Charge 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. 

Example 4. For a given lattice, a relationship is to be found between the lattice resistivity and temperature usiag the foUowiag variables mean free path F, the mass of electron Af, particle density A/, charge Planck s constant Boltzmann constant temperature 9, velocity and resistivity p. Suppose that length /, mass m time /, charge and temperature T are chosen as the reference dimensions. The dimensional matrix D of the variables is given by (eq. 55) ... 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

Integration of these component peaks, with appropriate corrections applied for different photoionization cross-sections and inelastic mean free paths, gives the electron populations listed in Table 4. The atomic charges obtained are consistent... 

A quite different aspect of local kinetics is that having to do with changes of charge state, e.g., between H+ and H° or H° and H. Such changes require emission or absorption of electrons or holes. Since the mean free paths of these carriers are large compared with atomic dimensions, it is customary (see for example Lax, 1960) to use a velocity-averaged cross section a as the key descriptor of the rate of a capture reaction such as H+ + e— H°. Explicitly, we write, for this case,... 

The above equations do not allow for kinetics associated with the mean free path discontinuity at the particle surface. A correction for this would increase the charging rate. As a first approximation, this can be allowed for by replacing Pp in Eqs. (75) and (77) with the product >p[l + (2A,/Z)p)]. This is based on the reasoning that ions migrating to within a mean free path of the particle surface will be deposited and that the ion concentration will drop effectively to zero within a mean free path of the surface. 

It is apparent from the values of ps that diffusional charging is primarily effective with very small particles, as might be expected. With particles as large as 10 microns the charge level produced in any reasonable time is small compared with what can be achieved with corona charging. For the 0.1-micron particle, however, the charge level attained by diffusion is of the same order and may be larger if the mean free path correction is allowed for. 

For a nuclide of mass M, abundance sensitivity is the ratio between the signal at mass M+ arising from the same species to the signal at mass M. Off-peak ions are present because of collisions behind the magnetic filter, of reflections on the tube wall, or of space-charge effects. As a result of the collisions, the energy of these ions is different from the energy of the main beam. They alter the apparent peak baseline in a continuous way. Abundance sensitivity decreases with the mean free path of ions, i.e., when pressure near the collector assembly... 

Chemical ionisation results from the gas-phase collision between the analyte and species formed from the reagent gas introduced concomitantly in the ion source and bombarded by electrons. Methane, ammonium or isobutane are often used as reagent gases (Fig. 16.17). The reagent gas is introduced into the ion source at a pressure of a few hundred pascals, which reduces the mean free path and favours collision. Chemical ionisation produces positively and negatively charged species. 

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