On the Effect of Particle Alignment in the DMA

Abstract

The Differential Mobility Analyzer (DMA) is designed to measure particle mobility diameter, which for spherical particles is equal to particle volume equivalent diameter. In contrast, the mobility diameter of aspherical particles is a function of the particle shape and orientation. The magnitude of the DMA electric fields is such that it can cause aspherical particles to align preferentially in a specific orientation. The same electric field and the sheath flow rate ( q _sh ) define the particle mobility diameter. But, the fact that particle orientation depends on the electric field makes the dynamic shape factor and hence the mobility diameter depend on q _sh . Here, we describe an operating procedure that relies on a tandem DMA system, in which the second DMA is operated at a number of q _sh , to obtain information about particle shape by measuring the effect of particle alignment on the particle mobility diameter. We show how the relationship between the mobility diameter and q _sh can even be used to physically separate particles according to their shapes. In addition we explore the use of simultaneous measurements of particle alignment and particle vacuum aerodynamic diameters to gain further information on particle shape and account for particle alignment in the calculations of dynamic shape factor. We first test this approach on doublets and compact triplets of PSL spheres, for which the orientation dependent dynamic shape factors are known. We then investigate applications on a number of polydisperse particle systems of various shapes.

INTRODUCTION

For spherical particles the mobility diameter is well defined and is equal to particle volume equivalent diameter. However, because particle mobility diameter is a measure of particle behavior and not of particle intrinsic property, for aspherical particles whose behavior in the DMA depends on the particle shape and the electric field, the relationship between the mobility diameter and volume equivalent diameter can be complex. Very little attention has been paid to the effects of asphericity on the particle mobility diameter and to how to use the relationship between the two to obtain information about particle shape.

With the advent of aerosol instrumentation it is becoming more common to use Differential Mobility Analyzers (DMAs) to classify or select particles with a narrow distribution of mobility diameters for interrogation by a second instrument to determine, for example, particle density (Katrib et al. 2004; McMurry et al. 2002; Slowik et al. 2004; Zelenyuk and Imre 2005; Zelenyuk et al. 2006), or hygroscopicity and composition (Buzorius et al. 2002). Combining a number of instruments in a series with a DMA upfront makes the need to take into account particle asphericity all the more important because the rigorous interpretation of these detailed measurements, must take particle shape into account. For particles of unknown shapes density has to be replaced with effective density and observed particle growth factors as a function of Relative Humidity (RH) can also be impacted by shape changes. In addition, in many of these complex experimental setups it is virtually impossible to keep the RH constant except for the cases where it is reduced to near zero. The consequence of operating at near zero RH is that a larger fraction of ambient particles become aspherical. As we show in this paper, the detailed interpretation of the measured mobility diameters of aspherical particles can be particularly complex because aspherical particles can and do become aligned in the electric field of the DMA and particle orientation, dynamic shape factor, and mobility diameter are all tightly coupled.

Despite the fact that many ambient and laboratory-generated particles are aspherical, the number of reported investigations of the effect of asphericity on the mobility diameter is extremely small. A study by Hansson and Ahlberg (1985) used a DMA to investigate the effect of shape on mobility diameter using agglomerates of Polystyrene latex (PSL) spheres. They concluded that particle alignment in the electric field of the DMA plays an important role for PSL doublets and triplets, but not for compact quadruplets and quintuplets. In addition they showed that particle alignment depends not only on the electric field but also on particle size. Kousaka et al. (1996) presented a study that used the DMA to measure the Dynamic Shape Factors (DSFs) of doublets and compact triplets of PSL agglomerates in the transition regime. They found that at low electric field both of these PSL agglomerates align at nearly 45° to the electric field, while at higher fields larger particles tend towards the parallel orientation whereas smaller particles do not reach the parallel orientation even at 10 KV/cm. Kousaka et al. (1996) concluded that particle orientation is a function of particle size and the electric field in the DMA. From these studies they were able to deduce the orientation dependent DSFs for the two PSL agglomerates. In a very recent publication Song et al. (2005) described the results of a very elegant experiment designed to investigate the relationship between the mobility diameter of gold nanoparticles and their shapes. The changes in the shape and the mobility diameters of gold nanoparticles as a function of temperature were observed using Scanning Electron Microscopy (SEM) and the DMA. Using SEM they observe that elevating the particles' temperature to 800°C transformed their shape from rods to nearly spherical resulting in a decrease of the particle mobility diameters from 55 nm to 25 nm.

A recent publication that focused on particle morphology by DeCarlo et al. (2004) presented a theoretical treatment of the relationship between particle shape and particle vacuum aerodynamic and mobility diameters. They explored the potentials and the limits of the information on particle shape which can be obtained from the simultaneous measurements of these two diameters. They point to the fact that these two diameters are measured under very different flow regimes and that because the magnitude of particle DSF generally depends on the flow regime it is not determinable without additional information. They suggest instead a simplifying approximation, in which the DSF is assumed to be constant with respect to the flow regime. They do not, however, consider the effect of particle alignment in the DMA on the particle DSF.

In a recent paper (Zelenyuk et al. 2006) we presented an experimental study of the effect of particle asphericity on the observed particle mobility and vacuum aerodynamic diameters. We used the DMA to classify particles with a narrow distribution of mobility diameters and our Single Particle Laser Ablation Time-of-flight mass spectrometer (SPLAT) to measure their vacuum aerodynamic diameters with great precision. The first part of that study focused on PSL agglomerates, for which it was possible to calculate precise DSFs for the transition and the free molecular regimes. The second part of that study describes the extension of the SPLAT/DMA system to a number of common aspherical particles for which approximate DSFs were calculated. One of the conclusions of that study was that particle alignment in the electric field of the DMA can affect the accuracy of the calculated approximate DSFs. We will show here that because the DSFs of asymmetric particles depend on particle orientation it is prudent to measure the mobility and vacuum aerodynamic diameters at the same or similar particle orientations.

The dependence of particle DSF on orientation means that it is a function of electric field in the DMA, whose magnitude determines the particle orientation in the first place. And because the electric field, at which a given particle is classified, depends on the sheath flow rate (q _sh ) that one can freely choose to operate the DMA with, the particle DSF is in essence a function of the q _sh . Moreover, because the particle mobility diameter is a function of its DSF, the mobility diameter of aspherical particles is dependent on the q _sh . In other words, the observed mobility diameter of an aspherical particle depends on q _sh . Therefore, the precise interpretation of the measured mobility diameters of aspherical particles requires knowledge of particle shape and of particle alignment in the DMA.

When considering the relationship between particle mobility diameter and particle shape it is worth reminding that changes in particle shape can result in large changes in mobility diameters, as it was illustrated in the recent study by Song et al. (2005), where the particles' mobility diameter decreased from 55 nm to 25 nm as a result of the change in their shape; from rod-like with an aspect ratio of 5.6 to nearly spherical. Since the present study focuses only on changes in particle orientation, while the particle shape remains constant, the corresponding changes in mobility diameter are expected to be smaller. To provide an approximate scale of the effect of orientation on the observed mobility diameter it is useful to point out that the mobility diameters of particles with aspect ratios smaller than 4 increases by ∼ 15% or less when they realign in the electric field of the DMA from the parallel to the random orientation, where random orientation corresponds to the statistically averaged particle orientation in the absence of an aligning field. But, it is also worth noting that this effect is sufficient in some cases to make it possible to physically separate particles on the basis of their shapes.

The goal of the present study is to explore the relationship between particle shape, alignment in the DMA, and mobility diameter to provide an additional tool to obtain real-time information on particle shape. In this article we describe the testing and then application of experimental procedures that quantify the effect of alignment of an arbitrary aerosol sample in real time. In the sections below we provide a brief theoretical background and the results and discussion of two types of studies: We begin with testing our measurement approach on agglomerates of PSL spheres, with precisely known shapes and volume equivalent diameters. The results from these measurements help quantify the system's capabilities and limits. We then follow with applications of this approach to sodium chloride, ammonium sulfate, graphite, alumina agglomerates, and three types of hematite particles—all aspherical polydisperse aerosol samples. In all cases particle shapes are verified by a simultaneous sampling of particles for Scanning Electron Microscopy (SEM) analysis. In addition we combine the measurements of mobility and vacuum aerodynamic diameters to make it possible to calculate particle effective density and approximate orientation dependent DSFs for a number of these systems. We conclude by demonstrating the use of the disparate sheath flow rate tandem DMA (TDMA) system to separate polydisperse particles on the basis of their shapes.

BACKGROUND

The observed mobility diameter, d _m , of a particle with a volume equivalent diameter, d _ve , is given by Equation (1) (DeCarlo et al. 2004; Zelenyuk et al. 2006):

χ _t,θ is the particles' DSF and the subscripts t and θ indicate that d _m is measured in the transition regime and, in general for aspherical particles (except for particles with special symmetry), the DSF and hence the mobility diameter are dependent on particle orientation. C _c (d _m ) and C _c (d _ve ) are the Cunningham slip correction factors calculated for the mobility diameter and the volume equivalent diameter, respectively. The dependence of the particle mobility diameter on the q _sh is due to the fact that the orientation of aspherical particles, and hence their DSF, in the DMA is a function of the electric field, which in turn is determined by the q _sh . The observed change in the particle mobility diameter as a function of electric field is a measure of the dependence of the DSF on particle orientation and therefore provides information about particle shape and symmetry.

Under most circumstances the volume equivalent diameter of the particles under study is not known, making it impossible to calculate the orientation dependent DSF. Instead we can resort to calculating relative changes in particle DSF by measuring the particle mobility diameters as a function of the q _sh . The ratio between the two DSFs is given in Equation (2):

d _{m lE} and d _{m hE} are the observed mobility diameters at two different particle orientations measured at low and high electric field and the behavior of the ratio χ _t,lE /χ _t,hE as a function of the DMA electric field contains the desired information on particle shape.

In general, at high electric fields particles in the DMA orient parallel to the electric field and their DSFs are at a minimum. At lower electric fields particles tend to the random orientation and their DSFs increase. The differences between the DSFs in these two orientations increase with particle aspect ratios and when comparing prolate spheroids with oblate spheroids with similar asphericity the changes are larger for prolates. Just to provide a guiding scale; for particles with χ _r < 2 (χ _r is the DSF in the random orientation) the differences between DSFs in the parallel and random orientations do not exceed ∼ 30%.

For particles with unknown volume equivalent diameters the measurement of mobility diameters alone cannot be used to calculate the particle DSF. DeCarlo et al. (2004) suggest that it is possible to compute an approximate DSF, for particles of known density from the ratio of the measured vacuum aerodynamic and mobility diameters, d _va /d _m using Equation (3):

Where ρ₀ and ρ _p are unit and particle densities respectively. The approximate DSF, in Equation (3) is assumed to be equal to χ _t,θ and χ _v,r , the DSFs in the DMA and in vacuum respectively ( = χ _v,r = χ _t,θ). To reiterate, in our case χ _t,θ relates to measurements in the transition regime and particle orientation that depends on the electric field in the DMA, while χ _v,r is the DSF in the free molecular regime and in the random orientation. Clearly, the physical interpretation of depends on the validity of the above assumption that the two DSFs are equal. The differences between χ _v,r and χ _t,θ reflect the fact that the two are measured under different flow regimes and also that particle alignment in the DMA can impact χ _t,θ. When possible, it would clearly be advantageous to use in Equation (3) the particle mobility diameter when it is in the random orientation, thereby minimizing the effect of alignment on the above approximation. Since particles approach the random orientation at the lowest electric fields the approximate DSF can, under these circumstances be labeled _r .

Returning to Equation (3), we note that because under most circumstances particle density is also unknown it is not possible to calculate even an approximate DSF. In these cases the simultaneous measurements of the two diameters d _va and d _m are still useful and can be used to yield an effective particle density defined as (Jimenez et al. 2003):

In the absence of internal voids, the effective density of spherical particles is equal to the particle density and is therefore a source of information about particle composition. Particle asphericity decreases the effective density by simultaneously lowering the vacuum aerodynamic diameter and raising the mobility diameter. To deconvolute the material density from the particle shape requires additional information. For example, in the present study we show how measurements of mobility diameter as a function of particle orientation isolate the effect of shape from density. Deploying instruments like SPLAT to measure, in addition to effective density and the effect of alignment, individual particle composition can help in defining reasonable limits on particle density.

EXPERIMENTAL

In the section below we present the results of two types of experiments designed to quantify the relationship between particle shape, particle alignment and particle mobility diameter: The first set of measurements uses a single DMA, which is part of a Scanning Mobility Particle Sizer (SMPS) (TSI Inc., Model 3936L25) and is suitable only for monodisperse samples like agglomerates of PSL spheres, while the second experimental setup that relies on a TDMA system is suitable for polydisperse aerosol samples. For these experiments the TDMA system is composed of a tandem of SMPSs, each operated at different q _sh .

For the PSL agglomerates experiments, PSL particles suspensions are aerosolized using an atomizer (TSI Inc., Model 3076), dried with two diffusion dryers (TSI Inc., Model 3062) before the mobility diameter is measured by the SMPS. The distribution of mobility diameters is measured with the DMA operated at a number of q _sh that range between 1.5 lpm to 15.0 lpm. For these measurements the ratio of the sheath to aerosol flow rates is kept at ∼ 10 or higher to maintain high sizing resolution. Since the maximal changes in measured mobility diameters, from the highest to lowest q _sh for the PSL doublets and triplets, are expected to be less than 10% it is recommended to test the DMAs' precision for each q _sh , using PSL spheres (Duke Scientific) as NIST certified size standards. In the second set of experiments that uses a TDMA each of the DMAs is tested using the NIST certified PSL particle size standards.

Particle mobility diameters are determined by analyzing the SMPS data in the 64 channels/decade size format and in the highly resolved raw-data format (see Figure 10a as an example). Each of the reported mobility diameters represents an average of a number of repeated measurements. The error bars in the figures represent the lowest estimate of reproducibility in these measurements.

FIG. 10 (a) Two mobility size distributions of 274 nm Lot 32 hematite particles obtained by the second DMA, presented in the highly resolved raw-data format. (b) A plot of the DSFs ratios for Lot 32 and Lot 46 hematite particles. (c) Vacuum aerodynamic size distributions of 274 nm Lot 32 particles selected by the second DMA at 1.5 lpm, to have mobility diameters of either 274 nm or 314 nm. The micrographs show the two particle types.

To measure the changes of the mobility diameters of polydisperse particles as a function of electric field in the DMA requires the use of a TDMA. The first DMA is used to select a narrow distribution of mobility diameters and the second DMA is used to probe the effect of electric field on particle alignment and the observed mobility diameter. In the present study the first DMA is operated at q _sh that vary between 7.0 lpm and 8.5 lpm and the second DMA is operated at numbers of different q _sh that ranged between 1.5 lpm and 12.0 lpm.

In most TDMA studies it is customary to use a neutralizer before the first DMA only, since a second neutralizer in front of the second DMAs results in a signal decrease. We find that to measure effects of particle alignment in the DMA it is actually advantageous to leave the second neutralizer in place. The equilibration of the singly charged particles, which are selected by the first DMA, by the second neutralizer generates multiply charged particles: a scan by the second DMA typically reveals a series of 3 to 4 peaks representing singly, doubly, triply, and quadruply charged particles. Since, as our data analysis suggests, particle orientation in this study is independent of particle charge, the existence of multiply charged particles results in a wider range of observed mobility diameter as a function of electric field in the DMA. In the present study this approach yields data for electric field strength that spans from 370 V/cm to nearly 10,000 V/cm.

The reported electric fields are calculated, based on the average voltages dialed on the SMPS display, to select the corresponding particle size for the experimental q _sh and the distance of 1.024 cm between DMA outer and inner electrodes, as reported by the manufacturer (TSI Inc.). Since the data are obtained in the SMPS scanning mode there are small differences between the exact value of the electric fields and the ones used in our plots. But, it is important to keep in mind that the interpretation of the data does not rely on knowing the electric fields with high precision.

Measurements of particle vacuum aerodynamic diameters are carried out with the SPLAT. A detailed description of this instrument is given in Zelenyuk and Imre (2005). Here we provide a brief description only. Particles enter the instrument through a 100 micron orifice into an aerodynamic lens inlet. The lens forms a very narrow low divergence particle beam and transmits the particles into the vacuum chamber with high efficiency. As the particles pass through the lens they acquire velocities that are function of their vacuum aerodynamic diameters. From the lens particles pass through two differentially pumped stages and enter the main chamber, which is equipped with two optical detection stages positioned 10.5 cm apart. In each optical detection stage a particle crosses a green laser beam, and the scattered light it generates is collected by ellipsoidal reflector and detected by a photomultiplier. Each particle is detected twice, once at each stage, and the time of flight between the two optical detection stages is recorded. Measuring the time of flight of PSL particles (Duke Scientific, density 1.05 g cm^{− 3}) of known diameter and density derives the time of flight to aerodynamic diameter calibration. Once detected and sized, particle composition is obtained by IR laser heating followed by UV laser ionization and time-of-flight mass spectroscopy. In the experiments described here the mass spectrometer is not used.

RESULTS and DISCUSSION

1. Mobility Diameter vs. Sheath Flow Rate for Doublets of PSL Spheres: Single DMA Experiments

The measurements described in this section are suitable only for monodisperse aerosol such as PSL agglomerates. Here we explore the magnitude of the effect of electric field in the DMA on the measured mobility diameter of singly charged well defined PSL doublets as a function of particle size. In Figure 1 we show an example of three mobility size distributions of PSL particles with 199 nm primary particle diameter obtained at three different q _sh s. The most intense peak in the figure corresponds to the singlets and the smaller peak to the right corresponds to the PSL doublets (the small peak to the left of the singlets matches the doubly charged doublets). Note that the mobility diameter of the doublets decreases with increasing q _sh . Changing the q _sh alters the electric field at which the PSL particles are classified, causing the asymmetric doublet to change its orientation from parallel at high electric fields to random at low electric field. Since the DSF of the doublet depends on its orientation so does its mobility diameter. By measuring the mobility diameters of the PSL doublets with 199 nm primary particle diameter at a number of q _sh and using the doublets' volume equivalent diameter it is possible to calculate the dependence of the DSFs on the electric field in the DMA. The results of this calculation are shown in the inset of Figure 1.

FIG. 1 Three mobility size distributions of PSL particles with 199 nm primary particle diameter measured at 6.5 lpm, 5.0 lpm, and 2.0 lpm DMA q _sh . The most intense peak corresponds to the singlet and the peak to the right corresponds to the doublets. The small peak at mobility diameters lower than the singlet corresponds to the doubly charged doublets. Note that the mobility diameter of the doublets decreases with increasing q _sh . By changing q _sh the electric field at which the doublets are selected is also changing and with it the doublets orientation. The inset provides a summary of the calculated DSFs for the doublets of 199 nm PSL spheres plotted as a function of the average electric field in the DMA.

In Figure 2 we present the calculated DSFs of the doublets of 129 nm, 199 nm, and 299 nm PSL spheres, obtained on the basis of measurements of their mobility diameters at a number of q _sh s. For comparison we have also included in the figure data from Kousaka et al. (1996) for the doublets of 100 nm PSL particles. The filled symbols indicate the asymptotic values of the DSFs for the corresponding doublets in the parallel orientation (high electric field) and random orientation (low electric field) (Cheng et al. 1988; Zelenyuk et al. 2006).

FIG. 2 A plot of the calculated DSFs of PSL doublets as a function of the electric field in the DMA showing our data for 299 nm, 199 nm, and 129 nm primary PSL particle diameters and the data from Kousaka et al. (1996) for the doublets of 100 nm PSL spheres. The filled symbols indicate the corresponding asymptotic values at high and at zero electric fields, for the parallel and the random orientations respectively. The data clearly indicate that particles change their alignment and tend towards the parallel orientation as the electric field in the DMA increases, with smaller particles requiring higher electric fields.

Figure 2 clearly illustrates that particle orientation in the DMA is a function of electric field and particle size. PSL doublets with primary particle size greater than 200 nm align parallel to the electric field when the electric field is above 5000 V/cm. In contrast, that data suggest that doublets with primary particle size smaller than 129 nm require significantly higher electric field to align parallel to the electric field. The dependence of particle orientation on particle size reflects the fact that parallel alignment is a result of electric field induced dipole, which provides the force to align the particle in the parallel orientation. For this process to be effective necessitates charge separation, which for smaller particles requires higher electric fields. This interpretation of the observed data suggests that the dependence of particle orientation on the electric field is, for the most part, determined by the particles longest dimension and that the larger this dimension is, the lower the electric field at which the particle orients parallel to the field is.

We note, on the basis of the data presented in Figure 2, that the sensitivity of particle orientation, and hence mobility diameter, to electric field is highest for particles with d _ve larger than ∼ 250 nm, and conclude that when applicable it is best to carry out the measurements of particle alignment on particles in the 200 nm to 400 nm size range.

2. Mobility Diameter vs. Flow Rate and Particle Charge for Doublets and Triplets of PSL Spheres: TDMA Experiments

To perform measurements of the effect of particle alignment in the DMA on polydisperse aerosol sample requires a TDMA: the first DMA is needed to select particles with narrow distributions of mobility diameters and the second DMA to measure their mobility diameters as a function of the electric field/sheath flow rate in the DMA.

We first test the application of the TDMA system on PSL doublets with 240 nm primary particle diameter. For this set of measurements the first DMA is operated at q _sh of 8.5 lpm and set to transmit the doublets of the 240 nm primary PSL particles and q _sh in the second DMA is varied. In Figure 3a we show two scans of the second DMA taken at q _sh of 2.0 lpm and 7.0 lpm. Since the second DMA is equipped with a neutralizer the charges on the singly charged doublets, selected by the first DMA, are equilibrated giving rise to the series of peaks that correspond to the multiply charged PSL doublets displayed in Figure 3a and labeled accordingly. Comparison of the two scans that are presented in the figure reveals the expected shift in particle mobility diameter as a function of q _sh in the second DMA. Note that the differences in particle mobility diameter as a function of q _sh are not large, but they are clearly measurable.

FIG. 3 (a) A plot of two mobility size distributions of doublets of 240 nm primary particle size PSL spheres taken by the scanning the second DMA, which is operated at q _sh of 7.0 lpm and 2.0 lpm. Particle charges are labeled by “+,” “++,” and so on. Note the shift in mobility diameter as a result of a change in q _sh . (b) A plot of the calculated DSFs of the doublets of 240 nm PSL spheres as a function of the average electric field in the DMA. The data form a single smooth trend, independent of particle charge, which is indicative of particle reorientation from random to parallel orientation, as the electric field is increased to ∼ 10,000 V/cm. Solid circles indicate the known values of the DSFs in the random and parallel orientations.

The data presented in Figure 3a are used to calculate a DSF from each of the observed peaks. The DSF of the singly charged particles is calculated using Equation (1) and the observed mobility diameters of the multiply charged particles are first converted to the equivalent singly charged mobility diameter and then used to calculate DSFs using the same equation. The calculated DSFs, for 10 different q _sh s are presented in Figure 3b in a plot of the calculated DSF vs. the electric field in the second DMA. We note that despite the fact that the data in Figure 3b contain particles with 4 different charges all the data points clearly form a single cohesive trend, which suggest that for these particles the induced dipole or higher moments dominate the forces that determine particle orientation and point charge interactions are less important.

Recently we reported the free molecular regime DSF of 1.145 for PSL doublets in random orientation (Zelenyuk et al. 2006), which can be compared with the DSF of 1.105 determined for randomly orientated 240 nm PSL doublets in the transition regime indicating a slight dependence on the flow regime. The application of Equation (3) to these data using the mobility diameter measured at low DMA electric field yields = 1.125, which is in close proximity to the two actual DSFs. Note, however, that if we had used in Equation (3) the mobility diameter measured at high electric field, when the particles are in the parallel orientation and their DSF is 1.01, the resulting approximate DSF would be 1.07 and the corresponding particle orientation would be undefined.

In our previous study (Zelenyuk et al. 2006) we also investigated the behavior of the compact PSL triplets as a function of the electric field in the DMA, and concluded that at q _sh of 5.0 lpm compact triplets with primary particle size greater than ∼ 200 nm are in the parallel orientation. In Figure 4 we present the calculated DSFs for the compact triplets of 199 nm PSL spheres as a function of the DMA electric field. The filled circle in the figure indicates the known values of the DSF in the parallel orientation and random orientations. The data presented in Figure 4 indicate that the compact triplets reorients from the parallel towards the random orientation as the electric field in the DMA is decreased. It is worth noting that the overall change in the DSF for the compact triplets from the highest to lowest electric field is ∼ 3%, yet it is detectable using the disparate sheath flow rate TDMA. When the observed changes in the DSF of the triplet are compared with those observed for the doublets we find the difference between the DSFs in the parallel and random orientations for the compact triplets to be smaller, which is a reflection of differences in particle shape (Cheng 1991).

FIG. 4 A plot of the calculated DSFs of the compact triplets of 199 nm PSL spheres as a function of the electric field in the DMA reflecting the process of particle reorientation. The filled black circles indicate the asymptotic values for the DSFs in the parallel and random orientations. The entire data set, regardless of particle charge forms a smooth trend indicative of particle reorientation from parallel towards random orientation, as the electric field is reduced from ∼ 6,500 V/cm to nearly zero. Note that the overall change in DSF is only ∼ 3%.

To summarize the observations for agglomerates of PSL spheres: We have demonstrated that the measurements conducted with a disparate sheath flow rate TDMA make it possible to identify and even quantify particle reorientation as a function of the electric field in the DMA even for particles with relatively small DSF. The behaviors of the DSFs of the PSL agglomerates are found to be in quantitative agreement with the known orientation dependent DSFs for these particles. Because the observed changes in particle mobility diameters are not significantly larger than the line width their precise quantification requires r data with high signal to noise ratios.

3. Application to Polydisperse Aerosol: Sodium Chloride, Ammonium Sulfate, Graphite, Aluminum Oxide, and Hematite

PSL agglomerates are the ideal particle systems for the study of the effects of particle shape on the behavior of aspherical particles. The results of the experiments described above put us in position to extend the measurements to the more complex systems of polydisperse aerosol samples with non-uniform shapes and unknown volume equivalent diameters. In this section we present the results of measurements for sodium chloride, ammonium sulfate, graphite particles, agglomerates of alumina nanoparticles, and hematite particles with a number of distinct shapes.

NaCl

We utilize the conditions our previous study (Zelenyuk et al. 2006) identified to consistently produce nearly cubic NaCl particles. NaCl particles are generated by atomizing a NaCl aqueous solution and drying the aerosol with two consecutive diffusion dryers. Three hundred nm mobility diameter NaCl particles are selected by the first DMA which is operated at q _sh of 7.0 lpm. After passing through the second neutralizer the mobility diameters of singly and multiply charged NaCl particles are measured by the second DMA which is operated at q _sh of 7.0 lpm and 3.0 lpm. The results of these two scans of the second DMA are shown in Figure 5. The inset in Figure 5 shows microscopic images of the DMA selected NaCl particles displaying their nearly cubic shapes. The fact that no differences between the two mobility diameter distributions are observed is in agreement with the behavior expected for these nearly isomeric particles (Horvath 1974).

FIG. 5 Plot of two mobility size distributions of the 300 nm NaCl particles obtained by scanning the second DMA at 7.0 lpm and 3.0 lpm q _sh s Particle charges are labeled by “+,” “++,” and so on. No detectable shift in mobility diameter is observed as a result of changes in q _sh . The inset shows micrographs of the DMA selected NaCl particles.

Ammonium Sulfate

In our previous study of ammonium sulfate particles we measured a DSF of 1.05 for particles with mobility diameter of 300 nm, and obtained microscopic images of the same particles. The DSF and the particle images are consistent with nearly spherical particles with slightly irregular shapes (Zelenyuk et al. 2006). Considering the small DSF and the irregular, nearly spherical particle shape, we expect the alignment effect for these particles be too small to be detected. Indeed the results of a set of measurements conducted on 300 nm ammonium sulfate particles at two different q _sh show no detectable changes in particle mobility diameter as a function of the electric field in the DMA.

Graphite Particles

Graphite particles with a 299 nm mobility diameter are generated by atomizing a water/isopropanol suspension of Aerodag G colloidal graphite (Acheson Colloids Corp.) and classified by the first DMA operated at q _sh of 7.0 lpm. As the micrographs presented in the inset in Figure 6a show, these DMA-classified graphite particles are thin irregularly shaped flakes. The observed mobility diameters of the singly and doubly charged 299 nm graphite particles, obtained by scanning the second DMA at q _sh of 7.0 lpm, 3.0 lpm, and 1.5 lpm are shown in Figure 6a. These mobility size distributions demonstrate that the mobility diameter of these asymmetric particles is a function of the electric field in the DMA and hence the DMA sheath flow rate. Figure 6b provides a summary of the measured mobility diameters in a plot of the calculated equivalent mobility diameters as a function of the electric field in the DMA. On the basis of our experience with PSL particles we conclude that Figure 6b indicates that the alignment of the flaky graphite particles changes from the parallel orientation, at high electric field, towards the random orientation at lower electric field. Using Equation (2) we can calculate the changes in DSF as a function of electric field and find the ratio of the highest to lowest DSFs to be 1.14. Considering that these flat particles are closer in their shape to oblates than prolates, the observed change in the DSF with particle orientation can qualitatively be compared with that observed for the compact triplets, for which we measured an increase in the DSF by only a factor of 1.03 over a similar range of electric fields. The significant difference between the two particle types indicates that the DSFs for the graphite particles are considerably larger than those for the compact triplets, which is consistent with the fact that graphite particles have a higher axis ratio.

FIG. 6 (a) Three mobility size distributions of graphite particles obtained by the second DMA at 3 flows. The inset shows (b) Particle equivalent mobility diameters as a function of electric field exhibiting a 30 nm shift. (c) Vacuum aerodynamic size distribution of the 300 nm graphite particles. The shaded peak is assigned to agglomerated particles.

Measuring, in addition to particles' mobility diameters, their vacuum aerodynamic diameters makes it possible to determine an effective density and an approximate DSF for these graphite particles. Figure 6c shows the observed vacuum aerodynamic size distribution of the graphite particles that were selected to have 299 nm mobility diameters at high q _sh . Three peaks are observed at 335 nm, 529 nm, and 736 nm, for singly, doubly, and triply charged particles. To minimize the effect of alignment on the calculated effective densities and approximate DSF for these particles we use the mobility diameter of 328 nm, corresponding to the measurement at lowest DMA electric field. The combination of vacuum aerodynamic and mobility diameters yield effective densities of 1.02 g cm^{− 3} for the singly charged particles and 0.94 g cm^{− 3} for the doubly and triply charged particles. When possible, it is instructive to compare the calculated effective densities, whose values depend on particle material density, porosity, and shape, to the known material density. In the case of graphite the bulk density is reported to be between 1.9 g cm^{− 3} and 2.3 g cm^{− 3} depending on the degree of porosity. The fact that the range of the reported densities is significantly higher than the calculated effective density of ∼ 1 g cm^{− 3} of the 299 nm graphite particles in this study is consistent with our conclusion above that the graphite particles have large DSF.

Despite the uncertainties in the exact value of graphite density in this study it is still informative to calculate the approximate DSF, _r , for the graphite particles using Equation (3). To minimize the differences between the measurements in SPLAT and those in the DMA that arise due to particle alignment we use in Equation [3] the low electric field mobility diameters of 328 nm, 560 nm, and 787 nm for singly, doubly, and triply charged particles respectively, yielding an approximate DFS of 1.5 ± 0.2 for all three particle sizes (using the reported densities of 1.9 g cm^{− 3} and 2.3 g cm^{− 3}).

A close examination of Figure 6c shows a fourth, lower intensity and broader peak centered at a vacuum aerodynamic diameter of ∼ 250 nm. The peak position and its broader width suggest that the particles that belong to this size distribution are most likely agglomerates of smaller, flaky particles that must also be present in the suspension. The combined mobility and vacuum aerodynamic diameters of these agglomerates yield an effective density of 0.83 g cm^{− 3} and an approximate DSF of ∼ 1.8.

Alumina Aggregates

Alumina particles are generated in our laboratory by atomizing a suspension of aluminum oxide nanoparticles with an average diameter of 37 nm (Nanophase Technologies Corporation). The aerosol flow is dried and size selected with the first DMA to produce a narrow distribution of 300 nm mobility diameter particles. The inset in Figure 7 shows micrographs of a few of the DMA selected alumina aggregates. Since these particles are asymmetric, they are expected to exhibit some electric field dependent alignment.

FIG. 7 A plot of the ratio of the DSFs at different electric fields for aluminum oxide agglomerates as a function of electric field in the DMA. The data indicate an overall shift of slightly less than 10% in DSF over the range of accessible electric fields. The inset shows micrographs of the DMA selected 300 nm aluminum oxide agglomerates.

In this set of measurements the first DMA is operated at q _sh of 8.5 lpm and set to select 300 nm mobility diameter particles, while the second DMA is operated at q _sh of 8.5 lpm and 3.0 lpm. We observe a small, but clearly measurable, shift in the mobility diameters of these particles as a function of the electric field in the DMA. The results are presented in Figure 7 in a plot of the equivalent mobility diameters as a function of the electric field in the DMA. We find for these complex particles that the mobility diameters increase by 18 nm, which translates to a 10% increase in the average particle DSF as a result of particle realignment from parallel to nearly random orientation. To put the alumina data in context it can be compared with our measured 10% increase of the DSF for the doublets of PSL spheres with primary diameter of 240 nm and volume equivalent diameter of 302 nm over a similar range of electric fields.

Hematite

What makes hematite particles particularly attractive for the present study is the fact that their sizes and shapes of these particles can be controlled systematically by the details of a reproducible gel-sol synthetic process (Sugimoto et al. 1998). In Figure 8 we show micrographs of three types of hematite particle synthesized in our laboratory following the procedures outlined by Sugimoto et al. (1998). The three particles labeled Lot 30 in Figure 8a are pseudocubic with 225 nm mobility diameters. Because of their nearly symmetric shapes they are expected to behave in a manner similar to the nearly cubic NaCl particles, we presented above, and exhibit an electric field independent mobility diameter. In contrast, the particles labeled Lot 32 and Lot 46 are nearly ellipsoidal in shape with average aspect ratios of ∼ 2.5 and ∼ 3.25 and mobility diameters of 274 nm and 219 nm, respectively. In this section we explore the differences in the behavior of these three particle types.

FIG. 8 Micrographs showing three types of hematite particles. (a) Three Lot 30 pseudocubic particles with mobility diameter of 225 nm. (b) A Lot 32 ellipsoidal particle with aspect ratio of ∼ 2.5 and mobility diameter of 274 nm. (c) A Lot 46 ellipsoidal particle with aspect ratio of ∼ 3.25 and mobility diameter of 219 nm.

We first present the results of measurements on the pseudocubic particles of Lot 30. Figure 9a shows three mobility size distributions obtained by scanning the second DMA with q _sh of 12.0 lpm, 3.0 lpm, and 1.5 lpm, and the first DMA set to select particles of 225 nm mobility diameters and operated with q _sh of 8.0 lpm. As expected, the data clearly show that the mobility diameters of these nearly symmetric pseudocubic hematite particles are independent of the electric field in the DMA. Because in this set of measurements the sample flow rate is kept constant, the decreasing q _sh results in the observed increase of the mobility size distributions line width.

FIG. 9 (a) Three mobility size distributions of Lot 30 hematite particles, obtained by the second DMA. No changes in mobility diameter are observed for these pseudocubic particles. (b) Vacuum aerodynamic size distribution of 219 nm Lot 30 particles. The inset shows micrographs of Lot 30 particles.

To further explore the properties of these pseudocubic particles we measure their vacuum aerodynamic diameters, the results of which are shown in Figure 9b. Here particles with 219 nm mobility diameter are selected with the first DMA and their observed vacuum aerodynamic diameter is found to be 880 nm. These two particle diameters yield an effective density of 4.0 g cm^{− 3}, to be compared with known hematite monocrystalline material density of 5.24 g cm^{− 3}.

On the basis of our previous measurements of cubic NaCl particles with rounded edges as well as measurements reported by Horvath (1974) it would be reasonable to estimate for these pseudocubic 219 nm hematite particles to be between 1.05 and 1.10. Using Equation (3) and the measured mobility and vacuum aerodynamic diameters of 880 nm and 219 nm respectively we calculate that the density of these hematite particles is 4.55 ± 0.2 g cm⁻³ or ∼13 ± 4% lower than the density of monocrystalline hematite. The lower density is a result of the experimentally confirmed polycrystalline porous structure of hematites, which is generated using gel-sol method (Cornell and Schwertmann 2004; Sugimoto et al. 1998; Park et al. 1996).

Next we present the results of a set of measurements on ellipsoidal hematite particles of Lot 32 with an aspect ratio of ∼ 2.5. For these particles we expect to find that alignment in the DMA plays a role and a measured mobility diameter that is dependent on the electric field in the DMA. In Figure 10a we present two observed mobility size distributions obtained by scanning the second DMA with q _sh of 11.0 lpm and 1.5 lpm, with the first DMA operated at q _sh of 7.5 lpm and set to select particles with 274 nm mobility diameter. To illustrate the level of the signal to noise ratio in these experiments we show the data in Figure 10a in the highly resolved raw-data format, which is used to extract mobility diameters throughout this entire study. The mobility diameter size distribution that is measured at high q _sh peaks at 274 nm, which is identical to the mobility diameter selected by the first DMA. Because for this scan the ratio of the q _sh to the aerosol sample flow rate is slightly over 40, the observed mobility size distribution exhibits a 3% line width. The second scan, taken at q _sh of 1.5 lpm, shows a broader peak that is shifted to 296 nm. The increased width reflects the decrease in the ratio of the q _sh and aerosol sample flow rate and is only slightly wider than expected on the basis of flow rates alone. The observed 22 nm shift in peak position is a result of the Lot 32 particles changing their orientation from being parallel to the DMA electric field towards being randomly orientated as the electric field is decreased.

An analogous set of measurements carried out on the Lot 46 particles with an aspect ratio of ∼ 3.25 and a high q _sh mobility diameter of 219 nm shows similar results. A summary of these measurements are presented in Figure 10b in a plot of the ratios of DSFs for high and low electric fields, calculated using Equation (2), for particles from Lot 32 and Lot 46 as a function of the average DMA electric field. The DSFs of both particle types exhibit an increase of slightly less than ∼ 15% as these particles reorient from the parallel to the random orientations. The theoretically calculated ratios of the DSFs in the parallel and random orientations of ellipsoidal particles with axis ratios of 2.5 and 3.25 in the continuum regime are 1.12 and 1.14 respectively (Cheng 1991), in very good agreement with our observed values.

It is interesting to note that the measurements of vacuum aerodynamic diameter of particles from Lot 32 reveal that in this lot there are two very different particle types, both of which are selected by the first DMA when it is set to select 274 nm mobility diameter particles. One particle type has a vacuum aerodynamic diameter of 920 nm, while the second has a vacuum aerodynamic diameter of 1266 nm. Given that the two particle-types have identical mobility diameters at high q _sh , the significant difference in their vacuum aerodynamic diameters suggests that they must have significantly different particle shape. Indeed, a careful examination of the micrographs of particles in Lot 32 confirms that it contains two particle types. The majority of the particles are ellipsoids with an aspect ratio of ∼ 2.5 and a small fraction of the particles in this lot are nearly spherical particles. We assign the peak with vacuum aerodynamic diameter of 1266 nm to the nearly spherical particles and the second peak at 920 nm to the ellipsoidal ones.

If our peak assignment is correct we expect to find: (a) that the mobility diameters of the two particle types behave very differently as a function of the electric field in the DMA and (b) that the SPLAT inlet transmission efficiency of the particles that correspond to these two peaks is significantly different.

We predict that the mobility diameters of the nearly spherical particles with larger vacuum aerodynamic diameters are independent of the q _sh , while the mobility diameters of the ellipsoidal particles shift to larger mobility diameters at low q _sh in the second DMA. To test this hypothesis we operate the second DMA with q _sh of 1.5 lpm and set it to select either 274 nm or 314 nm mobility diameter particles (both values are marked in Figure 10a) measuring in each case the vacuum aerodynamic diameter size distribution of the selected particles. The results of these two measurements are presented in Figure 10c, showing that the vacuum aerodynamic diameter of particles with unchanged mobility diameter of 274 nm is 1266 nm. In contrast particles with mobility diameters that shift to higher values at low q _sh have a vacuum aerodynamic diameter of 920 nm.

Measurements of relative transmission efficiencies of the SPLAT aerodynamic lens inlet for the two particle types reveal that the nearly spherical particles are transmitted by a factor of ∼ 10 more efficiently than the ellipsoidal particles. The significantly higher transmission efficiency of the nearly spherical particles is in good agreement with the known properties of this inlet.

We conclude that the mobility diameters of the nearly spherical particles are independent of the DMA electric field and that their DSF must be close to 1.0. In contrast the mobility diameters of the aspherical particles increase with increasing DSFs, while an opposite trend is observed for the vacuum aerodynamic diameters.

As we pointed out above, the hematite particles in this study are polycrystalline and have some degree of porosity. Consequently the true densities of the particles shown in the micrographs are not precisely known. However, on the basis of the measurements of the particle mobility and vacuum aerodynamic diameters we calculate effective densities of 4.6 g cm^{− 3} and 3.11 g cm^{− 3} for the nearly spherical and ellipsoidal particles respectively. In addition we use the SEM images and estimate the DSF of the nearly spherical particles to be between 1.0 and 1.02. Together, the estimated DSF and the measured mobility and vacuum aerodynamic diameters can be used to calculate a particle density of 4.7 ± 0.1 g cm^{− 3} for these particles; a value similar to that we estimated for the pseudocubic hematite particles. Assuming that all the particles in Lot 32 have the same density makes it possible to calculate _r , the approximate DSF of the ellipsoidal particles. Using the measured mobility diameter of 296 nm, the vacuum aerodynamic diameter of 920 nm and a 4.7 ± 0.1 g cm³ yields a DSF of 1.27 ± 0.02 for the ellipsoidal hematite particles in Lot 32.

It is worth noting that the last set of measurements on Lot 32 particles, presented in Figure 10c, demonstrates that it is not only possible to identify the particles' symmetry on the basis of their behavior as a function of q _sh in the DMA, but that it is even possible to select, with the second DMA when it is operated at low q _sh , either symmetric or asymmetric particles at will. In other words the TDMA system, operated at two different q _sh s is a potential tool for physically separating mixtures of particles, with identical high q _sh mobility diameters, by their shape.

CONCLUSION

We presented an experimental exploration of the relationship between particle shape and particle behavior in the DMA as a function of the electric field. We deployed a TDMA system, in which the first DMA was used to select particles with a narrow distribution of mobility diameters and the second DMA to explore the effect of the sheath flow rate and hence the electric field in the second DMA on the measured mobility diameters of the monodisperse particle population.

To examine the limits and potential of this approach to generate information about particle shape in real time we first tested it on PSL agglomerates with known shapes, and volume equivalent diameters. Their dynamic shape factors and their dependence on orientation and flow regime are also well known. Measuring the changes in the mobility diameters of the PSL doublets and compact triplets as a function of the electric field in the DMA established the relationship between the behavior of these particles in the DMA and the measured mobility diameters.

We find that in general asymmetric particles align parallel to the electric field at high electric field, but as the electric field is significantly decreased they approach a random orientation. Since the DSFs are at a minimum in parallel orientation the particle mobility diameters are smallest at the high electric field in the DMA. At low electric fields, as particles tend to the random orientation, the DSFs and the mobility diameters increase.

The electric fields at which particles change orientation are a function of particle shape and particle size. The data indicate that the forces that induce alignment in the parallel orientation are reliant on the electric field induced dipole or multipole moments. It is for that reason that the smaller the particle the higher the required electric field is to align the particle in the parallel orientation. We found, for example, that PSL doublets with a primary particle diameter of 129 nm and smaller require fields above 10 KV/cm to align in the parallel orientation. In contrast, doublets with primary particle diameters of 200 nm or larger align in the parallel orientation at electric fields above ∼ 6,000 V/cm. The data suggest that the electric field at which particle realignment takes place is closely related to the particles' longest dimension; the larger the longest dimension is, the lower the required electric field is, to achieve parallel orientation.

Our data clearly show that the alignment behavior of larger particles with up to four charges is independent of particle charge, indicating that the effects of particle induced dipole or multipole moment on particle orientation is dominant.

Particles with larger aspect ratios have larger DSFs and exhibit greater differences in DSFs as a function of orientations. Consequently, the change in particle mobility diameters as a function of the electric field is larger for particles with larger aspect ratios. It is also true that prolate spheroids display larger differences in DSFs with particle orientation than do oblates with the similar aspect ratio.

The measurements of mobility diameters of multiply charged particles yields datasets that span sufficiently wide range of electric fields to make it possible to accurately quantify the relationship between particle shape, particle alignment and particle mobility diameter. We demonstrated here a detection limit for changes in DSF that is below 3% while using commercially available instrumentation.

Table 1 summarizes the majority of the observed data for the nine particle types used in this study. The particle systems we investigated have DSFs that range from 1 to ∼ 1.5. The mobility diameters of the asymmetric particles were found to increase by nearly 10% while their DSFs increased by as much as 15% as they reorient from parallel to nearly the random orientation.

TABLE 1 A summary of the measured and calculated particle properties in this study

Particle type	ρ g cm^3	d m,hE nm ^a	d m,lE nm ^b	χ lE /χ hE ^c	r ^d
240 nm PSL doublet	1.05	305	326	1.10	1.13
199 nm PSL triplet	1.05	304	313	1.03	1.17
NaCl	2.17	300	300	1	1.10
(NH4)2SO4	1.77	300	300	1	1.05
Graphite	1.9–2.3	299	328	1.14	1.5 ± 0.2
Alumina	—	300	320	1.10	—
Hematite
Lot 30	∼4.6 ± 0.2	219	219	1	b1.05 – 1.10
Lot 32	4.7 ± 0.1	274	296	1.13	1.27 ± 0.02
Lot 46	—	219	242	1.15	—

Measurements of changes in particle mobility diameters as a function of the electric field provide insightful information about particle shape and particle symmetry, but alone they can not be used to obtain the particle DSF. However, the combined measurements of vacuum aerodynamic diameter and mobility diameter can be used to calculate an approximate DSF of particles of known densities. We demonstrated that when calculating the approximate DSFs of particles that exhibit alignment effects in the DMA yield it is best to use the mobility diameters that were measured at the lowest electric field. This approach minimizes the effect of alignment and gives a clearer meaning to the DSF with respect to particle orientation.

The measurement scheme we demonstrated here can be used to distinguish between particles on the basis of their symmetry. An observation of mobility diameter that changes as a function of DMA electric field indicates that the particles are asymmetric. The cases of NaCl, ammonium sulfate and the pseudocubic form of hematite particles demonstrate that unvarying mobility diameters do not indicate that the particles are spherical, but rather that they have special symmetry or that their asymmetries are too small to be detected in that manner.

We took advantage of the fact that Lot 32 of hematite particles contained two different particle shapes to illustrate how the disparate sheath flow rate TDMA system can be used to physically separate particles on the basis of their symmetry.

Acknowledgments

We thank Dr. Alexander Laskin and Dr. Yong Cai for their help with the Scanning Electron Microscope. Special thanks to Dr. Gary Holtom and Dr. Yong Cai for the help in generating hematite particles.

This work was supported by the U.S. Department of Energy Office of Basic Energy Sciences, Chemical Sciences Division. This research was performed in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research at Pacific Northwest National Laboratory (PNNL). PNNL is operated by the US Department of Energy by Battelle Memorial Institute under contract No. DE-AC06-76RL0 1830.

Notes

^a d _m,hE is the mobility diameter measured at high electric field in the DMA.

^b d _m,lE is the mobility diameter measured at low electric field in the DMA.

^c χ _lE /χ _hE is the ratio of the measured DSFs at low and high electric field in the DMA.

^d _r is an approximate DSF, in the random orientation, calculated using Equation (3).