Relationship between Diffusion and Chemical Exchange in Mixtures of

May 5, 2014 - The Center for Research Computing, University of Notre Dame, Notre Dame, Indiana 46556, United States. •S Supporting Information...
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Relationship between Diffusion and Chemical Exchange in Mixtures of Carbon Dioxide and an Amine-Functionalized Ionic Liquid by High Field NMR and Kinetic Monte Carlo Simulations Eric D. Hazelbaker,† Samir Budhathoki,‡ Han Wang,† Jindal Shah,‡,§ Edward J. Maginn,*,‡ and Sergey Vasenkov*,† †

Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States § The Center for Research Computing, University of Notre Dame, Notre Dame, Indiana 46556, United States ‡

S Supporting Information *

ABSTRACT: NMR exchange spectroscopy (EXSY) and NMR diffusion spectroscopy (PFG NMR) were applied in combination with kinetic Monte Carlo (MC) simulations to investigate self-diffusion in a mixture of carbon dioxide and an amine-functionalized ionic liquid under conditions of an exchange of carbon dioxide molecules between the reacted and unreacted states in the mixture. EXSY studies enabled residence times of carbon dioxide molecules to be obtained in the two states, whereas PFG NMR revealed time-dependent effective diffusivities for diffusion times comparable with and larger than the residence times. Analytical treatment of the PFG NMR attenuation curves as well as fitting of the PFG NMR effective diffusivities by KMC simulations enabled determination of diffusivities of carbon dioxide in the reacted and unreacted states. In contrast to carbon dioxide, the ion diffusivities were found to be diffusion time independent. SECTION: Liquids; Chemical and Dynamical Processes in Solution

D

The main focus is given to the relationship between CO2 diffusion and the process of CO2 exchange between the chemically bound, viz. reacted, and unreacted states in the mixture of CO2 and the TSIL. The experimental data are compared with the predictions of kinetic Monte Carlo (MC) simulations. The TSIL chosen for these studies is composed of the cation (2-aminoethyl)trimethylammonium or [(CH3)3N(CH2)2NH2]+ paired with a bis(trifluoromethyl)sulfonylamide or [(CF3SO2)2N]− anion. The expected stoichiometric reaction of CO2 with this TSIL is given by the following equation based on the proposed CO2 reaction mechanism for amine-functionalized TSILs

evelopment of highly efficient absorbents for the removal of CO2 from postcombustion flue gas, precombustion syngas, and natural gas has become an increasingly urgent task. Although processes based on CO2 capture by aqueous amine solutions currently find applications in natural gas sweetening, it has been realized that replacement of these solvents by other types of liquid absorbents that are more stable and require less energy for CO2 desorption would be extremely desirable. In addition, amine solvents are volatile and their use leads to undesirable fugitive emissions unless additional processing steps are taken. Ionic liquids, molten salts that are liquid at temperatures around room temperature, represent a promising class of absorbents for replacing traditional aqueous amine solvents. They can be tailored to exhibit a number of useful properties, including negligible vapor pressure and high thermal stability.1 It has been demonstrated that chemical modification of an ionic liquid by covalent tethering of an amine group to the cation results in a highly selective and reversible capture of CO2.2−5 A number of research articles have also been published reviewing the CO2 capture by functionalization of ionic liquids.6−8 One potential obstacle for using task-specific ionic liquids (TSIL) in which cation is functionalized with an amine group as CO2 absorbents is related to the observation that the TSIL viscosity increases significantly upon CO2 absorption,2 which can lead to transport limitations in the process of CO2 absorption. This Letter reports the first experimental studies of the microscopic diffusion properties of a mixture of CO2 and an amine-functionalized TSIL as well as those of the pure TSIL. © 2014 American Chemical Society

2(CH3)3 N(CH 2)2 NH 2+ + 2(CF3SO2 )2 N− + CO2 → (CH3)3 N+(CH 2)2 NH3+ + (CH3)3 N+(CH 2)2 NHCOO− + 2(CF3SO2 )2 N−

(1)

where the first and second product species are dication and zwitterion, respectively. In all cases, the CO2 concentration in the studied mixture was 0.06 CO2 molecules per anion−cation pair. Figure 1 shows examples of the 13C NMR spectra obtained by a one pulse sequence for [(CH3) 3N(CH2)2NH2]+Received: March 31, 2014 Accepted: May 5, 2014 Published: May 5, 2014 1766

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(selective π/2) − π/2 − τmix − π/2 − Acquisition13,14 with a selective excitation pulse (Selno of 1.5 ms width at 14 dB) was used. As discussed previously in refs 13−15, 1D EXSY can be a simpler and more efficient method for obtaining the exchange constants in comparison with a more traditional two-dimensional EXSY.16 1D EXSY measurements reported in this Letter can be viewed as relaxation-type experiments where the selective π/2 pulse was applied for the on-resonance spins of unreacted carbon dioxide and the NMR signals of both reacted and unreacted CO2 were monitored as a function of the mixing time τmix. To separate the effects of longitudinal T1 relaxation from the effects of chemical exchange during mixing time the standard inversion recovery measurements were also performed. Figure 2 shows the results of 1D EXSY and onedimensional inversion recovery (1D IR) measurements. It is important to note that the 1D EXSY data in Figure 2 are not corrected for the effect of the T1 NMR relaxation. The results in Figure 2 indicate that although the normalized signals measured by the 1D EXSY sequence experience an order of magnitude change when the mixing time is increased from around 0.0001 to 0.03 s, the corresponding normalized signals measured by the 1D IR sequence remain essentially unchanged for the same mixing time range. Hence, it can be concluded that the chemical exchange revealed by the 1D EXSY experiment occurs on a much shorter time scale than the T1 relaxation. This result allows a simplified analysis of the exchange data. In particular, the mean residence time of CO2 in the unreacted state can be estimated from the initial slope of the decay of the signal at 125 ppm shown in Figure 2b using17

Figure 1. NMR spectra of the pure ionic liquid [(CH3)3N(CH2)2NH2]+[CF3SO2)2N]− (a) and that containing 0.06 13CO2 molecules per anion−cation pair (b). The spectra were recorded by a 13C NMR one-pulse sequence. The chemical shifts are referenced to a doped dioxane in benzene standard.

[(CF3SO2)2N]− and a mixture of [(CH3)3N(CH2)2NH2]+[(CF3SO2)2N]− with CO2. In the [(CH3)3N(CH2)2NH2]+[(CF3SO2)2N]− spectrum (Figure 1a) the quartet centered at around 120 ppm originates from the anion, with the rest of the lines originating from the cation. It is seen that in comparison to this spectrum, the spectrum of the mixture in Figure 1b has two additional lines at around 161 and 125 ppm. The chemical shift of the former line corresponds to the known chemical shift of the carbamate group (HN13C(O)O−).9,10 Hence, this line can be assigned to the reacted CO2. The line at around 125 ppm originates from the unreacted CO2. Following this assignment, the lines at around 161 and 125 ppm were used to study diffusion and chemical exchange of CO2. The strongest anion lines at 119 and 120 ppm were used for determining the anion diffusivity. The cation diffusivity was obtained using the strongest overlapping cation lines at around 53 ppm. Hence, application of 13C PFG NMR allows obtaining diffusivities of all diffusing species using a single technique.11,12 In all cases, the reported diffusivities were calculated using the PFG NMR attenuation curves averaged over 3−5 repetitions of the same measurement. 13 C NMR exchange experiments (EXSY) were performed to investigate an exchange of CO2 between the reacted and unreacted states. One-dimensional (1D) EXSY sequence

Iunreacted(τmix ) = Iunreacted(0)exp( −τmix /tunreacted)

(2)

where Iunreacted is the intensity of the normalized signal at 125 ppm and tunreacted is the mean residence time in the unreacted state. This equation is expected to hold under the condition when during τmix the unreacted-to-reacted-state transitions that are followed by the transitions back to the unreacted state can be neglected.17 In particular, for Iunreacted(τmix)/Iunreacted(0) ≤ 0.5, this condition is expected to be satisfied because the equilibrium population of the reacted state is around 8.7 times larger than that of the unreacted state, as revealed by the ratio of the areas under the CO2 lines at 125 and 156 ppm in Figure 1b. In this case, the fraction of the CO2 molecules in the reacted state that experienced a transition from the unreacted

Figure 2. (a) Results of 13C NMR selective 1D EXSY experiments where the selective π/2 pulse was applied for the on-resonance spins of the unreacted carbon dioxide at 125 ppm. Also shown for comparison are the corresponding data obtained by a standard one-dimensional inversion recovery (1D IR) pulse sequence. (b) The same data for the line of the unreacted carbon dioxide at 125 ppm as in (a) shown for a smaller range of mixing times. Solid line shows the best fit of the exchange data for Iunreacted(τmix)/Iunreacted(0) ≤ 0.5 to eq 2. 1767

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state during τmix cannot significantly exceed 0.5 × (1/9.7) < 0.1, where 1/9.7 is the fraction of the CO2 molecules that were in the unreacted state at τmix = 0. Hence, the contribution of these molecules to the reacted-to-unreacted state transition can be neglected. Best fit of the 1D EXSY decay curve in Figure 2B to eq 2 for Iunreacted(τmix)/Iunreacted(0) ≤ 0.5 yields tunreacted = 8.8 ± 0.9 ms. The mean residence time in the reacted state (treacted) can be estimated by taking into account that for a two-state exchange the ratio of the equilibrium populations of molecules in the two states is equal to the corresponding ratio of the mean residence times. Using this consideration and noting that under our experimental conditions the ratio of the equilibrium populations of CO2 molecules in the reacted and unreacted states is around 8.7 we obtain for the mean residence time in the reacted state the value of 77 ± 8 ms. 13 C PFG NMR diffusion measurements for the ions and CO2 were performed using the standard stimulated echo PFG NMR sequence π/2 − τ1 − π/2 − τ2 − π/2 − τ1 − Acquisition where the magnetic field gradients were applied during the time intervals τ1. When performing diffusion measurements under the conditions of chemical exchange special care must be taken when choosing the duration of the time interval τ1 of the stimulated echo PFG NMR sequence. The choice of this time interval is important because the contribution of the CO2 molecules, which were in different chemical environments during the first and second time interval τ1 of the sequence, to the measured signal is expected to be proportional to cos(Δωτ1), where Δω is the difference between the precession frequencies in the reacted and unreacted states.18 Under our experimental conditions, the existence of such dependence was confirmed by performing measurements with the PFG NMR stimulated echo sequence at a fixed, small gradient strength. The measurements were carried out with different values of τ1 chosen such that the probed range of the values of Δωτ1 covered around 3π for each diffusion time used. The PFG NMR diffusion data reported in this Letter were obtained under conditions when cos(Δωτ1) = 1. This corresponds to the situation when the spins that were in different chemical environments during the first and second time interval τ1 of the sequence fully contribute to the measured signal. The measurements were carried out for the effective diffusion times comparable with and much larger than the values of the mean residence times of CO2 molecules in the unreacted and reacted states (tunreacted and treacted). Even when using large gradient amplitudes up to 30 T/m, it was not technically possible to perform 13C PFG NMR studies for diffusion times smaller than tunreacted. Figure 3 shows examples of the measured PFG NMR attenuation curves, viz. dependences of the normalized PFG NMR signal M(g)/M(g = 0) on the gradient amplitude g, for the ion lines discussed above as well as for the CO2 lines at 156 and 125 ppm. Due to signal-to-noise limitations in the PFG NMR measurements the maximum signal attenuation by diffusion did not exceed around 70% of the total signal at zero or small gradient strength. It is seen in Figure 3 that the measured attenuation curves do not show any significant deviations from the monoexponential behavior expected for normal diffusion with a single diffusivity D19,20 Ψ=

M (g ) = exp( −Dq2t ) M(g = 0)

Figure 3. Examples of the 13C PFG NMR attenuation curves measured for the cation, anion, and CO2, in the mixture of [(CH3)3N(CH2)2NH2]+[(CF3SO2)2N]− with CO2 for diffusion time t = 40 ms at 297 K. The attenuation curves for reacted and unreacted CO2 are those measured for the CO2 lines at 161 and 125 ppm, respectively. Solid lines show the best fit using eq 3. Dotted lines show the best fit data obtained from fitting all measured PFG NMR attenuation curves for the CO2 lines at 161 and 125 ppm using Supporting Information eqs S1 and S2.

In eq 3 Ψ is the PFG NMR signal attenuation, t is the diffusion time defined in refs 19 and 20, q = γgδ, where γ is the gyromagnetic ratio and δ denotes the effective duration of a field gradient pulse. The monoexponential behavior in agreement with eq 3 was also observed for all other diffusion times used in this study. The analytical formulas for PFG NMR attenuation curves in the case of diffusion under conditions of chemical exchange are presented in refs 21 and 22 and also shown in Supporting Information (eqs S1 and S2). The values of the initial magnetizations in these equations were modified to take into account T2 NMR relaxation of CO2 molecules in the reacted state with T2 = 1.4 ms and in the unreacted state with T2 = 3.9 ms during the first τ1 interval of the PFG NMR sequence. The T2 times were measured using the standard Carr−Purcell− Meiboom−Gill (CPMG) sequence. It was observed that in agreement with Supporting Information eqs S1 and S2 the effective diffusivities given by the initial slopes of the measured attenuation curves for the CO2 lines at 125 and 156 ppm are different at short diffusion times and approach the same diffusivity with increasing diffusion time (Figure 4). Figure 4 shows that for the largest diffusion time of 1.2 s both diffusivities are the same within the experimental uncertainty, indicating that the condition of fast exchange of CO2 molecules between the reacted and unreacted states is reached for this diffusion time. However, the apparent diffusivity associated with the unreacted CO2 is larger than that associated with the reacted CO2 for the diffusion time of 0.64 s (Figure 4), which is more than a factor of 8 larger than the mean residence time in the reacted state. This factor appears to be sufficiently large to ensure the conditions of fast exchange, which should result in no or little difference between the two diffusivities. In our opinion, the apparent diffusivity of the unreacted CO2 can be larger than what is expected under the fast exchange conditions because of the influence of T2 NMR relaxation. The T2 NMR relaxation time of the reacted CO2 is shorter than that of the unreacted CO2. As a result, T2 NMR relaxation would

(3) 1768

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kinetic MC simulations resulted in the CO2 diffusivity values which were found to be in satisfactory agreement with the results of analytical treatment using Supporting Information eqs S1 and S2 (Table 1). The KMC simulations were based on the reaction mechanism depicted in eq 1. The fact that the results from the KMC simulations agree remarkably well with those obtained experimentally suggests that the proposed reaction mechanism is likely to be operative in the TSIL examined in this work. Figure 4 and Table 1 show the cation and anion diffusivities obtained from fitting the measured PFG NMR attenuation curves by eq 3. It is seen that within the experimental uncertainty the ion diffusivities in the samples with and without CO2 are the same (Table 1) and do not depend on diffusion time (Figure 4). These results can be understood by noting that in the mixture sample the number of CO2 molecules is several times smaller than the number of the anion−cation pairs. As a result, at any particular time, the overwhelming majority of ions do not experience any interactions with CO2 molecules. It is important to note that due to small concentration of CO2 in the studied mixture sample the dications were not detected by natural abundance 13C PFG NMR. In this Letter, we report direct experimental observation of an exchange of CO2 molecules between the reacted and unreacted states and the related microscopic diffusion in a mixture of carbon dioxide and an amine-functionalized ionic liquid. 13C NMR exchange measurements allowed estimating residence times of CO2 molecules in both states, whereas 13C diffusion NMR studies revealed time-dependent diffusive dynamics of CO2 for diffusion times comparable with and larger than the residence times. Analysis of the NMR data using analytical treatment and fitting these data by kinetic MC simulations allowed obtaining diffusivities of carbon dioxide in the reacted and unreacted states. In agreement with expectations the diffusivities of the ions were found to be diffusiontime independent and much smaller than that of CO2 in the unreacted state.

Figure 4. Dependence of the effective self-diffusivities obtained from the initial slop of the PFG NMR attenuation curves for the cation, anion, and CO2 on the diffusion time in the mixture of [(CH3)3N(CH2)2NH2]+[(CF3SO2)2N]− with CO2 at 297 K (filled symbols). The diffusivities of reacted and unreacted CO2 are those measured for the CO2 lines at 161 and 125 ppm, respectively. Also shown are the corresponding effective diffusivities of CO2 obtained by KMC simulations (open symbols connected by lines).

preferentially reduce the weighting of the CO2 molecules that were in the reacted state during the time τ1 at the beginning of the PFG NMR sequence, thus increasing the apparent diffusivity associated with the unreacted CO2. Fitting the PFG NMR attenuation curves for CO2 to Supporting Information eqs S1 and S2 for the effective diffusion times between 30 ms and 1.2 s allowed estimating the diffusivities of carbon dioxide in the pure reacted and unreacted states. The resulting CO2 diffusivities in these states are shown in Table 1. Table 1. Diffusivities of Ions and CO2 in the Reacted and Unreacted States at 297 K. The Data for CO2 and Ions Were Obtained from Fitting the PFG NMR Attenuation Curves Measured for the Diffusion Times in the Range between 30 ms and 1.2 s to Supporting Information Eqs S1 and S2 and Eq 3, Respectively (PFG NMR)a



diffusivity × 10 , m /s 12

species CO2 in the unreacted state CO2 in the reacted state cation (mixture) anion (mixture) cation (pure TSIL) anion (pure TSIL)

2

PFG NMR

KMC simulations

± ± ± ± ± ±

40 ± 6 0.7 ± 0.2

35 0.9 0.5 0.44 0.6 0.6

7 0.4 0.1 0.1 0.1 0.1

EXPERIMENTAL SECTION

The TSIL composed of the cation (2-aminoethyl)trimethylammonium paired with a bis(trifluoromethyl)sulfonylamide anion was supplied by the group of Prof. James H. Davis (Department of Chemistry, University of South Alabama). The as-received ionic liquid sample was centrifuged to remove a trace amount of MgSO4 drying agent. Before loading with carbon dioxide, the sample was made sorbate free by keeping it at high vacuum at 357 K for at least 24 h. The 13C NMR spectrum of the sample (Figure 1a) is consistent with the TSIL structure. 13C NMR measurements were performed using a wide-bore 17.6 T Bruker BioSpin spectrometer. In PFG NMR diffusion studies, magnetic field gradients with the amplitude up to 30 T/m were generated using a Diff60 diffusion probe and a Great60 gradient amplifier (Bruker BioSpin). The effective width of gradient pulses was 2.9 ms. The use of a high field spectrometer affords high sensitivity and the ability to apply high gradients allows the possibility to measure slow diffusion of diffusing species (such as ions and CO2) on the millisecond time scale.11,12,23−26

a

Also shown are the CO2 diffusivities in the reacted and unreacted states obtained by fitting the effective experimental diffusivities for CO2 in Figure 4 to the results of kinetic MC simulations (KMC Simulations).

In addition to the exact analytical solution given by Supporting Information eqs S1 and S2, we have also used kinetic Monte Carlo (KMC) simulations of diffusion under the conditions of two-site exchange to estimate the diffusivities of carbon dioxide in the reacted and unreacted states. The simulation details are presented in Supporting Information. Fitting the effective diffusivities in Figure 4 to the results of the 1769

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Ionic Liquids: A Pulsed Field Gradient NMR study. J. Phys. Chem. B 2009, 113, 6353−6359. (12) Hazelbaker, E. D.; Budhathoki, S.; Katihar, A.; Shah, J. K.; Maginn, E. J.; Vasenkov, S. Combined Application of High Field Diffusion NMR and Molecular Dynamics Simulations to Study Dynamics in a Mixture of Carbon Dioxide and an ImidazoliumBased Ionic Liquid. J. Phys. Chem. B 2012, 116, 9141−9151. (13) Kessler, H.; Oschkinat, H.; Griesinger, C.; Bermel, W. Transformation of Homonuclear Two-Dimensional NMR Techniques into One-Dimensional Techniques Using Gaussian Pulses. J. Magn. Reson. 1986, 70, 106−133. (14) Kessler, H.; Mronga, S.; Gemmecker, G. Multi-Dimensional NMR Experiments Using Selective Pulses. Magn. Reson. Chem. 1991, 29, 527−557. (15) Bain, A. D.; Cramer, J. A. Slow Chemical Exchange in an EightCoordinated Bicentered Ruthenium Complex Studied by OneDimensional Methods. Data Fitting and Error Analysis. J. Magn. Reson., Ser. A 1996, 118, 21−27. (16) Bain, A. D. Chemical exchange in NMR. Prog. Nucl. Magn. Reson. Spectrosc. 2003, 43, 63−103. (17) Forsen, S.; Hoffman, R. A. Study of Moderately Rapid Chemical Exchange Reactions by Means of Nuclear Magnetic Double Resonance. J. Chem. Phys. 1963, 39, 2892−2901. (18) Chen, A.; Johnson, C. S.; Lin, M.; Shapiro, M. J. Chemical Exchange in Diffusion NMR Experiments. J. Am. Chem. Soc. 1998, 120, 9094−9095. (19) Kärger, J.; Ruthven, D. M.; Theodorou, D. N. Diffusion in Nanoporous Materials; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2012. (20) Callaghan, P. T. Principles of NMR Microscopy; Clarendon Press: Oxford, U. K., 1991. (21) Johnson, C. S. Effects of Chemical Exchange in DiffusionOrdered 2D NMR Spectra. J. Magn. Reson., Ser. A 1993, 102, 214−218. (22) Cabrita, E. J.; Berger, S.; Bräuer, P.; Kärger, J. High-Resolution DOSY NMR with Spins in Different Chemical Surroundings: Influence of Particle Exchange. J. Magn. Reson. 2002, 157, 124−131. (23) Mueller, R.; Kanungo, R.; Kiyono-Shimobe, M.; Koros, W. J.; Vasenkov, S. Diffusion of Ethane and Ethylene in Carbon Molecular Sieve Membranes by Pulsed Field Gradient NMR. Microporous Mesoporous Mater. 2013, 181, 228−232. (24) Mueller, R.; Kanungo, R.; Kiyono-Shimobe, M.; Koros, W. J.; Vasenkov, S. Diffusion of Methane and Carbon Dioxide in Carbon Molecular Sieve Membranes by Multinuclear Pulsed Field Gradient NMR. Langmuir 2012, 28, 10296−10303. (25) Dvoyashkin, M.; Wang, A.; Katihar, A.; Zang, J.; Yucelen, G. I.; Nair, S.; Sholl, D. S.; Bowers, C. R.; Vasenkov, S. Signatures of Normal and Anomalous Diffusion in Nanotube Systems by NMR. Microporous Mesoporous Mater. 2013, 178, 119−122. (26) Dvoyashkin, M.; Wang, A.; Vasenkov, S.; Bowers, C. R. Xenon in l-Alanyl-l-Valine Nanochannels: A Highly Ideal Molecular SingleFile System. J. Phys. Chem. Lett. 2013, 3263−3267.

ASSOCIATED CONTENT

S Supporting Information *

Details of processing of the PFG NMR data and details of the kinetic Monte Carlo Simulations are provided. This material is available free of charge via the Internet at http://pubs.acs.org.



AUTHOR INFORMATION

Corresponding Authors

*E. J. Maginn. Phone: +1 574 631 5687. Fax: +1 574 631 8366. E-mail: [email protected]. *S. Vasenkov. Phone: +1 352 392 0315. Fax: +1 352 392 0315. E-mail: [email protected]fl.edu. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS We are grateful for the financial support of this work by the NSF CBET awards (Nos. 0967458 and 0967703). We thank Prof. James H. Davis (University of South Alabama) for giving us the sample of the TSIL. NMR data was obtained at the Advanced Magnetic Resonance Imaging and Spectroscopy (AMRIS) facility in the McKnight Brain Institute of the University of Florida. The NMR measurement time is provided in the framework of the external user program of the National High Magnetic Field laboratory; AMRIS is gratefully acknowledged. Members of the Vasenkov Group would especially like to thank Dan Plant and Jim Rocca at AMRIS for help with NMR measurements. Computational resources were provided by Notre Dame’s Center for Research Computing. J.K.S. would like to acknowledge partial funding by the Center for Research Computing.



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