Predicting ion mobility as a function of the electric field for small ions in light gases

Ion mobility calculations of flexible all-atom systems at arbitrary fields using two-temperature theory

Ion mobility spectrometry (IMS) separates and analyzes ions based on their mobility in a gas under an electric field. When the field is increased, the mobility varies in a complex way that depends on the relative velocity between gas and ion, their electrostatic potential interactions, and the effects from direct impingement. Recently, the two-temperature theory, primarily developed for monoatomic ions in monoatomic gases, has been extended to study mobilities at arbitrary fields using polyatomic ions in polyatomic gases, with some success. However, this extension poses challenges, such as inelastic collisions between gas and ion and structural modifications of ions as they heat up. These challenges become significant when working with diatomic gases and flexible molecules. In a previous study, experimental mobilities of tetraalkylammonium salts were obtained using a FAIMS instrument, showing satisfactory agreement with numerical two-temperature theory predictions. However, deviations occurred at fields greater than 100 Td. To address this issue, this paper introduces a modified high-field calculation method that accounts for the structural changes in ions due to field heating. The study focuses on tetraheptylammonium (THA+), tetradecylammonium (TDA+), and tetradodecylammonium (TDDA+) salts. Molecular structures were generated at various temperatures using MM2 forcefield. The mobility was calculated using IMoS 1.13 with two-temperature trajectory method calculations up to the fourth approximation. Multiple effective temperatures were considered, and a linear weighing system was used to create mobility vs. reduced field strength plots. The results suggest that the structural enlargement due to ion heating plays a significant role in mobility at high fields, aligning better with experimental data. FAIMS' dispersion plots also show improved agreement with experimental results. However, the contribution of inelastic collisions and energy transfer to rotational degrees of freedom in gas molecules remains a complex and challenging aspect.

MobCal-MPI 2.0: an accurate and parallelized package for calculating field-dependent collision cross sections and ion mobilities

Ion mobility spectrometry (IMS), which can be employed as either a stand-alone instrument or coupled to mass spectrometry, has become an important tool for analytical chemistry. Because of the direct relation between an ion's mobility and its structure, which is intrinsically related to its collision cross section (CCS), IMS techniques can be used in tandem with computational tools to elucidate ion geometric structure. Here, we present MobCal-MPI 2.0, a software package that demonstrates excellent accuracy (RMSE 2.16%) and efficiency in calculating low-field CCSs via the trajectory method (≤30 minutes on 8 cores for ions with ≤70 atoms). MobCal-MPI 2.0 expands on its predecessor by enabling the calculation of high-field mobilities through the implementation of the 2^nd order approximation to two-temperature theory (2TT). By further introducing an empirical correction to account for deviations between 2TT and experiment, MobCal-MPI 2.0 can compute accurate high-field mobilities that exhibit a mean deviation of <4% from experimentally measured values. Moreover, the velocities used to sample ion-neutral collisions were updated from a weighted to a linear grid, enabling the near-instantaneous evaluation of mobility/CCS at any effective temperature from a single set of N₂ scattering trajectories. Several enhancements made to the code are also discussed, including updates to the statistical analysis of collision event sampling and benchmarking of overall performance.

First-Principles Modeling of Preferential Solvation in Mixed-Modifier Differential Mobility Spectrometry

Differential mobility spectrometry (DMS) separates ions based on mobility differences between high and low electric field conditions. To enhance resolution, solvents such as water and acetonitrile are often used to modify the collision environment and take advantage of differing dynamic clustering behavior between analytes that coelute in hard-sphere environments (e.g., N₂). When binary solvent mixtures are used to modify the DMS environment, one solvent can have a dominant influence over the other with respect to ion trajectories. For example, for quinoline derivatives, a 9:1 water:acetonitrile solvent mixture exhibited identical behavior to an environment containing only acetonitrile as a modifier. It was hypothesized that this effect arises due to the significantly different binding strengths of the two solvents. Here, we utilize a first-principles model of DMS to study analytes in single and binary solvent mixtures and explore the effects governing the dominance of one solvent over the other. Computed DMS dispersion curves of quinoline derivatives are in excellent agreement with those measured experimentally. For mixed-modifier environments, the predicted cluster populations show a clear preferential solvation of ions with the stronger binding solvent. The influence of ion-solvent binding energies, solvent concentration, and solvent molecule size is discussed in the context of the observed DMS behavior. This work can guide the usage of binary solvent mixtures for improving ion separations in cases where compounds coelute in pure N₂ and in single-solvent modifier environments. Moreover, our results indicate that binary solvent mixtures can be used to create a relative scale for solvent binding energies.

Investigation of Zero-/High-Field Ion Mobility Orthogonal Separation Using a Hyphenated DMA-FAIMS System and Validation of the Two-Temperature Theory at Arbitrary Field for Tetraalkylammonium Salts in Nitrogen

Toward greater separation techniques for ions, a differential mobility analyzer (DMA) has been coupled with field asymmetric waveform ion mobility spectrometry (FAIMS) to take advantage of two mobility-related but different methods of separation. The filtering effect of the DMA allows ions to be selected individually based on low-field mobility and studied in FAIMS at variable electric field, yielding mobility separations in two dimensions. Because spectra fully describe ion mobility at variable field strength, results are then compared with a two-temperature theory-predicted mobility up to the fourth-order approximation. The comparison yields excellent results up to at least 100 Td, beyond which the theory deviates from experiments. This is attributed to two effects, the enlargement of the structure due to ion heating and the inelasticity of the collisions with the nitrogen bath gas. The corrected mobility can then be used to predict the dispersion plot through a newly developed implicit equation that circumvents the possible issues related to the more elaborate Buryakov equation. Our results simultaneously show that the DMA-FAIMS coupling yields complete information on ion mobility versus the field-strength to gas-density ratio and works toward predicting such spectra from ion structures and gas properties.

Kinetics in DMS: Modeling Clustering and Declustering Reactions

Differential mobility spectrometry (DMS) uses high-frequency oscillating electrical fields to harness the differential mobility of ions for separating complex sample mixtures prior to detection. To increase the resolving power, a dynamic microsolvation environment is often created by introducing solvent vapors. Here, relatively large clusters are formed at low-field conditions which then evaporate to form smaller clusters at high-field conditions. The kinetics of these processes as the electrical field strength oscillates are not well studied. Here, we develop a computational framework to investigate how the different reactions (cluster association, cluster dissociation, and fast conformational changes) behave at different field strengths. We aim to better understand these processes, their effect on experimental outcomes, and whether DMS model accuracy is improved via incorporating their description. We find that cluster association and dissociation reactions for typical ion-solvent pairs are fast compared to the time scale of the varying separation fields usually used. However, low solvent concentration, small dipole moments, and strong ion-solvent binding can result in reaction rates small enough that a lag is observed in the ion's DMS response. This can yield differences of several volts in the compensation voltages required to correct ion trajectories for optimal transmission. We also find that the proposed kinetic approach yields generally better agreement with experiment than using a modified Boltzmann weighting scheme. Thus, this work provides insights into the chemical dynamics occurring within the DMS cell while also increasing the accuracy of dispersion plot predictions.

Improved First-Principles Model of Differential Mobility Using Higher Order Two-Temperature Theory

Differential mobility spectrometry is a separation technique that may be applied to a variety of analytes ranging from small molecule drugs to peptides and proteins. Although rudimentary theoretical models of differential mobility exist, these models are often only applied to small molecules and atomic ions without considering the effects of dynamic microsolvation. Here, we advance our theoretical description of differential ion mobility in pure N₂ and microsolvating environments by incorporating higher order corrections to two-temperature theory (2TT) and a pseudoequilibrium approach to describe ion-neutral interactions. When comparing theoretical predictions to experimentally measured dispersion plots of over 300 different compounds, we find that higher order corrections to 2TT reduce errors by roughly a factor of 2 when compared to first order. Model predictions are accurate especially for pure N₂ environments (mean absolute error of 4 V at SV = 4000 V). For strongly clustering environments, accurate thermochemical corrections for ion-solvent clustering are likely required to reliably predict differential ion mobility behavior. Within our model, general trends associated with clustering strength, solvent vapor concentration, and background gas temperature are well reproduced, and fine structure visible in some dispersion plots is captured. These results provide insight into the dynamic ion-solvent clustering process that underpins the phenomenon of differential ion mobility.