Energy properties and spatial plume profile of ionic liquid ion sources based on an array of porous metal strips

Either the positive or negative high voltage supply is connected to the distal electrode, and the extractor is grounded. In the positive mode, the voltage is regulated from 0 to +3000 V, and in the negative mode, the voltage is regulated from 0 to −3060 V. Both the emitted current, which is the current drawn by the emitter from the high voltage supply, and the intercepted current, which is defined as the current measured from the extractor to ground, are obtained by measuring the voltage drop across a 1 kΩ resistor.

The RPA test is performed to measure the energy distribution of the emitted particles. The actual acceleration voltage is usually smaller than the acceleration voltage applied between the distal electrode and the extractor from the high-voltage power supply. Thus, the RPA test can obtain the nonkinetic voltage losses. Further, ion fragmentation, which is the break-up of the emitted ion clusters, occurs during the ionic liquid electrospray process, and RPA test can measure the rates of fragmentation of ion clusters by analyzing the RPA curves.

As suggested in [27], a four-grid design is adopted in the RPA. The RPA device consists of a four-layer grid assembly, a metal shielding, and a collector, as depicted in figure 6. The first layer of the grid is grounded, and both the second and the fourth layers of the grids are connected to a voltage of −40 V to suppress the secondary electron emission. The third grid is the retarding grid, connected to the sweeping voltage generated from a signal generator and a high voltage amplifier. The RPA device is installed 95 mm away from the source. The center of the ILIS and the center of the RPA aperture are mounted coaxially. The flying particles enter the RPA device through the front aperture, pass the four layers of grids, and finally arrive at the collector. The collected currents are measured and recorded by a Keithley DMM 7510 digital multimeter.

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The spatial plume distribution is tested by measuring the collected current when rotating the ILISs either parallel to the strips or perpendicular to the strips, as shown in figure 7. The ILIS is installed on a rotating platform, and the rotating shaft traverses the emission plane. The rotary motion of the platform is driven by a turbine worm mechanism connected to a stepper motor, and the rotational speed can be regulated by the frequency of the pulse signal input. The rotational angular speed is set to six degrees per second in the test.

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The RPA collector is used to collect the emitted current, mounted 155 mm downstream from the source. Unlike the RPA test, all four layers of grids, including the retarding grid, are grounded. A similar method using the RPA device to collect the ion plume with the sweeping grid grounded was implemented in [23]. The ILIS center, aperture center, and collector center are installed coaxially. By rotating the ILIS, the plume with a certain divergence angle can selectively pass through the RPA aperture. Thus, the spatial plume distribution can then be measured from the collected current.

The variation of both emitted current and the intercepted current with the applied acceleration voltage is shown in figure 8. The startup voltage ${V}_{{\rm{start}}},$ which is defined as the minimum voltage that starts an electrospray emission, is 1280 V. Apart from the experimental value, the startup voltage can also be estimated by the following equation [28]

$$\begin{eqnarray}&&{V}_{{\rm{start}}}\sim \sqrt{\displaystyle \frac{\pi \gamma {R}_{{\rm{t}}}^{2}}{8{\varepsilon }_{0}{r}_{{\rm{p}}}}}\,\mathrm{ln}\left(\displaystyle \frac{4d}{{R}_{{\rm{t}}}}\right)\end{eqnarray} \tag{ 2 }$$

where $\gamma$ is the surface tension coefficient, ${R}_{{\rm{t}}}$ is the apex curvature radius of the emitter, ${r}_{{\rm{p}}}$ is the mean pore radius of the emitter, and $d$ is the distance between two electrodes. Given that the apex curvature radii and pore sizes fluctuate in a range, an accurate estimation of the startup voltage is not expected. Here, we take some typical values in the range to calculate the startup voltage. Taking $\gamma$ = 45.2 mN m⁻¹, $d$ = 140 μm, ${r}_{{\rm{p}}}$ = 3 μm, and ${R}_{{\rm{t}}}$ = 9 μm, the calculated startup voltage is 1217 V, with an error of 4.9% compared with the experimental value.

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Both the emitted current and the intercepted current grow with the increase of the applied acceleration voltage. In the positive polarity, the curve is similar to quadratic from the startup voltage to 2500 V while it is similar to linear form 2500 V to 3000 V. The emitted current reaches 804 μA at +3000 V, and −790 μA at −3060 V, and the intercepted current is within 6% of the emitted current, meaning that the ion transparency is up to 94%.

The normalized RPA curves for both positive and negative modes are plotted in figure 9. As the sweeping voltage of the retarding grid increases from zero to the acceleration voltage, the normalized collected current first holds steady, then experiences three stages of decline, and finally decreases to zero in both polarities. The overall RPA curves are generally consistent with some other RPA studies of ILISs [25, 29, 30]. According to the working principles of the ILISs, the emitted charged particles gain kinetic energy through electrostatic acceleration between emitter and extractor. If all the particles have the same kinetic energy, the collected current will maintain a steady value and dramatically decrease at a specific voltage. Therefore, the RPA curves indicate that the plume is not monoenergetic.

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The divergence of the energy distribution may be derived from ion extraction or ion fragmentation. Our previous time of flight test showed that the plume is mainly composed of monomers [31] (single ions, EMI⁺ or ${{\rm{BF}}}_{4}^{-}$) and dimers (single ions combined with a molecule, (EMI-BF₄)EMI⁺ or (EMI-BF₄)${{\rm{BF}}}_{4}^{-}$), very little, if any, trimer (single ions combined with two molecules, (EMI-BF₄)₂EMI⁺ or (EMI-BF₄)₂ ${{\rm{BF}}}_{4}^{-}$) or droplets. The relative molecular mass, molecular mass, charge, and charge to mass ratio of the ion species are listed in table 1. The inexistence of droplets contributes to concentrated extraction voltages. The energy of ions to be extracted from the ionic liquid is small (1–2 eV), which means there is little possibility of such significant energy dispersion (hundreds of eV) caused by ion extraction. Thus, only ion fragmentation effects need further consideration.

Table 1. Relative molecular mass, molecular mass, charge, and charge-to-mass ratio of the ion species.

Ion species	Relative molecular mass	Molecular mass (kg)	Charge (C)	Charge-to-mass ratio
EMI+	111.17	1.85 × 10−25	1.60 × 10−19	8.64 × 105
(EMI- BF4) EMI+	309.14	5.15 × 10−25	1.60 × 10−19	3.11 × 105
${{\rm{BF}}}_{4}^{-}$	86.80	1.45 × 10−25	1.60 × 10−19	1.11 × 106
(EMI-BF4) ${{\rm{BF}}}_{4}^{-}$	284.77	4.75 × 10−25	1.60 × 10−19	3.37 × 105

If the fragmentation occurs in the field-free region, as shown in figure 10, which means the acceleration process is completed, according to the principle of conservation of energy

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}\left({m}_{0}+{m}_{1}\right){{v}_{1}}^{2}={q}_{1}{V}_{{\rm{a}}}\end{eqnarray} \tag{ 3 }$$

where ${m}_{0}$ is the mass of a molecule, ${m}_{{\rm{1}}}$ is the mass of a monomer ion, ${v}_{1}$ is the velocity after electrostatic acceleration, ${q}_{1}$ is the charge of a monomer ion, and ${V}_{{\rm{a}}}$ is the applied acceleration voltage.

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Supposing that the velocity of the neutral molecule and the monomer ion remains unchanged after fragmentation, the accelerated ion travels at an invariable speed until it is stopped by the retarding grid

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}{m}_{1}{{v}_{1}}^{2}={q}_{1}{V}_{{\rm{RPA}}}\end{eqnarray} \tag{ 4 }$$

where ${V}_{{\rm{RPA}}}$ is the potential of the retarding grid. The ratio of ${V}_{{\rm{RPA}}}$ and ${V}_{{\rm{a}}}$ can be obtained from equations (3) and (4)

$$\begin{eqnarray}&&\displaystyle \frac{{V}_{{\rm{RPA}}}}{{V}_{{\rm{a}}}}=\displaystyle \frac{{m}_{1}}{{m}_{0}+{m}_{1}}\end{eqnarray} \tag{ 5 }$$

The ratio is a constant only depending on the masses of the monomer ion and the molecule. For EMI-BF₄, ${V}_{{\rm{RPA}}}/{V}_{{\rm{a}}}$ is 0.36 in positive mode and 0.30 in negative mode. The segment indicating fragmentation in the field-free region is marked in red in the RPA curve in figure 10.

If the dissociation of ion clusters takes place in the acceleration region, as shown in figure 11, both the molecule and the monomer ion are accelerated until they get to the departure position

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}\left({m}_{0}+{m}_{1}\right){{v}_{1,1}}^{2}={q}_{1}\left({V}_{{\rm{a}}}-{V}_{1}\right)\end{eqnarray} \tag{ 6 }$$

where ${v}_{1,1}$ is the velocity of the molecule and the monomer ion, and ${V}_{{\rm{1}}}$ is the electric potential of the departure position.

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After departure, the ion sustains acceleration up to leaving the acceleration region

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}{m}_{1}\left({{v}_{1}}^{2}-{{v}_{1,1}}^{2}\right)={q}_{1}{V}_{1}\end{eqnarray} \tag{ 7 }$$

where ${v}_{1}$ is the velocity of the monomer ion after ending the acceleration process. The accelerated ion travels at an invariable velocity until it is stopped by the retarding grid

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}{m}_{1}{{v}_{1}}^{2}={q}_{1}{V}_{{\rm{RPA}}}\end{eqnarray} \tag{ 8 }$$

The ratio of ${V}_{{\rm{RPA}}}$ and ${V}_{{\rm{a}}}$ can be derived from equations (6)–(8)

$$\begin{eqnarray}&&\displaystyle \frac{{V}_{{\rm{RPA}}}}{{V}_{{\rm{a}}}}=\displaystyle \frac{{V}_{1}}{{V}_{{\rm{a}}}}\left(1-\displaystyle \frac{{m}_{1}}{{m}_{0}+{m}_{1}}\right)+\displaystyle \frac{{m}_{1}}{{m}_{0}+{m}_{1}}.\end{eqnarray} \tag{ 9 }$$

The value of ${V}_{{\rm{1}}}$ ranges from 0 to ${V}_{{\rm{a}}},$ thus ${V}_{{\rm{RPA}}}/{V}_{{\rm{a}}}$ is within the limits of $\left[\tfrac{{m}_{1}}{{m}_{0}+{m}_{1}},1\right].$ In figure 10, the segment representing fragmentation in the acceleration region is marked in green in the RPA curve.

If no fragmentation occurs, the theoretical value of V_RPA/V_a is 1. The blue drop lines of the RPA curve in figures 10 and 11 denote the fraction of the ions without fragmentation.

Through the above analysis, the three segments of decline in the RPA curve imply different types of fragmentation. Since all the ion species are singly charged, the fragmentation rate at a certain applied acceleration voltage can be valued as the current fraction. From figure 9, there are no strong signs that ion fragmentation is affected by the acceleration voltage in the same polarity. The average fragmentation rates are calculated and presented in figure 12. The total fragmentation rate of the emitted particles accounts for 48.8% in positive mode and 59.8% in negative mode. Coles and Miller proposed and validated that ion clusters composed of complex ions tend to be more stable [29, 32]. The better stability of (EMI-BF₄)EMI⁺ than (EMI-BF₄)${{\rm{BF}}}_{4}^{-}$ is probably due to a more complex structure of (EMI-BF₄) EMI⁺ despite different polarities.

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Energy spectra of the ILIS can be derived from the derivative of the RPA curve. Figure 13 shows a series of normalized energy spectra of the ILIS at different acceleration voltages. It is found that there are two prominent peaks in each separate curve. This is due to the two sharp drop lines in the RPA curve, caused by fractions fragmented in the field-free region and fractions without fragmentation, respectively. After the calculation of the derivative, the signal intensity is therefore relatively high in the vicinity of these two positions, indicating that the plume contains two concentrated energy distributions.

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The voltage of the second peak, which indicates particles without fragmentation, is slightly smaller than the corresponding applied acceleration voltage. Since the unbroken particles obtained kinetic energy only by electrostatic field acceleration, the voltage loss of the ILIS can be obtained by analyzing the difference between the voltage of the second peak and the applied acceleration voltage. Further, energy efficiency, defined as the ratio of the actual acceleration voltage and the applied acceleration voltage, can also be calculated. Figure 14 illustrates voltage losses and energy efficiencies of the ILIS in positive and negative modes. Results indicate that the voltage loss is increased with the applied acceleration voltage. Correspondingly, the energy efficiency versus the applied acceleration voltage is decreased, though the decrease is relatively slight due to the simultaneous increase of the applied acceleration voltage. A similar trend was mentioned in references [30], though the material of the emitter is different. The voltage loss is probably due to the resistance of the propellant liquid or circuit.

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The spatial plume profiles both perpendicular and parallel to the strips of the ILIS are shown in figure 15. The collected current has been normalized to the height of the peak at an applied acceleration voltage of 3000 V or −3000 V. The main source of error is approximating the finite dimensions of the ILIS as a point source, which is estimated to be less than six degrees.

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It is found that the plume cross profile is approximately symmetric in the direction of either perpendicular or parallel to the strips, and better symmetry is found at higher acceleration voltages. This phenomenon is likely caused by the uneven distribution of the emission sites at lower voltages. At lower applied voltages, some parts of the emitters can form emission sites while others cannot [33], and this is likely due to the variation among the emission strips. This variability can be attributed to differences in apex geometry (mainly radii), emitter-to-extractor distance, and material properties (such as pore size) along the emitter apex. These differences lead to different startup voltages for emission site formation at the different parts of the strips. Thus, at lower voltages, only a part of the emission sites can produce emission and the distribution of the emission sites is uneven.

Besides, another interesting finding is that the plume perpendicular to the strips shows a higher divergence in both positive and negative modes compared with the plume parallel to the strips. Specifically, taking the angle containing 95% of the overall current as the plume angle, the half plume angle perpendicular to the strips is 41.2° at +3000 V and 40.1° at −3000 V, while the plume distribution parallel to the strips is more concentrated, 19.4° at +3000 V and 19.7° at −3000 V. To get an in-depth understanding of the plume divergence difference in two cross sections, numerical simulation is carried out via the software package COMSOL Multiphysics version 5.5.

In the simulation, a 3D model is established, as shown in figure 16(a). The sizes, materials, and circumstances are set the same as the experiments to reflect the actual conditions of the experiments. The combination of the extractor and the emitter array is placed in a sphere, which is defined as the calculation zone. The extractor is grounded, while the potential of the emitter array is set to either a positive or negative acceleration voltage. Particles (monomers and dimers) are released at an initial velocity of zero along the seven strips of the upper surface on the emitter array apex. The particle release position is marked in green in figure 16(b). The sequence type of meshing is set as a physics-controlled mesh, and the element size is selected as an extra-fine level so that the mesh of the emitter apex is fine enough to reflect the real geometry, as depicted in figure 16(c).

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Figure 17 shows the simulated trajectories of monomers and dimers at both V_a = 3000 V and V_a = −3000 V. Results further confirm that the plume divergence perpendicular to the strips is greater than parallel to the strips. From the COMSOL output file, the positions of the particles can be obtained. Taking the angle containing 95% of the total emitted particles as the plume angle, the simulated half plume angle perpendicular to the strips is 40.1° at +3000 V (an error of 2.7% with the measured value) and 39.7° at −3000 V (an error of 1.0% with the measured value), while this value parallel to the strips is 17.6° at +3000 V (an error of 9.3% with the measured value) and 18.1° at −3000 V (an error of 8.1% with the measured value). The simulated results are in good agreement with the experimental values.

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The accelerating particles are driven by the electric force provided by the electric field. Investigating the electric field distribution between two electrodes as shown in figure 18, the main electric field lines match well with particle trajectories perpendicular to the strips. Thus, it can be inferred that the spatial plume profile is influenced by the electric field distribution between the emitter and the extractor to a great extent.

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