(539a) Molecular Simulation of Adsorption Hysteresis of n-Alkanes in Nanoporous Materials

Adsorption of alkanes is crucial to a wide variety of applications ranging from adsorption cooling¹ to separations² to storage of natural gas.³ Previous studies have shown that porous materials such as zeolites and metal-organic frameworks (MOFs) can be useful for all these applications.^4,5 Despite the progress in these applications, capillary condensation and hysteresis, which may occur in such systems, are still not well understood. In addition, although hysteresis has been investigated for decades, most works, except for a few simulation studies,^6,7 have focused on simple molecules such as argon, nitrogen, and methane.^8,9

Here we present a computational study of hysteresis of C₁ to C₆ n-alkanes in selected MOFs from the ToBaCCo 1.0 MOF database of Colon et al.¹⁰ As complementary model systems, slit pores of varying widths were also studied. Two complementary simulation approaches were employed. First, we used grand canonical Monte Carlo (GCMC) and obtained the hysteresis loops (if any) by performing GCMC simulations sequentially “up and down” the isotherm, where the final configuration from a given pressure is used as the initial configuration for the simulation at the next pressure. In the second approach, we used canonical ensemble molecular dynamics (MD) simulations at fixed loadings combined with Widom insertions¹¹ that employ configurational-bias Monte Carlo (CBMC)^12,13 to determine the fugacities. Note the complementary nature of the approaches: GCMC sets the fugacity and calculates the loading, while MD plus Widom insertions sets the loading and calculates the fugacity. We show that the MD plus Widom approach is able to simulate the van der Waals (vdW) loop for an isotherm while GCMC cannot. GCMC simulations generate hysteresis loops, but they may suffer from sampling inefficiencies: at high loading, GCMC insertion and deletion moves have low acceptance rates due to the high density in the pores. A canonical simulation avoids these inefficiencies by fixing the number of molecules in the simulation box. Thus, a vdW loop serves as an additional proof that hysteresis observed in GCMC has a physical origin and is not simply due to poor sampling during the simulation. Utilizing these two methods, we were able to identify MOFs that exhibit hysteresis for n-butane and n-hexane at room temperature. The presence of hysteresis in these systems may affect their use in various applications.

We also tested the applicability of ideas from the principle of corresponding states as well as the Dubinin and Raduschekevich (DR) theory to n-alkane adsorption in MOFs. Following the concept of corresponding states, we simulated methane adsorption at the same reduced temperatures as for n-butane and n-hexane at 298 K, and we were able to observe hysteresis and vdW loops also for methane. Using the inverse of saturation loading as affinity coefficients for methane through n-hexane, we were able to collapse the isotherms from GCMC of these molecules onto a characteristic curve,¹⁴ although there is some scatter. We were also able to analyze the effect of size and flexibility of long chain molecules on adsorption and hysteresis comparing to small molecules: smaller molecules have smaller hysteresis loops and form plateaus before capillary phase transition, while larger and more complicated adsorbates broaden the hysteresis loops in terms of fugacity and loading ranges. These results indicate the usefulness of traditional adsorption and thermodynamic theories for novel sorbents such as MOFs and suggest future work to refine these theories.

References:

(1) Chen, H.; Chen, Z.; Farha, O. K.; Snurr, R. Q. High Propane and Isobutane Adsorption Cooling Capacities in Zirconium-Based Metal–Organic Frameworks Predicted by Molecular Simulations. ACS Sustainable Chem. Eng. 2019, 7 (22), 18242–18246. https://doi.org/10.1021/acssuschemeng.9b05368.

(2) Sholl, D. S.; Lively, R. P. Seven Chemical Separations to Change the World. Nature News 2016, 532 (7600), 435. https://doi.org/10.1038/532435a.

(3) Zhang, H.; Deria, P.; K. Farha, O.; T. Hupp, J.; Q. Snurr, R. A Thermodynamic Tank Model for Studying the Effect of Higher Hydrocarbons on Natural Gas Storage in Metal–Organic Frameworks. Energy & Environmental Science 2015, 8 (5), 1501–1510. https://doi.org/10.1039/C5EE00808E.

(4) Yaghi, O. M.; O’Keeffe, M.; Ockwig, N. W.; Chae, H. K.; Eddaoudi, M.; Kim, J. Reticular Synthesis and the Design of New Materials. Nature 2003, 423 (6941), 705–714. https://doi.org/10.1038/nature01650.

(5) R. Long, J.; M. Yaghi, O. The Pervasive Chemistry of Metal–Organic Frameworks. Chemical Society Reviews 2009, 38 (5), 1213–1214. https://doi.org/10.1039/B903811F.

(6) Jin, Z. Bubble/Dew Point and Hysteresis of Hydrocarbons in Nanopores from Molecular Perspective. Fluid Phase Equilibria 2018, 458, 177–185. https://doi.org/10.1016/j.fluid.2017.11.022.

(7) Rasmussen, C. J.; Vishnyakov, A.; Neimark, A. V. Calculation of Chemical Potentials of Chain Molecules by the Incremental Gauge Cell Method. J. Chem. Phys. 2011, 135 (21), 214109. https://doi.org/10.1063/1.3657438.

(8) Neimark, A. V.; Vishnyakov, A. Gauge Cell Method for Simulation Studies of Phase Transitions in Confined Systems. Phys. Rev. E 2000, 62 (4), 4611–4622. https://doi.org/10.1103/PhysRevE.62.4611.

(9) Zeng, Y.; Prasetyo, L.; Tan, S. J.; Fan, C.; Do, D. D.; Nicholson, D. On the Hysteresis of Adsorption and Desorption of Simple Gases in Open End and Closed End Pores. Chemical Engineering Science 2017, 158, 462–479. https://doi.org/10.1016/j.ces.2016.10.048.

(10) Colón, Y. J.; Gómez-Gualdrón, D. A.; Snurr, R. Q. Topologically Guided, Automated Construction of Metal–Organic Frameworks and Their Evaluation for Energy-Related Applications. Crystal Growth & Design 2017, 17 (11), 5801–5810. https://doi.org/10.1021/acs.cgd.7b00848.

(11) Widom, B. Some Topics in the Theory of Fluids. J. Chem. Phys. 1963, 39 (11), 2808–2812. https://doi.org/10.1063/1.1734110.

(12) Siepmann, J. I.; Frenkel, D. Configurational Bias Monte Carlo: A New Sampling Scheme for Flexible Chains. Molecular Physics 1992, 75 (1), 59–70. https://doi.org/10.1080/00268979200100061.

(13) Dubbeldam, D.; Calero, S.; Ellis, D. E.; Snurr, R. Q. RASPA: Molecular Simulation Software for Adsorption and Diffusion in Flexible Nanoporous Materials. Molecular Simulation 2016, 42 (2), 81–101. https://doi.org/10.1080/08927022.2015.1010082.

(14) Severson, B. L.; Snurr, R. Q. Monte Carlo Simulation of N-Alkane Adsorption Isotherms in Carbon Slit Pores. J. Chem. Phys. 2007, 126 (13), 134708. https://doi.org/10.1063/1.2713097.