Purdue University Graduate School

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Theoretical and numerical prediction of ion mobility for flexible all-atom structures under arbitrary fields and subject to structural rearrangement. An initial probing into the effects of internal degrees of freedom.

posted on 2024-04-18, 20:50 authored by Viraj Dipakbhai GandhiViraj Dipakbhai Gandhi

Ion mobility spectrometry (IMS), with its unparalleled ability to separate and filter ions based on their overall size before channeling them into a Mass Spectrometer, has placed itself as a cornerstone of the modern Analytical Chemistry field. IMS provides an orthogonal separation, aiding in the identification and analysis processes of various compounds. While there have been many inventions for ion mobility (IM) devices with exponential growth in the separation capability in the past few years, there is very little emphasis on the theoretical explanation. For example, most modern IMS devices often use a high ratio of electric field to gas concentration (E/n) as it provides better separation capabilities. However, the interaction between ion and gas at such E/n cannot be explained by current IM theories as they ignore several critical factors such as the increase in ion’s energy due to energetic collisions, the energy loss/transferred in the internal degree of freedoms, and change in the ion’s structure, requiring empirical data to identify ions after separation. The thesis presented here contributes towards bridging this gap by elucidating the complex interplay of forces and interactions that govern the ion separation process, thereby explaining on how these mechanisms can be further exploited for refined separation and advancing the computational approach to identify the separated ion.

To explain the ion-gas interaction under high E/n, this research extends the Two-Temperature Theory (2TT) up to the fourth order approximation. The central idea of the 2TT is to solve moments of the Boltzmann equation for the ion’s velocity distribution involving ion-gas collisions. The research shows a decreasing error between each subsequent approximations, indicating convergence. This advancement is demonstrated through the development and application of our in-house program, IMoS, and validated against experimental data for small ions in monoatomic gases. This research also justifies the mechanisms of increasing and decreasing mobility as the electric field is increased by explaining the interplay between the interaction potential and the collision energy.

Subsequent chapters investigate the impact of internal degrees of freedom (rotational and vibrational) on ion mobility. This includes pioneering work with the Structures for Lossless Ion Manipulations (SLIM) device to separate isotopomers, alongside computational advancements in simulating these effects, leading to the development of IMoS 2.0. In IMoS 2.0 software an ion is placed in a virtual drift tube with electric field, where it is free to rotate and translate upon collision. The research notably uncovers the role of rotational degrees of freedom in isotopomer separation, a previously underexplored area.

To ascertain the effect of the vibrational DoF and differentiate from the ion’s structural expansion and heating resulting from energetic collisions, a combined simulation of ion mobility and molecular dynamics (IM-MD) was performed. This analysis revealed that structural expansion plays a dominant role for the cause of deviation at high E/n, to such an extent that the vibrational DoF (or inelastic collisions) can normally be disregarded. Moreover, the research also indicates that using a combination of IM-MD simulation, one can identify accurate gas-phase structure of the ion at any temperature from a pool of probable structures.

Guided by these conclusions, the research now takes a significant step forward by aiming to accurately characterize protein structures in the gas phase using IM-MD simulation. Traditional MD simulations provide larger structures since the force field is not optimized for the gas-phase simulation. To address this, a biasing force towards the center of the protein is applied, compressing it. This method efficiently explores multiple feasible configurations, including those obscured by energy barriers. This strategy generated structures that closely align with the experimental evidence.


Division of Chemistry (CHE) - National Science Foundation


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Carlos Larriba-Andaluz

Advisor/Supervisor/Committee co-chair

Aaron Morris

Additional Committee Member 2

Ian Webb

Additional Committee Member 3

Alexander Laskin