Ion evaporation rate constants

Attempts were made to examine the validity of lEM by evaluation of the ion evaporation rate constant ki [see Eq. 1.11, where the (M (H20) ) for ions like Li, Na+, K +, and so on, were obtained from experimental data in the literature. The rate constants /ti(Li+), /ti(Na+), and so on, were compared with experimentally determined ion intensities, I(Li+), I(Na+), and so on, when equal concentrations of the salts LiX, NaX, and so on, were present in the solution. The observed ion abundance ratios should correspond to the evaluated rate constant ratios if IBM holds. The data used for the evaluation of AG°joi (M (H20) ) had error limits that led to some scatter of the evaluated AG gpi (M (H20) ) (see Table 1.1 in Kebarle and Peschke ). The results showed a trend of decreasing free energy of activation, AG (M " ") from Li to Cs, which should lead to increasing ion evaporation rate constants from Li to Cs. ... 

Unfortunately, the experimentally observed ion abundances determined in different laboratories did not agree. Results from this laboratory showed similar intensities for the Li -Cs series, while results from other laboratories such as Cole gave increasing intensities in the order Li" " to Cs" ", as expected on the basis of the calculated ion evaporation rate constants. The triple quadrupole mass spectrometer used in this labor-atory exhibited large decreases of ion transmission with increasing miz, and the corrections for the transmission changes used by Kebarle and Peschke could have been unreliable. 

Alloys, Alloys consist of two or more elements of different vapor pressures and hence different evaporation rates. As a result, the vapor phase and therefore the deposit constantly vary in compositions. This problem can be solved by multiple sources or a single rod- or wire-fed electron beam source fed with the alloy. These solutions apply equally to evaporation or ion-plating processes. 

Attachment is mainly by diffusion, although, if the decay products are ions, electrostatic attraction to charged nuclei of opposite sign makes a small additional effect (Bricard Pradel, 1966). The rate constant for attachment XA, is given by an equation originally applied to evaporation from small droplets (Fuchs, 1959). 

The equation assumes that the evaporation of the liquid takes place at or near the end of the capillary. However, it can be calcrrlated that the evaporation rate of water at 50°C from a 25-pm-lD tube is ca. 50 rrl/s. Therefore, the evaporation does not take place at or near the end of the capillary, but somewhere inside the capillary. The competition between evaporation rate F, and liqttid flow-rate F, is schematically depicted in Figure 4.2 [7]. The situation described above is marked (a) in Fignre 4.2. By increasing the inlet pressrrre it must be possible to go from the situation (a) to the ideal situation (b) or even to the situation (c). However, the resrrlting flow-rate will necessitate a larger pumping capacity of the vacuum system. The situation marked (c) does not resrrlt in stable ion sotuce pressures, because the evaporation surface area is not constant. 

The evaporative ensemble model is one in which the cluster ions have been generated in a broad distribution of cluster sizes and internal energies. Hence, the rate constant, k E), is inversely related to the reaction time, f, so that ln( ) = —ln(t) and cnn(A ) = —dln(t). This permits us to convert the derivative in Eq. (10.55) from dln(fe) to dln(f) (Lifshitz, 1993) as... 

Thomson 1979), the charge on droplets of this size that is required for this ion evaporation is lower than that required for Coulomb fission, i.e., ion evaporation replaces Coulomb fission as a means of relaxing the Coulombic repulsion at the droplet surface. The equation predicting the rate constant for ion evaporation from the droplets was derived on the basis of the transition state theory (see any text on physical chemistry) ... 

Another possible mechanism involves increases in the surface tension of the droplets as a result of high concentrations of co-eluting compounds (Mallet 2004). This effect would reduce the rate of solvent evaporation, and thus also the probability that the droplet will reach a sufficiently small size that ion evaporation can occur, and also increase the difficulty of ion evaporation itself via the term in the rate constant, see Equations [5.6-5.7]. Another effect that seems to be particularly important for biological sample extracts arises from the presence of involatile solutes, believed (King 2000) to cause ionization suppression not only via a strong effect on surface tension but also via co-precipitation of analyte as the droplets shrink in size. 

The 9 8 transition starts at z = 9 with a fairly uniform concentration of the various adducts, and ends at z = 8 with mostly the purely protonated and once sodiated peaks. The adducts with one and two TEA+ have both decreased drastically, so, again, the decay mechanism is by loss of one and two TEA+ units. The pattern in the z = 8->7 transition is similar. By careful analysis of these observable decay ratios in proteins of different radii, one could infer the dependence on charge state and radins of the rate constant for evaporation of TAA+ ions. This charge loss seems to be an activated process with a high activation energy, which is nonetheless considerably... 

Iribarne and Thomson derived an equation that provided detailed predictions for the rate of ion evaporation from the charged droplets.The treatment is based on transition state theory, used in chemical reaction kinetics. The rate constant ki for emission of ions from the droplets is given by... 

Schematic illustrations of the effect of temperature and surface density (time) on the ratio of two isotopes, (a) shows that, generally, there is a fractionation of the two isotopes as time and temperature change the ratio of the two isotopes changes throughout the experiment and makes difficult an assessment of their precise ratio in the original sample, (b) illustrates the effect of gradually changing the temperature of the filament to keep the ratio of ion yields linear, which simplifies the task of estimating the ratio in the original sample. The best method is one in which the rate of evaporation is low enough that the ratio of the isotopes is virtually constant this ratio then relates exactly to the ratio in the original sample.

It is a well recognized fact that in field ion microscopy field evaporation does not occur at a constant rate because of the atomic step structures of the tip surface. For the sole purpose of a compositional analysis of a sample, one should try to aim the probe hole at a high index plane where the step height is small and field evaporation occurs more uniformly. But even so, the number of atoms field evaporated per HV pulse or laser pulse within the area covered by the probe-hole will not be the same every time. It is reasonable to assume that the field evaporation events are nearly random even though there has been no systematic study of the nature of such field evaporation events. Let the average number of atoms field evaporated per pulse within the area covered by the probe-hole area be n. The probability that n atoms are field evaporated by a pulse is then given by the Poisson distribution... 

In a preliminary pulsed-laser atom-probe measurement,158 the critical ion energy deficits of Rh and W atoms, field evaporated from kink sites, are measured at a rate of 1010 layers per second at a temperature around 100 K. Using the system constants, i.e. the flight path constant and the... 

Special devices for the direct introduction of the sample into the ion-source chamber have been designed for substances that are unstable or have a very low volatility. Constancy of the rate of vapor flow is provided in this particular case by the constant evaporation temperature and by the presence of condensed phase. 

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