Crystallinity statistical

Production statistics on alkanolamines are not available, but they are sold in thousand-ton quantities and are available for bulk shipment except for DMAMP, AB, TRIS AMINO, and AMPD (the latter two being crystalline soHds). TRIS AMINO concentrate is available in bulk. AMPD is manufactured only in low volumes to meet limited demand in certain specialized uses. Similarly, 2-AB is manufactured only to meet demand for one end use. 

Statistical data on dry salt sales are available through 1994 (9). Dry salt includes salt produced as crystalline sodium chloride, but excludes salt in brine produced for production of chlor—alkah products and other chemicals. Table 7 gives United States dry salt sales for the period 1990—1994. 

Figure 6.4 Crystal structure of ar-tetragonal boron. This was originally thought to be B50 (4Bi2 + 2B) but is now known to be either B50C2 or B50N2 in which the 2C (or 2N) occupy the 2(b) positions the remaining 2B are distributed statistically at other vacant sites in the lattice. Note that this reformulation solves three problems which attended the description of the or-tetragonal phase as a crystalline modification of pure B ...

Random copolymers are similar to PEO but when the regular helical structure of the chains is demolished, the crystallinity is also destroyed. One of the simplest and most successful amorphous host polymers is an oxyethylene- oxymethylene structure in which medium length but statistically variable EO units are interspersed with methylene oxide groups. First described in 1990 [37], aPEO has the general structure... 

Structurally, plastomers straddle the property range between elastomers and plastics. Plastomers inherently contain some level of crystallinity due to the predominant monomer in a crystalline sequence within the polymer chains. The most common type of this residual crystallinity is ethylene (for ethylene-predominant plastomers or E-plastomers) or isotactic propylene in meso (or m) sequences (for propylene-predominant plastomers or P-plastomers). Uninterrupted sequences of these monomers crystallize into periodic strucmres, which form crystalline lamellae. Plastomers contain in addition at least one monomer, which interrupts this sequencing of crystalline mers. This may be a monomer too large to fit into the crystal lattice. An example is the incorporation of 1-octene into a polyethylene chain. The residual hexyl side chain provides a site for the dislocation of the periodic structure required for crystals to be formed. Another example would be the incorporation of a stereo error in the insertion of propylene. Thus, a propylene insertion with an r dyad leads similarly to a dislocation in the periodic structure required for the formation of an iPP crystal. In uniformly back-mixed polymerization processes, with a single discrete polymerization catalyst, the incorporation of these intermptions is statistical and controlled by the kinetics of the polymerization process. These statistics are known as reactivity ratios. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Based on the fact that pi-acids interact with the trinuclear gold] I) pi-bases, TR(carb) and TR(bzim), the trinuclear 3,5-diphenylpyrazolate silver(I) complex was reacted with each. Mixing [Au3(carb)3] or [Au3(bzim)3] with [Ag3(p,-3,5-Ph2pz)3] in CH2CI2 in stoichiometric ratios of 1 2 and 2 1 produced the mixed metal/mixed ligand complexes in the same gold-silver ratios. The crystalline products were not the expected acid-base adducts. It is suspected that the lability of the M-N bond (M=Au, Ag) in these complexes results in the subsequent cleavage of the cyclic complexes to produce the products statistically expected from the stoichiometry of materials used [74]. As a result of the lability of Au-N and Ag-N bonds, and the stability of... 

Molecular orientation increases the crystallization rate for two reasons the statistical probability of chain segments becoming suitably aligned to form a nucleus is increased and the entropic difference between the molten and crystalline states is reduced, which increases the driving force towards crystallization. 

If the statistical model of a paracrystalline stack is assumed, it turns out that the renormalization attenuates the influence of polydispersity on the position of the first zero. In general, the first-zero method is more reliable than the valley-depth method, although it is not perfect. Even the first-zero method is overestimating the value of V . The deviation is smaller than 0.05, if the found crystallinity is smaller than 0.35. If bigger crystallinities are found, the significance of the determination is... 

Figure 8.22. Testing the first-zero method for the determination of the linear crystallinity, V[, from the linear correlation function, yi (x/Lapp) with Lapp being the position of the first maximum in yi (x) (not shown here - but cf. Fig. 8.21). Model tested Paracrystalline stacking statistics with Gaussian thickness distributions. The interval of forbidden zeroes is shown. An additional horizontal non-linear axis permits to determine the linear crystallinity directly. A corresponding vertical axis shows the variation of the classical valley-depth method ... 

Properties and Application. The two independent statistical distributions of the two-phase stacking model are the distributions of amorphous and crystalline thicknesses, h (x) and ii2 x). Both distributions are homologous. The stacking model is commutative and consistent. If the structural entity (i.e., the stack as a whole) is found to show medium or even long-ranging order, the lattice model and its variants should be tested, in addition. As a result the structure and its evolution mechanism may more clearly be discriminated. 

Table 12 shows the equilibrium spreading pressures of each diacid. It is immediately apparent that for three of the diastereomeric pairs there are statistically significant differences. These distinctions relate stereochemical preferences in the spontaneous spreading of (+)- versus meso-monolayers in equilibrium with their respective crystalline phases. However, there appears to be no discernible trend in either the ( )- or meso-ESPs as a function of carbonyl position despite clear trends seen in their monolayer properties in the absence of any bulk crystalline phase. 

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