(10f) Systematic Atomistic Simulations of CO2 and N2 Permeabilities in Polymers

Recently, we have developed a computational approach ^[1,2] to screen the properties of physical solvents for specific gas separation applications through the integration of the NIST database, in-house computational database, in-house Monte Carlo and molecular dynamics simulations, and machine learning models. It is interesting but challenging to extend this computational approach to screen polymers for gas separation applications. The challenges include building a reliable database and identifying and computing feature variables for machine learning of gas permeability.

In this work, we aim to address one of the above challenges, that is, to study the factors (feature variables) which affect CO₂ and N₂ permeability and selectivity from atomistic simulations. We systematically calculated CO₂ and N₂ permeability in several different polymers, such as amorphous poly(ethylene) (PE), polydimethylsiloxane (PDMS), and poly[1-(trimethylsilyl)-1-propyne] (PTMSP), which cover a wide range of CO₂ permeabilities from 10-100,000 Barrer. Gas solubility was calculated both from the modified Widom-insertion method ^[3] and the advanced continuous fractional component (CFC) ^{[4, 5]} osmotic Monte Carlo (MC) simulation. The two methods were found to give consistent CO₂ solubility in PE. Gas diffusivity was obtained from NVE MD simulations using the Einstein relation. The simulated CO₂ solubility, diffusivity, and permeability in PE and PDMS polymers are comparable to the corresponding experimental data ^[6-9] with similar polymer molecular weight. Our simulation results clearly show that CO₂ diffusivity determines the order of magnitude for CO₂ permeability, while, CO₂/N₂ solubility selectivity determines the gas pair permeability selectivity.

For the CH₃- (C₂H₄)_n-CH₃ homologous compounds, it was found that the compound density, CO₂ solubility, diffusivity, and permeability correlate very well with 1/n for n between 4-100. This allows us to obtain the values for the PE polymer with n between 700-1400 through extrapolation. When n increases, the homologous compound density increases, while the compound free volume fraction, CO₂ solubility, diffusivity, and permeability decrease. Finally, it was found CO₂ absorption in PE at 20 bar expands the polymer volume by 4%, which in turn increases CO₂ diffusivity and permeability by two-fold. A similar increase in CO₂ permeability at elevated CO₂ pressure in PE was also experimentally determined in the literature ^[7]. This study will also be extended to other polymers and other gases very easily.

References:

1. Wei Shi, Robert L. Thompson, Megan K. Macala, Kevin Resnik, Janice A. Steckel, Nicholas S. Siefert, and David P. Hopkinson, “Molecular Simulations of CO₂ and H₂ Solubility, CO₂ Diffusivity, and Solvent Viscosity at 298 K for 27 Commercially Available Physical Solvents”, Invited paper to the J. Chem. Eng. Data, DOI: 10.1021/acs.jced.8b01228, 2019
2. Wei Shi, Robert L. Thompson, Megan K. Macala, S. Tiwari, Kevin Resnik, Janice A. Steckel, Nicholas Siefert, David P. Hopkinson, “Integration of Data Mining, Molecular Modeling, and Machine Learning to Screen Physical Solvents for Gas Separation”, 2018 AIChE Annual meeting, David L. Lawrence Convention Center, Pittsburgh, PA, Oct. 28-Nov.2, 2018.
3. Wei Shi, R. L. Thompson, E. Albenze, J. A. Steckel, H. B. Nulwala, D. R. Luebke. “Contribution of the acetate anion to CO2 solubility in ionic liquids: theoretical method development and experimental study”, J. Phys. Chem. B 2014, 118, 7388-7394.
4. Wei Shi, E. J. Maginn, “Continuous Fractional Component Monte Carlo: An Adaptive Biasing Method for Open System Atomistic Simulations”, J. Chem. Theory Comput. 2007, 3, 1451-1463.
5. Wei Shi, E. J. Maginn, “Atomistic Simulation of the Absorption of Carbon Dioxide and Water in the Ionic Liquid 1-n-Hexyl-3-methylimidazolium Bis (Trifluoromethylsulfonyl) imide ([hmim][Tf₂N])”, J. Phys. Chem. B 2008, 112, 2045-2055.
6. A. S. Michaels, R. B. Parker, Jr. “Sorption and Flow of Gases in Polyethylene”, J. Polym. Sci. 1959, XLI, 53-71.
7. S. A. Stern, S. S. Kulkarni, “TEST of a “Free-Volume” Model for Gas Permeation through Polymer Membranes. I. Pure CO₂, CH₄, C₂H₄, and C₃H₈ in Polyethylene”, J. Polym. Sci. 1983, 21, 467-481.
8. H. Lin, B. D. Freeman, “Gas solubility, diffusivity and permeability in poly(ethylene oxide)”, J. Membr. Sci. 2004, 239, 105-117.
9. T. C. Merkel, V. I. Bondar, K. Nagai, B. D. Freeman, I. Pinnau, “Gas Sorption, Diffusion, and Permeation in Poly(dimethylsiloxane)”, J. Polym. Sci. B: Polym. Phys. 2000, 38, 415–434.