Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2012.

Supporting Information for Adv. Funct. Mater., DOI: 10.1002/adfm.201201285 Gas Diffusion, Energy Transport, and Thermal Accommodation in Single-Walled Carbon Nanotube Aerogels Scott N. Schiffres, Kyu Hun Kim, Lin Hu, Alan J. H. McGaughey, Mohammad F. Islam, and Jonathan A. Malen*

S1

DOI: 10.1002/adfm.201201285

Supporting Information

Gas diffusion, energy transport, and thermal accommodation in single-walled carbon nanotube aerogels

Scott N. Schiffres,1 Kyu Hun Kim,2 Lin Hu,1 Alan J. H. McGaughey,1 Mohammad F. Islam,2

Jonathan A. Malen* 1,2

0.4 0.80 0.2 0.6 1 Spe

cific

Ads

orbe

d Vo

lum

e

!10

3 (c

c/g)

0

0.4

0.8

1.6

1.2

Adsorption

Desorption

P/P0

10 20 30 40 50

0.06

0.04

0.02

0

0.08

Pore Diamter (nm)

dV/d

r (cc

/g/n

m)

a)

b)

S2

Figure S1. Results of SWCNT nitrogen adsorption isotherms and BET derived specific pore

diameters. (a) Nitrogen adsorption isotherms. (b) This specific pore volume versus pore

diameter plot shows that the aerogel contains predominantly mesopores (2-50 nm diameter).

 

Figure S2. (a) Near-infrared fluorescence spectra from a dispersion recreated from SWCNT

aerogels with deoxycholic acid (DOC) indicating that SWCNTs remain intact during the

synthesis of SWCNT aerogels. The color bar indicates emission intensity in arbitrary units. (b)

Raman spectra from pristine SWCNT aerogels (top, red) and SG76 powder (bottom, black).

RBMs of the Raman spectra and the similar peak intensity ratios of D to G bands,

ID,aerogel/IG,aerogel =0.120 and ID,powder/IG,powder =0.128, suggest that SWCNTs remain undamaged

by the SWCNT aerogel synthesis.

a) b)

S3

Figure S3. An energy dispersive spectroscopy (EDX) spectra from the SWCNT aerogel shows

no peak for sodium (Na) and a small peak for Sulfur (S), which are chemical components of

SDBS surfactant. These results indicate that the SDBS surfactant was completely removed, and

thus, the aerogel is free of surfactant. Note that the quantitative value for sulfur (0.5 wt%) is

below the 1% quantitative analysis limit of EDX.

S4

Figure S4. Plot of effective total thermal conductivity for sample 2 versus gas pressure. Fits to

kinetic theory model (eq 5) are indicated with solid lines.

102 103 104 105 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Pressure [Pa]

Ther

mal

con

duct

ivity

[W/m

K]

Total thermal conductivity vs pressure

SWCNT aerogel + H2SWCNT aerogel + HeSWCNT aerogel + NeSWCNT aerogel + N2SWCNT aerogel + Ar

S5

Table S1. 12-6 Lennard-Jones parameters used in the MD simulations for predicting the

accommodation coefficients.

σ (Å) ε (meV)

C-C1 3.4 2.4

Ar-Ar1 3.4 10.61

Ne-Ne1 2.75 3.07

He-He2 2.56 0.88 1. Ackerman, D. M.; Skoulidas, A. I.; Sholl, D. S.; Karl Johnson, J. Diffusivities of Ar and Ne in Carbon Nanotubes. Molecular Simulation 2003, 29, 677–684. 2. Tuzun, R. E.; Noid, D. W.; Sumpter, B. G.; Merkle, R. C. Dynamics of Fluid Flow Inside Carbon Nanotubes. Nanotechnology 1996, 7, 241. Mixing rules for LJ parameters: !!" =

!!!!!!!!

, !!" = !!!!!!

 

S6

Alternative  Derivation  Relating  rs,  re,  and  α  

As an alternative to the recursive derivation presented in the main text, the relationship between

re, rs, and α can be derived by taking re to be a sum that captures the total distance traveled by

the energy of one molecule.

The contribution to re from the first collision with the solid is

!rs , (S1)

from the second collision is !(1!!)2rs , (S2)

and from the nth collision is !(1!!)n!1nrs . (S3)

Combining these gives

re =!rs +!(1!!)2rs +...+!(1!!)n!1nrs . (S4)

We are interested in the limit of n→∞, where

α1lim =

∞→s

e

n rr

. (S5)

This result is the same as eq 9.