Surface-area measurement of polydisperse particles with ...



Supplementary Information1. Order-of-magnitude analysis for adhesive forces between particles of an agglomerate and separation forces by vortex agitation To determine if the energy input to the powder in the tube by vortex shaking is high enough to break agglomerates or it is just sufficient to make them airborne, we compared two opposing forces, i.e., separation force and adhesive force; because we are only interested in comparing order of magnitudes of the opposing forces, we simplify the forces. We assume that separation forces created by vortex shaking are centrifugal force and shear force, and an adhesive force is van der Waals force. The centrifugal force of a rotating particle isFc= mrw2, (S1)where m is particle mass, r, radius of rotation (1.25 cm), and w angular speed (~ 3000 rpm).The shear stress of a particle near the wall in the flow undergoing orbital motion in a plane normal to the gravitational direction can be estimated as following (Salek et al., 2012)τw=μU0wν1/2, (S2)where U0 is the maximum rotating speed (~ rw), and ?, are dynamic and kinematic viscosities of the air, respectively. If the area of the particle is A, shear force acting on the particle is expressed as w A (= Fw).The adhesive force, van der Waals force, between particles (Hinds, 1999) isFv=Ad/(12 x2), (S3)where A is the Hamaker constant (~100x10-20 J), d is particle diameter, and x is an average distance between particles (~ 0.4 nm).Calculating the forces with given values results in Fc ~ 10-12 N, Fw ~ 10-11 N, and Fv ~ 10-8 N for 1?m spherical particle, and Fc ~ 10-15 N, Fw ~ 10-13 N and Fv ~ 10-7 N for 0.1?m spherical particle. Adhesive force is three orders of magnitude higher than the separation forces for the 1?m particle, confirming that the vortex shaking method we used will not impart sufficient energy to the aerosols to break them into smaller particles— in other word, it is just sufficient to make them airborne.2. Coagulation between particles with different sizesCoagulation coefficient K1,2 for coagulation between aerosol particles of different sizes is expressed (Hinds, 1999),K1,2=π (d1D1+ d1D2+ d2D1+ d2D2), (S4)where d1 and d2 are diameters of nanomaterial and background material, and D1 and D2 are diffusion coefficients for particle d1 and d2, respectively. We assume that a nanomaterial particle concentration (N10) is introduced as the initial condition at time t=0 as the result of an impulse injection with a given concentration of a background aerosol, and two concentrations are instantaneously mixed. Also, no constant source and ventilation flow are assumed. The change in nanomaterial number concentration N1 can be expressed as follows with these assumptions (Seipenbusch et al., 2008):dN1dt=-K11N12-N1N2K12, (S5)where K11 and K12 are the coagulation rate constants, respectively, for homogeneous and heterogeneous collisions. Given d1=200 nm and d2=10 nm, it is found that K11 and K12 are 5.5 x 10-16 m3 s-1 and 3.5 x 10-14 m3 s-1, respectively. K12 is larger than K11 by a factor of 64, indicating that the heterogeneous coagulation rate constant strongly depends on the ratio of the particle sizes d of the nanomaterial and the background. Thus, neglecting K11 and solving the eq we obtain the solution,N1N10=e-N2K12t, (S6)It is worth noting that if the particle sizes of the nanomaterial and background would be comparable, i.e., 200 nm, the concentration change of the nanomaterial would be only 5 %, indicating that the difference between the two particle sizes is a major factor affecting the coagulation. Based on this simple calculation of the change of the concentration of the nanomaterial particles, the morphology and density of the particles can be changed in case of high concentration of background aerosol. Kannosto et al. (2008) investigated the mode resolved density of atmospheric aerosol particles and showed that the densities for accumulation mode varied from 1.1 to 2 g cm-3 (average 1.5 g cm-3), for Aitken mode from 0.4 to 2 g cm-3 (average 0.97 g cm-3), and for 15 nm particles 1.2-1.5 g cm-3. By averaging the densities of all modes we obtain a density of 1.3 g cm-3. 3. Calculation of the change of airborne nanomaterial properties via coagulation with background aerosolSeveral studies on workplace monitoring showed that the number concentration of airborne carbon nanotubes and nanofibers generated during harvesting and production was in the range of 2 x 103 to 4 x 104 cm-3, with a mean background particle concentrations of 3.2 x 103 cm-3 (Dahm et al., 2013), and the number concentration of airborne carbon nanofibers released during the bag change and dryer dumping event was about 230 cm-3 and 3000 cm-3, respectively, with a mean background particle concentrations of 6.5 x 105 cm-3 (Evans et al., 2010). Based on this information, we assume that the concentration and diameter of nanomaterial particles is 3000 cm-3 and 200 nm, and that the concentration and diameter of background particles is 105 cm-3 and 10 nm. The rate of change of nanomaterial particle concentration N1 through coagulation with background particles (N2) is expressed as follows:N1N10=e-N2K12t, (S7)where N10 is the initial concentration of nanomaterial particles and K12 are the coagulation rate constants for heterogeneous collisions. The change in net concentration of nanomaterial particles in 10 min is found to be about 87.6 % decrease compared to the initial concentration. If the concentration of the background aerosol is 104 cm-3, the change in net concentration of the nanomaterial particles becomes 18.8 % reduction. We are concerned about how much the particle properties such as density and property-equivalent diameter would change via coagulation with background aerosols. We estimate a typical density of the background aerosol as 1.3 g cm-3 by averaging the densities of all modes based on data from Kannosto et al. (2008), as shown in the previous section. If the target particles (e.g., nanotubes) change their density (typically, 2.0 g cm-3) by coagulation of the background particles with a density of 1.3 g cm-3, and the resulting particles consist of 20% background particles and 80% nanotube particles by mass, the resulting particles will have a density of 1.86 g cm-3. 20 % background particle per nanotube particle by mass is equivalent to the number of about 3000 background particles per nanotube particle. This change of the density will bring 10.2 % increase in volume equivalent diameter dve for the same mass particle. In summary, depending on the concentration level of the background aerosol, coagulation rates are expected to be low. If the concentration of the background aerosol is high, it could change particle density somewhat, but particle volume equivalent diameter would be within 11 % even in the case of 20 % coagulation of the background particles by mass. This fact could justify that the properties measured in the laboratory experiments in this work are more or less relevant to real-world scenarios where mixed aerosols exist. ReferencesDahm, M. M., Evans, D. E., Schubauer-Berigan, M. K., Birch, M. E. and Deddens, J. A. (2013). Occupational Exposure Assessment in Carbon Nanotube and Nanofiber Primary and Secondary Manufacturers: Mobile Direct-Reading Sampling. Ann Occup Hyg 57:328-344.Evans, D. E., Ku, B. K., Birch, M. E., and Dunn, K. H. (2010). Aerosol Monitoring during Carbon Nanofiber Production: Mobile Direct-Reading Sampling. Ann. Occup. Hyg. 52:9–21. Hinds, W. C. (1999). Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles. New York, USA: John Wiley & Sons.Kannosto, J., Virtanen, A., Lemmetty, M., Makela, J. M., Keskinen, J., Junninen, H., Hussein, T., Aalto, P. and Kulmala, M. (2008). Mode resolved density of atmospheric aerosol particles. Atmos Chem Phys 8:5327-5337.Salek, M.M., Sattari, P., & Martinuzzi, R.J. (2012). Analysis of fluid flow and wall shear stress patterns inside partially filled agitated culture well plates. Annals of biomedical engineering, 40, 707-728.Seipenbusch, M., Binder, A. and Kasper, G. (2008). Temporal Evolution of Nanoparticle Aerosols in Workplace Exposure. Ann Occup Hyg 52:707-716.Table S1. Comparison of NanomaterialsNanomateriala Exponent b from eqs 1 and 2Exponent b from data fitting (Table 3)MWCNT1, VS-2.662-1.48802Graphene, ES1.0381.5444CNF, VS-1.058-0.78436SWCNT, VS1.970.08343a Obtained from a functional relation between particle mass and aerodynamic diameter and the assumption that aerodynamic diameter is not too different from mobility diameter.Table S2. Complete dataset of various particle properties for nanomaterials tested in this study.Materialdmob (nm)dae (nm)eff (kg/m3)dproj (nm)denv (nm)dve (nm)Total length based on project area Lproj (nm)Total length based on particle mass Lmass (nm)Aspect ratio based on particle mass (Lmass/dt)SWCNT, VS30043.177.61179.6695.1113.733749649982335701740087.109.21231.81186.2159.5780591137894298495950084.170.8775.6741.4174.285125717988981284927600120.180.31169.11247.4212.276670532516592322614MWCNT1, VS10060.8543.4139.7349.464.8882452.92320091340.6208.3497.3110.912802270.4114300109.9230.9244.01794.3146.130775195.8260400125170.1374.361186.2175.950819072.9454MWCNT1, PA10076.3713.8264.42482.5770.932932594.830200101.3390.5218.04313.80116.0225562603130300171.5425.2310.90564.96179.0531989566478400199.4329.1483.51768.68219.20779417554878MWCNT2, VS10083.8800.6--73.7---200141.8610.7--134.7---300167.2410.1--176.9---400189.7305.7--213.9---MWCNT3, VS100176.82173.3391.17-102.824042906.0200283.91718.3461.68-190.13348183337400351.7805.8678.82-295.472386875138600409.9514.7537.61-381.71178014822296800422.0321.7914.32-435.11313221965439MWCNT-OH, ES10072.3668.45192.17259.5669.40---200126.2520.92271.78479.70127.73---300256.9781.15286.18446.24219.29---Silver nanorods, ES8069.3839.9--59.91---120127.61085.7--97.89---150150.71006.9--119.3---200211.71088.7--163.3---C60, ES5033.72644.10--34.27---6543.73633.15--44.30---8038.86432.08--48.00---10043.37369.23--56.94---Graphene, ES3032.381086.4274.8392.524.5---5018.4336.9548.9595.227.6---8019.61206.7311.6419.337.5---10029.56242.11034.41384.849.5---Gold nanorods, ES4032.34791.3--29.4---5040.287783.8--36.6---6056.305928.6--46.5---CNF, VS100----81.168835.899.01.65200----150.922354.9636.610.6400----268.634087.63589.859.8List of FiguresFig. S1. TEM image analysis for envelop diameter, aspect ratio, project surface area, and posority. (a) Original TEM image, (b) Ellipse inscribing the particle of interest, and major and minor axes, and (c) Black and white image to obtain project area of the particle.Fig. S2 Comparison of aerodynamic diameters measured by ELPI and DMA-APM methods for MWCNT-OH particles.Fig. S3. Typical size distributions of airborne nanomaterial particles by different generation methods: (a) for MWCNTs generated by vortex shaking (VS), (b) for MWCNTs (10-20 nm) by pneumatic atomization (PA), (c) for silver nanorods by electrospraying (ES), (d) MWCNTs (60-100 nm) by VS, (e) graphenes by ES, (f) MWCNT-OH by ES, (g) fullerene (C-60) by ES, and (h) gold nanorods by ES. In the legend of the figure VS stands for vortex shaker, ES for electrospray, and PA for pneumatic atomizer.Fig. S4 Mass vs. mobility diameter for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, ES for electrospray, and PA for pneumatic atomizer.Fig. S5. Typical TEM images of various nanomaterials generated by different methods for different mobility diameters. (A) MWCNT1 aerosol generated by vortex shaking (B) MWCNT1 aerosol generated by pneumatic atomization (C) MWCNT-OH aerosol (D) SWCNT aerosol by dry dispersion (E) graphene aerosol (F) fullerene (C60) aerosolFig. S6. Characteristic diameter and open area vs. mobility diameter for different nanomaterial aerosols: (a) MWCNT aerosol generated by vortex shaking, (b) MWCNT aerosol generated by pneumatic atomization; (c) open area. Also shown is open area of a single fiber for reference (assumed fiber diameter is 25 nm). In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. In Fig. S6 (a) & (b), the error bar of the aerodynamic diameter is not included because its variation is small.Fig. S7. 2-D projected area scaling exponent calculated based on TEM image (assuming fractal theory) vs. mass scaling exponent measured by DMA-APM for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. A line included represents an equation, Df, 3 / Df, 2=1.1.Fig. S8. Total tube or fiber length calculated based on measured mass and tube diameter ((Lmass on y-axis)) and based on projected area and tube diameter of a particle from TEM images (Lproj on x-axis) for different nanomaterials. (a) MWCNT (dry dispersion), (b) MWCNT (liquid nebulization), (c) CNF, (d) SWCNT, and (e) Mitsui MWCNT. Lmass on y-axis was obtained with a formula, mass = tube cross section area times total tube length multiplied by the particle material density. An average tube diameter was assumed in the calculations based on the actual measurements from several TEM images. Lproj on x-axis was calculated with a relation of projected area = total tube length times tube diameter.Figure S9. Comparison of (a) measured mobility diameters with theoretically calculated values, and (b) measured aspect ratios with theoretically calculated values for chain-like nanotubes.Fig. S10 (a) Loading plot showing relationship between variables in the space of the first two principal components, and (b) dynamic shape factor vs. mass. In plot (a), we clearly see that dae, dve, dmob, mass and fc (friction coefficient) have heavy loadings for principal component 1, and that eff and DSF have heavy loadings for principal component 2. Plot (b) shows distinct grouping and mapping of data for each material.7600955448300Fig. S1 TEM image analysis for envelop diameter, aspect ratio, project surface area, and open area. (a) Original TEM image, (b) Ellipse inscribing the particle of interest, and major and minor axes, and (c) Back and white image to obtain project area of the particle.020000Fig. S1 TEM image analysis for envelop diameter, aspect ratio, project surface area, and open area. (a) Original TEM image, (b) Ellipse inscribing the particle of interest, and major and minor axes, and (c) Back and white image to obtain project area of the particle.-4933950(a)(a)10325102785110(c)(c)28534690EllipseMajor axis, aMinor axis, b(b)EllipseMajor axis, aMinor axis, b(b)8255004094480Fig. S2 Comparison of aerodynamic diameters measured by ELPI and DMA-APM methods for MWCNT-OH particles.00Fig. S2 Comparison of aerodynamic diameters measured by ELPI and DMA-APM methods for MWCNT-OH particles.5046456447095Fig. S3 Typical size distributions of airborne nanomaterial particles by different generation methods: (a) for MWCNT1 (10-20 nm) generated by vortex shaking (VS), (b) for MWCNT1 (10-20 nm) by pneumatic atomization (PA), (c) for silver nanorods by electrospraying (ES), (d) MWCNT3 (60-100 nm) by VS, (e) graphenes by ES, (f) MWCNT-OH by ES, (g) fullerene (C-60) by ES, (h) gold nanorods by ES, (i) MWCNT3 generated by VS and (j) SWCNT by dry dispersion.00Fig. S3 Typical size distributions of airborne nanomaterial particles by different generation methods: (a) for MWCNT1 (10-20 nm) generated by vortex shaking (VS), (b) for MWCNT1 (10-20 nm) by pneumatic atomization (PA), (c) for silver nanorods by electrospraying (ES), (d) MWCNT3 (60-100 nm) by VS, (e) graphenes by ES, (f) MWCNT-OH by ES, (g) fullerene (C-60) by ES, (h) gold nanorods by ES, (i) MWCNT3 generated by VS and (j) SWCNT by dry dispersion.35106164208984(b)00(b)365248497790(a)00(a)32448507608(c)00(c)19526855113655Fig. S3 Continued.020000Fig. S3 Continued.36334702007235(d)00(d)371983024765(e)00(e)36341052872141(f)00(f)18205695787126Fig. S3 Continued.020000Fig. S3 Continued.38119053613929(h)00(h)19729456837680Fig. S3 Continued.020000Fig. S3 Continued.380619080118(g)00(g)3964305128570(i)00(i)39008053075341(j)00(j)20643856320155Fig. S3 Continued.020000Fig. S3 Continued. 7340605506085Fig. S4 Mass vs. mobility diameter for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, ES for electrospray, and PA for pneumatic atomizer00Fig. S4 Mass vs. mobility diameter for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, ES for electrospray, and PA for pneumatic atomizer-182880-63500A00A2828925260286500-19050260286500283527526924000-228602724150.2 ?m0.2 ?m10287002231390(i) 100 nm 00(i) 100 nm 37623752257425(ii) 200 nm 00(ii) 200 nm 10382254622165(iii) 300 nm 00(iii) 300 nm 37719004622165(iv) 400 nm 00(iv) 400 nm 8324495627586Fig. S5 Typical TEM images of various nanomaterials generated by different methods for different mobility diameters. (A) MWCNT1 aerosol generated by vortex shaking (B) MWCNT1 aerosol generated by pneumatic atomization (C) MWCNT-OH aerosol (D) SWCNT aerosol by dry dispersion (E) graphene aerosol (F) fullerene (C60) aerosol, (G) gold nanorod aerosol and (H) silver nanorods aerosol.00Fig. S5 Typical TEM images of various nanomaterials generated by different methods for different mobility diameters. (A) MWCNT1 aerosol generated by vortex shaking (B) MWCNT1 aerosol generated by pneumatic atomization (C) MWCNT-OH aerosol (D) SWCNT aerosol by dry dispersion (E) graphene aerosol (F) fullerene (C60) aerosol, (G) gold nanorod aerosol and (H) silver nanorods aerosol.46990-185791B00B19366317479102Fig. S5 Continued.020000Fig. S5 Continued.176212549574450031146752642870002476502642870003114675137795002476501377950012192002271395(i) 100 nm 00(i) 100 nm 39528752271395(ii) 200 nm 00(ii) 200 nm 12287254633595(iii) 300 nm 00(iii) 300 nm 39624004633595(iv) 400 nm 00(iv) 400 nm 26384256948170(v) 500 nm 00(v) 500 nm 19963205321300Fig. S5 Continued.020000Fig. S5 Continued.-30480-6721C00C-76200391795200 nm 200 nm 33718502526665(ii) 200 nm 00(ii) 200 nm 6858002370455(i) 100 nm 00(i) 100 nm 2752725392166007524754687570(iii) 300 nm 00(iii) 300 nm -762002781300200 nm 200 nm -78740-313055D00D17348205456555Fig. S5 Continued.020000Fig. S5 Continued.-30480-160859E00E17602207979243Fig. S5 Continued.020000Fig. S5 Continued.7905757559304(v) 200 nm 00(v) 200 nm 7048502223770(i) 30 nm 00(i) 30 nm 38766752214245(ii) 50 nm 00(ii) 50 nm 7905754900295(iii) 80 nm 00(iii) 80 nm 38100004900559(iv) 100 nm 00(iv) 100 nm 2911475152400002937510287655000-50800287655000-41275548640000-76200152400009715518415F00F9823452418715(i) 80 nm 00(i) 80 nm 31254703371850048895337185004041775143510(ii) 100 nm 00(ii) 100 nm 10287079639G00G312610564770003810650340099695568325H00H3943350175260(ii) 60 nm 00(ii) 60 nm 883920154305(i) 40 nm 00(i) 40 nm 317588582500992042250979Aerosolized polydisperse silver particles 00Aerosolized polydisperse silver particles 21430412466340Fig. S5 Continued.020000Fig. S5 Continued.427008115306(a) 00(a) 4235453191510(b) 00(b) 35395936195(c) 00(c) 711679589615Fig. S6 Characteristic diameter and open area vs. mobility diameter for different nanomaterial aerosols: (a) MWCNT aerosol generated by vortex shaking, (b) MWCNT aerosol generated by pneumatic atomization; (c) open area. Also shown is open area of a single fiber for reference (assumed fiber diameter is 25 nm). In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. In Fig. S6 (a) & (b), the error bar of the aerodynamic diameter is not included because its variation is small.00Fig. S6 Characteristic diameter and open area vs. mobility diameter for different nanomaterial aerosols: (a) MWCNT aerosol generated by vortex shaking, (b) MWCNT aerosol generated by pneumatic atomization; (c) open area. Also shown is open area of a single fiber for reference (assumed fiber diameter is 25 nm). In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. In Fig. S6 (a) & (b), the error bar of the aerodynamic diameter is not included because its variation is small. 8680454267835Fig. S7 2-D projected area-scaling exponent calculated based on TEM image (assuming fractal theory) vs. mass scaling exponent measured by DMA-APM for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. A line included represents an equation, Df, 3 / Df, 2=1.1.00Fig. S7 2-D projected area-scaling exponent calculated based on TEM image (assuming fractal theory) vs. mass scaling exponent measured by DMA-APM for different nanomaterial aerosols. In the legend of the figure VS stands for vortex shaker, PA for pneumatic atomizer and ES for electrospray. A line included represents an equation, Df, 3 / Df, 2=1.1.29080365494020Fig. S8. Total tube or fiber length calculated based on measured mass and tube diameter ((Lmass on y-axis)) and based on projected area and tube diameter of a particle from TEM images (Lproj on x-axis) for different nanomaterials. (a) MWCNT (dry dispersion), (b) MWCNT (liquid nebulization), (c) CNF, (d) SWCNT, and (e) Mitsui MWCNT. Lmass on y-axis was obtained with a formula, mass = tube cross section area times total tube length multiplied by the particle material density. An average tube diameter was assumed in the calculations based on the actual measurements from several TEM images. Lproj on x-axis was calculated with a relation of projected area = total tube length times tube diameter.00Fig. S8. Total tube or fiber length calculated based on measured mass and tube diameter ((Lmass on y-axis)) and based on projected area and tube diameter of a particle from TEM images (Lproj on x-axis) for different nanomaterials. (a) MWCNT (dry dispersion), (b) MWCNT (liquid nebulization), (c) CNF, (d) SWCNT, and (e) Mitsui MWCNT. Lmass on y-axis was obtained with a formula, mass = tube cross section area times total tube length multiplied by the particle material density. An average tube diameter was assumed in the calculations based on the actual measurements from several TEM images. Lproj on x-axis was calculated with a relation of projected area = total tube length times tube diameter.-2622555168265E00E-231140-461010A00A3244215-386715B00B-3009902455545C00C28911552535555D00D198782-303(a) 00(a) 1506886985(b) 00(b) 620202124930Figure S9. Comparison of (a) measured mobility diameters with theoretically calculated values, and (b) measured aspect ratios with theoretically calculated values for chain-like nanotubes.020000Figure S9. Comparison of (a) measured mobility diameters with theoretically calculated values, and (b) measured aspect ratios with theoretically calculated values for chain-like nanotubes.1431230(a) 00(a) 2226372638646(b) 00(b) 4171956328039Fig. S10 (a) Loading plot showing relationship between variables in the space of the first two principal components, and (b) dynamic shape factor vs. mass. In plot (a), we clearly see that dae, dve, dmob, mass and fc (friction coefficient=3πμdmob/C(dmob)) have heavy loadings for principal component 1, and that eff and DSF have heavy loadings for principal component 2. Plot (b) shows distinct grouping and mapping of data for each material.00Fig. S10 (a) Loading plot showing relationship between variables in the space of the first two principal components, and (b) dynamic shape factor vs. mass. In plot (a), we clearly see that dae, dve, dmob, mass and fc (friction coefficient=3πμdmob/C(dmob)) have heavy loadings for principal component 1, and that eff and DSF have heavy loadings for principal component 2. Plot (b) shows distinct grouping and mapping of data for each material. ................
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