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Abstract
The distinct optical properties of solid and liquid silicon nanoparticles are exploited to determine the distribution of gas-borne solid and liquid particles in situ using line-of-sight attenuation measurements carried out across a microwave plasma reactor operated at 100 mbar. The ratio between liquid and solid particles detected downstream of the plasma varied with measurement location, microwave power, and flow rate. Temperatures of the liquid particles were pyrometrically-inferred using a spectroscopic model based on Drude theory. The phase-sensitive measurement supports the understanding of nanoparticle formation and interaction and thus the overall gas-phase synthesis process.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Growing interest in gas-phase synthesis routes for oxidic and non-oxidic nanomaterials is driven by their capability to generate high-purity materials of various compositions and morphologies and their scalability to industrial production levels [1–4]. Usually, vaporized or sprayed precursors are introduced into the respective reaction environments and heat provided by a flame, a plasma, or heated reactor walls causes the reactants to dissociate. The reaction products form a highly supersaturated vapor that condenses into liquid or solid nanoparticles downstream of the heat source. Gaining insight into the processes of initial particle formation, growth, and phase change via in situ optical methods [5] is a prerequisite for understanding the underlying reaction pathways and their interaction with the fluid flow [6].
In many synthesis processes, the nanoparticles undergo a phase transition. In plasma-initiated gas-phase synthesis of Si and Ge nanoparticles, the precursor-laden (SiH4, GeH4) gas flows through a microwave-generated plasma at high velocity (typically 100 m/s), leading to high-temperature residence times of approximately 1.2 ms duration, during which time the precursor decomposes and initial condensation of super-saturated vapor leads to homogeneous nucleation outside of this zone. The nucleation first leads to the formation of liquid nanodroplets, which then solidify [7] as the temperature of the carrier gas drops. Understanding the liquid-to-solid transition is of special importance because it strongly influences the morphology of the resulting material. Liquid droplets may collide, coalesce, and form larger spherical droplets that subsequently solidify into compact spherical monocrystalline or amorphous nanoparticles. In contrast, the interaction of solid particles in the reactor leads to the formation of loose aggregates, which, as a result of sintering, lead to fractal, often multicrystalline, structures. Depending on precursor concentration, total pressure, and residence time, the morphology, size, and crystal structure of the formed particles can be strongly affected [7]. Understanding the particle phase as a function of residence time and reaction conditions is thus important for a better understanding of the particle formation history, which in turn, would provide measures for directing the synthesis process towards desired particle properties and would be the basis for scale-up to industrial production scales [8].
Because the phase-transition temperature is a strong function of nanoparticle size, the location of the phase transition may also provide fundamental insight into the physics of nanoscale solid matter. In this paper, this process is investigated for silicon nanoparticles formed in a microwave plasma process, which exploits the distinctive optical properties in the liquid (i.e., metallic) and solid (i.e., semiconducting) states of silicon. Based on their similar properties [9], it is expected that the method would also be applicable to characterize the plasma-based synthesis of germanium nanoparticles [10].
Optical diagnostics techniques enable in situ quantitative measurements of, e.g., particle temperature, volume concentration (volume fraction), particle size, as well as chemical composition or crystal structure [5,7,11–14]. A line-of-sight representative particle temperature can be deduced from optical pyrometry [15] if the optical characteristics of the material (which can be wavelength and temperature dependent) are known or measured separately. This technique – exploiting emission at multiple wavelengths – has been widely applied to soot characterization in laminar flames [16,17] or engine combustion [18,19]. If the detection system is calibrated against a light source of known brightness, particle volume fractions can also be inferred from the absolute signal intensity [20–22]. Another diagnostics for acquiring optical properties of gas-borne particulate matter is spectrally-resolved line-of-sight attenuation (LOSA) [23–25]. In this method, broadband light (∼250–620 nm) is passed through an ensemble of nanoparticles to measure the wavelength-dependent extinction (absorption plus scattering) of nanomaterial in the pathway of the light beam. In this work, we apply spatially- and spectrally-resolved LOSA for the measurement of extinction coefficients, Kext,λ during gas-phase synthesis of Si nanoparticles in the exhaust flow of a plasma reactor. In the case of Si and Ge nanoparticles, the wavelength dependence of Kext,λ strongly depends on the phase of the material. In our previous work, spectrally-resolved extinction measurements were performed on liquid Si nanoparticles [26]. In this work, these data are used in the spectroscopic equation that is used for pyrometric temperature measurements. The extinction and pyrometric temperature measurements are performed for different experimental conditions to observe the variations in the qualitative fractions of solid and liquid nanoparticles in the line-of-sight and to see how temperature effects these variations. The experimental conditions include flow rate of precursor-laden gases into the plasma zone, microwave power used to generate the plasma and the measurement location through the particles.
2. Theoretical background
In the LOSA measurement, incident radiation from a light source (here a laser-driven light source, LDLS) is shone across a polydisperse aerosol of silicon or germanium nanoparticles that may be solid, liquid, or a mixture of the two phases. By assuming an optically thin environment, the detected intensity is given by the radiative transfer equation [27]
The bulk absorption and extinction coefficients of the aerosol are related to the spectral absorption and extinction cross-sections of the particles, Cλ,abs and Cλ,ext according to Ref. [28] by
The absorption and extinction cross-sections are functions of the size parameter x = πdp/λ and the complex permittivity of the bulk material, ɛ, which define their optical properties. In case of liquid silicon nanoparticles, these properties can be well described by Drude theory [24,29–31] as long as the particle size is larger than the mean free electron path [32]. Accordingly, the complex permittivity is
The extinction cross-sections of solid Si nanoparticles change dramatically with diameter, especially in the intensity and wavelength position of morphology-dependent resonances located in the near-UV and visible spectral range. The peaks correspond to resonances of bound oscillators, which is distinct from the spectrally-smooth cross-sections predicted by Drude theory, caused by intra (conduction) band electron transitions. In contrast to solid nanoparticles, the extinction coefficient of liquid silicon [24] and germanium [9] nanoparticles are smooth curves, with a peak in the UV region corresponding to a surface plasmon resonance followed by a monotonic decrease with increasing wavelength.
Fig. 2. Extinction spectra of (a) solid and (b) liquid silicon nanoparticles simulated by Mie theory for particle sizes between 10 and 90 nm. Peaks in solid Si represent morphology-dependent resonances, while peaks in the UV in liquid Si correspond to surface plasmon resonances.
The distinct optical properties between liquid and solid silicon nanoparticles can be exploited for in situ detection of the phase of gas-borne particles in a reactor environment. For the presented synthesis conditions, the particle diameters are expected to range between 20 to 50 nm. In this range, the additional peak in the solid phase corresponding to the morphology-dependent resonances will be the main criterion to differentiate between the two particle phases.
An effort was made to confirm the extinction measurements for liquid-phase silicon nanoparticles by modeling their extinction spectrum using the Drude model in combination with Mie theory. The required electrical permittivity value was inferred from ellipsometry [29,30] measurements.
3. Experimental procedure
Silicon nanoparticles are produced via gas-phase synthesis from silane (SiH4) as precursor in a microwave plasma. The reactor is described in detail in Ref. [26]. Schematics of the reactor and the optical setup for line-of-sight attenuation/extinction (LOSA) measurements are shown in Fig. 3. A flow of Ar and H2 with a small amount (around 10 Vol.% of the total flow) of SiH4 are injected through a nozzle centrally through the focus region of a circular microwave resonator (IPLAS, Cyrannus) where the plasma is generated. The plasma dissociates the precursor and the molecular fragments lead to the formation of Si nanoparticles, which then grow further downstream. An additional swirling flow of H2 and Ar is introduced tangentially around the central nozzle to confine the synthesized particles within a cylindrical shaped torch of approximately 12 mm diameter and to minimize thermophoretic deposition on the reactor walls. A luminous zone forms where light is emitted from thermal radiation of the formed particles. At a distance of 300 mm downstream the plasma region, extinction measurements are performed along horizontal lines-of sight through optical ports mounted in a cross piece.
Fig. 3. Schematics of the reactor and optical arrangement. a: Plasma reactor (side view), MW: Microwave radiation, NG: Nozzle gases, SF: Swirl gas flow. b: Optical setup (top view) for extinction measurements. LDLS: Laser-driven light source, PM: Parabolic mirror (effective focal length: 50 mm), A: Aperture, L: Lenses (focal length: L1 = 250 mm, L2 = 250 mm, L3 = 150 mm), NPT: Nanoparticle torch, SP: Spectrometer, distances d1 = 50 mm, d2 = 100 mm, d3 = d4 = 250 mm, d5 = 150 mm.
At the same location, particle samples are collected using a pneumatically-driven thermophoretic sampler [17] for ex situ TEM analysis. The TEM grid is exposed to particles for approximately 10–20 ms. The estimated gas temperature at this location is between 1500 and 1700 K according to previous measurements with multi-line NO-LIF temperature imaging in a similar arrangement [7]. Information on the spatial distribution of liquid and solid nanoparticles is derived from multiple extinction measurements through the particle stream by laterally-traversing the entire reactor through intervals of 1 mm. Additional extinction measurements were conducted in the off-gas of the reactor at room temperature in an optically accessible 6.79 cm3 test cell with purged windows (Artium).
In the optical setup, an off-axis parabolic mirror collimates the broadband light from a laser-driven plasma source (LDLS, Energetiq EQ-77), which is then focused onto the nanoparticle stream with a lens. The transmitted light is then collimated and focused by an assembly of two lenses onto the horizontal slit of a spectrometer (Acton, SP-150, grating: 300 lines/mm, f = 150 mm, f# = 4) equipped with an EMCCD camera (Andor, iXon DV887) as detector.
The proportion of solid and liquid particles in the probe volume, and the size distributions, can be modified by altering the operating conditions of the plasma reactor, e.g., by adjusting the microwave power, the gas pressure, the flow rate, and the composition of the precursor gas flow. In this work, measurements were carried out for four different operating conditions with different volume flow rates. Changing flow rates at fixed microwave power changes the energy intake per volume (and thus the temperature) as well as the residence time of the reactants within the plasma zone.
Nominal conditions are those used in our previous work [26], with 2.23 standard liter per minute (slm) of total gas mass-flow rates through the nozzle (0.03 slm SiH4, 2 slm Ar, 0.2 slm H2) and 800 W microwave power for plasma generation. Deviating operating conditions are then given by 70, 80, and 120% of the standard mass-flow rate, while maintaining the mixture composition with 1.35 Vol.% SiH4 for all cases. The swirl gas mass-flow rate is kept constant in all cases (6.6 slm Ar and 0.5 slm H2). The gas inlet flow rate to the plasma region, the silane concentration, and approximated residence time of gases are listed in Table 1. The residence time of the gas mixture inside the quartz tube is calculated for the distance between the nozzle and plasma region. If not stated otherwise, the microwave power for plasma generation is 800 W and the total pressure inside the reactor is 100 mbar. In a few measurements, the microwave power was also increased to 1000 and 1200 W to further increase the gas-phase temperature.
Table 1. Experimental conditions used in the experiment.
4. Results
4.1 Extinction measurements
In line-of-sight attenuation (LOSA) experiments, spectral intensities are measured for four conditions in succession (all along the same line-of-sight at a specific wavelength): (a) The combined transmitted and emitted intensities from the particle-laden volume, It+e,λ, (b) the intensity from the light source without particles in the flow, Ilamp,λ, (c) the emission from the particles with the light source off (only relevant in case of high temperatures), Ie,λ, and (d) the background without particles and without light source, Idark,λ. A quantitative measure of the opacity at the specific wavelength λ over the path length L can then be derived from
The spectrometer can record a wavelength range of 150 nm for a fixed grating position. To capture an extinction spectrum for a larger wavelength range (∼250–620 nm), three different grating positions were selected sequentially and the recorded spectra are patched together to produce one spectrum.
Figure 4 shows a measured extinction spectrum for a case with the standard flow conditions (2.23 slm flow rate at 300 mm downstream plasma zone through cross piece) but increased microwave power (1000 W). The simulated extinction spectrum using the Drude model in combination with Mie theory [34–37] based on liquid particles with a mean diameter of 25 nm (cf. Figure 2(b)) closely matches the experimentally-observed spectrum.
Fig. 4. Extinction spectrum for liquid silicon particles, measured with standard flow conditions but increased microwave power (1000 W) in comparison with simulations based on the Drude model in combination with Mie theory (dashed red line) for 25-nm diameter silicon droplets.
4.2 Extinction measurements on hot vs cold silicon nanoparticle aerosols
Extinction spectra obtained using microwave power (800 W) at same measurement location deviate from the result in Fig. 4 with the extent of the deviation depending on the flow rates (Fig. 5(a)). Under these operating conditions, the aerosols are sufficiently hot so that both liquid and solid particles may exist in the probe volume depending on the exact location in the flow and the respective local temperature. The monotonous decay in extinction towards longer wavelengths can be ascribed to the fraction of liquid particles following the Drude model in combination with Mie theory. The additional extinction in the 250–500 nm range is attributed to solid particles (cf. Figure 2(a)). Note: The additional features at ∼251 nm correspond to Si atomic emission [38] causing a reduction in apparent extinction presumably because the electronically-excited atomic species are at a higher temperature than the particles.
Fig. 5. Extinction spectra of Si nanoparticles measured in the plasma flow corresponding to two flow rates at 800 W for hot aerosols through the cross piece (a) and for cold aerosols through the downstream test cell (b). The dip in the extinction spectra around 251 nm is due to atomic-Si emission. The peaks in the 250–550 nm range indicate the presence of solid particles. An increased flow rate at fixed microwave power leads to partial solidification up to the measurement location. With increased microwave power of 1000 W (dotted curve) the particles remain liquid up to the measurement position also for the increased flow rate.
To better understand the solidification process and the optical extinction caused by solid Si nanoparticles, additional extinction measurements were carried out in an optically-accessible test cell installed downstream of the reactor (Fig. 3) where the gases are cooled down to room temperature and thus all particles are solid. The extinction spectra recorded for cold aerosols are shown in Fig. 5(b) for the same two flow rates as for the hot aerosols generated at 100 mbar gas pressure.
For the 1.56 slm gas inlet flow rate (blue curves) and the hot aerosol, there are no peaks visible in the extinction spectra that would indicate the presence of solid particles per Fig. 2(a). These peaks appear, however, in measurements further downstream in the test cell. This shows that most of the particles are in the liquid phase in the measurement location in the cross piece, which then solidify further downstream. In case of 2.23 slm for hot aerosols (solid red curves), there are already significant peaks visible in the spectrum indicating the larger fraction of solid as the increased gas flow at fixed microwave power leads to a reduced gas temperature at the measurement location. The spectra then change further for cold aerosols with 100% solid particles.
In order to estimate the fraction of solid and liquid Si inside the aerosol qualitatively, different measured extinction spectra can be fitted with a combined spectrum of two individual spectra in different ratios: the first spectrum corresponds to all solid, and the second to all liquid. The cold aerosols are in solid phase, but, the hot aerosols at 800 W are mixture of solid and liquid. Therefore, a spectrum is added in Fig. 5(a) for 1000 W with 2.23 slm flow rate that corresponds to all liquid particles (cf. Figure 4). The extinction spectra corresponding to liquid (hot aerosol at 1000 W) and solid (cold aerosol at 800 W) phase for 2.23 slm flow rate are added according to
To analyze the different mixing ratios of solid and liquid Si in the aerosols, a least-square regression has been performed to extinction spectra recorded through the cross piece for four flow rates using Eq. (7). Figure 6(a) shows the measured extinction spectra (solid lines) and the fitted curves (dashed line), while Fig. 6(b) shows the value of parameter α (solid number density fraction) for all these flow rates.
Fig. 6. Extinction spectra (solid lines) recorded through cross piece for hot aerosol for different flow rates fitted with Eq. (7) (dotted lines) (a) and the resulting values of parameter α (b) representing the contribution of solid to the fitting signal.
The results presented in this figure shows that the number density fraction of solid particles found at the measurement position first increases for flow rates between 1.56 and 2.23 slm and then drops again for a flow rate of 2.68 slm. The fraction of solid particles is expected to increase with decreasing gas temperature. It is, however, unlikely that the mean temperature changes when increasing the flow rate to 2.68 slm. The origin of this effect is therefore attributed to the complex structure of the reactive plasma flow where increased flow rates can also lead to a difference in temperature distribution and thus locally higher temperature. It will be interesting to relate these findings to gas-temperature measurements in future work, e.g., using NO [7] or SiO-LIF thermometry [39].
4.3 Pyrometric temperature measurements
The incandescence of particles detected by camera can be described by spectroscopic model [40]
The emission from solid nanoparticles is very small for the spectral range of interest (∼550–850 nm) relative to emission from the liquid nanoparticles (cf. Figure 2), and can be excluded. Therefore
If, it is also assumed that the scattering cross-section of liquid nanoparticles is negligible as compared to their absorption cross-section, the measured extinction spectrum will represent a path-integrated absorption cross-section
Equation (8) can then be written as
The emission spectra of the particle luminescence are recorded for 1.56 and 2.23 slm flow rates and fitted with Eq. (12) using least-squares regression (cf. Figure 7). The temperature dropped from 1610 ± 5 K to 1504 ± 5 K with the gas inlet flow rate increment from 1.56 to 2.68 slm. It validates the findings in Fig. 6, i.e., the larger density number fraction of solid in the aerosol for 2.23 slm flow rate as compared to 1.56 slm. Note that ± 5 K is mathematical uncertainty calculated by fitting procedure and it does not describe the accuracy in temperature measurements.
Fig. 7. Temperature measured from thermal radiation of hot Si nanoparticles for two gas inlet flow rates, i.e., 1.56 and 2.23 slm (Symbols: Measured spectra, Solid lines: Fitted curve with spectroscopic model).
The observed pyrometric temperature at the 2.23 slm condition of 1504 ± 5 K is below the melting point of macroscopic silicon (∼1560 K) [26], which seems to contradict the assumption that all incandescence is from liquid particles. It is, however, well established that the melting point of nanoparticles may be hundreds of Kelvin lower than that of the corresponding bulk material because of the surface energy contribution to the overall Gibbs free energy [41]. Therefore, these measurements present an opportunity to determine the melting point from the lowest observable temperature for gas-borne silicon nanoparticles. For the same reason, we can analyze the extinction measurements from Fig. 6 as a result from combined liquid and solid particles in the probe region.
4.4 Ex situ particle characterization
Under the current conditions, the coexistence and spatial distribution of both phases can be explained in various ways. One possibility is that the synthesized particles exhibit a broad size distribution, such that – at the same temperature – the smaller particles are in the liquid phase, while the larger ones are in the solid phase, as melting temperature reduces with the reduction of particle sizes [41,42]. However, histograms of particle diameters obtained from processed TEM images (Fig. 8) can be fitted to a log-normal size distribution
Fig. 8. TEM images and particles size distribution for 1.56 and 2.23 slm gas inlet flow rates. Solid lines represent the log-normal fit to the distribution.
4.5 Effect of temperature on solidification through variation of the microwave power
Increasing the microwave power at constant mass-flow rates increases the gas temperature in the plasma zone and will thus shift the high-temperature zone further downstream, which will leave almost all particles in the liquid state at the measurement position in the optical crosspiece. Figure 9 shows the extinction spectra recorded at microwave powers of 700 and 1200 W for the standard flow rate (2.23 slm). The extinction feature marking the solid phase disappears at the higher microwave power, i.e., higher temperatures.
Fig. 9. (a) Extinction spectra recorded for two different microwave powers at constant mass-flow rate. The peak in the 250–550 nm range disappears with increasing temperature inside the reactor. The solid lines are fits with Eq. (7) to the extinction spectra. (b) Thermal radiation of hot Si particles for same microwave powers. Symbols: Measured radiation, Solid lines: Fitted curve with spectroscopic model with Eq. (12).
Following the procedure as before, the temperature of the particle ensembles was determined from measured emission spectra assuming the particles emit thermal radiation. For the two microwave powers of Fig. 9(a), Eq. (12) is fitted to emission spectra recorded between 550 and 820 nm (Fig. 9(b)). It can be observed that the temperature increases by roughly 220 K when increasing the microwave power from 700 to 1200 W.
The temperature determination gives a strong indication that temperature has a major impact on the solidification process and thus the variation in extinction spectra. In Fig. 9, the impact of the solidification to the extinction coefficient is shown; the spectrally-resolved extinction spectrum changes from a structured spectrum (P = 700 W, Tpyro = 1504 ± 5 K) to a Drude-like spectrum (P = 1200 W, Tpyro = 1727 ± 5 K). Solid lines in the figure represent the fitting to the spectra with Eq. (7). The fitting indicates a value of 0.75 of parameter α for 700 W, while zero for 1200 W case. Because of the absence of the solid, the equation makes use of only spectrum corresponding to all liquid. We can assume that, at 1200 W microwave power and above, all particles are liquid.
4.6 Spatially-resolved analysis
For spatially-resolved detection of the solid vs. liquid particle ratio within a horizontal plane in the particle torch, extinction measurements are recorded by scanning the particle torch (i.e., the whole reactor) horizontally through the fixed analysis beam path, while all the other conditions are kept the same. Figure 10(a) shows the resulting extinction spectra for 850 W microwave power for different horizontal positions, marked as corresponding colored arrows in the top view sketch in the middle in the figure (b). It can be seen that when moving from the center of the particle torch to the edge, the peak corresponding to solid particles starts to appear between 360 and 420 nm, and the contribution of the solid increases (Fig. 10(c)). This result suggests that most of liquid particles can be found within the inner layers of the hollow cylindrically shaped particle flow, while the solid particles are distributed on the outer wall of the torch. This might be a consequence of the strong temperature gradient towards lower temperatures when moving from position 1 to 4 in the cross-sectional view in Fig. 10(c).
Fig. 10. a: Extinction spectra recorded for different horizontal positions of the particle torch within the analysis beam path, as illustrated in (b). Peaks representing the solid fraction appear while moving from center to the edge of the particle stream. c: The values of parameter α representing the contribution of solid to the fitting signal as a function of beam position through the particles stream (see text). The red dashed line in right graph represents the temperature trend (schematically) with respect to horizontal positions.
5. Conclusions
A line-of-sight-attenuation (LOSA) technique has been demonstrated to obtain qualitative in situ information upon the amount of the liquid- and solid-phase fraction of silicon nanoparticles synthesized in a plasma flow reactor. The method exploits the distinct optical absorption properties of liquid and solid silicon nanoparticles. This knowledge helps to elucidate the overall gas-phase synthesis process, which can be used to tune the process parameters towards production of phase-selected material for different operating conditions, e.g., gas inlet flow rate in the plasma region, total pressure and microwave power input. The solid particle phase can be identified by additional peaks in the extinction spectra in the near-UV and VIS range (250–550 nm) representing morphology-dependent resonances, providing the means to distinguish against the liquid fraction represented by the underlying monotonous decay of the spectral intensity towards longer wavelengths.
For the majority of operating conditions, particles from both phases were detected in the line-of-sight probe volume. The solid-to-liquid phase ratio at a selected position in the particle flow depends on the local gas-phase temperature, with lower temperatures corresponding to a larger fraction of solid nanoparticles. This was validated by recording the spectral emission of incandescing particles and determining an effective pyrometric temperature using a spectroscopic model derived from the radiative transfer equation.
In an additional optical cell downstream of the reactor where particles have cooled down below the melting point, spectra from the solid phase were recorded exclusively. In addition, it was observed that the percentage of solid increases as one moves from the center of the particle stream to the outer edge because of the temperature gradient towards the cold surrounding coflow. For a given flow rate (i.e., residence time) particle solidification shifts further downstream due to higher gas-phase temperature, such that in the line-of-sight analysis beam, most particles are in the liquid phase; this was validated by simulating the extinction spectra with a combined spectrum obtained by adding individual spectra of 100% solid and 100% liquid in different proportions.
Although the current work describes the distribution qualitatively, there is a potential for quantitative analyses by building a model which will include the optical properties of both liquid and solid Si. This will then enable the LOSA diagnostics to validate the optical properties of nanoparticles with both phases in the line-of-sight. This will then also allow us to investigate whether there are combinations of particle phase, temperature, and particle-size distribution that might lead to ambiguous results in the evaluation. The obtained optical properties (i.e., complex refractive index) can then be incorporated into spectroscopic models needed for other particle diagnostics methods, such as laser-induced incandescence (LII) for the determination of silicon nanoparticle size and volume fraction [24]. Future LOSA/LII experiments in the plasma reactor are directed towards determining optical properties of Si/Ge mixed-phase nanoparticle synthesis for later size and volume fraction measurements.
Funding
Deutsche Forschungsgemeinschaft (222540104, 262219004).
Acknowledgements
Funding by the German Research Foundation (DFG) is acknowledged through the projects No. 222540104 and 262219004. KD acknowledges funding through DFG’s Mercator Fellowship (Project No. 262219004)
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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