For nanoparticles with nonspherical morphologies, e.g., open agglomerates or fibrous particles, it is expected that the actual density of agglomerates may be significantly different from the bulk material density. It is further expected that using the material density may upset the relationship between surface area and mass when a method for estimating aerosol surface area from number and mass concentrations (referred to as “Maynard’s estimation method”) is used. Therefore, it is necessary to quantitatively investigate how much the Maynard’s estimation method depends on particle morphology and density. In this study, aerosol surface area estimated from number and mass concentration measurements was evaluated and compared with values from two reference methods: a method proposed by Lall and Friedlander for agglomerates and a mobility based method for compact nonspherical particles using well-defined polydisperse aerosols with known particle densities. Polydisperse silver aerosol particles were generated by an aerosol generation facility. Generated aerosols had a range of morphologies, count median diameters (CMD) between 25 and 50 nm, and geometric standard deviations (GSD) between 1.5 and 1.8. The surface area estimates from number and mass concentration measurements correlated well with the two reference values when gravimetric mass was used. The aerosol surface area estimates from the Maynard’s estimation method were comparable to the reference method for all particle morphologies within the surface area ratios of 3.31 and 0.19 for assumed GSDs 1.5 and 1.8, respectively, when the bulk material density of silver was used. The difference between the Maynard’s estimation method and surface area measured by the reference method for fractal-like agglomerates decreased from 79% to 23% when the measured effective particle density was used, while the difference for nearly spherical particles decreased from 30% to 24%. The results indicate that the use of particle density of agglomerates improves the accuracy of the Maynard’s estimation method and that an effective density should be taken into account, when known, when estimating aerosol surface area of nonspherical aerosol such as open agglomerates and fibrous particles.

Recent review articles and toxicology studies have indicated the potential occupational health risks associated with inhaling some types of nanoparticles and have suggested that evaluating exposures to such particles using aerosol surface area may be more appropriate under some circumstances (

Two near real-time methods for estimating aerosol surface area using number and mass concentrations have been suggested for analyzing exposures to nanoparticles in the atmosphere and workplace (

For this present study, the Maynard’s estimation method was evaluated and compared with mobility based methods for agglomerates and compact particles using well-defined polydisperse aerosols with controlled morphologies and known particle densities. The main aim of the study was to quantitatively investigate the effect of agglomerate particle density on the Maynard’s surface area estimation method. Polydisperse silver aerosol particles were generated by an aerosol generation facility developed by

^{3} to 10^{4} particles/cm^{3} for monodisperse aerosols and approximately 10^{7} particles/cm^{3} for polydisperse aerosols. Aerosol morphology is controlled using a sintering furnace at different temperatures ranging from room temperature (approximately 20°C) up to 900°C (near the melting point of 962°C for bulk silver).

The number size distributions of polydisperse aerosols generated at different sintering temperatures were measured using a scanning mobility particle sizer (SMPS, Model 3936, TSI, Inc.) together with a condensation particle counter (CPC, Model 3022a, TSI, Inc.). The SMPS was calibrated using standard monodisperse polystyrene latex (PSL) particles of diameters 20 and 100 nm (Duke Scientific Co.).

For aerosol mass measurements, an aerosol photometer (DustTrak, Aerosol Monitor Model 8520, TSI, Inc.) was used, together with filter media in parallel (0.6-

To control particle morphology, sintering temperatures were varied between 20°C (room temperature) and 500°C. Transmission electron microscopy (TEM) samples were collected using a thermophoretic precipitator (

To quantitatively evaluate the Maynard’s estimation method, reference surface areas were calculated on the basis of two different approaches for agglomerates and sintered compact particles, respectively.

To calculate surface area of agglomerates, a method proposed by _{p}_{m}

^{*} is the dimensionless drag force for agglomerates (^{*} = 6.62 for motion parallel to viscous flow of gas [

To calculate surface area of sintered compact particles, an SMPS was used to give a reference aerosol surface area from the measured number size distribution. Previous studies showed that the mobility diameter of an agglomerate or spherical particle is nearly equal to the diameter of a sphere with the same projected surface area measured by TEM for monodisperse open silver agglomerates below 100 nm and for TiO_{2} agglomerates below 400 nm (

This method is based upon the approach reported by

_{1} = _{2} = CMD, and _{3} = _{g}
^{(}GSD). Φ is the normalized lognormal function.

The difference between the expected values (_{ex} is the expected total number concentration and _{ex} is the expected mass concentration) and measured values (_{meas} and _{meas}) will be minimized when the following relation is met,

_{ma} is the diameter of average mass and d_{i}_{,min} and d_{i}_{,max} (index _{ma} = CMDe^{1.5ln2σg} can be used to evaluate _{g}, as shown in

Thus, if _{g} is fixed, _{meas}) concentration and mass concentration (_{meas}) were measured using the SMPS and CPC, and DustTrak and filter media, respectively.

Aerosol surface area concentration from two independent measurements of particle number and mass concentrations can be calculated as follows:
_{s} is the diameter of average surface and _{s} = CMDe^{ln2σg}.

It is worth noting that in

Differential mobility analyzer (DMA)-classified monodisperse agglomerates were provided into an aerosol particle mass analyzer (APM, Model 3600, Kanomax, Inc.) to measure mean particle mass. Briefly, the APM consists of two concentric cylinders that rotate together at a controlled rate. The outer cylinder (52 mm in radius) is electrically grounded, and a classifying voltage is applied to the inner cylinder (50 mm in radius). Charged particles introduced axially into the small annular gap experience centrifugal and electrostatic forces, which act in opposite directions. The concentration of particles downstream from the APM is measured as the classifying voltage is varied as shown in

Several definitions for effective density of agglomerates have been well discussed by

CMDs and GSDs obtained from TEM image analysis using ImageJ analyses are summarized in

^{2} corresponds to 0.06 and 0.05 for GSDs of 1.5 and 1.8, respectively. It may be reasonable to assume that the mass of the agglomerates measured by the filter media at 20°C is more reliable than the one measured by the DustTrak under the same condition because some errors associated with the particle-loaded filter weighing such as humidity and electrostatics effects were minimized when the particle mass was measured in the controlled environment. It is reported that the gravimetric uncertainty is mostly due to weighing procedure and initial and final mass filter conditioning (^{2} is 0.8155 and 0.8301, respectively (not shown in

All the surface areas estimated by the method are summarized in

The agglomerate particle sizes in this study ranged from 50 to 400 nm in diameter. The corresponding density was found to be in the range from 0.44 to 2.24 g cm^{−3}. The density of the agglomerates decreased as the size of the agglomerates increased, which means that the agglomerates have more open structure as size increases. Given that the bulk density of a spherical silver particle is 10.5 g cm^{−3}, the densities measured in the size range are significantly low. The estimates of surface area were obtained for DustTrak and filter with the assumed GSD = 1.8 using an effective density of the agglomerates and are shown in ^{−3}, which corresponds to the density of agglomerates with 200 nm. The contribution to surface area of agglomerates larger than modal diameter (approximately 50 nm) for the case of nonsintered particles is expected to be significant. It is therefore reasonable to assume that a representative density of the agglomerates in the whole size range will be the one for agglomerates at a modal diameter or mean diameter of a surface area-weighted size distribution. The surface area-weighted size distribution obtained from the number size distribution for nonsintered particles in ^{−3} for the surface area estimate, which corresponds to 100 and 150 nm, respectively, the estimate shows better agreement with the reference value within 23% compared with the estimate within 79% when the bulk density of silver was used. The results clearly show that the use of effective density of agglomerates improves the accuracy of the Maynard’s estimation method.

^{−3} as particle size increases from 50 to 150 nm. It is worth noting that particles in the size range of 50 to 100 nm have a similar density to one another and also have a density close to the bulk material density of silver. The difference between estimated surface area and reference surface area measured by the SMPS slightly decreases as particle density decreases from 8.61 to 5.39 g cm^{−3} and then increases significantly as particle density decreases from 5.39 to 1 g cm^{−3}. As can be seen in ^{−3}. The data from

^{−3}, while the deviation for spherical particles increases as particle density decreases. The minimum deviation, i.e., around 0%, occurs with particle density between 1.0 and 0.8 g cm^{−3} for agglomerates, while it occurs with particle density of about 6.0 g cm^{−3} for nearly spherical particles. The reason the use of effective particle density improves the accuracy of the Maynard’s estimation method is that agglomerate particles have a density lower than their material density, as shown in

In the previous section, it was shown that the effective particle density affects the accuracy of the Maynard’s estimation method. Because the effective density can span up to a range of about 24 (e.g., from 0.44 to 10.5 g cm^{−3}) for agglomerate particles, the difference between the estimated surface area and reference surface area was significant when the material density was used. On the other hand, the Maynard’s method was found to work well for nearly compact spherical particles assuming the material particle density. According to the measurement of effective density of the particles sintered at 500°C, most of particles with sizes smaller than 100 nm were found to have density of about 8.5 g cm^{−3}, which is 19% difference from the material density of silver. This fact justifies using the material density to estimate surface area of compact particles from the Maynard’s method.

The advantage of the Maynard’s estimation method is that it provides a means of estimating aerosol surface area exposure easily in the workplace where measurements of aerosol number and mass concentration are frequently made in parallel in real time. The aerosol photometer is used to measure aerosol mass concentration in the workplace and provides important insights into how exposures may occur (

One issue for use of the Maynard’s estimation method is that the assumed particle density, i.e., material density of the particle, causes a significant error in estimation of the particle surface area for silver agglomerates approximately 55% higher than the actual particle density. The error could be even more drastic for complex aerosols with high dynamic shape factors, such as carbon nanotube agglomerates. It is not expected that an aerosol generated in workplace will have spherical shape, particularly nanoparticles. For example, the aerosols generated from processes involving one dominant generation mechanism, such as welding, smelting, and powder handling, may have a single mode distribution and may also be agglomerates, not single spherical particles (

Another issue of the Maynard’s estimation method is that the particle surface physical characteristics, such as particle roughness and pores, and their contribution to surface area are not captured by the method. Particle roughness may increase particle surface area (

The estimates from the total number and mass concentration measurements were comparable to the reference methods for all morphologies of silver agglomerates within the surface area ratios of 3.31 and 0.19 for assumed GSDs 1.5 and 1.8, respectively, when the material density of silver was used. The difference between the estimate and surface area measured by the reference method for fractal-like agglomerates decreased from 79% to 23% when the measured effective particle density was used while the difference for nearly spherical particles decreased from 30% to 24%. The number and mass estimates correlated well with the two reference calculations when gravimetric mass was used, depending on the assumed value of GSD used for CMDs less than 100 nm. The results clearly show that the use of actual agglomerate density improves the accuracy of the Maynard’s estimation method and that the use of particle density of agglomerates should be taken into account, when known, when estimating surface area of nonspherical aerosol such as open agglomerates and fibrous particles. Particle effective density in the workplace could be determined using tandem mobility mass analysis even though highly specialized instruments such as SMPS and APM are needed.

The authors would like to thank Dr. Andrew Maynard, School of Public Health at the University of Michigan; Dr. Aleks Stefaniak, Division of Respiratory Disease Studies (DRDS)/National Institute for Occupational Safety and Health (NIOSH) in Morgantown, WV, for his invaluable comments and suggestions on this work; and Ellen Galloway for editorial assistance. This work was funded by the NIOSH through the Nanotechnology Research Center (NTRC) program (project CAN 927ZBCL).

This article not subject to United States copyright law.

The mention of any company or product does not constitute an endorsement by the Centers for Disease Control and Prevention. The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health.

Experimental setup (MFC, mass flow controller; HEPA, high-efficiency particulate air filter; SMPS, scanning mobility particle sizer; CPC, condensation particle counter; TEM, transmission electron microscopy).

Schematic diagram for measuring an effective density of single mobility size particles by a tandem mobility mass analysis (DMA: differential mobility analyzer; APM: aerosol particle mass analyzer; NT: neutralizer). Adapted from

Typical number concentration as a function of APM voltage for particles classified by the APM at a fixed rotating speed. The peak voltage corresponds to mean mass of the classified particles. (Color figure available online).

Typical size distributions measured by SMPS at different sintering temperatures (without sintering and with sintering at 500°C shown).

TEM images of polydisperse aerosols at different sintering temperatures.

TEM images (a) before and (b) after image processing by threshold for no sintering for particles sampled by a thermophoretic precipitator. (c) Normalized number size distributions measured from SMPS and TEM data for the particles.

Comparison of aerosol total mass concentrations measured by the DustTrak and filter media at different sintering temperatures. The error bar on the data was expressed as the standard deviation of three measurements made for the DustTrak and as a detection limit of the filter (

Estimation of aerosol surface-area from number and mass concentration measurements, assuming geometric standard deviation (_{g}) is 1.5 and 1.8 and particle density is 10.5 g cm^{−3}. Number concentration was taken from the size distribution measured with the SMPS and mass concentration measured using a DustTrak (TSI, Inc.) and filter media. Calculated surface areas for agglomerates at 20°C and 200°C and sintered particles at 300°C and 500°C were obtained, respectively, by the method by

Difference between estimated surface area and calculated surface area as a function of particle density for filter and DustTrak data. _{est} is estimated surface area and _{cal} is surface area calculated by either the method for agglomerates (

Statistics of number distributions measured by SMPS at different sintering temperatures

Sintering temperature (°C) | Number concentration (cm^{−3}) | CMD | GSD | Diameter of average mass (nm) |
---|---|---|---|---|

20 | 8.68E+06 | 45.2 | 1.79 | 75.2 |

200 | 8.54E+06 | 35.7 | 1.74 | 56.6 |

300 | 8.24E+06 | 30.5 | 1.58 | 41.7 |

500 | 8.41E+06 | 26.7 | 1.51 | 34.4 |

CMD means count median diameter.

GSD means geometric standard deviation.

Statistics of number and surface area distributions measured by SMPS and TEM

Number | SMPS | TEM (TP) | TEM (EP) | |||
---|---|---|---|---|---|---|

| ||||||

Sintering temperature (°C) | CMD | _{g} | CMD | _{g} | CMD | _{g} |

20 | 45.2 | 1.79 | 33.2 | 1.62 | — | — |

200 | 35.7 | 1.74 | 21.2 | 1.86 | 17.6 | 1.64 |

300 | 30.5 | 1.58 | 18.0 | 1.68 | 15.8 | 2.22 |

500 | 26.7 | 1.51 | — | — | 24.8 | 2.69 |

TP means thermophoretic sampling.

EP means electrostatic precipitator sampling.

Count median diameters estimated by Maynard’s method using number and mass concentrations, assuming GSD = 1.5 and GSD = 1.8

Sintering temperature (°C) | CMD (measured) | GSD = 1.5
| GSD = 1.8
| |
---|---|---|---|---|

CMD (estimated) | CMD (estimated) | |||

F | 20 (no sintering) | 45.2 | 79.4 | 22.0 |

F | 200 | 35.7 | 60.4 | 17.9 |

F | 300 | 30.5 | 64.3 | 18.8 |

F | 500 | 26.7 | 46.6 | 14.3 |

D | 20 (no sintering) | 45.2 | 37.1 | 21.0 |

D | 200 | 35.7 | 46.7 | 29.7 |

D | 300 | 30.5 | 43.9 | 27.2 |

D | 500 | 26.7 | 34.5 | 18.6 |

F stands for filter and D for DustTrak (TSI, Inc.).

Estimation of surface area from total number and mass concentrations, assuming GSD = 1.5 and GSD = 1.8

Sintering temperature (°C) | Reference surface area_{cal} (cm^{2} m^{−3}) | GSD = 1.5_{est} (cm^{2} m^{−3}) | SR_{est}/_{cal}) | %Δ^{*} (_{est} – _{cal})/ _{cal} | GSD = 1.8_{est} (cm^{2} m^{−3}) | SR (_{est}/_{cal}) | %Δ^{*} (S_{est} – S_{cal})/ _{cal} | |
---|---|---|---|---|---|---|---|---|

F | 20 (no sintering) | 1.69E+03 | 2.35E+03 | 1.39 | 39 | 3.50E+02 | 0.21 | −79 |

F | 200 | 1.09E+03 | 1.34E+03 | 1.23 | 23 | 2.73E+02 | 0.25 | −75 |

F | 300 | 4.49E+02 | 1.49E+03 | 3.31 | 231 | 2.82E+02 | 0.63 | −37 |

F | 500 | 3.30E+02 | 7.98E+02 | 2.42 | 142 | 2.30E+02 | 0.70 | −30 |

D | 20 (no sintering) | 1.69E+03 | 5.13E+02 | 0.30 | −70 | 3.29E+02 | 0.19 | −81 |

D | 200 | 1.09E+03 | 8.00E+02 | 0.73 | −27 | 5.30E+02 | 0.49 | −51 |

D | 300 | 4.49E+02 | 6.95E+02 | 1.55 | 55 | 4.53E+02 | 1.01 | 1 |

D | 500 | 3.30E+02 | 4.36E+02 | 1.32 | 32 | 2.83E+02 | 0.86 | −14 |

F stands for filter and D for DustTrak (TSI, Inc.).

Obtained by a method proposed by

Obtained from the scanning mobility particle sizer (SMPS) for sintered compact particles.

SR means a ratio of estimated surface area to reference surface area.

Estimation of surface area from total number and mass concentrations using measured effective particle densities for agglomerates (nonsintered particles), assuming GSD = 1.8

Diameter | Density^{−3}) | Reference surface area _{cal} (cm^{2} m^{−3}) | DustTrak, GSD = 1.8 estimated surface area _{est} (cm^{2} m^{−3}) | SR_{est}/_{cal}) | %Δ^{*} (_{est} – _{cal})/_{cal} | Filter, GSD = 1.8 estimated surface area_{est} (cm^{2} m^{−3}) | SR (_{est}/_{cal}) | %Δ^{*} (_{est} – _{cal})/_{cal} |
---|---|---|---|---|---|---|---|---|

50 | 2.24 | 1.69E+03 | 5.35E+02 | 0.32 | −68 | 9.02E+02 | 0.53 | −47 |

100 | 1.79 | 1.69E+03 | 5.83E+02 | 0.34 | −66 | 1.04E+03 | 0.62 | −38 |

150 | 1.29 | 1.69E+03 | 6.65E+02 | 0.39 | −61 | 1.29E+03 | 0.77 | −23 |

200 | 0.95 | 1.69E+03 | 7.55E+02 | 0.45 | −55 | 1.58E+03 | 0.93 | −7 |

250 | 0.78 | 1.69E+03 | 8.25E+02 | 0.49 | −51 | 1.80E+03 | 1.07 | 7 |

300 | 0.63 | 1.69E+03 | 9.08E+02 | 0.54 | −46 | 2.08E+03 | 1.23 | 23 |

350 | 0.56 | 1.69E+03 | 9.61E+02 | 0.57 | −43 | 2.25E+03 | 1.33 | 33 |

400 | 0.44 | 1.69E+03 | 1.08E+03 | 0.64 | −36 | 2.66E+03 | 1.57 | 57 |

Classified by a differential mobility analyzer (DMA).

Obtained from mass measurement of the DMA-classified particles by an aerosol particle mass analyzer (APM).

SR means a ratio of estimated surface area to reference surface area.

Estimation of surface area from total number and mass concentrations using measured effective particle densities for nearly spherical particles, assuming GSD = 1.8

Diameter | Density^{−3}) | Reference surface area_{cal} (cm^{2} m^{−3}) | DustTrak, GSD = 1.8 estimated surface area_{est} (cm^{2} m^{−3}) | SR_{est}/_{cal}) | %Δ^{*}(_{est} – _{cal})/ _{cal} | Filter, GSD = 1.8 estimated surface area _{est} (cm^{2} m^{−3}) | SR (_{est}/_{cal}) | %Δ^{*} (_{est} – _{cal})/_{cal} |
---|---|---|---|---|---|---|---|---|

50 | 8.61 | 3.30E+02 | 2.96E+02 | 0.90 | −10 | 2.49E+02 | 0.76 | −24 |

80 | 8.52 | 3.30E+02 | 2.97E+02 | 0.90 | −10 | 2.51E+02 | 0.76 | −24 |

100 | 8.36 | 3.30E+02 | 2.98E+02 | 0.90 | −10 | 2.53E+02 | 0.77 | −23 |

120 | 5.39 | 3.30E+02 | 3.32E+02 | 1.01 | 1 | 3.14E+02 | 0.95 | −5 |

150 | 3.55 | 3.30E+02 | 3.73E+02 | 1.13 | 13 | 3.97E+02 | 1.20 | 20 |

– | 1.00 | 3.30E+02 | 5.76E+02 | 1.75 | 75 | 8.72E+02 | 2.64 | 164 |

Classified by a differential mobility analyzer (DMA).

Obtained from mass measurement of the DMA-classified particles by an aerosol particle mass analyzer (APM) except unit density (1 g cm^{−3}).

SR means a ratio of estimated surface area to reference surface area.