Low-field condition

In the low-field condition, the quantization axis is defined by the EFG main component In this situation, and rj can both be determined from powder spectra when recorded in an externally applied field. Figure 4.14 shows simulated spectra as is often encountered in practice such as in applied-field measurements of diamagnetic compounds or fast-relaxing paramagnetic compounds at high temperatures. The simulated traces differ in detail from a single-crystal spectrum as shown in Fig. 4.13, but their features still correlate in a unique manner with rj and the sign of... 

Fig. 14. Mobility versus E/N, showing the change of the mobility coefficient K as the ions are clustered through the addition of a dopant (e.g., methylene chloride). Under high-field conditions, K stays practically unaltered, whereas under low-field conditions, K is decreased, which leads to an increase in A K.

Fig. 4.72. Under low-field conditions, there is a linear relation between the ionic current density and the field in the electrolyte.

Under low-field conditions pX 1, the exponentials can be expanded and linearized to give... 

This expression can be simplified further, first, by applying the low-field condition pX 1. It becomes... 

A so-called low-field condition in analytical IMS holds as long as EIN is below approximately 2 Td, and the previous discussion is a valid, although approximate, representation of the effect an external electric field has on the transport of ions in gases. 

From this, we can define that low-field conditions are not valid when the ion s drift velocity is no longer proportional to EIN as described in Equations 10.7 andlO.8. This will occur when the energy gained by the ion from the field is no longer small compared to the thermal energy, as shown in Equation 10.15 from Mason and McDaniel" ... 

From Equation 10.15, we can conclude that what may be low-field conditions for a heavy ion may still be high-held conditions for a light ion (or an electron) in a heavy gas. 

Two limiting cases are of practical importance. The low-field condition mjE4 kT means negligible orientation in the field direction, i.e., 1. Hence Eq. (3.29) reduces to... 

The ion mobility, K, is the ratio of the ion velocity, to the magnitude of the applied electric field, E. The ion mobility is constant under low-field conditions where the E/N quotient is typically less than 2Td (ITd = lOVcm ). Ion mobility can be determined from the experimental parameters as... 

For applications where IM is used to obtain structural information about the ion, such as those in structural proteomics and biophysics, the IM separations are performed using weak electrostatic fields ca. 20-30 V cm torr ). Provided the field strength is sufficiently weak, or under so-called low-field conditions, a closed equation for the ion-neutral collision cross section can be expressed from the kinetic theory of gases see Note 1). When the IM separations are performed in low-field conditions, i.e., constant 7C, the mobility is related to the collision cross section of the ion-neutral pair ... 

It is irrqiortant to recognize fiiat file electric field conditions normally employed in PTR-MS are not low field conditions and fiius the dependence of on cannot be ignored in an accurate quantitative treatment [24,26]. However, this makes any calculations which require file use of K considerably more complex and in what follows we opt for simplicity and ignore any d endence of K on E. However, file wise reader should be wary of such calculations and not attach too much accuracy to the numbws extracted. 

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