Aerosol detection efficiency in inductively coupled plasma mass spectrometry

Spectrochimica Acta Part B 119 (2016) 50–64

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Aerosol detection efficiency in inductively coupled plasma mass spectrometry☆ Joshua A. Hubbard ⁎, Joseph A. Zigmond Sandia National Laboratories, Albuquerque, New Mexico, USA

a r t i c l e

i n f o

Article history: Received 6 October 2015 Received in revised form 1 February 2016 Accepted 25 February 2016 Available online 2 March 2016 Keywords: Aerosol Inductively coupled plasma mass spectroscopy Particle size classification Refractory Volatile Heat transfer Mass transfer Evaporation Boiling Nanoparticles

a b s t r a c t An electrostatic size classification technique was used to segregate particles of known composition prior to being injected into an inductively coupled plasma mass spectrometer (ICP-MS). Size-segregated particles were counted with a condensation nuclei counter as well as sampled with an ICP-MS. By injecting particles of known size, composition, and aerosol concentration into the ICP-MS, efficiencies of the order of magnitude aerosol detection were calculated, and the particle size dependencies for volatile and refractory species were quantified. Similar to laser ablation ICP-MS, aerosol detection efficiency was defined as the rate at which atoms were detected in the ICP-MS normalized by the rate at which atoms were injected in the form of particles. This method adds valuable insight into the development of technologies like laser ablation ICP-MS where aerosol particles (of relatively unknown size and gas concentration) are generated during ablation and then transported into the plasma of an ICP-MS. In this study, we characterized aerosol detection efficiencies of volatile species gold and silver along with refractory species aluminum oxide, cerium oxide, and yttrium oxide. Aerosols were generated with electrical mobility diameters ranging from 100 to 1000 nm. In general, it was observed that refractory species had lower aerosol detection efficiencies than volatile species, and there were strong dependencies on particle size and plasma torch residence time. Volatile species showed a distinct transition point at which aerosol detection efficiency began decreasing with increasing particle size. This critical diameter indicated the largest particle size for which complete particle detection should be expected and agreed with theories published in other works. Aerosol detection efficiencies also displayed power law dependencies on particle size. Aerosol detection efficiencies ranged from 10−5 to 10−11. Free molecular heat and mass transfer theory was applied, but evaporative phenomena were not sufficient to explain the dependence of aerosol detection on particle diameter. Additional work is needed to correlate experimental data with theory for metal-oxides where thermodynamic property data are sparse relative to pure elements. Lastly, when matrix effects and the diffusion of ions inside the plasma were considered, mass loading was concluded to have had an effect on the dependence of detection efficiency on particle diameter. © 2016 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Inductively coupled plasma mass spectrometry Inductively coupled plasmas have long been used in analytical chemistry to excite chemical species for atomic emission spectrometry and mass spectrometry. This study focuses on thermal processes, which occur inside the inductively coupled plasma mass spectrometer. For this reason, a few basic characteristics of the ICP, and the plasma environment, lend to better understanding of aerosol-plasma interactions and experimental results obtained in this study. ☆ Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. ⁎ Corresponding author. E-mail address: [email protected] (J.A. Hubbard).

http://dx.doi.org/10.1016/j.sab.2016.02.015 0584-8547/© 2016 Elsevier B.V. All rights reserved.

Radio frequency (RF) power is coupled into the outer annulus of the plasma. Heat is conducted from the outer annulus in to the central aerosol flow where analyte and matrix species are atomized (broken down into atomic constituents) and ionized through collisions with electrons. The heavy particle temperature, or plasma gas temperature (Tg), is associated with atomization. The electron temperature is associated with ionization [1]. Most analyte elements are easily ionized in the normal analytical zone of the plasma torch [2]. As particles move along the axis of the torch, there is an increase in temperature between the initial radiation zone, at temperatures on the order of 1000 Kelvin (K), and the normal analytical zone [3]. Plasma temperature then decreases as the axial position transitions from the normal analytical zone to the plasma tail [4]. The plasma temperature along the axis of the torch, in the central aerosol flow, is cooler than in the outer annulus where RF power is coupled into the plasma. The plasma velocity in the central channel ranges from 15 to 25 m/s [5,6]. The gas-kinetic temperature decreases with increasing central gas flow rates [7] where the location of the initial

J.A. Hubbard, J.A. Zigmond / Spectrochimica Acta Part B 119 (2016) 50–64

hot region moves downstream along the axis even though the central velocity remains relatively unchanged [8,9]. Gas flowing through the torch is assumed to be a neutral plasma stream with an approximate gas kinetic temperature of 5000–6000 K in the normal analytical zone [9–11]. Argon ion densities are on the order of 1015 ions/cm3 at these temperatures [12]. The Saha equation has been applied to show that less than approximately 0.1% of argon gas is ionized in the ICP, which suggests the plasma can be treated as a hot gas to good approximation [13]. The effect of central gas flow rate on plasma gas kinetic temperature has been observed where the central flow was 1000 K cooler when the aerosol flow rate was increased from 0.25 to 0.5 L/min [14]. Local thermodynamic equilibrium is often assumed in both experimental and computational studies. Local thermal equilibrium (LTE) is defined as the condition at which electron temperature equals the gas kinetic temperature [15]. Deviations from LTE can occur due to differences in conductivity for gas particles and electrons. Non-LTE conditions can occur due to the presence of interferents and other conditions leading to local gas temperatures as much as 2000 K less than the local electron temperatures. LTE conditions are often assumed for atmospheric pressure plasmas which are the focus of this work. In actuality, both non-LTE and LTE conditions occur inside an ICP torch where the central core more closely satisfies the definition of LTE conditions and the peripheral does not. ICP plasma property modeling capabilities of electron density, electron temperature, and gas temperature are within 10–20% of experimentally observed values [16]. After analytes are atomized and ionized, ions undergo supersonic expansion as they are transported through the sampler cone where the pressure drops from atmospheric pressure to vacuum. ICP-MS signals result from analyte ions close to the center of the torch (within a millimeter) where the sampler cone draws gases from the torch [17]. The pressure is again reduced to lower vacuum through the skimmer section where ions are focused with ion optics and directed to the mass analyzer and ion detector. The total gas flow through skimmer is approximately 1% of the flow through the sampler, and the overall transfer efficiency from skimmer to detector is 0.02–0.2% [18]. Typical overall detection efficiencies of ICP-MS range from 10−5 to 10−6 [8] and result from losses in the torch, sampler, skimmer, and transport from the skimmer to the ion detector. In many ICP applications, sample materials are digested in acids and then sprayed into the ICP torch using carefully designed nebulizers to limit the size of droplets. In other applications, it is preferable to avoid acid digestion since it can be hazardous, a source of contamination, result in the loss of volatile materials, and introduces the potential for incomplete dissolution. Digestion also increases the time required for analysis, which is undesirable in some applications. Slurry atomization and laser ablation are two methods which have been used to characterize solid materials without digestion. In past works, the effect of droplets and solid particles on ICPs has been noted. Substantial fluctuations in signal intensities have been observed with time periods on the order of 10 μs. These fluctuations were attributed to incompletely desolvated droplets or incompletely vaporized particles [17]. Droplet desolvation refers to the process of evaporating aqueous components of the analyte droplet where the solute remains and is detected. Eliminating hydrogen and oxygen from the plasma also reduces polyatomic interferences where analytes form hydrides and oxides [19,20]. Hartley et al. utilized a thermoelectric cooler to desolvate slurries prior to injection into ICP-MS [19]. They attributed enhanced transport and atomization efficiencies to the removal of water jackets surrounding solid particles prior to entry into the plasma. RF power coupling into the plasma can also be affected by plasma impedance changes due to the presence of droplets [21]. Energy sinking required for desolvation can result in the reduction in ionization temperatures by approximately 500 K [4]. Others have found that incompletely desolvated droplets and vaporizing particles cool the plasma by 1000 K or more within 1–2 mm of the particle or droplet [22]. This cooling corresponds to 10-fold decrease in electron number density,

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which subsequently affects the number of analyte atoms that are ionized in the plasma [22]. From early works with slurry atomization, it was suggested that solid particles must be less than approximately 3 μm in diameter to be atomized efficiently [2]. Later works with particles of varying size measured atomization efficiencies of 20–25% for 10 μm silica particles and 60–70% for 5 μm particles [23]. When slurries were desolvated, it was found that 100% atomization efficiencies were possible for 8 μm solid particles, whereas a shift down to 4 μm particles was observed when plasma energy was diverted to the boiling off of the water jacket [19]. A significant body of literature exists aimed at understanding the fundamental interactions between aerosol droplets and solid particles and inductively coupled plasmas. 1.2. Laser ablation inductively coupled plasma mass spectroscopy (LA-ICP-MS) LA-ICP-MS is simply, or not so simply, coupling a laser ablation cell onto the front end of an ICP-MS to analyze solid samples directly by creating aerosols with laser ablation. This enables direct characterization of solid surfaces without sample digestion or wet chemistry. Spatial inhomogeneity of solid samples can also be characterized and material characterization can be performed more rapidly using LA-ICP-MS. Although promising, sample fractionation (preferential sampling and detection of certain elements) can occur and is difficult to mitigate without matrix-matched certified reference materials. This is partially due to complex aerosol generation processes, which occur during laser ablation and complex aerosol-plasma interactions which occur in the ICP. It has been recognized that laser ablation and ICP-MS technologies must be optimized for use with one another [24]. In this section, we present the complexity of laser ablation generated aerosols as motivation for studying particle-plasma interactions in ICP. Elemental fractionation represents a challenge for LA-ICP-MS [25]. There are numerous parameters affecting fractionation and the combination of those parameters is complex and difficult to model [26]. One common approach used to mitigate these complex effects is the use of external calibration methods via matrix-matched standards. Others have noted the need for internal calibration standards since ablation rates are material dependent and mass loading effects can be significant in some cases [27]. One suggestion for calibration, when matrix matched standards are not available, has been to co-inject calibration aerosols of known size and composition in parallel to the laser ablation aerosol [28]. Some studies have attempted this calibration technique using optical particle counters but OPCs are limited to particles larger than approximately 100 nm in size [29–31]. Complex thermal processes and aerosol transport that occur during the ablation step make it difficult to know, a priori, particle size distributions and compositions of aerosol particles aspirated by the ICP-MS. Subsequent thermal and transport processes in the ICP then govern detection efficiencies in ICP-MS by affecting the breakdown of aerosol particles into constituent atoms, the process of ionization, and transport through the sampler and skimmer. Again, the focus of Section 1.2 is to review aerosol processes, which occur during laser ablation to motivate additional study of how those particles are then processed inside the ICP. The effects of particle and plasma properties on ICP-MS detection efficiencies will be explored in greater detail in Sections 1.3 through 1.6. Aerosol generation processes have been characterized for metal and glass solid samples [32,33]. Glaus et al. showed that enhancements to LA-ICP-MS were achieved by moving from infrared laser wavelengths to deep ultraviolet wavelengths and reducing laser pulse durations from nanoseconds to femtoseconds [34]. These two modifications in laser characteristics lead to narrower particle size distributions which aid in efficient atomization in ICP-MS. There is a transition between thermal heating of the solid above a wavelength of 250 nm to breaking chemical bonds at wavelengths below 200 nm [27]. Thermal diffusion in the solid material is significant for picosecond and nanosecond laser

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J.A. Hubbard, J.A. Zigmond / Spectrochimica Acta Part B 119 (2016) 50–64

pulses [34]. When nanosecond laser ablation pulses are employed, particles grow from gas-to-particle conversion followed by agglomeration [34]. For femtosecond pulses, phase explosion has been described where a mixture of droplets and vapor is ejected from the ablation site [34]. Femtosecond ablation aerosols show less matrix dependence but larger spherical particles are enriched in refractory elements and nanoparticle agglomerates are enriched in volatile elements [34]. Ablation aerosols generated from metallic samples are primarily affected by pulse duration whereas wavelength effects are more significant for non-metallic samples [35]. Mixed gases in the ablation cell (e.g., He, Ne, Ar) have been shown to affect particle formation at the site of laser ablation [30] and also affect subsequent transport efficiencies of particles to the ICP-MS [36]. The addition of helium as a carrier gas enhanced detection efficiencies by as much as a factor of five with respect to particles transported in Argon [37]. Kovacs et al. have also employed helium as carrier gas to enhance the transport efficiency of particles from the surface being ablated [38]. They attributed better performance to higher gas thermal conductivity and its influence on aerosol expansion, more efficient vapor transport away from surface, and desirable effects on plasma operation. Aerosol transport efficiencies from the laser ablation cell to the ICP-MS lie in the range of 75–95% [39,40]. Vapor deposition in transport tubes has also been observed and contributes to sample fractionation through the loss of volatile materials [36]. Overall detection efficiencies for LAICP-MS are on the order of 10−8 to 10−5 for silicate glasses, zircon, and silicon. One study demonstrated the effects of reduced pressure on vapor generation, nucleation, condensation, and agglomeration where these processes were affected by slower cooling of the vapor phase and longer condensation times [41]. These processes and aerosol characteristics make it challenging to use laser ablation generated aerosols to quantify ICP-MS aerosol detection efficiencies because the composition and size of aspirated aerosols are a subject of study. In some LA-ICP-MS studies, laser ablation aerosols have been size segregated prior to their aspiration into the ICP-MS. This enables the characterization of fractionation effects occurring upstream of the ICP (i.e., due to laser ablation). A centrifugal flow separator was used to show that incomplete evaporation occurred for silicate particles larger than 500 nm [42]. Other studies have concluded that refractory silicate particles above 150 nm in diameter were not efficiently vaporized in ICP-MS [35,43]. Differential mobility analyzers have also been used to size segregate aerosols upstream of the ICP where particles are separated by their electrical mobility diameters [25–27,29,30,35,36,41,43,44]. Others have used electrothermal heating to augment laser ablation aerosol particle size and composition prior to ICP-MS to reduce deleterious effects. Intermediate measurements of aerosol properties are required to develop the coupling between laser ablation and ICP-MS. 1.3. Mixed gas ICP Mixed gas plasmas are often employed in ICPs to obtain some desired analytical effect such as the reduction of polyatomic interferences. There have been numerous fundamental studies on the effects of mixed gases on ICP temperatures. They are pertinent to this study as we added nitrogen gas to the central aerosol flow of argon during experiments. Sesi et al. studied the addition of nitrogen, hydrogen, and helium to an argon plasma [45]. In the central channel, nitrogen gas caused this region of the plasma to grow in width and contract in height. Sesi et al. attributed the changes in plasma properties to the higher heat capacity of nitrogen where nitrogen acted as an energy sink. The majority of RF power is coupled to the outer region and then transported to central region through diffusion and gas collisions. The addition of nitrogen to the central region caused a depression in gas kinetic temperature which was attributed to the energy sink effect. The effects of hydrogen were also studied [45]. Increased gas kinetic temperatures (2000 K) were observed when hydrogen was added to the central flow at volumetric concentrations on the order of 15%. This is often attributed to

the thermal conductivity of hydrogen, which is higher than argon. Similar effects were measured for helium gas added to the central gas flow: there was an increase of 1500 K in the gas kinetic temperature with the addition of 17% v/v helium/argon. The addition of helium gas can also enhance particle vaporization rates through secondary effects like vapor diffusivity [43]. Commercially available ICP-MSs are designed for use with pure argon. Extinction of the plasma has been observed when the impedance matching network of the RF generator and argon gas is altered in the presence of mixed gases, particles, or droplets. Nitrogen entrainment from ambient air, or injection of nitric acid, are common sources of nitrogen in argon ICPs. The maximum nitrogen concentration was found to be 5% v/v before torch extinction occurred in one study [46]. As opposed to commercially available ICP-MS instruments, aerosol measurement instruments operate optimally with air and nitrogen gases. The addition of air or nitrogen to the plasma flow can make the plasma unstable. The use of argon in electrostatic aerosol instruments affects electrical breakdown strengths and aerodynamic particle behavior due to differences in gas density and viscosity. For these reasons, it may be necessary to use gas exchange devices to obtain the desired results. Okada et al. employed argon gas inside a differential mobility analyzer to size classify particles in the 5–40 nm size range, which were subsequently injected into an ICP-MS [47]. In this study, we were unable to satisfactorily operate aerosol instruments using argon as the aerosol carrier gas. We therefore generated aerosols in nitrogen and mixed the nitrogen with argon prior to injection in the central flow of the ICP. Others have employed gas exchange techniques to optimize use of specific instruments. Nishiguchi et al. used a gas converter apparatus consisting of concentric tubes to exchange nitrogen for argon; the inner tube was porous and permitted the diffusional exchange of gas ions but did not permit the loss of particles [48]. Kovacs et al. also used a gas exchange device to replace air with argon before particle injection into the ICP-MS thereby enhancing ICP-MS performance through a reduction in oxide formation and polyatomic ion formation [38]. Myojo et al. used a similar approach, exchanging air for argon, but used the sheath and aerosol flows inside a Kanawa-type differential mobility analyzer to dilute the air with argon [49]. 1.4. Matrix effects Matrix elements have complicated effects on sample analysis through the suppression and enhancement of specific analyte ions [50]. These matrix effects are not observed in optical emission spectroscopy and are therefore attributed to the transport of ions through the sampler and skimmer of the ICP-MS [51,52]. These effects can be significant depending on the mass load of aerosol particulate and will therefore be mentioned here and used to analyze experimental results obtained in this study. As the neutral argon plasma is transported through the skimmer, free electrons are lost and the remaining stream of analyte ions possesses a net positive electrostatic charge. A volume of like charges creates its own electric field governed by the Poisson equation for electrostatics. The electric field then drives positively charged ions away from the axis of the ion beam and away from the region sampled by the mass analyzer and detector. This is called the space charge effect. The space charge effect is not governed by the ratio of matrix to analyte ions, rather the total concentration of matrix ions, which dictates the strength of electrostatic repulsion [53]. High mass ions (analyte or matrix) are deflected off-axis to a lesser degree than light ions due to the effect of ion kinetic energy. Thus, heavier elements enhance space charge effects since they remain on axis for longer periods [54]. A matrix concentration of 1% has been noted to cause substantial suppression where other reports have been made of 10–20% losses in analyte intensity at 0.1% matrix concentrations [2,55]. The combination of light analytes with heavy matrix elements represents the most significant space charge loss where sample dilution and plasma operating

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conditions can be used to mitigate these effects [14,18,56]. Closely matched internal standards are needed to correct analyte intensities in the presence of background matrix [57,58]. It has also been suggested that materials with low melting points also result in more severe matrix effects and that sample dilution can be used as a mitigation strategy [59]. 1.5. Diffusion and dispersion The matrix effect refers to electrostatic repulsion that occurs downstream of the sampling and skimmer cones. In the vacuum region of the ICP, diffusion is negligible compared to gas kinetics and electrostatics [60]. However, diffusion and dispersion in the ICP torch can also be responsible for the suppression of analyte intensities observed with ICP-MS. If ions are dispersed from the axis of the ICP, they will not be sampled efficiently since only centrally located ions are transported through the vacuum interface. Diffusion and dispersion thus represent a potential mass bias and will be discussed and included in the analysis of experimental data obtained in this study. Ion kinetic energy is proportional to atomic mass [18,61]. Gas kinetic temperature affects diffusion and dispersion of ions inside the ICP as well as the kinetic energy of ions transported through the sampler cone. Lighter elements have been found in relatively higher concentrations in the outer regions of the plasma, whereas heavy elements have higher concentrations along the central axis of the torch [1,18,56,62]. Diffusion coefficients have been measured and calculated in the range of 1–100 cm2/s where time resolved analyte intensities show the diffusion of a vapor clouds resulting from the desolvation of individual droplets [6]. Higher gas-kinetic temperatures and concentration gradients result in greater diffusion off the central axis of the ICP, thereby making the sampling depth (positioning of sampler cone at the point of complete vaporization) a critical parameter for optimal ion sampling [3,62–64]. 1.6. Heat and mass transfer The heat and mass transfer rates between particles and plasma inside the ICP is of critical importance to understanding detection efficiencies. A number of formative studies were conducted regarding heat and mass transfer to aerosol particles inside plasmas where the particle sizes typically ranged from 10 to 100 μm in particle diameter [65–75]. In these studies, the authors found that continuum heat and mass transfer correlations needed to be corrected for non-continuum effects inside the plasma. More recently, a number of studies have characterized aerosol processing inside plasmas. The commercially available software tool ANSYS Fluent has been used to model particle-plasma coupling and particle evaporation [76]. Conduction heat transfer within the particle was not modeled, and it was assumed that the particle reaches its melting point, the liquid phase fraction increases, and then the particle increases in temperature once it has completely melted giving rise to evaporative mass transfer. Aerosol processing in ICP has also been modeled with mixed-gas effects, and it was shown that higher gas temperatures were possible when helium was used as the injection medium thus resulting in the complete evaporation of larger droplets [77]. The vaporization of aerosol particles in ICP-OES and ICP-MS has been studied with noted differences in analyte detection efficiencies for pure metals and metal-oxides [63]. Fundamentally, the process of heat and mass transfer can be separated into categories of large and small particles. Unfortunately, developing absolute criteria for what constitutes large and small particles is challenging [78]. Sensible heat is transferred to an aerosol particle which results in an increase in particle temperature above the melting point of the material. If the process is heat transfer limited, and the boiling point of the material is higher than the gas kinetic temperature of the plasma, the particle will stay near its melting point and evaporate [78]. If the process is mass transfer limited, sensible heat will continue to be transferred to the particle until it reaches its boiling point where

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latent heat exchange (energy transfer from the particle) will then balance heat transfer to the particle. Thermodynamic properties of the material (e.g., enthalpy of vaporization) and plasma properties (e.g., gas kinetic temperature) dictate if the vaporization process is heat transfer limited or mass transfer limited. In the case of boiling, particles are unlikely to approach the plasma temperature but rather remain near the boiling point and exchange latent heat with the surroundings through mass transfer [62]. In the heat transfer limited regime, the square of the particle diameter is expected to be linearly related to time [79]. In the mass transfer limited regime, the particle diameter is expected to be linearly related to time [79]. It has also been suggested that the effect of a large number of small particles will be greater than a small number of large particles [19]. 2. Experiment Aerosols of known composition were generated in ultra-high purity nitrogen. The test apparatus is shown in Fig. 1. For good measure, the nitrogen was passed through carbon and HEPA capsule filters to ensure that no volatile gases or particulates were present. The nitrogen flow was regulated by a mass flow controller (Alicat MCRW), passed through an in-line bipolar gas ionizer (Simco-Ion Ioncell), and fed into an aerosol generation chamber constructed from a stainless steel tube 0.46 meters (m) in length and 0.2 m in diameter with two end flanges. A 180 kHz ultrasonic spray nozzle (Sonotek) was inserted into the top flange with an ISO-KF bulkhead fitting so the spray went directly into the chamber. The aerosol generation chamber was wrapped in a blanket heater (Briskheat 12 in. × 24 in.), which was controlled by an Omega temperature controller (CSI8DH). A T-type thermocouple was used to measure the gas temperature inside the chamber. The temperature was maintained at 43.3 °C (110 °F) to enhance droplet evaporation for low gas flows. Calculations were performed to ensure the nitrogen gas would accommodate the amount of water injected into the chamber without saturating, thereby desolvating droplets effectively upstream of the ICP-MS. Test powders were placed in 50 mL centrifuge tubes, mixed with water, sonicated, and then drawn into a sonic syringe (Sonotek) capable of keeping heavy particles suspended over many hours of testing. A syringe pump (Cole Parmer) was used to deliver a constant rate of 25 μL/min of solution to the Sonotek Nozzle. The aerosol was then passed through two desiccant diffusion driers (Topas DDU-570) to remove water vapor from the aerosol stream. From there, the dry aerosol was fed into an Electrostatic Classifier (TSI 3080 with 3088 advanced aerosol neutralizer and 3081 long DMA) to size segregate the particles. Size-segregated particles were then either fed into (1) a Condensation Particle Counter (TSI Inc. 3787) to measure particle concentration (#/ cm3 of N2) or (2) into a Perkin-Elmer Elan DRC II Inductively Coupled Plasma Mass Spectrometer. The ICP-MS injector was modified such that it could be connected to the outlet of the Electrostatic Classifier using 6 millimeter tubing. Initial attempts were made to operate the Electrostatic Classifier and Condensation Particle Counter with argon. These attempts were not successful, and for this reason, we generated aerosols into nitrogen with flow rates ranging from 0.1 to 0.25 liters per minute (lpm). After electrostatic size segregation, the aerosol stream was mixed with argon gas flowing at rates between 1.0 and 1.5 lpm. These argon flow rates were needed to keep the argon plasma stable with the presence of nitrogen. The introduction of nitrogen was necessary to perform classification with the Electrostatic Classifier and Condensation Particle Counter. Two nitrogen flows (QN2) were used during experiments, 0.1 lpm (low flow) and 0.25 lpm (high flow). The Electrostatic Classifier sheath:aerosol flow rate ratios for the low and high flow conditions were 10:1 and 7.2:1, respectively. Low sheath flow rates were required to extend the working range of the classifier up to 1000 nanometers in electrical mobility diameter. At low sheath:aerosol flow rate ratios (b5:1), the performance of the classifier is less optimal and the size

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Fig. 1. Experimental test apparatus used to generate aerosols of known size and composition, measure the aerosol gas concentration, and inject the aerosol directly into an ICP-MS.

classification is more broad than at a ratio of 10:1 [80]. The aerosol flow rate of the Condensation Particle Counter was adjusted to the low and high flow settings of 0.1 and 0.25 lpm using a DryCal gas flow calibrator (Mesa Labs). The two instruments, classifier and CPC, were operated as a scanning mobility particle sizer (SMPS), where the classifier voltage was ramped over time to give measurements of aerosol concentration from 100 to 1000 nanometers in electrical mobility diameter over a time period of 300 s. When classified and injected directly into the ICP-MS, the same 300 s ramp was used to deliver a stream of size-segregated particles to the ICP-MS over time. Thus, the instantaneous sample time for each ICP-MS measurement was directly correlated to particle size. ICP-MS flows were as follows: (1) argon nebulizer flow (premixed with the aerosol) of 1.5 lpm for the high flow condition and 1.0 lpm for the low flow condition, (2) argon auxiliary flow of 1.2 lpm, and (3) argon plasma flow of 15 lpm. The torch power was kept constant at 1400 W. The argon torch operated stably with these gas flows. ICP-MS software was used to setup measurement methods for each of the materials analyzed. Along with the analyte of interest, its most abundant oxidized forms and isotopes (e.g., 107Ag and 109Ag) were monitored. The argon dimer and water were also used as monitors for the performance of the ICP-MS. When switching from one material to the next, e.g., Ag to Au, the aerosol generation chamber was purged with argon at a rate of 10 lpm for 8–12 h to ensure that no aerosol particles were carried over from one experiment to the next. In addition to the oxide forms of the analyte of interest, the previous analyte of interest (last test material) was monitored to ensure there was no residual aerosol in the test system. Operational settings for the aerosol instruments and ICP-MS instrument are given below for the high and low flow test conditions (Table 1).

Five powders were selected to represent a range of volatile to refractory behavior inside the plasma: silver (Ag), gold (Au), aluminum oxide (Al2O3), cerium oxide (CeO2), and yttrium oxide (Y2O3). The supplier and the chemical identifier for each powder are given in Table 2 along with the minimum and maximum physical particle sizes provided by the manufacturer. For each material, molecular weight (MW), material density (ρm), melting point temperature (Tmp), boiling point temperature (Tbp), specific heat capacity (Cp), and thermal diffusivity (α) are given in Table 3. Silver and gold have relatively low melting points and thermal heat capacities with respect to the refractory species. We hypothesized that the aerosol detection efficiency would be higher for these two materials and lower for the refractory species. Scanning electron microscope images were also taken for each of the powders. For the SEM samples to be most representative of the aerosolized materials, the suspension sprayed into the chamber was first sonicated in a 50 mL centrifuge tube. A small drop of each solution was then placed on a separate electron microscopy stub for imaging. SEM images are shown in Fig. 2. In this study, particles were separated by their electrical mobility diameters (dm) in the TSI Electrostatic Classifier. The electrical mobility diameter is related to the volume equivalent diameter (dve) through the dynamic shape factor (χ), which is often used to characterize the aerodynamic drag on a non-spherical particle with respect to its volume equivalent sphere. When calculating particle volume and particle mass from electrical mobility measurements, corrections need to be applied to dm to account for non-spherical shape. Additional measurement techniques would be required to obtain accurate shape factors, but SEM images suggest particle morphologies do not differ substantially from particles that have been characterized in the literature. Volume shape

Table 1 Aerosol and ICP-MS instrument settings for the high and low flow test conditions.

Table 2 List of powders, manufacturer information, and manufacturer specified minimum and maximum physical particle sizes

Test condition Instrument setting

Unit

High N2 flow

Low N2 flow

EC sheath flow EC aerosol flow Sheath:aerosol flow ratio ICP-MS Ar nebulizer flow ICP-MS Ar auxiliary flow ICP-MS Ar plasma flow ICP-MS Ar torch power

(lpm) (lpm) (-) (lpm) (lpm) (lpm) (W)

1.8 0.25 7.2 1.5 1.2 15 1400

1 0.1 10 1 1.2 15 1400

Name

Symbol

Supplier

Purity

Model

Min. size

Max. size

(–)

(–)

(–)

(%)

(–)

(μm)

(μm)

Silver

Ag

99.95

47MR-01C

0.1

0.5

Aluminum oxide Gold Cerium oxide Yttrium oxide

Al₂O₃ Au CeO₂ Y2O3

Advanced materials Skyspring Alfa Aesar Skyspring Skyspring

99.99 99.96 99.9 99.995

1321DL 44636 2113CG 8211CG

0.3 0.5 0.1 0.5

0.8 0.8 1.0 1.0

J.A. Hubbard, J.A. Zigmond / Spectrochimica Acta Part B 119 (2016) 50–64 Table 3 Molecular weight (MW), material density (ρm), melting point temperature (Tmp), boiling point temperature (Tbp), specific heat capacity (Cp), thermal conductivity (kp), and thermal diffusivity (αp) for test materials. Name

MW

ρm

Tmp 3

Tbp

Cp

kp

αp

(-)

(g/mol) (g/cm ) (°C)

(°C)

(J/g⋅K) (W/mK) (m2/s)

Silver Aluminum oxide Gold Cerium oxide Yttrium oxide

107.87 101.96 196.96 172.12 225.81

2162 2977 2970 3500 4300

0.24 0.88 0.13 0.45 0.45

10.49 3.95 19.32 7.65 5.1

962 2072 1064 2400 2425

406 20 314 11 27

1.6E−04 5.8E−06 1.3E−04 3.1E−06 1.2E−05

the shape factors for particles in this study to be approximately 1.4, the midpoint between spherical particles and platelet like particles with dynamic shape factors approaching 1.8. We will use this correction to convert dm to dve. Estimates of uncertainty in dve will also incorporate particle shape since we cannot quantify, exactly, shape factors for each of the powders shown in Fig. 2. Shape factor corrections are employed extensively in aerosol measurement and are detailed in the literature [84,85]. The volume equivalent diameter is given by the following: dve ¼ dm

factors were measured for coal and quartz whose morphologies were non-spherical [81,82]. Dynamic shape factors of platelet like talc particles have also been calculated from measured data [83]. We estimate

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C c ðdve Þ 1 ; C c ðdm Þ χ

ð1Þ

where Cc is the particle slip correction factor. Stokes law for aerodynamic drag is corrected for non-continuum effects through Cc. Exact calculation

Fig. 2. Scanning electron microscope images of (a) silver (Ag), (b) gold (Au), (c) aluminum oxide (Al2O3), (d) cerium oxide (CeO2), and (e) yttrium oxide (Y2O3).

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of Cc will not be discussed here but is available in many standard references on aerosol transport and physics [86,87]. The slip correction factors, at 0.8 atmospheres of pressure (Albuquerque, New Mexico) and standard temperature, for 100 nm and 1000 nm particles are approximately 3.5 and 1.2, respectively. Eq. (1) was solved iteratively to determine the ratio of dve to dm, which is plotted in Fig. 3 against the electrical mobility diameter for shape factors of 1.0 and 1.4. The electrical mobility diameter is identical to the volume equivalent diameter for perfectly spherical particles. Fig. 3 shows the bias that dve is approximately 20–30% smaller than dm from 100 nm to 1000 nm. Again, this is an approximation to correct for non-spherical particle shape in the calculation of particle mass. We will use an uncertainty of 20% in dve to account for the assumption that all particles possess a shape factor of 1.4. In our assessment, this should adequately represent uncertainties which arise from non-spherical particle shape. In this study, we suspended test powders in water and then atomized the liquid to create aerosols. By spraying dilute solutions, we attempted to mitigate the occurrence of agglomerated particles. To confirm our assumption of non-agglomerated particles, particle density measurements could be made with proper instrumentation [88,89]. However, instrumentation required for these measurements was not available and we therefore assume that solid particles were not agglomerated primary particles with densities deviating significantly from the material density.

3. Results Fig. 4 shows the aerosol concentration (dW) in particles per cm3 of N2 as a function of volume equivalent diameter (dve) in nanometers. These specific data were generated with Ag aerosol. The median diameter was between 100 and 300 nanometers and agreed well with manufacturer provided data for the particle size distribution. Concentrations below 50 particles per cm3 were not included in data analysis or calculations of aerosol detection efficiencies due to higher uncertainty. ICP-MS data for ion intensity, nms (counts/second), are shown in Fig. 5. Only data for 107Ag and 107AgO are shown for illustration purposes. The most abundant oxide forms of analytes were monitored to check for incomplete vaporization, inefficient ionization, or polyatomic ion formation in the ICP. 109Ag and 107Ag are naturally occurring isotopes and occur at approximately equal abundances. Only 107Ag is shown in the figure, but 109Ag occurred with an equal ion intensity. At time zero, we began to ramp up aerosol particle size. This was controlled by the Electrostatic Classifier. The change in analyte intensity (107Ag

Fig. 3. Ratio of volume equivalent diameter (dve) and electrical mobility diameter (dm) as a function of dm for dynamic shape factors of 1.0, and 1.4 needed to calculate particle mass from electrical mobility diameter.

Fig. 4. Aerosol particle size distribution measured with Electrostatic Classifier and Condensation Particle Counter for Ag powder.

ions counted per second by the ion detector) is due to the following primary effects: (1) a change in aerosol-gas concentration and (2) a change in particle diameter. The analyte intensity (counts per second) is denoted as an atomic flow rate through the mass spectrometer, nms. Without both particle size and particle concentration measurements, it would not be possible to calculate the aerosol detection efficiency from ICPMS data. Coupling these two experimental capabilities is what makes this data unique. The relative standard deviation in 107Ag data was approximately 10%. 107AgO concentrations were on the order of 0.2–0.5% of the maximum 107Ag concentration. We suspect that these oxides formed inside the plasma with the trace amount of oxygen inside the argon and nitrogen. The 107AgO intensity was not dependent on time and the magnitude of this signal represents the background intensity. For the purposes of calculating aerosol detection efficiency, values of nms were only used if five times greater than background measurements (taken without aerosol being fed into the plasma).

Fig. 5. ICP-MS analyte intensity measurement (counts per second) as a function of equivalent volume diameter (dve) for 107Ag and 107AgO.

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The number of analyte atoms being fed into the ICP-MS per second was calculated from aerosol-gas concentration data. The aerosol atomic flow rate, na, was calculated according to the following equation: molanalyte π 1 3   N A  Q N2 na ¼ dW  ρm dve  6 MWcompound molcompound

ð2Þ

where NA was Avogadro's number. The aerosol detection efficiency, E, was then calculated according to the following equation: E¼

nms : na

ð3Þ

The method of Kline and McClintock (1949) was used to calculate uncertainties in calculated values of na and E. The major uncertainties propagating through the calculation are given below in Table 4. The uncertainty in na, Una, was calculated as h i1=2 ¼ 0:33: U na ¼ ð0:10Þ2 þ 9ð0:20Þ2 þ ð0:10Þ2 þ ð0:10Þ2

ð4Þ Fig. 6. Aerosol detection efficiency, E, as a function of equivalent volume diameter, dve for Ag aerosol.

The uncertainty in E, UE, was calculated as h i1=2 ¼ 0:35: U E ¼ ð0:33Þ2 þ ð0:10Þ2

ð5Þ

The uncertainty in E is mostly driven by uncertainties in particle diameter and particle concentration, which are used to calculate particle mass injected into the ICP-MS. Particle diameter is the most critical parameter since it is cubed in the calculation of aerosol atomic flow rates. Uncertainty in particle shape is reflected in these calculations. Aerosol concentration data in Fig. 4 and ICP-MS data in Fig. 5 were combined with Eqs. (2) and (3) and plotted in Fig. 6. The maximum aerosol detection efficiency was approximately 2 × 10−8. The aerosol detection efficiency then dropped between 250 nm and 1000 nm. We attribute this loss in aerosol detection efficiency to incomplete atomization (the breakdown of aerosol particles into atoms inside the plasma) due to particle size. Larger particles were not completely atomized in the plasma due to limited residence times and kinetically controlled heat and mass transfer rates. Below a certain size, e.g., 250 nm, aerosol detection efficiency should theoretically remain constant if all other factors remain constant and particles are completely atomized. Secondary effects like atom and ion diffusion in the plasma will be considered below. The logarithm of aerosol detection efficiency was plotted against the logarithm of particle size and then fitted with a piecewise function to represent the onset of particle size dependence at a critical particle diameter. We assumed the aerosol detection efficiency was constant below some critical value of particle diameter (dp,c). After the critical diameter, we assumed the aerosol detection efficiency decreased with particle size according to a power law function in agreement with

Table 4 Primary measurement uncertainties propagating through the calculation for aerosol detection efficiency E Uncertainty Parameter

(%)

dW Q dve ρm nms

10 10 20 10 10

experimental data. The piecewise fitting function was specified as follows: log10 ðEÞ ¼ a

for

log10 ðdve Þb ¼ k

ð6Þ

and log10 ðEÞ ¼

a−b log10 ðdve Þ þ b k

for

log10 ðdve ÞNk:

ð7Þ

In Eqs. (6) and (7), a, b, and k, are constants determined from curve fitting. The constant k was used to determine the critical diameter, dp,c = 10k. Taking the inverse logarithm of Eqs. (6) and (7) gives the following equations for aerosol detection efficiency: E ¼ 10a

for

dve b ¼ 10k

ð8Þ

and, E ¼ 10b dve

m

for

dve N10k

ð9Þ

where m is the functional dependence of detection efficiency on particle size, m¼

a−b : k

ð10Þ

Fig. 7 through Fig. 11 show the logarithm of aerosol detection efficiency as a function of the logarithm of volume equivalent diameter. High and low flow conditions are shown for silver, gold, aluminum oxide, yttrium oxide, and cerium oxide. The low flow condition for cerium oxide was not obtained due to plasma instability for that specific set of experimental parameters. Each experiment was performed in triplicate and all data are shown in the figures. Confidence interval bounds on curve fitting parameters were used to calculate the mean critical particle diameter, dp,c, mean slope, m, and associated uncertainties. Values are given in Table 5. Figs. 7 and 8 show calculated data for silver and gold, respectively. The more volatile species, silver and gold, had critical particle diameters ranging from 200 nm to 300 nm, whereas critical particle diameters were not observed for metal-oxides. We attributed larger critical

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Fig. 7. Log10(aerosol detection efficiency) vs. Log10(particle diameter) for silver aerosol particles.

Fig. 8. Log10(aerosol detection efficiency) vs. Log10(particle diameter) for gold aerosol particles.

particle diameters to complete particle vaporization occurring for larger particles which delayed the onset of particle size dependent atomization behavior. Data for Al2O3, Y2O3, and CeO2 are shown in Figs. 9, 10, and 11, respectively. The refractory particles did not show clear signs of a transition regime between complete atomization and size dependent vaporization (dp,c b 100 nm). If this transition occurs, it is likely to occur for particles smaller than those characterized in this study. Aerosol concentrations were low for particle diameters less than 300 nm for Al2O3 at 0.10 lpm N2. The same was true for Y2O3. Other powders could be used to increase aerosol concentrations at smaller particle sizes and extend the range over which aerosol detection efficiency can be calculated. The magnitude of m = dlog10(E)/dlog10(dve) reveals differences between volatile and refractory species and high and low flow conditions (i.e., residence time). Data for Ag and Au are somewhat inconclusive in this regard. The decreasing portion of the curve should be extended to larger particle sizes (1–5 μm) to more clearly identify the dependence of aerosol detection efficiency on particle size. Uncertainty in m made

dependence of detection efficiency on particle size. Those effects will be discussed separately below.

−2

4. Discussion 4.1. Mixed gas plasma effects Other works have shown that the addition of nitrogen to the central gas flow of the plasma torch results in depressions in gas kinetic temperature [45]. This would reduce the likelihood of complete particle vaporization in the plasma. For the materials tested here, analyte signals were observed for all tests, demonstrating that plasma temperatures were in excess of the material melting points (Tg N 2425 K for Y2O3) at the minimum. Oxide forms of each analyte (e.g., CeO2) were also monitored and signals elevated above the background were not observed. This shows that atoms liberated from the surface of particles were effectively ionized, which again shows plasma temperatures were sufficient

−3

and dve it difficult to conclude if there were well-defined dve regimes. Some data even suggested that the size dependence was −3

−4

higher than dve , e.g., dve . The effect of particle size on aerosol detection efficiency for oxides Y2O3 and Al2O3 was more significant (−3 N m N −5). In addition to particle surface area and volume, atomic dispersion in the ICP, and matrix effects, could also affect the

Table 5 Particle composition, nitrogen aerosol generation flow rate (high or low), critical particle diameter (dp,c), and slope (m) of the log10(E) vs. log10(dve) curve Particle

N2 flow

dp,c

m

Composition

(lpm)

(nm)

(–)

Ag Ag Al2O3 Al2O3 Au Au CeO2 Y2O3 Y2O3

0.1 0.25 0.1 0.25 0.1 0.25 0.25 0.1 0.25

250 ± 10 210 ± 10 b100 b100 300 ± 40 220 ± 40 b100 b100 b100

−3.1 ± 0.2 −1.9 ± 0.2 −3.3 ± 0.4 −4.0 ± 0.1 −2.4 ± 0.9 −1.4 ± 0.6 −2.9 ± 0.1 −4.8 ± 0.2 −4.5 ± 0.1

Fig. 9. Log10(aerosol utilization efficiency) vs. Log10(particle diameter) for aluminum oxide aerosol particles.

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59

to viscous forces: ρg  U  dve : μg

Re ¼

ð12Þ

In Eq. (12), ρg and μg are the gas density and dynamic gas viscosity, respectively, and U is the relative velocity between the particle and fluid. Gas densities and viscosities for argon at high temperature were taken from Carpenter et al. [90] and Murphy et al. [91], respectively. For Re bb 1, the flow around the particle is considered viscous and Nu = 2. In this limiting case, the convective heat transfer coefficient is directly proportional to the thermal conductivity of the fluid and inversely related to particle diameter. As particle diameter approaches the mean free path of the gas, continuum fluid assumptions are no longer valid. There is a transition from continuum to free molecular physics regimes indicated by the dimensionless Knudsen number, Kn, Kn ¼

Fig. 10. Log10(aerosol detection efficiency) vs. Log10(particle diameter) for yttrium oxide aerosol particles.

to atomize and ionize a portion of the aerosol particles. Suppressions in gas kinetic temperatures may have occurred but did not eliminate atomization and ionization. It is difficult to determine the magnitude of temperature suppression without direct measurements of plasma gas kinetic temperature. 4.2. Heat transfer effects The ratio of convective and conductive heat transfer rates at the boundary of a particle is given by the Nusselt number, Nu,

Nu ¼

h  dve ; kg

ð11Þ

where h is the convective heat transfer coefficient and kg is the thermal conductivity of the surrounding fluid. Re is the particle Reynolds number. The particle Reynolds number gives a ratio of fluid inertial forces

2λg : dve

ð13Þ

In Eq. (13), λg is the mean free path of gas atoms or molecules. The mean free path was calculated according to the following relationship [92]: λg ¼

  μ g 2kB T g −0:5 ; ρg πmg

ð14Þ

where the Boltzmann constant is kB =1.381 ⋅ 10−23 J/K, and the gas molecule mass is mg = 6.634 ⋅ 10−26 kg for Argon. The average molecular speed, c, is given by c¼

 0:5 8kB T g : πmg

ð15Þ

Kennard [93] derived the heat transfer rate (q) to a particle in the free molecular regime (subscript fm),  2   dve P g c γ þ 1 T p −1 ; qfm ¼ απ 2 2 γ−1 T g

ð16Þ

where the accommodation coefficient, α, is assumed to be on the order of unity, γ is the specific heat capacity ratio taken to be a constant independent of temperature, γ = 1.667(argon), Pg is gas pressure (0.8 atm), and Tp is particle temperature. In the continuum regime (subscript c), the heat flux to the particle, qc, is given by qc ¼ 4π

    dve kg T p −T g : 2

ð17Þ

Fuchs [94] derived the ratio of actual heat flux, q, to the continuum heat flux, qc, as a function of Kn, and the free-molecular and continuum heat fluxes: q ¼ qc

Fig. 11. Log10(aerosol detection efficiency) vs. log(particle diameter) for cerium oxide aerosol particles.



1 q þ c 1 þ Kn qfm

−1

:

ð18Þ

Eq. (18) is valid over the entire range of Kn. A more detailed description of continuum-transition-free-molecular regime heat transfer can be found in the literature for laser-induced incandescence of aerosol particles [95]. The ratio q/qc is plotted against Kn in Fig. 12. The following values were assumed: Tp = 1000 K, Tg =5000 K, and k = 0.15 W/mK, where the thermal conductivity of argon can be taken from Devoto et al. [96] for Tg N 5000 K and Hoshino et al. [97] for Tg b 5000K. The crossover from the continuum regime to the transition regime occurs at Kn

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conclude that internal particle temperature gradients do not have a significant effect on particle atomization. This is not always the case (e.g., large particles), and others have accounted for internal temperature gradients in their numerical models of aerosol evaporation [99]. The Fourier number, Fop, gives the ratio of thermal diffusion to thermal storage within the interior of the particle: Fop ¼

Fig. 12. Ratio of actual heat transfer (q) to nanoparticle to heat transfer in the continuum regime (qc) as a function of particle Knudsen number (Kn). Mean free path of argon was calculated at 5000 K.

~ 0.01. The crossover from the transition regime to free molecular regime occurs at Kn ~10. The ratio q/qc is plotted against dve in Fig. 13. According to our analysis, the free molecular to transition regime crossover occurs at approximately 2.0 μm. All data collected here were in the free-molecular regime. The heat transfer rate to a 10 μm is approximately 50% of the continuum limit. Not until particle diameter reaches approximately 50–70 μm is the heat transfer rate 95% of the continuum limit. 4.3. Equilibrium temperature The particle Biot number, Bip, is given by Bip ¼

h  dve kp

ð19Þ

and gives the ratio of heat transfer resistances at the surface (convection) to the interior conduction resistance. If Bip ≤ 0.1, it is generally assumed that the interior of the particle is at uniform temperature. This is often called a lumped capacitance model [98]. For the particle materials and gas conditions in this study, 10−3 ≤ Bip ≤ 10−2. We thus

αp τ dve

2

:

ð20Þ

In Eq. (20), the particle thermal diffusivity, αp, is given by αp = kp/ ρpCp, where Cp is the particle thermal heat capacity. For Eq. (20), we will use the characteristic time, τ, of 1 ms, which is the approximate bulk torch velocity (~ 20 m/s) normalized by the length of torch in which particle atomization occurs (~ 0.0254 m). For the particle materials and gas conditions in this study, 103 ≤ Fop ≤ 105. We thereby conclude that the time over which particle atomization occurs is long with respect to the thermal equilibration time of the particle; particle temperature is not assumed to be transient but rather assumed to reach its equilibrium temperature very quickly. Under steady-state, equilibrium, evaporative conditions, the heat transfer to the particle is balanced by the energy carried away from the particle by mass transfer, mevap, and phase change: q ¼ mevap  hfg ;

ð21Þ

where hfg is the enthalpy of vaporization. Theoretical heat transfer rates for Au and Ag particles were calculated according to the methods outlined in Section 4.2. Only Au and Ag were considered here due to the complexity of calculating enthalpy of phase change, and the sparsity of vapor pressure data, for oxidized materials. Vapor pressure data for Au and Ag are also readily available [100]. Our analysis indicated that the particle temperature would need to exceed the boiling point of these materials, 2162 K and 2970 K for Ag and Au, respectively, for the heat transfer rate to be balanced by mass transfer and associated phase change. These temperatures are plausible even with the addition of N2 gas to the central gas flow. The influence of enthalpy of vaporization can be observed in other ICP-MS sample injection techniques where dissolved analyte atoms are injected in the form of dilute aqueous droplets. The relatively low heat of vaporization of water, with respect to silver and gold, results in the reduction of droplet temperatures below the boiling point of water [101]. 4.4. Evaporation In addition to the simple equilibrium condition assumed in Eq. (21), evaporative behavior can be modeled by the kinetic theory of gases. The particle diameter at arbitrary time t, dve(t), is given by the following equation for evaporation in the free-molecular regime [111]: dve ðt Þ−dve;0 ¼ −

1 cMP v t; 2 ρp RT p

ð22Þ

where Pv is the vapor pressure at the surface of the particle, dve,0, is the initial particle diameter, and R is the universal gas constant. The aerosol detection efficiency, E, is defined as the fraction of particle atomized, is then given by " #3  3 dve; f 1 cMP v τ 1 ¼ 1− 1− E ¼ 1− dve;0 2 ρp RT p dve;0 Fig. 13. Ratio of actual heat transfer (q) to nanoparticle to heat transfer in the continuum regime (qc) as a function of particle diameter. Mean free path of argon was calculated at 5000 K.

ð23Þ

where dve, f is the final particle diameter and τ is again a characteristic time scale.

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61

We then define a parameter, ψ¼

1 cMP v τ ; 2 ρp RT p

ð24Þ

such that Eq. (23) can be written more succinctly and utilized for data fitting operations,   ψ 3 E ¼ 1− 1− ; dve;0

ð25Þ

where only initial particle diameter is known a priori. Au and Ag data were fitted with Eq. (25) and replotted in Fig. 14 and Fig. 15, respectively. From Eqs. (23) and (25), one can see that 0 ≤ 1 − ψ/dve , 0 ≤ 1 due to limitations on dve , f/dve , 0. In this range of values, the size dependence of E varies from d0ve to d−1 ve . The symbols represent empirical data of the form of Eq. (7). The dashed lines represent curve fits with the form of Eq. (25). The dotted line was added to show a slope of − 1, or a functional dependence of d−1 ve . As can be seen in the figure, evaporative phenomena do not predict the functionality (e.g., E ~ d−3 ve ) observed in experimental data. Once again, we observe data trends that suggest purely evaporative phenomena are not sufficient to describe the process of nano-particulate aerosol detection in an inductively coupled plasma. Under theoretical evaporative conditions, the dependence of aerosol detection efficiency on particle size varies according to Eq. (25); thus, disparities in slope presented in Table 5 would be expected depending on the dimensionless parameter ψ/dve , 0; m at the low and high flow conditions for silver should not be necessarily be equal due to the shift in ψ/dve,0. To explain functional dependencies greater than d−1 ve , rapid particle boiling, or explosive phenomena, may also result in particle fragmentation which could act to disperse material away from the torch centerline where it could be sampled. Complex phase change phenomena have been noted elsewhere where the explosive shattering of metal-oxide particles may occur due to the liberation of gases within the solid particle resulting in fracture [80]. More work is needed to analyze boiling behavior and the behavior of oxidized materials. Vapor pressure and enthalpy data are available, but the chemical kinetics, and decomposition of oxidized materials, are complex [102–106]. In subsequent sections, we examine the effects of dispersion and space charge on the functional dependence of E on dve.

Fig. 15. Log10(aerosol detection efficiency) vs. Log10(particle diameter) for Ag aerosol: (a) power law curve fit, Eq. (7), symbols; (b) evaporative theory curve fit, Eq. (25), dashed lines; and (c) power law with a slope of −1, dotted line.

4.5. Diffusion effects in the ICP The method outlined in Flamigni et al. was used to calculate the relative diffusion of each analyte species considered in this work [63]. The objective of this analysis was not to quantify absolute diffusion rates but rather to assess the role of analyte diffusion on the detection efficiencies measured in this study. The binary diffusion coefficient of gas A and analyte B, DAB, is given by DAB

pffiffiffiffiffiffiffiffi  1 :5 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=π kB  T g 1 1 ; ¼ þ 3 P g  σ AB mA mB

ð26Þ

where kB is the Boltzmann constant, Tg is gas temperature, Pg is gas pressure, σABis the collision cross section, and mA and mB are the atomic masses of the gas and analyte, respectively. The atomic mass of gas A is calculated as the molar weighted average of argon and nitrogen: mA ¼ χ Ar  mAr þ χ N2  mN2 :

ð27Þ

In Eq. (27), the mole fraction of argon, χAr, is calculated as χAr = nAr/ ntotal, where n is the molar flow rate of gas. The collision cross section is calculated according to the following equation: h  2  2 i σ AB ¼ π χ Ar  r Ar þ r analyte þ χ N2  rN2 þ r analyte :

Fig. 14. Log10(aerosol detection efficiency) vs. Log10(particle diameter) for Au aerosol: (a) power law curve fit, Eq. (7), symbols; (b) evaporative theory curve fit, Eq. (25), dashed lines; and (c) power law with a slope of −1, dotted line.

ð28Þ

In Eq. (28), r is the van der Waals radius whose values are tabulated in the literature [107–110]. If one simply wants to look at relative diffusion, atomic masses and collision cross sections are sufficient. Absolute diffusion coefficients were calculated in the range of 5–10 cm2/s at 5000 K. The ratios of molar flow rates in the central gas flow of the ICP were as follows: (1) 86% Ar and 14% N2 at the high flow condition and (2) 91% Ar and 9% N2 at the low flow condition. Table 6 gives the atomic masses, collision cross sections, and binary diffusion coefficients for all analytes considered in this study, where values were normalized by the maximum value for all analytes. Gold had the heaviest atomic mass but cerium had the highest collision cross section. Looking at the diffusion coefficients, cerium is the least likely element to diffuse and disperse off the central axis of the ICP and aluminum, the lightest element, is the most likely to diffuse. It would be desirable to calculate the reduction of analyte atoms along the central axis of the ICP so that the magnitude of detection

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Table 6 Analyte (B), analyte atomic mass (mB) normalized by the maximum analyte atomic mass of all analytes considered in this study, collision cross section (σAB) normalized by the maximum collision cross section of all analytes considered in this study, and binary diffusion coefficient (DAB) normalized by the maximum binary diffusion coefficient of all analytes considered in this study B

mB/mB,max

σAB/σAB,max

DAB/DAB,max

Ce Au Y Ag Al

0.71 1.00 0.45 0.55 0.14

1.28 1.12 1.22 1.10 1.00

1.00 1.11 1.11 1.20 1.76

ion loading of the plasma. The effects of increased mass loading and decreased residence time act lower the total detection efficiency. For the refractory species, Y2O3, Al2O3, and CeO2, atom flow rates for yttrium were the lowest. This may partially explain why the absolute detection efficiency for yttrium was the highest of the refractory species. Lower on-axis concentrations of yttrium ions would result in less ion dispersion in the torch. Table 6 shows the relative diffusion coefficient of yttrium, with respect to the other analytes, is low, approximately 11% higher than the diffusion rate of cerium. Relatively low concentrations in the ICP and low relative diffusivity would result in enhanced ion intensities in the ICP-MS with respect to other analytes. 4.6. Matrix effects

efficiency could be correlated to atomic mass. Although diffusion coefficients can be calculated, exact quantification of the absolute effects of diffusion on detection efficiency is a challenge. Assuming complete evaporation, which is not a valid assumption in this case, it would be necessary to know the exact plasma temperature, analyte vapor concentration gradient in the radial direction along the central axis, and the axial location of complete vaporization. The location of complete vaporization is dependent on material properties and heat and mass transfer kinetics which are the subject of the current study. Estimates of vapor concentrations can be made based on measured aerosol concentrations. The vapor concentration is proportional to the cube of volume equivalent diameter; thus, diffusion in the ICP could result in a functional dependence of detection efficiency on particle size. Fig. 16 shows the atomic aerosol flow rate, na, as a function of volume equivalent diameter for all analytes and nitrogen gas flow rates used in this study. It can be seen that over the range of volume equivalent diameters, gas flow rates, and test materials, the total atomic intensity varies over four orders of magnitude. One would expect this to have an effect on ion intensities measured in the ICP-MS because higher atomic concentrations in the plasma, and higher concentration gradients, would result in increased diffusion out of the central region of the plasma into the outer region of the plasma. The first observation from Fig. 16 is that higher nitrogen flow rates generally resulted in increased transport from the aerosol generation chamber to the ICP-MS. Settling velocities for heavy particles (e.g., gold) are non-negligible even for nanoparticles. In measurements of detection efficiency, we attributed lower E to decreased residence time in the plasma. We also see the general trend that higher nitrogen flow rates resulted in increased

In this study, the matrix ions have the same composition as the analyte ions. Matrix effects would become significant if the total ion population were large enough to cause significant space charge downstream of the sampler and skimmer. Measured aerosol concentrations were used to assess the relative influence of total ion concentration on space charge losses in the ICP. Fig. 16 shows atom flow rates of 109–1013 atoms per second. Assuming all of these atoms were ionized, and transported through the sampler and skimmer, the resultant ionic charge would be approximately 0.0001–1 μA. The actual ionic charge would be less than these calculated values due to incomplete atomization and ionization, ion dispersion in the ICP, and transport losses through the sampler and skimmer. Niu et al. calculated the maximum ionic current under which no space charge effects were to be expected, Imax = 0.4 μA [18]. Thus, space charge effects may be present where na N 1012 atoms/s. Based on these calculations, it is plausible that space charge affected the functional dependence of E on dve, where aerosol concentrations were sufficiently high. 5. Conclusions Aerosols of known particle size, composition, and gas concentration were generated and injected directly into an inductively coupled plasma mass spectrometer (ICP-MS). To do so, polydisperse aerosols were generated and size segregated in an Electrostatic Classifier providing size control between 100 nm and 1000 nm. After size segregation, particles were either counted in a condensation nuclei counter or injected into an ICP-MS. An aerosol detection efficiency for the ICP-MS was calculated using the calculated atomic injection rate (aerosol particles in) and atomic count rate of the ICP-MS (atoms detected). Torch residence time, particle size, and particle composition were observed to affect the aerosol detection efficiency. The aerosol detection efficiencies of gold and silver were relatively constant up to approximately 300 nm to 400 nm in size after which the detection efficiency decreased with increasing particle size. The particle size dependence varied with carrier gas flow rate and particle composition. Empirical data suggested that aerosol detection efficiencies varied with the volume equivalent −4 particle diameter from d−2 ve to dve . Free-molecular heat and mass transfer theory was applied to experimental data but did not adequately predict the particle size dependence observed in aerosol detection efficiencies. Calculations also suggested that particle temperatures were elevated above the boiling point temperature, but more work is needed to model the behavior of metal-oxides due to challenges in calculating enthalpy of phase change and sparse vapor pressure data. Lastly, an analysis of ion mass loading in the plasma suggests diffusion in the torch, and space charge effects downstream of the sampler, likely contributed to the functional dependence of ion detection efficiency on particle diameter. References

Fig. 16. Aerosol atom flow rate, na, vs. volume equivalent diameter (dve) for all analytes and gas flow rates tested in this study.

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