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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: [email protected] (Piotr Kowalczyk)

1

mailto:%[email protected]

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

2

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.

12

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 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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