General calculation of the collision integral for the linearized Boltzmann transport equation

Ion-mobility spectra of a set of aliphatic linear aldehydes with the number of carbon atoms from 3 to 7 are obtained. Values of the mobility corresponding to two most intense peaks, considered to be those of a monomer and dimer, are determined according the spectra. Based on mobility, collision cross sections are calculated using the Mason-Schamp equation. The linear increase in the collision cross sections upon an increase in molecular weight is determined. According to the experimental results, the contribution to the cross section that has no dependence on molecular weight diminishes with the formation of dimers. It is established using quantum chemical calculations that this is associated with a reduction in the dipole moment upon the formation of dimers.

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“…Collision cross sections can be calculated based on the values of mobility from the Mason-Schamp equation [31][32][33] ,…”

Section: Resultsmentioning

confidence: 99%

Structure of aldehyde cluster ions in the gas phase, according to data from ion mobility spectrometry and ab initio calculations

Lantsuzskaya

Krisilov²,

Levina³

2015

Russ. J. Phys. Chem.

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“…T eff can be envisioned as the relative collision temperature; when the ions and neutral gas molecules follow respective Maxwellian distributions at temperature T i and T , the relative velocity distribution will be a Maxwellian with temperature T eff . The equations used for the evaluation of the a rs ( l ) , can be found in the Supporting Information (SI), section S1.1. These equations are easily coded, and the matrix elements can be directly obtained from the known collision integrals.…”

Section: Introductionmentioning

confidence: 99%

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

Haack

Bissonnette

Ieritano

et al. 2022

J. Am. Soc. Mass Spectrom.

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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.

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“…This latter work includes expressions for matrix elements and an explanation of technical points in the use of Burnett functions. A more limited study covering some of the same points has been made by Aisbett et al (1974).…”

Section: (Iii) Matrix Elements and Collision Integralsmentioning

confidence: 99%

Kinetic Theory of Charged Particle Swarms in Neutral Gases

Kumar¹,

Skullerud²,

Robson³

1980

Aust. J. Phys.

328

208

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The kinetic theory of charged test particles in a neutral gas, in the presence of static and uniform electric and magnetic fields, is reviewed. The effects of inelastic processes and reactions are included. The general space-time development of the swarms is considered and the relation between the nonhydrodynamic anQ hydrodynamic developments is pointed out. The transport coefficients are identified as statistical averages over the configuration-space and phase-space distributions. The evaluation of these averages by computer simulations is briefly discussed.The main emphasis, however, is on the Boltzmann equation treatment of the problem. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann equation. These equations have similar structure and may be solved by similar methods. Methods of solution are classified and examined in detail for precise calculation of drift and diffusion. Illustrative examples are given.Several representations of the Boltzmann collision integral suitable for use in these calculations are examined. A discussion of the calculation of matrix elements and the relationship between different matrix representations is given. Complete expressions to all orders in the Fokker-Planck expansion and in the expansions for the operator components of the spherical harmonic decomposition in the differential form are given. The advantages of using the adjoint of the collision operator and the cold gas collision operator in these derivations and in applications are shown and utilized. Phys., 1980, 33, 343-448 AbstractThe kinetic theory of charged test particles in a neutral gas, in the presence of static and uniform electric and magnetic fields, is reviewed. The effects of inelastic processes and reactions are included. The general space-time development of the swarms is considered and the relation between the nonhydrodynamic anQ hydrodynamic developments is pointed out. The transport coefficients are identified as statistical averages over the configuration-space and phase-space distributions. The evaluation of these averages by computer simulations is briefly discussed. The main emphasis, however, is on the Boltzmann equation treatment of the problem. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann equation. These equations have similar structure and may be solved by similar methods. Methods of solution are classified and examined in detail for precise calculation of drift and diffusion. Illustrative examples are given.Several representations of the Boltzmann collision integral suitable for use in these calculations are examined. A discussion of the calculation of matrix elements and the relationship between different matrix representations is given. Complete expressions to all orders in the Fokker-Planck expansion and in the expansions for the operator components of the spherical harmonic ...

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General calculation of the collision integral for the linearized Boltzmann transport equation

Cited by 21 publications

References 2 publications

Structure of aldehyde cluster ions in the gas phase, according to data from ion mobility spectrometry and ab initio calculations

Structure of aldehyde cluster ions in the gas phase, according to data from ion mobility spectrometry and ab initio calculations

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

Kinetic Theory of Charged Particle Swarms in Neutral Gases

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