmetry of diameters of the eomponents and a very large differenee in the eoneentration of eomponents, here we restriet ourselves to the deseription of the struetural properties of the model. Our interest in this model is due, in part, to experimental findings eoneerning the potential of the mean foree aeting between eolloids in a eolloidal dispersion in the presenee of a matrix of obstaeles [12-14]. 

Chapter 9, on entropy and molecular rotation in crystals and liquids, is concerned mostly with statistical mechanics rather than quantum mechanics, but the two appear together in SP 74. Chapter 9 contains one of Pauling s most celebrated papers, SP 73, in which he explains the experimentally measured zero-point entropy of ice as due to water-molecule orientation disorder in the tetrahedrally H-bonded ice structure with asymmetric hydrogen bonds (in which the bonding proton is not at the center of the bond). This concept has proven fully valid, and the disorder phenomenon is now known to affect greatly the physical properties of ice via the... 

Asymmetrical Peaks are rarely found in WAXS from polymers, but they are ubiquitous in the MAXS of liquid crystalline polymers. For asymmetrical peaks in isotropic patterns it is best to determine the peak position from the maximum of the peak, if peak asymmetry is a result of linear or planar disorder. Linear disorder means that the crystals are more or less one-dimensional (a tower of unit cells). Planar disorder means that the crystallites are made from only very few layers of unit cells (cf. Guinier [6] Chap. 7). 

Microfibrillar structure in isotropic materials makes asymmetrical peaks, because microfibrils are materials with linear disorder. Steep is the increase from small scattering angle. The peak shape can be quantitatively analyzed (S tribeck [106]) yielding extra information on the lateral extension of the microfibrils. 

Usually the discussion of the ODT of highly asymmetric block copolymers in the strong segregation limit starts from a body-centred cubic (bcc) array of the minority phase. Phase transitions were calculated using SOFT accounting for both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy [129]. Results indicate that the ODT occurs between ordered bcc spheres and disordered micelles. 

The EXAFS, which occurs at higher energies above the edge, is due to the interference between the outgoing and the backscattered photoelectron waves (10-14). EXAFS provides information about the local structure of the x-ray absorbing atom. Typically, nearest neighbor bond lengths and coordination numbers can be determined to 0.02 A (1%) and one atom in four (25%) (4 ). The accuracy of these determinations is somewhat worse for outer-shell atoms, for disordered systems, or for systems with asymmetric distributions of atoms within a shell (15,16). 

An example of the second effect is provided by mono-sec-butyl phthalamide (17a) (56). In the crystal the two enantiomers of this molecule are miscible in all proportions. The racemate crystallizes in space group PI (two general positions in the unit cell) with four molecules per unit cell. Thus there are two molecules in the asymmetric unit. The sec-butyl moieties adopt the anti conformation (the two geometries are shown schematically in 17b) and exhibit conformational disorder to different extents at the two symmetry-independent sites. 

There are a number of possible explanations for the formation of more than one photodimer. First, due care is not always taken to ensure that the solid sample that is irradiated is crystallographically pure. Indeed, it is not at all simple to establish that all the crystals of the sample that will be exposed to light are of the same structure as the single crystal that was used for analysis of structure. A further possible cause is that there are two or more symmetry-independent molecules in the asymmetric unit then each will have a different environment and can, in principle, have contacts with neighbors that are suited to formation of different, topochemical, photodimers. This is illustrated by 61, which contrasts with monomers 62 to 65, which pack with only one molecule per asymmetric unit. Similarly, in monomers containing more than one olefinic bond there may be two or more intermolecular contacts that can lead to different, topochemical, dimers. Finally, any disorder in the crystal, for example due to defective structure or molecular-orientational disorder, can lead to formation of nontopochemical products in addition to the topochemical ones formed in the ordered phase. This would be true, too, in those cases where there is reaction in the liquid phase formed, for example, by local melting. 

Photodimerization of cinnamic acids and its derivatives generally proceeds with high efficiency in the crystal (176), but very inefficiently in fluid phases (177). This low efficiency in the latter phases is apparently due to the rapid deactivation of excited monomers in such phases. However, in systems in which pairs of molecules are constrained so that potentially reactive double bonds are close to one another, the reaction may proceed in reasonable yield even in fluid and disordered states. The major practical application has been for production of photoresists, that is, insoluble photoformed polymers used for image-transfer systems (printed circuits, lithography, etc.) (178). Another application, of more interest here, is the use that has been made of mono- and dicinnamates for asymmetric synthesis (179), in studies of molecular association (180), and in the mapping of the geometry of complex molecules in fluid phases (181). In all of these it is tacitly assumed that there is quasi-topochemical control in other words, that the stereochemistry of the cyclobutane dimer is related to the prereaction geometry of the monomers in the same way as for the solid-state processes. 

Fig. 10.5. Molecular surface of the archaeal (A), the euka otic 20S (B) and the HsIV proteasome (C). The accessible surface is colored in blue, the clipped surface (along the cylinder axis) in white. To mark the position of the active sites, the complexes are shown with the bound inhibitor calpain (yellow). (A) The disorder of the first N-terminal residues in the archaeal a-subunits generates a channel in the structure of the CP, (B) whereas the asymmetric but well-defined arrangement of the a N-terminal tails seals the chamber in eukaryotic CPs. (C) The eubacterial "miniproteasome" has an open channel through which unfolded proteins and small peptides can access the proteolytic sites. (D) Ribbon plot of the free...

The F -ion conductor first discovered by Faraday represents a more complex order-disorder transition to fast ionic conduction. At all temperatures, PbF2 is reported to have the fluorite structure in which the F ions occupy all the tetrahedral sites of a face-centred-cubic Pb -ion array however, the site potential of the Pb ions is asymmetric, and a measurement of the charge density with increasing temperature indicates that the F ions spend an increasing percentage of the time at the... 

At Oak Ridge, the focus was to develop specific-sequence DNA to improve the diffraction quality of NCP crystals. The positioning of the DNA on the histone core has to be precise so that all the NCPs are identical. A project was undertaken to understand the DNA sequence effects on nucleosome phasing [25]. Second, a DNA palindrome was developed to extend the two-fold symmetry of the histone core to the DNA. The objective was to eliminate the two-fold disorder caused by the indeterminacy of packing of an asymmetric particle into the crystal lattice. A palindrome based on one-half of the primary candidate sequence was constructed and methods were developed to produce the palindrome fragment in large quantities for reconstitution of NCPs. 

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