A critical review of the two-temperature theory and the derivation of matrix elements. High field ion mobility and energy calculation for all-atom structures in light gases using a 12-6-4 potential

Abstract

Ion mobility has become a ubiquitous tool in many aspects of Analytical Chemistry due to its ability to separate compounds in the gas phase prior to feeding them to a Mass Spectrometer. To understand how this complex separation occurs, it is necessary to thoroughly explain the ion-gas interaction. In particular, this manuscript aims to describe the physics behind the collisions at high fields using the two-temperature approximation. The two-temperature theory has been recently employed to describe the mobility of polyatomic ions quite successfully and thus a proper account is warranted. A concise description is provided along with rigorous mathematical arguments behind its success at predicting the ion's drift velocity. Moreover, a thorough procedure for obtaining the equations (including the matrix elements) for higher-order mobility approximations is also provided with high detail, making this work suitable for beginners and experts in ion mobility. In particular, a discussion is brought forth on the choice of the base temperature and its relation to both the effective temperature and the drift velocity of the ion. A comparison between a 12-6-4 potential and the Maxwell model is made, pointing at the possible errors of using the Maxwell model for low- and high-field calculations. Using our in-house algorithm IMoS, successive approximations up to the fourth are tested against previous ones and against experimental results, showing both, asymptotic convergence, as well as a good agreement for monoatomic gases and small ions.

Keywords

• Two-temperature theory
• Ion-mobility
• High-field
• Higher-order approximation
• Collision cross section