J. Phys. Chem. C 2007, 111, 9305-9313
9305
Experimental and Theoretical Studies of Gas Adsorption in Cu3(BTC)2: An Effective Activation Procedure Jinchen Liu,† Jeffrey T. Culp,‡ Sittichai Natesakhawat,§ Bradley C. Bockrath,§ Brian Zande,⊥ S. G. Sankar,⊥ Giovanni Garberoglio,| and J. Karl Johnson*,†,§ Department of Chemical Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260, Parsons Project SerVices, Incorporated, Post Office Box 618, South Park, PennsylVania 15129, National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236, AdVanced Materials Corporation, Pittsburgh, PennsylVania 15220, and Dipartimento di Fisica dell’ UniVersita` di Trento, 38100 Italy ReceiVed: February 20, 2007; In Final Form: April 28, 2007
We have improved the activation process for CuBTC [Cu3(BTC)2, BTC ) 1,3,5-benzenetricarboxylate] by extracting the N,N-dimethylformamide-solvated crystals with methanol; we identify material activated in this way as CuBTC-MeOH. This improvement allowed the activation to be performed at a much lower temperature, thus greatly mitigating the danger of reducing the copper ions. A review of the literature for H2 adsorption in CuBTC shows that the preparation and activation process has a significant impact on the adsorption capacity, surface area, and pore volume. CuBTC-MeOH exhibits a larger pore volume and H2 adsorption amount than any previously reported results for CuBTC. We have performed atomically detailed modeling to complement experimentally measured isotherms. Quantum effects for hydrogen adsorption in CuBTC were found to be important at 77 K. Simulations that include quantum effects are in good agreement with the experimentally measured capacity for H2 at 77 K and high pressure. However, simulations underpredict the amount adsorbed at low pressures. We have compared the adsorption isotherms from simulations with experiments for H2 adsorption at 77, 87, 175, and 298 K; nitrogen adsorption at 253 and 298 K; and argon adsorption at 298 and 356 K. Reasonable agreement was obtained in all cases.
1. Introduction
TABLE 1: Summary of the Results from the Literature for Gas Adsorption in CuBTC
Metal-organic frameworks (MOFs) are interesting materials for studying gas adsorption1,2 because they can be made in high purity, are highly crystalline, and have a very narrow range of pore sizes with virtually all of their pore volume falling within the IUPAC microporous regime. MOFs can be tailored fairly easily, and they have high pore volume and surface area. One of their potential applications is H2 adsorption and storage.3 CuBTC [Cu3(BTC)2, BTC ) 1,3,5-benzenetricarboxylate] (also known as HKUST-1) has garnered a good deal of attention since it was first reported by Chui et al. in 1999.4 There have been continuous efforts to improve the synthesis and activation of CuBTC.5-10 Most studies have focused on the gas adsorption properties of CuBTC, with special emphasis on molecular hydrogen. A summary of the results from the literature for gas adsorption in CuBTC is presented in Table 1. Wang et al.5 measured the adsorption isotherms for 10 different gases and proposed that CuBTC could be used for separation of gas mixtures, on the basis of analysis of their pure gas adsorption isotherms. We note, however, that mixture isotherms or ideal adsorbed solution theory should be used to predict selectivities. It is interesting to note that the uptake measured by different groups at nominally the same conditions varies considerably. For example, the maximum uptake measured at 77 K and 1 bar ranged from 1.33 to 2.6 wt %.8-13 The high pressure uptake at
ref
5 N2, O2, CO, CO2, N2O, CH4, 295 C2H4, C2H6, n-C12H26, H2O
Pmax (bar)
maximum H2 uptake (wt %)
1a
18 Ar
87
1.01
11 H2
77 87
1.01 1.01
1.44 1.07
7 H2
77
25
16 CO2
298
42
9 H2
77 87 195
14 H2
77 87 200 298
12 H2
77
15 H2
77
88
3.2
8 H2
77 87
1 1
2.18 1.56
13 H2
77
1
2
10 H2 D2 NO
†
University of Pittsburgh. ‡ Parsons Project Services, Incorporated. § National Energy Technology Laboratory. ⊥ Advanced Materials Corporation. | Universita ` di Trento.
T (K)
adsorbate
77 77 77 196, 298
17 Ar a
66-143
1.01 1.01 1.01 50 43 60 65 0.92
1 10 0.8 1
3.3 2.6 1.9 450 °C (expected wt % of 3 CuO for Cu3(BTC)2 anhydrous, 39.4%; found, 39.0%). TGA analysis in air at 5 °C/min showed all solvents removed below 150 °C, with no further weight loss before the onset of decomposition at T > 300 °C. The N2 BET surface area and pore volume of the sample were determined to be 1482 m2/g and 0.828 cm3/g, respectively. 2.1.2. Methylene Chloride SolVent: CuBTC-CH2Cl2. This sample was prepared following the method of Rowsell and Yaghi.9 Specifically, 1.0 g H3BTC was dissolved in 30 mL of 1:1 DMF/EtOH then added to a 15 mL solution of 2.0 g Cu(NO3)2·2.5 H2O in a sample vial. The resulting blue solution was stirred for 15 min, and then the vial was capped and heated in an oven at 85 °C for 20 h. The mixture was decanted while hot, and rinsed with DMF. The resulting blue microcrystals were soaked in 25 mL of methylene chloride for 3 days, with the solvent decanted and refreshed daily. The structure of the methylene chloride exchanged material was verified by X-ray powder diffraction. The material gave a N2 BET surface area and pore volume of 698 m2/g and 0.39 cm3/g, respectively. The TGA on the sample after exchange with methylene chloride
Gas Adsorption in Cu3(BTC)2 showed a weight loss equivalent to ∼2.3 DMF per Cu3(BTC)2 formula unit beginning at 170 °C, indicating that the exchange of DMF with methylene chloride was incomplete (see Supporting Information Figure S1). Difficulties associated with removal of the residual DMF are likely responsible for the lower surface area and pore volume (see Section 4). 2.2. Adsorption Measurements. Low pressure sorption isotherms (10-6-1 bar) of N2 and H2 were collected using a Quantachrome Autosorb-1-C analyzer. Prior to the measurements, samples (120-130 mg) were degassed under vacuum at 85 °C overnight, then for 2 h at 115 °C (CuBTC-MeOH) or under vacuum at 170 °C for 24 h (CuBTC-CH2Cl2). BET and Langmuir surface areas and total pore volumes of the samples were determined from N2 adsorption isotherms at 77 K. Multipoint BET and Langmuir measurements were taken at relative pressures in the range of P/P0 ) 0.1-0.3. The N2 pore volume was calculated from the N2 adsorption at 77 K at P/P0 ) 0.995. H2 sorption measurements were performed at 77 K. High pressure isotherms were collected on a pressure-composition isotherm measurement system (Advanced Materials Corporation) for pressures up to ∼60 bar for Ar and N2 and ∼50 bar for H2 at 77, 87, 175, and 298 K. This volumetric instrument is capable of collecting isotherms over a wide range of pressures (0.01-200 bar) and temperatures (77-1173 K). Prior to the measurements, samples (∼800 mg) were degassed under vacuum at 85 °C overnight, then for 2 h at 115 °C (CuBTCMeOH) or at 170 °C for 24 h (CuBTC-CH2Cl2). On the basis of the N2 BET pore volume measurements, porosities of 73% and 34% were used to calculate the excess gas adsorption for the methanol solvated and methylene chloride solvated samples, respectively (see Supporting Information). 3. Calculation Details 3.1. Model for the MOFs. We have used a rigid structure to model the MOF. The atomic positions of the MOF were obtained from published X-ray diffraction data,4 from which we removed the atoms belonging to the solvent molecules. For comparison, we also used the structure obtained from neutron powder diffraction analysis of the desolvated material.13 The adsorption isotherms obtained from these two sets of structural data are essentially identical. Thus, we only present results from calculations using the X-ray diffraction data. We used the universal force field (UFF) of Rappe´ et al.27 for the framework atoms in our simulations. Sagara et al.26 computed the binding of H2 on IRMOF-1 framework atoms using quantum mechanical methods and developed an ad hoc potential for H2 interacting with IRMOF-1. They computed effective framework charges on the atoms from density functional theory and combined these with a point-charge representation of the quadrupole moment on H2 to represent the classical H2-framework interaction potential. Garberoglio et al.24 found that the electrostatic charges on the framework atoms substantially increase the amount adsorbed at 77 K and low pressures but have a marginal effect at high pressures. (We note in passing that the Zn potential from the DREIDING force field28 was used by mistake in Figure 4 of ref 24, resulting in ∼0.3 wt % higher adsorption than if the UFF potential had been used.) Moreover, Garberoglio et al. found that Sagara’s results are similar to those obtained using the Buch potential29 without any fluid-solid charge interactions for adsorption of H2 in IRMOF-1.24 Fluid-solid charge interactions should be incorporated for accurate modeling of H2 adsorption in MOFs at low pressures. However, inclusion of the charge effects in a consistent fashion is difficult, since addition of a quadrupole term can make the H2-H2 interactions
J. Phys. Chem. C, Vol. 111, No. 26, 2007 9307 TABLE 2: Lennard-Jones Potential Parameters for the Adsorbate Molecules Used in This Work adsorbate
ref
/k (K)
σ (Å)
H2 N2 N2 (two-center LJ) Ar
29 30 31 32
34.20 93.98 37.29 119.80
2.960 3.572 3.310 3.400
L (Å)
1.090
artificially too attractive.24 In this paper, we are mainly interested in the behavior of the adsorption isotherms at high pressure, so we defer development of a H2 potential that includes charge interactions to another paper. 3.2. Model for Adsorbates. We have used the LennardJones (LJ) 12-6 potential to model the adsorbate molecules. Spherical models were used for all fluids but N2, for which both spherical and two-center LJ models were used. The fluid-fluid interaction potential parameters used in this work are reported in Table 2. The Lorentz-Berthelot mixing rules were employed to calculate the fluid-solid LJ cross-interaction parameters in the simulations. The fluid-fluid and fluid-solid intermolecular potentials were truncated at 17 Å, and no long-range corrections were applied. 3.3. Simulation Techniques. We have used the conventional GCMC technique in this work to calculate adsorption isotherms,33,34 wherein we specified the temperature and fugacity of the adsorbing gas and calculated the number of adsorbed molecules at equilibrium. Simulations at the lowest pressure for each system were started from an empty MOF matrix. Each subsequent simulation at higher fugacity was started from the final configuration of the previous run. Simulations consisted of a total of 8×106 trial moves, with the last half of the configurations used for data taking. A move is defined as an attempted translation, creation, or deletion of a molecule for spherical adsorbates. An additional reorientation move was included for a two-center LJ model for N2. The probability of attempting molecule creation and deletion was set to 0.3 in the simulations. To obtain the relationship between the bulk pressure and the fugacity, the Lennard-Jones 12-6 equation of state35 was used for spherical LJ models of nitrogen and argon; equations of state based on experimental data were used for hydrogen36 and the two-center LJ model of nitrogen.37 We have converted the total adsorption obtained from simulation to excess adsorption in order to compare with experimental data. The details of the conversion can be found in the Supporting Information. 3.4. Quantum Effects. Quantum diffraction effects can be important for light molecules, such as H2, leading to significant differences in the thermodynamic properties compared with those for corresponding classical fluids. The importance of quantum effects on the adsorption of H2 and D2 on carbons and other porous materials at cryogenic temperatures has been known for several decades.38-40 The importance of quantum effects in the adsorption of H2 in MOFs must be assessed in order to compare simulation results with experiments. Garberoglio et al. indicated that quantum effects reduce the amount of H2 adsorbed in IRMOF-1 and IRMOF-8 at 77 K.24 We have employed two different methods to account for quantum effects of H2 adsorbed in CuBTC. We use the path integral Monte Carlo (PIMC) method41,42 as the reference standard, since this method is essentially exact. We also use the Feynman-Hibbs effective potential method,43,44 which is much more computationally efficient than the PIMC method. 3.4.1. Path Integral Monte Carlo. We have used the path integral formalism41,42 adapted to the GCMC ensemble33,41,45 to account for quantum effects for simulating adsorption of H2;
9308 J. Phys. Chem. C, Vol. 111, No. 26, 2007
Liu et al.
this same method was used previously by Garberoglio et al.24 The simulations were performed at 77 and 298 K using one unit cell as the simulation box and a Trotter number of 30 beads at 77 K and 8 beads at 298 K. For each state point, the number of equilibration configurations was 106, starting from the result of the previous computation, followed by 4×106 configurations for production. The probability of creation/deletion was set to 49%, with 2% probability of performing a hybrid Monte Carlo move. 3.4.2. Feynman-Hibbs Effective Potential. The FeynmanHibbs effective potential (FH)43,44 can be obtained from a Taylor series expansion about a Gaussian Feynman-Hibbs potential.46,47 The FH effective potential truncated at the quadratic term has been shown to represent the thermodynamic and structural properties of 4He gas and liquid Ne fairly well when compared with PIMC results over a range of conditions.46,47 The FH effective Buch potential truncated at the quadratic term has the following form:
UFH(r) ) ULJ(r) +
( )
p2 ∇2ULJ(r) 24µkT
(1)
Figure 1. Fluid-fluid interaction potential for H2 at 77 K. The solid line is the Lennard-Jones 12-6 Buch potential for H2, the dotted line is the Feynman-Hibbs correction term given by the second term in eq 1, and the dashed line is the Feynman-Hibbs effective Buch potential for H2 at 77 K.
where ULJ(r) is the LJ interaction potential, r is the moleculemolecule distance, p is Planck’s constant divided by 2π, µ is the reduced mass, k is the Boltzmann constant, and T is the absolute temperature. The Laplacian of the potential is given by
(
)
2 132σ12 30σ6 - 8 ∇2ULJ(r) ) U′′LJ(r) + U′LJ(r) ) 4 r r14 r
(2)
For H2-H2 interactions, µ ) m/2, and for H2-sorbent interaction, µ ) m, where m is the mass of H2 molecule. We can therefore write
2.005 p2 ) (H2-H2) 24µkT T
(3)
1.002 p2 ) (H2-sorbent) 24µkT T
(4)
The units of eqs 3 and 4 are Å2. The classical Buch potential, the FH correction term (second term in eq 1), and the FH effective Buch potential for H2 at 77 K are plotted in Figure 1. The bulk isothermal properties of H2 at 77 K have been calculated from GCMC simulations using the classical Buch potential and the FH effective Buch potential. Quantum effects lead to a decrease in the bulk density of ∼20% at pressures >100 bar compared with classical Buch potential, as can be seen in Figure 2. The equation of state for H2 is accurately reproduced by the FH effective Buch potential. We should also mention that PIMC simulations with Buch potential have been shown to reproduce the H2 bulk equation of state over a fairly wide range of temperatures and pressures.45,48 4. Results and Discussion 4.1. Effect of Synthesis and Activation Technique on Porosity and H2 Adsorption. We have observed that the CuBTC‚(solvent) complex is highly stable at ambient conditions, unaffected by oxygen or humidity. However, the Cu2+ centers are susceptible to reduction by solvent or guests at elevated temperatures. This susceptibility was highlighted in the original report by Chui et al.4 Many attempts at improving the synthesis and stability of the material have been reported, with the
Figure 2. Bulk properties for H2 at 77 K. The experimental data49 are plotted as the solid line; the simulation results from the FH effective Buch potential are represented by filled circles, and the deviations are represented by empty circles. The simulation results from the classical Buch potential are represented by filled squares and the deviations are represented by empty squares.
majority focused on lowering the synthesis temperature.5,6,8-10 The lowest synthesis temperature was employed in the method of Rowsell and Yaghi, which used a solvent mixture of water, ethanol, and DMF at 85 °C with a reaction time of 20 h.9 We have verified that this procedure gives a product of high purity. However, we sought an improved method of removing the highboiling DMF, since replacement with methylene chloride (the procedure of Rowsell and Yaghi) in our hands appeared to leave a significant portion of the DMF in the crystals, as shown by a weight loss at ∼170 °C in the TGA run (see Supporting Information Figure S1). We found that extraction via Soxhlet of the DMF solvated crystals for ∼12 h with methanol was very effective at removing the DMF and gave a TGA trace that showed all solvents removed below 150 °C. This improvement in the preparation of the material allowed the activation prior to the gas adsorption measurements to be performed at a much lower temperature. Indeed, evacuation at 85 °C overnight, followed by a brief heating to 115 °C for 2 h was sufficient to completely remove the solvent. Extraction with methanol may be more effective at removing DMF than extraction with CH2-
Gas Adsorption in Cu3(BTC)2
J. Phys. Chem. C, Vol. 111, No. 26, 2007 9309
TABLE 3: Comparison of Surface Areas and Pore Volumes for Different CuBTC Samplesa ref this work (CuBTC-MeOH) this work (CuBTC-CH2Cl2) this work (simulation)
hydrothermal hydrothermal
4 5 18 6 11 7 16 9 14 12 15 8
hydrothermal hydrothermal hydrothermal hydrothermal hydrothermal electrochemical hydrothermal hydrothermal electrochemical
10 17
ABET, m2/g
synthesis method
hydrothermal “ambient pressure synthesis” hydrothermal hydrothermal
1482 (P/P0 ) 0.1-0.3) 698 (P/P0 ) 0.1-0.3) 1635 (P/P0 ) 0.1-0.3) 1504 (P/P0 ) 0.1-0.4) 692.2 964, 1333 (different batch)
AL, m2/g
Vp, cm3/g
2302 (P/P0 ) 0.1-0.3) 1078 (P/P0 ) 0.1-0.3) 2205 (P/P0 ) 0.1-0.3)
0.828 (P ) 0.995 atm) 0.390 (P ) 0.9 atm) 0.820 (P ) 1 atm)
917.6
0.333 0.658 0.37b 0.41 0.40b
∼1500b 1820
1781 1507 (P/P0 ) 0.02-0.3) 1154 1944 (P/P0 ) 0.02-0.1) 1239 (P/P0 ) 0.3)
2175 1958 872 2257 (P/P0 ) 0.02-0.35)
886b
0.75 0.27 0.62 (P/P0 ) 0.2) 0.684 0.32b
a The data were obtained from N adsorption isotherms at 77 K, except where noted. See Figures S4 and S5 for the N adsorption isotherms from 2 2 this work. b From argon adsorption at 87 K.
Cl2 due to the higher affinity of methanol for the polar pore environment and the ability of methanol to hydrogen bond with the existing solvents (ethanol and water) in the pores. Activation of the material at lower temperature greatly minimizes the danger of reducing the copper ions, as compared to heating at elevated temperatures with reactive guests still present in the material. This procedure has been repeated several times and has given consistent adsorption results from sample to sample. Furthermore, we have verified that once the reactive solvents, such as alcohols and DMF, have been removed, the material is stable at 115 °C under vacuum for at least 48 h, as determined by reproducible isotherms measured at intermittent times. Thus, it is our estimate that the inconsistencies in the reported gas adsorption properties of the material are most likely due to sample decomposition through either elevated temperatures used in the synthesis or activation procedure. The improved technique we have developed for synthesis and activation of CuBTC is reflected in the larger N2 BET pore volume of 0.828 cm3/g and higher H2 uptake measured on the material. In Table 3, we have summarized the specific BET and Langmuir surface areas and pore volumes from this work and the literature. We see that CuBTC-MeOH has the largest pore volume when compared with other reported results. We have also synthesized CuBTC following the method of Rowsell and Yaghi9 for verification purposes. The pore volume for this material, CuBTC-CH2Cl2, is comparable to Chui et al.,4 Vishnyakov et al.,18 Schlichte et al.,6 Lee et al.,11 and Krungleviciute et al.,17 but smaller than Wang et al.,5 Krawiec et al.,8 Rowsell and Yaghi,9 and Xiao et al.10 The pore volume and surface area of the sample we have prepared by the method of Rowsell and Yaghi gives a smaller surface area and pore volume than originally reported;9 however, the hydrogen uptake we have measured at high pressure is similar to a separate report on the material prepared by the same method.15 The difference in pore volumes for CuBTC-CH2Cl2 from this work and from Rowsell and Yaghi9 using the same synthetic procedure could be a result of the material’s being very sensitive to the synthesis conditions, for example, the volume of methylene chloride used in the extraction, batch size, or both. The batch size effect has been noted by Wang et al.5 Nevertheless, the pore volumes of the materials produced by the previously reported synthesis procedures under hydrothermal conditions are smaller than the pore volume of CuBTC-MeOH. The pore volume for the
material synthesized using an electrochemical method is unavailable for comparison.7,14 We also show the pore volume for the ideal crystal of CuBTC from simulations in Table 3. This value was calculated by dividing the amount of N2 adsorbed at P/P0 ) 1 as calculated from simulations by the bulk N2 density at 77 K. This is the same approach used in the experiments and, therefore, provides consistency between the pore volumes measured from experiments and calculated from simulations. The experimental value of 0.828 cm3/g agrees very well with the simulation value of 0.820 cm3/g, indicating that the material is remarkably free of guest molecules and defects. We also list the specific surface areas in Table 3, as calculated from the BET and Langmuir models. Note that these two methods give different results. We have found that the specific surface areas are very sensitive to the pressure region used for the calculations. For example, a specific BET surface area of 1635 m2/g was obtained by using the simulated adsorption data in the range P/P0 ) 0.1-0.3; however, this value decreases to 1504 m2/g if the data in the range P/P0 ) 0.1-0.4 are used. We have listed the pressure ranges used in the literature for calculating the specific surface area when such information was available. The specific surface area for CuBTC-MeOH is similar to those given by Yaghi and co-workers9,15,16 and is larger than the other groups. We have compared our experimental H2 adsorption isotherms in CuBTC at 77 K with data from the literature. The CuBTCMeOH sample exhibits the largest uptake comparing with literature data in the low-pressure regime, as shown in Figure 3. Our adsorption isotherm for CuBTC-CH2Cl2 agrees with data from Wong-Foy et al.,15 Lee et al.,11 and Prestipino et al.12 The adsorption isotherms from Rowsell and Yaghi,9 Xiao et al.,10 Krawiec et al.,8 and Peterson et al.13 fall between our isotherms for CuBTC-MeOH and CuBTC-CH2Cl2; this is consistent with the magnitude of pore volumes shown in Table 3. Interestingly, two adsorption isotherms, both from the Yaghi group,9,15 shown in Figure 3 as filled squares and half-filled squares, are not in agreement with each other. The disagreement in the data is probably due to the data’s being measured on two different instruments, with the high-pressure instrument not intended to provide precise subatmospheric data.50 Our data for CuBTC-CH2Cl2 are in agreement with the latter data set. The high pressure adsorption isotherms are shown in Figure 4. Here again, adsorption in CuBTC-MeOH yields the largest
9310 J. Phys. Chem. C, Vol. 111, No. 26, 2007
Figure 3. Comparison of experimental H2 adsorption isotherms in CuBTC at 77 K from different groups at low pressure, 0 < P < 1 bar. Filled circles, this work (CuBTC-MeOH); filled squares, Rowsell and Yaghi;9 filled down-triangles, Xiao et al.;10 filled stars, Krawiec et al.;8 crosses, Peterson et al.;13 half-filled squares, Wong-Foy et al.;15 halffilled circles, this work (CuBTC-CH2Cl2); filled diamonds, Lee et al.;11 filled up-triangles, Prestipino et al.12
Liu et al.
Figure 5. Comparison of simulated H2 adsorption isotherms in CuBTC at 77 K using the classical Buch potential (diamonds), PIMC (squares), and the FH effective Buch potential (circles). Lines are drawn as a guide to the eye.
Figure 6. Comparison of simulated H2 adsorption isotherms in CuBTC at 298 K using the classical Buch potential, PIMC, and the FH effective Buch potential. Symbols are the same as in Figure 5. Figure 4. Comparison of experimental H2 adsorption isotherms in CuBTC at 77 K from different groups for the high-pressure regime, 0 < P < 50 bar. Filled circles, this work (CuBTC-MeOH); filled downtriangles, Xiao et al.;10 filled squares, Panella et al.;14 filled diamonds this work (CuBTC-CH2Cl2); filled up-triangles, Wong-Foy et al.15
uptake, reaching ∼4.1 wt % at P ) 26 bar, which is ∼30% larger than the adsorption in CuBTC-CH2Cl2. The latter agrees very well with data of Wong-Foy et al.15 The adsorption data from Panella et al.14 and Xiao et al.10 lies between the isotherms of our two materials. We have seen that CuBTC-MeOH has the largest pore volume (Table 3) and H2 adsorption (Figures 3 and 4) compared with literature data. This increase is associated with the combination of a low-temperature synthesis that reduces the probability of introducing defects by inadvertent reduction of copper ions and the complete removal of solvents by our new activation procedure. 4.2. Impact of Quantum Effects. Simulation data using the FH effective Buch potential are compared with data from PIMC and the classical simulations for H2 adsorption in CuBTC at 77 K in Figure 5. The excess adsorption, including quantum effects (with both PIMC and FH approach), is about 15-20% less at 77 K over the whole range of pressures compared with classical simulations. Thus, quantum effects are significant for H2
adsorption in CuBTC at low temperatures, and they must be taken into account in the simulations to accurately compare with experiments. The agreement between the FH and PIMC simulations, as seen in Figure 5, is fairly good. The FH effective Buch potential appears to overestimate the importance of quantum effects, leading to ∼4% reduction in the amount of H2 adsorbed relative to the PIMC simulations. We have used the FH approach in our calculations to compare with experiments because of the significant computational savings of the FH method over the PIMC method. We have also compared the FH effective Buch potential with PIMC and classical Buch potential for H2 adsorption in CuBTC at 298 K. The difference in excess adsorption between the FH and classical Buch potential seen in Figure 6, is ∼7% at 85 bar, but the difference between the classical and PIMC results is only ∼2% at 85 bar. Use of the FH formalism at high temperature is not recommended because it overestimates quantum effects at these conditions. It may be surprising that there is even a 2% difference between classical and quantum isotherms at 298 K. The reason that quantum effects are nonzero at 298 K is that at this temperature, the thermal de Broglie wavelength of a hydrogen molecule is still a sizable fraction of
Gas Adsorption in Cu3(BTC)2
J. Phys. Chem. C, Vol. 111, No. 26, 2007 9311
Figure 8. Comparison of simulated and experimental H2 adsorption isotherms in CuBTC-MeOH at 87, 175, and 298 K. Experimental results are represented by squares, diamonds, and triangles for 87, 175, and 298 K, respectively. Simulations results are represented by dashed, dotted, and solid lines for 87, 175, and 298 K, respectively.
Figure 7. Comparison of simulated and experimental H2 adsorption isotherms in CuBTC-MeOH at 77 K. (a) P ) 0-1 bar measured with the Quantachrome Autosorb-1-C analyzer. (b) P ) 0-50 bar measured with pressure-composition isotherm measurement system (Advanced Materials Corporation). The experimental results are represented by filled circles. The simulation results using classical Buch and FH effective Buch potentials are represented by dashed and solid lines, respectively.
the hard-core diameter. The importance of quantum diffraction is enhanced at high densities because the molecules are more localized. 4.3. Comparison of Simulations with Experiments for H2 Adsorption. We plot our experimentally measured H2 isotherm at 77 K for CuBTC-MeOH along with predictions from our simulations in Figure 7. Both classical and FH calculations are plotted. The low pressure isotherm plotted in Figure 7a was measured using the Quantachrome Autosorb-1-C analyzer. Neither the quantum corrected nor the classical simulations agree quantitatively with the low-pressure data in Figure 7a. The poor agreement between simulations and experiments at low pressures may largely be due to ignoring charge-quadrupole interactions between H2 and the framework. The inclusion of chargequadrupole interactions in a self-consistent way will be addressed in a separate publication. The high-pressure experimental isotherm (Figure 7b) has a loading of ∼3.8 wt % at the highest pressure of 50 bar. The classical simulations give a loading of 4.4 wt % at P ) 27.6 bar, and the FH approach gives 3.6 wt % at P ) 29.3 bar. The FH effective Buch potential gives the best
agreement with experiments at the highest pressures but underestimates the amount adsorbed over the entire range, probably due to a combination of factors, including (1) lack of charge-quadrupole interactions in the model, (2) overcorrection for quantum effects by the FH approach, and (3) errors in the solid-fluid potentials. Peterson et al. noted that the lattice constant of CuBTC changes with D2 loading.13 However, the maximum change in the lattice constant is only 0.021 Å,13 which is unlikely to affect the equilibrium amount adsorbed. Simulations with the classical Buch potential overestimate the experimental data for pressure >5 bar and underestimate the experimental data for pressure
