Taylor fraction

There is also considerable uncertainty as to the fraction of the surface atoms that act as active sites. As mentioned, results that support a Taylor fraction near unity are opposed by other results from which this fraction is concluded to be small. As pulse experiments such as those done by Dautzenberg et al. are open to, among other factors, the criticism that the hydrogenation pulse could have introduced artifacts, it would be desirable to check the product distribution in experiments in which chemically, the steady state is well defined, but pulses are used where normal synthesis gas is replaced... 

We note that the use of N2 chemisorption on iron, for example, really amounts to measuring the atoms per active site as a function of FE. This procedure is merely an alternative to the one we have adopted, in which we reason about the number of sites involving a given configuration of atoms per unit of exposed atoms. This quantity has been called the Taylor fraction (367). Similar concepts have been discussed recently by Carberry (368). 

The number of active centres is therefore generally less than the total number of surface atoms,the ratio of the two being termed the Taylor fraction Fj (or Taylor ratio). A.A. Balandin attempted to make Taylor s ideas more precise by proposing a Multiplet Hypothesis by which each type of reaction required a multiplet of several atoms to be an active centre. So for example to chemisorb a benzene molecule either for its hydrogenation or in its formation by dehydrogenation, a hexagonal multiplet with one central atom as found in the fcc(l 11) plane would be needed. If the number of atoms composing the multiplet (or ensemble as it was called by Kobozev ) is the Balandin number Nb, then... 

Burdett, R.A., L.W. Taylor and L.C. Jones Jr (1955), Determination of aromatic hydrocarbons in lubricating oil fractions by far UV absorption spectroscopy , p. 30. In Molecular Spectroscopy Report Conf. Institute of Petroleum, London. 

Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Plow 28 1411-1435 Kawaji M (1999) Fluid mechanics aspects of two-phase flow Flow in other geometries. In Kand-likar SG, Shoji M, Dhir VK (eds) Handbook of phase change boiling and condensation. Taylor and Francis, Washington, DC, pp 205-259... 

There was thus the need for optical experiments showing the flaws of classical electrodynamics. An important difference between a wave and a particle is with respect to a beam splitter a wave can be split in two while a photon can not. An intensity correlation measurement between the two output ports of the beamsplitter is a good test as a wave would give a non zero correlation while a particle would show no correlation, the particle going either in one arm or the other. However, when one takes an attenuated source, such as the one used by Taylor, it contains single photon pulses but also a (small) fraction of two... 

Fig. 53.—Molecular weight distribution in poly-(hexa-methylene adipamide) as obtained by fractionation (points) compared with curves calculated from Eq. (3) for two values of p, (Taylor. )...

Oxygen isotopic fractionation factors used for the calculation were taken from Taylor (1997). Initial 8 0 value of hydrothermal solution (0%o) was estimated from 8 0 values of K-feldspar and quartz in the veins and homogenization temperatures (Shikazono and Nagayama, 1993), and that of groundwater (—7%c) was estimated from meteoric water value of the south Kyushu district (—7%c) (Matsubaya et al., 1975). 

General Reeerences Van t Land, Industrkd CrystaUizaUon ofMdts, Taylor Francis, New York, 2004. Mullin, CrystaiUzathn, 4th ed., Butterworth-Heinemann, 2001. Myerson, Handbook of Industrkd CrystaUizaUon, 2d ed., Butterworth-Heinemann, 2001. Pfann, Zone Melting, 2d ed., Wiley, New York, 1966. U.S. Patents 3,621,664 and 3,796,060. Zief and Wilcox, Fractional Solidification, Marcel Dekker, New York, 1967. 

The simplest method for propagation of the analytical errors into the °Th/U age equation (Eqn. 1) involves linear expansion (Albarede 1995, ch. 4.3) of the effect on the calculated age of very small perturbations of the measured ratios (in effect, a Taylor expansion using only the first term). As long as the effect of the errors of the measured ratios on the age is not a large fraction of the age itself, this method will yield acceptably accurate age-errors with minimal effort. 

MRI has been used as a non-invasive quantitative visualization technique to investigate a class of complex Taylor-Couette-Poiseuille (TCP) flows, which constitute a prototype of many mixing or fractionation processes. Here we focused on the vicinity of the Stationary Helical Vortex (SHV) regime characterized by a... 

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

FIGURE 17.25 LCCC separation of a poly(l,6-hexanediol adipate) (a) and SEC analysis of the functionality fractions (b) from Kriiger et al., 1994 (Copyright 1994 from Journal of Liquid Chromatography, 1994, p. 17 by Kruger et al. Reproduced by permission of Taylor Francis Group, LLC., http //www.taylorandfrancis.com). 

Figure 4.1. Removal of carbonate from Israeli arid soils as indicated by the X-ray diffractograms after extraction of the carbonate fraction by NaOAc-HOAc solutions at various pHs for 16 hours. C calcite d = 3.04 A, and D dolomite, d = 2.89 A. Number 1, 2, 3, 4, 5, and 6 indicate non-treated soil (No. 1), treatments (No. 2-6) with NaOAc-HOAc solutions at pH 7.0, 6.0, 5.5, 5.0 and 4.0, respectively (after Han and Banin, 1995. Reprinted from Commun Soil Sci Plant Anal, 26, Han and Banin A., Selective sequential dissolution techniques for trace metals in arid-zone soils The carbonate dissolution step, p 563, Copyright (1995), with permission from Taylor Francis US)...

Figure 4.2. Dissolution of Ca from Israeli arid soils by NaOAc-HOAc solutions at various pHs after the extraction of the exchangeable fraction (after Han and Banin, 1995. Reprinted from Commun Soil Sci Plant Anal, 26, Han and Banin A., Selective sequential dissolution techniques for trace metals in arid-zone soils The carbonate dissolution step, p 568, Copyright (1995), with permission from Taylor Francis US)...

Figure 6.1. The fractional loading isotherms of Cu in a contaminated Israeli loessial soil at an initial (one hour) period and after 48 weeks. The soil was treated with increasing levels of metal nitrates and was incubated under the field capacity regime. Horizonal solid line represents the native content of Cu in the nonamended soil (Figure 6.1 - Figure 6.4, after Han and Banin, 2001. Reprinted from Commun Soil Sci Plant Anal, 32, Han F.X and Banin A.,The fractional loading isotherm of heavy metals in an arid-zone soil, pp 2700-2703, Copyright (2001), with permission from Taylor Francis)...

Figure 6.28. Initial changes of Co concentrations in the main solid-phase fractions of two Israeli arid soils. Soils were incubated under the saturated paste regime (after Han et al., 2002b. Reprinted from J Environ Sci Health, Part A, 137, Han F.X., Banin A., Kingery W.L., Li Z.P., Pathways and kinetics of transformation of cobalt among solid-phase components in arid-zone soils, p 188, Copyright (2003), with permission from Taylor Francis)...

With little error the exponential in the numerator of the rightmost fraction of Eq. (7.2) is expanded in a Taylor series resulting in... 

Taylor RS et al. Proteomics of rat liver Golgi complex minor proteins are identified through sequential fractionation. Electrophoresis 2000 21 3441-3459. 

Riley and Taylor [39] have studied the uptake of about 30 organics from seawater onto the resin at pH 2 - 9. At the 2 - 5 p,g/l level none of the carbohydrates, amino acids, proteins or phenols investigated were adsorbed in any detectable amounts. Various carboxylic acids, surfactants, insecticides, dyestuffs, and especially humic acids are adsorbed. The humic acids retained on the XAD-1 resin were fractionated by elution with water at pH 7, M aqueous ammonia, and 0.2 M potassium hydroxide. 

Taylor, R. E., Slota, P., Fraction Studies on Marine Shell and Bone Samples for Radiocarbon Analyses, In Radiocarbon Dating, pp. 422-432, Berkeley University of California Press, 1979. 

Bowers and Taylor (1985) were the first to incorporate isotope fractionation into a reaction model. They used a modified version of EQ3/EQ6 (Wolery, 1979) to study the convection of hydrothermal fluids through the oceanic crust, along midocean ridges. Their calculation method is based on evaluating mass balance equations, as described in this chapter. 

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