Aerosol Particle Collection Efficiency of Holey Carbon Film-Coated TEM Grids

Abstract

A simple sampling method to collect aerosol particles for transmission electron microscope (TEM) analysis was developed by R’mili and others in 2013. The method involves passing air through a holey carbon film-coated copper mesh TEM grid (holey carbon grid) and sampling particles by filtration. In this study, we proposed a modified calculation method to represent the collection efficiencies of holey carbon grids, taking into consideration the porosity of the copper mesh. We then evaluated the particle collection efficiencies of holey carbon grids both theoretically and experimentally. We tested the collection efficiency of two types of holey carbon grids, with nominal pore sizes of 1.2 and 0.6 μm, using particles of monodispersed polystyrene latex (PSL) and potassium chloride. The overall collection efficiency of each grid (E_grid) was determined by the downstream/upstream concentration ratio measured by condensation particle counters (CPCs). In addition, for PSL particles, the collection efficiency of the holey carbon film (E_film) was determined by the ratio of the number of particles on the film (counted on a scanning electron microscope) to the number of inflow particles (counted by a CPC). We compared model calculations against the experimental results obtained in this study and those reported by R’mili and others in 2013. These data showed that the calculated E_grid values were in reasonably good agreement with the experimental E_grid values. However, although the model calculation indicated that E_film ≈ E_grid, there was an inconsistency between the experimental E_film and E_grid, which requires further investigation in order to determine its cause.

Copyright 2014 American Association for Aerosol Research

1. INTRODUCTION

A transmission electron microscope (TEM), often used in conjunction with an energy-dispersive X-ray analytical system, is an effective tool for the analysis of aerosol particles. It can accurately determine particle size, morphology, and composition. For example, in studies on the risks associated with nanomaterials, TEM observation is a reliable way to verify the presence and form of aerosolized nanomaterials, and to differentiate between nanomaterials and background particles (Methner et al. 2010).

The success of TEM observation is strongly dependent on the particle sampling method used. It is necessary to collect particles onto a grid specifically used for TEM observation (i.e., a TEM grid), which typically has a diameter of approximately 3 mm. Various methods have been proposed for direct particle collection, such as electrostatic precipitation (Cheng et al. 1981; Dixkens and Fissan 1999; Fierz et al. 2007; Miller et al. 2010), thermophoretic precipitation (Bang and Murr 2002; Lyyränen et al. 2009; R’mili et al. 2011), inertial impaction (Birch et al. 2011), or Brownian motion (Tsai et al. 2009). Meanwhile, an indirect method commonly used to measure asbestos involves dissolution of the filter after particle collection so that the particles are transferred onto a TEM grid (National Institute for Occupational Safety and Health [NIOSH] 1994; International Organization for Standardization [ISO] 1995; Methner et al. 2010). However, all these methods have drawbacks in that a specific device is required, collection efficiency is low or unknown, or preparation is time-consuming.

A simple sampling method for collecting aerosol particles on a TEM grid has recently been proposed and developed by Lyyränen et al. (2009) and R’mili et al. (2011, 2013). In this method, air is passed through a holey carbon film-coated copper mesh TEM grid (holey carbon grid) and particles are sampled by filtration (Figure 1). This method is low-cost, compact, and portable, and sample preparation is not required. Although collection efficiency with this method depends on particle size, efficiency is nevertheless relatively high compared to other collection techniques. R’mili et al. (2013) evaluated the collection efficiency of two types of holey carbon grids: the first had uniformly-sized circular pores arranged regularly, while the second had nonuniformly-sized irregular pores distributed randomly. Collection efficiency was tested using monodispersed copper (Cu) and sodium chloride (NaCl) particles with a particle size of 5–150 nm at a volume flow rate of 0.3 L·min⁻¹. They reported a minimum collection efficiency of 15%–18% at a particle size of around 30 nm.

FIG. 1 Diagram of an aerosol particle collection system using a holey carbon film-coated TEM grid.

Like Nuclepore filters, holey carbon grids have circular pores. Therefore, the collection efficiencies of holey carbon grids can be estimated by employing models developed for calculating the collection efficiencies of Nuclepore filters. R’mili et al. (2013) used this technique to calculate the collection efficiencies of holey carbon grids, and reported a good agreement between the model calculation and the experimental results. However, their calculation method has room for improvement. First, they did not consider the porosity of the copper mesh, which was approximately 50%. As a result, the actual velocity of the flow approaching and passing through the pores of the carbon film was approximately two times higher than the value they assumed; this is problematic because flow velocity affects the calculated collection efficiencies by both impaction and diffusion. Second, although the effect of impaction largely depends on particle density (Pich 1964), the difference in densities between the Cu and NaCl particles was not considered in the model calculation. Third, Equation (15) in R’mili et al. (2013), which was used to calculate the collection efficiency due to Brownian diffusion, was invalid for this situation as it only expressed single-fiber efficiency by diffusion. An additional factor was needed in order to apply this single-fiber theory and obtain the efficiency of the entire film (Yamamoto et al. 2005). Furthermore, the equation to obtain Kuwabara's hydrodynamic factor (Ku), used in Equation (15) of R’mili et al. (2013), differs from the original equation (Kirsch and Fuchs 1968; Hinds 1999).

In this article, we propose a modified calculation method to represent the collection efficiencies of holey carbon grids, taking into consideration the porosity of the copper mesh. We then compare the model calculation with experimental results reported by R’mili et al. (2013), and with those obtained in this study. We experimentally tested the collection efficiency of two types of holey carbon grids, with nominal pore sizes of 1.2 and 0.6 μm, using monodispersed polystyrene latex (PSL) spherical particles and potassium chloride (KCl) particles. The overall collection efficiency of each grid was determined by the downstream/upstream concentration ratio measured by condensation particle counters (CPCs). In addition, for PSL particles, the collection efficiency of the holey carbon film on each grid was determined by the ratio of the number of particles on the grid (visually counted on a SEM) to the number of inflow particles (counted by a CPC).

2 MATERIALS AND METHOD

2.1 Holey Carbon Grids and Sampling System

In this study, we used two types of holey carbon grids. Both were 200-mesh copper grids coated with a carbon support film, and both had circular pores. The first had a nominal pore size of 1.2 μm and nominal pore spacing of 1.3 μm (Quantifoil R1.2/1.3 on 200 mesh Cu, Agar Scientific, Stansted, UK; hereafter Grid-1); the second had a nominal pore size of 0.6 μm and nominal pore spacing of 1 μm (Quantifoil R0.6/1 on 200 mesh Cu, Agar Scientific; hereafter Grid-2). In contrast, R’mili et al. (2013) used 400-mesh copper grids coated with a carbon support film; circular pores in these grids had a nominal pore size of 1.2 μm and nominal pore spacing of 1.3 μm (Quantifoil R1.2/1.3 on 400 mesh Cu, Agar Scientific; hereafter Grid-3). The structural characteristics of all three grids are summarized in Table 1.

TABLE 1 Structural characteristics of the holey carbon film-coated TEM grids

	Grid-1: Quantifoil R1.2/1.3	Grid-2: Quantifoil R0.6/1	Grid-3: Quantifoil R1.2/1.3
Characteristic parameters	on 200-mesh Cu	on 200-mesh Cu	on 400-mesh Cu
Holey carbon film
Pore diameter, dfilm (μm)	1.2 (nominal)^a,	0.6 (nominal)^a,	1.2 (nominal)^a,
	1.67 ± 0.060 (n = 34)^b	0.93 ± 0.17 (n = 34)^b	1.3^c
Pore pitch, pfilm (μm)	2.5^a,b	1.6^a,b	—
Pore density, Nfilm (number·m^−2)	1.60 × 10^11d	3.91 × 10^11d	1.3 × 10^11c
Porosity, Pfilm	0.35^e	0.27^e	0.17^c
Thickness, Lfilm (μm)	∼0.02^a	∼0.02^a	∼0.02^a
Copper mesh
Hole width, wmesh (μm)	100^b (reverse: 90^a,b)	100^b (reverse: 90^a,b)	44^b (reverse: 37^a,b)
Hole pitch, pmesh (μm)	125^a,b	125^a,b	62^a,b
Porosity, Pmesh	0.64^f	0.64^f	0.50^f
Thickness, Lmesh (μm)	16^a	16^a	12^a

^aValues provided by the manufacturer.^bValues measured in this study. For pore diameter, more than 100 pores on each of the 34 grids used in the collection efficiency tests were measured. The mean and the standard deviation are based on a grid-to-grid variation.^cValues measured by R’mili et al. (2013).^dN_film = 10¹²/p_film².^eP_film = (π / 4) × (d_film/p_film)².^fP_mesh = (w_mesh/p_mesh)².

A field-emission SEM (Quanta 250 FEG, FEI Company, USA) was used to measure structural characteristics for both Grid-1 and Grid-2, which were compared to nominal values provided by the manufacturer (Table 1). The measured pore diameters were somewhat different from the nominal values. Although there was relatively little variation in the diameter of pores within a grid, there was large variation in the diameter of pores among grids (grid-to-grid variation), especially with Grid-2. In contrast, the measured pore pitch (= pore diameter + pore spacing) was fairly stable and consistent with the nominal pore pitch. The measured width and pitch of the square holes in the copper mesh were also fairly stable. The width of the hole at the front of the mesh, to which the holey carbon film was attached, was somewhat larger than at the back (Table 1).

Figure 1 is a diagram of an aerosol particle collection system with a holey carbon grid; it is the same as the one used by R’mili et al. (2013). A holey carbon grid with a copper joint (hole grid Cu 2000 μm, Agar Scientific; external diameter = 3.05 mm, internal diameter = 2 mm) was placed in a TEM grid holder (Mini Particle Sampler, MPS, Ecomesure, Janvry, France) developed by the Institut National de l’Environnement Industriel et des Risques, (INERIS, France) (R’mili et al. 2013). The volume flow rate was fixed at 0.3 L·min⁻¹. This value was recommended by Lyyränen et al. (2009) in order to avoid deterioration of the carbon film on the TEM grid, and was used by R’mili et al. (2013). Pressure-drops occurring through the holey carbon grids at this volume flow rate were 1.1 ± 0.14 kPa for Grid-1 and 1.7 ± 0.51 kPa for Grid-2 (values are given as mean ± standard deviation; n = 29 and 28, respectively).

2.2 Experimental Setup for Evaluating the Collection Efficiency

The experimental setup used for evaluating the collection efficiency of the holey carbon grids is shown in Figure 2. Conductive silicone tubing and stainless steel connectors were used to transmit the particles. An atomizer (model ATM-226, Topas, Dresden, Germany), followed by a silica gel drier, were used to generate PSL spherical particles 100 and 300 nm in size, and KCl particles 30, 50, and 100 nm in size. In addition, an electrospray (model 3480, TSI, Shoreview, MN, USA) was used to generate PSL spherical particles of 30 and 50 nm, and KCl particles of 5, 10, and 15 nm. The KCl concentrations in solutions for the atomizer and electrospray were 0.02–0.07 and 0.25 g·L⁻¹, respectively. The aerosolized particles were neutralized by a radioactive source (americium [Am]-241) to establish an equilibrium charge distribution. These were then classified by a differential mobility analyzer (DMA; model 3081 or 3085, TSI) with a platform (model 3080, TSI) to obtain monodispersed particles, and to remove the residuals of ultrapure water used for the PSL and KCl solutions. The charges on the monodispersed particles passing through the DMA were subsequently removed by another Am-241 source. The number concentrations of particles upstream and downstream of the TEM grid holder were measured by two separate CPCs (models 3776 and 3775, TSI, respectively). The lines from the bifurcation to the upper CPC and the TEM grid holder were the same lengths in order to avoid differing particle losses in the two sets of tubing. The number concentrations of particles upstream of the TEM grid holder were recorded as being on the order of magnitude of 10²–10³ particles·cm⁻³. The sampling time ranged between a few minutes and a few hours, depending on the concentration and particle size. Tests for each size and composition of particles were repeated at least three times.

FIG. 2 Schematic diagram of the experimental setup.

2.3 Determination of the Collection Efficiency

Penetration (P_t) is expressed by: [1] where C_up and C_down are the number concentrations of particles upstream and downstream of the TEM grid holder, respectively. The overall collection efficiency of the holey carbon grid (E_grid) was calculated according to the ratio of penetrations with (P_t,with) and without (P_t,without) the holey carbon grid; in the latter case, only the copper joint was used (Figure 1). This calculation took into account the counters’ own intrinsic differences and the loss of particles through the holder and tubing: [2]

For PSL particles, the collection efficiency of the holey carbon film on the grid (E_film) was also determined by the ratio of particles on the holey carbon film (visually counted on an SEM) to inflow particles (counted by a CPC): [3] where N_dep represents the total number of particles deposited on the holey carbon film, and N_in is the total number of particles entering the grid. N_dep and N_in were calculated as: [4] [5] where A_film is the effective filtration area of the holey carbon film, N_SEM is the total number of particles on the holey carbon film counted on the SEM, A_SEM is the total area of the holey carbon film observed on the SEM, and V is the total sampling air volume (= volume flow rate × sample collection time). A_film was calculated as: [6] where d_j is the internal diameter of the copper joint (2 mm) and P_mesh is the fraction of the opening area (porosity) of the copper mesh (Table 1).

More than 100 particles deposited on over 20 different regions in each grid were counted. Prior to SEM observation for 30- and 50-nm PSL particles, the TEM grids containing particle deposits were coated with platinum–palladium (approximately 2 nm in thickness) in order to make identification clearer. While we used the SEM in this analysis for cost-saving reasons, some samples were also examined using a TEM (JEM-1010, JEOL, Tokyo, Japan).

3 THEORY

3.1 Models

Like Nuclepore filters, porous TEM grids have circular pores. Therefore, the collection efficiencies of holey carbon grids can be estimated by employing models developed for calculating the collection efficiencies of Nuclepore filters (Pich 1964; Spurny et al. 1969; Manton 1978, 1979). Particle collection by a Nuclepore filter is generally expressed by separate filtration mechanisms: inertial impaction on the filter surface, interception at the pore opening, and Brownian diffusion to the pore wall and front surface of the filter (Cyrs et al. 2010; Chen et al. 2013).

Collection efficiency due to impaction (E_I) is calculated as (Pich 1964; Spurny et al. 1969): [7] [8] [9] [10] where Stk is the Stokes number defined in terms of r₀, P is the filter porosity, m is the mass of a single aerosol particle, U₀ is the face velocity, C_c is the Cunningham slip correction factor (Kim et al. 2005), η is the dynamic viscosity of the flow (≈1.8 × 10⁻⁵ Pa·s for air), r₀ is the pore radius, ρ_p is the particle density, and r_p is the particle radius. Although the original papers (Pich 1964; Spurny et al. 1969) did not consider C_c in the Stokes number, Equation (10) includes it (Cyrs et al. 2010; Chen et al. 2013).

Collection efficiency due to interception (E_R) is calculated as (Marre and Palmeri 2001): [11] [12] [13] where N_r is the particle radius normalized for the pore radius (= r_p /r₀), N_g is the slip parameter (= l_g /r₀), l_g is the slip length (=1.126λ; Marre et al. 2004), and λ is the mean free path of gas molecules (≈0.065 μm for air). When N_r > 1, the efficiency is equal to 1 and the formula is invalid. This model is based on the assumption of Poiseuille flow with flow slip.

Manton (1978) pointed out a problem in considering impaction and interception separately. The former process is calculated without accounting for the finite size of a particle, while the latter ignores the inertia of a particle relative to the flow. Manton (1978) therefore calculated the collection efficiency due to the combined mechanisms of impaction and interception on the filter (E_IR) from the computed trajectories of particles, and proposed an approximate expression for E_IR: [14] [15] [16] [17] [18] where a and b are functions of an inertia parameter I: a₁ = 0.688500 − 1.473959P + 0.286458P², a₂ = 7.754343 − 46.535261P + 72.737760P², a₃ = 1.296234 − 4.525388P + 6.554401P², b₁ = 2.720000 − 33.125000P + 65.625000P², b₂ = 16.117649 − 36.715870P + 27.829932P², and b₃ = − 10.611610 + 28.831488P − 31.098401P². Stk’ is the Stokes number defined in terms of the radius (D₀) of the cylindrical flow approaching a pore (where D₀ = r₀/, as D₀ is defined based on the porosity: P = πr₀²/πD₀² = the sectional area of a pore/the sectional area of the flow approaching a pore). a₁, a₂, a₃, b₁, b₂, and b₃ were derived from the calculation for the cases of I = 0.25, 2, and 100, and P = 0.04, 0.16, and 0.36. Equation (14)[14] is valid within the limits: I ≤ 100 and 0.04 ≤ P ≤ 0.36. Although Manton (1978) did not consider C_c in the Stokes number, Equation (18) includes it. Manton (1978) proposed I to specify the collection efficiency for a parameter that depends on the filter geometry, flow conditions, and particle density, but not on particle size. However, when C_c is taken into account, I is expressed as a function of C_c, which does depend on particle size.

The collection efficiency due to diffusion to the pore wall of the filter (E_W) can be calculated as (Gormley and Kennedy 1949; Twomey 1962; Spurny et al. 1969): [19] where N_D = LD_pP/r₀²U₀, L is the filter thickness (pore length), and D_p is the particle diffusion coefficient.

The collection efficiency due to diffusion to the front surface of the filter (E_DS) can be calculated as (Manton 1979): [20] where α₁ = 4.57 − 6.46P + 4.58P², α₂ = 4.5, and is the normalized particle diffusion coefficient (= D_p/D₀U₀). The function α₁ (P) was determined by a least-squares fitting of data from a series of solutions for P = 0.05, 0.32, and 0.64; therefore, Equation (20)[20] is valid for filter porosities (P) in the range 0.05–0.64.

The overall collection efficiency (E_O) can be expressed as: [21]

These models are valid when the flow approaching a pore is laminar, which occurs at a low Reynolds number (Re). The Re of a flow approaching a pore can be calculated as (Manton 1978): [22] where ν is the kinematic viscosity of the flow (≈1.5 × 10⁻⁵ m²·s⁻¹ for air).

3.2 Application of the Models to the Collection Efficiency of the Holey Carbon Grid

For each holey carbon grid, we considered the collection efficiencies of the holey carbon film (E_film) and the copper mesh (E_mesh) separately. We calculated the collection efficiencies of the three types of holey carbon grids listed in Table 1; Grid-1 and Grid-2 were used for the tests conducted in this study, while Grid-3 was used for the tests conducted in R’mili et al. (2013).

The individual collection efficiencies, E_I, E_R, E_IR, E_W, and E_DS, of the holey carbon film were calculated by Equations (7), (11), (14), (19), and (20), respectively. In these calculations, the pore radius (d_film/2), porosity (P_film), and thickness (L_film) of the holey carbon film, and the velocity of the flow approaching a pore in the holey carbon film (U_film) were used instead of r₀, P, L, and U₀, respectively. The values of d_film, P_film, and L_film are summarized in Table 1. U_film can be obtained by: [23] where Q is the volume flow rate (0.3 L·min⁻¹).

The total collection efficiency of the holey carbon film (E_film) was calculated as: [24]

TABLE 2 Conditions of the flow through the holey carbon film-coated TEM grids^a

	Grid-1: Quantifoil R1.2/1.3	Grid-2: Quantifoil R0.6/1	Grid-3: Quantifoil R1.2/1.3
	on 200-mesh Cu	on 200-mesh Cu	on 400-mesh Cu
Flow approaching a pore in the holey carbon film
Flow velocity, Ufilm (m·s^−1)	2.5	2.5	3.2
Reynolds number, Re	0.23	0.15	0.33
Inertia parameter, I	15	7.4	11
Flow approaching a hole in the copper mesh
Flow velocity, Umesh (m·s^−1)	1.6	1.6	1.6
Reynolds number, Re	7.5	7.5	3.7
Inertia parameter, I	887	887	346

^aValues were calculated using the structural characteristics of each grid given in Table 1, alongside the following sampling conditions: volume flow rate Q = 0.3 L·min⁻¹, internal diameter of the copper joint d_j = 2 mm, particle density ρ_p = 1,000 kg·m⁻³ = 1 g·cm⁻³, and Cunningham slip correction factor C_c = 1.

We used E_IR, instead of E_I and E_R, since E_IR gave better estimates (see results and discussion).

Although the copper mesh has square holes, its approximate individual collection efficiencies, E_I, E_R, E_W, and E_DS, were calculated from Equations (7)[7] , (11)[11] , (19)[19] , and (20)[20] , respectively. E_IR could not be determined because the I of the flow approaching a hole in the copper mesh substantially exceeded the limits of validity for Equation (14)[14] ; this is discussed further below. In these calculations, the sectional area-equivalent circular-based hole radius (r_mesh), porosity (P_mesh), and thickness (L_mesh) of the copper mesh, and the velocity of the flow approaching a hole in the copper mesh (U_mesh), were used instead of r₀, P, L, and U₀, respectively. The values of P_mesh and L_mesh are summarized in Table 1. The sectional area-equivalent circular-based hole radius (r_mesh) was calculated as: [25] where w_mesh is the width of the square hole in the copper mesh (Table 1). U_mesh can be obtained by: [26]

The total collection efficiency of the copper mesh (E_mesh) was calculated as: [27]

The overall collection efficiency (the combined efficiency of E_film and E_mesh) of the holey carbon grid (E_grid) was calculated as: [28]

Table 2 summarizes the velocities, Reynolds numbers, and inertia parameters (for the case of C_c = 1) of flows that approach a pore in the holey carbon film and a hole in the copper mesh.

U_film and U_mesh are 2.5–3.2 and 1.6 m·s⁻¹, respectively; these are relatively higher than those generally set for Nuclepore filters (e.g., 0.02–0.18 m·s⁻¹; Cyrs et al. 2010; Chen et al. 2013). The flow approaching a pore in the holey carbon film has Re < 1, whereas the flow approaching a hole in the copper mesh has Re < 10, indicating that the flow is laminar in both cases. These data show that the above models would therefore be valid.

For the case of C_c = 1, a range of 7–15 was obtained for I of the flow approaching a pore in the holey carbon film, which is within the limits of validity for Equation (14)[14] (i.e., I < 100). However, as particle size decreases, C_c increases and, consequently, I increases. For example, in the case of Grid-1, the I of particles with sizes below 40 nm and ρ_p = 1 g·cm⁻³ exceeded the limits of validity for Equation (14)[14] . Although some errors may arise, Equation (14)[14] was still used to calculate E_IR for the holey carbon film, even when I > 100.

In contrast, the I of the flow approaching a hole in the copper mesh substantially exceeded the limits of validity for Equation (14)[14] ; hence, E_I and E_R, instead of E_IR, were used to calculate the collection efficiency of the copper mesh.

4 RESULTS AND DISCUSSION

Experimental measurements for overall collection efficiencies (E_grid) for KCl and PSL particles, and collection efficiencies of the holey carbon film (E_film) for PSL particles are summarized in Table 3.

TABLE 3 Results of measured particle collection efficiency^a

		Grid-1: Quantifoil R1.2/1.3 on 200-mesh Cu			Grid-2: Quantifoil R0.6/1 on 200-mesh Cu
	Particle diameter (nm)	Collection efficiency of the holey carbon film, Efilm	Overall collection efficiency, Egrid	Ratio	Collection efficiency of the holey carbon film, Efilm	Overall collection efficiency, Egrid	Ratio
KCl	5	—	0.23 ± 0.032	—	—	0.32 ± 0.033	—
KCl	10	—	0.11 ± 0.0046	—	—	0.15 ± 0.0034	—
KCl	15	—	0.068 ± 0.0087	—	—	0.080 ± 0.026	—
KCl	30	—	0.070 ± 0.0043	—	—	0.10 ± 0.0076	—
KCl	50	—	0.052 ± 0.025	—	—	0.11 ± 0.0028	—
KCl	100	—	0.25 ± 0.021	—	—	0.33 ± 0.029	—
PSL	30	0.031 ± 0.0021	0.050 ± 0.0059	0.62 ± 0.033	0.053 ± 0.010	0.098 ± 0.017	0.56 ± 0.18
PSL	50	0.049 ± 0.012	0.073 ± 0.019	0.69 ± 0.16	0.085 ± 0.019	0.17 ± 0.060	0.54 ± 0.17
PSL	100	0.12 ± 0.041	0.11 ± 0.012	1.04 ± 0.37	0.24 ± 0.064	0.25 ± 0.059	1.01 ± 0.35
PSL	300	0.60 ± 0.060	0.55 ± 0.032	1.09 ± 0.12	0.71 ± 0.13	0.63 ± 0.15	1.16 ± 0.19

^aValues are given as mean ± standard deviation (n = 3–5).

Representative SEM and TEM images of particles collected on the holey carbon grids are presented in Figure 3. The PSL particles were almost spherical, whereas the KCl particles were close to cubic, but could be approximated as spheres. Although KCl particles were classified by a DMA to obtain monodispersed particles, KCl particles larger than the selected size were also found, as shown in Figure 3d. This was likely due to the effects of the multiple charges.

FIG. 3 SEM images of (a) 100-nm PSL particles collected on Grid-1, and (b) 100-nm PSL particles collected on Grid-2. TEM images of (c) 100-nm PSL particles collected on Grid-1, and (d) 50-nm KCl particles collected on Grid-1.

4.1 Comparison of Filtration Mechanisms

Figure 4 presents the theoretical collection efficiencies for particles with ρ_p = 1 g·cm⁻³ due to individual filtration mechanisms for Grid-1. The collection efficiencies E_I, E_R, E_IR, E_W, and E_DS are based on the individual filtration mechanisms of the holey carbon film, whereas E_mesh represents the total collection efficiency of the copper mesh. The overall collection efficiencies (E_grid) of PSL particles (ρ_p ≈ 1 g·cm⁻³) found in the experiment are also presented in Figure 4 for comparison.

FIG. 4 Particle collection efficiency by size for Grid-1 according to individual filtration mechanisms. The theoretical collection efficiency of particles with ρ_p = 1 g·cm⁻³ at a volume flow rate of 0.3 L·min⁻¹ was calculated for each mechanism using parameters related to the structural characteristics of Grid-1 (Table 1). E_I, E_R, E_IR, E_W, and E_DS are based on the individual filtration mechanisms of the holey carbon film, whereas E_mesh represents the total collection efficiency of the copper mesh. Filled symbols indicate the experimental overall particle collection efficiency (E_grid) for PSL particles (n = 3–5; shown as mean ± standard deviation).

This simulation shows that diffusion to the front surface (E_DS) is the prevailing mechanism for the collection of smaller particles, whereas the contribution of diffusion to the pore wall (E_W) is negligible. For the collection of larger particles, impaction (E_I) and interception (E_R) are the prevailing mechanisms. Although the combined mechanisms of impaction and interception on the filter (E_IR) obtained from Manton's model had a lesser effect than the combination of separately obtained impaction (E_I) and interception (E_R), E_IR was in better agreement with the experimental data.

The collection efficiency of the copper mesh (E_mesh) was smaller than that of the holey carbon film (the combination of E_IR, E_W, and E_DS). This was reasonable, because the pore diameter of the holy carbon film (<2 μm) is smaller than the hole width of the copper mesh (∼100 μm) by approximately two orders of magnitude.

Similar findings were also obtained from the model calculations for Grid-2 and Grid-3 (data not shown).

4.2 Comparison Between Experimental and Theoretical Collection Efficiencies

The experimental and theoretical overall collection efficiencies (E_grid) for Grid-1, Grid-2, and Grid-3 are presented in Figures 5, 6, and 7, respectively. The experimental data in Figure 7 are those reported by R’mili et al. (2013). Because the collection efficiency due to impaction depends on ρ_p, Figures 5 and 6 show the theoretical collection efficiencies of particles with ρ_p = 1 g·cm⁻³ (PSL) and 2 g·cm⁻³ (KCl). Similarly, Figure 7 shows the theoretical collection efficiency of particles with ρ_p = 1.8 g·cm⁻³, which is the true density of NaCl particles. Although the experimental data reported by R’mili et al. (2013) include the collection efficiency of Cu particles (Figure 7), the theoretical collection efficiency of particles with a density corresponding to that of Cu particles could not be calculated. This was due to two factors: (1) the density of the generated Cu particles was unknown, as the effective density of Cu particles produced by a spark-type generator would be lower than the true density of Cu (≈9 g·cm⁻³) (Hering and Stolzenburg 1995; Evans et al. 2003); and (2) I for high-density particles like this substantially exceeded the limits of validity for Equation (14)[14] .

FIG. 5 Overall particle collection efficiency (E_grid) by size for Grid-1. The solid and dotted lines indicate the theoretical collection efficiencies of particles with ρ_p = 1, and 2 g·cm⁻³, respectively, which were calculated using parameters related to the structural characteristics of Grid-1 (Table 1) and a volume flow rate of 0.3 L·min⁻¹. Open and filled symbols indicate the experimental efficiency for KCl and PSL particles, respectively (n = 3–5; shown as mean ± standard deviation).

FIG. 6 Overall particle collection efficiency (E_grid) by size for Grid-2. The solid and dotted lines indicate the theoretical collection efficiencies of particles with ρ_p = 1 and 2 g·cm⁻³, respectively, which were calculated using parameters related to the structural characteristics of Grid-2 (Table 1) and a volume flow rate of 0.3 L·min⁻¹. Open and filled symbols indicate the experimental efficiency for KCl and PSL particles, respectively (n = 3–5; shown as mean ± standard deviation).

FIG. 7 Overall particle collection efficiency (E_grid) by size for Grid-3. The solid line indicates the theoretical collection efficiencies of particles with ρ_p = 1.8 g·cm⁻³, calculated using parameters related to the structural characteristics of Grid-3 (Table 1) and a volume flow rate of 0.3 L·min⁻¹. Open and filled symbols indicate the experimental efficiency for Cu and NaCl particles, respectively, reported by R’mili et al. (2013) (n = 3; shown as mean ± standard deviation).

Regardless of the grid type and given conditions, the theoretical overall collection efficiencies were in reasonably good agreement with the experimental overall collection efficiencies. A slight gap between the theoretical and experimental efficiencies for KCl particles in Figures 5 and 6 would be partly explained by the contributions of particles larger than the selected size. The theoretical minimum collection efficiency diameter was between 25 and 40 nm, which corresponds to the transition region between the two prevailing mechanisms, E_DS and E_IR (Figure 4).

4.3 Differences in Efficiency Among Types of Holey Carbon Grid

The minimum overall collection efficiencies obtained experimentally in the given conditions were approximately 5%, 8%, and 15% for Grid-1, Grid-2, and Grid-3, respectively. Notably, Grid-1 and Grid-2 had a different pore size for the holey carbon film, and, as expected, a smaller pore had a higher efficiency in this case. However, the highest collection efficiency was observed for Grid-3, despite its pore size being larger than that of Grid-2. One key difference between Grid-3 and the others was the mesh size. The 400 copper mesh of Grid-3 had a lower porosity (Table 1), which resulted in a higher face velocity of the flow approaching the pores of the holey carbon film when the volume flow rate (Q) was uniform. Although a higher face velocity can decrease the deposition by diffusion, it increases the deposition by impaction, and thus increases the minimum overall collection efficiencies in the given conditions. If Q is adequately adjusted to obtain the same face velocity, the difference in efficiency between 200- and 400-mesh grids would be eliminated. However, as R’mili et al. (2013) reported, 400-mesh grids (e.g., Grid-3) may be better since their small mesh holes can minimize the risk of damage to the holey carbon film under the pressure induced by flow during sampling.

As reported in Section 2.1, there was a discrepancy between actual and nominal pore sizes for Grid-1 and Grid-2. In addition, there was a large grid-to-grid variation in pore sizes, especially for Quantifoil R0.6/1 (Grid-2); consequently, the results for Grid-2 varied widely (Table 3). As Chen et al. (2013) suggested for Nuclepore filters, performance of pressure-drop checks by sampling clean air before conducting the sampling is recommended in order to check the uniformity of pore sizes. In addition, performing occasional pressure-drop checks during sample collection may alert the user of damage to a holey carbon film (when the pressure decreases) or of clogging (when the pressure increases).

4.4 Collection Efficiency Obtained from Counting Particles on an Electron Microscope

The theoretical model calculation indicated that only a small number of particles were collected on the copper mesh; in fact, very few PSL particles were observed during SEM analysis on the copper mesh of the grid in any of the cases during the experiments. This finding indicates that the collection efficiency of the holey carbon film (E_film) will be nearly equal to the overall collection efficiency (E_grid). As expected, the experimentally measured E_film for 100- and 300-nm PSL particles were comparable to the experimentally measured E_grid (Table 3). On the other hand, the experimentally measured E_film values for 30- and 50-nm PSL particles were approximately 30%–50% lower than the experimentally measured E_grid values (Table 3). This inconsistency may have been caused by errors in the determination of E_film, since the experimentally measured E_film values were determined in a complex manner. Underestimation of E_film values may have resulted from particle loss during the SEM observation preparation process or during the SEM observation. Further studies are needed to reveal the cause of this inconsistency, which could represent a problem when particle number concentration in the air is estimated from the number of particles observed on the holey carbon film using an electron microscope.

5 CONCLUSIONS

This study evaluated the particle collection efficiencies of holey carbon film-coated copper mesh TEM grids both theoretically and experimentally; this approach can be used as a simple sampling method to collect aerosol particles for TEM analysis. We proposed a modified calculation method to represent the collection efficiencies of holey carbon grids that included consideration of the porosity of the copper mesh. Regardless of the grid type and given conditions, the calculated overall collection efficiencies were in reasonably good agreement with the experimental overall collection efficiencies. Although the theoretical calculations indicated that the collection efficiency of the holey carbon film (E_film) would be nearly equal to the overall collection efficiency (E_grid), there was an inconsistency between the experimentally determined E_film and E_grid. Further investigation is needed in order to reveal the cause of this inconsistency, and to establish a method for estimating the particle concentration in the air from the number of particles observed on the holey carbon film using an electron microscope.

FUNDING

The authors would like to thank the New Energy and Industrial Technology Development Organization of Japan (NEDO) for funding the study under a grant for “Innovative carbon nanotubes composite materials project toward achieving a low-carbon society” (No. P10024).