Supplementary Information

1. 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 is

Fc= 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)

τ w=μU 0(wν )

1/2

, (S2)

where U0 is the maximum rotating speed (~ rw), and µ, 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) is

Fv=Ad/(12 x2), (S3)

1

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 1µm spherical particle, and Fc ~ 10-15 N, Fw ~ 10-13 N and Fv ~ 10-7 N for 0.1µm

spherical particle. Adhesive force is three orders of magnitude higher than the separation

forces for the 1µm 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 sizes

Coagulation coefficient K1,2 for coagulation between aerosol particles of different sizes is

expressed (Hinds, 1999),

K 1,2=π (d1 D1+d1 D 2+d2 D1+d2 D2), (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):

d N1

dt=−K11 N1

2−N1 N2 K 12, (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

2

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,

N 1

N 10=e−N2 K12 t, (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 aerosol

Several 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

3

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:

N 1

N 10=e−N2 K12 t, (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

4

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.

5

References

Dahm, 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.

6

Table S1. Comparison of Nanomaterials

Nanomaterial a Exponent b from eqs 1 and 2

Exponent b from data fitting (Table 3)

MWCNT1, VS -2.662 -1.48802

Graphene, ES 1.038 1.5444

CNF, VS -1.058 -0.78436

SWCNT, VS 1.97 0.08343

a Obtained from a functional relation between particle mass and aerodynamic diameter and the assumption that aerodynamic diameter is not too different from mobility diameter.

7

Table S2. Complete dataset of various particle properties for nanomaterials tested in this

study.

Material

dmob (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, VS 300 43.1 77.6 1179.6 695.1 113.7 337496 499823 357017

400 87. 109.2 1231.8 1186.2 159.5 780591 1378942 984959500 84.1 70.8 775.6 741.4 174.2 851257 1798898 1284927600 120.1 80.3 1169.1 1247.4 212.2 766705 3251659 2322614

MWCNT1, VS 100 60.8 543.4 139.7 349.4 64.8 882 452.9 23

200 91 340.6 208.3 497.3 110.9 1280 2270.4 114300 109.9 230.9 244.01 794.3 146.1 3077 5195.8 260400 125 170.1 374.36 1186.2 175.9 5081 9072.9 454

MWCNT1, PA 100 76.3 713.8 264.42 482.57 70.93 2932 594.8 30

200 101.3 390.5 218.04 313.80 116.02 2556 2603 130300 171.5 425.2 310.90 564.96 179.05 3198 9566 478400 199.4 329.1 483.51 768.68 219.20 7794 17554 878

MWCNT2, VS 100 83.8 800.6 - - 73.7 - - -

200 141.8 610.7 - - 134.7 - - -300 167.2 410.1 - - 176.9 - - -400 189.7 305.7 - - 213.9 - - -

MWCNT3, VS 100 176.8 2173.3 391.17 - 102.8 2404 290 6.0

200 283.9 1718.3 461.68 - 190.1 3348 1833 37400 351.7 805.8 678.82 - 295.4 7238 6875 138600 409.9 514.7 537.61 - 381.7 11780 14822 296800 422.0 321.7 914.32 - 435.1 13132 21965 439

MWCNT-OH, ES 100 72.3 668.45 192.17 259.56 69.40 - - -

200 126.2 520.92 271.78 479.70 127.73 - - -300 256.9 781.15 286.18 446.24 219.29 - - -

Silver nanorods, ES

80 69.3 839.9 - - 59.91 - - -

120 127.6 1085.7 - - 97.89 - - -

8

150 150.7 1006.9 - - 119.3 - - -200 211.7 1088.7 - - 163.3 - - -

C60, ES 50 33.72 644.10 - - 34.27 - - -65 43.73 633.15 - - 44.30 - - -80 38.86 432.08 - - 48.00 - - -100 43.37 369.23 - - 56.94 - - -

Graphene, ES 30 32.38 1086.4 274.8 392.5 24.5 - - -

50 18.4 336.9 548.9 595.2 27.6 - - -80 19.61 206.7 311.6 419.3 37.5 - - -100 29.56 242.1 1034.4 1384.8 49.5 - - -

Gold nanorods, ES

40 32.34 791.3 - - 29.4 - - -

50 40.287 783.8 - - 36.6 - - -60 56.305 928.6 - - 46.5 - - -

CNF, VS 100 - - - - 81.168 835.8 99.0 1.65200 - - - - 150.92 2354.9 636.6 10.6400 - - - - 268.63 4087.6 3589.8 59.8

9

List of Figures

Fig. 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) aerosol

Fig. 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

10

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

11

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.

12

13

Fig. 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.

(a)

(c)

(b)

Minor axis, b

Major axis, a

Ellipse

14

Fig. S2 Comparison of aerodynamic diameters measured by ELPI and DMA-APM methods for MWCNT-OH particles.

15

(a)

(b)

Fig. 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.

16

(c)

(d)

Fig. S3 Continued.

17

Fig. S3 Continued.

(e)

(f)

18

Fig. S3 Continued.

(g)

(h)

19

Fig. S3 Continued.

(j)

(i)

20

21

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) aerosol, (G) gold nanorod aerosol and (H) silver nanorods aerosol.

(iv) 400 nm (iii) 300 nm

(ii) 200 nm (i) 100 nm

0.2 µm

A

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

22

(i) 100 nm (ii) 200 nm

(iii) 300 nm (iv) 400 nm

(v) 500 nm

Fig. S5 Continued.

B

23

C

(i) 100 nm (ii) 200 nm

(iii) 300 nm

200 nm

200 nm

Fig. S5 Continued.

24

Fig. S5 Continued.

D

25

(i) 30 nm (ii) 50 nm

(iii) 80 nm (iv) 100 nm

(v) 200 nm

Fig. S5 Continued.

E

26

Aerosolized polydisperse silver particles

H

(ii) 100 nm (i) 80 nm

F

(i) 40 nm (ii) 60 nm

G

Fig. S5 Continued.

27

(b)

(a)

28

Fig. 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.

(c)

29

30

E

A B

C D

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.

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.

31

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.

(b)

(a)

32

(b)

(a)

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=3 πμ dmob /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.