pubs.acs.org/Langmuir © 2009 American Chemical Society
Theoretical Insight of Physical Adsorption for a Single Component Adsorbent + Adsorbate System: II. The Henry Region Anutosh Chakraborty,† Bidyut Baran Saha,*,† Kim Choon Ng,*,† Shigeru Koyama,‡ and Kandadai Srinivasan§ † Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore, ‡Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga Koen, Kasuga Shi, Fukuoka 816-8580, Japan, and §Frigrite Limited, 27 Grange Road, Cheltenham, Victoria 3192, Australia
Received January 19, 2009. Revised Manuscript Received April 6, 2009 The Henry coefficients of a single component adsorbent + adsorbate system are calculated from experimentally measured adsorption isotherm data, from which the heat of adsorption at zero coverage is evaluated. The first part of the papers relates to the development of thermodynamic property surfaces for a single-component adsorbent + adsorbate system1 (Chakraborty, A.; Saha, B. B.; Ng, K. C.; Koyama, S.; Srinivasan, K. Langmuir 2009, 25, 2204). A thermodynamic framework is presented to capture the relationship between the specific surface area (Ai) and the energy factor, and the surface structural and the surface energy heterogeneity distribution factors are analyzed. Using the outlined approach, the maximum possible amount of adsorbate uptake has been evaluated and compared with experimental data. It is found that the adsorbents with higher specific surface areas tend to possess lower heat of adsorption (ΔH) at the Henry regime. In this paper, we have established the definitive relation between Ai and ΔH for (i) carbonaceous materials, metal organic frameworks (MOFs), carbon nanotubes, zeolites + hydrogen, and (ii) activated carbons + methane systems. The proposed theoretical framework of Ai and ΔH provides valuable guides for researchers in developing advanced porous adsorbents for methane and hydrogen uptake.
1. Introduction The adsorption in porous solid adsorbents is a complex process with respect to the nature of the solid adsorbent surface and adsorbate. Generally, adsorption sites are characterized by different energies distributed over the adsorbent surface. Therefore, one theoretically expects a distribution in the “microscopic” Henry’s regime.2 The Henry region represents the rudimental model between an adsorbate particle and the solid adsorbent surface and defines how much a fluid can be adsorbed on the surface or in the confined space of pores and how adsorption varies with temperature.3-6 The Henry constants are obtained experimentally from the measurements of adsorption isotherms at various temperatures using either a volumetric or gravimetric method or from chromatography. The classical and statistical thermodynamics suggest that the Henry constant always exists at zero loading, from which one can easily calculate the isosteric heat of adsorption.7,8 The Henry’s region is the low pressure and low uptake regime, where each gas molecule can explore the whole adsorbent surface independently and the gases in the adsorbed phase are most strongly attracted to the adsorption sites with the *Corresponding authors. E-mail:
[email protected] (B.B.S.); mpengkc@ nus.edu.sg (K.C.N.). (1) Chakraborty, A.; Saha, B. B.; Ng, K. C.; Koyama, S.; Srinivasan, K. Langmuir 2009, 25, 2204. (2) Do, D. D. Adsorption Analysis: Equilibria and Kinetics; Imperial College: London, 1998; Vol. 2, p 250. (3) Do, D. D.; Tran, K. N. Langmuir 2003, 19, 5656. (4) Nguyen, C.; Do, D. D. J. Phys. Chem. B 2001, 105, 1823. (5) Derachits, N. A.; Gubkina, M. L.; Nikolaev, K. M.; Polyakov, N. S. Russ. Chem. Bull. 1997, 46, 1778. (6) Silva da Rocha, M.; Iha, K.; Faleiros, A. C.; Jose Corat, E.; Encarnacion Vazquez, M.; Iha, S. J. Colloid Interface Sci. 1998, 208, 211. (7) Steele, W. A. The interaction of gases with solid surfaces. The International Encyclopedia of Physical Chemistry and Chemical Physics; Pergamon Press: Oxford, 1974; Vol. 3. (8) Bottani, E. J.; Ismail, I.; Bojan, M.; Steele, W. A. Langmuir 1994, 10, 3805.
Langmuir 2009, 25(13), 7359–7367
highest energies; that is, the adsorption energy (ΔH) shows the maximum value in the Henry’s regime. At low pressures and uptakes, the isotherms tend to be linear and the slope of these isotherms determines the suitability of an adsorbent + adsorbate pair. The thermodynamic limit for adsorption at low surface loading expresses the fact that there is no interaction among the adsorbed molecules, and this behavior is presented theoretically by the Henry adsorption isotherms as expressed by the relationship x = KHP, where x is the amount of adsorbate uptake, P denotes the pressure, and KH is the Henry coefficient. The universal adsorption isotherm possesses the Henry’s constant at low pressures and concentrations even though some adsorption isotherm equations such as the Freundlich, Sips, and Dubinin models do not follow Henry’s behavior. Using the ultrahigh vacuum techniques, Hobson and Armstrong9 measured the adsorption isotherms of nitrogen and argon on Pyrex glass in the range of relative pressures between l0-13 and 10-8 and in the range of relative coverage between 10-6 and 0.3. They found that the Dubinin-Raduskevich (DR) isotherm equation was able to empirically describe all the data. They also suggested a simple analytical hypothesis for the extrapolation of isotherms on heterogeneous surfaces to the region of Henry’s law. This work inspires the efforts to improve the DR isotherm by incorporating the Henry law limit.10 However, in a prior work,11,12 a method for describing the initial region of adsorption isotherms using the isotherm parameters of the Dubinin model has been proposed, and this is performed by using the tangent to the isotherm and extrapolating this tangent to zero pressure. The DR equation fails in the limit of the pressure approaching zero, where the slope of (9) Hobson, J. P.; Armstrong, R. A. J. Phys. Chem. 1963, 67, 2000. (10) Kapoor, A.; Ritter, J. A.; Yang, R. T. Langmuir 1989, 5, 1118. (10) Kapoor, A.; Ritter, J. A.; Yang, R. T. Langmuir 1989, 5, 1118. (11) Jakubov, T. S.; Mainwaring, D. E. J. Colloid Interface Sci. 2002, 252, 263. (12) Sundaram, N. Langmuir 1993, 9, 1568.
Published on Web 05/01/2009
DOI: 10.1021/la900217t
7359
Article
Chakraborty et al.
the isotherm incorrectly approaches zero and this equation cannot be applied.13 However, “a purge and trap method” is used to extend the lower limits of adsorption equilibria into the Henry’s law region for calculating the Henry coefficient.13 The theoretical maximum isosteric heat of adsorption (ΔH) is found in the Henry’s region and is calculated as a function of the width of slit-shaped pores.14 The theoretical maximum ΔH decreases with the increase of adsorbent pore width. In another reference,6 a statistical adsorption model is applied for the low value of adsorption uptake to establish conditions for the Freundlich isotherm model such that this model obeys Henry’s law with its physical significance. An expression of the Henry’s law constant in terms of the sticking coefficient has been derived, and it is found that it has an increasing function with respect to temperature and is directly related to the entropy factor.15 In part I,1 the thermodynamic property surfaces for a singlecomponent adsorbent + adsorbate system has been developed from the viewpoint of classical thermodynamics, thermodynamic requirements of chemical equilibrium, Gibbs law, and Maxwell relations. It solved the information gap with respect to the state of adsorbed phase and dispelled the confusion as to what is the actual state of the adsorbed phase. In this Article, we present the Henry’s coefficient (KH) in terms of sticking coefficient (β) and the average residence time (τ) of adsorbate molecules on the adsorbent surface, where the nonideality of the gaseous phase is taken into account. We employ the experimentally measured adsorption isotherm data available from the literature that are of practical interest to calculate KH and ΔH. The main objective of this paper is to mathematically formulate the specific surface area (Ai) of a solid adsorbent using the theoretical rigor of Boltzmann distribution function, Henry’s coefficient, isosteric heat of adsorption at zero loading, and specific surface area of adsorbate molecules. The maximum amount of adsorbate uptake is also formulated in terms of ΔH, surface-energy (R), and surface-structural (γ) heterogeneity factors. Based on the experimentally measured adsorption isotherms at low pressure and concentration, it is possible to establish a thermodynamic relationship between ΔH and Ai of porous adsorbents + adsorbates, and such an approach provides a guide to researchers toward the development of advanced porous adsorbents.
2. Adsorption in Henry’s Region The physical adsorption system as shown in Figure 1a is an ensemble of adsorbed gas plus adsorbent enclosed by a surface. It also gives the representation of the huddle of adsorbate molecules into adsorbent pores for various adsorbate uptakes ranging from the Henry region to monolayer. The changes in the energy flow of adsorbate molecules can be tracked by integrating in succession between the limits of P = 0 and P, T0 and any temperature (T), and x = 0 and x with T, x; P, x; and P, T being held constant, respectively. T0 is the initial reference temperature for any adsorbent + adsorbate system. A graphical representation of the process of adsorption is depicted with an initial state (P = 0, T0, x = 0) to the Henry region (P f 0, T, x f 0) for various temperatures and is shown in Figure 1b. It is evident from the general consideration that the amount of adsorbate adsorbed per unit surface area (q; unit g g-1 m-2) is given by15 q = Ncτβ, that is, the amount of adsorbate uptake becomes ð1Þ x ¼ Nc βτAs (13) Schindler, B. J.; Buettner, L. C.; LeVan, M. D. Carbon 2008, 46, 1285. (14) Schindler, B. J.; LeVan, M. D. Carbon 2008, 46, 644. (15) Asnin, L. D.; Chekryshkin, Yu. S.; Federov, A. A. Russ. Chem. Bull. 2003, 52, 2747.
7360 DOI: 10.1021/la900217t
where As defines the adsorbent surface area, Nc (in m-2 s-1) is the number of collisions per unit time of adsorbate molecules with the solid adsorbent surface, β is the sticking coefficient, and τ defines the average residence time of a molecule on the adsorbent. The numbers of collisions of molecules are evaluated from the kinetic theory of gas, that is, Nc = P/(2πmKBT)1/2, where m is the molecular weight and KB indicates the Boltzmann constant. Here, τ is estimated in the form of the well-known Frenkel equation and this is given by τ = τ0 exp(Ed/RT),15 where τ0 represents the lattice fluctuation time, on the order of 10-13 s, Ed (in J mol-1) is the activation energy during desorption, and R defines the universal gas constant. Representing the adsorption system, comprising an adsorbed phase and compressed gaseous phase, the net change pressure with respect to temperature (dP/dT) is equal to dP/dT at adsorbed phase {(∂P/∂T)x} plus that of gaseous phase {(dP/dT)g}. Here, (dP/dT)g is taken into account to make a correction due to the nonideality of gaseous phase. Hence, the subscript “g” defines the gaseous phase. A more accurate representation of the isosteric heat of adsorption (ΔH, in J mol-1) becomes16 RT 2 DP dP ΔH ¼ þ Tvg ð2Þ dT g P DT x The amount of adsorbate uptake x is a function of pressure (P) and temperature (T), that is, x = f (P, T). Using the Jacobians, we have17 (∂P/∂T)x = -[(∂P/∂T)P/(∂x/∂P)T]. The partial derivative of the number of collisions of molecules with respect to P at constant T can be written as (∂Nc/∂P)T = 1/(2πmKBT)1/2 = P/(2πmKBT)1/2 (1/P) = Nc/P, and (∂Nc/∂T)P = -(Nc/2T). The derivative of τ with respect to T becomes dτ/dT = -τ(Ed/RT2). From eq 1, Nc = x/βτAs. The partial derivate of uptake x with respect to P at constant T is (∂x/∂P)T = AsNcβτ/P. The partial derivate of uptake x with respect to T at constant P is written as Dx Ed 1 1 dβ ð3Þ ¼ Nc βτAs þ DT P RT 2 2T β dT Equation 2 is now expressed with respect to the sticking coefficient (β) as ΔH 1 ðDx=DTÞP dP ¼ þ Tv g 2 RT P ðDx=DPÞT dT g Ed 1 1 dβ dP ¼ þ þ Tv g dT g RT 2 2T β dT 1 dβ ðEd -ΔHÞ 1 1 dP þ ¼ þ β dT RT 2 2T P dT g dðln βÞ Ea 1 1 dP þ ¼ þ dT RT 2 2T P dT g
ð4Þ
where the activation of energy (Ea) is represented by (Ed - ΔH). Integrating eq 4 from initial state (T = T0, β = β0) to any state (T, β), where β0 is the sticking coefficient at T0. The final form of eq 4 becomes ( ) 1=2 Z T T -Ea 1 1 1 dP þ exp dT β ¼ β0 T0 R T T0 T0 P dT g ð5Þ (16) Chakraborty, A.; Saha, B. B.; Koyama, S.; Ng, K. C. Appl. Phys. Lett. 2006, 89, 171901. (17) Chakraborty, A.; Saha, B. B.; Koyama, S.; Ng, K. C. Appl. Phys. Lett. 2007, 90, 171902.
Langmuir 2009, 25(13), 7359–7367
Chakraborty et al.
Article
Figure 1. (a) Schematic of an adsorption system where the blue dotted lines are the “captured” molecules under the influenced of the van der Waals forces ranging from the Henry region to monolayer. The Henry region is shown in the adsorption isotherm diagram. (b) Graphical representation of the process of adsorption from an initial state (P = 0, T0, x = 0) to the Henry region (P f 0, T, x f 0) for various temperatures (T1, T2, T3, ...).
Now, the sticking coefficient is presented as a function of T. The amount of adsorbate uptake as given by eq 1 is expressed as τ0 β0 Ea x ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp RT0 2πmKB T0 ( ) Z T ΔH 1 dP þ dT As P ð6Þ exp RT T0 P dT g The Henry constant (KH in g g-1 Pa-1) is calculated as dx x ¼ lim ¼ KH ¼ lim Pf0 dP Pf0 P ( ) Z T τ 0 β 0 As Ea ΔH 1 dP pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp þ exp dT ð7Þ RT RT0 2πmKB T0 T0 P dT g The Henry’s coefficient is expressed in terms of energy and entropy factors.18 It can be shown that the sticking coefficient can be computed from the experimentally measured KH, and this (18) Kolyadina, O. A.; Murinov, Y. I.; Voronkov, M. G.; Pozhidaev, Y. N. Russ. Chem. Bull. 2000, 49, 2000.
Langmuir 2009, 25(13), 7359–7367
is given by β ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KH 2πmKB T τAs
ð8Þ
3. Specific Surface Area from Henry Region: A Theoretical Insight It is well-known that the Henry coefficient has been expressed in terms of interaction energy φ of one adsorbate molecule with the surrounding adsorbent and the Brunauer-Emmett-Teller R (BET) surface area. This is given by19 KH = (Ai/RT) z0max{exp [-φ(z)/kBT] - 1}dx, where z is the distance perpendicular to the surface and zmax is integration constant depending on the structure of the solid adsorbent. The major challenge in calculating Henry coefficients is the quantitative determination of the interaction energy φ as a function of z. Brunauer et al.20 have established the most widely used method for the determination of the specific surface area (Ai in m2 g-1) of solids. However, the Adamson21 myth remains unsolved for the calculation of (19) Do, D. D.; Nicholson, D.; Do, H. D. J. Colloid Interface Sci. 2008, 324, 15. (20) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (21) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990.
DOI: 10.1021/la900217t
7361
Article
Chakraborty et al.
surface area, “How can molecular adsorption determine the surface area?” Kaneko and Ishii22 have proposed a new method for the measurement of superhigh BET surface area of microporous carbons. They also described the structural reason why the geometrical specific surface area of microporous carbons can be more than the limiting value of 2630 m2 g-1 and briefly proposed a method of obtaining superhigh surface area.23 In the present analysis, we assume that (i) the functional adsorbent surface distinguishes different zones by means of binding energy εi of surface atoms; (ii) the surface atoms are noninteracting, that is, the binding energy of each surface atom is independent of surrounding atoms; and (iii) the number of adsorbent surface atoms (Ni) with binding energy εi is related to the number, N0, of atoms in the adsorbate state energy (ε0) level. Using the Boltzmann distribution law, we can write24 Ni expð -εi =kTÞ -ðεi -ε0 Þ ¼ exp ¼ ð9Þ kT N0 expð -ε0 =kTÞ where T is the temperature at which the surfaces are in equilibrium condition and k is the Boltzmann constant. The atoms with binding energy, εi, are collected and patched to the specific surface area, Ai, being proportional to Ni. On the other hand, the adsorbate atoms having binding energy ε0 are proportional to adsorbate surface area A0. Applying this hypothesis, eq 9 can be written as Ai -ðεi -ε0 Þ -ðji -j0 Þ ¼ exp ð10Þ ¼ exp kT RT A0 Here, ji = NAεi and j0 = NAε0. NA indicates the Avogadro constant (NA = 6.023 1023 mol-1). The adsorbate surface area is given by A0 = NAa0, where a0 (in cm2) is the molecular area of the adsorbate, and is calculated as25 a0 = 1.091(m/FlNA)2/3. Here, m (in g mol-1) is the molecular weight of the adsorbate and Fl denotes the liquid phase density in g cm-3. It should also be noted here that if the adsorption is completely localized, the adsorbed molecules residing on the adsorption sites would have their positions determined by the crystal structure of the adsorbent; that is, the surface area of adsorbate molecules, A0, is determined not only by the molecular size of the adsorbate but also by the lattice parameters of the adsorbent. When the adsorbate is mobile, A0 is determined by the size and shape of the molecules as well as their packing pattern; that is, the ordering is similar to that of the liquid. The adsorbed phase volume is given by26 va = vb exp[R(T - Tb)], where vb is the specific volume at boiling point temperature (Tb) and R defines the thermal expansion coefficient. The density of the adsorbed phase is written as Fa = 1/va. In the present analysis, a0 is calculated as a0 = 1.091(m/FaNA)2/3. From eq 10, we have Ai ¼ 1:091NA
m Fa NA
¼ 1:091NA
m Fa NA
!2=3
-j exp RT
f ðQr Þ ¼ f ðQ0, r Þ þ
f 0 ðQ0, r Þ ðQr -Q0, r Þ þ 1!
f 00 ðQ0, r Þ f ðQ0, r Þ ðQr -Q0, r Þ2 þ ðQr -Q0, r Þ3 þ 2! 3! ...
f ðQr Þ ¼
X f γ ðQ0, r Þ γ!
ðQr -Q0, r Þγ ð12Þ
where f γ(Q0,r) denotes the γth derivative of f(Qr) at the point Q0,r (= Q0/RT) [Q0 is the least adsorption energy, and γ is an integer (γ = 1, 2, 3, ...n)]. According to Maclaurin’s development, eq 12 is valid for Q0,r < Qst,r < Qr (as shown in Figure 1), where Qst,r (= Qst/RT) is the reduced isosteric heat of adsorption. Equation 12 is modified by28 ¥ ¥ X γ X Q -Q0 γ jr ¼ Dγ Qr -Q0, r ¼ δγ RT γ ¼1 γ ¼1 ¼ δ1
Q -Q0 RT
þ δ2
Q -Q0 RT
2
þ
jr ≈R
...
þ δn
Q -Q0 RT
n
Q -Q0 γ RT
where δγ or R gives information concerning the nature of the adsorbent surface energy distribution function for a given adsorbate. At Henry’s region,7 Q ≈ ΔH and ΔH = -RT2 (dln KH/dT). Equation 11 is now written as 8 !γ 9 !2=3 < m ΔH 0 -Q0 = Ai ¼ 1:091NA exp -R ð13Þ : ; Fa NA RT
!2=3 expf -jr g
ð11Þ
(22) Kaneko, K.; Ishii, C. Colloids Surf. 1992, 67, 203. (23) Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. Carbon 1992, 30, 1075. (24) Cerofolini, G. F.; Jaroniec, M.; Sokolowski, S. Colloid Polym. Sci. 1978, 256, 471. (25) Sing, K. S. W.; Rouquerol, F.; Rouquerol, J. Adsorption by powders and solids; Academic: London, 1999. (26) Ozawa, S.; Kusumi, S.; Ogino, Y. J. Colloid Interface Sci. 1976, 56, 83.
7362 DOI: 10.1021/la900217t
where j (= ji - j0) is the extra energy27 and jr (= j/RT) indicates the reduced extra energy. Areas with higher values of extra energy are those on which surface molecules have a higher degree of insaturation. The unsaturated forces of these molecules are available for establishing bonds with adsorbed molecules. So it is assumed that the adsorption energy (Q) on a given surface area is an increasing function of the extra energy on that surface, that is, Qr = f(jr), where Qr = Q/RT. It should be noted here that jr g 0. The heterogeneity of adsorbent surface is a direct consequence of the Boltzmann distribution function.24 Equation 10 permits a bridge between the surface and adsorption properties. The adsorption takes place initially on the unstable adsorbent face with the maximum isosteric heat of adsorption. Since adsorption energy is the main contribution to free-energy loss following adsorption, in that case we can admit that the adsorption energy (Q) on a given adsorbent surface face is an increasing function of the extra energy on that surface face, which indicates that there exists the smallest possible adsorption energy (Q0) in a single component adsorbent-adsorbate system. Obviously, it is difficult to express analytically the dependence of jr on Q. However, it is not too restrictive to assume a Maclaurin’s development. Using Maclaurin’s development,27 we have
The unit of Ai (eq 13) is cm2 mol-1. The monolayer capacity of any adsorbent + adsorbate system is defined as the maximum amount of adsorbate uptake, which can be accommodated in a completely filled single molecular layer. It is related to the specific (27) Chakraborty, A.; Saha, B. B.; Koyama, S.; Ng, K. C.; Yoon, S. H. Appl. Phys. Lett. 2008, 92, 201911. (28) Rudzinski, W.; Everett, D. H. Adsorption of gases on heterogeneous surfaces; Academic Press: 1992; pp 141.
Langmuir 2009, 25(13), 7359–7367
Chakraborty et al.
surface area of solid adsorbent,25 that is, Ai = xmA0. The maximum possible amount of adsorbate uptake (xm, in g g-1) for a single component adsorbent-adsorbate system is given by 8 !γ 9 < 0 ΔH -Q0 = ð14Þ xm ¼ exp -R : ; RT Hence, the energy distribution (Φ) of the solid adsorbent surface is given by dxm Φ ¼ dfΔH 0 =ðRTÞg 8 !γ -1 !γ 9 < ΔH 0 -Q0 ΔH 0 -Q0 = exp -R ð15Þ ¼ -γR : ; RT RT We have introduced quasi-statistical thermodynamic treatment for calculating the specific surface area. This is a very simple way to handle the distribution function for the fractional area occupied by the chemical species for a given adsorption enthalpy or energy level. In reality, this approach assumes that the system is completely under isochoric (isotropic and constant volume) conditions. That approach works for those cases where the system is very close to complete thermodynamic equilibrium under pressure and moderate temperatures.
4. Results and Discussion In this work, we make use of the experimentally measured isotherm data for the adsorption of hydrogen and methane on carbonaceous materials, carbon nanotubes, zeolites, and metal organic frameworks29-38 to show the present findings. At first, the Henry’s coefficient and the heat of adsorption at zero surface coverage are calculated. Using the proposed formulation, the specific surface area and the maximum amount of adsorbate uptake for solid porous adsorbent are obtained as a function of R, γ, ΔH, and T. The critical temperature of hydrogen is 33.2 K. So, the adsorptive storage of hydrogen, at ambient temperature or cooled by liquid nitrogen (77 K), is absolutely based on supercritical adsorption. We have analyzed the physical adsorption in Henry’s region on the basis of published data of the adsorption of hydrogen by carbonaceous porous materials,29-31 crystalline microporous MOFs,32-34 zeolites,35,36 and carbon nanotubes29 at temperatures 77 and 303 K and varying pressures up to 10 MPa. The hydrogen-accumulating properties or uptakes of MOFs are compared with those of traditional materials (charcoals and zeolites) and nanocarbon systems. We have examined the experimentally measured adsorption isotherm data29-38 to calculate the Henry’s coefficient (KH) as a function of temperature, and finally ΔH is calculated. Table 1 (29) Xu, W.-C.; Takahashi, K.; Matsuo, Y.; Hattori, Y.; Kumagai, M.; Ishiyama, S.; Kaneko, K.; Iijima, S. Int. J. Hydrogen Energy 2007, 32, 2504. (30) Panella, B.; Hirscher, M.; Roth, S. Carbon 2005, 43, 2209. (31) de la Casa-Lillo, M. A.; Lamari-Darkrim, F.; Cazorla-Amoro’s, D.; Linares-Solano, A. J. Phys. Chem. B 2002, 106, 10930. (32) Qu, D. Chem.;Eur. J. 2008, 14, 1040. (33) Wong-Foy, A. G.; Matzger, A. J.; Yaghi, O. M. J. Am. Chem. Soc. 2006, 128, 3494. (34) Rowsell, J. L. C.; Yaghi, O. M. J. Am. Chem. Soc. 2006, 128, 1304. (35) Li, Y.; Yang, R. T. J. Phys. Chem. B 2006, 110, 17175. (36) Langmi, H. W.; Walton, A.; Al-Mamouri, M. M.; Johnson, S. R.; Book, D.; Speight, J. D.; Edwards, P. P.; Gamesonb, I.; Anderson, P. A.; Harris, I. R. J. Alloys Compd. 2003, 356-357, 710. (37) Himeno, S.; Komatsu, T.; Fujita, S. J. Chem. Eng. Data 2005, 50, xxx. (38) Lozano-Castello, D.; Alcaniz-Monge, J.; de la Casa-Lillo, M. A. Cazorla-Amoros, D.; Linares-Solano, A. Fuel 2002, 81, 1777.
Langmuir 2009, 25(13), 7359–7367
Article
summarizes the values of ΔH, KH (error ranges from 2 to 5%), maximum amount of adsorbate uptake including the BET surface area, and initial sticking coefficient for the adsorption of H2 on carbonaceous materials, MOFs, carbon nanotubes, nanohorns, and zeolites. A plot of specific surface area (Ai) versus ΔH for the adsorption of hydrogen on various functional porous adsorbents is shown in Figure 2, and the isosteric heat of adsorption (ΔH) is found to decrease with a higher Ai and approaches the least adsorption energy (Q0), and their gradients are found to be steeper, indicating the higher mobility of the hydrogen molecules. The functional carbonaceous material (Maxsorb III, activated carbon fibers, etc.) and MOFs consist mainly of micropores with different widths. At very low pressures (P f 0), it is found that ΔH is higher compared with Q0 for adsorbents with low surface area, that is, a0 . Ai as hydrogen molecules adsorb rapidly onto sites of high energy. On the other hand, the values of ΔH are found to be lower for adsorbents with higher surface area, and ΔH approaches Q0 for Ai = a0. In the case of lower Ai, the adsorbate molecules first penetrate into narrower pores, resulting in a stronger interaction between the adsorbate and the adsorbent. This implies a higher value of ΔH. Adsorbate molecules are gradually accommodated in the pores of adsorbents with higher specific surface area, in which the amount of adsorbate uptake becomes stronger and ΔH becomes weaker. Therefore, a linear decrease in ΔH as a function of specific surface area is observed. The amount of hydrogen uptake (measured experimentally at 77 K, 303 K, and 10 MPa) varies linearly with the specific surface area and this is shown in Figure 3. The limiting amount of hydrogen uptake (xm) on functional porous materials is also shown in Figure 3. It is found from eq 9 that the sticking coefficient (β) depends on the Henry coefficient from which β at any reference temperature is calculated. A plot of β versus Ai of functional adsorbents is plotted in Figure 4. At low surface coverage, β provides the maximum value and decreases with the higher specific surface area. The porous materials with higher Ai have a lower sticking coefficient, indicating the higher amount of adsorbate uptake due to relatively lower enthalpy and entropy of adsorption. One of the most important problems in physical adsorption is the evaluation of adsorbent heterogeneity from adsorption isotherm data. The heterogeneity is mainly due to various atoms and functional groups exposed at the porous adsorbent surface, imperfections of this surface, and impurities strongly bonded with the surface. The main source of the adsorbent heterogeneity is the complex porous structure containing micropores of different dimensions. The heterogeneity of functional porous materials is analyzed by means of adsorption energy and surface structural distribution functions. The surface energy distribution functions (Φ) versus ΔH - Q0 for the adsorption of hydrogen on different functional porous materials are plotted in Figure 5. The least adsorption energy Q0 represents the characteristic of adsorbent + adsorbate pairs, and this value is very close to but higher than the enthalpy of vaporization of adsorbates. The parameters R and γ provide useful information about the nature of the energy distribution function of hydrogen on various carbonaceous materials, zeolites, MOFs, single wall nanotubes (SWNTs), and single wall nanohorns (SWNHs). A comparison of the energy distributions as presented in Figure 5 shows that the functions Φ for carbonaceous materials, MOFs, and zeolites + hydrogen systems (a-c) differ from those evaluated for nanotubes (d and e), especially in their shapes. These distribution functions show a resemblance for the systems (i) a-c and (ii) d, e, which suggest their similar adsorption properties with DOI: 10.1021/la900217t
7363
Article
Chakraborty et al.
Table 1. Experimentally Measured ΔH, KH, Uptakes, Specific Surface Surface Area, and Initial Sticking Coefficient (Hence Initial Reference Temperature T0 = 34 K) for the Adsorption of Hydrogen on Carbonaceous Materials, SWNTs, SWNHs, MOFs, and Zeolites (in This Analysis, τ is Considered 10-16 s) name Maxsorb III ACF A20 AC2 SWNH SWNH-623 SWNH-693 SWNH-773 S-SWNT S-SWNT-693 r-SWNT n-SWNT MOF-74 HKUST-1 IRMOF-11 IRMOF-6 IRMOF-11 IRMOF-20 MOF-177 MOF-5 Cu3(BTC)2 NaCsRHO CdRHO CdA CdX CdY NaX NaY
ΔH (J mol-1) (at 77 K) 5800 ( 100 7000 ( 250 7800 ( 200 8000 ( 300 7400 ( 100 7150 ( 150 6900 ( 200 6750 ( 100 6200 ( 150 6500 ( 60 6560 ( 200 7800 ( 100 7420 ( 70 7390 ( 200 6900 ( 100 6500 ( 80 6250 ( 150 5800 ( 90 5800 ( 160 7100 ( 100 19 500 ( 300 15 200 ( 300 10 700 ( 100 10 350 ( 50 10 200 ( 100 9800 ( 200 9600 ( 100
KH (kg kg-1 kPa-1) (at 77 K)
% uptake (x) (at 77 K)
0.002310 0.004763 0.008798 0.005077 0.003140 0.003046 0.002828 0.000910 0.000883 0.001283 0.001184 0.007820 0.005832 0.005668 0.003595 0.002695 0.002258 0.002150 0.003010 0.013758 1.690000 0.020465 0.018130 0.010495 0.010794 0.028893 0.011384
5.60 ( 0.28 4.20 ( 0.21 2.65 ( 0.13 1.44 ( 0.07 2.80 ( 0.14 3.19 ( 0.16 4.19 ( 0.20 2.11 ( 0.11 3.78 ( 0.19 3.68 ( 0.18 2.69 ( 0.13 2.23 ( 0.11 3.25 ( 0.16 3.47 ( 0.17 4.81 ( 0.24 5.18 ( 0.31 6.66 ( 0.30 7.47 ( 0.32 5.10 ( 0.22 2.23 ( 0.11 0.01 ( 0.00 0.08 ( 0.00 1.21 ( 0.06 1.42 ( 0.07 1.47 ( 0.07 1.79 ( 0.08 1.90 ( 0.09
BET surface area (m2 g-1) 3306 1984 1060 296 775 1202 1536 337 1190 937 832 1100 2280 2380 3340 4210 4610 5670 2296 1154 3 90 383 526 594 622 725
β0As (m2) 3.3096 10-5 6.8241 10-5 0.00012605 7.2740 10-5 4.4988 10-5 4.3641 10-5 4.0518 10-5 1.2651 10-5 1.8382 10-5 1.6963 10-5 0.00011204 8.3557 10-5 8.1208 10-5 5.1507 10-5 3.8612 10-5 3.2351 10-5 3.0804 10-5 4.3125 10-5 0.00019712 0.00029321 0.00025975 0.00015037 0.00015465 0.00041396 0.00016310
Figure 2. Specific surface area as a function of the enthalpy of adsorption at zero surface coverage for the adsorption of hydrogen on (i) carbonaceous materials, (ii) single wall carbon nanotubes (SWNTs), (iii) single wall nanohorns (SWNHs), (iv) MOFs, and (v) zeolites. Experimental data are for 77 K and 10 MPa.
Figure 3. Amount of hydrogen uptake as a function of specific surface area for (i) 77 K and 10 MPa and (ii) 303 K and 10 MPa. The limiting amount of hydrogen uptake calculated by the present formulation (eq 14) is also shown.
respect to hydrogen molecules. The functions Φ as shown in Figure 5 provide information about the nature of the energetic and structural heterogeneity of activated carbons, MOFs, zeolites, and carbon nanotubes with respect to hydrogen adsorption. The distribution function Φ also indicates that the carbonaceous materials (type Maxsorb III, activated carbon fiber, etc.) possess more micropores of smaller dimensions than MOFs, zeolites, and nanotubes. This means that the Φ of carbonaceous materials + H2 systems shows the greater number of adsorption sites of higher energies. The influences of γ for the adsorption of carbonaceous materials, MOFs, SWNTs, and SWNHs on hydrogen are shown in Figure 6. It is interesting to observe that, as the exponent γ increases, the energy distribution function changes from a right-handed widened function toward a left-handed
widened Gaussian-like function, which indicates the nature of adsorbent surface heterogeneity. It is found from the present analysis that (i) until today, Maxsorb III is the best material for hydrogen storage, (ii) SWNTs and SWNHs with high specific surface area provide some promising results, and (iii) MOFs with specific surface area as high as 6000 m2/g exhibit the maximum hydrogen uptake of 7.2% at 77 K and 10 MPa. It is also necessary to consider a more realistic physical picture to take into account the fact that the adsorption energy of a molecule depends not only on the adsorbent surface heterogeneity factor (γ) but also on the adsorption energy distribution factor (R), which depends on temperature. It should be noted here that R is defined by the ratio of thermal energy to characteristic energy of the adsorbentadsorbate system. It is observed from Table 2 that R depends on
7364 DOI: 10.1021/la900217t
Langmuir 2009, 25(13), 7359–7367
Chakraborty et al.
temperature, and the energy distribution function Φ as a function of ΔH and R for the adsorption of hydrogen depends on (i) functional porous carbonaceous materials and (ii) single wall carbon nanotubes as shown in panels a and b, respectively, of Figure 7. The distribution function is a belt-shaped curve very similar to the Gaussian distribution. At higher temperature, the surface energy factor (R) increases, and Φ(ΔH) is shifted
Figure 4. Sticking coefficient of hydrogen on functional porous adsorbents for various specific surface areas. It is found that the βAs values of SWNTs are smaller than those of other adsorbents presented here.
Article
especially in the region of high ΔH values, which indicates that more adsorption energy is consumed for hydrogen adsorption. From the present analysis, γ = 1.2 for activated carbons, different activated carbon fibers, MOFs, and zeolites + hydrogen systems, whereas γ = 2 for different SWNTs and SWNHs + hydrogen
Figure 5. Surface energy distribution function as a function of ΔH found in the Henry region for the adsorption of hydrogen on carbonaceous materials, MOFs, zeolites, SWNTs, and SWNHs. It is found that the surface energy and structural distribution factors are different but the nature of functional carbonaceous porous materials, MOFs, and zeolites is the same. SWNTs and SWNHs are found to be of the same nature.
Figure 6. Plot of Ai and ΔH - Q0 as a function of surface structural distribution factor (γ) for (a) functional porous carbonaceous materials + H2 system, (b) MOFs + H2 system, (c) SWNTs + H2 system, and (d) SWNHs + H2 system. Langmuir 2009, 25(13), 7359–7367
DOI: 10.1021/la900217t
7365
Article
Chakraborty et al.
Table 2. Values of Surface Energy and Surface Structural Distribution Factors for the Adsorption of Hydrogen on Functional Porous Materials at 77 and 303 K 77 K
carbonaceous materials + H2 SWNTs + H2 SWNHs + H2 MOFs + H2 zeolites + H2
303 K
R
γ
R
γ
0.212 0.039 0.052 0.180 0.177
1.2 2.0 2.0 1.2 1.2
1.20 0.60 0.64
1.2 2.0 2.0
Figure 8. Specific surface area as a function of the enthalpy of adsorption at Henry’s regime for the adsorption of methane on carbonaceous materials. In this analysis, “ACF” indicates activated carbon fiber, “LFC” means activated carbon fiber with CO2 activation, “AC” defines activated carbon, and “KUA” represents the activated carbons prepared by KOH activation of Spanish anthracite.
Figure 9. Amount of methane uptake as a function of Ai for 298 K and 5 MPa. The limiting amount of methane uptake calculated by the present formulation (eq 14) is also shown. It is found from this curve that the maximum amount of methane uptake (0.5 g/g) can be captured by decreasing temperatures and increasing pressures with the use of Maxsorb III.
Figure 7. Plot of Ai and ΔH- Q0 as a function of surface energy distribution factor (R) for (a) functional porous carbonaceous materials + H2 and (b) SWNTs + H2 systems.
systems. It is concluded that the adsorption energy distribution function depends not only on the nature of the interactions between solid and adsorbate atoms but also on the conditions under which the adsorbent solid surface in formed. Another point to note is that the energy involved for porous materials and hydrogen is much higher than that corresponding to liquefaction of hydrogen (at normal boiling point), that is, ΔH|H2 . hfg|H2, and this means that the conventional types of adsorbent have difficulty in storing hydrogen at large capacity. Using the thermodynamic method of evaluation, it is projected that, by applying advanced surface controlled treatment on the carbonaceous materials where a pore areas could reach realistically as high as 5000 m2/g, the hydrogen uptakes are predicted to be (i) 12% at 77 K and 10 MPa and (ii) 1.8% at room temperature and 10 MPa for both carbon nanotubes and nanohorns. 7366 DOI: 10.1021/la900217t
The adsorption characteristics of carbonaceous materials (Norit R1 Extra, BPL, Maxsorb III, different types of KUA and LFC) and methane systems are discussed from experimentally measured adsorption isotherm data37,38 at very low pressure and concentration. A plot of specific surface area versus ΔH for various carbonaceous materials + methane is shown in Figure 8, and the maximum value of isosteric heat of adsorption (ΔH) is found to be lower with a higher specific surface area. The amount of methane (measured experimentally at 298 K and 5 MPa) varies linearly with the specific surface area of different carbonaceous materials, and this is shown in Figure 9. From the present analysis, it is observed that type KUA41701 and Maxsorb III show the higher uptakes and lower ΔH. It is also found from the present analysis that the energy ratio of heat of adsorption and enthalpy of liquefaction for methane on Maxsorb III is nearly equal to 2, that is, (ΔH/hfg)|CH4 ≈ 2, indicating that the Maxsorb III-methane system exhibits a more rapid uptake pattern. By applying advanced surface controlled treatment, the surface area of carbonaceous materials could realistically be reached as high as 5000 m2/g. The predicted methane uptakes are predicted to be Langmuir 2009, 25(13), 7359–7367
Chakraborty et al.
Article
Table 3. Experimentally Measured ΔH, KH, Specific Surface Surface Area and Initial Sticking Coefficient (Hence Initial Reference Temperature T0 = 34 K), and Sticking Coefficient at the Temperature of 298 K for the Adsorption of Methane on Carbonaceous Materials (in This Analysis, τ is Considered 10-16 s) name
ΔH (J mol-1) (at 298 K)
KH (kg kg-1 kPa-1) (at 298 K)
surface area (m2 g-1)
βAs (m2)
β0As (m2)
LFC 14 LFC 30 LFC 47 LFC 54 LFC 73 ACF type LFC BPL Norit R1 Extra Maxsorb III KUA11701 KUA41701
20 100 ( 250 18 500 ( 300 14 700 ( 200 114 200 ( 250 13 800 ( 160 13 136 ( 150 16 700 ( 150 15 900 ( 100 12 600 ( 150 19 200 ( 300 12 000 ( 200
0.003322 0.002090 0.001445 0.001291 0.001073 0.000841 0.001720 0.001540 0.000485 0.002311 0.000549
520 930 1760 1930 2400 2862 1150 1450 3250 726 3290
0.6755 0.4250 0.2938 0.2625 0.2182 0.1710 0.3497 0.3132 0.0986 0.4699 0.1116
0.005709 0.005027 0.007720 0.007241 0.006925 0.006240 0.006037 0.006395 0.004028 0.004798 0.005171
important in many ongoing efforts to create new synthetic carbonaceous materials such as carbon nanotubes, carbon nanofibers, metal organic frameworks, and carbon-silica composites. We have shown here that, under atmospheric conditions, carbonaceous materials are not suitable for hydrogen storage but could be acceptable for methane storage if new materials are designed with higher Ai. Acknowledgment. The authors wish to thank King Abdullah University of Science & Technology (KAUST) for the generous financial support through the project (WBS R265-000-286-597). Note Added after ASAP Publication. This article was released ASAP on May 1, 2009. Figure 4 was replaced, and the correct version of the article was posted on May 27, 2009.
Appendix Figure 10. Isosteric heat of adsorption in Henry’s region as a function of pore width.
50% at room temperature and 5 MPa pressure. Table 3 furnishes the values of ΔH, KH, βAs, β0As, and the BET surface area for the adsorption of CH4 on carbonaceous materials. The effects of ΔH on adsorbent pore width (w) for the adsorption of H2 and CH4 on functional carbonaceous materials are shown in Figure 10. The ΔH calculated by using the parallel slit model14 is also shown in Figure 10, where ΔH ranges from 24 to 14 kJ mol-1 for the activated carbon + methane system as the pore width varies from 4 to 10 A˚. It should be noted here that ΔH ranges from 12 to 5 kJ mol-1 for the carbonaceous material + H2 system. The ΔH value of the parallel slit model is matched well with the ΔH data of the Maxsorb III + methane/hydrogen system. For the carbonaceous material + methane system, the results14 obtained from the parallel slit model are 5-10% higher than those calculated by the present analysis. On the other hand, the ΔH data of SWNTs and SWNHs + hydrogen systems as shown in Figure 10 are about 15-20% higher than those calculated by the parallel slit model. The reason is due to the fact that the graphite parallel slit pore model ignores the effects of surface energy and surface structural heterogeneity factors.
5. Conclusions In this paper, it is found that the heat of adsorption at Henry’s region determines the limiting amount of adsorbate uptakes. We have developed a model to calculate the specific surface area as a function of the adsorption energy and compared the model with various experimental data. The knowledge of isosteric heat of adsorption for a molecule as a function of Ai can help in the design of new materials. From this analysis, it can be said that it is Langmuir 2009, 25(13), 7359–7367
1. Derivation of (∂x/∂P)T: As DNc D x 1 Dx 1 Dx ¼ ¼ w DP βτ T βτ DP T βτ DP T DP T As N c Dx Nc βτAs w ¼ ¼ DP T P P 2. Derivation of (∂x/∂T)P: The partial derivative of Nc with respect to T at constant P is written as As DNc D x ¼ DT P DT βτ P 1 Dx x D 1 x D 1 ¼ þ þ βτ DT P β DT τ P τ DT β P 1 Dx Nc τβAs D 1 dτ Nc τβAs D 1 dβ ¼ þ þ βτ DT P Dτ τ dT Dβ β dT β τ ! 1 Dx -1 Ed -1 dβ -τ þ Nc βAs ¼ þ Nc τAs 2 βτ DT P τ RT 2 β2 dT 1 Dx Nc Ed As Nc As dβ þ ¼ βτ DT P RT 2 β dT Nc As 1 Dx Nc Ed As Nc As dβ þ w¼ βτ DT P 2T RT 2 β dT
Dx As Nc βτEd As Nc βτ As Nc βτ dβ ¼ þ DT P 2T β dT RT 2 Dx Ed 1 1 dβ ¼ Nc βτAs þ wDT P RT 2 2T β dT
w-
DOI: 10.1021/la900217t
7367
