Post on 06-Aug-2019
Molecular Simulation Aided Nanoporous Carbon Design
for Highly Efficient Low-Concentrated Formaldehyde
Capture
Piotr Kowalczyk*1, Jin Miyawaki2,3, Yuki Azuma3, Seong-Ho Yoon2,3, Koji
Nakabayashi2,3, Piotr A. Gauden4, Sylwester Furmaniak4, Artur P. Terzyk4, Marek
Wisniewski4, Jerzy Włoch5, Katsumi Kaneko6 and Alexander V. Neimark7
1School of Engineering and Information Technology, Murdoch University,
Perth, Western Australia 61502Institute for Materials Chemistry and Engineering, Kyushu University,
6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
3Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka, 816-8580, Japan.
4 Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group,
Nicolaus Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń,
Poland5 Faculty of Chemistry, Synthesis and Modification of Carbon Materials
Research Group, Nicolaus Copernicus University in Toruń, Gagarin Street 7,
87-100 Toruń, Poland
6 Center for Energy and Environmental Science, Shinshu University, Nagano
380-8553, Japan 7 Department of Chemical and Biochemical Engineering, Rutgers, The State
University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854-8058,
United States Corresponding author. Email: P.Kowalczyk@murdoch.edu.au (Piotr Kowalczyk)
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Supporting Information
TABLE OF CONTENTS
Section 1: Experimental Details
1.1. Elemental CHN analysis
1.2. Nitrogen measurements (77 K) and porosity analysis
1.3. Surface carbon and oxygen content by XPS analysis
Section 2: Detailed computational methods
2.1. Molecular models
2.2. Formaldehyde adsorption isotherms (stable, metastable, and unstable states)
2.3. Isosteric heat of adsorption
2.4. Efficiency factor computed at zero-coverage
2.5. Analysis of formaldehyde-oxygen functionalities hydrogen bonds
2.6. Total pair correlation function calculations: wide-angle X-ray scattering
from adsorbed formaldehyde
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REFERENCES
[1S] A. V. Neimark, Y. Lin, P. I. Ravikovitch, M. Thommes, Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons, Carbon 47 (2009) 1617-1628.[2S] [W. L. Jorgensen, D. S. Maxwell, J. Tirado-Rives, Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc. 118 (1996) 11225-11236.[3S] G. Hantal, P. Jedlovszky, P. N. M. Hoang, S. Picaud, Calculation of the adsorption isotherm of formaldehyde on ice by grand canonical Monte Carlo simulation, J. Phys. Chem. C 111 (2007) 14170-14178.[4S] M. Jorge, Ch. Schumacher, N. A. Seaton, Simulation study of the effect of the chemical heterogeneity of activated carbon on water adsorption, Langmuir 18 (2002) 9296-9306.[5S] M. P. Allen, D. J. Tildesley, Computer simulation of liquids, Oxford: Clarendon, 1987.[6S] P. Kowalczyk, R. Holyst, H. Tanaka, K. Kaneko, Distribution of carbon nanotube sizes from adsorption measurements and computer simulation, J. Phys. Chem. B 109 (2005) 14659-14666.[7S] C. J. Fennel, D. Gezelter, Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics, J. Chem. Phys. 124 (2006) 234104-234108.[8S] D. Nicholson, N. G. Parsonage, Computer Simulation and Statistical Mechanics of Adsorption, London: Academic Press, 1982.[9S] P. Kowalczyk, P. A. Gauden, A. P. Terzyk, A. V. Neimark, Screening of carbonaceous nanoporous materials for capture of nerve agents, Phys. Chem. Chem. Phys. 15 (2013) 291-298.[10S] P. A. Kollman, L. C. Allen, The theory of the hydrogen bond, Chem. Rev. 72 (1972) 283-303.[11S] M. C. Gordillo, J. Martí, Hydrogen bond structure of liquid water confined in nanotubes, Chem. Phys. Lett. 329 (2000) 341-345.[12S] K. Jurkiewicz, Ł. Hawełek, K. Balin, J. Szade, F. L. Braghiroli, V. Fierro, A. Celzard, A. Burian, Conversion of natural tannin to hydrothermal and graphene-like carbons studied by wide-angle X-ray scattering, J. Phys. Chem. A 119 (2015) 8692-8701.[13S] J. H. Hubbell, Wm. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, Atomic form factors, incoherent scattering functions, and photon scattering cross sections, J. Phys. Chem. Ref. Data 4 (1975) 471-538.[14S] R. Kaplow, S. L. Strong, B. L. Averbach, Radial density functions for liquid mercury and lead, Phys. Rev. 138 (1965) A1336-A1345.
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Section 1: Experimental Details
1.1. Elemental CHN analysis We performed an elemental analysis of carbon, hydrogen, nitrogen and oxygen of the
hydrogen treated (-H) and oxidized (-Ox) samples of ACF using a CHN Elemental Analyzer
(MT-5, Yanako, Japan). The samples were desiccated thoroughly before measurements (in a
vacuum oven at 60 0C for 4 h). The assay of O content (Odiff.) was defined by subtracting the
sum of the contents of C, H, and N from 100%. The CHN results are collected in Table 1S.
Sample Elemental composition (wt. %)C H N Odiff.
*
H-5Å 93.98 1.0 0.67 4.35H-7Å 94.21 0.93 0.70 4.16Ox-5Å 85.89 1.23 0.98 11.90Ox-7Å 86.31 1.14 0.68 11.87
Odiff.* (%) = 100 – C(%)-H(%)-N(%).
Table 1S. Elemental composition determined by CHN analysis.
1.2. Nitrogen measurements (77.4 K) and porosity analysisWe measured nitrogen adsorption isotherms on pitch-based ACF at 77.4 K using
BELSORP-max-S (BEL Japan Inc.). Prior to adsorption measurements, the samples were
pretreated at 150 0C under vacuum (p < 10-4 Pa) for 2 h. We compute the pore volume
distributions from quenched solid density functional theory (QSDFT) using in-house code
[1S]. We use the QSDFT kernel of local N2 adsorption isotherms generated for slit-shaped
carbon pores with disordered pore walls [1S].
1.3. Surface carbon and oxygen content by XPS analysis X-ray photoelectron spectra (XPS) were measured on pitch-based P5 activated carbon
fiber using a monochromatized AlKα x-ray 12 kV source (AXIS-ULTRA, Kratos). Surface
carbon and oxygen content by XPS analysis: carbon 90 % and oxygen 10 %.
Oxygen-containing functional groups Content, (%)
4
C=O in quinones, carbonyl groups 28
Oxygen of the carbonyl group (C=O)
present in lactones, anhydrides, oxygen
atom of
hydroxyl groups (-OH)
46
Oxygen atom in lactones and anhydrides
(-C-O-C-)
21
Oxygen atom in carboxyl groups
(-COOH or COOR)
5
Table 2S. Deconvolution analysis of O1s peak.
For comparison, the surface oxygen content of Madagascar graphite, grafoil, and less-
crystalline graphite was in the range of 2 to 7 %)
Section 2: Detailed computational methods
2.1. Molecular modelsWe used a rigid potential model for formaldehyde belonging to the OPLS-AA family
[2S]. In the planar formaldehyde model the H-C and C=O bonds are 1.101 and 1.203 Å long,
respectively, and the H-C=O angle is 121.80. In the OPLS-AA model only the C and O atoms
carry fractional charges (Table 2S), hence the 2.6 D dipole moment of the model points along
the C=O double bond (Stockmayer-type molecule). In Table 2S, we list all (12,6) Lennard-
Jones (LJ) parameters and Columbic point charges for formaldehyde. We would like to point
out that the OPLS-AA model has been recently used for the modeling of formaldehyde
adsorption on ice by the grand canonical Monte Carlo simulations [3S].
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Formaldehyde
Interaction site (Å) /kB (K) q (e)C 3.75 52.9 +0.45O 2.96 105.8 -0.45H 2.42 7.6 0.00
Table 3S. Interaction parameters for the formaldehyde potential model used in the
simulations [2S].
For carbon adsorbents, we used all interaction parameters (e.g. LJ parameters, point
charges and geometries of functional groups belonging to OPLS-AA family) from the work
of Jorge et al. (Table 4S and 5S) [4S]. We applied the Lorentz-Berthelot combining rules to
compute the cross-species LJ parameters [5S].
Molecule/group Interaction site (Å) /kB (K) q (e)C*) C*) 3.40 28.0 -***)
Hydroxyl
C**) 3.40 28.0 + 0.20
O 3.07 78.2 – 0.64
H -****) -****) + 0.44
Carboxyl
C**) 3.40 28.0 + 0.08
C 3.75 52.8 + 0.55
=O 2.96 105.7 – 0.50
O 3.00 85.6 – 0.58
H -****) -****) + 0.45*) an atom of carbon structure non bounded with hydroxyl and/or carboxyl.**) an atom of carbon structure bounding a group.
***) LJ type centre without charge.
****) a centre treated only as a point charge and not as a LJ centre.
Table 4S. Interaction parameters for the structural carbon models used in the
simulations[4S].
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Molecule/
groupBond type
Bond
length
(Å)
Angle typeValue of the angle
(degrees)
HydroxylC*)O 1.364 C*)OH 110.5
OH 0.960
Carboxyl
C*)C 1.520 C*)CO 111.0
C=O 1.214 OCO 123.0
CO 1.364 COH 107.0
OH 0.970*)an atom of the carbon structure bounding the groups.
Table 5S. Geometric characteristics of the surface oxygen groups introduced in adsorbents.
[4S]
2.2. Formaldehyde adsorption isotherms (stable, metastable, and unstable
states) We simulated formaldehyde adsorption isotherms in structural atomistic models of
pure and oxidized carbons at 303 K (including: stable, metastable and unstable states) using
in-house grand canonical Monte Carlo (GCMC) and gauge-cell meso-canonical Monte Carlo
(MCMC) simulation codes [6S]. For all GCMC simulations, we used a minimum of 5108
MC steps (where step includes equal-probability insertion, deletion, displacement, and
rotation moves) for equilibration and an additional 5108 MC steps for data collection. For all
GMC simulations, we used a minimum of 5108 MC steps (where step includes equal-
probability displacement, rotation, and swap moves) for equilibration and an additional 5108
MC steps for data collection. We kept rigid atom positions for model adsorbents in all
simulations. We computed the interactions energies between atoms (including formaldehyde-
formaldehyde and formaldehyde-adsorbent atoms) using (12,6) Lennard-Jones (LJ) plus
Coulomb (C) potential with the Fennel-Gezelter correction for long-range electrostatic
interactions [7S]:
U (rij )=U LJ ( rij)+U c (r ij ) (1S)
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U LJ (r ij )=4 εij[( σ ij
rij )12
−(σ ij
r ij )6] (2S)
UC (rij )={ q iq j
4 π ε0 [ erfc (α r ij)r ij
−erfc ( α rcut )
rcut+( erfc (α rcut )
r cut2 + 2α
√πexp (−α2 rcut
2 )r cut ) (r ij−r cut )]r ij<rcut
0.0 rij ≥ rcut}
(3S)
where rij is the interatomic distance between the i th and j th LJ or C centre, q i and q j are
the values of the point charges, ε 0=8.8543 10−12 [ C2
Jm ]is the dielectric permittivity of free
space, α=0.2 [ 1Å ] is the damping factor, and erfc ( x ) is the complementary error function
[7S]. In all GCMC and GMC simulations we used a cut-off distance of 12.5 [Å] for both
fluid-fluid and solid-fluid interactions.
2.3. Isosteric heat of adsorptionWe computed the isosteric heat of formaldehyde adsorption at 303 K from thermal
fluctuations [8S]:
qst=RT + ⟨U ⟩ ⟨N ⟩−⟨UN ⟩⟨ N 2 ⟩− ⟨ N ⟩2
(4S)
In eq. 4S,R is the universal gas constant, 𝑇 is the temperature, U is the configurational
(internal) energy of the system, N is the number of molecules in the system, and brackets
denote ensemble average quantities [8S]. The method of eq. 4S is the standard procedure to
probe the isosteric heat of adsorption using Monte Carlo simulations in the grand canonical
ensemble.
2.4. Efficiency factor computed at zero-coverageFor each pore size, H, we define and compute the efficiency factor, α (H ), which is a
measure of the effectiveness of binding of formaldehyde to oxidized carbon (‘ox’) over pure
carbon (‘p’) [8S]:
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α (H )=kox ( H )k p ( H )
(5S)
were k ox ( H ) and k p ( H ) corresponds to the Henry constants computed for oxidized and pure
carbon, respectively. For each pore size, we computed the Henry constant from the well-
known statistical mechanical expression [4S]:
k ( H )=⟨exp(−U
k B T )⟩kB T
(6S)
where k B is the Boltzmann’s constant. We sampled the Boltzmann factor (angular brackets in
eq. 6S) by repeatedly inserting a formaldehyde molecule at random position and orientation
in the structural atomistic models and calculating solid-fluid part of the configuration energy
due to this insertion (Usf). Details of the in-house Monte Carlo integration method used for
sampling are given elsewhere [9S].
2.5. Analysis of formaldehyde-oxygen functionalities hydrogen bondsThe formaldehyde does not engage in strong hydrogen bonds (H-bonds) by itself.
However, formaldehyde molecules act as a hydrogen bond acceptor. This means that
formaldehyde can engage in H-bonding with another compound that does have positive
hydrogen. Indeed, in the presence of another protic compound, e.g. water, hydrogen fluoride,
ammonia, etc., strong H-bonds are formed [10S]. Therefore, it is expected that confined
formaldehyde molecules are able to form H-bonds with oxygen-containing functional groups
(hydrogen bond donors). The number of H-bonds per formaldehyde molecule is sensitive to
micropore size, type of surface oxygen groups and the adsorbed density. To understand this
dependence, for each selected point on the adsorption isotherm, we collect a minimum of 50
configurations of formaldehyde adsorbed in structural atomistic models of pure and oxidized
carbons from NVT Monte Carlo simulations. Next, we used the Gordillo and Martı́ algorithm
[11S] to compute the average number of H-bonds per adsorbed formaldehyde molecule.
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2.6. Total pair correlation function calculations: wide-angle X-ray scattering from
adsorbed formaldehyde
The principal experimental method used for determining the structure of fluids,
including fluids adsorbed in nanomaterials, is X-ray diffraction. From the analysis of the
angular distribution of the scattered intensity, a structure factor and pair correlation function
can be derived which can be compared with those determined from structural atomistic
models.
We computed the theoretical structure factor from the atomistic configurations of
formaldehyde adsorbed in pure and oxidized carbons using Debye equation [12S]:
S (Q )=1+ 1N [∑i=1
N
∑j=1
N f i f j
⟨ f ⟩2sin (Q r ij )
Q rij ]i ≠ j
(7S)
were N is the total number of atoms in adsorbed formaldehyde (e.g. 2 ∙ M ∙H , M ∙ O, and
M ∙C, where M is the number of adsorbed formaldehyde molecules,H 2CO), rij is the
interatomic distance between the i th and j th atoms, Q=4 sinθ / λ, where 2 θ is the scattering
angle and λ is the wavelength of the incident X-ray beam, ⟨ f ⟩=∑i=1
n
ci f i, where c i and f i are the
concentration and the atomic scattering factor of the i th atomic elements, respectively,n=3
is the number of atomic elements in formaldehyde molecule [13S]. The unwanted small-
angle X-ray scattering contribution (or the Debye’s volume scattering) was eliminated from
the theoretical S (Q ) function as described by Kaplow et al. [14S].
We converted the theoretical structure by the sine Fourier transform to the real space
representation of the theoretical diffraction data in the form of the total pair correlation
function (TPCF) [12S]:
G (r )= 2π ∫
0
Qmax
Q [S (Q )−1 ] sin (Qr )sin ( Q
Qmax )πQQmax
dQ (8S)
were Qmax=22 Å−1 is assumed maximum value of scattering vector, r is the interatomic
distance in the real space, and the last term refers to the Lorch dumping function that
suppresses the undesirable termination ripples from the total pair distribution function [12S].
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Our algorithm for computation of TPCF from the Monte Carlo simulations consists of
three steps. In the first step, we collected a minimum of 50 configurations of formaldehyde
adsorbed in pure and oxidized carbons from NVT Monte Carlo simulations. We used the
GCMC configurations of formaldehyde at 303 K and 2 atm as the initial configurations in all
NVT MC simulations. In the second step, we computed a minimum of 50 theoretical S (Q )
functions from these configurations using eq. 7S. Finally, we averaged the S (Q ) and
calculated the theoretical TPCF from eq. 8S. Note that C-O and C-H bond lengths in
formaldehyde molecule are 1.37 Å and 1.0 Å , respectively. Therefore, all peaks ¿ 2 Å on
theoretical TPCF correspond to intra-molecular correlations in formaldehyde molecules.
Theoretical TPCFs are presented for r>2 Å (Figure 6 in main article), and thus they are
provided information about intermolecular correlations between formaldehyde molecules
adsorbed in pure and oxidized carbons.
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Figure 1S. Left panel shows a fixed-bed column filled with ACF adsorbent. Right panel presents the in-house apparatus used for measurements of formaldehyde breakthrough curves at 303 K.
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Figure 2S. Snapshots of equilibrium configurations for the nanoconfined formaldehyde in pure and oxidized 3.8 Å ultramicropores at 2 atm and 303 K. Note excluded volumes generated by carboxylic groups. It should be noted that the graphics collected in this figure are created using the VMD program [34].
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Figure 3S. Snapshots of equilibrium configurations for the nanoconfined formaldehyde in pure and oxidized 5.0 Å ultramicropores at 2 atm and 303 K. It should be noted that the graphics collected in this figure are created using the VMD program [34].
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Figure 4S. Snapshots of equilibrium configurations for the nanoconfined formaldehyde in pure and oxidized 6.0 Å ultramicropores at 2 atm and 303 K. It should be noted that the graphics collected in this figure are created using the VMD program [34].
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Figure 5S. Snapshots of equilibrium configurations for the nanoconfined formaldehyde in pure and oxidized 10.0 Å ultramicropores at 2 atm and 303 K. It should be noted that the graphics collected in this figure are created using the VMD program [34].
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Figure 6S. Upper panels display formaldehyde adsorption isotherms in pure and carboxylic carbons simulated from GCMC (open symbols) and MCMC (closed symbols) techniques at 303 K. Bottoms panels present comparison between GCMC and Henry adsorption isotherms (solid lines) at very low pressures.
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