Figure 1 provides a schematic of the system. The EDB was previously designed and built at ETH Zurich and has been described elsewhere (Colberg, 2001). In brief, the EDB follows a “double-ring” design in which the electric field trapping the particle originates from a pair of rings acting as high-voltage AC electrodes and two center-drilled endcaps maintaining a DC potential (Davis et al., 1990). The particle originates from a droplet-on-demand generator based on a commercial inkjet printer cartridge (Hewlett–Packard 51633M) and is then charged inductively by passing through a charged coil. While held in the EDB, the particle is illuminated by a small diode-pumped, solid-state laser producing 532 nm light (Lasermate GMA-532-5A9P2) and imaged with a compact CCD camera (JAI CV-A50).

The transfer and ionization source assemblies were newly designed and built at Harvard. The transfer assembly was constructed of aluminum and stainless steel and kept entirely electrically grounded. Within an outer tube that supports the EDB atop the ionization source, the transfer tube (0.25 in. OD, length ∼ 14 cm) extends at its top to directly below the lower (grounded) DC endcap of the EDB. A funnel attached to the top of the transfer tube helps reduce turbulence by adapting the inner diameter of the endcap to that of the transfer tube. The transfer tube terminates at its bottom within the ionization source, directly above the vaporization platform.

The ionization source assembly was designed to mount in front of the inlet region of a commercial time-of-flight mass spectrometer (JEOL AccuTOF). The curved face of the assembly's cylindrical housing includes an entrance hole for the transfer tube at the top, two side ports for a 0.5 in. viewing window and camera, two threaded 0.25 in. ports to control how much the MS inlet draws in lab air compared to gas from the EDB, and a bottom port that can be used for mounting the vaporization platform or a laser. The flat front face of the housing, opposite the MS inlet, contains a Teflon disc with an adjustable mount for a 0.30 mm diameter needle used to generate the ionizing corona discharge (typical current through MS orifice plate ∼ 200–300 nA).

The vaporization platform is built around a disk-shaped ceramic positive temperature coefficient (PTC) resistor (TDK B59060) whose temperature self-regulates to 220 ∘C when a 12 V potential is applied. The resistor is sandwiched between two copper foil electrodes, which in turn are surrounded by two circular glass cover slips (12 mm diameter, 0.14 mm thickness). The stack of materials is secured to a polyether ether ketone (PEEK) base with screws. Upon exiting the transfer tube, the particle strikes the heated top cover slip and vaporizes. The vapors are drawn immediately into the MS inlet, after first undergoing gas-phase ionization via interaction with the corona discharge.

Electronic control of the EDB system and ionization source was managed via a custom dataflow program (Keysight VEE). The AC voltage for the EDB ring electrodes was generated from a function generator signal (Stanford Research Systems), amplified through a high-voltage amplifier (Matsusada). Control, data acquisition, and data analysis from the mass spectrometer were performed using a commercial software suite (JEOL MassCenter). Relative humidity (RH) and temperature were measured using a combined sensor (Sensirion SHT21) installed in the flow directly upstream of the EDB.

Immediately after particle introduction into the EDB, “spring point” measurements were made to determine initial diameter (Davis, 2001). The spring point method is based on the equations describing the stability regions of the EDB. These equations can be shown to relate two parameters that describe the field strength and the drag on the particle at the transition between stable and unstable trapping of a particle – the “spring point”. The parameters are related to measured DC amplitude, AC amplitude and frequency, particle diameter, and the “geometrical constant” of the EDB via Eqs. () and (): 1β×b=2gVacω2Vdc,2α=36μρdp2ω, where β is the field strength parameter; b is the geometrical constant for the specific EDB; α is the drag parameter; g is the gravitational constant (taken as 9.80665 ms-2); Vac and Vdc are the amplitudes of the AC and DC components, respectively, on the ring electrodes and endcaps;  ω is the angular frequency of the AC component; ρ is the particle's density; dp is the particle's diameter; and μ is the viscosity of the surrounding gas (taken as 1.846 × 10-5 kgm-1s-1).

To relate α and β×b at the spring point, single solid polymethyl methacrylate (PMMA) spheres of known 18 µm diameter (Microbeads AS) were injected into the EDB. The spring point of each sphere was measured for a number of different AC amplitude–frequency combinations, with a total of 22 spring point measurements over 4 different PMMA spheres. We ruled out the possibility of doublets or larger aggregates by observation of the droplet behavior by eye. Agglomerates show distinct scattering intensity fluctuations because of Brownian rotational motion in the EDB, which are easily detected by observing the image of the particle. Additionally, if the spring point had been measured using an aggregate with mass twice that of a single sphere or greater, the value would have been clearly anomalous and discarded. From each spring point measurement, α and β×b were calculated using Eqs. () and (), and the data were fit empirically to a second-order polynomial function. This polynomial function was used to convert β×b for each PEG particle, calculated via Eq. (), to α, which in turn was used to calculate a particle diameter via Eq. ().

We found this method of determining particle diameters to provide values consistent with an alternate calculation method, in which α and β are related using the stability curves tabulated in Davis et al. (1990), and b for this EDB is taken to be 2.8 × 10-3 (determined by optimizing the evaporation model fit to data for tetraethylene glycol (PEG-4) evaporation in the polyethylene glycol, average molecular weight 200 (PEG-200), evaporation experiment described below).

Solutions were prepared using commercially available polyethylene glycol, average molecular weight 200 (PEG-200, TCI), and monodisperse triethylene glycol (PEG-3), tetraethylene glycol (PEG-4), pentaethylene glycol (PEG-5), and hexaethylene glycol (PEG-6) (99 % except 97 % PEG-3; Sigma Aldrich). Reliable operation of the inkjet cartridge droplet generator, which requires a liquid with suitable viscosity and surface tension, required all PEG solutions to be dissolved in deionized water. Best performance was found when the PEG was diluted to a weight fraction between 0.20 and 0.30, which optimized the trade-off between consistent droplet generation (sufficiently high concentration of water) and production of larger particles that were easier to transfer to the ionization assembly (sufficiently high concentration of PEG). Once mixed, samples were pipetted into the well of the inkjet cartridge for particle injection. Because of the dry environment of the EDB in these experiments (< 5 % RH), effectively all of the water was assumed to evaporate out of the particles after injection on the timescale of seconds, leaving behind a PEG particle with a starting mass proportional to the PEG weight fraction of the prepared solution. Running the evaporation model (described below) with a mole fraction of water of 0.05 (corresponding to ∼ 5 % RH, Ninni et al., 1999) confirmed that the presence of water under these dry conditions was predicted to have a negligible effect on the evaporation rate and hence could be safely disregarded.

A droplet (initial injection volume ∼ 140 pL) was injected from an inkjet cartridge into the electrodynamic balance. The droplet was negatively charged by passing through a coil held at +300 Vdc. The electric field in the electrodynamic balance was created from a superposition of an AC field (Vpp = 5 kV, f = 100 Hz) and a DC field (Vdc = +10 to +20 V).

For particles that were sized, the following procedure was completed within the first 2 min after the droplet was injected into the trap to determine the droplet's spring point: the DC amplitude was adjusted until the droplet was vertically centered in the EDB. The AC frequency was decreased and the AC amplitude was increased (up to 6 kV) until the particle was just at the cusp of no longer being stably trapped. Then, at a fixed AC frequency, the AC amplitude was slowly increased in 0.01 kV increments until the droplet was observed by eye to no longer be stably trapped in the center of the trapping potential (i.e., when it started tracing a vertically stretched path). The AC adjustment procedure was repeated at a second pair of lower AC frequency and amplitude values when possible. Each trio of DC amplitude, AC frequency, and AC amplitude values allowed for the size of the droplet at that moment to be calculated (Sect. 2.2). The average of the two calculated diameters using the two sets of AC measurements was taken to be the starting diameter of the particle.

Some particles were then immediately ejected from the EDB to the vaporization and ionization region (see ejection procedure below) and hence resided in the EDB for 3 to 5 min before mass spectral analysis. Other particles resided in the EDB for longer amounts of time before ejection. For these particles, after the sizing procedure was complete, a 80 sccm purge flow of nitrogen (Airgas, industrial grade) was introduced from the top of the EDB. The DC trapping voltage was increased to approximately 50 V to keep the droplet near the center of the EDB with this flow. The purge flow remained at this level until droplet ejection.

The droplet ejection procedure started with increasing the nitrogen flow and the DC trapping voltage in tandem so that the droplet's vertical position in the EDB remained constant as the flow increased. It was found that with the current experimental geometry, droplet transfer was most reliable with a nitrogen flow of approximately 200 to 250 sccm and a counterbalancing DC voltage of approximately 200 to 350 V, depending on the droplet mass and charge. Once the flow and voltage were increased, the 0.25 in. threaded ports on the ionization region were fully or partially closed (by means of adjustable valves) so that the nitrogen flow into the EDB matched that of the flow entering the mass spectrometer inlet via the transfer tube. The correct extent to close the valves was determined by centering the droplet's horizontal alignment. A centrally aligned droplet was taken to mean the flow out of the bottom of the EDB to the ionization region matched the flow from the top of the EDB. (Horizontal displacement of the droplet was taken as a sign of gas flowing through the EDB's side droplet injection port due to a mismatch between the nitrogen flow into the top of the EDB and out of the bottom.) Once the flow was set appropriately the DC voltage was switched to 0 V, and the droplet was pulled with the nitrogen flow out of the EDB, down the transfer tube, and onto the vaporization platform in the ionization region.

The particle mass spectra were quantified for each mass channel of interest, working at unit m/z mass resolution, using the MS software's “chromatogram” viewer. The height of the peak above the surrounding background, in time, was taken to be the signal strength. The software peak-finding algorithm was used to define the peak height and background, with correct peak identification confirmed by eye. Figure 2 presents a sample time trace of selected ion signals arising from ejection and ionization of a 20 µm diameter PEG-200 particle.

To account for particle-to-particle variability in MS signal, peaks were normalized to the PEG-6 parent ion signal at 283 m/z. PEG-6 was chosen as an internal standard due to its minimal evaporation over the timescale of these experiments and presence in appreciable amounts. To obtain molar ratios (relative to PEG-6) that can be compared to a model, the normalized peak intensities were then corrected for the molar sensitivity of the specific PEG molecule compared to PEG-6, as determined by measurements of binary droplets of known composition of PEG-6 mixed with PEG-3, PEG-4, or PEG-5 (Table A1).

Mass spectra were also collected for particles consisting of pure PEG-3 through PEG-6 to assess the extent of fragmentation and check for mass coincidence problems. Negligible mass coincidence was found for the parent ion peaks used here, and all molecules were found to have a majority of their signal at the parent ion, with the exception of PEG-3, which had three roughly equal peaks: the parent ion and two fragment ions (Table A2).

A kinetic model was developed to describe the evaporation of a single PEG droplet levitated in the EDB. The model is initialized with a distribution of PEG components and a particle diameter. The particle is assumed to be an ideal mixture in equilibrium at every instant with the gas phase at the surface, as in Eq. (): 3csi=XiPvapikT, where csi is the gas-phase surface concentration of species i, Xi is the particle-phase mole fraction of species i, Pvapi is the pure component vapor pressure of species i at temperature T inside the EDB, and k is the Boltzmann constant.

The evaporation of species i is then assumed to proceed via Maxwellian flux (Seinfeld and Pandis, 2006), as in Eq. (): 4dnidt=4πrDgi(c∞i-csi), where r is the particle radius, Dgi is the gas-phase diffusion constant of species i, and c∞i is the gas-phase concentration of species i at infinite distance from the particle surface (here always taken to be zero). This description of evaporation is strictly true for conditions with no gas flow, whereas we operate with a small nitrogen purge flow (80 sccm) to prevent buildup of PEG vapor within the EDB. However, we conclude our combination of EDB geometry and flow rate leads to a negligible increase in the evaporation rate (Zhang and Davis, 1987).

Parameters used to describe PEG molecules in model calculations are taken from Krieger et al. (2017) and described in Table B1. The model was implemented in Python using the SciPy package's implementation of the LSODA ordinary differential equation solver.

For each experimental data set, the model was run twice as bracketing cases to reflect the uncertainty in literature vapor pressures, as well as particle-to-particle variability in initial diameter and EDB temperature. The slow-evaporation-limit model run used the lowest measured temperature (298.0 K), the largest measured starting particle radius of the particles for a given experiment, and the lower bounds of the literature vapor pressure values (reported as 95 % confidence intervals in Krieger et al., 2017), with the exception of the PEG-6 internal standard, whose vapor pressure was taken as the upper bound of the literature confidence interval. Conversely, the fast-evaporation-limit model run used the highest measured temperature (299.5 K), the smallest measured particle radius, and the upper bounds of the literature vapor pressure confidence intervals, except for the lower bound of PEG-6's vapor pressure. The starting particle radius was typically between 9 and 11 micron, with variability on the order of 10 %. The most important contributors to the model output ranges were the uncertainties in vapor pressure and variations in starting radii.

The model's performance was checked by comparison to an experiment performed with a PEG-4 + PEG-6 particle of known starting composition trapped in a similar EDB at ETH Zurich, equipped with a spectrometer that continuously sized the particle via scattering measurements (as in Zardini et al., 2006). The measured change in radius over multiple days was consistent with the model-derived radius (Fig. B1).

Using the EDB–MS system, we obtained the mass spectrum of single particles that were trapped inside the EDB and then transmitted to the ionization source for vaporization and ionization. A sample mass spectrum of a PEG-200 particle (Fig. 3) shows that the signal from droplets with diameters on the order of 20 µm can be easily detected.

The measurement and model were compared for droplets of three different compositions: two binary mixtures and one more complex mixture.

The above analysis uses a model to check the appropriateness of the observed evaporation rates. However, one future utility of such an experimental system may be calculating the vapor pressure (or activity) of a compound for which the value is not known. Thus, we also assessed how well we can constrain the vapor pressures of compounds by optimizing the model fit to the experimental measurements. For both the PEG-3 + PEG-6 and PEG-4 + PEG-6 binary mixtures, we iteratively ran the model with the PEG-3 or PEG-4 reference vapor pressure (at 298.15 K) as the free variable (assuming PEG-6 to represent a reference compound with well-constrained vapor pressure). We performed the analysis twice for each mixture, fixing the temperature and initial diameter to each of the bracketing cases described above. We calculated the root-mean-squared deviation (RMSD) of the binned data points from the model output at the bin's midpoint time and searched for convergence to a minimum RMSD. In each case, we found model convergence to the binned data. The extracted vapor pressures of PEG-3 and PEG-4 averaged over the two bounding temperature–diameter cases (48 ± 12 mPa for PEG-3 and 14.6 ± 2.2 mPa for PEG-4) are consistent with the literature vapor pressures (66.8-9.5+11.0 and 16.9-1.0+1.1 mPa for PEG-3 and PEG-4, respectively), when their respective uncertainties are considered. The results demonstrate that the current data set allows calculating vapor pressures with uncertainty within a factor of 2. Because vapor pressure values derived from different experimental techniques can vary by orders of magnitude, even the precision obtained in this proof-of-concept measurement can represent a helpful constraint for compounds less well-studied than PEG (Bilde et al., 2015). The variability in the starting diameter and temperature are the dominant sources of uncertainty in this model fit, so the precision of extracted vapor pressures is expected to improve with better constraints on the particle-to-particle variability in EDB temperature and starting diameter.

We have shown the experimental results to be consistent with expectations reflected in a kinetic model and, further, that meaningful vapor pressure values can be extracted if the values are assumed to be unknown. However, it can also be seen from Figs. 4 and 5 that there is considerable particle-to-particle variability in the signal for replicates collected after the same EDB residence time. Additionally, this variability appears to differ between evaporation data sets: the PEG-4 + PEG-6 binary particle data appears much more tightly clustered than the PEG-3 + PEG-6 data set, for instance, meaning averaging over fewer points is required. This variability highlights the importance of averaging over multiple particles to obtain a quantitative picture of the change in droplet composition. We investigated possible sources of this variability in order to understand possible sources of improvement for future iterations of this system.

Because this variability is observed for particles for which little evaporation has occurred, it seems unlikely that variability in the rate of evaporation is the cause. Instead, the variability more likely originates from vaporization, ionization, or the mass spectral measurement itself.

We investigated a number of possible factors contributing to the variability in signal. Within the size range of particles analyzed during the evaporation experiments, variability in the particle diameter (approx. ±10 %), measured with the spring point method, did not correlate to particle-to-particle variability in apparent evaporation rates, or to particle-to-particle variability in absolute signal. For two populations of PEG-200 particles with masses varying by a factor of approximately 2.5, higher variability in raw signal was observed for the smaller particles. In this data set the decreased particle-to-particle variability in normalized signal can also be readily observed (Fig. A1). From these analyses we conclude that though the particle-to-particle variability in raw signal may be affected by significant differences in particle mass, the variability in the normalized evaporation data was not explained by the variability in measured starting particle diameter. We compared the variability in signal for particles that were trapped in the EDB to particles that were allowed to travel directly to the ionization region, either by passing through the EDB without first being charged or by ejection out of the droplet generator positioned directly above the top of the transfer tube. Comparing the two sets of measurements on a solution-by-solution basis, we did not find that the particles first trapped in the EDB systematically demonstrated a larger variability in signal. This implies the trapping process is not a dominant source of variability in the signal.

Because there was particle-to-particle variability in the total amount of particle-derived signal measured by the MS, we looked for a correlation between normalized signal variability and the total raw counts, both for particles trapped in the EDB and immediately ejected, and for particles that were never trapped. Our data set was too sparse to make statistically rigorous conclusions, but it did not appear as if there was a consistent relationship for all studied solutions between total raw counts and the normalized signal variability, once we filtered out data with raw PEG-6 peak intensities judged too low (< 1000 countss-1) to allow for accurate peak height determination.

We also considered the possibility that the 1 s MS sampling time used for these experiments could be undersampling the pulse of a signal from the vaporized particle, which could lead to added signal variability. To check this, we compared the variability in normalized peak signals of PEG-200 particles when the MS sampling interval was 1 or 0.1 s. In each case, the PEG-200 particles were injected into the EDB and then immediately transferred to the ionization region, without trapping. We found no difference in the variability in the normalized PEG-3 through PEG-7 signals between the 1 and 0.1 s sampling data.

Another factor to consider is the possibility of variability in the vaporization process. The quantification procedure presumes the vaporization of analyte molecules is virtually instantaneous, for every particle measured. If the vaporization process were not instantaneous for certain lower-volatility analyte molecules, this would manifest itself as the signal intensity being spread out over a longer time interval, with diminished peak intensity. The peak signals for most particles showed a consistent sharp peak shape on all analyte signal channels. In a small number of cases, it was observed that heavier molecular weight (i.e., lower volatility) PEG showed an anomalously broad distribution of signal in time, with a smaller peak intensity, whereas lighter molecular weight PEG showed the normal sharp peak. These cases were ascribed to irregular vaporization, perhaps due to misalignment of the particle transfer, and discarded from further analysis. Had these data not been discarded, they would have contributed extremely large “normalized signals” for lighter molecular weight PEG, since the PEG-6 peak intensities were weakened due to broadening. If irregular vaporization contributed to the variability in normalized signal observed in Figs. 4 or 5, it would have needed to have arisen from cases in which the broadening of the lower-volatility signals was too subtle to be screened out by eye.

From these checks, we observed what appeared to be an inherent variability of approximately ±20–30 % in the normalized peak intensities, regardless of the raw signal strength, initial particle diameter, the MS sampling rate, or whether or not the particle was held in the EDB prior to transfer to the ionization region. The origin of the apparent somewhat greater variability for some data, such as the first time bin for the PEG-3 + PEG-6 binary particles, has not been determined. Future work is needed to determine whether such variability persists in future studies with refinements to the experimental design.

An additional limiting factor for this experiment, beyond the signal variability and consequent need for averaging, was the difficulty of transfer from the EDB to the vaporization region for some particles. It was found that the transfer protocol described above worked with near-100 % success for transferring particles that were ejected from the EDB relatively quickly after their initial formation. However, the transfer success rate for some particles was found to become appreciably lower when residence times in the EDB extended to hours or days. We hypothesize this is a result of the smaller remaining particle mass after a significant portion of the particle's starting material has evaporated: the less massive the particle is, the more buffeted it is by any turbulence it encounters during the transfer step and less likely to strike the vaporization platform. Future experiments with this system would be aided by an improved transfer design in which lighter particles also reach the ionization source with near-100 % efficiency or an experimental design in which the final droplet mass is not much smaller than the initial.

We envision future experiments using this EDB–MS system to study linked chemical and physical transformations of particles, particularly with relevance to atmospheric aerosol particles. The strength of this system lies in its ability to couple the strengths of trapped single particle experiments – in which a single particle transforms over a timescale of minutes, hours, or days, with careful control of both condensed- and gas-phase compositions – with the chemical specificity of mass spectrometric analysis. These strengths make the EDB–MS a complimentary technique to existing experimental and modeling approaches.

Even using laboratory-generated aerosol particles with diameters on the order of 10 µm, results from future lab studies can be used to improve our understanding of submicron atmospheric aerosol particles. Physical and chemical constants, such as reaction rate constants and diffusion coefficients, are equally applicable to both laboratory and smaller atmospheric particles. The effect of other size-dependent factors, such as changing surface-to-volume ratio, radius-dependent mixing timescale of a viscous particle, or the Kelvin effect on growth of small nanoparticles, can be accounted for by calculation if the appropriate parameters are known. Trapping a submicron particle within the EDB–MS would require further development. One approach may be to transfer particles to the ionization region using a linear quadrupole geometry; this geometry has been used by other research groups (Duft et al., 2015; Jacobs et al., 2017; Sivaprakasam et al., 2017). Detection limitations for the mass spectrometer would also need to be assessed.

One class of future experiments is to measure evaporation rates. By fitting to a model, evaporation data can be used to determine vapor pressures of compounds when the levitated particle represents an ideal mixture, as was demonstrated in the current work. In addition, particles can be prepared for which evaporation is not expected to proceed as for an ideal mixture. For instance, the compound being studied may be expected to have an activity coefficient in the particle mixture deviating significantly from unity, or evaporation might be kinetically limited due to physical properties (slow diffusion or phase separation). If the vapor pressure of the compound under study is known, the observed evaporation rate can be compared quantitatively to a model representation of that nonideality. The use of a mass spectrometer as the analytical technique in these cases means the presence of all MS-detectable components of the particle can be tracked with time, providing a more detailed data set than an equivalent experiment measuring particle diameter alone.

Beyond measurements of evaporation in ideally and nonideally mixed particles, the EDB–MS can be used to track chemical reactions in particles. A condensed-phase mixture that itself is reactive can be prepared and injected as a particle, or the composition of the bath gas can be changed to induce changes in the particle's composition. One example would be to change the RH of the gas, which can change the water activity in the particle and consequently affect condensed-phase chemistry by either serving as a plasticizer to help speed diffusion in a kinetically “frozen” particle or affecting equilibrium of a chemical reaction in which water directly plays a role, such as hydrolysis. A second example would be to add an oxidant such as ozone or the hydroxyl radical (OH) to the gas, which can cause organic molecules in the particle to undergo rounds of oxidative “aging”.

In all of these examples, the EDB–MS is well-suited to studying chemical transformations over “long” timescales of hours or days, which are of interest because of their relevance to the atmospheric lifetime of aerosol particles. One approach in laboratory studies of aerosol chemistry has been to speed up the reaction of interest by increasing the concentration of a reactive species, for example, ozone or OH, compared to typical atmospheric concentrations. The technique presumes the chemical changes an aerosol particle undergoes over multiple days can be accurately compressed to a shorter timescale by working at higher concentrations. However, it may be the case that working at higher concentrations masks other processes that are important on a longer timescale but do not speed up under the selected concentration conditions. Unimolecular reactions are an example of a class of such processes. Working with the EDB–MS would provide an opportunity to check whether the results from high concentration experiments can in fact be extrapolated to slower, lower-concentration conditions in the atmosphere.

This system therefore represents a valuable analytical tool for better understanding fundamental physicochemical processes of aerosol particles, whose value in part lies in providing improved model representations of these processes, enabling a better understanding of the role of aerosol particles in human health and climate.