Believability

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

There is a significant difference between the results shown in Figure 2 and calculated results given in Brit. Chem. Eng. Proc. Tech. 16 1036 (1971). We believe the latter to be in error. 

Appendix C-5 lists selected UNIQUAC binary parameters and characteristic binary parameters for noncondensable-condensable interactions for 150 binary pairs. For any binary pair, the parameters shown are believed to be the best now available. Parameters listed here were chosen from the more extensive lists in Appendix C-6 and C-7. A12 and A21 correspond to the UNIQUAC... 

Other techniques such as X-ray diffusion or small angle neutron diffusion are also used in attempts to describe the size and form of asphaltenes in crude oil. It is generally believed that asphaltenes have the approximate form of very flat ellipsoids whose thicknesses are on the order of one nanometer and diameters of several dozen nanometers. 

Note that styrenes are believed to react incompletely with the anhydride. 

We believe to have shown here that the RVP of gasoline is a primary characteristic for quality resulting from a delicate compromise between the demands for vehicle performance, optimization of refinery operations and environmental protection. 

It is believed that to avoid any risk of explosion, the electrical conductivity of jet fuel should fall between 50 and 450 pS/m. This level is attained using anti-static additives which are metallic salts (chromium, calcium) added at very low levels on the order of 1 ppm. 

The presence of thiophene and its derivatives in crude oils was detected in 1899, but until 1953, the date at which the methyl-thiophenes were identified in kerosene from Agha Jari, Iran crude oil, it was believed that they came from the degradation of sulfides during refining operations. Finally, their presence was no longer doubted after the identification of benzothiophenes and their derivatives (Table 8.9), and lately of naphthenobenzothiophenes in heavy cuts. 

It is believed that the majority of clastic reservoir rocks are water wet, but the subject of wettability is a contentious one. 

Exciting developments based on electromagnetic induction raced along from that time, giving us the sophisticated products our everyday lives depend on. During most of the period productive uses for eddy current technology were few and few people believed in it as a usefiil tool eddy currents caused power loss in electrical circuits and, due to the skin effect, currents flowed only in the outer surfaces of conductors when the user had paid for all the copper in the cable. The speedometer and the familiar household power meter are examples of everyday uses that we may tend to forget about. The brakes on some models of exercise bicycle are based on the same principle. 

In this preliminary work we have investigated composite objects with a simple geometry. In future work the proposed approach will be applied to more complicated objects, in particular glued structures. Since we for such objects expect to have a less distinct back wall echo, we have reason to believe that the preprocessing method that was used in this work has to be somewhat modified. 

The mechanism of the Fischer-Tropsch reactions has been the object of much study (note Eqs. XVI11-55-XV111-57) and the subject of much controversy. Fischer and Tropsch proposed one whose essential feature was that of a metal carbide—patents have been issued on this basis. It is currently believed that a particular form of active adsorbed carbon atoms is involved, which is then methanated through a series of steps such as... 

Typical results for a semiconducting liquid are illustrated in figure Al.3.29 where the experunental pair correlation and structure factors for silicon are presented. The radial distribution function shows a sharp first peak followed by oscillations. The structure in the radial distribution fiinction reflects some local ordering. The nature and degree of this order depends on the chemical nature of the liquid state. For example, semiconductor liquids are especially interesting in this sense as they are believed to retain covalent bonding characteristics even in the melt. 

It is widely believed that gases are virtually ideal at a pressure of one atmosphere. This is more nearly tnie at relatively high temperatures, but at the nonnal boiling point (roughly 20% of the Boyle temperature), typical gases have values of pV/nRT that are 5 to 15% lower than tlie ideal value of unity. 

Figure A2.5.22 shows [6] the experimental heat eapaeity of p-brass (CiiZn) measured by Moser in 1934. Note that the experimental eiirve is sharper and goes imieh higher than any of the theoretieal eurves in figure A2.5.21 however, at that time it was still believed to have a finite limit.

Nearly all experimental eoexistenee eurves, whether from liquid-gas equilibrium, liquid mixtures, order-disorder in alloys, or in ferromagnetie materials, are far from parabolie, and more nearly eubie, even far below the eritieal temperature. This was known for fluid systems, at least to some experimentalists, more than one hundred years ago. Versehaflfelt (1900), from a eareflil analysis of data (pressure-volume and densities) on isopentane, eoneluded that the best fit was with p = 0.34 and 8 = 4.26, far from the elassieal values. Van Laar apparently rejeeted this eonelusion, believing that, at least very elose to the eritieal temperature, the eoexistenee eurve must beeome parabolie. Even earlier, van der Waals, who had derived a elassieal theory of eapillarity with a surfaee-tension exponent of 3/2, found (1893)... 

The scientific shidies of the early 1970s are fiill of concern whether the critical exponents detemiined experimentally, particularly those for fluids, could be reconciled with the calculated values, and at times it appeared that they could not be. However, not only were the theoretical values more uncertain (before RG calculations) than first believed, but also there were serious problems with the analysis of the experiments, in addition to those associated with the Wegner... 

An experimental teclmique that is usefiil for structure studies of biological macromolecules and other crystals with large unit cells uses neither the broad, white , spectrum characteristic of Lane methods nor a sharp, monocliromatic spectrum, but rather a spectral band with AX/X 20%. Because of its relation to the Lane method, this teclmique is called quasi-Laue. It was believed for many years diat the Lane method was not usefiil for structure studies because reflections of different orders would be superposed on the same point of a film or an image plate. It was realized recently, however, that, if there is a definite minimum wavelengdi in the spectral band, more than 80% of all reflections would contain only a single order. Quasi-Laue methods are now used with both neutrons and x-rays, particularly x-rays from synclirotron sources, which give an intense, white spectrum. 

Contradictory evidence regarding the reaction to fonn 8 and 9 from 7 led the researchers to use TREPR to investigate the photochemistry of DMPA. Figure B1.16.15A shows the TREPR spectrum ofthis system at 0.7 ps after the laser flash. Radicals 6, 7 and 8 are all present. At 2.54 ps, only 7 can be seen, as shown in figure B1.16.15B. All radicals in this system exliibit an emissive triplet mechanism. After completing a laser flash intensity sPidy, the researchers concluded that production of 8 from 7 occurs upon absorption of a second photon and not tiiemially as some had previously believed. 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

Lattice models are particularly suited for answering the questions posed. We will show that the two physical restrictions are sufficient to rationalize the emergence of very limited (believed to be only of the order of a thousand... 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

It is generally believed that in the first stage of a passivation reaction—just below —a precursor film is fonned... 

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