Experimental fractional

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

Mo+ and Mc>2+ one may resort to a multinomial expansion coefficient analysis. Let us represent the fractional abundances of the 7 Mo isotopes by a, b, c, d, e, f and g. The calculated and experimental fractional abundances of the 15 mass lines in Mo + are listed in Table 2.4. When the calculated abundances are compared with the experimental abundances, one reaches the conclusion that the spectrum shown in Fig. 2.17 contains few if any Mo+ ions. If on the other hand, a fraction of the ions are Mo+, say p, then the relative abundances of each mass line can also be calculated. For example, that of Min = 92 should be [pa + (1 — p)a2], and that of M/n = 94 should be [pb + (1 — p)(b2 + 2ad), etc. Thus the fraction p can be obtained by best fit of theoretical abundances and experimental abundances of different Min mass lines. 

A more significant test is the comparison of calculated and experimental fractionation ratios with particle sizes. Crocker, Kawahara, and Freiling (2) have presented Small Boy experimental 89Sr fractionation ratios vs. particle sizes. Figure 10 is a reproduction of their plot with... 

Experimental fraction of protons bound to polyprotic acid... 

Table 4.1. Ore model parameters for both standard and modified Ore approaches (Fmin, / max, F °d and F °d), and the experimental fractions F for the noble gases and a variety of molecules. Note that when Eex < EPS, the minimum predictions have been set to zero see equation (4.38). See Charlton (1985a) for the origin of the measurements. In general, the fractions for the molecular gases have been found to be both density and temperature dependent. The value quoted here is for low densities and is thus expected to be the Ore contribution to the overall positronium fraction in these gases at higher densities...

Figure 8 shows a comparison of experimental fraction of n-butane undecomposed (X) vs. Xcalc from Equation 13. While the four sets of data show some systematic differences, it is clear that Equation 13 represents the rate of conversion of n-butane nearly as well as it does for propane. (Set 4, variable time at 750°C, gives mainly higher conversions than predicted Sets 1, 2, and 3 about as predicted or a little lower.) Experimental X varies from calculated X by an average of —. 023 d=. 03. 

Fractionation Research, Inc. Topical Report No. 18—Efficiency Comparisons AIChE Design Manual and FRl Experimental Fractionation Research, Inc. Alhambra, CA, May 29, 1959. 

The cumulative weight fraction of all species up to length x, which is the most convenient function for comparison with an experimental fractionation will be... 

Hydrothermal- and carbonate-exchange techniques. The majority of available experimental fractionation data are for oxygen isotope fractionations involving minerals. Much of the data, particularly the early data, were obtained using water as the isotopic exchange medium. These experiments were either done at ambient pressure (typically synthesis experiments), or in cold-seal pressure vessels at pressures of 1 to 3 kbar (e.g. O Neil and Taylor 1967 O Neil et al. 1969 Clayton et al. 1972). Later experiments were done in a piston cylinder apparatus (at 15 kbar) to exploit the pressure enhancement of exchange rates (Clayton et al. 1975 Matsuhisa et al. 1979 Matthews et al. 1983a,b). 

The values of K thus obtained depended upon the rate of light absorption according to the Expression 3, where F(C) was the experimental fraction of I0 absorbed at a particular concentration, C, of solute. 

Experimental fraction of dose evaporated extrapolated to f =o (except for XI and XII) (Kasting and Saiyasombati, 2001). ° Estimated value, corrected as in Kasting and Saiyasombati (2001). 

For comparison with experimental fractionation results, we have to find the total number of monomeric molecules which are contained in chains of a definite length. This number, as a function of the chain length, would give us the distribution curve of the molecular weight fractions, as defined on page 323. As a chain of s links contains (s + 1) monomeric molecules, the total number of fundamental molecules embodied in chains with s links would be... 

At a direct inspection of experimental fractional independent yields and their fits by Gaussian curves one can observe that yield values with even proton and/or neutron numbers tend to lie above the curve and those with odd numbers tend to lie below it. This is taken into account by two factors EOZ and EON, the even-odd (or odd-even) factors for protons and neutrons, respectively. These values may be given in percentage. In this way, an EOZ-value of, e.g., 15% corresponds to a factor 1.15 by which a value read from the Gaussian curve has to be multiplied (even-Znuclide) or divided (odd-Znuclide) in order to obtain the predicted yield. 

These three theoretical distributions describe only a very small portion of the diversity of polymer microstructures that are produced every day in academia and industry. Even for the polymerization systems they describe, they are only strictly valid as instantaneous distributions. If conditions in the polymerization reactor fluctuate as a function of time or spatial location, the distributions for the polymer product may be considerably more complex. In this case, it is very difficult to And a mathematical model precise enough to describe the complete polymer microstructure, and we must rely solely on experimental fractionation for its determination. In fact, the comparison of experimentally-measured mi-crostructural distributions with the ones predicted by theory is a powerful tool to investigate pol5mierization mechanisms and imderstand polymer reactor nonidealities. Nonetheless, these distributions are essential to realize the complexity of polymer microstructure and the interdependency of the distributions of molecular weight, chemical composition (or tacticity), and long-chain branching. This interdependency should always be kept in mind when interpreting the firactionation data from any experimental technique. 

Fractionation Equipment. Until recently, no fiilly automated instrument existed to perform batch fractionation of polymers. Most of the older experimental apparatuses consisted of simple glassware equipment that required considerable operator time and the manipulation of sizeable amounts of solvent. Some of these experimental fractionation systems have been thoroughly described by Francuskiewicz (8). 

The fact that cations with larger alkyl side chains seem to exhibit lower normal boiling point temperatures may seem in contradiction with experimental fractional distillation results (Earle et al. [23] and Widegren et al. [38]) that indicate that in a... 

The current results within the relaxed model (p ) shows a very good reproduction of the experimental fraction of Ge atoms involved in homopolar bonds. The fraction of corner sharing Ge atoms is improved upon previous simulation, this stems from the substantial change of the shape of the third goece peak. 

The Freundlich adsorption isotherm (Adamson, 1990) resulted to be the best one to describe the specific interaction of CER with glassy carbon electrodes by using a fitting procedure of experimental fractional surface coverage vs. c cer-... 

Figure 11. Potential dependence of the fractional coverage of chemisorbed xanthate on silver and silver-gold alloys in solutions of pH 9.2 containing 10 mol dm ethyl xanthate. Solid lines are isotherms for silver (1), 50 50 wt. % Ag-Au alloy (2), and 20 80 wt. % Ag-Au alloy. Data points are experimental fractional coverages for the 50 50 (o) and 20 80 alloys (A). (From Woods et al )...

This method, referred to as the generalized Beall method (/2, /3) and Schulz s procedure can both be applied to the calculated fractionation data described in the following. In these hypothetical cases, unlike in most expaimental fractionations, the result of the Schulz and generalized Beall evaluations can be compared with the true initial distribution. In the majority of the experimental fractionation studies reported the latter is not known, so that the reliability of the curves cannot be checked. 

Triad sequence distributions were used to calculate diad concentrations, probability parameters, number average sequence lengths and the comonomer mole fractions in the copolymers. The experimental fractions of all the ten A centred and ten M centred triad cotactic sequences were found to be in excellent agreement with those calculated using the probabilities parameters. 

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