A contribution to the amaranthine quarrel between true and average electrical mobility in the free molecular regime

Landau and Lipschitz's approach—termed here H&B due to the use of Happel and Brenner's slow rotation approximation—for calculating the average electrical mobility over all orientations of an ion in the free molecular regime is shown in this manuscript to be an invalid assumption for non-globular ions when a fixed electrical field is present. The reason behind the invalidity seems to be the confusion between average “settling” velocity (the calculation intended by H&B) and the average mobility (drag) in the direction of the field. When a missing orientation is taken into account by rotating the drag tensor, the average mobility obtained through Landau's approach coincides with well-known orientationally averaged Kinetic Theory Methods such as those of Mason and McDaniel (M&M). H&B's averaging approach, however, can be related to the true mobility displacement of the ion or, in other words, the displacement occurring in the direction of the velocity. This true mobility displacement only agrees with the average mobility displacement if ion velocity and electrical field have always the same direction, which only happens under special cases. Analytical and numerical calculations of collision cross-sections of linear and planar structures using a momentum transfer kinetic theory approach are chosen here as a means to prove that a single rotation of the drag tensor is sufficient to show agreement between both methods. A projected area approach is also used to prove the inadequacy of the H&B method

Modeling of an Inverted Drift Tube for Improved Mobility Analysis of Aerosol Particles

A new mobility particle analyzer, which has been termed Inverted Drift Tube, has been modeled analytically as well as numerically and proven to be a very capable instrument. The basis for the new design have been the shortcomings of the previous ion mobility spectrometers, in particular (a) diffusional broadening which leads to degradation of instrument resolution and (b) inadequate low and fixed resolution (not mobility dependent) for large sizes. To overcome the diffusional broadening and have a mobility based resolution, the IDT uses two varying controllable opposite forces, a flow of gas with velocity v gas , and a linearly increasing electric field that opposes the movement. A new parameter, the separation ratio Λ = v drift /v gas , is employed to determine the best possible separation for a given set of nanoparticles. Due to the system’s need to operate at room pressure, two methods of capturing the ions at the end of the drift tube have been developed, Intermittent Push Flow for a large range of mobilities, and Nearly-Stopping Potential Separation, with very high separation but limited only to a narrow mobility range. A chromatography existing concept of resolving power is used to differentiate between peak resolution in the IDT and acceptable separation between similar mobility sizes

Analysis of Ion Motion and Diffusion Confinement in Inverted Drift Tubes and Trapped Ion Mobility Spectrometry Devices

Ion motion in trapped ion mobility spectrometers (TIMS) and inverted drift tubes (IDT) has been investigated. The two-dimensional (2D) axisymmetric analytical solution to the Nernst–Planck equation for constant gas flows and opposed linearly increasing fields is presented for the first time and is used to study the dynamics of ion distributions in the ramp region. It is shown that axial diffusion confinement is possible and that broad packets of ions injected initially into the system can be contracted. This comes at the expense of the generation of a residual radial field that pushes the ions outward. This residual electric field is of significant importance as it hampers sensitivity and resolution when parabolic velocity profiles form. When radio frequency (RF) is employed at low pressures, this radial field affects the stability of ions inside the mobility cell. Trajectories and frequencies for stable motion are determined through the study of Mathieu’s equation. Finally, effective resolutions for the ramp and plateau regions of the TIMS instrument are provided. While resolution depends on the inverse of the square root of mobility, when proper parameters are used, resolutions in the thousands can be achieved theoretically for modest distances and large mobilities

Optimization of long range potential interaction parameters in ion mobility spectrometry

The problem of optimizing Lennard-Jones (L-J) potential parameters to perform collision cross section (CCS) calculations in ion mobility spectrometry has been undertaken. The experimental CCS of 16 small organic molecules containing carbon, hydrogen, oxygen, nitrogen, and fluoride in N2 was compared to numerical calculations using Density Functional Theory (DFT). CCS calculations were performed using the momentum transfer algorithm IMoS and a 4-6-12 potential without incorporating the ion-quadrupole potential. A ceteris paribus optimization method was used to optimize the intercept σ and potential well-depth ϵ for the given atoms. This method yields important information that otherwise would remain concealed. Results show that the optimized L-J parameters are not necessarily unique with intercept and well-depth following an exponential relation at an existing line of minimums. Similarly, the method shows that some molecules containing atoms of interest may be ill-conditioned candidates to perform optimizations of the L-J parameters. The final calculated CCSs for the chosen parameters differ 1% on average from their experimental counterparts. This result conveys the notion that DFT calculations can indeed be used as potential candidates for CCS calculations and that effects, such as the ion-quadrupole potential or diffuse scattering, can be embedded into the L-J parameters without loss of accuracy but with a large increase in computational efficiency

Modeling and Experimenting a Novel Inverted Drift Tube Device for Improved Mobility Analysis of Aerosol Particles

Ion Mobility Spectrometry (IMS) is an analytical technique for separation of charged particles in the gas phase. The history of IMS is not very old, and in this century, the IMS technique has grown rapidly in the advent of modern instruments. Among currently available ion mobility spectrometers, the DTIMS, FAIMS, TWIMS, DMA are notable. Though all the IMS systems have some uniqueness in case of particle separation and detection, however, all instruments have common shortcomings. They lack in resolution, which is independent of mobility of different charged particles and they are not able to separate bigger particles (20 120 nm) with good accuracy. The work presented here demonstrates a new concept of IMS technique at atmospheric pressure which has a resolution much higher than that of the currently available DTIMS (Drift Tube Ion Mobility Spectrometry) instruments. The unique feature of this instrument is the diffusion auto-correction. Being tunable, It can separate the wide range of particles of different diameters. The working principle of this new IMS technique is different from the typical DTIMS and to simply put, it can be considered as an inversion of commonly used technique, so termed as Inverted Drift Tube (IDT).The whole work performed here can be divided into three major phases. In the first phase, the analytical solution was derived for two new separation techniques: IPF (Intermittent push flow) and NSP (Nearly stopping potential) separations. In the next phase, simulations were done to show the accuracy of the analytical solution. An ion optics simulator software called SIMION 8.1 was used for conducting the simulation works. These simulations adopted the statistical diffusion (SDS) collision algorithm to emulate the real scenario in gas phase more precisely. In the last phase, a prototype of experimental setup was built. The experimental results were then validated by simulated results