Diffusion of CO 2 in large crystals of Cu-BTC MOF

Transcription

1 Supporting Information Diffusion of CO 2 in large crystals of Cu-BTC MOF Trenton M. Tovar, 1 Junjie Zhao, 2 William T. Nunn, 2 Heather F. Barton, 2 Gregory W. Peterson, 3 Gregory N. Parsons, *2 and M. Douglas LeVan *1 1 Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, Tennessee Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina Edgewood Chemical Biological Center, U.S. Army, Aberdeen Proving Ground, Maryland S1

2 Experimental Methods Materials. Commercial adsorbents used in this study were Cu-BTC powder purchased from Sigma Aldrich and BPL activated carbon (lot no ) in 6x16 mesh form obtained from Calgon Carbon Corp. Research grade helium, pure CO 2, and 1% CO 2 in He were purchased from Air Liquide. Cu-BTC Single Crystal Synthesis. A low temperature solvothermal method was used to synthesize large Cu-BTC single crystals g copper nitrate trihydrate (Cu(NO 3 ) 2 3H 2 O) was dissolved in 3 ml of deionized water g benzene-1,3,5-tricarboxylic acid (H 3 BTC) was dissolved in 3 ml of ethanol (slight heating was needed to fully dissolve this organic linker). The Cu(NO 3 ) 2 solution was first mixed with 3 ml of N,N-dimethylformamide (DMF) in a 20 ml scintillation vial. The H 3 BTC solution and 12 ml of glacial acetic acid (modulator) were subsequently added to the mixed solution as well. The scintillation vial was then placed in a furnace where the reaction was allowed to proceed at 55 C for 3 days. After the solvothermal synthesis, only the Cu-BTC crystals that nucleated and grew on the glass wall of the vial were collected by hand, since the MOF particles at the bottom of the vial tend to aggregate and may have defects due to the precipitate homogenously nucleated in the solution. All the crystals were soaked in ethanol for at least 3 days for solvent exchange and dried in vacuum at 120 C overnight before CO 2 adsorption measurements. Crystal Characterization. Cu-BTC single crystals were imaged using an Olympus BX60 optical microscope equipped with a ProgRes C5 camera. Optical microscopic images were captured and analyzed with ProgRes CapturePro software. SEM images of Cu-BTC crystals were obtained with an FEI Phenom bench-top SEM. Crystals were mounted on conductive carbon taps and sputter-coated with 5-10 nm of Au-Pd before imaging. X-ray diffraction patterns of the Cu-BTC single crystals and powders were collected using a PANalytical Empyrean X-ray diffractometer. The unit cell of our Cu-BTC single crystals was also determined by single crystal X-ray diffraction at 210 K using Bruker-Nonius X8 Kappa APEXII diffractometer. The unit cell dimension was refined by least squares method against 750 reflections covering a range out to 58 degrees (2θ). BET surface area of Cu-BTC single crystals and powders was measured using a Quantachrome Autosorb-1C surface area and pore size analyzer. 10 mg of Cu-BTC was vacuum dried at room temperature for h before the measurement of a N 2 adsorption isotherm. BET surface area was calculated based on the isotherm within the P/P o range of Thermogravimetric analysis (TGA) was measured with a Discovery TGA from TA Instruments. Pure CO 2 isotherms were measured using a Rubotherm gravimetric analyzer. A sample was degassed at 25 C for approximately 12 hours using a turbo molecular pump until no weight change was detected. The sample was then dosed with CO 2 at a specified pressure and allowed to equilibrate until no more weight change was S2

3 detected. After equilibration, the CO 2 pressure was increased to the next specified value. This process was repeated for the pressure range of the isotherm, from 0.5 to 800 mmhg. The CO 2 loading was calculated by the weight gain of the sample at each pressure step. Diffusion Measurement. CO 2 diffusion was measured using a concentration-swing frequency response apparatus (figure S1). The apparatus consists of two MKS mass flow controllers; one for the adsorbate feed and one for a pure helium stream. The two streams combine in a zero-volume tee and enter a small mixing region made of a 3 cm length of 1/16 tubing that feeds a shallow adsorption bed. A shallow bed is used to prevent bed effects such as axial dispersion and consists of a 2 cm length of ¼ tubing with an inner diameter of 4 mm. The resulting bed volume is approximately 0.25 cm 3. After the sample is loaded, the remainder of the bed is filled with 2 mm diameter glass beads to further reduce void space in the bed. The small volume of the system is important in order to maintain low residence times which helps avoid artificial dampening of the amplitude ratio at faster frequencies. The small bed and flow through experiment also help to reduce the impact of heat of adsorption effects. The pressure in the adsorbent bed was controlled at 1 bar by a MKS Baratron pressure controller, and effluent gas from the adsorbent bed was sampled by an Agilent 5975 mass spectrometer. For sample preparation, approximately mg of adsorbent was regenerated for 8 hours under vacuum (at 25 C for Cu-BTC crystals, at 250 C for BPL activated carbon) for accurate weight measurement. The sample was then loaded into the adsorption bed and placed under vacuum at room temperature with a 1 sccm He flow through the bed for 16 hours. Next, a CO 2 stream was mixed with the pure He stream and the ratio of the two flow rates determined the gas-phase concentration. All experiments were performed with a flowrate of 20 sccm. For gas-phase concentrations of 0.1% and 0.5%, a specialty 1% CO 2 /He tank was used with flowrates of 2 sccm or 10 sccm for the adsorbate stream and either 18 sccm or 10 sccm for the pure helium stream. For the 10% CO 2 gas phase concentration experiments, a pure CO 2 tank is used for the adsorbate feed with a flowrate of 2 sccm and helium flow of 18 sccm. To run an experiment, the system was allowed to reach steady-state as determined by a constant signal from the mass spectrometer. Then the mass flow controllers were used to introduce sinusoidal perturbations to the flowrates of each stream but 180 degrees out of phase. This resulted in a feed stream to the adsorbent bed that has a constant flow rate with a sinusoidal concentration swing around the desired steady-state gas-phase concentration. To maintain linearity in the system, the perturbations were small with the swing in the flowrates being ±10% of the adsorbate feed; ie. for experiments with a 2 sccm CO 2 feed, the amplitude of the swing is 0.4 sccm from a low of 1.8 sccm to a high of 2.2 sccm. The perturbations were performed at different frequencies in the range of to 0.1 Hz. The collected data are presented as plots of the amplitude ratio (AR) as a function of the perturbation frequency, where the AR is calculated from the amplitude of the concentration swing of the gas exiting the adsorbent bed divided by the S3

4 amplitude of the gas entering the adsorbent bed. The diffusion mechanism and rate parameters can be extracted by fitting the data to a mathematical model derived from transfer functions. Detailed mathematical models for a CSFR apparatus have been described elsewhere. 1,2 Figure S1. Schematic of the concentration-swing frequency response apparatus. S4

5 Figure S2. Optical microscopic images of Cu-BTC crystals obtained from a three-day solvothermal synthesis. The crystal size ranges from 500 µm to 1.3 mm. (Crystal size measurements are labelled on the images.) Scale bars represent 400 µm. S5

6 (200) (400) Cu-BTC Single Crystal (600) Intensity (a.u.) (800) (111) (222) (333) (444) (555) Cu-BTC Single Crystal (666) Simulated Cu-BTC Diffraction Pattern θ (degree) Figure S3. XRD patterns of a Cu-BTC single crystal for the planes parallel to (100) (black) and the planes parallel to (111) (red), and simulated diffraction pattern for Cu-BTC (blue). The fact that only peaks associated with targeted parallel crystal planes appear in the diffraction patterns and that optical micrographs show negligible defects confirm the formation of high-quality single crystals. S6

7 Figure S4. (a) N 2 isotherms for Cu-BTC single crystals and fine powder. (b) BET surface area and (c) pore volume calculated from N 2 isotherms. The surface area is 1980 and 1825 m 2 /g for the single crystals and the fine powder respectively. Pore volumes are 0.85 and 0.79 cm 3 /g for the large crystals and powder samples respectively. S7

8 Figure S5. Thermogravimetric analysis (TGA) for Cu-BTC single crystals (red) and fine powder (black). Cu-BTC powder shows a steeper initial mass drop compared to the large crystals due to the shorter diffusion length in small particles for solvent evaporation. We also noticed that the mm-scale crystal exhibits a sharper mass decrease than the fine powder in the decomposition regime ( o C), possibly because of slower heat transfer and less impurities in the large crystals. S8

9 Figure S6. The correlation between the mass per crystal and the crystal dimension. The error bar indicates the standard deviation of the crystal sizes in a mass measurement group. S9

10 Figure S7. Increase of Cu-BTC crystal size as a function of reaction time. The red curve is fit by a Gompertz function described below. Crystal Growth Mechanism The crystal size was measured after specific growth times (1-5 d), and Figure S7 shows that the size of the largest crystal increases as a function of synthesis time. A nucleation delay period was observed in the first day of growth, and the crystal size quickly ramps up to ~1.3 mm at 3 days. After 3 days, the change in crystal size is very small, indicating the termination of crystal growth. We used a Gompertz function (Equation S1), a common mathematical model to describe such growth behavior, and the data fit well to the model. Taking the mass-size correlation into account (Figure S6 and Equation S2), this growth function can be converted into a plot similar to the classic La Mer diagram (Figure S8). 3 At the beginning of the synthesis, secondary building units (SBUs) of Cu-BTC MOF start to form in the solution. As the reaction proceeds and the SBU concentration reaches supersaturation (after ~1 d), heterogeneous nucleation occurs on the wall of the scintillation vial as it is more thermodynamically favorable. The crystal growth rate depends on the SBU concentration and stops once the concentration drops below the supersaturation point (after ~4 d). S10

11 We used Gompertz function for fitting the growth curve in Figure S7: exp exp Equation S1 Where L (mm) is the size of the large crystal obtained from particular reaction time, (mm) is the pre-exponential factor, k (d -1 ) is the kinetic factor, t and t c (in units of d) are the growth time and transition time (for fitting purpose), respectively. After fitting the data to the Gompertz function, we get 1.34 mm, t c = 1.78 d, k = 2.18 d -1. Figure S4 shows the correlation between the mass and crystal dimension. We used a power law to fit the data: Equation S2 Where m (mg) is the mass per crystal, L (mm) is the size of the large crystal (crystal dimension), is power, is the density factor. After fitting, we get n = 2.14, The reaction kinetics can be derived by substituting L in Eqn S2 with Eqn 1 and taking a derivative of Eqn S2: exp exp exp Equation S3 Figure S8. (a) Crystal mass increase rate (dm/dt) as a function of reaction time based on Eqnation S3. (b) La Mer diagram adapted from Ref. 3. When the concentration of SBU exceeds the supersaturated point (C s ), heterogeneous nucleation can happen. S11

12 Figure S9. (a) Pore size distribution of BPL carbon. (b) CO 2 CSFR curves on BPL activated carbon at varying concentrations. BPL Activated Carbon BPL activated carbon is a bituminous coal-based carbon that is steam activated. The coal is pulverized and reagglomerated using a petroleum pitch binder. The carbon is then activated which creates a predominantly microporous structure with some mesopores. 4 The pore size distribution in Figure S9 shows that the vast majority of pores are between 5-25 Å. A previous study on the diffusion of hydrocarbons in BPL found that the diffusion is micropore controlled. 5 The intersecting curves in the CSFR plot is a clear indicator that the regressed D s /R 2 values change significantly, as is seen by Table 2 in the paper. If macropore diffusion was the controlling resistance, the diffusivity should not change much as gas-phase concentration changes because the diffusion is governed more by collisions of molecules rather than by interaction with the surface. Therefore, the diffusivity should be comparable to bulk diffusion of CO 2 in helium and is pressure independent. Since the measured D s /R 2 values vary significantly, the only way to calculate a similar diffusivity at each concentration is if the diffusion length varies. Since the same sample was used for measurements at each concentration, the diffusion length does not change and macropore diffusion does not make sense as the controlling mechanism. The only explanation for the changing D s /R 2 is that interactions between the adsorbate and surface change with concentration and impact the diffusivity. The concentration dependence of surface diffusivity (ie. micropore diffusion) has been well studied. 6 S12

13 Adsorption Isotherms To ensure that CO 2 adsorption in the single crystals is similar to Cu-BTC powder, a CO 2 isotherm was measured and compared with literature values. Figure 2 shows the CO 2 isotherm measured at 25 C on Cu-BTC crystals of various sizes. The isotherm fits well to a Toth model given by 7 = n bp [ 1+ ( bp) ] Equation S4 s n t 1/ t where n is the loading, P is the pressure, n s is the saturation loading, b describes the adsorption affinity, and t is a measure of the adsorbent heterogeneity. The fitted parameters n s, b, and t are 10.5 mol/kg, mmhg -1, and 0.95 respectively. Figure S10 also shows some of the representative CO 2 isotherms reported in the literature. We plotted these curves based on parameters for a Sips fit from Aprea et al. 8 and a Langmuir fit from Hamon et al. 9 Select data points at 1 bar were also adapted from Yazaydin et al., 10 Millward and Yaghi, 11 and Wang et al. 12 While most isotherms in the literature were measured at high pressure, due to the large capacity of Cu-BTC, CO 2 isotherms at low pressures are important for comparison to diffusion measurements at low CO 2 concentrations. It is clear that the isotherm for the large Cu-BTC single crystals compares favorably with the MOF powder at low CO 2 pressure where the diffusion measurements take place. 5 Loading (mol/kg) Cu-BTC crystals Aprea 8 Hamon 9 Yazaydin 10 Milward 11 Wang Figure S10. Gravimetric CO 2 isotherm on large Cu-BTC single crystals at 298 K fit by a Toth isotherm model (red curve). Also shown are data points from literature isotherms of CO 2 on powder Cu-BTC at 298 K. 600 Pressure (mmhg) S13

14 Amplitude Ratio Frequency (Hz) Figure S11. Error analysis plot for a 0.5% CO 2 CSFR experiment on 0.7 mm Cu-BTC crystals. Error bars show a 95% confidence interval based on repeated cycles at each frequency. The three fits show the line of best fit (solid), a fit through the upper confidence limit (dashed), and a fit through the lower confidence limit (dotted) CSFR Reproducibility Frequency response experiments are highly repeatable. This is mainly due to elimination of human error as the data are taken based on a cycling frequency that is set rather than an initial start time that the user must record. For higher frequency data points the relative error is usually less than 1%, although slower frequency data can have higher errors up to 5%. The reason for this is two-fold, more data can reasonably be collected at faster frequencies which results in smaller confidence limits based purely on sample size. Experimentally, the apparatus was not in a temperature controlled environment and it is possible that temperature fluctuations in the room on the same time scale as the slower oscillations can impact the adsorption cycles. Figure S11 shows amplitude ratio data with error bars representing 95% confidence intervals based on a minimum of 5 cycles at each frequency. Three curves were independently fit through the average, upper confidence limit, and lower confidence limit. The regressed D s /R 2 values were , , and respectively. This is typical of CSFR data and gives a relative error in the D s /R 2 of approximately 10% for each individual data set. While the CSFR experiments using the same exact sample give very low error, more uncertainty is added when different samples are compared. Due to the non-spherical shape of the Cu-BTC crystals, a correlation had to be used in order to calculate an effective diffusion radius. From the main paper, R eff is defined by S14

15 R 1/ 3 3 1/ 3 x / 3 eff = α L meas 4ρπ Equation S6 where ρ is the crystal density, L meas is the longest measured dimension of the crystal, and α and x are the power law mass correlation parameters from Figure S6. Uncertainties in α, L meas, and x propagate through the calculation of the effective diffusion length which is ultimately used to get the micropore diffusivity. The uncertainty in R eff is given by 2 2 Reff Reff Reff δ R + + eff = δα δlmeas δx Equation S7 α Lmeas x = c 1 L 3 x / 3 meas α 2 3 δα 2 1 x 3 + α L 3 x 1 3 meas δl meas α L 3 x / 3 meas ln ( L ) where c is the constant term in equation S6, α is 0.52, δα is 0.015, x is 2.14, δx is 0.17, L meas depends on the sample and is either 0.7, 1, or 1.3, and δl meas is 0.1. The effective diffusion radius is given for each set of crystal sizes along with the uncertainty in Table S1. Table S1. Effective diffusion length and uncertainty for different crystal sizes. Crystal Size Reff δreff (mm) (mm) (mm) meas 2 S15

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