A benchmark comparison between two ion mobility and collision cross-section (CCS) calculators, MOBCAL and IMoS, is presented here as a standard to test the efficiency and performance of both programs. Utilizing 47 organic ions, results are in excellent agreement between IMoS and MOBCAL in He and N when both programs use identical input parameters. Due to a more efficiently written algorithm and to its parallelization, IMoS is able to calculate the same CCS (within 1%) with a speed around two orders of magnitude faster than its MOBCAL counterpart when seven cores are used. Due to the high computational cost of MOBCAL in N, reaching tens of thousands of seconds even for small ions, the comparison between IMoS and MOBCAL is stopped at 70 atoms. Large biomolecules (>10000 atoms) remain computationally expensive when IMoS is used in N (even when employing 16 cores). Approximations such as diffuse trajectory methods (DHSS, TDHSS) with and without partial charges and projected area approximation corrections can be used to reduce the total computational time by several folds without hurting the accuracy of the solution. These latter methods can in principle be used with coarse-grained model structures and should yield acceptable CCS results. Graphical Abstract ᅟ.
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 N 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.
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.Charged gas phase nanoparticles can be subject to drift and separation by means of electric fields. The charge divided by the friction coefficient of the nanoparticle under such fields is defined as electrical mobility and its accurate reckoning is key to the determination of particle size distribution functions. In Aerosol Science, and when dealing with globular particles, a particle's electrical mobility is linked to its diameter, d p , through the well-known equation 1, 2 :where qe is the net charge on the particle (the product of the integer charge state and the unit electron charge), µ is the dynamic viscosity and λ is the mean free path. C c is the Cunningham's correction factor and is a function of the Knudsen number. Most often, mobility based size distribution functions are measured with differential mobility analyzers (DMA) 3 coupled to Condensation Nucleus Counters CNCs 4 , and operated in series as a scanning mobility particle sizer (SMPS) 5,6 . While the SMPS combination has been incredibly successful, there are several shortcomings to its use which could be improved upon employing different techniques. Because the residence time -length divided by sheath velocity-of transmitted particles in a DMA is fixed and independent of particle size, diffusional broadening leads to degradation of instrument resolution for sub 20 nm particles 7,8 . For particles larger than 20 nm, the resolution, defined as Z/ΔZ, is fixed and with values of approximately <10 for most operating commercial devices. This results in adequate resolution but sometimes insufficient -a 90 nm monodisperse distribution is barely distinguishable from a 100 nm monodisperse distribution assuming a resolution of 6-. Similarly, SMPSs typically require sev...
Ion motion in Trapped Ion Mobility Spectrometers (TIMS) and Inverted Drift Tubes (IDT) has been investigated. The 2D axi-symmetric 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 outwards. This residual electric field is of significant importance as it hampers sensitivity and resolution when parabolic velocity profiles form. When 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.
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 nonglobular 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.
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