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Hydrogen storage in a series of Zn-based MOFs studied by Sanchez–Lacombe equation of state
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e6
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Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state Sajjad Javidi Alesaadi, Fatemeh Sabzi* Department of Chemical Engineering, Shiraz University of Technology, Shiraz 71555-313, Iran
article info
abstract
Article history:
One of the most famous porous adsorbents used for separation and storage of hydrogen is
Received 12 October 2014
metal organic framework (MOF). In this study, the experimental data related to hydrogen
Received in revised form
adsorption on and desorption from five adsorbents including MOF-5, MOF-177, MOF-200,
25 November 2014
MOF-205 and MOF-210 is adopted. Then, the hydrogen sorption is modeled by applying
Accepted 2 December 2014
SanchezeLacombe Equation of State (SL EoS). The amount of hydrogen uptake in the ad-
Available online xxx
sorbents is obtained through hydrogen-adsorbents phase equilibrium calculations at temperature 77 K and various pressures up to 80 105 Pa. The result is compared with the
Keywords:
experimental data to show the precision of SL equation of state in predicting the hydrogen
Hydrogen
sorption trend. SL EoS predicts the experimental results satisfactorily, even though in
Zn-based MOFs
comparison with PHSC EoS, the latter shows a little reduction in average absolute
Sorption
deviation.
Porosity
Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
SanchezeLacombe equation of state
Introduction Nowadays, fossil fuels provide most of the world energy requirement for transportation and heating. Meeting this energy demand while maintaining or reducing our current environmental footprint is challenging and need significant changes in the way we produce, distribute and use energy [1]. Hydrogen is a promising alternative energy carrier, since it has the highest possible energy density and is a carbon-free fuel not producing undesirable greenhouse gas CO2. Therefore, the development of hydrogen infrastructures is crucial to facilitate the transition to a sustainable, carbon-neutral energy economy tomorrow [2]. One of the barriers to the advancement of hydrogen technologies is storage. Compressed gas and liquid hydrogen storage methods are unlikely to meet the aggressive energy targets for H2 storage systems [3]. Alternatives, such as
solid state storage systems where a host material is used as gas carrier, offer improved volumetric energy densities [4,5]. In general, hydrogen storage materials can be divided into two classes, those that bind atomic hydrogen via strong chemisorption process like metal hydrides [1], and those that trap molecular hydrogen via weak van der Waals interactions known as physisorption like activated carbons [6] and metal organic frameworks (MOFs) [7e13]. Designing MOFs includes the assembly of metal-carboxylate subunits as nodes of the framework and of organic linkers in the network topology. The properties of MOFs, for example pore dimensions, porosity and surface area, depend upon the choice of the metal ions and the organic ligand [7,14]. In 2003, the first measurement of hydrogen storage on a MOF material, i.e. Zn4O(BDC)3 with BDC ¼ 1,4-benzenedicarboxylate, referred as MOF-5was reported by Rosi et al. [15]. Since then, numerous metal-organic frameworks have been synthesized
* Corresponding author. E-mail addresses: [email protected], [email protected] (F. Sabzi). http://dx.doi.org/10.1016/j.ijhydene.2014.12.008 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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experimentally [7,8,16] for further modification and in order to predict novel properties. Among them, Furukawa et al. produced MOF-177, connecting Zn4O unit with three 4,40 ,400 -benzene-1,3,5-triyl-tribenzoate(BTB) as organic linkers. They also constructed the expanded forms of MOF-177 from 4,40 ,400 -[benzene-1,3,5-triyl-tris(benzene-4,1-diyl)]tribenzoate (BBC) to obtainMOF-200, and used mixed 4,40 ,400 -benzene-1,3,5-triyl-tribenzoate (BTB)/2,6-naphthalenedicarboxylate(NDC) and BTE/ biphenyl-4,40 -dicarboxylate(BPDC) links to gainMOF-205 and 210 [17]. They presented the crystal structures of MOFs and reported their hydrogen adsorption at 77 K and 80 bar. Augmenting theoretical knowledge of hydrogen sorption in metal organic frameworks is important for our understanding of physisorption in these materials. Equations of state have been widely used to seek the structure-property relationships of the adsorption of gases in polymers. Perturbed Hard Sphere Chain Equation of State (PHSC EoS) has been previously chosen for investigating the sorption of CO2, C2H2and C2H4in a kind of macromolecule with high porosity called hydrogen-bonded organic framework (HOF-1a) successfully [18]. This model has been also used to predict the hydrogen [19] and methane [20] storage in five adsorbents including MOF-5, MOF-177, MOF200, MOF-205 and MOF-210. In this work, the SanchezeLacombe (SL) equation of state has been selected to examine its capability for interpreting hydrogen sorption data in above-mentioned macromolecules. The well-known latticefluid model of SL has been previously applied to study the properties of binary or multi-component ordinary compounds and polymeric systems [21e24]. There is also some monolayer and multilayer adsorption models all based on fitting several adjustable parameters [25e28] which account for example lattice coordination number and pore heterogeneity but not structure of the adsorbent. For gas solubility prediction in SL model, the knowledge of three characteristic parameters, i.e. the characteristic density, r*, the characteristic pressure, P*, and the characteristic temperature, T*, is needed. These parameters have been calculated for both hydrogen molecules and MOFs in order to use as constants to correlate sorption data points.
Following the original developments of Sanchez and Lacombe, the general SanchezeLacombe equation of state can be written as [29,30]: (1)
where r is the reduced density, P the reduced pressure and T the reduced temperature of a pure component. The reduced parameters are obtained by characteristic constants as follows: r¼
r P T ; P ¼ *; T ¼ * r* P T
(2)
where T is the absolute temperature, P the pressure and r the density of a pure substance. r is a size parameter that shows the number of lattice sites occupied by a molecule and can be related to the molecular weight according to the below relation: r ¼ P* M
* * RT r
T* ¼
ε* ε* M ; P* ¼ * ; r* ¼ * rn R n
(4)
where, ε* , n* , R and M are the interaction energy per mer, the close-packed volume of a mer, the universal gas constant and the molar mass or molecular weight of molecules, respectively. For a polymer-gas mixture, it needs to use a mixing rule for the calculation of, n*mix , ε*mix and rmix based on the corresponding values of the pure component parameters. In this work, the van der Waals mixing rule has been applied for calculating the mixture properties as follows [23]: n*mix ¼
Nc X Nc X i¼1
fi fj n*ij
(5)
j¼1
where n*ij ¼
n*ii þ n*jj 2
! 1 nij
(6)
The parameter nij accounts for possible deviation of n*ij from the arithmetic mean of the corresponding values n*ii and n*jj of the pure components. Here, the value of the interaction parameter nij has been assumed zero. Accordingly, the values of ε*mix and rmix have been obtained by the following equations: ε*mix ¼
r1 mix ¼
Nc X Nc 1 X
n*mix
i¼1
fi fj
0:5 ε*ii ε*jj 1 kij n*ij
(7)
j¼1
Nc .
X fj rj
(8)
j¼1
where kij is a binary interaction parameter for the ith and jth components' interaction in the mixture. fi is the volume fraction of the ith component in the mixture expressed in terms of the mass fraction ui and the characteristic values of r*i and n*i of the pure components: 2 !31 Nc uj 5 ui 4 X fi ¼ * * ri ni j¼1 r*j n*j
Theory
1 r2 þ P þ T lnð1 rÞ þ 1 r ¼ 0 r
For a high molecular weight polymer the value of r can be considered to be infinite. T*, P* and r* are the characteristic parameters defined as [23]:
(9)
The chemical potential of each component in the gas and polymer þ gas phases must be equal at the equilibrium state, i.e. mGi ¼ mPi . Following the developments of McHugh and Krukonis [31], the chemical potential of the ith component in a multicomponent system can be written as: ri mi ¼ RT ln fi þ 1 rmix 2 1 33 2 0 Nc Nc X X 2 * * * * * þri 4 r4 * @ fj nij εij εmix fj nij A þ εmix 55 n j¼1 j¼1 3 2 r RTn ð1 rÞlnð1 rÞ þ lnr ri 7 6 7 6 7 6 1 þri 6 7 7 6 Nc P 5 4 * A þPn 2 fj nij nmix
(10)
j¼1
(3)
where Nc denotes the number of components in the mixture.
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e6
and the percentage of average absolute deviation (AAD%) calculated from the following expression:
Results and discussions There are three pure component characteristic parameters, T*, P* and r*in SL EoS to produce the phase behavior diagram. Because of the lack of metal organic frameworks' vaporeliquid equilibrium (VLE) or PVT data, pure compound characteristic parameters cannot be estimated directly. Therefore these parameters have been calculated by group contribution method. For this purpose and at the first step the macromolecule structure has beenbrokendown to its functional groups. By making use of Eqs. 11e13 developed by Boudouris et al., the characteristic properties have been obtained through summing the first and second order contribution of each group in one specific property [22]: T* ¼ P* ¼ r* ¼
X X X
X
Ni T*1i þ W Ni P*1i þ W Ni r*1i þ W
X X
. Mw
(11)
. Mw
(12)
. Mw
(13)
Mj T*2j þ T*+ Mj P*2j þ P*+
Mj r*2j þ r*+
Ni is the number of first-order groups and Mj is the number of second-order groups. W is a constant equal to zero when just the first-order contributions are included and is equal to one when the second order contributions are added.T , P and r are adjustable parameters which set equal to 1674 K, 5225 MPa and 405 kg/m3,respectively. Table 1 shows the characteristic parameters for Zn metal element, molecular hydrogen and the individual metal organic frameworks of interest including: MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210. The characteristic parameters of Zn are needed to obtain the characteristic parameters of macromolecules. In this work, the binary interaction parameter (Kij ) has been determined by fitting the experimental data of isothermal sorption of hydrogen on the afore-mentioned macromolecules at 77 K for each binary system. The binary interaction parameter has been finally obtained by minimization of the following objective function [24]: NdP exp X Pcal i Pi OF ¼ exp Pi i¼1
!2 (14) exp
and Pi are the number of equilibrium data whereNdp ,Pcal i points, calculated and experimental vapor pressures, respectively. Table 2 represents the binary interaction parameters
AAD% ¼
NdP cal exp 100 X Pi Pi NP i¼1 Pexp i
(15)
In Table 2, the average absolute deviation without optimizing the adjustable parameter, i.e. Kij ¼ 0 , has been also shown in order to establish the validity of SL equation of state for recalculating the sorption data points without using a scaling constant. In this work, the adsorption and desorption of hydrogen on MOF-5, MOF-177, MOF-200, MOF-205 and MOF210 has been predicted at 77 K and pressures up to 80 105 Pa by GC-SL EoS setting the local equilibrium in both sides of membrane, feed and permeate. The experimental sorption data points which is in terms of the mass of hydrogen sorbed in the mass unit of MOFs has been converted to volume fraction in order to use in equilibrium calculations. It is worth to notice that SL EoS is based on the lattice-fluid theory assuming that the potential energy is pair-additive for each pair of molecules and that only the nearest neighbors are considered in this sum. This means that the model considers the interaction energy, ε*mix , between the hydrogen molecules situated immediately next to MOF surface and MOF unit cell, i.e. excess uptake. As the experimental hydrogen sorption also shows excess hydrogen uptake, then SL EoS is applicable for estimating hydrogen uptake capacity in MOFs. MOF-5 was introduced for the first time in 1999 by Yaghi's research group [32]. MOF-5 has a crystal structure, in which Zn4O unit has been joined with three 1,4-benzene dicarboxylate (BDC) as organic linkers. The amount of adsorption and desorption of hydrogen in MOF-5 at 77 K was measured by Furukawa et al. [17]. Geometric surface area, pore volume and crystal density are the main parameters affecting the sorption of gas at constant temperature and pressure. Chahine and Bose [33] reported pore volume and BET (Brunauer-EmmettTeller) surface area as 1.55 cm3 g1 and 3800 m2 g1. In this work, hydrogen sorption on MOF-5 at 77 K and various pressures up to 90 105 Pa with using Kij or without using has been modeled via SL EoS. The amount of the calculated and experimental adsorption and desorption of hydrogen in MOF5 has been shown in Fig. 1. The comparison of experimental and theoretical curves shows that suggested model either with using Kij or without using it, can predict the sorption data well.
Table 2 e Adjusted binary interaction parameters and statistical errors from SL equation of state. Table 1 e Pure component characteristic parameters used in the SL EoS model. Component H2 [29] Zn [30] MOF-5 MOF-177 MOF-200 MOF-205 MOF-210
*
*
*
T (K)
P (MPa)
r (Kg/m )
45.89 7128.00 551.06 846.84 803.32 723.38 662.51
100.00 8602.79 505.82 672.08 572.84 573.38 522.03
152.66 6110.00 975.37 1332.95 1122.18 1324.27 1002.63
3
Pairs Hydrogen-MOF-5 (adsorption) Hydrogen-MOF-5 (desorption) Hydrogen-MOF-177 (adsorption) Hydrogen-MOF-177 (desorption) Hydrogen-MOF-200 (adsorption) Hydrogen-MOF-200 (desorption) Hydrogen-MOF-205 (adsorption) Hydrogen-MOF-205 (desorption) Hydrogen-MOF-210 (adsorption) Hydrogen-MOF-210 (desorption)
Kij 0.07 0.71 0.27 0.20 0.11 0.43 0.05 0.31 0.01 0.48
AAD% AAD% (Kij ¼ 0) 1.63 2.08 1.73 2.55 1.67 2.87 1.14 2.07 1.63 2.22
1.86 2.86 2.14 4.01 2.46 4.19 1.66 3.13 2.04 3.35
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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In spite of better pore texture and higher adsorption amount for hydrogen gas, the number of publications on MOF177 is less than that on MOF-5. The pore volume and BET surface area have been reported by Chen et al. [34] as 1.89 cm3 g1 and 4500 m2 g1. The experimental amount of hydrogen sorption in MOF-177 was measured by Furukawa et al. [17] at 77 K and 90 105 Pa. Fig. 2 compares the measured amounts of hydrogen adsorption and desorption in MOF-177 with the calculated values obtained from SL equation of state. The maximum hydrogen sorption capacity of MOF-177 is 75 mg g1 while that of MOF-5 is 50 mg g1. It would be reasonable that hydrogen is more largely adsorbed in MOF177, which has higher pore volume and surface area. Accordingly, a non-interpenetrating expansion of MOF-177 was targeted by Furukawa et al. [17] using BBC to make the highly porous material MOF-200. The unit cell volume of MOF200 is 2.6 times greater than that of MOF-177. They found that BET surface area of MOF-200 is 4530 m2 g1 which is not much different from that of MOF-177. Fig. 3 exhibits the calculated, with or without using Kij , and experimental hydrogen uptake values in MOF-200. It has been demonstrated that despite the higher pore volume of 3.59 cm3 g1relative to that of MOF-177, MOF-200 does not show larger hydrogen uptake. It seems that hydrogen adsorption is favored in small micropores, which is largely due to van der Waals interactions with the internal wall structure and to weak electrostatic forces associated with the metal-oxide cluster. Other MOFs of nets were constructed by using mixed BTB/ NDC and BTE/BPDC to obtain MOF-205 and -210 [17]. Furukawa et al. [17] recognized that MOF-205 has less surface area and pore volume than MOF-200 (4460 m2 g1 and 2.16 cm3 g1) and therefore, less hydrogen uptake value. Amongst the five macromolecules studied here, MOF-210 has the highest BET surface area and pore volume as 6240 m2 g1 and 3.6 cm3 g1. Figs. 4 and 5 represent the calculated and experimental hydrogen adsorption on and desorption from MOF-205 and -210, respectively. It is obvious that MOF-210 with ultrahigh surface area would exhibit exceptional gas storage capacity.
Fig. 1 e Comparison of H2 sorption and desorption in MOF5 with experimental data [17].
Fig. 2 e Comparison of H2 sorption and desorption in MOF177 with experimental data [17].
In the above five cases, two factors, i.e. surface area and pore volume, are important for MOFs to be ideal for hydrogen storage purposes. As a general principle, MOFs with smaller surface area have smaller pores and should demonstrate smaller hydrogen uptake capacity. But practically there is no linear relationship between these two factors. It can be concluded that MOFs with the smallest pore size show the strongest hydrogen-binding energy while the highest hydrogen uptake is achieved in the macromolecules with the largest surface area. Zhao et al. [35] and Culp et al. [36] indicated that the ideal MOF to be chosen for hydrogen storage should have high surface area for higher capacity and appropriate pore size for strong binding with hydrogen. In order to examine the ability of SanchezeLacombe model in describing hydrogen sorption experimental results, the AAD% obtained in this work has been compared with AAD%
Fig. 3 e Comparison of H2 sorption and desorption in MOF200 with experimental data [17].
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e6
5
molecular size and energy parameters which are meaningful, while SL EoS depends on temperature, pressure and density characteristic parameters which do not make sense for macromolecular nets such as MOFs.
Conclusion
Fig. 4 e Comparison of H2 sorption and desorption in MOF205 with experimental data [17].
taken from our previously published hydrogen storage in MOFs studied by PHSC equation of state [19]. Table S1 in supplementary material shows the AAD% extracted from PHSC modeling of hydrogen sorption in the above-mentioned MOFs with and without using Kij through Eq. (15). In the zero parameter method, i.e. Kij ¼ 0, the mean deviations of 2.77 and 1.83 are observed for SL and PHSC equation of state, respectively. While, with binary interaction parameter taking into account, the mean deviations reduce to 1.96 and 1.59, consecutively. In both cases, using fitted mixture interaction parameters in the model resulted in better predictions of sorption isotherms for all MOFs. Moreover, in comparison with SanchezeLacombe model, PHSC equation of state leads to a noticeably better agreement with experimental sorption data points. It is reasonable, because the PHSC EoS is based on
In this study, hydrogen adsorption on and desorption from MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 have been investigated by applying SanchezeLacombe Equation of State at temperature 77 K and a wide range of pressure 0e80 105 Pa with reasonable precision. The SL EoS requires three molecular characteristic parameters, namely, the characteristic density, r*, the characteristic pressure, P*, and the characteristic temperature, T*, calculated using group contribution method. There is only one adjustable scaling constant which is calculated from the regression of isothermal hydrogen sorption experimental data. The results gained without applying the scaling constant demonstrates that the modeling is a successful predictive analysis and the inclusion of Kij does not reduce it to a simple data fitting process. It seems that the PHSC equation of state is more successful in accomplishing the prediction duty, even though SL equation of state performs well, too. Hydrogen sorption in metal organic frameworks studied here, is growing with pressure, reaching a stable and constant amount. Among all aforementioned MOFs, MOF-210 with ultrahigh surface area and pore volume represents exceptional hydrogen storage capacity.
Acknowledgments The authors wish to thank the computer facilities provided by Shiraz University of Technology.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijhydene.2014.12.008
references
Fig. 5 e Comparison of H2 sorption and desorption in MOF210 with experimental data [17].
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Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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ScienceDirect journal homepage: www.elsevier.com/locate/he
Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state Sajjad Javidi Alesaadi, Fatemeh Sabzi* Department of Chemical Engineering, Shiraz University of Technology, Shiraz 71555-313, Iran
article info
abstract
Article history:
One of the most famous porous adsorbents used for separation and storage of hydrogen is
Received 12 October 2014
metal organic framework (MOF). In this study, the experimental data related to hydrogen
Received in revised form
adsorption on and desorption from five adsorbents including MOF-5, MOF-177, MOF-200,
25 November 2014
MOF-205 and MOF-210 is adopted. Then, the hydrogen sorption is modeled by applying
Accepted 2 December 2014
SanchezeLacombe Equation of State (SL EoS). The amount of hydrogen uptake in the ad-
Available online xxx
sorbents is obtained through hydrogen-adsorbents phase equilibrium calculations at temperature 77 K and various pressures up to 80 105 Pa. The result is compared with the
Keywords:
experimental data to show the precision of SL equation of state in predicting the hydrogen
Hydrogen
sorption trend. SL EoS predicts the experimental results satisfactorily, even though in
Zn-based MOFs
comparison with PHSC EoS, the latter shows a little reduction in average absolute
Sorption
deviation.
Porosity
Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
SanchezeLacombe equation of state
Introduction Nowadays, fossil fuels provide most of the world energy requirement for transportation and heating. Meeting this energy demand while maintaining or reducing our current environmental footprint is challenging and need significant changes in the way we produce, distribute and use energy [1]. Hydrogen is a promising alternative energy carrier, since it has the highest possible energy density and is a carbon-free fuel not producing undesirable greenhouse gas CO2. Therefore, the development of hydrogen infrastructures is crucial to facilitate the transition to a sustainable, carbon-neutral energy economy tomorrow [2]. One of the barriers to the advancement of hydrogen technologies is storage. Compressed gas and liquid hydrogen storage methods are unlikely to meet the aggressive energy targets for H2 storage systems [3]. Alternatives, such as
solid state storage systems where a host material is used as gas carrier, offer improved volumetric energy densities [4,5]. In general, hydrogen storage materials can be divided into two classes, those that bind atomic hydrogen via strong chemisorption process like metal hydrides [1], and those that trap molecular hydrogen via weak van der Waals interactions known as physisorption like activated carbons [6] and metal organic frameworks (MOFs) [7e13]. Designing MOFs includes the assembly of metal-carboxylate subunits as nodes of the framework and of organic linkers in the network topology. The properties of MOFs, for example pore dimensions, porosity and surface area, depend upon the choice of the metal ions and the organic ligand [7,14]. In 2003, the first measurement of hydrogen storage on a MOF material, i.e. Zn4O(BDC)3 with BDC ¼ 1,4-benzenedicarboxylate, referred as MOF-5was reported by Rosi et al. [15]. Since then, numerous metal-organic frameworks have been synthesized
* Corresponding author. E-mail addresses: [email protected], [email protected] (F. Sabzi). http://dx.doi.org/10.1016/j.ijhydene.2014.12.008 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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experimentally [7,8,16] for further modification and in order to predict novel properties. Among them, Furukawa et al. produced MOF-177, connecting Zn4O unit with three 4,40 ,400 -benzene-1,3,5-triyl-tribenzoate(BTB) as organic linkers. They also constructed the expanded forms of MOF-177 from 4,40 ,400 -[benzene-1,3,5-triyl-tris(benzene-4,1-diyl)]tribenzoate (BBC) to obtainMOF-200, and used mixed 4,40 ,400 -benzene-1,3,5-triyl-tribenzoate (BTB)/2,6-naphthalenedicarboxylate(NDC) and BTE/ biphenyl-4,40 -dicarboxylate(BPDC) links to gainMOF-205 and 210 [17]. They presented the crystal structures of MOFs and reported their hydrogen adsorption at 77 K and 80 bar. Augmenting theoretical knowledge of hydrogen sorption in metal organic frameworks is important for our understanding of physisorption in these materials. Equations of state have been widely used to seek the structure-property relationships of the adsorption of gases in polymers. Perturbed Hard Sphere Chain Equation of State (PHSC EoS) has been previously chosen for investigating the sorption of CO2, C2H2and C2H4in a kind of macromolecule with high porosity called hydrogen-bonded organic framework (HOF-1a) successfully [18]. This model has been also used to predict the hydrogen [19] and methane [20] storage in five adsorbents including MOF-5, MOF-177, MOF200, MOF-205 and MOF-210. In this work, the SanchezeLacombe (SL) equation of state has been selected to examine its capability for interpreting hydrogen sorption data in above-mentioned macromolecules. The well-known latticefluid model of SL has been previously applied to study the properties of binary or multi-component ordinary compounds and polymeric systems [21e24]. There is also some monolayer and multilayer adsorption models all based on fitting several adjustable parameters [25e28] which account for example lattice coordination number and pore heterogeneity but not structure of the adsorbent. For gas solubility prediction in SL model, the knowledge of three characteristic parameters, i.e. the characteristic density, r*, the characteristic pressure, P*, and the characteristic temperature, T*, is needed. These parameters have been calculated for both hydrogen molecules and MOFs in order to use as constants to correlate sorption data points.
Following the original developments of Sanchez and Lacombe, the general SanchezeLacombe equation of state can be written as [29,30]: (1)
where r is the reduced density, P the reduced pressure and T the reduced temperature of a pure component. The reduced parameters are obtained by characteristic constants as follows: r¼
r P T ; P ¼ *; T ¼ * r* P T
(2)
where T is the absolute temperature, P the pressure and r the density of a pure substance. r is a size parameter that shows the number of lattice sites occupied by a molecule and can be related to the molecular weight according to the below relation: r ¼ P* M
* * RT r
T* ¼
ε* ε* M ; P* ¼ * ; r* ¼ * rn R n
(4)
where, ε* , n* , R and M are the interaction energy per mer, the close-packed volume of a mer, the universal gas constant and the molar mass or molecular weight of molecules, respectively. For a polymer-gas mixture, it needs to use a mixing rule for the calculation of, n*mix , ε*mix and rmix based on the corresponding values of the pure component parameters. In this work, the van der Waals mixing rule has been applied for calculating the mixture properties as follows [23]: n*mix ¼
Nc X Nc X i¼1
fi fj n*ij
(5)
j¼1
where n*ij ¼
n*ii þ n*jj 2
! 1 nij
(6)
The parameter nij accounts for possible deviation of n*ij from the arithmetic mean of the corresponding values n*ii and n*jj of the pure components. Here, the value of the interaction parameter nij has been assumed zero. Accordingly, the values of ε*mix and rmix have been obtained by the following equations: ε*mix ¼
r1 mix ¼
Nc X Nc 1 X
n*mix
i¼1
fi fj
0:5 ε*ii ε*jj 1 kij n*ij
(7)
j¼1
Nc .
X fj rj
(8)
j¼1
where kij is a binary interaction parameter for the ith and jth components' interaction in the mixture. fi is the volume fraction of the ith component in the mixture expressed in terms of the mass fraction ui and the characteristic values of r*i and n*i of the pure components: 2 !31 Nc uj 5 ui 4 X fi ¼ * * ri ni j¼1 r*j n*j
Theory
1 r2 þ P þ T lnð1 rÞ þ 1 r ¼ 0 r
For a high molecular weight polymer the value of r can be considered to be infinite. T*, P* and r* are the characteristic parameters defined as [23]:
(9)
The chemical potential of each component in the gas and polymer þ gas phases must be equal at the equilibrium state, i.e. mGi ¼ mPi . Following the developments of McHugh and Krukonis [31], the chemical potential of the ith component in a multicomponent system can be written as: ri mi ¼ RT ln fi þ 1 rmix 2 1 33 2 0 Nc Nc X X 2 * * * * * þri 4 r4 * @ fj nij εij εmix fj nij A þ εmix 55 n j¼1 j¼1 3 2 r RTn ð1 rÞlnð1 rÞ þ lnr ri 7 6 7 6 7 6 1 þri 6 7 7 6 Nc P 5 4 * A þPn 2 fj nij nmix
(10)
j¼1
(3)
where Nc denotes the number of components in the mixture.
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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and the percentage of average absolute deviation (AAD%) calculated from the following expression:
Results and discussions There are three pure component characteristic parameters, T*, P* and r*in SL EoS to produce the phase behavior diagram. Because of the lack of metal organic frameworks' vaporeliquid equilibrium (VLE) or PVT data, pure compound characteristic parameters cannot be estimated directly. Therefore these parameters have been calculated by group contribution method. For this purpose and at the first step the macromolecule structure has beenbrokendown to its functional groups. By making use of Eqs. 11e13 developed by Boudouris et al., the characteristic properties have been obtained through summing the first and second order contribution of each group in one specific property [22]: T* ¼ P* ¼ r* ¼
X X X
X
Ni T*1i þ W Ni P*1i þ W Ni r*1i þ W
X X
. Mw
(11)
. Mw
(12)
. Mw
(13)
Mj T*2j þ T*+ Mj P*2j þ P*+
Mj r*2j þ r*+
Ni is the number of first-order groups and Mj is the number of second-order groups. W is a constant equal to zero when just the first-order contributions are included and is equal to one when the second order contributions are added.T , P and r are adjustable parameters which set equal to 1674 K, 5225 MPa and 405 kg/m3,respectively. Table 1 shows the characteristic parameters for Zn metal element, molecular hydrogen and the individual metal organic frameworks of interest including: MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210. The characteristic parameters of Zn are needed to obtain the characteristic parameters of macromolecules. In this work, the binary interaction parameter (Kij ) has been determined by fitting the experimental data of isothermal sorption of hydrogen on the afore-mentioned macromolecules at 77 K for each binary system. The binary interaction parameter has been finally obtained by minimization of the following objective function [24]: NdP exp X Pcal i Pi OF ¼ exp Pi i¼1
!2 (14) exp
and Pi are the number of equilibrium data whereNdp ,Pcal i points, calculated and experimental vapor pressures, respectively. Table 2 represents the binary interaction parameters
AAD% ¼
NdP cal exp 100 X Pi Pi NP i¼1 Pexp i
(15)
In Table 2, the average absolute deviation without optimizing the adjustable parameter, i.e. Kij ¼ 0 , has been also shown in order to establish the validity of SL equation of state for recalculating the sorption data points without using a scaling constant. In this work, the adsorption and desorption of hydrogen on MOF-5, MOF-177, MOF-200, MOF-205 and MOF210 has been predicted at 77 K and pressures up to 80 105 Pa by GC-SL EoS setting the local equilibrium in both sides of membrane, feed and permeate. The experimental sorption data points which is in terms of the mass of hydrogen sorbed in the mass unit of MOFs has been converted to volume fraction in order to use in equilibrium calculations. It is worth to notice that SL EoS is based on the lattice-fluid theory assuming that the potential energy is pair-additive for each pair of molecules and that only the nearest neighbors are considered in this sum. This means that the model considers the interaction energy, ε*mix , between the hydrogen molecules situated immediately next to MOF surface and MOF unit cell, i.e. excess uptake. As the experimental hydrogen sorption also shows excess hydrogen uptake, then SL EoS is applicable for estimating hydrogen uptake capacity in MOFs. MOF-5 was introduced for the first time in 1999 by Yaghi's research group [32]. MOF-5 has a crystal structure, in which Zn4O unit has been joined with three 1,4-benzene dicarboxylate (BDC) as organic linkers. The amount of adsorption and desorption of hydrogen in MOF-5 at 77 K was measured by Furukawa et al. [17]. Geometric surface area, pore volume and crystal density are the main parameters affecting the sorption of gas at constant temperature and pressure. Chahine and Bose [33] reported pore volume and BET (Brunauer-EmmettTeller) surface area as 1.55 cm3 g1 and 3800 m2 g1. In this work, hydrogen sorption on MOF-5 at 77 K and various pressures up to 90 105 Pa with using Kij or without using has been modeled via SL EoS. The amount of the calculated and experimental adsorption and desorption of hydrogen in MOF5 has been shown in Fig. 1. The comparison of experimental and theoretical curves shows that suggested model either with using Kij or without using it, can predict the sorption data well.
Table 2 e Adjusted binary interaction parameters and statistical errors from SL equation of state. Table 1 e Pure component characteristic parameters used in the SL EoS model. Component H2 [29] Zn [30] MOF-5 MOF-177 MOF-200 MOF-205 MOF-210
*
*
*
T (K)
P (MPa)
r (Kg/m )
45.89 7128.00 551.06 846.84 803.32 723.38 662.51
100.00 8602.79 505.82 672.08 572.84 573.38 522.03
152.66 6110.00 975.37 1332.95 1122.18 1324.27 1002.63
3
Pairs Hydrogen-MOF-5 (adsorption) Hydrogen-MOF-5 (desorption) Hydrogen-MOF-177 (adsorption) Hydrogen-MOF-177 (desorption) Hydrogen-MOF-200 (adsorption) Hydrogen-MOF-200 (desorption) Hydrogen-MOF-205 (adsorption) Hydrogen-MOF-205 (desorption) Hydrogen-MOF-210 (adsorption) Hydrogen-MOF-210 (desorption)
Kij 0.07 0.71 0.27 0.20 0.11 0.43 0.05 0.31 0.01 0.48
AAD% AAD% (Kij ¼ 0) 1.63 2.08 1.73 2.55 1.67 2.87 1.14 2.07 1.63 2.22
1.86 2.86 2.14 4.01 2.46 4.19 1.66 3.13 2.04 3.35
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
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In spite of better pore texture and higher adsorption amount for hydrogen gas, the number of publications on MOF177 is less than that on MOF-5. The pore volume and BET surface area have been reported by Chen et al. [34] as 1.89 cm3 g1 and 4500 m2 g1. The experimental amount of hydrogen sorption in MOF-177 was measured by Furukawa et al. [17] at 77 K and 90 105 Pa. Fig. 2 compares the measured amounts of hydrogen adsorption and desorption in MOF-177 with the calculated values obtained from SL equation of state. The maximum hydrogen sorption capacity of MOF-177 is 75 mg g1 while that of MOF-5 is 50 mg g1. It would be reasonable that hydrogen is more largely adsorbed in MOF177, which has higher pore volume and surface area. Accordingly, a non-interpenetrating expansion of MOF-177 was targeted by Furukawa et al. [17] using BBC to make the highly porous material MOF-200. The unit cell volume of MOF200 is 2.6 times greater than that of MOF-177. They found that BET surface area of MOF-200 is 4530 m2 g1 which is not much different from that of MOF-177. Fig. 3 exhibits the calculated, with or without using Kij , and experimental hydrogen uptake values in MOF-200. It has been demonstrated that despite the higher pore volume of 3.59 cm3 g1relative to that of MOF-177, MOF-200 does not show larger hydrogen uptake. It seems that hydrogen adsorption is favored in small micropores, which is largely due to van der Waals interactions with the internal wall structure and to weak electrostatic forces associated with the metal-oxide cluster. Other MOFs of nets were constructed by using mixed BTB/ NDC and BTE/BPDC to obtain MOF-205 and -210 [17]. Furukawa et al. [17] recognized that MOF-205 has less surface area and pore volume than MOF-200 (4460 m2 g1 and 2.16 cm3 g1) and therefore, less hydrogen uptake value. Amongst the five macromolecules studied here, MOF-210 has the highest BET surface area and pore volume as 6240 m2 g1 and 3.6 cm3 g1. Figs. 4 and 5 represent the calculated and experimental hydrogen adsorption on and desorption from MOF-205 and -210, respectively. It is obvious that MOF-210 with ultrahigh surface area would exhibit exceptional gas storage capacity.
Fig. 1 e Comparison of H2 sorption and desorption in MOF5 with experimental data [17].
Fig. 2 e Comparison of H2 sorption and desorption in MOF177 with experimental data [17].
In the above five cases, two factors, i.e. surface area and pore volume, are important for MOFs to be ideal for hydrogen storage purposes. As a general principle, MOFs with smaller surface area have smaller pores and should demonstrate smaller hydrogen uptake capacity. But practically there is no linear relationship between these two factors. It can be concluded that MOFs with the smallest pore size show the strongest hydrogen-binding energy while the highest hydrogen uptake is achieved in the macromolecules with the largest surface area. Zhao et al. [35] and Culp et al. [36] indicated that the ideal MOF to be chosen for hydrogen storage should have high surface area for higher capacity and appropriate pore size for strong binding with hydrogen. In order to examine the ability of SanchezeLacombe model in describing hydrogen sorption experimental results, the AAD% obtained in this work has been compared with AAD%
Fig. 3 e Comparison of H2 sorption and desorption in MOF200 with experimental data [17].
Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e6
5
molecular size and energy parameters which are meaningful, while SL EoS depends on temperature, pressure and density characteristic parameters which do not make sense for macromolecular nets such as MOFs.
Conclusion
Fig. 4 e Comparison of H2 sorption and desorption in MOF205 with experimental data [17].
taken from our previously published hydrogen storage in MOFs studied by PHSC equation of state [19]. Table S1 in supplementary material shows the AAD% extracted from PHSC modeling of hydrogen sorption in the above-mentioned MOFs with and without using Kij through Eq. (15). In the zero parameter method, i.e. Kij ¼ 0, the mean deviations of 2.77 and 1.83 are observed for SL and PHSC equation of state, respectively. While, with binary interaction parameter taking into account, the mean deviations reduce to 1.96 and 1.59, consecutively. In both cases, using fitted mixture interaction parameters in the model resulted in better predictions of sorption isotherms for all MOFs. Moreover, in comparison with SanchezeLacombe model, PHSC equation of state leads to a noticeably better agreement with experimental sorption data points. It is reasonable, because the PHSC EoS is based on
In this study, hydrogen adsorption on and desorption from MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 have been investigated by applying SanchezeLacombe Equation of State at temperature 77 K and a wide range of pressure 0e80 105 Pa with reasonable precision. The SL EoS requires three molecular characteristic parameters, namely, the characteristic density, r*, the characteristic pressure, P*, and the characteristic temperature, T*, calculated using group contribution method. There is only one adjustable scaling constant which is calculated from the regression of isothermal hydrogen sorption experimental data. The results gained without applying the scaling constant demonstrates that the modeling is a successful predictive analysis and the inclusion of Kij does not reduce it to a simple data fitting process. It seems that the PHSC equation of state is more successful in accomplishing the prediction duty, even though SL equation of state performs well, too. Hydrogen sorption in metal organic frameworks studied here, is growing with pressure, reaching a stable and constant amount. Among all aforementioned MOFs, MOF-210 with ultrahigh surface area and pore volume represents exceptional hydrogen storage capacity.
Acknowledgments The authors wish to thank the computer facilities provided by Shiraz University of Technology.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijhydene.2014.12.008
references
Fig. 5 e Comparison of H2 sorption and desorption in MOF210 with experimental data [17].
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Please cite this article in press as: Alesaadi SJ, Sabzi F, Hydrogen storage in a series of Zn-based MOFs studied by SanchezeLacombe equation of state, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/ j.ijhydene.2014.12.008