GPU Assisted Simulation Study of Ion-Ion Reactions Within Quadrupole Ion Traps

GPU Assisted Simulation Study of Ion-Ion Reactions within Quadrupole Ion Traps Supplementary Information

Dan Guo,1 Muyi He,1 Yuzhuo Wang,1 Xingchuang Xiong,2 Xiang Fang2 and Wei Xu1*

1School of Life Science, Beijing Institute of Technology, Beijing 100081, China

2National Institute of Metrology, Beijing 100013, China

*Corresponding Author: Wei Xu School of Life Science Beijing Institute of Technology Haidian, Beijing, 100081, China Email: [email protected] Phone: +86-10-68918123

1. The calculation of ion-ion reaction rate in 3D ion trap

Because of buffer gas cooling, an ion cloud will reach thermal equilibrium inside a 3D ion trap and the ion cloud distributions could be approximated as

Gaussian distributions. The distribution of ion cloud in 3D ion trap was discussed in our previous work in details.1 The ion number density in 3D ion trap can be written as:

(S1) where N is the total number of ions, a is standard deviation of ion cloud and u is the distance from the point of interest to trap center.

Assume that anions have a Gaussian distribution with standard deviation and the standard deviation of cations is . As ion density within ion trap is not uniform,

Equation 4 in the main text has an integration expression,

(S2) where is the total number of anions, is the total number of cations and is the average kinetic energy.

After calculation of the integration in Equation S2, its expression is

The standard deviation of ion cloud has an expression as:

In which Dr and Dz represent the pseudopotential well depth, Q is the total charge inside the 3D ion trap, K is the Boltzmann constant, is the permittivity of vacuum and

T is the temperature of the ion cloud.

The expression of a can be simplified by ignoring the minimum terms and symbolic substituting uninteresting parameters with constants.

(S5) in which and are constants determined by ion trap size and temperature. ,

In this study, characters of anions are fixed, so Equation S3 can be approximated by the function with following form:

(S6) in which and are constants determined by anions and the average kinetic energy of ions.

In the simulation condition of ions with different m/z values, the first term on the right side of Eq. S5 can be replaced by a constant term, since the value and variation of the first term are small compared to the second term. And because the size of anion cloud has small variation along with the increase of m/z value of cations, reaction rate is approximately in inverse proportion to m/z submitting a1 in Eq. S6 with Eq. S5.

When it comes to the situation of ions with different charges, is nearly in proportion to q2 (cation charge).

2. Flow chart of ion-ion reaction simulation procedure

In this simulation, r* is set as 2*10-7 m. When two ions approach a distance r*, the coulombic force between two ions will be the dominant force on one ion, so the effect of trapping electric force can be ignored. Moreover, the value of r* is far smaller than the average distance between two ions, so the situation of several ions interacting was not taken into consideration for its low probability. E0 is the total energy of ion-ion system, same as the definition in the main text.

An anion with high velocity may pass by an anion and not being considered for ion-ion reaction, if the product of the time step and relative velocity of the ion is larger than r*. As shown in Figure S1, anions in the orange area would be calculated for ion-ion reactions. However, an anion in the blue area might also react with the cation but not counted in the simulation, since the distance the anion moved (, v average ion velocity) in a single time step (t) could be larger than the actual distance of these two ions, thus pass by the cation. Therefore, a scale factor was used to compensate this phenomenon. The scale factor was calculated as the ratio of the total area over the green plus orange areas, which is .

ሺݒȀ ʹ ሻݐ

ʹ ݒȀ +כݎ -

Figure S1 The schematic diagram of reaction rate factor.

3. The motion of low q ions

Experiment shows that the electric field generated by oppositely charged ion population could be used to trap high mass ions.2 Ions with low q value are difficult to be trapped by the electric field of an ion trap, while they can be trapped when oppositely charged ion population exists (see Figure S2). The electric field generated by space charge was modeled with the theoretical model used in Ref.1 - 3 x 1 0 - 3 x 1 0 1 1

0 . 5 0

- 2 - 0 . 5

- 3 - 1 2 - 4 1 2 4 1 0 - 3 0 2 x 1 0 - 1 0 - 3 - 3 - 1 x 1 0 x 1 0 - 1 0 - 2 - 3 - 2 - 2 - 3 x 1 0 - 2 - 4 (a) (b)

Figure S2 The difference of ion motion with (a) and without (b) the electric field generated by oppositely charged ion population was explored by simulation. qx =

6 0.00098, qz = 0.00196 and the number of oppositely charged ion population is 1*10 .

References

1. Guo, D.; Wang, Y.; Xiong, X.; Zhang, H.; Zhang, X.; Yuan, T.; Fang, X.; Xu, W., Space Charge Induced Nonlinear Effects in Quadrupole Ion Traps. Journal of the American Society for Mass Spectrometry 25, (3), 498-508. 2. McLuckey, S. A.; Wu, J.; Bundy, J. L.; Stephenson, J. L.; Hurst, G. B., Oligonucleotide mixture, analysis via electrospray and ion/ion reactions in a quadrupole ion trap. Analytical Chemistry 2002, 74, (5), 976-984.