Ion-Molecule Collision Energies

In addition to a thermal translational energy, ions travelling along a drift tube are given an additional energy by the applied electric field. An expression for the total mean ion kinetic energy was derived by Wannier [33,34] and takes the following form  

The first term on the right-hand side of Equation 3.22 is simply the thermal contribution to the kinetic energy of the ion. The second term represents the kinetic energy of the ion as it is driven along the drift tube at velocity Va. However, Wannier also suggested an additional contribution, the third and final term in Equation 3.22, which derives from collisions between the ions and buffer gas molecules (of mass mb) and gives rise to an additional, but randomly oriented, velocity contribution. 

Although Equation 3.22 was derived as early as 1953, there was some doubt about its validity until the mid-1970s, when careful experiments were carried out on ion motion in various buffer gases, which showed the Wannier expression to be a good approximation to the real mean ion kinetic energy [35]. 

Notice that the molecule of mass m refers to the neutral molecule involved in the collision (which is an unreactive collision with a buffer gas molecule or a reactive collision with an analyte molecule). 

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In terms of the reactivity contribution, significant differences can occur from one type of analyte molecule to another. For example, owing to its high proton affinity (812 kJ mor ) acetone reacts via a proton transfer process as readily with H3O+(H2O) as it does with H3O+ and therefore on a quadrupole-based PTR-MS system a value of Xm 0.5 will be appropriate. However, Xm has a much lower value for toluene and benzene, since both possess a higher proton affinity than H2O but a lower proton affinity than (H20)2 (see Section 2.2.4.2 for a more detailed discussion of the reactivity of toluene with H3O+(H2O)). Note that the value of Xm may also depend on the value of E N and the temperature of the drift mbe. Toluene is a good example of this since the rate of its endothermic reaction with H30+(H20) will increase as the ion-molecule collision energy increases. An illustration of the effect of humidity is shown in Figure 4.3. 

The hard-core limiting forms of U(r) do not lead to physically acceptable results. We conclude that this is caused by a complete neglect of the effect of the attractive forces on the slope of the repulsive part in U(r). If the interaction energy is assumed as the sum of a Morse exponential function and the polarization energy evaluated at r = r°, the resulting transition probabilities appear useful for analyzing ion-molecule collisions. 

A necessary condition for ion-molecule reactions that has not been considered thus far is that of continuity between reactant and product potential energy surfaces. Many reactions of ions and molecules take place with / a transition from one potential energy surface to another. If no suitable crossings between the respective surfaces exist, then obviously orbiting ion-molecule collisions cannot produce chemical reac-... 

Since the ionic states formed by high-energy radiation seem to be the chemically important ones, let us consider their reactions. The reactions between ions and neutral molecules in the gas phase can be studied directly in a mass spectrometer. Under ordinary operating conditions the pressure in the ionizing chamber of the mass spectrometer is about 10 6 mm. and the ions formed have little chance to collide with a molecule during their brief lifetime (10-5 sec.) before collection. Therefore, mainly unimolecular decomposition reactions occur and it is the products of these that are detected. The intensity of these primary ions increases with the first power of the pressure in the ionization chamber. However, when the pressure becomes great enough so that ion molecule collisions can occur readily, additional secondary ions which are the products of these ion molecule Collisions appear. The intensity of these secondary product ions depends on the concentrations of both the molecules and the primary ions, and thus on the square of the pressure. 

In addition to the processes just discussed that yield vibrationally and rotationally excited diatomic ions in the ground electronic state, vibrational and rotational excitations also accompany direct electronic excitation (see Section II.B.2.a) of diatomic ions as well as charge-transfer excitation of these species (see Section IV.A.l). Furthermore, direct vibrational excitation of ions and molecules can take place via charge transfer in symmetric ion molecule collisions, as the translational-to-internal-energy conversion is a sensitive function of energy defects and vibrational overlaps of the individual reactant systems.312-314... 

R. C. Bhattacharjee and W. Forst, Statistical Theory of Energy Transfer in Ion-Molecule Collisions, paper presented at Seventh International Mass Spectrometry Conference, Florence, 1976. 

G. H. Bearman, H. H. Harris, P. B. James, and J. J. Leventhal, Molecular Excitation in Low Energy Ion-Molecule Collisions, paper presented at 19th Annual Gaseous Electronic Conference, Cleveland, October 1976. 

It has been mentioned that phase space theory, i.e. assuming a loose transition state, has been able to explain the translational energy releases in the decomposition of certain ion—molecule collision complexes [485] and in some unimolecular decompositions measured by PIPECO (see Sect. 8.2). There is a larger number of translational energy releases from PIPECO and a body of data as to translational energy releases in source reactions of positive ions formed by El [162, 310] (Sect. 8.3.1) with which the predictions of phase space theory are in poor agreement. The predicted energy releases are too low. 

If a reactant gas is introduced into the collision cell, ion-molecule collisions can lead to the observation of gas-phase reactions. Tandem-in-time instruments facilitate the observation of ion-molecule reactions. Reaction times can be extended over appropriate time periods, typically as long as several seconds. It is also possible to vary easily the reactant ion energy. The evolution of the reaction can be followed as a function of time, and equilibrium can be observed. This allows the determination of kinetic and thermodynamic parameters, and has allowed for example the determination of basicity and acidity scales in the gas phase. In tandem-in-space instruments, the time allowed for reaction will be short and can be varied over only a limited range. Moreover, it is difficult to achieve the very low collision energies that promote exothermic ion-molecule reactions. Nevertheless, product ion spectra arising from ion-molecule reactions can be recorded. These spectra can be an alternative to CID to characterize ions. 

Another consequence of these forces is that reactive ion-molecule collisions ( ion-molecule reactions ), in contrast to neutral gas reactions, in many cases do not possess activation energy barriers and thus proceed at the collision rate [37]. 

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