Sensitivity of electrospray molecular dynamics simulations to long-range Coulomb interaction models

Molecular dynamics (MD) electrospray simulations of 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-${\mathrm{BF}}_4$) ion liquid were performed with the goal of evaluating the influence of long-range Coulomb models on ion emission characteristics. The direct Coulomb (DC), shifted force Coulomb sum (SFCS), and particle-particle particle-mesh (PPPM) long-range Coulomb models were considered in this work. The DC method with a sufficiently large cutoff radius was found to be the most accurate approach for modeling electrosprays, but, it is computationally expensive. The Coulomb potential energy modeled by the DC method in combination with the radial electric fields were found to be necessary to generate the Taylor cone. The differences observed between the SFCS and the DC in terms of predicting the total ion emission suggest that the former should not be used in MD electrospray simulations. Furthermore, the common assumption of domain periodicity was observed to be detrimental to the accuracy of the capillary-based electrospray simulations.

Figure 1

All-atom (a) and corresponding coarse-grained model (b) of EMIM-${\mathrm{BF}}_4$. For the all-atom model, atom colors are as follows: C (teal, larger light gray), H (silver, smaller light gray), N (blue, dark gray), B (pink, larger), and F (green, smaller). Each EMIM-${\mathrm{BF}}_4$ is approximately 6 $\AA$ across in dimension.

Figure 2

Schematic of an MD electrospray simulations (a) and boundary conditions used for extrusion simulations (b).

Figure 3

Emission current of monomer (a) and dimer (b) species sampled at the extraction plane, shown as a cumulative moving average at every 5 ps for mass flow rates of $1.22\times {10}^{-12}$, $2.44\times {10}^{-12}$, $4.88\times {10}^{-12}$, $7.32\times {10}^{-12}$, and $9.76\times {10}^{-12}$ kg/s.

Figure 4

Emission current of trimer (a) and droplets (b) sampled at the extraction plane, shown as a cumulative moving average at every 5 ps for mass flow rates of $1.22\times {10}^{-12}$, $2.44\times {10}^{-12}$, $4.88\times {10}^{-12}$, $7.32\times {10}^{-12}$, and $9.76\times {10}^{-12}$ kg/s.

Figure 5

Ion (sum of monomer, dimer, and trimer) (a) and total (b) emission current sampled at the extraction plane, shown as a cumulative moving average at every 5 ps for mass flow rates of $1.22\times {10}^{-12}$, $2.44\times {10}^{-12}$, $4.88\times {10}^{-12}$, $7.32\times {10}^{-12}$, and $9.76\times {10}^{-12}$ kg/s.

Figure 6

Comparison of number of ions emitted (a) and Coulomb energy per ion of emitted ions (b) for the DC and DC + PPPM coupled Coulomb interactions, for an EMIM-${\mathrm{BF}}_4$ electrospray simulation at a mass flow rate of $1.22\times {10}^{-12}$ kg/s and extraction potential of $-13$ V.

Figure 7

Emission snapshot for the DC (a) and coupled DC + PPPM (b) method. The copper colored particles are the platinum sites that form the capillary, the light blue colored particles represent the M1 CG site, silver colored represent the IM CG site, red colored particles represent the MR CG site, dark blue colored particles represent the M2 CG site, and yellow colored particles represent the anion of BF4 CG sites.

Figure 8

Comparison of kinetic (a) and Coulombic energy (short+long range) (b) for the direct Coulomb (DC) with $R_c$ = 20 Å and $R_c$ = 40 Å, and DC + PPPM method with $R_c$ = 12 Å and 20 Å.

Figure 9

Comparison of number of ions emitted (a) and Coulombic energy per ion of emitted ions (b) for the direct Coulomb (DC) with $R_c$ = 20 Å and $R_c$ = 40 Å, and DC + PPPM method with $R_c$ = 12 Å and 20 Å.

Figure 10

Comparison of ion counts (a) and evaluation of Eq. (3) as a function of $r^{\prime }$ (b) for the direct Coulomb (DC) simulation at a mass flow rate of $1.22\times {10}^{-12}$ kg/s. The green curve (circle symbols) in (a) shows the number of ions inside the capillary within $R_c=20\AA$ from the ions at the base of the Taylor cone $\sim 1\AA$ above the meniscus.

Figure 11

Emission currents obtained for the direct Coulomb (DC) with $R_c$ = 20 Å (a) and $R_c$ = 40 Å (b).

Figure 12

Emission currents obtained for the DC + PPPM method with $R_c$ = 12 Å (a) and 20 Å (b).

Figure 13

Plan view ($x\text{−}y$ plane) of the domain images (blue, dashed) created around the actual domain (red, solid) due to periodicity. Sides of the square represent 500 Å.

Figure 14

Comparison of Coulombic energy (short+long range) (a) and kinetic energy (b) for the nonperiodic direct Coulomb (DC) with $R_c=20$ Å and nonperiodic DC + PPPM method with $R_c=20$ Å.

Figure 15

Comparison of number of ions emitted (a) and Coulombic energy per ion of ions emitted (b) for the nonperiodic direct Coulomb (DC) with $R_c=20$ Å and nonperiodic DC + PPPM method with $R_c=20$ Å.