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Temperature and Loading-
Dependent Diffusion of
Light Hydrocarbons
in ZIF-8
as Predicted through
Fully Flexible Molecular ...
New Separation
Strategies
INTRODUCTION 1
Replace cryogenic distillation with…
processes that utilize nanoporous
materials
...
Representative System: ZIF-8
THEORY 2
• ZIF-8 Attributes
Small window diameter (3.4 Å)
Large cavities (11.4 Å)
Robust s...
Permeabilities to Rates
Permeability
P =
𝐽
∆𝑃/𝑙
= Ɗ 𝑡 𝑆
𝑚𝑜𝑙
𝑚∙𝑠∙𝑃𝑎
where Ɗ 𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 and 𝑆 is the sor...
Diffusion can be modeled as an activated
hopping process between low energy regions
METHODS 4
Biased sampling method:
umbr...
TST and Dynamical Corrections
METHODS 5
• Transition state theory translates the free
energy barrier into a hopping rate
•...
• Umbrella sampling method predicts
quantitatively the diffusion coefficients
of hydrocarbons in ZIF-8
(benchmark: within ...
• Constrained the center of mass of the adsorbate
to the window using a spring during a MD
simulation; window sizes measur...
Does ZIF-8 undergo the LL-HL transition
upon hydrocarbon loading?
RESULTS 8
• Osmotic Framework Adsorbed Solution
Theory (...
Applying dcTST to Higher Loadings
RESULTS 9
• Umbrella sampling is
easily applied to
simulate higher loadings
• Track one ...
Simulated Hydrocarbon Transport
Diffusivities in ZIF-8
RESULTS 10
• Self-diffusivities combined with
thermodynamic correct...
Permeability
Predictions
RESULTS 11
Image from Bux et al.1
• Order of magnitude
agreement with experimental
data
• Disagre...
4. First study to use dcTST to study effect of finite loadings while
maintaining full framework flexibility; all results c...
QUESTIONS?
THE END 13
Ross Verploegh
ross.verploegh@chbe.gatech.edu
E&ST 3312
Georgia Institute of Technology
School of Ch...
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Talk on hydrocarbon Diffusion in MOFs given at the 15AIChE Conference

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Temperature and Loading-Dependent Diffusion of Hydrocarbons in ZIF-8 using Fully Flexible Molecular Simulations

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Talk on hydrocarbon Diffusion in MOFs given at the 15AIChE Conference

  1. 1. Temperature and Loading- Dependent Diffusion of Light Hydrocarbons in ZIF-8 as Predicted through Fully Flexible Molecular Simulations Ross Verploegh, Dr. Sankar Nair, Dr. David Sholl November 11, 2015 2015 AIChE Annual Meeting Salt Lake City, UT ENGINEERING NOVEL MATERIALS THROUGH SIMULATIONS -SHOLL GROUP
  2. 2. New Separation Strategies INTRODUCTION 1 Replace cryogenic distillation with… processes that utilize nanoporous materials (1) Thermodynamic separations (e.g. adsorption) (2) Kinetic separations (e.g. membranes)
  3. 3. Representative System: ZIF-8 THEORY 2 • ZIF-8 Attributes Small window diameter (3.4 Å) Large cavities (11.4 Å) Robust synthesis process, in- expensive, water-stable well studied Low Loading ZIF-8 High Loading ZIF-8 Transition occurs upon nitrogen loading of ~50 molecules/unit cell  Force field available (“off the shelf”)3 • Molecular sieving potential for C3 alkenes and alkanes1 • Intra-framework dynamics characterized by swinging of the organic linker2 (1) Pan, Y.; Li, T.; Lestari, G.; Lai, Z., Effective separation of propylene/propane binary mixtures by ZIF-8 membranes. J. Membr. Sci. 2012, 390, 93-98. (2) Coudert, F. X.; Boutin, A.; Jeffroy, M.; Mellot-Draznieks, C.; Fuchs, A. H.,Thermodynamic methods and models to study flexible metal-organic frameworks. ChemPhysChem 2011, 12 (2), 247-58. (3) Zhang, L.; Hu, Z.; Jiang, J., Sorption-Induced Structural Transition of Zeolitic Imidazolate Framework-8: A Hybrid Molecular Simulation Study. J. Am. Chem. Soc. 2013, 135 (9), 3722-3728.
  4. 4. Permeabilities to Rates Permeability P = 𝐽 ∆𝑃/𝑙 = Ɗ 𝑡 𝑆 𝑚𝑜𝑙 𝑚∙𝑠∙𝑃𝑎 where Ɗ 𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 and 𝑆 is the sorption coefficient Transport Diffusivity to Self-Diffusivity Ɗ 𝒕,𝒊 = Ɗ 𝒔,𝒊( 𝝏𝒍𝒏𝒑 𝝏𝒍𝒏𝒄) where Ɗ 𝑠,𝑖 = Ɗ 𝑡0,𝑖 by assuming mixing effects are negligible; function of loading Self-Diffusivity to Hopping Rate Ɗ 𝑠,𝑖 = 1 6 𝑘𝑖,𝐴→𝐴𝐿𝐿 𝐸𝑋𝐼𝑇 𝜆2 where 𝑘𝑖,𝐴→𝐴𝐿𝐿 𝐸𝑋𝐼𝑇 = the rate through one “pore” times the number of possible exits THEORY 3 Hollow Fiber Module and Hollow Fiber with ZIF-8 Layer Representative MOF Frameworks Transport Diffusion (Left) and Self-Diffusion (Right) What is the physical interpretation of the rate? How is the rate calculated?
  5. 5. Diffusion can be modeled as an activated hopping process between low energy regions METHODS 4 Biased sampling method: umbrella sampling Free energy curve: reactants to products WHAM Weighted Histogram Analysis Method
  6. 6. TST and Dynamical Corrections METHODS 5 • Transition state theory translates the free energy barrier into a hopping rate • Transmission coefficient: probability for an adsorbate to settle in the opposite cage assuming it has reached the transition state • Dynamical corrections are needed to account for: 1. Fast recrossings 2. Geometry of the adsorbent around the transition state 3. Presence of other adsorbates 4. Morphology and DOFs of the adsorbate 0, 35, 100, 150 °C Molecular diameters: 3.64, 4.16, 5.0 Å
  7. 7. • Umbrella sampling method predicts quantitatively the diffusion coefficients of hydrocarbons in ZIF-8 (benchmark: within an order of magnitude) • Quantitative simulation of slow diffusion rates • A less sharp separation of propylene/propane is observed with the simulations than experiments1 (Sim. ideal selectivity ~20; Exp. ideal selectivity ~140) • Exp. data gathered through round-robin procedures more reliable2 Comparison of Simulated and Experimental Self-Diffusivities in ZIF-8 at 35°C RESULTS 6 Red region indicates the limiting region of conventional MD (1) Zhang, C.; Lively, R. P.; Zhang, K.; Johnson, J. R.; Karvan, O.; Koros, W. J. The Journal of Physical Chemistry Letters 2012, 3, 2130. (2) Eum, K.; Jayachandrababu, K. C.; Rashidi, F.; Zhang, K.; Leisen, J.; Graham, S.; Lively, R. P.; Chance, R. R.; Sholl, D. S.; Jones, C. W.; Nair, S. Journal of the American Chemical Society 2015.
  8. 8. • Constrained the center of mass of the adsorbate to the window using a spring during a MD simulation; window sizes measured with a grid based percolation method • Adsorbates brace the window open while they are at (or close to) the dividing surface • Calculations cannot ignore coupling between large adsorbates and the framework DOFs • Diffusion of large molecules at infinite dilution is not associated with a structural transition of ZIF-8 LL PLD=3.4 Å, HL PLD=3.9 Å Effect of the Crossing Event on the ZIF-8 Window Diameter RESULTS 7 Infinite dilution and 35 °C
  9. 9. Does ZIF-8 undergo the LL-HL transition upon hydrocarbon loading? RESULTS 8 • Osmotic Framework Adsorbed Solution Theory (OFAST)1 • Grand potential: • Transition from the LL to HL ZIF-8 structure is not thermodynamically favorable upon C1-C4 hydrocarbon loading at 35°C • Recent experimental work has confirmed this prediction Increasing hydrocarbon chain length 0 ( ,T) ( ,f) ( ) f e host n f T U TS PV RT df f       (1) Coudert, F.-X.; Jeffroy, M.; Fuchs, A. H.; Boutin, A.; Mellot-Draznieks, C., Thermodynamics of Guest-induced Structural Transitions in Hybrid Organic-Inorganic Frameworks. J. Am. Chem. Soc. 2008, 130 (43), 14294-14302.
  10. 10. Applying dcTST to Higher Loadings RESULTS 9 • Umbrella sampling is easily applied to simulate higher loadings • Track one adsorbate, consider all others as background potential • For all the hydrocarbons, the free energy barrier decreases faster than the transmission coefficient (dynamical correction) decreases Free energy curves for various propane loadings Transmission coefficient curves for various propane loadings • Decrease occurs from an increase in molecular collisions 2.5-10 Propane Molecules / UC and 35 °C
  11. 11. Simulated Hydrocarbon Transport Diffusivities in ZIF-8 RESULTS 10 • Self-diffusivities combined with thermodynamic correction factors from GCMC simulations • Data points at highest fractional loadings correspond to loadings at 10 bar bulk pressure • Quantitative agreement with C1-C3 experimental IRM studies1 (1) Chmelik, C. Microporous and Mesoporous Materials 2015. At 35 °C
  12. 12. Permeability Predictions RESULTS 11 Image from Bux et al.1 • Order of magnitude agreement with experimental data • Disagreements arise from: (1) force fields (2) neglecting defects on nano and microscale levels (3) inaccuracy in measuring film thickness (4) possible surface resistances at interfaces Exp. permeance data taken from published work by Zhang et al., Pan et al., Brown et al., Bux et al (1) Bux, H.; Chmelik, C.; Krishna, R.; Caro, J., Ethene/ethane separation by the MOF membrane ZIF-8: Molecular correlation of permeation, adsorption, diffusion. J. Membr. Sci. 2011, 369 (1–2), 284-289.
  13. 13. 4. First study to use dcTST to study effect of finite loadings while maintaining full framework flexibility; all results consistent with experimental diffusion and permeance data Summary CONCLUSIONS 12 2. Possible to compute self-diffusivities of adsorbates in ZIF-8 using “off the shelf” force fields; MD biased sampling methods allow us to probe slow diffusion 3. Large adsorbates can locally brace open the window of ZIF-8, demonstrating the necessity of using simulation methods that account for this behavior 1. Simulations examine diffusion of a wide selection of adsorbates in ZIF- 8; exhibiting a continuum of fast to slow diffusing species
  14. 14. QUESTIONS? THE END 13 Ross Verploegh ross.verploegh@chbe.gatech.edu E&ST 3312 Georgia Institute of Technology School of Chemical and Biomolecular Engineering Sholl Group Sponsor: Phillips 66 Acknowledgements: Sholl Group

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