Supplementary Information
Carbon Nanotube Penetration through Fiberglass and Electret Respirator Filter and Nuclepore Filter Media: Experiments and Models
Sheng-Chieh Chen
1
, Jing Wang
2,3
, Yeon Kyoung Bahk
2,3
, Heinz Fissan
4,5
, David Y.H.
Pui
1*
1
Particle Technology Laboratory, Mechanical Engineering, University of Minnesota,
111 Church St., S.E., Minneapolis 55455, USA
2
Institute of Environmental Engineering, ETH Zurich, Stefano-Franscini-Platz 3,
8093 Zurich, Switzerland
3
Analytical Chemistry, Empa, Ueberlandstrasse 129, 8600 Dübendorf, Switzerland
4
Institute of Energy and Environmental Technology (IUTA e.V.), Bliersheimer Str. 60,
47229 Duisburg, Germany
5
Center for Nanointegration Duisburg-Essen (CENIDE), Carl Benz-STR. 199, 47057
Duisburg, Germany
*Corresponding author. Tel.: +1 612 625 2537 fax: +1 612 625 6069
E-mail address: dyhpui@umn.edu
400,000
Total number conc.= 2.5*10 5 #/cm 3
Number median diameter= 90 nm
Mode=102 nm
300,000
200,000 water residues
100,000
0
10 20 50 100 200 mobility diameter, nm
500
Fig. S1 Size distribution of aerosolized functionalized MWCNTs for penetration tests
1

of different respirator media measured by the SMPS.
Single Fiber Theory
This study investigated the theoretical particle penetration, P theo
, due to mechanical effect of NaCl and MWCNTs through the fiberglass filter using single fiber theory as (Bahk et al. 2013; Wang et al. 2007, 2011):
P theo
 exp

 d
4

E
T f

1
 t

 
, (S1) where
 is the solidity of the filter, t is the thickness of the filter, d f
is the fiber diameter in the filter media and E
T
is the total single fiber efficiency. E
T
is the total efficiency due to diffusion ( E
D
), interception ( E
R
), interception of diffusing particles
( E
DR
) and impaction ( E
I
) and determined as:
E
T

1


1

E
D

1

E
R

1

E
DR

1

E
I

. (S2)
The E
D
, E
R
, E
DR
and E
I
are calculated as (Wang et al. 2007, 2011):
E
D

0 .
84 Pe

0 .
43 , (S3)
E
R

1

R
2 Ku




2 ln

1

R


1
  
1
1

R
2

1

2


2

1

R

2



, (S4)
E
DR

1 .
24

Ku

R 2 3
Pe

1 2 and
E
I

1

2 Ku

2
 
29 .
6

28
 0 .
62

R
2 
27 .
5 R
2 .
8

Stk ,
(S5)
(S6) where Pe is the Peclet number, Ku is the Kuwabara hydrodynamic parameter, R is the ratio of particle diameter to the fiber diameter and Stk is the Stokes number. The Pe and Ku are calculated as:
Pe
 d f
U
0
D and
Ku

 ln

2

3
4
  

2
4
,
(S7)
(S8)
2

where U
0
is face velocity. The definitions of R and Stk are different between NaCl and MWCNT due to the generic dynamics (Wang et al. 2011). Briefly, the particle diameter used in the interception depositions, Equations (S4) and (S5), for MWCNTs should use the effective length, L eff
(determined from SEM analysis) and introduce an angle of 40 o
for the assumption of random orientation as (Wang et al. 2011):
R

L eff
 sin 40 0 d f
. (S9)
The Stk for NaCl is calculated as:
Stk

 p d p
2
C c
U
18
 d f
0 , (S10) where
 p
is NaCl density (2.2 g cm
-3
), d p
is the particle mobility diameter, C c
is the
Cunningham slip correction factor and
 is the air viscosity (Ns m
-2
). For the Stk of
MWCNTs, the aerodynamic radius proposed by Spurny (1986) should be introduced to account for the effect of orientation on the impaction depositions. For more details, please refer to Equations (S8-S11) of Wang et al. (2011). However, since the impaction deposition was very low for the current MWCNTs due to the low Stokes number of <0.01, the mechanism was neglected in this study.
Mechanical and Electrostatic Deposition in Electret Filters
To calculate the single fiber efficiency of the tested electret filter which is a split type (Lathrache et al. 1986; Baumgartner et al. 1986) bipolar charged fibrous filter (Li et al. 2012), a superposition of mechanical and electrostatic collection effects should be carried out in the model. Therefore Equation (S2) should be revised for taking the electrostatic attraction deposition, E q
, into account as:
E
T

1


1

E
D

1

E
R

1

E
DR

1

E
I
 
1

E q

. (S11)
For charged particles in bipolarly charged fibers, due to Coulombic effect, the
Coulombic electrostatic deposition efficiency, E qC
, was calculated as (Lathrache and
Fissan 1986):
E qC


Ku

1 8
1


2

N
CD
N
CD
1 4
. (S12)
3

N
CD
is a dimensionless parameter for charged particles through bipolarly charged fibrous filter and defined as:
N
CD

3

0

C c
1


 q f
 d p
U
0
, (S13) where
 is the charge density of the fiber (C m
-2
), q is the carried charge of particle
(C),
 f
is the fabric dielectric constant (1.5 for the polypropylene of current electret media) and

0
is the permittivity of the vacuum (8.85×10
-12
C
2
N
-1 m
-2
).
For uncharged particles through bipolarly charged fibers, dielectrophoretic effect dominates the deposition, especially for larger particles. The dielectrophoretic deposition efficiency, E qD
, was calculated as (Lathrache and Fissan 1986):
E qD


Ku
2 5
1


2

N
DD
N
DD
2 3
(S14) and
N
DD

3

0
2 C

2

1
 c
 f d

2
2 p d f
U
0
 p
 p

1

2
, (S15) where N
DD
is a dimensionless parameter for uncharged particles through bipolarly charged fibrous filter, and
 p
is the relative permittivity of the particle, which is 6 for
NaCl and 2.5 for carbon black and was used for the MWCNT in this study.
Because the tested particles were in charge equilibrium, the charge distribution of particles was necessary to be considered in the calculation of electrostatic attraction deposition. The charging models developed by Wen et al. (1984), Wiedensohler et al.
(1986) and Wiedensohler (1988) were applied for the MWCNT and NaCl, respectively. In the model, the aspect-ratio and the minor axis diameter of the
MWCNT were determined from SEM analysis, and NaCl particles were treated as spherical. Results showed that the MWCNTs tended to have a smaller neutral fraction compared to sphere-like NaCl of the same mobility size. The reduced fraction was about 5, 3, 2 and 2% for 20, 50, 100 and 300 nm mobility diameter, respectively, and the reduced fractions of MWCNT were distributed to singly and higher charged particle fractions. The results here show that the MWCNTs hold more charges than spheres of the same mobility diameter on average, in agreement with previous results for agglomerates (Wang et al. 2010; Shin et al. 2010). Thus the Coulombic attraction
4

for MWCNTs will be stronger than for NaCl. The dielectrical effect is also stronger for MWCNTs. So qualitatively, the electrostatic deposition efficiency for CNTs should be higher than that for NaCl. This effect, together with the longer interception length, makes the electret filter more efficient for MWCNTs.
Based on the charging distribution results, Equations (S14) and (S15) were used for the penetration calculation of uncharged NaCl and MWCNT particles. On the other hand, Equations (S12) and (S13) should be used for charged particles. Therefore, the total electrostatic penetration should be:
P theo
 f
 exp

 d
4

E
T f

1

0 t


 n

10  n
 n


0
10 f
 exp

4

E
T
 d f
1

 
 n
 t
 
, (S16) where f (0) is the fraction of particles remained neutral and f ( n ) is the fraction of particles with n of unit charge. The E
T0
and E
T
( n ) are defined as:
E
T 0

1


1

E
D

1

E
R

1

E
DR

1

E
I
 
1

E qD

(S17) and
E
T
 

1


1

E
D

1

E
R

1

E
DR

1

E
I
 
1

E qC

, (S18) respectively, where E qC
( n ) represented the Coulombic electrostatic deposition efficiency for the particles carrying charges from negative 10 all the way to positive
10 and particles carrying more than 11 charges were neglected. As mentioned earlier, impaction deposition was neglected for MWCNTs, therefore E
I
was equal to zero in
Equations (S17) and (S18) for MWCNTs but not for NaCl.
The depositions of polydisperse MWCNTs with the mobility diameter of 20-500 nm on HD-2583 and 3M #1 filters are shown in Figure S2.
5

(a) (b)
Fig. S2 Deposition of polydisperse MWCNTs (d m
=20-500 nm) on HD-2583 (left) and
3M electret #1 (right) filters.
Effective Length of Different Mobility Diameter MWCNT
Since the effective length is the crucial parameter on the MWCNT filtration for the tested respirator filter media and Nuclepore filter and it usually dominates the filter deposition as shown earlier, here, we are presenting the SEM analysis result of their effective length as function of mobility diameter to help clarify the MWCNT deposition mechanisms. Figure S3(a) shows the effective length distributions of the monodisperse MWCNTs with 50 and 100 nm mobility diameters and those for 150,
200, 300, 400 and 500 nm mobility diameters are shown in Figure S3(b). The monodisperse MWCNTs were found to have a broad distribution as that found in Seto et al. (2010). Figure S3(a) indicates that multiple charge MWCNTs were collected on the samples, obviously in the 100 nm sample. Because these unintentionally obtained larger MWCNTs did not affect the penetration in Nuclepore and respirator filters significantly (< 1% of penetration), the effect was neglected in this study. In comparison, the multiple charge effect was not obvious in larger mobility diameter
MWCNTs as shown in Figure S3(b). This was because the classified larger monodisperse MWCNTs were at the right hand side (larger mobility diameter) of the peak of the polydisperse MWCNT distribution.
6

0.2
0.1
0.4
(a)
0.3
d m
=50 nm,
 g
=1.51
d m
=100 nm,
 g
=1.27
0
0-
50
50
-1
00
10
0-
15
0
15
0-
20
0
20
0-
25
0
25
0-
30
0
30
0-
35
0
35
0-
40
0
40
0-
45
0
45
0-
50
0
50
0-
55
0
55
0-
60
0
60
0-
65
0 effective length, nm
0.5
(b)
0.4
0.3
d m
=150 nm,
 g
=1.47
d m
=200 nm,
 g
=1.35
d m
=300 nm,
 g
=1.55
d m
=400 nm,
 g
=1.43
d m
=500 nm,
 g
=1.39
0.2
0.1
0
0-
20
0
20
0-
40
0
40
0-
60
0
60
0-
80
0
80
0-
10
00
10
00
-1
20
0
12
00
-1
40
0
14
00
-1
60
0
16
00
-1
80
0
18
00
-2
00
0
20
00
-2
20
0
22
00
-2
40
0
24
00
-2
60
0 effective length, nm
Fig. S3 Effective length distribution of the MWCNTs with 50 and 100 nm mobility diameter (a) and 150, 200, 300, 400 and 500 nm mobility diameter (b) determined by
Image J.
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