ARTICLE pubs.acs.org/JPCC
Methane-Induced Deformation of Porous Carbons: From Normal to High-Pressure Operating Conditions Piotr Kowalczyk,*,† Sylwester Furmaniak,‡ Piotr A. Gauden,‡ and Artur P. Terzyk‡ †
Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia ‡ Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
bS Supporting Information ABSTRACT: Applying developed recently thermodynamic model of adsorption-induced deformation of microporous carbons (Kowalczyk, P.; Ciach, A.; Neimark, A. Langmuir 2008, 24, 6603), we study the deformation of carbonaceous porous materials due to adsorption of methane at 313 K and pressures up to 19 MPa. The internal adsorption stress induced by adsorbed/compressed methane is very high in the smallest micropores (for instance, adsorption stress in 0.315 nm ultramicropore reaches 1.8 GPa at 19 MPa). Model calculations show that depending on pore structure both monotonic (i.e., expansion) and nonmonotonic (i.e., initial contraction and further expansion) methane stressstrain isotherm are theoretically predicted. Our calculations reproduce quantitatively the methane stressstrain isotherm on carbide-derived activated carbon at 313 K and experimental pressures up to 5.9 MPa. Moreover, we extrapolate methane stressstrain isotherm measured by the dilatometric method up to 19 MPa to mimic high pressure operating conditions. We predict that expansion of the studied carbon sample reaches 0.3% of volume at 19 MPa and 313 K. From our extrapolation of experimental dilatometric deformation data to high pressure conditions, we predict that the reduction of pressure from 19 to 1 MPa is accompanied by shrinkage of carbon sample by about 0.28% of volume. Comparison with recent study due to Yang et al. (Yang, K.; Lu, X.; Lin, Y.; Neimark, A. V. Energy Fuels 2010, 24, 59555964) shows that studied activated carbon is more resistant to adsorption stress than various coal samples. Presented study can be useful for optimization of operating conditions used in methane gas-extraction technologies.
1. INTRODUCTION The phenomenon of adsorption-induced deformation recently attracted considerable attention owing to its relevance to the various problems of adsorption science and technology, such as characterization of porous materials, molecular sieving and equilibrium separation of fluid mixtures by porous sieves, carbon dioxide geosequestration and coal bed methane recovery, mechanical stability of various porous bodies, and so on.118 Guest molecules adsorbed in nanopores cause a substantial stress in the host matrix (the order of GPa) leading to its contraction or swelling and sometimes to morphological transitions.1,7,11 Although various experimental manifestations of adsorptioninduced deformation have been known for a long time,1921 a rigorous molecular-level description of this phenomenon has been proposed recently.27 However, we are still far from a complete understanding of the complex mechanisms that govern adsorptioninduced deformation of various porous materials. Deformation of porous materials due to desorption of methane fluid entrapped inside small carbonaceous pores is not only the fundamental problem of adsorption science but it also pays a crucial role in optimization of operating conditions used in gas-extraction technologies.2224 Increase in exploration of natural methane r 2011 American Chemical Society
sources (i.e., natural gas, coal-bed methane, shale gas, and others) is being driven by rising energy demands, mandates for cleaner burning fuels, and the economics of energy use. Directional drilling and hydraulic-fracturing technologies are allowing expanded natural gas extraction from organic-rich shales and unmined coals.2225 Nevertheless, strong scientific foundations are crucial to address the public concerns involving safety of those technologies. As has been recently shown by Osborn et al.,25 in active gas-extraction areas, average and maximum methane concentrations in drinking-water wells increases with proximity to the nearest well and were 19.2 and 64 mg CH4 L1. In contrast, the concentration of methane in drinking water within similar geologic formations and hydrogeologic regimes average only 1.1 mg CH4 L1. Why does methane gas released from organic-rich shales contaminate drinking water? Although there is no simple answer to this question, we believe that understanding of carbonaceous matrix shrinkage upon methane extraction at high pressures is an important point to address. When methane molecules are desorbed from small carbonaceous pores Received: September 28, 2011 Revised: December 8, 2011 Published: December 16, 2011 1740
dx.doi.org/10.1021/jp209364x | J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
ARTICLE
Figure 1. Stack consists of homogeneous slit-shaped carbon pores with effective pore width Heff = H σCC, where H = 0.655 nm, and σCC = 0.34 nm. For this pore size, we used the stack consists of 6 basic units.
during gas-extraction processes, they induce elastic stress in the host carbonaceous matrix and cause its shrinkage. Reduction in transportation channel sizes may affect the permeation of desorbed methane fluid and can cause its uncontrolled release to drinking water or atmosphere. High concentration of realized underground methane may potentially pose explosion hazards as well as significant contribution to greenhouse effect.24,25 The aim of the present paper is to study the microscopic mechanism of adsorption-induced deformation of porous carbonaceous materials upon adsorption/desorption of methane at 313 K and high pressures. We want to answer the following questions: (1) Why do carbonaceous solids consisting of very small micropores shrink during desorption of supercritical methane? (2) What is the magnitude of this adsorption-induced sample deformation? To address these questions, we present novel fully atomistic implementation of the thermodynamic approach developed recently by Kowalczyk et al.7 We employ Monte Carlo simulations to compute the adsorption stress in atomistic slit-shaped carbon pores of various sizes.7,9 Next, we use a microscopic model of adsorption-induced deformation to explain the expansion of an activated carbon sample upon adsorption of methane at 313 K studied in ref 26. Finally, we predict a methane stressstrain isotherm on a studied sample of carbide-derived AUK activated carbon at pressures up to 19 MPa in order to mimic methaneextraction operating conditions.
2. THEORY OF THE ELASTIC STRESS IN MICROPOROUS CARBONS As previously,7,9 we represent the carbon sample as a macroscopically isotropic disordered three-dimensional medium composed of stacks of slit-shaped pores of various sizes embedded in an amorphous matrix. We assume that the basic element of the porous structure, a stack of slit-shaped pores, consists of homogeneous pores. We assume further that the carbon matrix is incompressible and it transfers the adsorption stress isotropically. This assumption arises from the observation that stacks of
slit-shaped pores embedded in the amorphous carbon matrix are randomly oriented. Following our previous studies,7,9 the volumetric strain measured in dilatometric experiments is given by j ε ¼ ½σ̅ s p ð1Þ k In the above equation, the effective adsorption stress and bulk modulus are respectively expressed by7,9 Z Hσ s ðH, pÞSðHÞ dH Z ð2Þ σ̅ s ¼ HSðHÞ dH
K ¼
k j
ð3Þ
Here, j denotes porosity, k denotes the elastic modulus, S(H) dH is the surface area of pores of width (H, H + dH), and σs(H,p) is the adsorption stress in a single slit-shaped pore of width H. In order to calculate the volumetric strain given by eq 1, one has, first of all, to compute the adsorption stress in individual slit-shaped carbon pores and, next, to average this stress with the pore size distribution function. In our previous studies7,9 we used the simplest structureless slit-shaped pore model to extract σs(H,p) from molecular simulations. In the current work we propose to compute the adsorption stress from derivative of the grand thermodynamic potential Ωp of the adsorbed phase with respect to the volume V of the model stack consists of homogeneous atomistic slit-shaped carbon pores (note that V = mVC, where VC and m = 1, 2, ... denote the volume and the number of unit cells in our model stack, respectively) at fixed temperature T and adsorbate chemical potential μ (see Figure 1)7,9,11,13 ∂Ωp σ s ðV , pÞ ¼ ∂V 1741
ð4Þ T, μ
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
ARTICLE
ε/kB, (K)
q, (e)
0.66
Methane CC
0.34
55.055
HH CH
0.265 0.3025
7.901 30.6
0.165
Carbon C
0.34
28.0
σ and ε/kB denote (12,6) Lennard-Jones collision diameter and well depth, respectively, kB is the Boltzmann constant, and q represents point charges attached to carbon and hydrogen atom.28 a
This method requires the thermodynamics integration along the simulated isotherm to compute the grand thermodynamic potential, and, subsequently, the differentiation of the grand thermodynamic potential with respect to V7,9 Ωp ðμ, TÞ ¼ Ωp ðμr , TÞ
Z μ μr
N dμ
ð5Þ
Here, N(V,T,μ) is the number of adsorbed molecules per V at given environmental conditions, chemical potential μ, and temperature T. The grand potential and adsorption stress was calculated from eq 5 and 4 by thermodynamic integration along the isotherm starting from a reference ideal gas state at a sufficiently low vapor pressure, Ωp(μr,T) = kbN(μr)T.7,9 Here, we want point out advantages of the current model in comparison to the previous one.7 First, we treated both adsorbate and adsorbent by fully atomistic model. This is important at high pressures when molecular roughness of carbon pores and detailed shaped of methane molecules may affect the computed adsorption isotherms and stresses. Second, the accuracy of thermodynamic calculations can be easily adjusted by the size of our model stack consists of homogeneous slit-shaped carbon pores. Finally, the proposed fully atomistic model of porous material is very flexible. All additional information about studied porous carbon can be easily incorporated into microscopic model displayed in Figure 1, for example, the shape and the wall thickness of carbon pores, functional groups, water content, mineral contaminations, and others.
3. SIMULATION METHODOLOGY 3.1. FluidFluid Interaction Potential. We model methane as an atomistic rigid molecule using the revised five-site model proposed by Sun et al.27 In the atomistic simulations, we express the intermolecular potential between two methane molecules A and B as a sum of sitesite terms2830
U A, B ðqÞ ¼
i¼1 j¼1
∑5 ∑5 uijðrijA, BÞ
ð6Þ
)
)
where the sum is taken over all sites i of molecule A and the sites j of molecule B, q t {rAi rBi }i,j=1,2,3 is the set of separations between each atom in molecule A and each atom in molecule B, rijA,B = rAi rBi is the distance between two sites i and j on the molecules A and B, respectively, and uij(r) denotes distance dependent sitesite interaction potential. Depending on the type of the site, uij(r) is given by a pairwise dispersion or electrostatic interaction energy. We assume that the dispersion
The parameters of the potential, i.e. σA,B and εA,B, are taken from force field developed by Sun et al.27 and revised by Terzyk et al.28 (see Table 1). We model electrostatic force via the Coulomb law of electrostatic potential31,32 B uA, i, j ¼
A B 1 qi qj 4πε0 rijA, B
ð8Þ
where ε0 is the permittivity of free space (ε0 = 8.85419 1012 C2 N1 m2), qAi denotes the value of the point charge i on the molecule A, qBj denotes the value of the point charge j on the molecule B, rA,B ij is the distance between two charges i and j on molecules A and B, respectively. The values of the point charges are taken from the force field developed by Sun et al.27 and revised by Terzyk et al.28 (see Table 1). 3.2. SolidFluid Interaction Potential. In the atomistic simulations we express the intermolecular potential between methane molecule A and nanomaterial consists of NC carbon atoms as follows:28 U A, C ðqÞ ¼
5
NC
uij ðrijA, C Þ ∑ ∑ i¼1 j¼1 2
C ¼ 4εA, C 4 uA, ij
σ rijA, C
A, C
!12
ð9Þ
σ rijA, C
A, C
!6 3 5
ð10Þ
where the first sum is taken over all sites i of the molecule A and the second one over all carbon atoms NC in the simulation box, q t {rAi rCi }i,j=1,2,3 is the set of separations between each atom in the molecule A and each carbon atom, rijA,C = rAi rCi is the distance between site i on the molecule A and carbon atom, and uijA,C (r) denotes distance dependent sitesite (12,6) LennardJones interaction potential. The parameters of the potential for carbon are taken from our previous studies28,3335 (see Table 1). 3.3. Simulation Details. The adsorption isotherms were computed by the grand canonical Monte Carlo method (GCMC).31,32 We adopted the simulation setup displayed in Figure 1 for all GCMC simulations, that is, cubic simulation box of size 3.936 nm 3.83476 nm H with periodic boundary conditions and minimum image convention for computing molecular interactions in x, y, and z directions.31,32 Note that the box size in x and y direction was adjusted to simulate perfect graphene sheet. The number of basic units in each studied stack consists of homogonous slit-shaped carbon pores were adjusted to ensure the high accuracy of computed statistical averages. The absolute value of methane adsorption is simply the average number of methane molecules per volume of the simulation box, ÆNæ/V.36 The grand canonical ensemble simulations utilized 5 107 configurations; the first 2.5 107 configurations were discarded to guarantee equilibration. Then 68 adsorption isotherms of methane at 313 K and pressures from 1 106 to 28 MPa were computed. All simulated adsorption isotherms of methane consisted of 114 points and covered the range of pore 1742
)
σ, (nm)
parameter
energy of interaction is given by the (12,6) Lennard-Jones equation31,32 2 !12 !6 3 A, B σA, B 5 A, B A, B 4 σ ð7Þ uij ¼ 4ε A, B rijA, B rij
)
Table 1. Parameters Used for Modelling of Methane Methane and MethaneCarbon Interactions28a
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
Figure 2. Top panel: Adsorption stress of methane at 313 K versus bulk pressure for selected slit-shaped carbon pore sizes. Note that the size of the pore is displayed on the plot in (nm). Bottom panel: Adsorption stress of methane at 313 K versus slit-shaped carbon pore size computed for bulk pressures from 0.01 to 19 MPa. Maximum adsorption stress corresponds to slit-shaped carbon pore width ∼0.315 nm (see snapshot given by A), and a minimum is found in pores of pore width ∼0.46 nm. Note the high adsorption stress in the smallest micropores of pore width ∼0.31 nm.
sizes, Heff ∈ [0.2,5.0] nm, where Heff = H 0.34 nm is the effective pore width). The thermodynamic integration was performed according to eq 5 with an ideal gas as a reference state, whereas the adsorption stress was computed from eq 4.
4. RESULTS AND DISCUSSION 4.1. Methane-Induced Deformation of Carbide-Derived Activated Carbon. The impact of the pore size on adsorption
stress is crucial for understanding the adsorption-induced deformation at an atomistic level.2,3,7,9 When the adsorption stress is negligible, the stack consists of homogeneous slit-shaped carbon pores is stable because the mechanical equilibrium is established. A lower pressure than external pressure is interpreted as the tendency of the stack to shrink until the pressure inside the carbon pores is equal to the external one. Negative adsorption stress is expected when the packing of methane molecules is strongly restricted by pore geometry.7 A higher pressure inside carbon pores than external one will induce a stack swelling.7,9 The repulsive forces responsible for swelling phenomenon are generated from dense solidlike/compressed liquidlike layers of adsorbed methane. Supercritical methane is strongly adsorbed in
ARTICLE
Figure 3. Theoretical cumulative pore volume distributions used for the investigation of adsorption-induced deformation of microporous activated carbon upon methane adsorption at 313 K. For all considered model samples of activated carbons, we assume the total pore volume of 0.51 cm3/g.
studied carbon stacks at given operating conditions, as is presented in Figure 2. As would be expected, the computed adsorption stress is very high in the carbon stacks consist of the smallest micropores, when methane molecules are tightly packed. As an example, the adsorption stress in a 0.315 nm micropore reaches 1.8 GPa at 19 MPa. Further expansion of the pore size results in fast reduction of the adsorption stress. This so-called quasi-high-pressure effect of the slit-shaped nanopore spaces has been confirmed by a series of experiments.3739 As pore size reaches 0.4 nm, adsorption stress crosses zero and is further negative. Microscopic configurations of adsorbed methane in 0.450.46 nm micropores show imperfect packing of adsorbed molecules (see Figure 2 and movie in the Supporting Information). Near pore sizes of 0.54 and 0.68 nm, we observe second and third maximum of adsorption stress, respectively. Due to the high operating temperature (i.e., T/Tc = 1.6, where Tc denotes critical temperature for methane), the pore size dependence of the adsorption stress is rapidly damped.7 Therefore we concluded that, at studied operating conditions, only micropores contribute to the methane-induced deformation of slit-shaped porous materials. Adsorption-induced deformation of heterogeneous carbons can be easily predicted from assumed pore size distribution and bulk modulus. As previously,7,9 we model pore size distribution by the Gaussian functions (see Figure 3). The corresponding 1743
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
ARTICLE
Figure 4. Methane stressstrain isotherms at 313 K computed on the basis of pore volume distributions displayed in Figure 3. The assumed bulk modulus K is 10 (circles), 20 (triangles), 30 (squares), and 40 GPa (diamonds).
methane-induced deformation curves at 313 K are shown in Figure 4. The internal pore structure greatly impacts the deformation curves, since the adsorption stress is strongly affected by the size of the slit-shaped carbon pores. Interestingly, we predict both monotonic and nonmonotonic shapes of stressstrain isotherms due to adsorption of methane at the studied operating conditions. For sample A, we observe expansion in the whole range of pressures. This is because the assumed pore size distribution corresponding to carbon sample A contains only the smallest micropores with pore size below 0.45 nm. The great excess of the internal pressure computed for the smallest micropores causes the porous solid to swell, and the bulk modulus controls the extent of expansion, as is displayed in Figure 4. It is worth underlining that, for the investigated values of bulk modulus, the maximum theoretical expansion of the carbon sample due to adsorption of methane at 313 K and 19 MPa is around 3.5%. Comparing to our previous study of carbon dioxide-induced deformation,9 we notice that adsorbed methane induced lower deformation of porous carbon than carbon dioxide. It can be explained by the fact that carbon dioxide molecules access smaller carbon pores with stronger binding energy. Moreover, the binding energy in wider micropores accessible for methane molecules is always greater for carbon dioxide. Samples BD are more structurally heterogonous than sample A. They contain a different fraction of wider slit-shaped carbon pores with pore size above 0.45 nm. That is why methaneinduced deformation curves computed for samples BD are nonmonotonic with an initial contraction and further expansion (see Figure 4). Micropores with positive adsorption stress tend
to expand to reduce the internal pressure. On the other hand, micropores with negative adsorption stress tend to contract. As for sample A, we notice that bulk modulus controls the extent of sample deformation. However, because the adsorption stress is much smaller in wider micropores, methane-induced deformation of samples B-D is much smaller than that of sample A. We may therefore conclude that samples B-D are good approximation to a real sample of heterogeneous porous carbon and dry coal with high carbon content (for example anthracene). The simulation model was employed to describe the experimental data collected on a carbide-derived AUK activated carbon during methane adsorption at 313 K characterized by the micropore volume of 0.51 cm3/g, characteristic adsorption energy 29 kJ/mol, and effective micropore width 0.41 nm.26 Here, we want to underline that high quality carbide-derived activated carbon is composed of stacks of slit-shaped pores of various sizes embedded in an amorphous matrix.26,40,41 A high value of the characteristic adsorption energy and small value of the effective micropore size indicates microporus character of studied carbon. Methane stressstrain isotherm collected by dilatometric experiment cover the range of pressures up to 5.9 MPa,26 as is presented in Figure 5. The proposed model reproduces the nonmonotonic behavior of the experimental dilatometric curve reasonably well. The studied sample of activated carbon expands up to 0.15% at 5.9 MPa and 313 K. The predicted bulk modulus of the investigated carbide-derived AUK activated carbon is 8 GPa. This value is comparable with the reported data for vitreous carbons and polycrystalline graphite.7 Moreover, our previous estimation of bulk modulus of 7 GPa for 1744
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
Figure 5. Dependence of the deformation of carbide-derived AUK activated carbon on the methane adsorption at 313 K measured by the dilatometric method26 (open triangles) and computed from the proposed thermodynamic model (solid line). Dashed line in the bottom panel shows extrapolation of the stressstrain isotherm up to 19 MPa.
carbide-derived activated carbon from an argon dilatometric experiment at 243 K is close to the current prediction.7 One great advantage of the microscopic model of adsorption-induced deformation is its ability to extrapolate dilatometric experiment to different operating conditions.9,18 Knowing the pore size distribution and bulk modulus of the investigated porous carbon, we compute methane stressstrain isotherm up to 19 MPa. Here, we want to point out that the assumed linear stressstrain relation is justified by the fact that the strain measured for microporous materials (e.g., zeolites and activated carbons) is small, typically in fractions of a percent.1 In other words, the stress associated with adsorption is very small relative to the bulk modulus that characterizes porous material. Because of this, we expected that for the studied activated carbon the linear Hooke law should hold at higher pressures. As pointed by Neimark et al.,11 it is not true for adsorption-induced deformation (e.g., breathing and gate opening) of flexible metalorganic frameworks.1116 From the extrapolation of the experimental data to high pressure operating conditions, we found that the expansion of studied carbon sample reaches 0.3% by volume at 19 MPa (see bottom panel in Figure 5). Finally, let us consider the shrinkage of studied porous carbon upon desorption of methane. From our extrapolation of experimental dilatometric deformation data to high pressure operating conditions, we predict that the reduction of pressure from 19 to 1 MPa is
ARTICLE
accompanied by shrinkage of the carbon sample of 0.28% of volume. We believe that the estimation of carbon shrinkage upon desorption of methane combined with geological information is very useful for controlled and safe extraction of methane from organic-rich shales or unmined coals. Incorporation of functional groups and water content into the model structure of porous carbon will be the subject of our future works. 4.2. Methane-Induced Deformation of Coals and CarbideDerived Activated Carbon: Similarities and Differences. It is particularly interesting to compare the elastic properties of studied carbide-derived activated carbon with similar properties corresponding to different samples of colas.18 Here we would like stress that coals and activated carbons are different materials. Coal is a complex heterogeneous sedimentary organic rock, made of fossilized plant matter and incorporated inorganic matter.42,43 The maceral compositions indicates the botanic precursors and depositional histories for a coal and are divided into three groups:42 “vitrinite” (remains of various plant matter such as bark, stems, roots, etc), “liptinite” (cuticles, spores, resin, and algal remains) and “inertinite” (oxidized plant material, fungal remains, fossilized charcoal, etc). Various molecular representations for the structure of coal have been proposed.44 However, it is commonly accepted that coal is a three-dimensional macromolecular network structure consisting of polyaromatic and alkyl substituted aromatic units linked by covalent and noncovalent bonds (hydrogen bonds, van der Waals interactions, electrostatic interactions, and ππ interactions44). In recent work Yang et al.18 used an effective model to study the methane-induced deformation of different coal samples. The authors combined quenched solid density functional theory45 with the microscopic model of Kowalczyk et al.7 In the light of recent studies,46,47 it seems clear that the approximation of coal internal structure by the stacks of slit-shaped amorphous carbon pores embedded in the amorphous matrix (i.e., independent pore model) is poor approximation to the complex structure of this porous material. Nevertheless, as we show later by direct comparison with the current results, calculations due to Yang et al.18 are consistent and capture the essential physics of adsorption-induced deformation process. Let us compare the molecular modeling in both studies. Similarly to the current work, Yang et al.18 used a slit-shaped carbon pore model for generation of adsorption stresses in different pore sizes upon methane loading at high pressures. Next, in both studies, the roughness of the solid surfaces was taken into account. The essential difference between our work and the previous one18 is the structure of solid surfaces around pores. The carbon surface around the slit-shaped pores of carbide-derived activated carbon is composed of graphene sheets, i.e., crystalline surfaces. In contrast, Yang et al.18 did not describe the atomistic structure of solid surfaces around the slitshaped pores, but calibrated their potentials of solidfluid interaction on experimental data of adsorption on a surface of Cabot BP-280 carbon black,45 i.e., on an amorphous surface. This point is essential to explain the differences and similarities between the both studies. As would be expected, both microscopic models generate two types of methane stressstrain isotherm. Type I shows monotonic expansion in the whole pressure range (see Figure 4, and Figure 4 in ref 18). In both studies this elastic behavior of porous material is expected for samples consisting small micropores (i.e., with pore size below 0.5 nm, as is shown in Figures 2 and 3, and Figure 4 in ref 18). Type II displays initial contraction at low pressures followed by expansion. This elastic behavior of porous material results from the heterogeneous nature 1745
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C of both coals and activated carbons (i.e., distribution of pore sizes). The essential difference between the both studies is the computed values of adsorption stresses and bulk modulus for studied carbonaceous materials. As would be expected, the adsorption stress in graphitic slit-shaped carbon pores is much higher that this corresponding to their amorphous counterparts. We found that adsorption stress in small micropores reaches 1800 MPa at external pressure of 19 MPa (see Figure 2). In contrast, Yang et al.18 found that adsorption stress in small amorphous micropores is around 250 MPa at the same operating conditions (see Figure 3 in ref 18). It is not surprising because adsorption stress depends on the packing of methane molecules in carbon nanospaces. Amorphous nature of solid surfaces around carbon micropores affected the packing of adsorbed particles. Disorder in adsorbed layers induced from amorphous carbon walls inevitably reduces the adsorption stress. Computed bulk modulus of different coals is around 23 GPa. In contrast, the predicted bulk modulus of studied activated carbon is 8 GPa. This indicates that coals are softer porous materials than studied activated carbon. It seems obvious if one takes into account the fact that coal is natural three-dimensional polymer consists of small cross-linked carbon fringes. Soft-matter materials (i.e., polymers, gels, colloid crystals, etc.) are less resistant to adsorption stress in comparison to hard materials.
5. CONCLUSIONS We study adsorption-induced deformation of carbonaceous amorphous porous materials due to adsorption of methane at 313 K and high pressures. We show that adsorbed and compressed methane molecules induce very high adsorption stress in the smallest micropores with pore size ∼0.315 nm. At 19 MPa, the adsorption stress in 0.315 nm micropore reaches 1.8 GPa. As pore size increases the adsorption stress is rapidly damped in the range of micropores because thermal fluctuations smooth the packing effects at 313 K. Model calculations as well as dilatometric experiment show both monotonic and nonmonotonic methane strainstress isotherms. The shape of deformation curve strongly depends on the internal pore structure of porous body. On the other hand, the bulk modulus scales the extent of sample deformation. Our calculations reproduce quantitatively the methane stressstrain isotherm on carbide-derived AUK activated carbon at 313 K and experimental pressures up to 5.9 MPa. The predicted bulk modulus of studied carbon of 8 GPa is characteristic for vitreous carbons and polycrystalline graphite. Finally, we extrapolate stressstrain dependence measured by dilatometric method to higher pressures to mimic geological conditions. From the thermodynamic model of adsorptioninduced deformation, we predict that expansion of studied carbon sample reaches 0.3% at 19 MPa and 313 K. Desorption of methane trapped inside carbon pores at 19 MPa up to 1 MPa results in sample shrinkage of 0.28% of volume. ’ ASSOCIATED CONTENT
bS
Supporting Information. Snapshots of methane adsorbed in selected stacks of micropores. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: +61 8 9266 7800. E-mail:
[email protected].
ARTICLE
’ ACKNOWLEDGMENT P.K. acknowledges partial support by the Office of Research & Development, Curtin University of Technology, Grant CRF10084. S.F., P.G., and A.T. acknowledge the use of the computer cluster at the Poznan Supercomputing and Networking Centre as well as the Information and Communication Technology Centre of Nicolaus Copernicus University (Torun, Poland). P.K. gratefully acknowledges the use of the supercomputer EPIC (epic.ivec.org) for CPU time ’ REFERENCES (1) Tvardovskiy, A. V. Sorbent deformation; Elsevier Ltd.: Oxford, U.K., 2007. (2) Ravikovitch, P. I.; Neimark, A. V. Langmuir 2006, 22, 10864–10868. (3) Ustinov, E. A.; Do, D. D. Carbon 2006, 44, 2652–2663. (4) G€unther, G.; Prass, J.; Paris, O.; Schoen, M. Phys. Rev. Lett. 2008, 101, 086104. (5) G€unther, G.; Schoen, M. Phys. Chem. Chem. Phys. 2009, 11, 9082–9092. (6) G€unther, G.; Schoen, M. Mol. Simul. 2009, 35, 138–150. (7) Kowalczyk, P.; Ciach, A.; Neimark, A. V. Langmuir 2008, 24, 6603–6608. (8) Balzer, Ch.; Wildhage, T.; Braxmeier, S.; Reichenauer, G.; Olivier, J. P. Langmuir 2011, 27, 2553–2560. (9) Kowalczyk, P.; Furmaniak, S.; Gauden, P. A.; Terzyk, A. P. J. Phys. Chem. C 2010, 114, 5126–5133. (10) Gor, G. Y.; Neimark, A. V. Langmuir 2011, 27, 6926–6931. (11) Neimark, A. V.; Coudert, F. X.; Boutin, A.; Fuchs, A. H. J. Phys. Chem. Lett. 2010, 1, 445–449. (12) Gor, G. Y.; Neimark, A. V. Langmuir 2010, 26, 13021–13027. (13) Neimark, A. V.; Coudert, F. X.; Triguero, C.; Boutin, A.; Fuchs, A. H.; Beurroies, I.; Denoyel, R. Langmuir 2011, 27, 4734–4741. (14) Kondo, A.; Noguchi, H.; Carlucci, L.; Proserpio, D. M.; Ciani, G.; Kajiro, H.; Ohba, T.; Kanoh, H.; Kaneko, K. J. Am. Chem. Soc. 2007, 129, 12362–12363. (15) Kondo, A.; Noguchi, H.; Ohnishi, S.; Kajiro, H.; Tohdoh, A.; Hattori, Y.; Xu, W. C.; Tanaka, H.; Kanoh, H.; Kaneko, K. Nano Lett. 2006, 6, 2581–2584. (16) Tanaka, D.; Nakagawa, K.; Higuchi, M.; Horike, S.; Kubota, Y.; Kobayashi, T. C.; Takata, M.; Kitagawa, S. Angew. Chem., Int. Ed. 2008, 47, 3914–3918. (17) Li, D.; Kaneko, K. Chem. Phys. Lett. 2001, 335, 50–56. (18) Yang, K.; Lu, X.; Lin, Y.; Neimark, A. V. Energy Fuels 2010, 24, 5955–5964. (19) Bangham, D. H.; Fakhoury, N. Nature (London) 1928, 122, 681–682. (20) Bangham, D. H. Trans. Faraday Soc. 1937, 33, 805–811. (21) Maggs, F. A. P. Trans. Faraday Soc. 1946, 42, 284–288. (22) Kerr, R. A. Science 2010, 328, 1624–1626. (23) Tour, J. M.; Kittrell, C.; Colvin, V. L. Nat. Mater. 2010, 9, 871–874. (24) Pacala, S.; Socolow, R. Science 2004, 305, 968–972. (25) Osborn, S. G.; Vengosh, A.; Warner, N. R.; Jackson, R. B. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 8172–8176. (26) Shkolin, A. V.; Fomkin, A. A. Colloid J. 2009, 71, 119–124. (27) Sun, Y.; Spellmeyer, D.; Pearlman, D. A.; Kollman, P. J. Am. Chem. Soc. 1992, 114, 6798–6801. (28) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Kowalczyk, P. Adsorption Sci. Technol. 2009, 27, 281–296. (29) Kowalczyk, P.; Gauden, P. A.; Ciach, A. J. Phys. Chem. B 2009, 113, 12988–12998. (30) Kowalczyk, P.; Gauden, P. A.; Ciach, A. J. Phys. Chem. B 2011, 115, 6985–6994. (31) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, U.K., 1987. (32) Frenkel, D.; Smit, B. Understanding Molecular Simulation From Algorithms To Applications; Academic Press: London, 1996. 1746
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
The Journal of Physical Chemistry C
ARTICLE
(33) Kowalczyk, P.; Tanaka, H.; Holyst, R.; Kaneko, K.; Ohmori, T.; Miyamoto, J. J. Phys. Chem. B 2005, 109, 17174–17183. (34) Kowalczyk, P.; Bhatia, S. K. J. Phys. Chem. B 2006, 110, 23770–23776. (35) Kowalczyk, P.; Holyst, R.; Terrones, M.; Terrones, H. Phys. Chem. Chem. Phys. 2007, 9, 1786–1792. (36) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, 1982. (37) Imai, J.; Souma, M.; Ozeki, S.; Suzuki, T.; Kaneko, K. J. Phys. Chem. 1991, 95, 9955–9960. (38) Saeki, T.; Hashimoto, K.; Kimura, N.; Omata, K.; Fujishima, A. J. Electroanal. Chem. 1996, 404, 299–302. (39) Simon, P.; Gogotsi, Y. Nat. Mater. 2006, 7, 845–854. (40) Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Science 2006, 313, 1760–1763. (41) Gogotsi, Y.; Dash, R. K.; Yushin, G.; Yildirim, T.; Laudisio, G.; Fischer, J. E. J. Am. Chem. Soc. 2005, 127, 16006–16007. (42) van Krevelen, D. W. Coal: Typology, Chemistry, Physics, Constitution; Elsevier Science: Amsterdam, 1993. (43) Milligan, J. B.; Thomas, K. M.; Crelling, J. C. Energy Fuels 1997, 11, 364–371. (44) Marzec, A. Fuel Process. Technol. 2002, 7778, 25–32. (45) Neimark, A. V.; Lin, Y.; Ravikovitch, P. I.; Thommes, M. Carbon 2009, 47, 1617–1628. (46) Van Niekerk, D.; Mathews, J. P. Fuel Process. Technol. 2011, 92, 729–34. (47) Mathews, J. P.; van Duin, A.; Chaffee, A. Fuel Process. Technol. 2011, 92, 718–28.
1747
dx.doi.org/10.1021/jp209364x |J. Phys. Chem. C 2012, 116, 1740–1747
