Vacuum mean free path

In a vacuum (a) and under the effect of a potential difference of V volts between two electrodes (A,B), an ion (mass m and charge ze) will travel in a straight line and reach a velocity v governed by the equation, mv = 2zeV. At atmospheric pressure (b), the motion of the ion is chaotic as it suffers many collisions. There is still a driving force of V volts, but the ions cannot attain the full velocity gained in a vacuum. Instead, the movement (drift) of the ion between the electrodes is described by a new term, the mobility. At low pressures, the ion has a long mean free path between collisions, and these may be sufficient to deflect the ion from its initial trajectory so that it does not reach the electrode B. 

Molecular distillation occurs where the vapor path is unobstmcted and the condenser is separated from the evaporator by a distance less than the mean-free path of the evaporating molecules (86). This specialized branch of distillation is carried out at extremely low pressures ranging from 13—130 mPa (0.1—1.0 p.m Hg) (see Vacuum technology). Molecular distillation is confined to appHcations where it is necessary to minimize component degradation by distilling at the lowest possible temperatures. Commercial usage includes the distillation of vitamins (qv) and fatty acid dimers (see Dimeracids). 

Vacuum Flow When gas flows under high vacuum conditions or through very small openings, the continuum hypothesis is no longer appropriate if the channel dimension is not very large compared to the mean free path of the gas. When the mean free path is comparable to the channel dimension, flow is dominated by collisions of molecules with the wall, rather than by colhsions between molecules. An approximate expression based on Brown, et al. J. Appl. Phys., 17, 802-813 [1946]) for the mean free path is... 

For gas flow through porous media with small pore diameters, the slip flow and molecular flow equations previously given (see the Vacuum Flow subsec tion) may be applied when the pore is of the same or smaller order as the mean free path, as described by Monet and Vermeulen (Chem. E/ig. Pi og., 55, Symp. Sei , 25 [1959]). 

According to Ktiudsen if a small circular orifice of diameter less than the mean free path of the molecules in a container, is opened in the wall of the container to make a connection to a high vacuum sunounding the container, the mass of gas effusing tlnough the orifice, of area A, is given by an equation derived from the kinetic theoty, where tire pressure is in amiospheres. 

Characterization techniques become surface sensitive if the particles or radiation to be detected come from the outer layers of the sample. Low energy electrons, ions and neutrals can only travel over distances between one and ten interatomic spacings in the solid state, implying that such particles coming off a catalyst reveal surface-specific information. The inherent disadvantage of the small mean free path is that measurements need to be carried out in vacuum, which conflicts with the wish to investigate catalysts under reaction conditions. 

In situ characterization. Catalysts should preferably be investigated under the conditions under which they are active in the reaction. Various reasons exist why this may not be possible, however. For example, lattice vibrations often impede the use of EXAFS, XRD and Mossbauer spectroscopy at reaction temperatures the mean free path of electrons and ions dictates that XPS, SIMS and LEIS are carried out in vacuum, etc. Nevertheless, one should strive to choose the conditions as close as possible to those of the catalytic reaction. This means that the catalyst is kept under reaction gases or inert atmosphere at low temperature to be studied by EXAFS and Mossbauer spectroscopy or that it is transferred to the vacuum spectrometers under conditions preserving the chemical state of the surface. 

Improved vacuum conditions effect an elongated mean free path for the ions and thus a lower risk of collision on their transit through the TOF analyzer. The background pressure in the analyzer is directly reflected by the resolution. [40] Despite improvements of resolving power in the order of a factor of two can be realized (Fig. 4.9), enhanced pumping systems alone are not able to effect a breakthrough in resolving power. 

Note The need for almost perfect vacuum, i.e., extremely long mean free paths, in FT-ICR mass spectrometers arises from the combination of high ion velocities of several 10 m s observation intervals in the order of seconds, and the effect of collisions on peak shape. 

The second most apparent limitation on studies of surface reactivity, at least as they relate to catalysis, is the pressure range in which such studies are conducted. The 10 to 10 Torr pressure region commonly used is imposed by the need to prevent the adsorption of undesired molecules onto the surface and by the techniques employed to determine surface structure and composition, which require relatively long mean free paths for electrons in the vacuum. For reasons that are detailed later, however, this so-called pressure gap may not be as severe a problem as it first appears. There are many reaction systems for which the surface concentration of reactants and intermediates found on catalysts can be duplicated in surface reactivity studies by adjusting the reaction temperature. For such reactions the mechanism can be quite pressure insensitive, and surface reactivity studies will prove very useful for greater understanding of the catalytic process. 

In the Knudsen effusion method a substance is enclosed in a sealed container into which a very small hole is drilled. This hole must be knife-edged and the mean free path of the vapour must be 10 times the diameter of the hole. In its simplest form an experiment proceeds as follows. The Knudsen cell, with sample in it, is carefully weighed and then heated in a vacuum at the requisite temperature for a set time. The cell is then re-weighed and the weight loss is measured. However, it is now more usual to continuously measure the weight of the cell. If the molecular weight and surface area of the sample is known the vapour pressure can be found. 

Used to calculate the mean free path length X for any arbitrary pressures and various gases are Table III and Fig. 9.1 in Chapter 9. The equations in gas kinetics which are most important for vacuum technology are also summarized (Table IV) in chapter 9. 

Model concept Gas Is pourable (fluid) and flows In a way similar to a liquid. The continuum theory and the summarization of the gas laws which follows are based on experience and can explain all the processes in gases near atmospheric pressure. Only after it became possible using ever better vacuum pumps to dilute the air to the extent that the mean free path rose far beyond the dimensions of the vessel were more far-reaching assumptions necessary these culminated in the kinetic gas theory. The kinetic gas theory applies throughout the entire pressure range the continuum theory represents the (historically older) special case in the gas laws where atmospheric conditions prevail. 

Laminar flow In circular tubes with parabolic velocity distribution Is known as Poiseuille flow. This special case is found frequently in vacuum technology. Viscous flow will generally be found where the molecules mean free path is considerably shorter than the diameter of the pipe X d. 

Molecular flow prevails In the high and ultrahigh vacuum ranges. In these regimes the molecules can move freely, without any mutual Interference. Molecular flow Is present where the mean free path length for a particle Is very much larger than the diameter of the pipe X d. 

---