Electrospray molecular dynamics simulations using an octree-based Coulomb interaction method

A new octree-based Coulomb interaction model is developed to model the electrospray of ionic liquids (ILs) in molecular dynamics. Using an octree-based method, Coulomb interactions are categorized as intra- and interleaf Coulomb interactions based on a criterion related to the Bjerrum length of the IL. The octree-based method is found capable of reproducing Coulomb energy in agreement with established and computationally more expensive models, such as the direct Coulomb and the damped shifted force (DSF) method in the absence of an external electric field. In the presence of an external electric field, the octree-based method produces distinctly different results compared to that obtained by the direct Coulomb method. The time required to form Taylor's cone was shorter for the octree method compared to the direct Coulomb approach. While no emission larger than monomers was observed from the direct Coulomb simulation, emission of larger species such as dimers and trimers was observed when the octree-based Coulomb interaction model was used. Furthermore, the octree-based model forms a smaller ion emission cone compared to that from the direct Coulomb method.

Figure 1

Molecular structure and atom types of EAN. Subscripts are used to differentiate the carbon and hydrogen atoms based on their position in the molecular skeleton [31]. Atom colors are as follows: C (teal), H (silver), N (blue), and O (red). The EAN molecule is approximately 5.0 Å across in dimension. Partial charge on each atom is as labeled.

Figure 2

Example of an arbitrary octree structure constructed with $R_{\mathrm{inner}}=20\AA$; particles A–E denote notional ion pairs. Figure on the right shows a three-dimensional view of the octree leaf ($m=10$).

Figure 3

Radial distribution function of ammonia and nitrate nitrogen atoms of EAN.

Figure 4

Comparison of Coulomb energy convergence for a single snapshot taken at a time of 35 ps of atom positions of 2000 ion pairs representing a EAN primary droplet at a temperature of 5.0 K. Direct Coulomb and DSF method ($R_S=320\AA$, ${\alpha }_d=0.005$) comparison shown in the left panel and octree-based Coulomb interaction method shown in the right.

Figure 5

Comparison of Coulomb energy and total (potential + kinetic) energy of an isolated primary droplet. Coulomb energy calculated using direct [Eq. (4)], DSF [Eq. (5)], and octree-based method [Eqs. (7) and (10) with $R_S=\infty$ and ${\alpha }_d=0.0]$ shown in (a). Coulomb energy calculated using DSF and octree-based methods [Eqs. (7) and (10)] shown in (b). Total energy of simulations using direct, DSF, and octree-based method ($R_S=\infty$ and ${\alpha }_d=0.0$) shown in (c). Total energy of simulations using octree-based methods shown in (d).

Figure 6

Snapshots of the simulation with constrained cation moving away from the primary droplet surface. Distance between cation and the droplet surface in (a), (b), (c), (d) is 0, 10, 30, and 60 Å, respectively.

Figure 7

Comparison of Coulomb energy of the constrained cation with potential energy contribution from other sources shown in (a). Comparison of Coulomb energy of the constrained cation from damped octree-based Coulomb interaction model shown in (b).

Figure 8

Snapshots of the primary droplet simulation in the presence of an external electric field. This case is performed with damped octree-based Coulomb interaction method with $R_S=320\AA$ and ${\alpha }_d=0.005$. Droplet structure in (a), (b), and (c) is at a simulation time of 2.5, 5.0, and 7.5 ps, respectively.

Figure 9

Octree structure generated by the damped octree-based method for the droplet simulation in the presence of external electric field at 7.5 ps [see Fig. 8]. Top and bottom: isometric and front view. The smallest leaves are of size equal to $R_{\mathrm{inner}}=10\AA$.

Figure 10

Comparison of number of secondary monomers emitted from the primary droplet in the presence of external electric field.

Figure 11

Comparison of Coulomb energy and total energy per atom of the primary droplet in the presence of external electric field shown in (a) and (b), respectively.

Figure 12

Snapshot of atomic partial charge positions at 30 ps (a) for the capillary electrospray simulation performed with damped octree-based Coulomb interaction method, and front (b) and isometric (c) views of the generated corresponding octree structure. Radius of the capillary is 59 Å.

Figure 13

Snapshots of the Taylor's cone formation during the capillary electrospray simulation. This case is performed with damped octree-based Coulomb interaction method with $R_S=320\AA$, intraleaf Coulomb ${\alpha }_d=0.005$, and interleaf Coulomb ${\alpha }_d=0.1$. The radius of the cylinder is 59 Å. Snapshots at simulation times of 2.5, 25, and 35 ps are shown in (a), (b), and (c), respectively.

Figure 14

Comparison of Coulomb (a), total energy per atom (b), emission currents (c), and number of atoms present in the simulation (d) during the capillary extrusion simulations. Figures 14, 14, and 14 use MD data collected over the entire domain and include both anions and cations.

Figure 15

Comparison of the cation monomer (a) and dimer (b) emission currents as a function of distance from the capillary tip, obtained from the octree-based and direct Coulomb methods for 2000 frames after 20 ps simulation time.

Figure 16

Comparison of the cation trimer emission currents as a function of distance from the capillary tip, obtained from the octree-based and direct Coulomb methods for 2000 frames after 20-ps simulation time.

Figure 17

Comparison of the normalized $X$ (a) and $Y$ (b) velocity distribution functions of the atomic partial charges emitted at the tip of the capillary, obtained from the octree-based and direct Coulomb methods for cations after 20 ps for 2000 time frames.

Figure 18

Comparison of the normalized $Z$ (c) velocity distribution functions of the atomic partial charges emitted at the tip of the capillary, obtained from the octree-based and direct Coulomb methods for cations after 20 ps for 2000 time frames.

Figure 19

Comparison of the normalized emission probability distribution functions of both cations and anions emitted between 20 and 45 ps, obtained from the octree-based and direct Coulomb methods. Capillary tip is located at $z=290\AA$.