Length multiple

Organic acids are hydrocarbons that are characterized by their carboxylate function (COOH). Their hydrocarbon structure can vary considerably from aliphatic to aromatic, saturated to unsaturated, and straight chain to branched. Other variations in structure include varying chain lengths, multiple carboxylate groups (e.g., di- or tricarboxylic acids), and presence of hydroxyl- and ketofunctions. Organic acids with different molecular structures obviously differ in their physical and chemical properties. 

The expense is justified, however, when tackling polymer chains, where reconstruction of an entire chain is expressed as a succession of atomic moves of this kind [121]. The first atom is placed at random the second selected nearby (one bond length away), the third placed near the second, and so on. Each placement of an atom is given a greater chance of success by selecting from multiple locations, as just described. Biasing factors are calculated for the whole multi-atom move, forward and reverse, and used as before in the Metropolis prescription. For fiirther details see [122, 123. 124. 125]. A nice example of this teclmique is the study [126. 127] of the distribution of linear and branched chain alkanes in zeolites. 

As in the case of ions we can assign values to covalent bond lengths and covalent bond radii. Interatomic distances can be measured by, for example. X-ray and electron diffraction methods. By halving the interatomic distances obtained for diatomic elements, covalent bond radii can be obtained. Other covalent bond radii can be determined by measurements of bond lengths in other covalently bonded compounds. By this method, tables of multiple as well as single covalent bond radii can be determined. A number of single covalent bond radii in nm are at the top of the next page. 

Note that the denominator in each case is equal to the volume of the unit cell. The fact that a, b and c have the units of 1/length gives rise to the terms reciprocal space and reciprocal latlice. It turns out to be convenient for our computations to work with an expanded reciprocal space that is defined by three closely related vectors a , b and c, which are multiples by 2tt. of the X-ray crystallographic reciprocal lattice vectors ... 

UV/Vis detectors are among the most popular. Because absorbance is directly proportional to path length, the capillary tubing s small diameter leads to signals that are smaller than those obtained in HPLC. Several approaches have been used to increase the path length, including a Z-shaped sample cell or multiple reflections (Figure 12.44). Detection limits are about 10 M. 

Traditionally, cyclone dimensions are multiples of outiet pipe diameter D. Typical barrel diameters are 2D but efficiency increases at constant up to a 3Z9 barrel diameter. Efficiency also improves as barrel and cone length are increased at constant up to the natural length of the vortex. At constant inlet velocity, efficiency increases as outiet diameter (and all ratioed dimensions in a family of cyclones) is decreased. Improved efficiency is attained at the... 

Nonparenthetical values are zero additional uncertainty. Parenthetical values are 0.5% additional uncertainty. AU. straight lengths are expressed as multiples of the pipe diameter D. They are measured from the upstream face of the primary device. 

Isolation of radioactive wastes for long periods to allow adequate decay is sought by the use of multiple barriers. These include the waste form itself, the primary containers made of resistant materials, overpacks as secondary layers, buffer materials, concrete vaults, and finally the host rock or sod. Barriers limit water access to the waste and minimize contamination of water suppHes. The length of time wastes must remain secure is dependent on the regulatory limit of the maximum radiation exposure of individuals in the vicinity of the disposal site. 

At the beginning of 1992, the largest Hquids pipelines in the United States, based on pipeline length, were Amoco Pipeline Co., 19,096 km Mobil Pipe Line Co., 15,026 km Exxon Pipeline Co., 14,983 km and Conoco Pipe Line Co., 12,980 km. Distances do not include 1316 km of the Trans-Alaska Pipeline with multiple ownership. In both 1991 and 1992, the product pipeline company with the most product deHveries was Colonial Pipeline with 104,990,000 m, more than double the amount deHvered by Santa Ee Pacific Pipelines, Inc. The top pipeline in terms of cmde oil deHveries was the Alyeska Pipeline Service Co., operator of the Trans-Alaska Pipeline System, with movement of 105,735,000 m (3). 

For systems having multiple legs, the displacement to be absorbed by each leg is distributed proportionally to the cube of the length of the legs as shown in Figure 10. 

---