Dynamics of reactive ions and ion mobility

Molecular mass spectrometry necessarily requires that a sample of matter be vaporised and converted into ions (ionised), as the individual molecular particles of the sample must interact with electric or magnetic fields for analysis. Although molecules change their molecular properties during ionisation, they do not lose them: in particular, ionised molecules are also chemically reactive and exhibit a range of chemical transformation processes equivalent to that of neutral molecules. However, this chemical reactivity takes place under conditions that differ from those under which neutral molecules react: ions are subjected to significant forces or interactions via electric fields through the Coulomb force.

As a result, ions react particularly strongly to external electric fields. They are accelerated by the force exerted by an electric field, which increases their velocity and thus their kinetic energy. If the electric field – and thus the accelerating force – is strong enough, this additional kinetic energy can reach values far exceeding the thermal equilibrium energy.

Effective ion temperature and reaction temperature

If the background gas pressure at which the electrical acceleration of the ions takes place is still high enough for collisions with neutral particles of the background gas to occur, the electrical acceleration of the ions also increases the collision energy between the ions and the background gas particles. This has far-reaching consequences for the chemical reactivity of the ions, but also for the ions themselves: the high-energy collisions provide a high effective reaction temperature for chemical reactions. This generally alters which reactions are likely to occur and with what probability. Furthermore, high-energy inelastic collisions with background gas particles lead to the excitation of internal energy states (such as vibrational states) in molecules. This often results in fragmentation reactions: molecular ions break up into several fragments, which may themselves be highly reactive. Large molecules can undergo significant changes in their geometric shape due to the energy stored internally. Since the probability of an ion colliding with neutral gas particles naturally also depends on the ion’s geometric structure, a complex coupling arises between the external electric field strength, the internal degrees of freedom of a molecular ion, the ion’s interaction cross-section with the background gas, and the effective reaction temperature of the ion.

The PTC seeks to understand these couplings and the resulting phenomena on the basis of molecular processes and to describe them using models and numerical simulations. Experimentally, in addition to the analysis of conversion products of chemically reactive ions, the determination of the mobility of molecular ions in an electric field (ion mobility) is an important method for gaining insights into their molecular dynamics.

When ions move in an electric field within a neutral background gas, they quickly reach a constant drift velocity as a result of collisions with the background gas particles. The ratio between the drift velocity $v_d$ and the electric field strength $E$ is the ion mobility $K$: 
$$ v_d = K E $$

However, partly due to the coupling mentioned above between internal degrees of freedom (or the reaction temperature) and the electric field strength, the ion mobility is generally not a constant, but itself a complex function of the electric field strength: 
$$ v_d = K\left(E\right) E $$

There are several significant analytical methods based on the measurement of ion mobility at a given field strength or on the behaviour of the mobility function as a function of field strength. The most important of these are ion mobility spectrometry (IMS) and differential ion mobility spectrometry (DMS).

The description of the ion mobility observable experimentally under various conditions, using theoretical models and numerical simulations, is a significant current area of research at the PTC. In addition to understanding the fundamental dynamic processes, this work also opens up avenues for improving the performance of ion mobility-based analytical methods.

As electrically charged particles, ions interact with one another via the Coulomb interaction. In groups of ions, the motion of individual particles is therefore always dependent on the motion of the other particles in the group. As a result, larger groups of ions in analytical instruments such as mass spectrometers often do not exhibit ideal, collective behaviour. This phenomenon is known as space charge. In ion-trap mass analysers and similar components of mass spectrometers in particular, such space charge effects can have a very significant impact on the performance of the instruments.

Modelling these space charge effects is computationally intensive: since the motion of an ion depends, amongst other things, on every other ion, a naive numerical model must determine the distance between each ion and every other ion. This results in a computational cost that increases quadratically (with $\mathcal{O}\left(n^2\right)$). This is generally far too computationally intensive for modelling real-world problems. Consequently, for most problems, numerical approximation methods must be used to describe the space-charge coupling between the ions.

The PTC uses various simulation programmes to model the motion of ions in mass spectrometers and similar instruments, taking into account space charge effects, chemical reactivity and interactions with background gases. In some cases, we develop our own simulation tools tailored to specific research questions.