To determine the adverse health effects of inhalable particles, the lung regional deposition fraction must be investigated (Chuang et al., 2016; Haddrell et al., 2015). The lung regional deposition fraction is closely associated with the density and morphology of submicron particles that can be derived from their mass measurement (Broday and Rosenzweig, 2011; Salma et al., 2002; Shi et al., 2015). Therefore, mass distribution and particle density play pivotal roles in the study of associated health effects. However, obtaining measurements of the morphology or density of aerosol particles in the environment is not easy (Bau et al., 2014; DeCarlo et al., 2004), and particles in an ambient environment are generally irregular and nonspherical. In this regard, Liu et al. (2013) demonstrated that the morphological parameter of a fractal soot particle, namely the fractal dimension (Df), could affect the particle's radiative properties. In addition, according to theoretical calculations, He et al. (2015) reported that aged soot aggregates with partially encapsulated or externally attached structures have weaker absorption properties than do fresh soot aggregates.

Nevertheless, theoretical simulations and experimental studies on the effects of aerosols on human health and the atmosphere all require certain assumptions regarding particle morphology or density to be made to enable the conversion of number concentration to mass concentration or volume concentration (Hand and Kreidenweis, 2002). To experimentally retrieve the density of submicron-to-nanometre-sized particles, a differential mobility analyser (DMA) system coupled with a low-pressure impactor was developed to measure the aerodynamic sizes of particles of known electric mobility size. By further assuming that the particles were all spherical, the “effective” or “apparent” density was derived (Kelly and McMurry, 1992; Schleicher et al., 1995; Skillas et al., 1998). A similar system combining a scanning mobility particle sizer and electrical low-pressure impactor in parallel was reported and applied to study diesel particulate matter and ambient aerosols (Maricq et al., 2000; Ristimäki et al., 2002; Symonds et al., 2007; Van Gulijk et al., 2004; Virtanen et al., 2004). Furthermore, Ehara et al. (1996) developed the aerosol particle mass analyser (APM), which is an aerosol instrument that classifies particle mass by balancing the centrifugal force and electrostatic force. Based on an identical classification mechanism but utilizing a different rotating scheme to create centrifugal force, the Couette centrifugal particle mass analyser is another commercially available instrument. With such advances in aerosol instrumentation, McMurray et al. (2002) proposed using the APM to directly measure the mass of monodispersed particles classified by a DMA (tandem DMA–APM system) instead of using an impactor to probe the particle aerodynamic size. This DMA–APM scheme is capable of revealing the density or mass distribution of targeted aerosol particles in real time. Throughout the past decades, this scheme has also been adopted extensively to determine the Df of aerosol aggregates (Lall et al., 2008; McMurry et al., 2002; Park et al., 2003, 2004a, b; Scheckman et al., 2009) and atmospheric aerosols (Kuwata and Kondo, 2009; Kuwata et al., 2011).

A growing number of APM experiments are being conducted in outdoor environments in relation to the dual interest in human health and climate change (Leskinen et al., 2014; Rissler et al., 2014). However, when experiments are conducted in the field, environmental conditions such as temperature (T) and pressure (P) vary spatially and temporally, particularly at high-altitude sites. The viscosity (μ=μrTr+SuT+SuTTr1.5) and mean free path (l=μPπRT2M=lrPrPTTr2Tr+SuT+Su) of ambient air change continuously (Kulkarni et al., 2011), thereby influencing the performance and range of detection limits (classifiable region) for the APM. Therefore, in this study, air, oxygen, and carbon dioxide were selected as carrier gases to experimentally evaluate the effect of gas viscosity and the mean free path on the performance of the APM, including the classifiable region and detection limits. On the other hand, argon would be required as the carrier gas if the APM were used as an aerosol particle classifier coupled with inductively coupled plasma mass spectrometry (ICP-MS; in a similar manner to the DMA–ICP-MS system) (Myojo et al., 2002). Therefore, the effects of changing the carrier gas in the APM's transfer function require investigation. In this regard, the experimental and simulated transfer functions for the APM operated for various carrier gases were explored and are compared in this paper. The results provide a valuable insight into the performance of the APM when operated under various conditions.

The APM was first proposed by Ehara et al. (1996), and a compact version was recently developed by Tajima et al. (2013). The instrument consists of two electrodes, namely coaxial and rotating cylindrical electrodes, between which a narrow annular space is created for mass classification (classification zone). When the APM is initialized, the inner and outer electrodes rotate at the same speed (ω) to generate centrifugal force, and a high voltage is applied to the inner electrode to create a “counter” electrostatic force. The governing equations of particle movements in radial and axial directions inside the classification zone are expressed as follows (Ehara et al., 1996): mτ⋅drdt=m⋅r⋅ω2-q⋅Vr⋅ln⁡ro/ri(in  a  radial  direction),mτdzdt-υr=0(in  an  axial  direction),τ=ρp⋅dp,m2⋅Ccdp,m18μ,Sc=mq=Vrc2⋅ω2⋅ln⁡r0/ri. Particles are then classified based on the balance between the centrifugal force and counter electrostatic force, and only particles with a designated mass-to-charge ratio (S) pass through the classification zone. The mass-to-charge ratio for particles that remain in the central line (rc) within the classification zone is defined as the “critical” S (Sc; Eq. (4). Based on this definition, the classified particle mass (m), rotation speed (ω), and voltage applied (V) are linearly correlated on a log scale, as shown in Eq. (5): logm=log⁡q-2log⁡rc-log⁡ln⁡r0/ri+log⁡V-2log⁡ω. Tajima et al. (2011, 2013) depicted the classifiable region for the APM by using a log–log mass-versus-rotation-speed plot. However, because of the physical limits of the operational voltage and rotation speed of the APM, a parallelogram of potential classifiable regions was reported.

The transfer function (Ω) is generally used to characterize the classification performance of the DMA, and by defining the penetration probability of particles under a designed condition, the transfer function is employed to evaluate the performance of the APM. The nondiffusive transfer function for the APM (ΩAPM) can be indexed by the penetration at the Sc (t(Sc)) and the resolution parameter (ΔS) (Tajima et al., 2013); t(Sc) is the maximum height of the transfer function, and ΔS can be estimated theoretically as follows: t(Sc)=exp⁡-λc,ΔS=rc4δtanh⁡λcλc22. Both parameters are closely related to λc, which is the major dimensionless performance parameter defined by Ehara et al. (1996) for APM operation. The ΩAPM is a strong function of λc: λc=2τ⋅ω2⋅Lυ¯=2⋅ρp⋅dp,m218⋅ω2⋅LQa/πro2-ri2⋅Ccdp,mμ=2m3dp,m⋅ω2⋅LQa/ro2-ri2⋅Ccdp,mμ. λc can be interpreted as the ratio of the timescale for axial and radial particle movements in the classification zone. When the value of λc is larger, the APM has a superior classification resolution. Generally, the axial traversal timescale (LLυ¯υ¯) is considered constant because the aerosol flow rate is fixed when the instrument is operated. Thus, the classification performance can be improved by decreasing the radial traversal timescale (112τ⋅ω22τ⋅ω2). A shorter radial traversal time enables easier removal of incompetent particles by deposition onto the electrodes, which denotes lower penetration possibility for particles with a mass-to-charge ratio other than Sc. In other words, the transfer function is narrower, or ΔS is smaller, for a larger value of λc, which suggests a higher classifying resolution. However, the trade-off for operating the APM at a larger λc is that the maximum penetration of the transfer function (t(Sc)) is lower. Tajima et al. (2011) recommended that the APM be operated at a constant λc (with a fixed ΩAPM) within the range of 0.25 to 0.5 when the aerosol flow rate is 0.3 L min-1.

For a constant value of λc, a unique curve in the log–log mass-versus-rotation-speed plot can be determined iteratively through Eq. (8), and this intercepts the APM classifiable region. This constant-λc curve generally acts as the lower boundary for the APM classifiable region. As observed in Eq. (8), λc is a function of the APM rotation speed (ω) and depends on particle mass and density with respect to relaxation time (τ). The value of τ is closely related to gas viscosity (μ) and the Cunningham slip factor (Cc). At a given λc, the ω for classifying particles with a certain mass decreases with an increasing Cc-to-μ ratio (Ccμ). For air, oxygen, argon, and carbon dioxide, limited variations in the values of Ccμ are observed, and their constant-λc curves are closely clustered. By contrast, the long mean free paths of low-molecular-weight gases such as hydrogen and helium can lead to a relatively high Ccμ. Consequently, when the APM is operated with hydrogen and helium, the classifiable mass range needs to be extended to a much lower detection limit without sacrificing the resolution or modifying the APM hardware (Fig. 1). However, an implicit problem is that the breakdown voltages of inert gases are generally approximately 1 order of magnitude lower than that of air (Schmid et al., 2002) (values of gas-specific parameters and the corresponding detection limits are listed in Table 1).

The expression of Ccμ can be further rewritten to reveal the effects of temperature, pressure, and the carrier gas species as Eq. (9): Ccdpμ=1μ+2l2ldpdpμα+β⋅exp⁡-γ2l2ldpdp=T+SuTr+SuTTr-1.5⋅1μr+PrPTTr0.5⋅2lr2lrdpdpμrα+β⋅exp⁡PPrTTr-2T+SuTr+Su⋅-γ2lr2lrdpdp, where α=1.142, β=0.558, and γ=0.999 (Allen and Raabe, 1985). As shown in Fig. 2, compared to pressure, Ccμ is somewhat invariant with temperature; when the temperature changes from 273 to 318 K, the difference of Ccμ for all gas species is less than 6 %. However, the Ccμ for 100 nm particles increases by 42 % when the air pressure decreases to 65 kPa (Fig. 3); therefore, when operating the APM at high-altitude sites, the detection limits need to be lowered or the resolution needs to be improved. By contrast, based on the analytical predictions, Eq. (4) is unaffected by Ccμ, and the classification accuracy remains unchanged.

Figure 4 depicts the experimental evaluation system. The particles were generated by an aerosol atomizer (TSI, Model 3076) and dehumidified by two desiccant dyers connected in series to remove excess water content. To experimentally evaluate the classification accuracy, 50 and 100 nm polystyrene latex (PSL) spheres certified by the National Institute of Standards and Technology (Thermo Fisher Scientific, cat. no. 3050A and 3100A) were used here. The mean diameters of the size distributions of the 50 and 100 nm PSL given by the manufacturers are 46±2 and 100±3 nm, respectively. These PSL particles were classified using the DMA (TSI 3081) and then delivered to the APM (Kanomax model II-3601) to determine particle mass. The overall aerosol flow rate of the DMA–APM system was controlled by the downstream CPC (condensation particle counter, TSI 3022A) and fixed at 0.3 L min-1. To optimize the size of the classification resolution, the sheath flow rate of the DMA was set at 3.0 L min-1. In addition to air, carbon dioxide (CO2) and oxygen (O2) with purity levels of 99.99 % were supplied as carrier gases. Before conducting measurements, the selected gas was used to purge all apparatus for at least 5 min to ensure that no residual contaminant gases remained, and the flow rates of the DMA's sheath flow and aerosol flow were calibrated using a volumetric flow meter (Gilian Gilibrator 2, Sensidyne, St. Petersburg, FL, USA). Because the DMA–APM was used to investigate the effects of carrier gases on the APM's performance, it was necessary to first study the sizing accuracy of the DMA for various carrier gases. The results showed that the differences between the measured modal diameters and nominal sizes of 50 and 100 nm certified PSL particles were within 6 % for air, CO2, and O2. Therefore, no significant effects of gas species on DMA sizing accuracy were observed, which was consistent with the findings of Schmid et al. (2002).

The classifying accuracy of aerosol instruments under various conditions is generally characterized by a normalized indicator relative to a known reference (Karg et al., 1992; Marlow et al., 1976; Ogren, 1980; Schmid et al., 2002). The normalized mass-to-charge ratio (S¯=SgasSair) was used in the present study to analyse the APM's performance at a constant rotation speed (ω) and constant sizing resolution (λ) operation. For the constant λ operation, λ values of 0.24 and 0.45 were chosen for both 50 and 100 nm PSL spheres. The operation of DMA–APM is identical to Kuwata and Kondo (2009) and Kuwata et al. (2011), in which the DMA selects particles with +1 charge and predetermined mobility diameters and then subjects them to the APM. Subsequently, the APM was set to scan across a range of voltage (V), while the number concentration (CN) of the passing particles was measured by a CPC. The peak of the CN–V distribution was subsequently inspected to determine the particle mass (m).

The APM's stepping CN–V spectrum was converted to the transfer function and compared with the simulated transfer function. The transfer function is a kernel function used to theoretically evaluate the concentration of downstream particles and is critical for evaluating the performance of the APM (Ehara et al., 1996; Emery, 2005; Tajima et al., 2013). In the present study, two computer programs, namely the TRANSFER program and SIM_APM program (developed by the National Institute of Advanced Science and Technology (AIST) of Japan) were utilized to theoretically evaluate the operational performance of the APM (Tajima et al., 2011, 2013). The TRANSFER program calculated the theoretical APM transfer function at a fixed rotation speed and voltage, and the SIM_APM program simulated particle distribution at the APM outlet based on the known particle distribution at the APM inlet (the size distribution was classified by the front DMA). Both simulated results were compared with experimental APM measurements.

In this study, the effects of temperature (“T” hereafter), pressure (“P” hereafter), and gas viscosity (“μ” hereafter) on the performance of the APM were evaluated analytically and experimentally. The analytical results revealed that the APM's detection limit can be lowered simply by increasing the Cc / μ ratio without modifying the hardware of the APM or its classifying resolution. Under a constant λ and fixed T and P, the use of a low-molecular-weight carrier gas such as H2 or He can lower the mass detection limit to approximately <10-2 fg. Similarly, a reduction in operating P lowers the detection limit or improves the resolution. Under these circumstances, the effects of T on the APM's detection limit are relatively minor.

Our experimental results under constant λ or ω values reveal that the use of a carrier gas other than air reduces accuracy. Specifically, a carrier gas with a lower μ than air such as CO2 yields an underestimation of mass, whereas one with a higher μ such as O2 yields an overestimation. A subsequent flow field simulation revealed variations in flow velocity in an angular direction at the APM's inlet and outlet when air and other carrier gases were used. The flow velocity decreased with μ but increased with ω. Thus, the effects of T are expected to affect the APM's performance, and changes in μ, density, and diffusivity in the carrier gas likely alter the radial acceleration of flow in the APM; however, further research is recommended for these aspects.