Info: Ion-Gas Collisions

From SIMION

"Is it possible to simulate ions flying through non-vacuum conditions (i.e. ions colliding with background gas)?"

Yes, a number of models can be specified for this.

First, why simulate collisions? Normally, SIMION assumes that ions fly through perfect vacuum, and often this is a valid approximation. However, this assumption is not always appropriate. For example, the effect is significant in ion mobility mass spectrometry. In ion traps, ion funnels, and similar devices, a non-negligible buffer gas is often used to kinetically cool and focus ions.

How are collisions simulated? A collision model can be introduced into a simulation via a A SIMION user program. This works well in SIMION 8 though is also supported via a lower-level programming language in 6 and 7. A number of pre-built collision models are included as examples in SIMION 8, such as Stokes' Law (drag), hard-sphere (HS1), and high-pressure (SDS), but sure to download the latest 8.0.x update. A number of models have also been described in the literature below and can be found for version 7. If desired, you can customize these models or program your own. The way the models work is that at each time-step, such a user program applies an adjustment to the ion motion (typically in other_actions or accel_adjust segment) according to some equation or algorithm depending on the desired collision model.

The following main types of models are typically used:

• Viscous damping
• Hard sphere collision model

The viscous damping models apply a force that is a function of the particle velocity vector. Often, this is Stokes' law in which the force is proportional to ion velocity vector, particle radius, and fluid viscosity (see [Stokes' law (http://en.wikipedia.org/wiki/Stokes_law)]).

The hard-sphere collision models are based on the kinetic theory of gases in which, unlike the viscous damping models, the individual collisions between ion and gas particles are modeled. The expected frequency of collisions, measured as a distance (the mean-free-path) is predicted by the kinetic theory of gases as a function of the known pressure, temperature, and collisional cross sections of colliding particles. Collisions between ion and gas particles result in positive and negative energy transfers as well as scattering (deflection of ion velocity vectors), or even absorptions (e.g. in electron-gas collisions). The energy transfers provide for the kinetic cooling of a fast moving ion as well as the kinetic heating of a slow moving ion. Usually, we treat the colliding particles as hard-spheres. Often we assume that the collisions are elastic. Generally, the background gas is non-stationary and has a Maxwell-Boltzmann distribution of velocities, which is a function of temperature. The proposed reference model for hard sphere elastic collisions is Collision_Model_HS1 (an updated version of which is included in SIMION 8).

Some newer models are hybrids and have been successful at higher pressures.

Links

Below are links that include SIMION code for collision models.

Combined viscous and hard-sphere, hybrid, or other collision models

• The special Hydrodynamics version of Virtual Device (http://www.simion.com/virtual_device/#hydrodynamics) contains a collision model for ion movement in gas plus a model of a supersonic jet, with a detailed description of the math/physical model, tests against experiments, and PRG code. Uses mobility and monte-carlo collisions with large step optimization. In supersonic jet ions typically travel from ~1 atmosphere to 10 Pa. Under 1 atmosphere for length of travel 0.2 mm (one trajectory), it takes approximately half an hour (using small step algorithm) or only two minutes (using big step algorithm). Collision model and model of supersonic jet is in PRG code, with supersonic jet a semianalytical model verified from hydrodynamics software that outputs arrays of pressure, density, temperature, adn velocity of gas. Documentation and some results online.
• [1] (http://dx.doi.org/10.1016/j.ijms.2005.03.010) Anthony D. Appelhans, David A. Dahl. "SIMION ion optics simulations at atmospheric pressure." International Journal of Mass Spectrometry, 244 (2005) 1-14. (source code is included with the electronic version online). --"The statistical diffusion simulation (SDS) user program avoids the computationally intensive issues of high collision rates by employing collision statistics to simulate the effects of millions of collisions per time step. Ion motions are simulated by a combined viscous ion mobility and random ion jumping approach." (suitable for atmospheric pressures) -- Note: A Lua version of this is available and is included in SIMION 8.0.3. The SDS model is further analyzed in the [2] (http://dx.doi.org/10.1016/j.ijms.2007.07.008) David A. Dahl1, a, Timothy R. McJunkina and Jill R. Scott. "Comparison of ion trajectories in vacuum and viscous environments using SIMION: Insights for instrument design" International Journal of Mass Spectrometry. Volume 266, Issues 1-3, 1 October 2007, Pages 156-165.

Hard-sphere collision models

• D. Manura 2005. Collision_Model_HS1 - A fairly complete hard-sphere collision model: elastic, ion-neutral, non-stationary backgroung gas with Maxwell-Boltzmann distribution, random collision angles, mean-free-path a function of relative velocity. SL code. (Note: an updated version of this is included in SIMION 8.0.2.)
• D. Dahl. (dahl_drag.prg (http://www.simion.com/examples/dahl_drag.prg)) - Hard-sphere collision model: elastic, ion-neutral, non-stationary backgroung gas with Maxwell-Boltzmann distribution, random collision angles, constant mean-free-path. PRG code. Compared to Collision_HS1, some algorithms are less elegant, mean-free-path is constant, and it's implemented in PRG code.
• [3] (http://dx.doi.org/10.1016/S1387-3806(02)00627-9) A. Appelhans and D. Dahl. "Measurement of external ion injection and trapping efficiency in the ion trap mass spectrometer and comparison with a predictive model." International Journal of Mass Spectrometry. Volume 216, Issue 3, 15 May 2002, pp. 269-284 (see link in the References/Documentation page.) - A simple hard-sphere collision model: elastic, ion-neutral, stationary backgroung gas, head-on/frontal collisions with random deflection angles, constant mean-free-path. Includes a small section of PRG code. Compared to Collision_HS1, background gas is stationary, elastic collision model is simpler, mean-free-path is constant, and it's implemented in PRG code.
• D. Dahl. _Trap example (INJECT.PRG) in SIMION 7.0 - very simple and limited hard-sphere collision model: elastic, head-on/frontal collisions, stationary background gas. PRG code. Simulates simple kinetic cooling but not kinetic heating. This is much more limited that Collision_HS1.
• [4] (http://www.sinica.edu.tw/~ccswww/zj-AN-1999-P923.pdf) Hui-Fen Wu, Li-Wei Chen, and Ya-Ping Lin. Simulation of the Collisional Cooling Effect in a Quadrupole Ion Trap Mass Spectrometer. J. Chin. Chem. Soc., Vol. 46, No. 6, 1999. -- Applies Langevin theory, whose implementation is described in some detail.

Stoke's Law viscosity models

• D. Dahl. _Drag (drag) example in SIMION 7.0 or 8.0. See also p. I-29 to I-30 of the SIMION 7.0 manual. This model is based on Stoke's Law viscosity.

Below are links that discuss collision models in SIMION.

Hard-sphere collision models.

• [5] (http://dx.doi.org/10.1016/S1387-3806(02)00921-1) Li Ding, Michael Sudakav, Sumio Kumashiro. "A simulation study of the digital ion trap mass spectrometer". International Journal of Mass Spectrometry, Volume 221, Issue 2, 15 November 2002, Pages 117-138. - Hard-sphere collision model: elastic, ion-neutral, non-stationary backgroung gas with Maxwell-Boltzmann distribution, random collision angles, mean-free-path a function of relative velocity.
• [6] (http://dx.doi.org/10.1016/j.ijms.2004.09.005) An electrostatic focusing ion guide for ion mobility-mass spectrometry, Kent J. Gillig, Brandon T. Ruotolo, Earle G. Stone and David H. Russell, - Collision model using a Maxwell-Boltzman distribution for the collision gas energy and accomodating collisions from behind the ion.
• [7] (http://www.spectroscopynow.com/Spy/pdfs/JMS341219.pdf) M. W. Forbes, M. Sharifi, T. Croley, Z. Lausevic, and R.E. March. Simulation of Ion Trajectories in a Quadrupole Ion Trap: a comparison of Three Simulation Programs. Journal of Mass Spectrometry, 34, 1219-1239, 1999. -- Discusses collision models in SIMION, ITSIM, ISIS, and in general, especially with respect to ion traps. A bit dated in some aspects (limited SIMION collision model).
• [8] (http://dx.doi.org/10.1002/(SICI)1097-0231(19970830)11:13%3c1467::AID-RCM54%3e3.0.CO;2-X) Ling He and David M. Lubman. Simulation of External Ion Injection, Cooling and Extraction Processes with SIMION 6.0 for the Ion Trap/Reflectron Time-of-flight Mass Spectrometer. Rapid Communications in Mass Spectrometry, 11, 1467-1477 (1997). Hard-sphere collision model: elastic, ion-neutral, non-stationary backgroung gas (without Maxwell-Boltzmann distribution?), random but orthogonal collision angles, mean-free-path a function of relative velocity.
• [9] (http://dx.doi.org/10.1016/S1387-3806(02)00960-0) Aleksey V. Tolmachev, Harold R. Udseth and Richard D. Smith. Modeling the ion density distribution in collisional cooling RF multipole ion guides. International Journal of Mass Spectrometry. Volume 222, Issues 1-3 , 1 January 2003, Pages 155-174.

Comparison of viscous drag and ion/neutral collision models and more theory:

• [10] (http://www3.interscience.wiley.com/cgi-bin/abstract/55000418/ABSTRACT) Chris M. Lock, Edward W. Dyer. Simulation of ion trajectories through a high pressure radio frequency only quadrupole collision cell by SIMION 6.0 Rapid Communications in Mass Spectrometry, Volume 13, Issue 5 , Pages 422 - 431. 1999. --"Two collision modeling programs were designed and compared, one based on viscous drag cooling which is applicable to ions of high m/z, and the other on discrete ion/neutral collision phenomena for ions of low m/z. The latter approach included an ion scattering model (the theory of which is described here) to simulate changes in trajectory with each binary collision."
• [11] (http://csnwww.in2p3.fr/amdc/experimental/pacifrfq.pdf) S. Henry, I. Martel-Bravo, M. de Saint Simon, M. Jacotin, J.-F. Képinski, and D. Lunney. Beam Cooling Using a Gas-Filled RFQ Ion Guide
  • [12] (http://csnwww.in2p3.fr/amdc/experimental/cooling.pdf) M.D. Lunney, R.B. Moore. Cooling of mass-separated beams using an RFQ ion guide - supports viscous dampening over hard-sphere collisions for low KE.
• [13] (http://www.physics.mcgill.ca/~moore/Notes/BeamCooling.pdf) R.B. Moore. Buffer Gas Cooling of ion Beams. January 2002 (58 pages)--"This note summarizes the principles involved in the containment of the motion of ions in buffer gas and in the resultant cooling of the ion motion."

A few posters at ASMS 2004 described use of collision models:

• Modelling Ion Trajectories in an Ion Mobility Drift Tube using SIMION Michael M. Sakal; Robert R. Hudgins; York University , Toronto, ON, Canada (ion mobility, using collision model based code from David Dahl.
• Transmission of Ions Through Conductance Pathways from Atmospheric Pressure Ross C. Willoughby; Edward W. Sheehan; Chem-Space Associates, Pittsburgh, PA (adapted SIMION to include viscous flow components)
• Characterization of Higher Order Fields in a Compensated Cylindrical Ion Trap Desmond A. Kaplan; Gary L. Glish; The University of North Carolina, Chapel Hill, NC

Some at ASMS 2005 used collisions models too.