Disparity

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

Tuckerman, M.E., Berne, B.J., Martyna, G.J. Molecular dynamics algorithm for multiple time scales systems with disparate masses. J. Chem. Phys. 94 (1991) 1465-1469. 

A reasonable approach for achieving long timesteps is to use implicit schemes [38]. These methods are designed specifically for problems with disparate timescales where explicit methods do not usually perform well, such as chemical reactions [39]. The integration formulas of implicit methods are designed to increase the range of stability for the difference equation. The experience with implicit methods in the context of biomolecular dynamics has not been extensive and rather disappointing (e.g., [40, 41]), for reasons discussed below. 

There is often a fundamental disparity between the graphic ability of computer monitors and that of printers. Monitors may use anywhere from 8-bit color (256 colors) to 24-bit color (16 million colors). Printers, except for dye sublimation models, use four colors, which are printed in a pattern that tricks the eye into seeing all colors. Monitors generally use about a 72-dpi (dots per inch) screen resolution, as compared to printer resolutions of 300 dpi or better. 

Solids can be crystalline, molecular crystals, or amorphous. Molecular crystals are ordered solids with individual molecules still identihable in the crystal. There is some disparity in chemical research. This is because experimental molecular geometries most often come from the X-ray dilfraction of crystalline compounds, whereas the most well-developed computational techniques are for modeling gas-phase compounds. Meanwhile, the information many chemists are most worried about is the solution-phase behavior of a compound. 

The relationship of the selectivity of an electrophile to its reactivity is a separate issue, because the above quantitative correlations of reactivity can be used empirically, without accepting that they allow comment about the reactivity of electrophiles. There is no direct evidence for the view that differences in the selectivities of electrophiles are related in a simple way to their different reactivities. Indeed, it is difficult to grasp the meaning of comparisons attempted between electrophiles of very different structures, which bring about reaction under disparate conditions by different mechanisms. 

The coupled methods, GC/MS and LC/MS, form very powerful combinations for simultaneous separation and identification of components of mixtures. Hence, these techniques have been used in such widely disparate enterprises as looking for evidence of life forms on Mars and for testing racehorses or athletes for the presence of banned drugs. 

We are most often concerned with solutions which are dilute with respect to polymer. This means that nj Vj polymer molecule is so much greater than that of the solvent, the disparity in the number of moles is even more extreme than for the same approximation applied to compounds of comparably sized molecules. Since the approximation Xj = n2/(ni -I- n2) = nj/nj apphes to dilute solutions, we can write... 

In choosing fhe examples of lasers discussed in Sections 9.2.1 to 9.2.10 many have been left ouf. These include fhe CO, H2O, HCN, colour cenfre, and chemical lasers, all operating in fhe infrared region, and fhe green copper vapour laser. The examples fhaf we have looked af in some defail serve to show how disparate and arbifrary fhe materials seem to be. For example, fhe facf fhaf Ne atoms lase in a helium-neon laser does nof mean fhaf Ar, Kr and Xe will lase also - fhey do nof. Nor is if fhe case fhaf because CO2 lases, fhe chemically similar CS2 will lase also. 

Over 90% of the HCl produced ia the United States origiaates as a coproduct from various chlorination processes direct generation of HCl from and CI2 accounts for only about 8% of the total production. Table 11 describes the production contribution of HCl from significant sources through the period 1980 to 1992 (72). Figure 6 illustrates the historical production growth of HCl ia the United States (73). The growth rate, about 5—6% from 1955 to 1975, slowed to - 1% because of disparity between supply and demand (see Table 12). The production capacity ia 1993 was about 2.92 million metric tons, down 9.6% from the 1992 production of 3.24 million metric tons (74). 

Worldwide, approximately 85% of acetone is produced as a coproduct with phenol. The remaining 17% is produced by on-purpose acetone processes such as the hydration of propylene to 2-propanol and the dehydrogenation of 2-propanol to acetone. The cost of production of 2-propanol sets the floor price of acetone as long as the acetone demand exceeds the coproduct acetone supply. However, there is a disparity in the growth rates of phenol and acetone, with phenol demand projected at 3.0%/yr and acetone demand at 2.0%/yr. If this continues, the coproduct supply of acetone will exceed the total acetone demand and on-purpose production of acetone will be forced to shut down the price of acetone is expected to fall below the floor price set by the on-purpose cost production. Projections indicate that such a situation might occur in the world market by 2010. To forestall such a situation, companies such as Mitsui Petrochemical and Shinnippon (Nippon Steel) have built plants without the coproduction of acetone. 

Pigments Aftertreatments. The surfaces of pigment particles can have different properties and composition than the particle centers. This disparity can be caused by the absorption of ions during wet milling, eg, the —OH groups, on the surface. In some cases, surfaces are modified intentionaHy to improve the pigments appHcation properties, interaction with the organic matrix, and weather resistance. 

The cross-linking reaction mechanism is also influenced by the presence of other monomers. Methyl methacrylate is often used to improve the uv resistance of styrene-based resins. However, the disparate reaction rates of styrene and methacrylate monomer with the fumarate unsaturation not only preclude the use of more than 8% of the methacrylate monomer due to the significant slowing of the cross-linking reaction but also result in undercured products. 

A catalyst is a substance that iacreases the rate of approach to equiUbrium of a chemical reaction without being substantially consumed itself. A catalyst changes the rate but not the equiUbrium of the reaction. This definition is almost the same as that given by Ostwald ia 1895. The term catalysis was coiaed ia ca 1835 by Ber2eHus, who recognized that many seemingly disparate phenomena could be described by a single concept. For example, ferments added ia small amounts were known to make possible the conversion of plant materials iato alcohol and there were numerous examples of both decomposition and synthesis reactions that were apparendy caused by addition of various Hquids or by contact with various soHds. 

Such marked disparities are not observed in the MCD spectra of indole, benzo[6]furan and benzo[6 Jthiophene (80T1521, 81BCJ1511), nor those of dibenzofuran and dibenzothioph-ene (81BCJ1511). 

Even if the interfacial tension is measured accurately, there may be doubt about its applicability to the surface of bubbles being rapidly formed in a solution of a surface-active agent, for the bubble surface may not have time to become equihbrated with the solution. Coppock and Meiklejohn [Trans. Instn. Chem. Engrs., 29, 75 (1951)] reported that bubbles formed in the single-bubble regime at an orifice in a solution of a commercial detergent had a diameter larger than that calculated in terms of the measured surface tension of the solution [Eq. (14-206)]. The disparity is probably a reflection of unequihbrated bubble laminae. 

If the blending process is between two or more fluids with relatively low viscosity such that the blending is not affected by fluid shear rates, then the difference in blend time and circulation between small and large tanks is the only factor involved. However, if the blending involves wide disparities in the density of viscosity and surface tension between the various phases, then a certain level of shear rate may be required before blending can proceed to the required degree of uniformity. 

Sorption activity differences of listed elements on aerosile A-300 and K-7-30 have been established depending from pH media. It was marked that disparity of pH sorption optimum values (pH, ) is caused by changes of composition and stmcture of hydrated cover ot sorbents. The presence of hydrated and a solvate surface layer on K-7-30 is the reason of differences at degree of hydrolysis of taken elements and composition of their hydrolyzed forms. 

As mentioned earlier, if there is a large disparity in sttiicture at the film-substrate interface, such as a crystalline phase growing on an amorphous, glassy, substrate, the film may detach and grow a separate morphology. 

However, for these parameters of the barrier, the cross-over temperature would exceed 500 K, while the observed values are 50 K. If one were to start from the d values calculated from the experimental data, the barrier height would go up to 30-40 kcal/mol, making any reaction impossible. This disparity between Vq and d is illustrated in fig. 34 which shows the PES cuts for the transition via the saddle-point and for the values of d indicated in table 2. 

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