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					                                                       Molecular Modeling of Structure and Dynamics
                                                                  in Fuel Cell Membranes
                                                                               A. Roudgar, Sudha N.P. and M.H. Eikerling
                                                                Department of Chemistry, Simon Fraser University, Burnaby, Canada,V5A 1S6


I. Introduction
                                                                                                                                  III. Computational simulation of arrays of the simplest and
  Proper understanding of the relations between structure formation and mobility is critical for the development
  of highly performing proton conducting membranes for fuel cells. It is, however, impossible to study the
                                                                                                                                  shortest sidechain (CF3SO3H)
  complete scale of structural details in real membranes with quantum mechanical approaches (DFT and
  AIMD). Feasible routes are to utilize combinations of quantum mechanical and classical approaches or to
                                                                                                                                  Part 1: Geometry Optimization
  consider small substructures of the membrane. Here we apply ab-initio approaches to simplified model                            Computational details                                      Top view                        Side view
  systems. The objective is to understand co-operative phenomena in proton transport and explore effects of
  length, chemical structure and arrangements of polymeric side chains.                                                           • Two-dimensional hexagonal array with fixed
                                                                                                                                     positions of carbon atoms.
                                                                                                                                  • 3 sidechains + 3 water molecules per unit cell
Architecture of Membranes
                                                                                                                                  • Vienna Ab-initio Simulation Package (VASP)
Nature of backbone                                                         Chemical architecture of the side chains               • Only Γ point is considered in total energy                                            Fixed carbons
                                                                                                                                    calculation
                                                                                                                                  • Projected Augmented Wave (PAW)
                                                                                                                                    pseudopotential with cut-off energy Ecut=400 eV
                                                                                                                                  • PW-91 Functional
 S-PBI butane                                                                             PS-g-mac PSSA(21) (graft polymer)      Binding energy as a function of sidechain - sidechain distance
                                 PAN-g-macPSSA graft copolymers (32)
Conductivity 0.01 Scm-1(80°C)                                                             Conductivity 0.08 Scm -1
                                 (graft polymer). Conductivity 0.1 Scm-1                                                                                                                    A C-C distance of d=6.18Å corresponds to the largest
                                                                                                                                                                                             binding energy - fully dissociated array.
Distance between side             Length of the side chain
chains
                                                                                                                                                                                            The transition between fully dissociated and fully non-
                                                                                                                                                                                             dissociated array occurs at d=7.2Å.

                                                                                                                                                                                            In similar calculations for CH3SO3H the transition
                                                                                                                                                                                             between fully-dissociated and fully non-dissociated
                                                                                       S-PPBP
                                                                                       Conductivity 0.001 Scm-1                                                                             array occurs at d=6.7Å (weaker acid).
 Partially sulfonated styrene
 ethylene. Conductivity 0.002                                                                                                                                                               We expect a high probability of proton transfer in the
 Scm-1 when x=9.                                                                                                                            Top-view                     Top-view            region of d~7.2Å, where the difference in energies
                                                                                                                                                                                             is small.

Morphology of Nafion
The ionomer consists of an hydrophobic backbone with side chains that are terminated by acid
groups. Good proton conductivity of the membrane is due a spontaneous “nanophase segregation”
in the presence of water.
                                                                                                                                          Dissociated acid          Non dissociated acid

                                                                                                                                   Part 2: Ab-initio Molecular Dynamics
                                                                                                                                  Computational details

                                                                                                                                  • Two dimensional hexagonal arrays with C-C fixed distance d=7.2
                                                                                                                                  • 3 sidechains + 3 water molecules per unit cell

                                                                                                                                  • Constant temperature T=300K
                                                                                                                                  • Nose-Hoover thermostat with Nose mass Q=0.05
                                                                                                                                  • PW-91 Functional
                                                                                                                                                                   t=0                                                          t=2.1 ps

                                                                                                                                  In initial configuration                            At t>0.5ps the acid head
                                                                                                                                  (t=0) all acids groups                              groups start to approach
                                                                                                                                   are non-dissociated                                each. Local clusters are
                                                                                                                                                                                      formed. A partially
                                                                                                                                                                                      dissociated state develops.


                          The complexity and large number of involved atoms demand simple
                          but reliable models for computational simulation of such a system.                                       At t>4.1ps the system evolves towards a transition state.   t=5.7 ps

                                                                                                                                   The potential energy drops.
II. Model System and Approaches                                                                                                    Acid groups become fully dissociated
                                                                                                                                   The energy of the new structure is 1eV lower
                                                                                                                                     than the initial (non-dissociated) configuration
Step 1: We consider a two-
dimensional regular array
of sidechains anchored to a
substrate.
                                                                                                                              IV. Conclusion
                                                                                                                               We study effects of molecular structure on proton, solvent and polymer dynamics in PEMs.
                                                                                        Compare the dynamics of the
                                                                                                                               Our model consists of a minimally hydrated 2-D array of sidechains with fixed end points.
                                                                                        sidechains with and without the
                                                                                                                               We perform full quantum mechanical calculations using VASP.       T
                                                                                        substrate (frequency spectra).
                                                                                                                               Total energy calculation as a function of C-C distance was performed.
Step 2: We remove                                                                                                              Upon increasing the C-C distance, a transition from dissociated to non-dissociated state occurs.
the substrate and fix                                                                                                          We have performed a molecular dynamics simulation for 3(CF2SO3H + H2O) at fixed C-C distance d=7.2Å. Our
the positions of the                                                                                                            results show that a transition occurs at t=4.1ps and a new and more stable structure is formed at t=5ps.
endpoint atoms at
their initial position.
                                                                                                                              Acknowledgement
                                                                                                                                 We gratefully acknowledge the funding of this work by NSERC.


                                                                                                                              References
                                Important characteristics of model system                                                     •Carmen Chuy, Jianfu Ding,Edward Swanson, Steven Holdcroft,Jackie Horsfall,and Keith V. Lovell, JECS,150(5)
                                                                                                                               E271-E279(2003).
   • Length of sidechains.                                           • Nature of acid groups.                                 •M.Eikerling, A.A.Kornyshev, Journal of Electroanalytical Chemistry,502(2001),1-14.
   • Distance between sidechains.                                    • Number of acid groups on sidechain.                    •K.D.Kreuer, Journal of Membrane Science,185 (2001),29-39.
   • Chemical structure of sidechains                                • Water content.                                         •E.Spohr, P.Commer, and A.A.Kornyshev, J.Phys.Chem.B 2002,106,10560-10569.
                                                                                                                              •M.Eikerling, A.A.Kornyshev, and U.Stimming, J.Phys.Chem.B 1997,101,10807-10820.

				
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