Minimally Hydrated Arrays of Acidic Surface Groups: Model Systems for Proton Transport in Fuel Cell Membranes

A. Roudgar, Sudha P.Narasimachary. and M.H. Eikerling

Department of Chemistry, Simon Fraser University, Burnaby, Canada,V5A 1S6

Morphology of Nafion

I. Introduction Polymer electrolyte fuel cells are environmentally friendly and highly efficient power sources. They play a

key role in the worldwide search for alternative energy solutions, driven by increasing energy demands, global warming and dwindling fossil fuel supplies. Major efforts in research focus on polymer electrolyte membranes (PEM), which must exhibit good proton conductivity and high stability in the harsh fuel cell milieu. Theoretical relationships between chemical architecture, morphology and proton conductivity are crucial for the design of advanced Polymer Electrolyte Membranes (PEMs) for fuel cells. It is, however, impossible to study the 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 consider small substructures of the membrane. Here, we apply ab-initio approaches to simplified model 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.

II. Model System and Approaches

Computational details

• Two-dimensional hexagonal array with fixed positions of carbon atoms.• 3 sidechains + 3 H2O per unit cell• Vienna Ab-initio Simulation Package (VASP)

Step 1: We consider a two-dimensional regular array of sidechains anchored to a substrate.

Step 2: We remove the substrate and fix the positions of the endpoint atoms at their initial position.

The complexity and large number of involved atoms demand simple but reliable models for computational simulation of such a system.

We compare the dynamics of thesidechains with and without the substrate (frequency spectra).

II. Ionomer moleculesbackbone properties, length and separation of sidechains

I. Acid/water clustersacid strength, hydration,dissociation

III. Aggregatessize and shape, effective density of acid groups

IV. Heterogeneous PEMmicrophaseseparation,effective properties (transport, stability)

chemical architecture

structural evolution

macroscopic performance

hydrophobic region

hydrophilic clusters

PEM: from chemical architecture to performance

The ionomer consists of an hydrophobic backbone with sidechains that are terminated by acid groups. Good proton conductivity of the membrane is due a spontaneous “nanophase segregation” in the presence of water.

Array of sidechains with fixed endpoint

Important characteristics of model system

• Length of sidechains.• Distance between sidechains.• Chemical architecture of sidechains

• Nature of acid groups.• Number of acid groups on sidechain.• Number of water molecules per sidechain.

III. Computational simulation of minimally hydrated arrays of the simplest and shortest “acid surface group” (R-SO3H with R=CF3)

Chemical structure of Nafion

–[(CF2 – CF2)n – CF – CF2]m

O – CF2CFCF3

O – CF2CF2SO3H

I

I5<n<13.5

100<m<1000

•Only Γ point is considered in total energy calculation• Projected Augmented Wave (PAW) pseudopotential with cut-off energy Ecut= 400 eV• PW-91 Functional

Hydration energy as a function of sidechain separation (C-C distance)

Structure B.1. Tilted fully dissociated structure

IV. Results

Structure B.2. Tilted partially dissociated structure

Structure B.3. Titled non-dissociated structure

A C-C distance of d = 6.23 Å gives the largest hydration energy (E = -2.78 eV) corresponding to the fully dissociated array of structure A. Upon increasing sidechain separation there is a transition from structure A to structure B at d = 6.7Å. A transition from structure A to structure B has been seen by performing a molecular dynamics calculation based on DFT at d = 7.4 Å within 6.1ps. Upon further increasing d, structure B can be found in 3 different states: fully dissociated, partially dissociated and non-dissociated. We expect high probabilities of proton transfer in the regions of d ~ 7.6 Å and d ~ 8.5 Å where the relevant energy differences are small.

Discussion

IV. Conclusion We study effects of molecular structure on proton, solvent and polymer dynamics in PEMs. Our model consists of a minimally hydrated 2-D array of sidechains with fixed endpoints. We perform full quantum mechanical calculations using VASP. Variation of the sidechain separation triggers a number of structural transitions in minimally hydrated arrays (upright, tilted, fully dissociated, partially dissociated, fully non-dissociated). The minimally hydrated structure is very stable at small sidechain separations. Extra water molecules are weakly bound. The considered model could provide valuable insight into proton transport mechanisms in minimally hydrated PEMs at elevated temperature.

T

Acknowledgement We gratefully acknowledge the funding of this work by NSERC.

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Binding energy of an extra water as a function of C-C distance

The binding energy as a function of C-C distance shows a small binding energy at small d and strong binding of the extra water molecule at large d.

The required energy to remove one water molecule from the system is large for small sidechain separation.

The required energy to remove one water molecule (E) as a function of sidechain separation

The small binding energy of an extra water and large require energy to remove one water molecule shows that the minimally hydrated systems are very stable and will persist at T>400K. Sidechain separation has a strong effect on structure and stability of hydrated arrays.

The two most stable geometries of structure B.2 with one extra water molecule.

Required energy to remove one water molecule as a function of C-C distance

Binding energy contour plot of structure B.2 partially

dissociated. There are two points correspond to the maximum binding energy

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Structure A. Upright fully dissociated structure