Presentation given at the Annual Meeting of the American Institute of Chemical Engineers 2013 in San Francisco. The talk showed how gas permeation can be simulated directly by constructing a thin slice polymer model of a given microporous polymer and by perturbing the system at the boundary, pressure differences can be created and gas flow observed throughout the steady-state simulation. The simulation data allows an inquiry into the permeation rates, preferred permeation paths and mining of simulation statistics to obtain virtual CT scans of the polymer on a molecular level.

1. Direct simulations of gas
permeation in polymeric
membrane materials for
separation processes
Hendrik Frentrup, Kyle E. Hart, Coray M. Colina, Erich A. Müller
Department of Chemical Engineering, Imperial College London
Department of Materials Science and Engineering, Pennsylvania State University

2. Materials for gas separation: PIM-1
PIM-1 is a microporous polymer with good gas separation properties
PIM-1 Structure
PIM-1 Membrane
PIM-1 Molecular Model
N. B. McKeown , P. M. Budd Macromolecules 43 (12) 2010
Picture courtesy of Kyle E. Hart
● Time-lag analysis
● Gas chromatography
● Endless chemical
diversity
● Grand Canonical MC → Adsorption isotherm
● Simulated pycnometry → Surface Area
● ...and more!
Permeability

3. Outline
• Molecular simulation of gas transport in polymers
• Direct permeation simulations via Non-Equilibrium MD
• Permeability and gas uptake from NEMD simulations
• Molecular motion of penetrant gases

4. Molecular simulations of gas transport in
polymers
Solution-diffusion model applied to PIM-1
• Equilibrium Molecular Dynamics
• → Self-Diffusion Coefficient
Adsorption isotherm
CO2
Exp.
Abbott, Hart & Colina Theor. Chem. Acc 132 1334 (2013)
P=D⋅S
● Grand Canonical Monte Carlo
● → Solubility and Adsorption Isotherm
CO2

5. In silico permeation experiments via NEMD
• Generate a 2D slice of
PIM–1 with tested force-field
• Confine between 2 walls
that are ”invisible” for
gases
• Insert gas in bulk regions
next to the polymer
• Equilibrate and allow
gases to diffuse into the
polymer

6. In silico permeation experiments via NEMD
• Apply external field and
allow to reach steady-state
• Measure the gas
uptake by integrating
the density distribution
• Measure pressure
difference and gas flux
through polymer, apply
darcy's law to calculate
permeability
H. Frentrup, E. A. Müller et al. Molecular Simulation 38, 540 (2012)

7. Results: Gas uptake and permeability
Simulations
[*] Abbott et al. Macromolecules 44 4511 (2011)
exp. Budd et al. J. Mem. Sci. 251 263 (2005) & 325 851 (2008)
[1] Heuchel et al. J. Mem. Sci. 318 84 (2008) [3] Fang et al. J. Phy. Chem. C 115 14123 (2011)
[2] Fang et al. Mol Sim. 36 992 (2010) [4] Chang et al. RSC Adv. 3 10403 (2013)
GCMC Sim.
NEMD Sim.

8. Molecular diffusion path
• Positions of one single CO2
molecule are plotted for 3
ns.
• Periodic boundary
conditions apply.
• The molecule is adsorbed at
the polymer gas interface
• It crosses the void and
enters the polymer on the
left side, quickly diffusing
through the polymer
• It spends a long time on the
interface before it crosses
the void again.

9. “CT scan” of the diffusion paths
White: High gas density
distribution
Red: intermediate density
→ Bulk Gas
Inside polymer
Gas region
Green: not accessible to gas
→ Polymer

10. “CT scan” of the diffusion paths

11. “CT scan” of the diffusion paths

12. Conclusions: Advantages of NEMD
• One single simulation for S and P
• Mixtures can be simulated
• Mixed-matrix membranes
• Complex molecules
• Complex geometries
• Simulation approach:
• Robust, scalable, efficient, parallel

13. Acknowledgements
• Kyle E. Hart
• Coray M. Colina
• Erich A. Müller
• EPSRC
• NSF