The Collision Cross Sections of Iodide Salt Cluster Ions in Air via Differential Mobility Analysis-Mass Spectrometry


To date, most collision cross section (CCS) predictions have invoked gas molecule impingement-reemission rules in which specular and elastic scattering of spherical gas molecules from rigid polyatomic surfaces are assumed. Although such predictions have been shown to agree well with CCSs measured in helium bath gas, a number of studies reveal that these predictions do not agree with CCSs for ions in diatomic gases, namely, air and molecular nitrogen. To further examine the validity of specular-elastic versus diffuse-inelastic scattering models, we measured the CCSs of positively charged metal iodide cluster ions of the form [MI]n[M+]z, where M = Na, K, Rb, or Cs, n = 1 – 25, and z = 1 – 2. Measurements were made in air via differential mobility analysis mass spectrometry (DMA-MS). The CCSs measured are compared with specular-elastic as well as diffuse-inelastic scattering model predictions with candidate ion structures determined from density functional theory. It is found that predictions from diffuse-inelastic collision models agree well (within 5 %) with measurements from sodium iodide cluster ions, while specular-elastic collision model predictions are in better agreement with cesium iodide cluster ion measurements. The agreement with diffuse-inelastic and specular-elastic predictions decreases and increases, respectively, with increasing cation mass. However, even when diffuse-inelastic cluster ion predictions disagree with measurements, the disagreement is of a near-constant factor for all ions, indicating that a simple linear rescaling collapses predictions to measurements. Conversely, rescaling cannot be used to collapse specular-elastic predictions to measurements; hence, although the precise impingement reemission rules remain ambiguous, they are not specular-elastic.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6


  1. 1.

    Mesleh, M.F., Hunter, J.M., Shvartsburg, A.A., Schatz, G.C., Jarrold, M.F.: Structural information from ion mobility measurements: effects of the long-range potential. J. Phys. Chem. 100(40), 16082–16086 (1996)

    Article  CAS  Google Scholar 

  2. 2.

    Shvartsburg, A.A., Jarrold, M.F.: An exact hard-spheres scattering model for the mobilities of polyatomic ions. Chem. Phys. Lett. 261(1/2), 86–91 (1996)

    Article  CAS  Google Scholar 

  3. 3.

    Shvartsburg, A.A., Mashkevich, S.V., Baker, E.S., Smith, R.D.: Optimization of algorithms for ion mobility calculations. J. Phys. Chem. A 111(10), 2002–2010 (2007)

    Article  CAS  Google Scholar 

  4. 4.

    Hogan, C.J., Fernandez de la Mora, J.: Ion mobility measurements of non-denatured 12–150 kda proteins and protein multimers by tandem differential mobility analysis - mass spectrometry (DMA-MS). J. Am. Soc. Mass Spectrom. 22, 158–172 (2011)

    Article  CAS  Google Scholar 

  5. 5.

    Larriba, C., Hogan, C.J., Attoui, M., Borrajo, R., Fernandez-Garcia, J., Fernandez De La Mora, J.: The mobility-volume relationship below 3.0 nm examined by tandem mobility-mass measurement. Aerosol Sci. Technol. 45, 453–467 (2011)

    Article  CAS  Google Scholar 

  6. 6.

    Counterman, A.E., Valentine, S.J., Srebalus, C.A., Henderson, S.C., Hoaglund, C.S., Clemmer, D.E.: High-order structure and dissociation of gaseous peptide aggregates that are hidden in mass spectra. J. Am. Soc. Mass Spectrom. 9(8), 743–759 (1998)

    Article  CAS  Google Scholar 

  7. 7.

    Saucy, D.A., Ude, S., Lenggoro, I.W., Fernandez De La Mora, J.: Mass analysis of water-soluble polymers by mobility measurement of charge-reduced ions generated by electrosprays. Anal. Chem. 76(4), 1045–1053 (2004)

    Article  CAS  Google Scholar 

  8. 8.

    Ku, B.K., Fernandez De La Mora, J., Saucy, D.A., Alexander, J.N.: Mass distribution measurement of water-insoluble polymers by charge-reduced electrospray mobility analysis. Anal. Chem. 76(3), 814–822 (2004)

    Article  CAS  Google Scholar 

  9. 9.

    Mcdaniel, E.W., Mason, E.A.: The Mobility and Diffusion of Ions in Gases. Wiley, New York (1973)

  10. 10.

    Shvartsburg, A.A., Mashkevich, S.V., Siu, K.W.M.: Incorporation of thermal rotation of drifting ions into mobility calculations: drastic effect for heavier buffer gases. J. Phys. Chem. A 104(42), 9448–9453 (2000)

    Article  CAS  Google Scholar 

  11. 11.

    Fernandez-Lima, F.A., Becker, C., Gillig, K., Russell, W.K., Nascimento, M.A.C., Russell, D.H.: Experimental and theoretical studies of (csi)(n)cs+ cluster ions produced by 355 nm laser desorption ionization. J. Phys. Chem. A 112(44), 11061–11066 (2008)

    Article  CAS  Google Scholar 

  12. 12.

    Beitz, T., Laudien, R., Löhmannsröben, H.-G., Kallies, B.: Ion mobility spectrometric investigation of aromatic cations in the gas phase. J. Phys. Chem. A 110(10), 3514–3520 (2006)

    Article  CAS  Google Scholar 

  13. 13.

    Kinnear, B.S., Kaleta, D.T., Kohtani, M., Hudgins, R.R., Jarrold, M.F.: Conformations of unsolvated valine-based peptides. J. Am. Chem. Soc. 122(38), 9243–9256 (2000)

    Article  CAS  Google Scholar 

  14. 14.

    Liu, B., Lu, Z.Y., Pan, B.C., Wang, C.Z., Ho, K.M., Shvartsburg, A.A., Jarrold, M.F.: Ionization of medium-sized silicon clusters and the geometries of the cations. J. Chem. Phys. 109(21), 9401–9409 (1998)

    Article  CAS  Google Scholar 

  15. 15.

    Shvartsburg, A.A., Jarrold, M.F.: Tin clusters adopt prolate geometries. Phys. Rev. A 60(2), 1235–1239 (1999)

    Article  CAS  Google Scholar 

  16. 16.

    Fernandez-Lima, F.A., Wei, H., Gao, Y.Q., Russell, D.H.: On the structure elucidation using ion mobility spectrometry and molecular dynamics. J. Phys. Chem. A 113(29), 8221–8234 (2009)

    Article  CAS  Google Scholar 

  17. 17.

    Bleiholder, C., Wyttenbach, T., Bowers, M.T.: A novel projection approximation algorithm for the fast and accurate computation of molecular collision cross sections (i). method. Int. J. Mass Spectrom. 308(1), 1–10 (2011)

    CAS  Google Scholar 

  18. 18.

    Wyttenbach, T., Bleiholder, C., Bowers, M.T.: Factors contributing to the collision cross section of polyatomic ions in the kilodalton to gigadalton range: application to ion mobility measurements. Anal. Chem. 85(4), 2191–2199 (2013)

    Article  CAS  Google Scholar 

  19. 19.

    Thalassinos, K., Slade, S.E., Jennings, K.R., Scrivens, J.H., Giles, K., Wildgoose, J., Hoyes, J., Bateman, R.H., Bowers, M.T.: Ion mobility mass spectrometry of proteins in a modified commercial mass spectrometer. Int. J. Mass Spectrom. 236(1/3), 55–63 (2004)

    CAS  Google Scholar 

  20. 20.

    Shvartsburg, A.A., Smith, R.D.: Fundamentals of traveling wave ion mobility spectrometry. Anal. Chem. 80(24), 9689–9699 (2008)

    Article  CAS  Google Scholar 

  21. 21.

    Bush, M.F., Hall, Z., Giles, K., Hoyes, J., Robinson, C.V., Ruotolo, B.T.: Collision cross sections of proteins and their complexes: a calibration framework and database for gas-phase structural biology. Anal. Chem. 82, 9557–9565 (2010)

    Article  CAS  Google Scholar 

  22. 22.

    Martinez-Lozano, P., Rus, J.: Separation of isomers l-alanine and sarcosine in urine by electrospray ionization and tandem differential mobility analysis-mass spectrometry. J. Am. Soc. Mass Spectrom. 21(7), 1129–1132 (2010)

    Article  CAS  Google Scholar 

  23. 23.

    Jiang, J.K., Attoui, M., Heim, M., Brunelli, N.A., Mcmurry, P.H., Kasper, G., Flagan, R.C., Giapis, K., Mouret, G.: Transfer functions and penetrations of five differential mobility analyzers for sub-2 nm particle classification. Aerosol Sci. Technol. 45(4), 480–492 (2011)

    Article  CAS  Google Scholar 

  24. 24.

    Epstein, P.S.: On the resistance experienced by spheres in their motion through gases. Phys. Rev. 23, 710–733 (1924)

    Article  CAS  Google Scholar 

  25. 25.

    Millikan, R.A.: The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev. 22, 1–23 (1923)

    Article  Google Scholar 

  26. 26.

    Ku, B.K., Fernandez De La Mora, J.: Relation between electrical mobility, mass, and size for nanodrops 1–6.5 nm in diameter in air. Aerosol Sci. Technol. 43(3), 241–249 (2009)

    Article  CAS  Google Scholar 

  27. 27.

    Campuzano, I., Bush, M.F., Robinson, C.V., Beaumont, C., Richardson, K., Kim, H., Kim, H.I.: Structural characterization of drug-like compounds by ion mobility mass spectrometry: comparison of theoretical and experimentally derived nitrogen collision cross sections. Anal. Chem. 84(2), 1026–1033 (2012)

    Article  CAS  Google Scholar 

  28. 28.

    Kim, H.I., Kim, H., Pang, E.S., Ryu, E.K., Beegle, L.W., Loo, J.A., Goddard, W.A., Kanik, I.: Structural characterization of unsaturated phosphatidylcholines using traveling wave ion mobility spectrometry. Anal. Chem. 81(20), 8289–8297 (2009)

    Article  CAS  Google Scholar 

  29. 29.

    Larriba, C., Hogan, C.J.: Free molecular collision cross section calculation methods for nanoparticles and complex ions with energy accommodation. J. Comput. Phys. 251, 344–363 (2013)

    Article  CAS  Google Scholar 

  30. 30.

    Ude, S., Fernandez De La Mora, J.: Molecular monodisperse mobility and mass standards from electrosprays of tetra-alkyl ammonium halides. J. Aerosol Sci. 36(10), 1224–1237 (2005)

    Article  CAS  Google Scholar 

  31. 31.

    Larriba, C., Fernandez De La Mora, J.: The gas phase structure of coulombically stretched polyethylene glycol ions. J. Phys. Chem. B 116, 593–598 (2012)

    Article  CAS  Google Scholar 

  32. 32.

    Larriba, C., Hogan, C.J.: Ion mobilities in diatomic gases: measurement versus prediction with non-specular scattering models. J. Phys. Chem. A 117, 3887–3901 (2013)

    Article  CAS  Google Scholar 

  33. 33.

    Ruotolo, B.T., Giles, K., Campuzano, I., Sandercock, A.M., Bateman, R.H., Robinson, C.V.: evidence for macromolecular protein rings in the absence of bulk water. Science 310, 1658–1661 (2005)

    Article  CAS  Google Scholar 

  34. 34.

    Ruotolo, B.T., Benesch, J.L.P., Sandercock, A.M., Hyung, S.J., Robinson, C.V.: Ion mobility-mass spectrometry analysis of large protein complexes. Nat. Protoc. 3(7), 1139–1152 (2008)

    Article  CAS  Google Scholar 

  35. 35.

    Scarff, C.A., Thalassinos, K., Hilton, G.R., Scrivens, J.H.: Traveling wave ion mobility mass spectrometry studies of protein structure: biological significance and comparison with x-ray crystallography and nuclear magnetic resonance spectroscopy measurements. Rapid Commun. Mass Spectrom. 22(20), 3297–3304 (2008)

    Article  CAS  Google Scholar 

  36. 36.

    Uetrecht, C., Rose, R.J., Van Duijn, E., Lorenzen, K., Heck, A.J.R.: Ion mobility mass spectrometry of proteins and protein assemblies. Chem. Soc. Rev. 39, 1633–1655 (2010)

    Article  CAS  Google Scholar 

  37. 37.

    Van Duijn, E., Barendregt, A., Synowsky, S., Versluis, C., Heck, A.J.R.: Chaperonin complexes monitored by ion mobility mass spectrometry. J. Am. Chem. Soc. 131(4), 1452–1459 (2009)

    Article  Google Scholar 

  38. 38.

    Hamilton, J.V., Renaud, J.B., Mayer, P.M.: Experiment and theory combine to produce a practical negative ion calibration set for collision cross-section determinations by travelling-wave ion-mobility mass spectrometry. Rapid Commun. Mass Spectrom. 26(14), 1591–1595 (2012)

    Article  CAS  Google Scholar 

  39. 39.

    Knapman, T.W., Berryman, J.T., Campuzano, I., Harris, S.A., Ashcroft, A.E.: Considerations in experimental and theoretical collision cross-section measurements of small molecules using travelling wave ion mobility spectrometry-mass spectrometry. Int. J. Mass Spectrom. 298(1/3), 17–23 (2010)

    CAS  Google Scholar 

  40. 40.

    Hogan, C.J., Fernandez De La Mora, J.: Tandem ion mobility-mass spectrometry (IMS-MS) study of ion evaporation from ionic liquid-acetonitrile nanodrops. Phys. Chem. Chem. Phys. 11(36), 8079–8090 (2009)

    Article  CAS  Google Scholar 

  41. 41.

    Rus, J., Moro, D., Sillero, J.A., Royuela, J., Casado, A., Estevez-Molinero, F., Fernandez De La Mora, J.: IMS-MS studies based on coupling a differential mobility analyzer (DMA) to commercial API-MS systems. Int. J. Mass Spectrom. 298, 30–40 (2010)

    Article  CAS  Google Scholar 

  42. 42.

    Hogan, C.J., Fernandez De La Mora, J.: Ion-pair evaporation from ionic liquid clusters. J. Am. Soc. Mass Spectrom. 21(8), 1382–1386 (2010)

    Article  CAS  Google Scholar 

  43. 43.

    Cloupeau, M., Prunet-Foch, B.: Electrostatic spraying of liquids in cone-jet mode. J. Electrost. 22(2), 135–159 (1989)

    Article  CAS  Google Scholar 

  44. 44.

    Fernandez De La Mora, J., Loscertales, I.G.: The current emitted by highly conducting taylor cones. J. Fluid Mech. 260, 155–184 (1994)

    Article  CAS  Google Scholar 

  45. 45.

    Bush, M.F., Campuzano, I.D.G., Robinson, C.V.: Ion mobility mass spectrometry of peptide ions: effects of drift gas and calibration strategies. Anal. Chem. 84(16), 7124–7130 (2012)

    Article  CAS  Google Scholar 

  46. 46.

    Aguado, A., Ayuela, A., Lopez, J.M., Alonso, J.A.: Structure and bonding in small neutral alkali halide clusters. Phys. Rev. B 56(23), 15353–15360 (1997)

    Article  CAS  Google Scholar 

  47. 47.

    Aguado, A., Ayuela, A., Lopez, J.M., Alonso, J.A.: ab initio calculations of structures and stabilities of (nai)(n)na + and (csi)(n)cs + cluster ions. Phys. Rev. B 58(15), 9972–9979 (1998)

    Article  CAS  Google Scholar 

  48. 48.

    Kim, J.H., Mulholland, G.W., Kukuck, S.R., Pui, D.Y.H.: Slip correction measurements of certified psl nanoparticles using a nanometer differential mobility analyzer (nano-dma) for knudsen number from 0.5 to 83. J. Res. Natl. Inst. Stand. Technol. 110(1), 31–54 (2005)

    Article  CAS  Google Scholar 

  49. 49.

    Borysik, A.J., Robinson, C.V.: The 'sticky business' of cleaning gas-phase membrane proteins: a detergent oriented perspective. Phys. Chem. Chem. Phys. 14(42), 14439–14449 (2012)

    Article  CAS  Google Scholar 

  50. 50.

    Krückeberg, S., Schooss, D., Maier-Borst, M., Parks, J.H.: Diffraction of trapped (csi)(n) cs+: the appearance of bulk structure. Phys. Rev. Lett. 85(21), 4494–4497 (2000)

    Article  Google Scholar 

  51. 51.

    Becke, A.D.: Density-functional thermochemistry. 3. the role of exact exchange. J. Chem. Phys. 98(7), 5648–5652 (1993)

    Article  CAS  Google Scholar 

  52. 52.

    Bradshaw, J.A., Gordon, S.L., Leavitt, A.J., Whetten, R.L.: Adsorption of water molecules on selected charged sodium-chloride clusters. J. Phys. Chem. A 116(1), 27–36 (2012)

    Article  CAS  Google Scholar 

  53. 53.

    Hay, P.J., Wadt, W.R.: ab initio effective core potentials for molecular calculations - potentials for the transition-metal atoms sc to hg. J. Chem. Phys. 82(1), 270–283 (1985)

    Article  CAS  Google Scholar 

  54. 54.

    Hay, P.J., Wadt, W.R.: ab initio effective core potentials for molecular calculations— potentials from k to au including the outermost core orbitals. J. Chem. Phys. 82(1), 299–310 (1985)

    Article  CAS  Google Scholar 

  55. 55.

    Wadt, W.R., Hay, P.J.: ab initio effective core potentials for molecular calcualtions - potentials for main group elements na to bi. J. Chem. Phys. 82(1), 284–298 (1985)

    Article  CAS  Google Scholar 

  56. 56.

    Aguado, A.: An ab initio study of the structures and relative stabilities of doubly charged (nacl)(m)(na)(2) (2+) cluster ions. J. Phys. Chem. B 105(14), 2761–2765 (2001)

    Article  CAS  Google Scholar 

  57. 57.

    Dugourd, P., Hudgins, R.R., Jarrold, M.F.: High-resolution ion mobility studies of sodium chloride nanocrystals. Chem. Phys. Lett. 267(1/2), 186–192 (1997)

    Article  CAS  Google Scholar 

  58. 58.

    Wyttenbach, T., Bushnell, J.E., Bowers, M.T.: Salt bridge structures in the absence of solvent? the case for the oligoglycines. J. Am. Chem. Soc. 120(20), 5098–5103 (1998)

    Article  CAS  Google Scholar 

  59. 59.

    Wyttenbach, T., Witt, M., Bowers, M.T.: On the stability of amino acid zwitterions in the gas phase: the influence of derivatization, proton affinity, and alkali ion addition. J. Am. Chem. Soc. 122(14), 3458–3464 (2000)

    Article  CAS  Google Scholar 

  60. 60.

    Niwa, M., Yamazaki, K., Murakami, Y.: Separation of oxygen and nitrogen due to the controlled pore-opening size of chemically vapor deposited zeolite a. Ind. Eng. Chem. Res. 30(1), 38–42 (1991)

    Article  CAS  Google Scholar 

  61. 61.

    Tammet, H.: Size and mobility of nanometer particles, clusters and ions. J. Aerosol Sci. 26(3), 459–475 (1995)

    Article  CAS  Google Scholar 

  62. 62.

    Happel, J., Brenner, H.: Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers, The Hague (1983)

  63. 63.

    Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge (1991)

  64. 64.

    Trimpin, S., Clemmer, D.E.: Ion mobility spectrometry/mass spectrometry snapshots for assessing the molecular compositions of complex polymeric systems. Anal. Chem. 80(23), 9073–9083 (2008)

    Article  CAS  Google Scholar 

  65. 65.

    Gamero-Castano, M., Fernandez De La Mora, J.: Kinetics of small ion evaporation from the charge and mass distribution of multiply charged clusters in electrosprays. J. Mass Spectrom. 35(7), 790–803 (2000)

    Article  CAS  Google Scholar 

  66. 66.

    Iribarne, J.V., Thomson, B.A.: On the evaporation of small ions from charged droplets. J. Chem. Phys. 64(6), 2287–2294 (1976)

    Article  CAS  Google Scholar 

  67. 67.

    Chan, P., Dahneke, B.: Free-molecule drag on straight chains of uniform sphere. J. Appl. Phys. 52, 3106–3110 (1981)

    Article  CAS  Google Scholar 

  68. 68.

    Zhang, C., Thajudeen, T., Larriba, C., Schwartzentruber, T.E., Hogan, C.J.: Determination of the scalar friction factor for non-spherical particles and aggregates across the entire Knudsen number range by direct simulation Monte Carlo (DSMC). Aerosol Sci. Technol. 46, 1065–1078 (2012)

    Article  CAS  Google Scholar 

Download references


This work was supported by NSF grant CHE-1011810. C.L. acknowledges support from the Ramon Areces Foundation and D.O. acknowledges support from a NSF Graduate Research Fellowship. The authors thank the Minnesota Supercomputing Institute for providing the computational resources needed for density functional theory calculations.

Author information



Corresponding author

Correspondence to Christopher J. Hogan Jr..

Electronic Supplementary Material

Below is the link to the electronic supplementary material.


Table S1, listing experimentally determined collision cross sections, a description of the procedure used to find the “best fit” values of the momentum scattering coefficients, ξ, for KI, RbI, and CsI clusters, and the coordinates and energies of the DFT determined structures in this work are provided. (PDF 1086 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ouyang, H., Larriba-Andaluz, C., Oberreit, D.R. et al. The Collision Cross Sections of Iodide Salt Cluster Ions in Air via Differential Mobility Analysis-Mass Spectrometry. J. Am. Soc. Mass Spectrom. 24, 1833–1847 (2013).

Download citation

Key words

  • Ion mobility
  • Differential mobility analysis
  • Collision cross section
  • Gas molecule
  • Scattering
  • Ion induced dipole potential
  • Cluster ion