Effect of Time, Temperature, and Kinetics on the Hysteretic Adsorption

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Effect of Time, Temperature, and Kinetics on the Hysteretic Adsorption
Desorption of H2, Ar, and N2 in the Metal
Organic Framework Zn2(bpdc)2(bpee) Sarmishtha Sircar,† Haohan Wu,§ Jing Li,§ and Angela D. Lueking*,†,‡ †

Department of Energy & Mineral Engineering and ‡Department of Chemical Engineering, EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States

bS Supporting Information ABSTRACT: The intriguing hysteretic adsorption
desorption behavior of certain microporous metal
organic frameworks (MMOFs) has received considerable attention and is often associated with a gate-opening (GO) effect. Here, the hysteretic adsorption of N2 and Ar to Zn2(bpdc)2(bpee) (bpdc = 4,40 -biphenyldicarboxylate; bpee = 1,2-bipyridylethene) shows a pronounced effect of allowed experimental time at 77 and 87 K. When the time allowed is on the order of minutes for N2 at 77 K, no adsorption is observed, whereas times in excess of 60 h is required to achieve appreciable adsorption up to a limiting total coverage. Given sufficient time, the total uptake for N2 and Ar converged at similar reduced temperatures, but the adsorption of Ar was significantly more rapid than that of N2, an observation that can be described by activated configurational diffusion. N2 and Ar both exhibited discontinuous stepped adsorption isotherms with significant hysteresis, features that were dependent upon the allowed time. The uptake of H2 at 77 K was greater than for both N2 and Ar but showed no discontinuity in the isotherm, and hysteretic effects were much less pronounced. N2 and Ar adsorption data can be described by an activated diffusion process, with characteristic times leading to activation energies of 6.7 and 12 kJ/mol. Fits of H2 adsorption data led to activation energies in the range 2
7 kJ/mol at low coverage and nonactivated diffusion at higher coverage. An alternate concentration-dependent diffusion model is presented to describe the stepwise adsorption behavior, which is observed for N2 and Ar but not for H2. Equilibrium is approached very slowly for adsorption to molecularly sized pores at low temperature, and structural change (gate opening), although it may occur, is not required to explain the observations.

’ INTRODUCTION Microporous metal
organic frameworks (MMOFs) have recently received considerable attention for applications in gas storage,1
6 separations,4,5,7
11 catalysis,12
15 and sensing and detection devices.13,16
19 The adsorption behavior in MMOFs may exhibit unusual features, one of which is significant adsorption
desorption hysteresis. Such hysteretic adsorption
desorption behavior may be a strategy by which to realize significant gas trapping for a novel means of adsorptive separation. Although hysteretic adsorption
desorption is a well-known phenomenon, previous studies of adsorption
desorption hysteresis are typically associated with mesopores in which isotherm discontinuities are indicative of capillary condensation within the pores and hysteresis arises because of metastable transition states.20,21 Such an effect may explain discontinuities in the adsorption isotherm for MMOFs under certain conditions (e.g., CO2 adsorption to MOF-5,22 i.e. [OZn4] [O2C
C6H4
CO2]3). Alternatively, hysteretic adsorption may be a sign of insufficient equilibrium time because of mass-transfer limitations. For this to occur, the window size of the pore would be on the order of the kinetic diameter of the diffusing gaseous species, thus impeding the transfer rate of the gas into the adsorbate. If the kinetic energy r 2011 American Chemical Society

of the gas is low (i.e., at low T) or the allowed time is short, then these mass-transfer limitations present themselves as adsorption
desorption hysteresis in which the gaseous species may still be diffusing upon completion of each sorption step. A third type of adsorption hysteresis is a result of sorptioninduced structural changes. This gas-induced structural changing in MMOFs has received increasing attention in the literature, although such behavior has been described in amorphous carbon materials23
27 and polymers.28 The behavior in MMOFs is particularly novel because it can be quite pronounced, involving very large changes in volume upon the removal or addition of a guest. Such behavior may give rise to distinct features in the adsorption isotherm. For example, the pressure at which a sharp discontinuity occurs in the isotherm was referred to as a gateopening (GO) pressure for adsorption (N2, Ar, and CO2) to [Cu(bpy)(BF4)2(H2O)2](bpy) (bpy = 1,4-bipyridine) at 77, 77, and 273 K, respectively. In a subsequent discussion, the pressure at which such a discontinuity occurs will be referred to simply as PA. Received: July 22, 2011 Revised: September 30, 2011 Published: October 05, 2011 14169

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Langmuir Here, the behavior was attributed to the disruption of hydrogen bonding between a BF4 anion and water molecules in adjacent layers at elevated pressure.29 Similar PA values, along with abrupt discontinuities in the desorption isotherm (PD), were seen for the supercritical adsorption of N2, O2, and CH4 at 298 K to [Cu(dhbc)2(4,40 -bpy)] (dhbc = 2,5-dihydroxybenzene dicarboxylate)30 and supercritical CO2 and N2 (at various T values) adsorption on a pillared Ni(1,2-bis(4-pyridyl)ethylene)[Ni(CN)4] compound by Culp et al.31 In the former case, the large pressure differential between the gate-opening and gateclosing pressures was attributed to the displacement of π
π stacked layers and the stabilization of the expanded crystal by the adsorbate. In the case presented by Culp et al.,31 XRD suggested that the structural transformation was due to a variation in the tilt angle of the pillars of the layered structure upon guest adsorption, but no evidence for this transformation was found in XRD or adsorption when the chemical identity of the pillar was varied. Zhao et al. saw a similar effect for supercritical H2 adsorption at 77 K for Ni2(bipy)3(NO3)4 (where bipy is 4,4-bipyridyl). Here, the hysteresis was attributed to the dynamic opening of the windows between pores under pressure.3 In situ synchrotron X-ray diffraction techniques have conclusively shown lattice swelling of MOF structures upon CO2 adsorption.32 Similarly, neutron powder diffraction and vibration spectroscopy33,34 were used to confirm that H2 hysteretic adsorption
desorption in MIL-53 (i.e., CrIII(OH) 3 (O2C
C6H4
CO2) 3 (HO2C
C6H4
CO2H}x 3 H2Oy) was due to a gate-opening mechanism. The use of neutron methods confirmed adsorption-induced structural transformations in MIL-53 and also demonstrated that H2 remained trapped in closed pores, even at low P values and 77 K.35 The rate of adsorption in GO-MMOFs has been described with a GO diffusion model36 that incorporates a double-exponential (DE) diffusion process37 and describes the GO transition via the formation of an intermediate. It thus builds from and shows similarities to other models of adsorption in rigid MMOFs.38
44 However, diffusion limitations in carbon materials45,46 and zeolites47
51 have been addressed previously and have demonstrated that diffusion limitations in porous materials are particularly pronounced at low temperature. Thus, it is notable that many of the studies of adsorption in GO-MMOFs neglect to mention the adsorption
desorption allowed time, particularly for studies that involve low temperature. This article demonstrates how insufficient time can have a drastic impact on the interpretation of GO effects in adsorption. Both condensing (N2 and Ar) and supercritical (H2) adsorption behavior are considered, and the allowed time and temperature are varied. Future work will address the detailed mapping of the role of temperature, pressure, other adsorptive gases, and the history of GO on subsequent adsorption measurements.

’ MATERIALS [Zn2(bpdc)2(bpee)] 3 2DMF or RPM3-Zn was synthesized according to a published procedure.52 XRD results of the structure have been reported previously: the structure changes reversibly upon removal and refill of the solvent. The crystal structure of as-synthesized, solvated RPM3-Zn is shown in Figure 1, where guest molecules are omitted for clarity. The guest-free structure has not yet been matched against the guest-free XRD data. To synthesize RPM3-Zn, crystals of [Zn2(bpdc)2(bpee)] 3 2DMF were synthesized using Zn(NO3)2 3 6H2O, 4,40 -biphenyldicarboxylic acid (H2bpdc) and 1,2-bipyridylethene (bpee)

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Figure 1. Crystal structure of solvated Zn2(bpdc)2(bpee). Structure determined by the single-crystal X-ray diffraction method with guest molecules (not shown). (Zn: aqua; C: gray; O: red; N: blue). in a molar ratio of 1:1:1 in a 15 mL DMF solution. The reaction was carried out at 165 °C for 3 days before cooling to room temperature. Colorless crystals of RPM3-Zn were isolated by filtering and washing with DMF and ethyl ether. Freshly made sample was immersed at room temperature in methanol and dichloromethane consecutively to exchange the solvent, followed by pumping under vacuum to give guestfree RPM3-Zn.

’ METHODS A commercial volumetric adsorption unit (ASAP 2020, Micromeritics) was used for adsorption measurements of subcritical gases at cryogenic temperatures at pressures of less than 1 bar. Temperature was maintained using a bath of liquid nitrogen (77 K) or liquid argon (87 K), which was replenished every 48 h for long experiments. Prior to the first isotherm, the sample was outgassed at high vacuum (∼5  10
3 mmHg) at 135 °C for at least 8 h. Unless otherwise noted, each adsorption isotherm was collected sequentially on the same sample with an additional pretreatment at 120 °C for 4 h prior to the next measurement. The convergence of the capacity of similar isotherms indicates that this was sufficient to remove adsorbate from the prior measurement or N2 introduced during backfill. As is typical for commercial volumetric equipment, the ASAP determines the allowed experimental time at each isotherm point based on the pressure stability. Because the experimental allowed time (ta) cannot be varied directly on this instrument, we have varied the frequency of the stability checks to arrive at different allowed times, as denoted by dt in sample notation. In certain cases (isotherm D and Ar at 77 K) a screening experiment was done to ensure that the given dt was sufficient to observe GO. The actual ta is often much greater than the minimum in the regions in which there is a steep increase in the adsorbed amount, as illustrated for select data in Figure 2 and specified more fully in the Supporting Information (Table S1
S9). Because of the inherent leakage associated with the equipment (e0.0007 mmHg/min) and the extended ta, we conservatively estimate the error bar to be 10 cm3 (STP)/g for a 50 mg sample.53 Additional details are provided in the Supporting Information. Hydrogen isotherms were collected for up to 20 bar using a highpressure gravimetric unit (Hiden IGA-003) to accommodate higher adsorption pressures for supercritical H2. Pressure control of the equipment is conducted through an admit valve and an exhaust valve such that the pressure remains constant after the initial ramping period. The operation of this equipment has been described in detail in previous reports54 as well as in the Supporting Information. The error bar at ∼300 °C and 20 bar is ∼3 cc (STP)/g, which represents a conservative estimate of the conditions used here. The effect of buoyancy on the sample weight was addressed by measuring the sample density with helium at 25 °C. In contrast to the ASAP, ta is specified by the user rather than based on stability criteria. 14170

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Figure 2. Nitrogen adsorption at 77 K shows a pronounced effect of allowed time: (A) dt = 5 s, (B) dt = 20 s, and (D, E) dt = 360 s. (C) Collected at Rutgers using a fresh sample and different adsorption equipment (Autosorb-1 MP, Quantachrome Instruments); the allowed time varied from 6 min to 3.7 h for adsorption. A history effect is also observed in which the number of data points affects the uptake (e.g., screening experiment D with 4 points vs full isotherm E with 45 points). Times (from the previous data point) for select points are Di = 67 h, Dii = 8.5 h, Ei = 62 h, Eii = 20 h, and Eiii = 14 h. The total times for adsorption (in hours) are A ≈ B (∼1) < C (16) < D (80) < E (135). Prior to the sharp rise, curves C
E follow the A and B curves. To analyze the rate of N2 and Ar adsorption, we have determined an average characteristic time of adsorption in the active region of the isotherm in two ways. First, we report the maximum time required for stability for a particular isotherm. Second, we compute an average characteristic time in the active portion of the isotherm (i.e., the region where there is a sharp discontinuity in the isotherm). The latter considers the cumulative time of adsorption from the initial inflection point of the isotherm (i.e., PA) to the point in the isotherm where it levels off and is divided by the number of points in this region. Both times are meant to serve as estimates of the true equilibration time. For the H2 isotherms collected on the gravimetric equipment, adsorption data versus time is available, and thus the rate data is fit directly to the kinetic model below. Data are fit to the short-time micropore diffusion (MPD) model, up to ϑ < 0.85 (eq 9) because the short-time model is accurate only up to ϑ ≈ 0.85.39 The model is fit against experiment using kc and qo as adjustable parameters. The last data point collected after ta is used as an initial estimate of qo, but both kc and qo are ultimately varied to minimize the sum of the least squares. All rate data are compared at equivalent uptakes. Because the volumetric and gravimetric equipment use different methods to consider the time necessary for stability, the time data from the two separate instruments are not compared in the analysis of the rate data below. Capacity, however, is directly comparable between the two instruments because both instruments have been calibrated with the same standard materials under the conditions of interest.

’ RESULTS The adsorption of subcritical N2 to Zn2(bpdc)2(bpee) at 77 K exhibited a pronounced effect of allowed time on the adsorption isotherm (Figure 2). A short duration (dt = 5 s) showed no appreciable adsorption (Figure 2A,B), whereas increased time (dt = 360 s; Figure 2D,E) showed sharp discontinuities in the adsorption isotherm (denoted PA), a feature that has been previously attributed to GO for other MMOFs.3,30,31 At PA, the necessary time always significantly exceeded the minimum required time (i.e., 11dt) to meet the stability criterion. Regions of the isotherm that were flat (including those with dt = 5) often

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did not exceed the minimum time. This observation is true for N2 at 77 K as well as for subsequent isotherms collected on the volumetric equipment. (Full time data are provided in the Supporting Information.) For example, E required 62 h for GO (Ei at P/Po = 0.14), ∼20 h for the subsequent point (Eii at P/ Po = 0.17), and ∼14 h for the second step in the isotherm (Eiii at P/Po = 0.23). Points after Eiii generally took 1.1 h to meet the stability criteria, which is the minimum time expected (i.e., 11dt). Both maximum and average characteristic times in the active region, as defined above, are summarized in Table 1. An average characteristic time is reported as an initial indicator, where some subsequent data below suggest that each point has not reached equilibrium, despite meeting the stability criteria of the instrument. Such slow structural transition dynamics have also been reported for MIL-53(Al) at 77 K with large temperature hysteresis.35 Typically, the number of points collected in an isotherm affects the refinement of the features of the isotherm. For example, there are two pronounced adsorption steps in E that have the maximum number of points; the adsorption steps are less pronounced when fewer adsorption points are collected (i.e., four points for D). However, the overall adsorption uptake is significantly decreased when insufficient adsorption time is allowed. Sample C represents data collected at Rutgers University for a fresh preparation of the sample52 with an intermediate adsorption time (max ta was 3.7 h at Ci). The cumulative adsorption time may also affect the data, with a decreased number of points for D decreasing the uptake relative to E: specifically, at P/Po = 0.45, the uptake of D is 80% that of E, which exceeds the anticipated error bar. Thus, the total adsorped amount is governed by both the allowed time at any given point and the cumulative time that the sample is exposed to gas prior to that data point. Such behavior is consistent with uptake that is diffusion-limited and, more generally, with any model that purports to explain hysteresis. Despite this diffusion-limited uptake, the overall uptake of the material is consistent between the two laboratories, ranging from 90 to 96 cc(STP)/g, despite differences in time settings, laboratories, and sample history. However, the reduced adsorption branch for C suggests that the intermediate allowed time achieved at Rutgers led to incomplete adsorption, despite once again meeting the equipment stability criteria. Uptake is reduced by 20% of N2 at P/Po = 0.03 (C and E, Figure 2); decreasing pressure further leads to 59% desorption (C, P/Po ≈ 1.7  10
5). The desorption time for E typically varied from 1 to 5 h for P/Po > 0.03; at P/Po = 0.03, desorption stability required 13 h. Incomplete desorption for GO-MMOFs has been observed previously and attributed to both (1) large cavities relative to the window size, with both being on the order of the kinetic diameter of the diffusing species,3 and (2) the slow dynamics of the structural transitions.35 Increasing the N2 adsorption temperature to 87 K significantly decreased the relative PA compared to that of N2 adsorption at 77 K (from P/Po = 0.14 at 77 K to 0.06 at 87 K, Figure 3). The 87 K N2 adsorption isotherms were collected only to P/Po = 0.3
0.35 to maintain the total pressure within the limits of the equipment (i.e., ∼1 bar). With this partial isotherm, it is interesting that the isotherm continues to increase as the pressure is decreased for the desorption branch, demonstrating insufficient allowed time even though the stability criteria were met. This increase in uptake on the desorption branch was observed for two sequential tests of N2 at 87 K. At least three steps are observed in both 87 K adsorption isotherms. In general, the two sequential isotherms 14171

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Table 1. Summary of Allowed Time for Adsorption in the Active Regiona gas, T, dt N2, 77 K, 360 (E)

active region (P/Poand

cumulative time for

no. of points in

average ta in active

percentage of final uptake)b

active region (h)c

active region

region (h)

maximum ta (h)

110 (118)

10 (6)

11

62

57

19

3

19

48 (79)

17 (19)

3

26

0.2

1.7

P/Po = 0.14
0.34 50
85%

N2, 87 K, 90 (H)

P/Po = 0.01
0.12 17
87%

N2, 87 K, 90 (I)

P/Po = 0.01
0.14 17
87%

Ar, 87 K, 5 (F)

P/Po = 0.17
1.00 45
100%

2.6 (4.8)

17 (28)

Ar, 77 K, 360 (J)

P/Po = 0.1

15

1

15

60 cc/g a Full time data is available in the Supporting Information. b Region of the isotherm where the transition from a flat to S shape takes place. c Cumulative time taken for adsorption by the entire active region after the offsetting time for points that fall in the initial flat portion ( 104 > 5  103 > 103 > 500 > 100 s from top to bottom) on the average adsorption amount when the diffusion time constant is kc = 10
5/s. (b) Effect of decreasing the diffusion time constant (from 1 to 10
6/s) on the average adsorption amount when the time for equilibration is 100 s for each data point. kc (diffusion time constant) and t (time) are fit to the MPD model.39

at comparable temperature.65 This is borne out by molecular dynamics simulations of diffusion into rigid Zn(tbip), in which H2 diffusivity was 1 to 2 orders of magnitude higher than for CH4 at 298 K.66 These differences may be even more pronounced at low temperature. We explore the effect of slow diffusion on the adsorption isotherm, considering a hypothetical material that has true adsorption equilibrium that is borrowed from the experimental H2 data at 77 K for RPM3-Zn (i.e., 180 min data at 77 K from Figure 5 is taken as qo in eq 8 for this hypothetical case). For a constant diffusivity (kc = 10
5 s
1), the average adsorption at the conclusion of a given time interval (q), as calculated by eq 8, is significantly less than the equilibrium value for t j 104 s (Figure 7a). One can see the data start to converge to the true isotherm when kct f 1 (Figure 7a). The interplay between kc and t is similarly illustrated in Figure 7b: the true isotherm is reproduced when kct f 1 and is significantly underpredicted when kct , 1 One can see that a 2 orders of magnitude change leads to a quite pronounced decrease in the isotherm; a 6 orders of magnitude change in the diffusivity will lead to practically no adsorption if the equilibration time is maintained at a constant value. This analysis reproduces the effect of the equilibration time seen for H2 adsorption at 77 K. Implicit in eq 8 is the initial boundary condition, q0 o, which is influenced by incomplete equilibration at previous points. Thus, slow diffusion coefficients, which can be quite pronounced in porous materials, necessitate long times, and insufficient time would change the chemical potential driving force prior to equilibration and be manifest as adsorption
desorption hysteresis because the gaseous species may still be diffusing upon completion of each sorption step. Such behavior in and of itself may lead to adsorption
desorption hysteresis and features in which the desorption branch actually increases relative to the adsorption branch (as was seen here for N2 87 K isotherms). A similar trend was seen for hysteretic H2 adsorption to Co-MOF [Co(1,4benzenedipyrazolate)] at 65 K as presented by Choi et al.55 The above hypothetical analysis assumes a constant diffusivity over the course of the measurement. The situation becomes even more complicated if the diffusivity changes over the course of the experiment. It is not uncommon for configurational diffusion to exhibit a concentration dependence, as demonstrated both theoretically67,68 and experimentally.37,38,60,69 In small pores, a concentration dependence arises as a natural consequence of steric hindrance between diffusing species.70

In extreme cases, diffusion in molecular sieves may be single file or occur in clusters.71 As one example, methane diffusivity in Zn(tbip) at 298 K varied by 2.5 orders of magnitude.66 Concentration-dependent diffusion has been described by a correlative model (Darken’s equation)61 Dapp ¼ Dc

∂ ln P ∂ ln qo

ð11Þ

where Dapp is the effective diffusivity that takes into account any concentration dependence and Dc is the concentration-independent crystalline diffusion coefficient. Equation 11 indicates that the apparent diffusivity is likely due to increases at higher gas loadings. Increased diffusivity at high loading in zeolites has been attributed to (1) repulsive interactions between diffusing species decreasing the activation energy for diffusion and (2) multiple molecules per cage or adsorbent site increasing the rate of mass transfer.61 To consider the effect of concentration-dependent diffusion, we extend the hypothetical analysis above to a simplified concentration-dependent case in which diffusion occurs in two regimes: a slow regime (S) followed by a fast regime (F). We arbitrarily take the transition region to be 5 bar. The slow and fast regimes may also correspond to a GO event. Interestingly, the two-diffusion-regime hypothetical material leads to an S-shaped isotherm (Figure 8). The step in the isotherm becomes more pronounced as the ratio of the diffusion constants in the two regimes increases. To achieve a truly flat portion of the isotherm prior to the inflection point, low diffusion coefficients are needed (Figure 8a). Similarly, when we keep the ratio of diffusivities constant and vary the allowed time, the steplike behavior becomes even more pronounced when time is insufficient in the first regime and sufficient in the second regime (Figure 8b). In all cases, the inflection point of the isotherm, PA, remains consistent regardless of the allowed time (Figure 8b). We would anticipate, however, that it would be dependent upon the refinement of the number of points in the isotherm. As the parameter kc incorporates the square of the effective diffusion length L, the transition point would also be highly sensitive to L, either through variations in particle size or partial GO within the particle. The issue of mass-transfer limitations becomes exacerbated when a stability criterion based on the rate of change of the amount adsorbed is used to determine the allowed time. Most commercial volumetric measurements, including ours, move to 14176

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Figure 8. (a) Effect of different diffusion time constants on the average adsorption amount and shape of the isotherm when the time for equilibration is 100 s. The diffusion time constant is assumed to be different for the initial slow (S) and a later fast (F) regime when the diffusion regime changes at an inflection point of ∼5 bar. (b) Effect of decreasing the allowed time on the average adsorption amount and shape of the isotherm when the diffusion time constant for the slow regime (S) is 10
8/s and that for the fast regime (F) is 10
5/s. The order of decreasing time in seconds is A(106) > B(105) > C(104) > D(5  103) > E(103) > F(500) > G(100).

the next point when the first derivative of pressure is below a certain user-specified tolerance, ε. Assuming that adsorption follows the MPD model given above and noting that the pressure in a volumetric experiment is proportional to moles adsorbed, we write the first derivative of eq 8 as ∞ ∂ϑ ¼ 6kc expð
n2 π2 kc tÞ < E ∂t n¼1

∑

ð12Þ

where the inequality incorporates the user-defined stability criterion, ε. For realistic values of diffusion in pores, the kc prefactor dominates eq 12 and dϑ/dt is essentially a constant. Equation 12 illustrates that the stability criterion should be chosen to be on the order of kc. An additional hypothetical analysis in which kc(t) is included in the Supporting Information (Figure S3) explains why the stability criterion in the volumetric measurements were met in a short time at low pressures, in a long time at intermediate pressures, and in a short time at high pressures. The results of this hypothetical diffusion case suggest that the S-shaped isotherm seen by N2 and Ar can be explained fully by mass-transfer limitations. It is unclear at this time whether the S-shaped isotherm seen for N2 and Ar is due to GO in RPM3-Zn that occurs only above a particular pressure. Structural changes have in fact been observed with diffraction studies combined with in situ gas exposure for RPM3-Zn.52,72 The analysis does reiterate that the isotherm shape is not sufficient information to demonstrate a structural transition, where sigmoidal isotherms may also result from masstransfer limitations, even when the structure is rigid. Furthermore, a GO event would likely lead to a significant change in diffusivity. The hypothetical analysis presented here does show that models of the GO process need not assume the complete absence of adsorption prior to a particular PA. One might also anticipate a partial opening and two diffusion regimes operating simultaneously. The fraction of open pores is likely to be an insignificant parameter only if GO is rapid relative to diffusion, and in fact the opposite has been observed. Concentrationdependent diffusion provides an alternate view on the kinetic behavior for MOFs that have an S-shaped isotherm. This concept has been previously applied to diffusion in rigid zeolites, but GO seems either consistent with or an alternative to a GO

mechanism to describe the uptake in MOFs that exhibit an S-shaped isotherm.

’ SUMMARY AND CONCLUSIONS Zn2(bpdc)2(bpee), or RPM3-Zn, shows very large adsorption
desorption hysteresis at 77 and 87 K for the subcritical adsorption of N2 and Ar. The degree of hysteresis between adsorption and desorption as well as the inflection point in the S-shaped isotherm were heavily dependent on the allowed time at each data point and also on the cumulative gas exposure time. The hysteresis and isotherm shape are associated with mass-transfer limitations expected at these temperatures. Mass-transfer limitations at low temperature are not unique to this material and will be exacerbated at low temperature for materials with molecularly sized pores and when the equipment stability tolerance is set to be much larger than the mass-transfer coefficient. If any one of these factors is involved, then the reported experimental isotherm may significantly underpredict the true equilibrium. Here, to obtain a significant adsorption of N2 at 77 K, we had to make significant changes to our normal experimental procedure, and the observed capacity may still not be the true equilibrium. Given sufficient time, the rate data followed an Arrhenius-type behavior with temperature. For N2 and Ar, an insufficient allowed time at 77 K led to negligible adsorption and no S-shaped isotherm. Increasing temperature also led to enhanced uptake and an S shape for the Ar isotherm even with a short allowed time. Fitting the N2 and Ar characteristic times to an activated solid-vibrational configurational diffusion model indicated activation energies of 6.7 and 12 kJ/mol, respectively. For supercritical H2 adsorption up to 20 bars, discontinuities in the adsorption isotherm were not observed, despite a 50% increased capacity relative to N2 and Ar at equivalent temperatures. Mass-transfer limitations for H2 demonstrated themselves as increased capacity and the degree of hysteresis with increasing allowed time. Insufficient allowed time had an equivalent effect of increasing the temperature by 10 K. Fitting the H2 rate data to a micropore diffusion model led to an activation energy for diffusion of 2
7 kJ/mol at low to moderate coverage and ∼0 kJ/mol at high coverage. Interestingly, the H2 uptake exceeded that of N2 or Ar, despite the lack of a discontinuity in the adsorption isotherm, which has been previously associated with a GO effect. A hypothetical 14177

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Langmuir analysis showed that all of the collected adsorption data was consistent with diffusion-limited adsorption: the H2 isotherm was consistent with simple micropore diffusion coupled with insufficient allowed time; the S shape in the isotherm was consistent with concentration-dependent diffusion, with increased diffusivity at high coverages. Rate limitations become exacerbated when the experimental stability time was set on the basis of the first derivative of the adsorbed amount. Slow diffusion makes slow progress to equilibrium whereas a change in diffusivity over the course of the experiment can lead to long stability times. Although this has been stated in previous papers, this work reiterates that the S-shaped isotherm is insufficient evidence for a gas-induced structural transformation. Concentration-dependent diffusion is a useful lens through which to view the rates of uptake in MMOFs whether the structure is rigid or flexible, particularly if any adsorption-induced structural changes that occur do so at a finite rate. Regardless of the model used to describe uptake in materials, it is clear that a sufficient adsorption time is required to avoid mass-transfer limitations that affect the measured adsorption isotherm.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional experimental details. Raw data to illustrate the cumulative and differential times required for the N2, Ar, and H2 isotherms. Calculation of theoretical time ratios for Knudsen diffusion. Calculation of the activation energy and attempts to fit the characteristic time data to GT and SV configurational models. Generation of observed isotherms for the hypothetical material to consider the effect of the diffusion time constant and the allowed time using the micropore diffusion model. Generation of hypothetical observed uptake to consider the effect of the diffusion time constant and the time when diffusion occurs in two regimes—slow and fast— using the MPD model. Generation of hypothetical observed uptake for kc(t). Fits of H2 data to MPD and DE models. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: 814-876-0005.

’ ACKNOWLEDGMENT This work was supported by the U.S. Department of Energy, Energy Efficiency and Renewable Energy program, award DEFG36-08GO18139. We thank Qixiu Li for collecting the H2 isotherms, Chunshan Song for useful discussions regarding configurational diffusion, and Milton Cole for useful discussions regarding the adsorption isotherms in this article. ’ REFERENCES (1) Millward, A. R.; Yaghi, O. M. J. Am. Chem. Soc. 2005, 127, 17998. (2) Mulfort, K. L.; Hupp, J. T. J. Am. Chem. Soc. 2007, 129, 9604. (3) Zhao, X. B.; Xiao, B.; Fletcher, A. J.; Thomas, K. M.; Bradshaw, D.; Rosseinsky, M. J. Science 2004, 306, 1012. (4) Czaja, A. U.; Trukhan, N.; Muller, U. Chem. Soc. Rev. 2009, 38, 1284.

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(5) Li, J.-R.; Kuppler, R. J.; Zhou, H.-C. Chem. Soc. Rev. 2009, 38, 1477. (6) Murray, L. J.; Dinca, M.; Long, J. R. Chem. Soc. Rev. 2009, 38, 1294. (7) Yaghi, O. M.; Li, G. M.; Li, H. L. Nature 1995, 378, 703. (8) Matsuda, R.; Kitaura, R.; Kitagawa, S.; Kubota, Y.; Belosludov, R. V.; Kobayashi, T. C.; Sakamoto, H.; Chiba, T.; Takata, M.; Kawazoe, Y.; Mita, Y. Nature 2005, 436, 238. (9) Hamon, L.; Llewellyn, P. L.; Devic, T.; Ghoufi, A.; Clet, G.; Guillerm, V.; Pirngruber, G. D.; Maurin, G.; Serre, C.; Driver, G.; van Beek, W.; Jolimaitre, E.; Vimont, A.; Daturi, M.; Ferey, G. J. Am. Chem. Soc. 2009, 131, 17490. (10) Stavitski, E.; Pidko, E. A.; Couck, S.; Remy, T.; Hensen, E. J. M.; Weckhuysen, B. M.; Denayer, J.; Gascon, J.; Kapteijn, F. Langmuir 2011, 27, 3970. (11) Couck, S.; Denayer, J. F. M.; Baron, G. V.; Remy, T.; Gascon, J.; Kapteijn, F. J. Am. Chem. Soc. 2009, 131, 6326. (12) Hasegawa, S.; Horike, S.; Matsuda, R.; Furukawa, S.; Mochizuki, K.; Kinoshita, Y.; Kitagawa, S. J. Am. Chem. Soc. 2007, 129, 2607. (13) Seo, J. S.; Whang, D.; Lee, H.; Jun, S. I.; Oh, J.; Jeon, Y. J.; Kim, K. Nature 2000, 404, 982. (14) Lee, J.; Farha, O. K.; Roberts, J.; Scheidt, K. A.; Nguyen, S. T.; Hupp, J. T. Chem. Soc. Rev. 2009, 38, 1450. (15) Ma, L.; Abney, C.; Lin, W. Chem. Soc. Rev. 2009, 38, 1248. (16) Beauvais, L. G.; Shores, M. P.; Long, J. R. J. Am. Chem. Soc. 2000, 122, 2763. (17) Allendorf, M. D.; Bauer, C. A.; Bhakta, R. K.; Houk, R. J. T. Chem. Soc. Rev. 2009, 38, 1330. (18) Pramanik, S.; Zheng, C.; Zhang, X.; Emge, T. J.; Li, J. J. Am. Chem. Soc. 2011, 133, 4153. (19) Lan, A.; Li, K.; Wu, H.; Olson, D. H.; Emge, T. J.; Ki, W.; Hong, M.; Li, J. Angew. Chem., Int. Ed. 2009, 48, 2334. (20) Gatica, S. M.; Cole, M. W. Phys. Rev. E 2005, 72. (21) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders and Porous Solids: Principles, Methodology, and Applications; Academic Press: San Diego, 1999. (22) Walton, K. S.; Millward, A. R.; Dubbeldam, D.; Frost, H.; Low, J. J.; Yaghi, O. M.; Snurr, R. Q. J. Am. Chem. Soc. 2008, 130, 406. (23) Inagaki, M.; Tashiro, R.; Washino, Y.; Toyoda, M. J. Phys. Chem. Solids 2004, 65, 133. (24) Park, C.; Anderson, P. E.; Chambers, A.; Tan, C. D.; Hidalgo, R.; Rodriguez, N. M. J. Phys. Chem. B 1999, 103, 10572. (25) Kobayashi, N.; Enoki, T.; Ishii, C.; Kaneko, K.; Endo, M. J. Chem. Phys. 1998, 109, 1983. (26) Suzuki, T.; Takahiro, K.; Kaneko, K. Chem. Phys. Lett. 1992, 191, 569. (27) Dresselhaus, M. S.; Dresselhaus, G. Adv. Phys. 2002, 51, 1. (28) Hibbs, M. R.; Hickner, M. A.; Alam, T. M.; McIntyre, S. K.; Fujimoto, C. H.; Cornelius, C. J. Chem. Mater. 2008, 20, 2566. (29) Li, D.; Kaneko, K. Chem. Phys. Lett. 2001, 335, 50. (30) Kitaura, R.; Seki, K.; Akiyama, G.; Kitagawa, S. Angew. Chem., Int. Ed. 2003, 42, 428. (31) Culp, J. T.; Smith, M. R.; Bittner, E.; Bockrath, B. J. Am. Chem. Soc. 2008, 130, 12427. (32) Kondo, A.; Noguchi, H.; Ohnishi, S.; Kajiro, H.; Tohdoh, A.; Hattori, Y.; Xu, W. C.; Tanaka, H.; Kanoh, H.; Kaneko, K. Nano Lett. 2006, 6, 2581. (33) Ferey, G.; Latroche, M.; Serre, C.; Millange, F.; Loiseau, T.; Percheron-Guegan, A. Chem. Commun. 2003, 2976. (34) Serre, C.; Millange, F.; Thouvenot, C.; Nogues, M.; Marsolier, G.; Louer, D.; Ferey, G. J. Am. Chem. Soc. 2002, 124, 13519. (35) Liu, Y.; Her, J. H.; Dailly, A.; Ramirez-Cuesta, A. J.; Neumann, D. A.; Brown, C. M. J. Am. Chem. Soc. 2008, 130, 11813. (36) Tanaka, D.; Nakagawa, K.; Higuchi, M.; Horike, S.; Kubota, Y.; Kobayashi, L. C.; Takata, M.; Kitagawa, S. Angew. Chem., Int. Ed. 2008, 47, 3914. (37) Fletcher, A. J.; Cussen, E. J.; Bradshaw, D.; Rosseinsky, M. J.; Thomas, K. M. J. Am. Chem. Soc. 2004, 126, 9750. 14178

dx.doi.org/10.1021/la202842m |Langmuir 2011, 27, 14169–14179

Langmuir

ARTICLE

(38) Fletcher, A. J.; Cussen, E. J.; Prior, T. J.; Rosseinsky, M. J.; Kepert, C. J.; Thomas, K. M. J. Am. Chem. Soc. 2001, 123, 10001. (39) Bao, Z. B.; Yu, L. A.; Ren, Q. L.; Lu, X. Y.; Deng, S. G. J. Colloid Interface Sci. 2011, 353, 549. (40) Skoulidas, A. I. J. Am. Chem. Soc. 2004, 126, 1356. (41) Salles, F.; Jobic, H.; Maurin, G.; Koza, M. M.; Llewellyn, P. L.; Devic, T.; Serre, C.; Ferey, G. Phys. Rev. Lett. 2008, 100, 245901. (42) Jhon, Y. H.; Cho, M.; Jeon, H. R.; Park, I.; Chang, R.; Rowsell, J. L. C.; Kim, J. J. Phys. Chem. C 2007, 111, 16618. (43) Liu, J.; Lee, J. Y.; Pan, L.; Obermyer, R. T.; Simizu, S.; Zande, B.; Li, J.; Sankar, S. G.; Johnson, J. K. J. Phys. Chem. C 2008, 112, 2911. (44) Skoulidas, A. I.; Sholl, D. S. J. Phys. Chem. B 2005, 109, 15760. (45) Marsh, H.; Wynnejones, W. F. K. Carbon 1964, 1, 269. (46) Sweatman, M. B.; Quirke, N. Langmuir 2001, 17, 5011. (47) Dubbeldam, D.; Calero, S.; Maesen, T. L. M.; Smit, B. Phys. Rev. Lett. 2003, 90. (48) Karger, J.; Kortunov, P.; Vasenkov, S.; Heinke, L.; Shah, D. R.; Rakoczy, R. A.; Traa, Y.; Weitkamp, J. Angew. Chem., Int. Ed. 2006, 45, 7846. (49) Rittig, F.; Coe, C. G.; Zielinski, J. M. J. Phys. Chem. B 2003, 107, 4560. (50) Cao, D. V.; Mohr, R. J.; Rao, M. B.; Sircar, S. J. Phys. Chem. B 2000, 104, 10498. (51) Jobic, H.; Karger, J.; Bee, M. Phys. Rev. Lett. 1999, 82, 4260. (52) Lan, A. J.; Li, K. H.; Wu, H. H.; Kong, L. Z.; Nijem, N.; Olson, D. H.; Emge, T. J.; Chabal, Y. J.; Langreth, D. C.; Hong, M. C.; Li, J. Inorg. Chem. 2009, 48, 7165. (53) See the Supporting Information (54) Jain, P.; Fonseca, D. A.; Schaible, E.; Lueking, A. D. J. Phys. Chem. C 2007, 111, 1788. (55) Choi, H. J.; Dinca, M.; Long, J. R. J. Am. Chem. Soc. 2008, 130, 7848. (56) Park, H. J.; Suh, M. P. Chem. Commun. 2010, 46, 610. (57) Quinn, D. F. Carbon 2002, 40, 2767. (58) Noguchi, H.; Kondoh, A.; Hattori, Y.; Kanoh, H.; Kajiro, H.; Kaneko, K. J. Phys. Chem. B 2005, 109, 13851. (59) The critical point is related directly to the well depth of the interparticle interaction (∼1.33 times the well depth). In turn, the gas
surface well depth is often related to the intermolecular potential and the characteristic energy of the solid (i.e., eab = (ea  eb)1/2) as a general rule of thumb. Assuming the characteristic energy of the solid can be treated as a constant, the trend in PA at a temperature equal to the critical temperature would suggest that the data correlates with either the gas
gas or gas
surface potential. (60) Fletcher, A. J.; Thomas, K. M. Langmuir 2000, 16, 6253. (61) Xiao, J. R.; Wei, J. Chem. Eng. Sci. 1992, 47, 1123. (62) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH: New York, 1994. (63) Yang, Q.; Zhong, C. J. Phys. Chem. B 2005, 109, 11862. (64) Sircar, S. Ind. Eng. Chem. Res. 2006, 45, 5435. (65) Vidali, G.; Ihm, G.; Kim, H. Y.; Cole, M. W. Surf. Sci. Rep. 1991, 12, 133. (66) Liu, J.; Lee, J. Y.; Pan, L.; Obermyer, R. T.; Simizu, S.; Zande, B.; Sankar, S. G.; Li, J.; Johnson, J. K. Mol. Simul. 2011, 37, 640. (67) Skoulidas, A. I.; Sholl, D. S. AIChE J. 2005, 51, 867. (68) Liu, J. C.; Lee, J. Y.; Pan, L.; Obermyer, R. T.; Simizu, S.; Zande, B.; Sankar, S. G.; Li, J.; Johnson, J. K. Mol. Simul. 2011, 37, 640. (69) Sircar, S.; Wu, H.; Li, J.; Lueking, A. D. Langmuir 2011accepted for publication. (70) Sholl, D. S.; Skoulidas, A. I. J. Phys. Chem. B 2005, 109, 15760. (71) Sholl, D. S.; Fichthorn, K. A. Phys. Rev. Lett. 1997, 79, 3569. (72) Wu, H.; Reali, R. S.; Smith, D. A.; Trachtenberg, M. C.; Li, J. Chem.—Eur. J. 2010, 16, 13951.

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