High Vacuum Case

In many applications of industrial interest, the ajl3 term is small compared to the 1/13 term. This permits an even further simplification of Eq. (12.2.1), namely, 

In the event that the piping or ducting is not circular, the equivalent 

A worked example, illustrating the use of this method is included in Appendix 12.A. 

In most applications of interest absolute pressure is of sufficient magnitude to cause the mean free path of the gas molecules to be much smaller than the particles feeding the cyclone. This mean free path is the average distance a gas molecule travels between collisions with another molecule. Under such conditions the gas behaves as a continuum and, if the particle Reynolds number is sufficiently small (less than 1 in any case), the familiar Stokes law may, as discussed in Chap. 2, express the drag force acting on a particle moving through the gas 

As we also mentioned in Chap. 2, if the particles and/or the absolute pressure is sufficiently small, a factor called the slip or Cunningham correction factor, Cf, is introduced into Eq. (12.3.1)  

---

If the pump is a filter pump off a high-pressure water supply, its performance will be limited by the temperature of the water because the vapour pressure of water at 10°, 15°, 20° and 25° is 9.2, 12.8, 17.5 and 23.8 mm Hg respectively. The pressure can be measured with an ordinary manometer. For vacuums in the range lO" mm Hg to 10 mm Hg, rotary mechanical pumps (oil pumps) are used and the pressure can be measured with a Vacustat McLeod type gauge. If still higher vacuums are required, for example for high vacuum sublimations, a mercury diffusion pump is suitable. Such a pump can provide a vacuum up to 10" mm Hg. For better efficiencies, the pump can be backed up by a mechanical pump. In all cases, the mercury pump is connected to the distillation apparatus through several traps to remove mercury vapours. These traps may operate by chemical action, for example the use of sodium hydroxide pellets to react with acids, or by condensation, in which case empty tubes cooled in solid carbon dioxide-ethanol or liquid nitrogen (contained in wide-mouthed Dewar flasks) are used. 

Sodium ethoxide [141-52-6] M 68.1. Hygroscopic powder which should be stored under N2in a cool place. Likely impurity is EtOH which can be removed by warming at 60-80" under high vacuum. Hydrolysed by H2O to yield NaOH and EtOH. Other impurities, if kept in air for long periods are NaOH and Na2C03 In this case the powder cannot be used if these impurities affect the reactivity and a fresh sample should be acquired [IR J Org Chem 21 156 1956]. 

The activation of silylene complexes is induced both photochemically or by addition of a base, e.g. pyridine. A similar base-induced cleavage is known from the chemistry of carbene complexes however, in this case the carbenes so formed dimerize to give alkenes. Finally, a silylene cleavage can also be achieved thermally. Melting of the compounds 4-7 in high vacuum yields the dimeric complexes 48-51 with loss of HMPA. The dimers, on the other hand, can be transformed into polysilanes and iron carbonyl clusters above 120 °C. In all cases, the resulting polymers have been identified by spectroscopic methods. 

Similar considerations apply to the selection of pressure drops where there is freedom of choice, although a full economic analysis is justified only in the case of very expensive units. For liquids, typical values in optimised units are 35 kN/m2 where the viscosity is less than 1 mN s/m2 and 50-70 kN/m2 where the viscosity is 1-10 mN /m2 for gases, 0.4-0.8 kN/m2 for high vacuum operation, 50 per cent of the system pressure at 100- 200 kN/m2, and 0 per cent of the system pressure above 1000 kN/m2. Whatever pressure drop is used, it is important that erosion and flow-induced tube vibration caused by high velocity fluids are avoided. 

A mass spectrometer provides an example of a molecular beam, in this case a beam of molecular ions. Molecular beams are used in many studies of fundamental chemical interactions. In a high vacuum, a molecular beam allows chemists to study the reactions that take place through specifically designed types of collisions. For example, a crossed-beam experiment involves the intersection of two molecular beams of two different substances. The types of substances, molecular speeds, and orientations of the beams can be changed systematically to give detailed information about how chemical reactions occur at the molecular level. Chemists also have learned how to create molecular beams in which the molecules have very little energy of motion. These isolated, low-energy molecules are ideal for studies of fundamental molecular properties. 

The free evaporation situation is obtained only in the case of vaporization in a high vacuum. 

Metal atoms can be incorporated into polymers using two approaches. For probing new reactions between metal atoms and polymers a small-scale spectroscopic approach, sometimes referred to as the Fluid Matrix Technique (11), is used. The coreactant polymer matrix, containing on the order of 0.5 fll of polymer, is preformed on an optical surface. In the case of viscous fluids such as 2 the material is painted on the substrate and held at temperatures ranging typically from 200 to 270 K. The temperature is chosen to maintain low volatility but retain mobility. Under high vacuum [10 6 torr]... 

In a highly idealized case representing the case of steady-state evaporation into a vacuum (pG = 0), Hsu and Graham (1976) use Eq. (2-92) to compute the rates of... 

In contrast to the other ion sources, the MALDI source may operate under high vacuum or under atmospheric pressure. In the latter case the acronym AP-MALDI (atmospheric pressure matrix assisted laser desorption ionization) is used. 

The methodology of surface electrochemistry is at present sufficiently broad to perform molecular-level research as required by the standards of modern surface science (1). While ultra-high vacuum electron, atom, and ion spectroscopies connect electrochemistry and the state-of-the-art gas-phase surface science most directly (1-11), their application is appropriate for systems which can be transferred from solution to the vacuum environment without desorption or rearrangement. That this usually occurs has been verified by several groups (see ref. 11 for the recent discussion of this issue). However, for the characterization of weakly interacting interfacial species, the vacuum methods may not be able to provide information directly relevant to the surface composition of electrodes in contact with the electrolyte phase. In such a case, in situ methods are preferred. Such techniques are also unique for the nonelectro-chemical characterization of interfacial kinetics and for the measurements of surface concentrations of reagents involved in... 

As with XRF, electron microscope-based microanalysis is relatively-insensitive to light elements (below Na in the periodic table), although this can be improved upon with developments in thin-window or windowless detectors which allow analysis down to C. It is better than XRF because of the high vacuum used ( 10-8 torr), but a fundamental limitation is the low fluorescent yield of the light elements. As with XRF analysis it is surface sensitive, since the maximum depth of information obtained is limited not by the penetration of the electron beam but by the escape depth of the fluorescent X-rays, which is only a few microns for light elements. In quantitative analysis concentrations may not add up to 100% because, if the surface is not smooth, some X-rays from the sample may be deflected away from the detector. It may be possible in such cases to normalize the concentration data to 100% if the analyst is certain that all significant elements have been measured, but it is probably better to repeat the analysis on a reprepared sample. 

---