Transient Mass and Thermal Transport during Methane Adsorption

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Transient mass and thermal transport during methane adsorption into the metal-organic framework HKUST-1 Hasan Babaei, Alan J. H. McGaughey, and Christopher Eli Wilmer ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b13605 • Publication Date (Web): 19 Dec 2017 Downloaded from http://pubs.acs.org on December 21, 2017

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ACS Applied Materials & Interfaces

Transient mass and thermal transport during methane adsorption into the metal-organic framework HKUST-1 Hasan Babaei,a,b* Alan J. H. McGaughey,b and Christopher E. Wilmera a

b

Department of Chemical & Petroleum Engineering, University of Pittsburgh, 3700 O’Hara St, Pittsburgh, PA, 15261

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA.

Abstract Methane adsorption into the metal-organic framework (MOF) HKUST-1 and the resulting heat generation and dissipation are investigated using molecular dynamics simulations. Transient simulations reveal that thermal transport in the MOF occurs two orders of magnitude faster than gas diffusion. A large thermal resistance at the MOF/gas interface (equivalent to 127 nm of bulk HKUST-1), however, prevents fast release of the generated heat. The mass transport resistance of the MOF/gas interface is equivalent to 1 nm of bulk HKUST-1 and does not present a bottleneck in the adsorption process. These results provide important insights into the application of MOFs for gas storage applications.

Keywords: metal-organic framework, gas adsorption, transient thermal transport, transient mass transport, gas/solid interface

*

Corresponding author. E-mail address: [email protected]

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Introduction Metal-organic frameworks (MOFs), which are nanoporous crystals with extremely high internal surface areas, are promising materials for gas storage, gas separation, and catalysis.1–4 One important, and often neglected, challenge related to gas storage in MOFs is the heat generated during gas adsorption. This heat increases the system temperature5 and, in turn, reduces the amount of gas that can be adsorbed. Efficient thermal transport can reduce this effect by facilitating heat dissipation. In this regard, previous studies have investigated the thermal conductivity of empty MOFs using atomistic modeling6–8 and experiments.9–11 One experimental work has studied the effect of adsorbed gas on MOF thermal conductivity.12 Our recent modeling studies addressed the mechanisms of thermal transport in nanoporous crystals containing adsorbed gases13 and the effects of pore shape and size on these mechanisms.14 Heat generation during adsorption, however, is a fundamentally transient effect, and these previous studies only considered equilibrium behavior. During gas adsorption, multiple phenomena occur simultaneously that make the problem complex. With reference to Figure 1, these phenomena are: (1) gas diffusion through the gas-MOF interface, (2) heat generation as gas molecules adsorb within the MOF pores, (3) thermal transport within the MOF by both phonons in the lattice and by gas molecules, (4) gas diffusion within the MOF pores, (5) gas molecule collisions with the MOF framework, resulting in phonon scattering, (6) thermal transport at the gas-MOF interface, and finally (7) thermal transport in the pure gas region. Some of these phenomena have been studied previously, but in isolation. For example, thermal transport in empty and gas-filled MOFs (as mentioned above) and gas diffusion have been studied separately in MOFs.15,16 Measurements17–21 and simulations22–24 have also been used to study gas diffusion


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through gas-zeolite interfaces (another nanoporous crystal), focusing on the permeability of the interface. In this paper, we address transient effects of gas adsorption in MOFs with the objective of identifying bottlenecks in mass and thermal transport that would limit their use in gas storage applications. We use molecular dynamics (MD) simulations of methane (a technologicallyrelevant gas for storage applications) adsorption into slabs of HKUST-1 (a typical MOF) of different thicknesses. Spatially- and temporally-resolved gas density and lattice temperature are obtained and the timescales associated with gas diffusion and thermal diffusion are extracted. Using the transient simulations and additional non-equilibrium MD simulations, we also calculate the interface thermal conductance and permeability.

Figure 1 Coupled mass and thermal transport during gas adsorption in a MOF.


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Structures and Methodology Methane was modeled as a point particle with the TraPPE force field.25 The force field developed by Zhao et al.26 was used for the interactions between atoms in HKUST-1, which has a simple cubic structure with 624 atoms in the unit cell and a lattice constant of 2.63 nm. HKUST-1 contains large pores of diameter 10 Å connected by channels of diameter 3.5 Å to smaller tetrahedral pores of diameter 5 Å. Lorentz–Berthelot mixing rules27 were used to model interactions between gas molecules and the framework atoms. The MD simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)28 software with a time step of 0.5 fs and with periodic boundary conditions applied in all directions. Simulation boxes containing initially-empty HKUST-1 with layer thicknesses of 4, 6, 8, 10, and 12 unit cells, all with a 1×1 unit cell cross sectional area, were considered. Each MOF slab shares two interfaces with a gas-only region (see Figure 2a, which shows the simulation box for the 4 unit cell system). To construct the MOF/gas interface, the HKUST-1 structure was truncated at the Cu-O bonds in the [100] direction and the dangling oxygen atoms were capped with hydrogen atoms. We note that there have only been theoretical studies on the effect of terminal groups on the HKUST-1 free surface morphology29 and that our work presents a bestcase scenario for interfacial mass transport. The number of gas molecules and the length of the gas region were chosen so that the gas pressure was initially 50 bar and reduced to 35 bar in both the gas and MOF regions upon the completion of adsorption [see Table S1 of the Supporting Information (SI)]. The corresponding steady-state density of gas molecules in the MOF, which is required to determine the initial number of gas molecules, was calculated using grand canonical Monte Carlo simulations.30


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The transient nature of the adsorption process adds complexity to the simulations. Notably, it is important that both the pure gas and the MOF be at equilibrium before the gas adsorption begins. We used artificial walls to prevent gas molecules from entering the MOF during the initial equilibration. These walls were located at the MOF-gas interface and interacted with gas molecules via a Lennard-Jones (LJ) potential that had the same length (3.73 A) and energy (1.23 kJ/mol) scales as those for the methane molecules. After equilibrating the gas and MOF separately at a temperature of 300 K in the canonical ensemble for one million time steps, the artificial walls were removed and the gas molecules were allowed to infiltrate the MOF in the microcanonical ensemble. Depending on the thickness of the MOF, the transient simulations were run for five to fifteen million time steps. During this time period, gas molecules diffuse into the MOF and are adsorbed, heat is generated, and thermal transport occurs. Throughout the simulation, we monitored the spatial and temporal variations of gas density, gas temperature, and MOF temperature. A snapshot of the 4 unit cell system in its final equilibrium state (i.e., complete adsorption) is shown in Figure 2b.


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Figure 2 Simulation box with 4 unit cells of HKUST-1: (a) before adsorption begins and (b) equilibrium state after adsorption is complete. Periodic boundary conditions are applied such that there are two MOF/gas interfaces. Grey, red, gold, light grey, and blue spheres represent carbon, oxygen, copper, hydrogen, and methane.

An energy drift occurs during the simulations that leads to a temperature rise in addition to that associated with the adsorption. No drift is observed in a bulk MOF/gas simulation that contains no interfaces. While the drift is thus most likely caused by the interfaces, its precise origin is unknown. The temperature rise for the 4, 6, and 8 unit cell systems is ~1 K/ns, which is comparable to previous benchmark MD simulations (e.g., 2.5, 0.5, and 10 K/ns for simulations of dihydrofolate reductase in water using the GROMACS, Desmond, and NAMD packages).31–35 The 4, 6, and 8 unit cell systems reach a mass- and thermal- steady state condition before the drift significantly affects the MOF temperature. For the 10 and 12 unit cell systems, however, longer equilibration times and larger drift (~5 K/ns) prevent these systems from reaching a thermal steady state condition. As such, we present the mass transport results for all MOF thicknesses, but the thermal transport results are only presented for the 4, 6, and 8 unit cell systems. Plots of MOF temperature versus time for all systems are provided in Figure S1.


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Results and Discussion Spatial resolution of time-dependent gas density and framework temperature A pertinent quantity that we sought to determine is the ratio of timescales for thermal and mass transport in the MOF during gas adsorption. To do so, we calculated the spatial profiles of the gas density and framework temperature in the MOF as a function of time. The gas densities for MOFs of thicknesses of 4 and 12 unit cells are plotted in Figures 3a and 3b at seven different times. The results for the other three MOF thicknesses are provided in Figure S2. The vertical axis provides the number of gas molecules located in 4 Å wide bins. These values were calculated based on time averages over 5 ps for total simulation times below 100 ps and over 100 ps for total simulation times beyond 100 ps. At the start of each simulation, the number of gas molecules in the MOF is zero. After the artificial walls are removed, gas molecules begin to diffuse into the MOF, starting from the interfaces and moving towards the center. A non-uniform spatial distribution is evident over a significant portion of the simulation time for all thicknesses before equilibrium is reached. At steady state, the distribution of gas molecules is also not uniform, with a slightly higher density near the interface. For the 12 unit cell MOF, the gas density near the interface is 0.36 molecules/nm3 higher than in the central region. The higher density of loaded gas near the interface may be a result of the lower potential energy felt by the gas molecules in this region compared to the bulk MOF, where there is a competing potential energy from clusters of MOF atoms located in the corners of pores. Two mechanisms with different time scales govern gas diffusion in HKUST-1: (i) bulklike diffusion characterized by travel from large pores to large pores, and (ii) travel between


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large and small pores. The timescale for (i) is small and can be calculated using MD simulations. The time scale for (ii), however, is longer due to the high energy barrier associated with the hopping events. These two mechanisms can be observed by tracing the potential energy of a single molecule (see Figure S3). While (ii) could be important in diffusion through channeled zeolites,21,24,36 in HKUST-1 the dominant diffusion path is (i), through the large pore openings due to a lower energy barrier for gas molecule motion. The time evolution of the spatially-resolved framework temperature for the 4 unit cell MOF is plotted in Figure 4. Comparing this plot to those for the gas density (Figures 3a and 3b) shows that, in contrast, the temperature is spatially uniform at any given point in time (i.e., from a thermal standpoint, the MOF can be considered as a lumped system). This finding indicates that the heat generated due to adsorption and gas-MOF interactions is conducted more easily than the gas molecules diffuse. Similar results are found for all MOF thicknesses. To quantify this behavior, we calculated the ratio of thermal diffusivity to mass diffusivity,

k / ρc , where k, ρ , and c are the effective thermal conductivity, density, and D

specific heat for the whole system and D is the diffusivity of gas molecules inside the MOF. Using reported values for HKUST-1 (MD-based k = 2.2 W/m K,13 experimental ρ = 600 kg/m3,37 and c = 700 J/kg K38) and D =5×10-8 m2/s,39 we find

k / ρc ≈ 100, supporting our D

observation of a uniform temperature profile and a non-uniform gas profile during gas adsorption. We also found that the gas molecules in the pure gas region become thermally equilibrated at times longer than the adsorption times. This effect can be observed from the


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difference between the temperatures of the gas molecules within the MOF and those in the pure gas region for the 6 unit cell system, as plotted in Figure S4. This finding indicates that the heat generated in the MOF during gas adsorption cannot be efficiently transferred to the pure gas region due to high thermal resistances at the gas-MOF interface and in the pure gas region.

Figure 3 Time evolution of gas adsorption into MOF slabs with thicknesses of (a) 4 and (b) 12 unit cells. The spatial average corresponds to the data at a time of 2.5 ns (4 unit cells) and 13.2 ns (12 unit cells).


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Figure 4 Time evolution of framework temperature inside the 4 unit cell thick MOF slab. Time evolution of adsorbed gas mass and system temperature The time evolution of the amount of adsorbed gas, from the beginning of adsorption (i.e., when the artificial walls are removed) until the system reaches equilibrium, is plotted in Figure 5a for each MOF thickness. The amount of gas, M(t), where t is time, is scaled by the equilibrium value, M∞. Each curve represents the average of four simulations with different initial velocity distributions (see Figure S5 for the individual curves for the 4 unit cell system). For all thicknesses, the amount of adsorbed gas increases monotonically with time and converges to an equilibrium value. We define a characteristic adsorption time as when the adsorbed gas density is 99% of the final value. This time is specified using the fitting procedure described later in the paper and is plotted in Figure 5b as a function of the MOF thickness. As expected, this time increases with increasing MOF thickness, from 1 ns for the 4 unit cell system to 5 ns for the 12 unit cell system. As shown in Figure 5c, the adsorbed gas density decreases as the MOF thickness increases and the higher interfacial gas concentration diminishes in its overall importance (see Figures 3a and 3b). We next calculated the heat generated during gas adsorption and the resulting temperature rise inside the MOF region (separately for the MOF and the gas). The heat generated was calculated as the difference in kinetic energy of the whole system (Figure S6) between the start and end of the gas adsorption and is plotted in Figure 5d as a function of MOF thickness. The heat generated increases linearly with the MOF thickness. The equilibrium temperatures of the gas molecules and the framework atoms in the MOF region are plotted in Figure 5e. The 4, 6, and 8 unit cell MOFs reach the thermal equilibrium


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state by 1.5, 2, and 2.5 ns, which are longer than the corresponding adsorption times. The gas and MOF temperatures are close for all MOF thicknesses and differences can be attributed to the finite-time averaging. For both the gas and the MOF, the equilibrium temperatures are nearly independent of the MOF thickness, falling within a range of ±2 K.


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Figure 5 (a) Adsorbed gas mass normalized by its final mass as a function of time for MOFs with different numbers of unit cells. (b) Adsorption time, (c) final adsorbed gas density (d) heat generated, and (e) temperatures of gas molecules and MOF atoms as a function of MOF thickness (plotted as a function of the number of unit cells).

Interface transport properties As noted above, the MOF-gas interface presents a resistance to thermal transport. We now quantify this resistance (using the interface thermal conductance) and the accompanying interface permeability. We used the direct method (i.e., non-equilibrium MD40) to calculate the interface thermal conductance, G, with the heat flux perpendicular to the MOF-gas interface. The interface thermal conductance is the ratio of the heat flux, q, to the temperature difference between the gas and MOF sides of the interface, ∆T, i.e., G = q/ ∆T. To predict interface thermal conductance, the 4 unit cell MOF slab was studied using a smaller gas region. After reaching equilibrium, a heat flux of 500 MW/m2 was applied from the gas to the MOF by adding/removing energy to/from two regions of the simulation box (the source is in the middle of the gas and the sink is in the middle of MOF) for fifteen million time steps. After the system reached steady state, temperature profiles were obtained. The steady-state temperature profile is plotted in Figure 6 and the predicted thermal conductance is 17.4 MW/m2 K. Taking the thermal conductivity of HKUST-1 to be 2.2 W/m K,13 this thermal conductance is equivalent to the thermal resistance of an HKUST-1 slab of thickness of 127 nm (i.e., about 50 unit cells) This quantity is known as the Kapitza length. This result indicates that the MOF-gas interface presents a bottleneck in the ability of the MOF to dissipate heat to its surroundings.


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Figure 6 Steady-state temperature profile for the application of a heat flux through the simulation box containing a 4 unit cell thick MOF. The blue/green points were used to extract the temperatures on the gas and MOF sides on the interfaces. The average temperature difference from the two interfaces was used to calculate the interface thermal conductance. The change in temperature slope near the source is due to the thermal resistance between the heat source and the neighboring gas molecules. The relevant mass transport property for the interface is the permeability, , which is defined as17,41: → ∞ ,

(1)

where j(t) and cs(t) are the mass flux across and gas concentration at the interface. Using this interface boundary condition and the diffusion equation,

, within the MOF, where

x is the direction perpendicular to the gas-MOF interface, the time dependence of the amount of adsorbed gas can be written as:41

1

! #$

" & % ∑+ ,-. ' (' ) )* . " "

(2)

Here, L = 0/ , l is half of the MOF thickness, and the 2, are the positive roots of 2, 342, 5. For each MOF thickness, we use Eq. (2) to extract the diffusivity and the permeability by fitting to the data in Figure 5a (see Figure S7). The average of the predicted diffusivity and permeability values are 9.2×10-8 m2/s and 87 m/s.42 We can define a characteristic length for


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interfacial mass transport that is analogous to the Kapitza length. This quantity, given by /, represents the length of MOF that provides the same resistance to mass transfer as the interface. This length for methane adsorption into HKUST-1 is ~1 nm which is much smaller than the Kapitza length of 127 nm. Thus, the interface, which for our simulation is hydrogen-terminated, plays a more important role in thermal transport than it does in mass transport. Summary We applied molecular dynamics simulations to study the coupled thermal and mass transport that occurs during the adsorption of methane into the MOF HKUST-1. Our transient simulations capture the full process, shown in Figure 1, including gas adsorption, the resulting heat generation, and subsequent thermal transport. From the spatial distribution (Figures 3a, 3b, and 4), time evolution (Figure 5a), and equilibrium condition (Figures 5b-5e) of gas density, gas temperature, and MOF temperature, we found that thermal transport in MOFs occurs two orders of magnitude faster than mass transport. As such, the MOF temperature is spatially uniform at any given time during the adsorption process (Figure 4). Nonetheless, a large thermal resistance at the MOF/gas interface and within the pure gas region prevent fast release of heat generated during adsorption. The MOF/gas interface does not present an appreciable resistance to mass transport for our hydrogenterminated MOF. We also found that the gas density near the MOF/gas interface is higher than in the bulk, suggesting a benefit for using small MOF particles in gas storage applications. Use of small MOF particles, however, leads to poor thermal transport because of the greater relative contribution of the MOF/gas interface. An optimal strategy may exist by combining small MOF


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particles with high thermal conductivity materials (e.g., carbon nanotubes/nanofibers or graphene).43–46 In general, we believe the insights described in this work may be useful in designing adsorbents where trade-offs between storage capacity and thermal conductivity, and thereby filling rates, are inescapable. Supporting Information. Additional data and information on simulation methodology supplied as Supporting Information.

Acknowledgements C.E.W. and H.B. gratefully acknowledge the Donors of the American Chemical Society Petroleum Research Fund for support of this research. They also acknowledge both the Swanson School of Engineering and the Center for Simulation and Modeling (SAM) at the University of Pittsburgh for early financial support, and for providing computational resources, respectively. A.J.H.M acknowledges support from NSF award DMR-1507325.


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(20) Hibbe, F.; van Baten, J. M.; Krishna, R.; Chmelik, C.; Weitkamp, J.; Kärger, J. In-Depth Study of Mass Transfer in Nanoporous Materials by Micro-Imaging. Chem. Ing. Tech. 2011, 83 (12), 2211–2218. (21) Hibbe, F.; Chmelik, C.; Heinke, L.; Pramanik, S.; Li, J.; Ruthven, D. M.; Tzoulaki, D.; Kärger, J. The Nature of Surface Barriers on Nanoporous Solids Explored by Microimaging of Transient Guest Distributions. J. Am. Chem. Soc. 2011, 133 (9), 2804–2807. (22) Inzoli, I.; Kjelstrup, S.; Bedeaux, D.; Simon, J. M. Transport Coefficients of N-Butane into and through the Surface of Silicalite-1 from Non-Equilibrium Molecular Dynamics Study. Microporous Mesoporous Mater. 2009, 125 (1–2), 112–125. (23) Inzoli, I.; Simon, J. M.; Bedeaux, D.; Kjelstrup, S. Thermal Diffusion and Partial Molar Enthalpy Variations of N-Butane in Silicalite-1. J. Phys. Chem. B 2008, 112 (47), 14937–14951. (24) Zimmermann, N. E. R.; Smit, B.; Keil, F. J. Predicting Local Transport Coefficients at Solid–Gas Interfaces. J. Phys. Chem. C 2012, 116 (35), 18878–18883. (25) Martin, M. G.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 1. United-Atom Description of n-Alkanes. J. Phys. Chem. B 1998, 102 (14), 2569–2577. (26) Zhao, L.; Yang, Q.; Ma, Q.; Zhong, C.; Mi, J.; Liu, D. A Force Field for Dynamic Cu-BTC Metal-Organic Framework. J. Mol. Model. 2010, 17 (2), 227–234. (27) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids, Reprint edition.; Oxford University Press: Oxford England; New York, 1989. (28) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117 (1), 1–19. (29) Amirjalayer, S.; Tafipolsky, M.; Schmid, R. Surface Termination of the Metal-Organic Framework HKUST-1: A Theoretical Investigation. J. Phys. Chem. Lett. 2014, 5 (18), 3206–3210. (30) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. Prediction of Adsorption of Aromatic Hydrocarbons in Silicalite from Grand Canonical Monte Carlo Simulations with Biased Insertions. J. Phys. Chem. 1993, 97 (51), 13742–13752. (31) Friedrichs, M. S.; Eastman, P.; Vaidyanathan, V.; Houston, M.; Legrand, S.; Beberg, A. L.; Ensign, D. L.; Bruns, C. M.; Pande, V. S. Accelerating Molecular Dynamic Simulation on Graphics Processing Units. J. Comput. Chem. 2009, 30 (6), 864–872. (32) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4 (3), 435–447. (33) Götz, A. W.; Williamson, M. J.; Xu, D.; Poole, D.; Le Grand, S.; Walker, R. C. Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born. J. Chem. Theory Comput. 2012, 8 (5), 1542–1555. (34) Bowers, K. J.; Chow, E.; Xu, H.; Dror, R. O.; Eastwood, M. P.; Gregersen, B. A.; Klepeis, J. L.; Kolossvary, I.; Moraes, M. A.; Sacerdoti, F. D.; Salmon, J.K. Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters. In Proceedings of the 2006 ACM/IEEE Conference on Supercomputing; SC ’06; ACM: New York, NY, USA, 2006. (35) Fitch, B. G.; Rayshubskiy, A.; Eleftheriou, M.; Ward, T. J. C.; Giampapa, M.; Pitman, M. C.; Pitera, J.; Swope, W. C.; Germain, R. S. Chapter 6 Blue Matter: Scaling of N-Body Simulations to One Atom per Node. Curr. Top. Membr. 2008, 60, 159–180. (36) Heinke, L.; Kärger, J. Correlating Surface Permeability with Intracrystalline Diffusivity in Nanoporous Solids. Phys. Rev. Lett. 2011, 106 (7), 074501. (37) Mason, J. A.; Veenstra, M.; Long, J. R. Evaluating Metal–organic Frameworks for Natural Gas Storage. Chem. Sci. 2013, 5 (1), 32–51. (38) Mu, B.; Walton, K. S. Thermal Analysis and Heat Capacity Study of Metal–Organic Frameworks. J. Phys. Chem. C 2011, 115 (46), 22748–22754. (39) This value is an average value from ref 14 (2×10-8 M2/s) and calculated here using Green-Kubo method (2.1×10-8 M2/s) and transient MD simulations (9.25×10-8 M2/S).


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(40) Schelling, P. K.; Phillpot, S. R.; Keblinski, P. Comparison of Atomic-Level Simulation Methods for Computing Thermal Conductivity. Phys. Rev. B 2002, 65 (14), 144306. (41) Crank, J. The Mathematics of Diffusion; Clarendon Press, 1979. (42) The solution provided by Eq. (2) assumes the diffusivity to be independent of temperature and gas density. To check this assumption, we performed equilibrium Green-Kubo based simulations to predict the diffusivity. The result, plotted in Figure S8 of the SI, indicates that within the temperature and gas density ranges of our transient simulations, the diffusivity varies from 2.1×108 2 m /s at T = 300 K to 2.7×10-8 m2/s at T = 350 K). (43) Jabbari, V.; Veleta, J. M.; Zarei-Chaleshtori, M.; Gardea-Torresdey, J.; Villagrán, D. Green Synthesis of Magnetic MOF@GO and MOF@CNT Hybrid Nanocomposites with High Adsorption Capacity towards Organic Pollutants. Chem. Eng. J. 2016, 304, 774–783. (44) Wen, P.; Gong, P.; Sun, J.; Wang, J.; Yang, S. Design and Synthesis of Ni-MOF/CNT Composites and RGO/Carbon Nitride Composites for an Asymmetric Supercapacitor with High Energy and Power Density. J. Mater. Chem. A 2015, 3 (26), 13874–13883. (45) Mao, Y.; Li, G.; Guo, Y.; Li, Z.; Liang, C.; Peng, X.; Lin, Z. Foldable Interpenetrated Metal-Organic Frameworks/Carbon Nanotubes Thin Film for Lithium–sulfur Batteries. Nat. Commun. 2017, 8, ncomms14628. (46) Pachfule, P.; Balan, B. K.; Kurungot, S.; Banerjee, R. One-Dimensional Confinement of a Nanosized Metal Organic Framework in Carbon Nanofibers for Improved Gas Adsorption. Chem. Commun. 2012, 48 (14), 2009–2011.


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Table Of Contents (TOC)


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Figure 1 Coupled mass and thermal transport during gas adsorption in a MOF. 82x75mm (300 x 300 DPI)


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Figure 2 Simulation box with four unit cells of HKUST-1: (a) before adsorption begins and (b) equilibrium state after adsorption is complete. Periodic boundary conditions are applied such that there are two MOF/gas interfaces. Grey, red, gold, light grey, and blue spheres represent carbon, oxygen, copper, hydrogen, and methane. 177x75mm (300 x 300 DPI)



Figure 3 Time evolution of gas adsorption into MOF slabs with thicknesses of (a) 4 and (b) 12 unit cells. The spatial average corresponds to the data at a time of 2.5 ns (4 unit cells) and 13.2 ns (12 unit cells). 165x107mm (300 x 300 DPI)


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Figure 4 Time evolution of framework temperature inside the 4 unit cell thick MOF slab. 163x55mm (300 x 300 DPI)



Figure 5 (a) Adsorbed gas mass normalized by its final mass as a function of time for MOFs with different numbers of unit cells. (b) Adsorption time, (c) final adsorbed gas density (d) heat generated, and (e) temperatures of gas molecules and MOF atoms as a function of MOF thickness (plotted as a function of the number of unit cells). 82x179mm (300 x 300 DPI)


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Figure 6 Steady-state temperature profile for the application of a heat flux through the simulation box containing a 4 unit cell thick MOF. The blue/green points were used to extract the temperatures on the gas and MOF sides on the interfaces. The average temperature difference from the two interfaces was used to calculate the interface thermal conductance. The change in temperature slope near the source is due to the thermal resistance between the heat source and the neighboring gas molecules. 165x48mm (300 x 300 DPI)


Transient Mass and Thermal Transport during Methane Adsorption

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