Comparison of particle-in-cell simulations with experimentally observed frequency shifts between ions of the same mass-to-charge in Fourier transform ion cyclotron resonance mass spectrometry

Abstract

It has been previously observed that the measured frequency of ions in a Fourier transform mass spectrometry experiment depend upon the number of trapped ions, even for populations consisting exclusively of a single mass-to-charge. Since ions of the same mass-to-charge are thought not to exert a space-charge effect among themselves, the experimental observation of such frequency shifts raises questions about their origin. To determine the source of such experimentally observed frequency shifts, multiparticle ion trajectory simulations have been conducted on monoisotopic populations of Cs(+) ranging from 10(2) ions to 10(6) ions. A close match to experimental behavior is observed. By probing the effect of ion number and orbital radius on the shift in the cyclotron frequency, it is shown that for a monoisotopic population of ions, the frequency shift is caused by the interaction of ions with their image-charge. The addition of ions of a second mass-to-charge to the simulation allows the comparison of the magnitude of the frequency shift resulting from space-charge (ion-ion) effects versus ion interactions with their image charge.

Figure 1

Experimentally observed frequency shifts observed for a monoisotopic Cs⁺ population, acquired by varying the concentration of a CsI electrospray solution and ion accumulation time in a storage hexapole prior to injection into the FTICR analyzer (replotted from data published in Reference 13.) Simulated frequencies vary from these experimental frequencies by ~ 2 kHz because simulations were conducted at exactly 7.0 T whereas the experimental magnetic field is on the order of 7.02 T.

Figure 2

Simulated frequency shifts for a cubic and quadrupolar trapping potential for Cs⁺ populations ranging from 100 to 750,000 at 35 % cell radius. The inset shows an expansion of the low ion number region of the curve.

Figure 3

Simulated frequency shifts for ion orbital radii ranging from 15% to 85% of the cell radius for Cs⁺ populations ranging from 100 to 1,000,000 in a quadrupolar trapping potential.

Figure 4

Simulated frequency shifts as a function of orbital radius for selected Cs⁺ numbers in a quadrupolar trapping potential.

Figure 5

Simulated frequency shifts in Cs⁺ when a second ion is added to the FTICR-MS analyzer employing a quadrupolar trapping potential. Orbital radii from 15% to 60% of the cell radius are shown. The dashed line represents the frequency shifts present at 35% cell radius for a population of only Cs⁺, for comparison.