Order metrics

The first crystal-independent structural order metric that we will explore is the translational parameter l w an integral measure of the amplitude of the material s total correlation function h(r),... 

Figure 4 The path traversed in structural order-metric space as liquid water (SPC/E) is compressed isothermally at two different temperatures. Filled diamonds represent T = 260 K, and open triangles represent T = 400 K. The arrows indicate the direction of increasing density. A and C are states of maximum tetrahedral order at the respective temperatures, whereas B is a state of minimum translational order. Reprinted with permission from Ref. 29. 

One aim of studying olfaction has been to gain an understanding of how the physical features of odor molecules correlate with their perceptual qualities. Unfortunately, the perceptual qualities do not often follow an easily ordered metric that can be simply related to molecular structures. We might, therefore, speak of a dual problem in attempting to relate odor perception to the features of the corresponding molecules no obvious metric is available to describe either the space of odor perceptions or the space of odor chemistry. 

The matrix gp, represents the components of a covariant second-order tensor called the metric tensor , because it defines distance measurement with respect to coordinates To illustrate the application of this definition in the... 

A great number of monoaza or polyaza. either symmetrica] or unsym-metrical, mono trimethine thiazolocyainines have been synthesized in order to verify or to obtain semiempirical rules, more or less based on the resonance theory, concerning the relation between the color of a thiazolo dye and the number and place of nitrogen atoms in the chromophoric chain. For example. Forster s rule applies to ionic dyes and stipulates that the will increase with the decreasing tendency of chromophoric atoms lying between the two auxochromes to take up the characteristic charges (90). 

Every continent, except Antarctica, grows com 40% of the present world crop is produced in the United States. In the 1987—1988 crop year, 12 states (Iowa, HI., Nebr., Minn., Ind., Ohio, Wis., Mo., S. Dak., Mich., Kans., and Tex. in order of production) produced 157.5 million metric tons (6.2 biUion bushels) that was 88% of the United States and 36% of the world s crop (66). Yield is influenced by many factors, including climate, pest control, planting density, and fertilization. Yield in the United States has increased from about 1.5 metric tons /hectare in the 1930s to about 7.5 metric tons /hectare. In 1985, a test plot produced 23.2 metric tons /hectare and yields approaching 40 metric tons /hectare are considered possible com is the most productive of the principal food crops. 

Fine chemicals are generally considered chemicals that are manufactured to high and weU-defined standards of purity, as opposed to heavy chemicals made in large amounts to technical levels of purity. Fine chemicals usually are thought of as being produced on a small scale and the production of some fine chemicals is in tens or hundreds of kilograms per year. The production of others, especially fine chemicals used as dmgs or food additives (qv), is, however, in thousands of metric tons (see Pharmaceuticals). For example, the 1990 U.S. production of aspirin [50-78-2] and acetaminophen [103-90-2] was on the order of 20,500 t and 15,000 t, respectively. 

Historically, the annual consumption of nickel fluoride was on the order of a few metric tons. Usage is droppiag because nickel fluoride is Hsted ia the EPA and TSCA s toxic substance iaventory. Nickel fluoride tetrahydrate is packaged ia 200—500-lb (90.7—227-kg) dmms and the 1993 price was 22/kg. Small quantities for research and pilot-plant work are available from Advance Research Chemicals, Aldrich Chemicals, Johnson/Matthey, Pfalt2 and Bauer, PCR, and Strem Chemicals of the United States, Fluorochem of the United Kingdom, and Morita of Japan. 

Units. The unit of sound absorption is the metric sabin, which is equivalent to one square meter of "perfect" absorption, eg, one square meter of a material with a = 1.0. The Knglish unit of sound absorption is the sabin, which is equivalent to one square foot of perfect absorption. In order to avoid confusion, the designation metric should always be used when referring to metric sabins. The number of metric sabins of absorption provided by an area of material is calculated by multiplying its area by its sound-absorption coefficient. For example, 10 m of material having a sound-absorption coefficient of 0.75 provides 7.5 metric sabins of absorption. 

This process is one of the three commercially practiced processes for the production of acetic anhydride. The other two are the oxidation of acetaldehyde [75-07-0] and the carbonylation of methyl acetate [79-20-9] in the presence of a rhodium catalyst (coal gasification technology, Halcon process) (77). The latter process was put into operation by Tennessee Eastman in 1983. In the United States the total acetic anhydride production has been reported to be in the order of 1000 metric tons. 

Phthahc anhydride (1) is the commercial form of phthaUc acid (2). The worldwide production capacity for the anhydride was ca 3.5 x 10 metric tons ia 1993, and it was used ia the manufacture of plasticizers (qv), unsaturated polyesters, and alkyd resins (qv) (see Polyesters, unsaturated). Sales of terephthahc acid (3) and its dimethyl ester are by far the largest of any of the benzenepolycarboxyhc acids 14.3 x 10 t were produced in 1993. This is 80% of the total toimage of ah. commercial forms of the benzenepolycarboxyhc acids. Terephthahc acid is used almost exclusively for the manufacture of poly(ethylene terephthalate), which then is formed into textiles, films, containers, and molded articles. Isophthahc acid (4) and trimehitic anhydride (5) are commercial products, but their worldwide production capacities are an order of magnitude smaller than for terephthahc acid and its dimethyl ester. Isophthahc acid is used primarily in the production of unsaturated polyesters and as a comonomer in saturated polyesters. Trimehitic anhydride is used mainly to make esters for high performance poly(vinyl chloride) plasticizers. Trimesic acid (6), pyromehitic dianhydride (7), and hernimehitic acid (8) have specialized commercial apphcations. The rest of the benzenepolycarboxyhc acids are not available commercially. 

Annual worldwide production is probably on the order of 2500 metric tons. Total worldwide production capacity is likely to be about 5000 metric... 

Economic Aspects. A peakia calcium cyanamide production was probably reached ia 1962 when the world production for fertilizer use was of the order of 1,000,000 metric tons of calcium cyanamide per year, and for iadustrial use approximately 300,000 t (excluding the then USSR). In 1990, the total production of cyanamide products was about half that of 1962. The largest producers are ia Japan, Germany, and Canada. 

Air emissions for processes with few controls may be of the order of 30 kilograms lead or zinc per metric ton (kg/t) of lead or zinc produced. The presence of metals in vapor form is dependent on temperature. Leaching processes will generate acid vapors, while refining processes result in products of incomplete combustion (PICs). Emissions of arsine, chlorine, and hydrogen chloride vapors and acid mists are associated with electrorefining. 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

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