The total energy as a function of collective coordinates, , for upright and tilted structures are plotted. Two types of frequency spectrum are calculated:

1.Coupled system: a geometry optimization is performed, collective coordinates are fully coupled with other degrees of freedom

2.Uncouple system: only a wavefunction optimization has been performed, no coupling with other degrees of freedom are considered

The results are well described with a Morse potential of form

The frequency of normal modes for both sidechain rotation and tilting are calculated from parameters D and .

Interfacial Structure and Dynamics in Fuel Cell MembranesAta Roudgar, Sudha P. Narasimachary and Michael Eikerling

Hydronium motion

Sidechain tilting

Sidechain rotating

2. Model of Hydrated Interfaces inside PEMs

1. Introduction

Effective properties (proton conductivity, water transport, stability)

hydrophobic phase

hydrophilic phase

Primary chemical structure• backbones• side chains • acid groups

Molecular interactions (polymer/ion/solvent), persistence length

Self-organizationinto aggregatesand dissociation

Secondary structure• aggregates • array of side chains• water structure

“Rescaled” interactions (fluctuating sidechains,mobile protons, water)

Heterogeneous PEM• random phase separation• connectivity• swelling

Focus on Interfacial Mechanisms of PT

Insight in view of

fundamental

understanding and

design:

Objectives

Correlations and mechanisms

of

proton transport in interfacial

layer

Is good proton conductivity

possible

with minimal hydration?

Assumptions:

decoupling of aggregate and side chain

dynamics

map random array of surface groups onto

2D array

terminating C-atoms fixed at lattice

positions

remove supporting aggregate from

simulation

Feasible model of hydrated interfacial layer

2. Stable Structural Conformation

Side view

fixed carbon positions

__3 3 23 x CF SO H + H O Unit cell:

Ab-initio calculations based on

DFT (VASP)

formation energy as a function

of dCC

effect of side chain modification

binding energy of extra water

molecule

energy for creating water defect

2D hexagonal array of surface groups

dCC

Structure

Collective

coordinate

Freq. of

couple system

(cm-1)

Freq. of

uncouple

system (cm-1)

Frequency of

normal mode

(cm-1)

upright Sidechain

tilting, θ

77.82 84.76

120- 150tilted 59.68 91.68

upright Sidechain

rotation, φ

95.87 217.44

tilted 74.59 227.55

Upon increasing sidechain there is a transition from “upright” to “tilted” structure occurs at dCC = 6.5Å

independent highly correlated

Formation energy as a function of sidechain separation for regular array of Triflic acid, CF3-SO3-H

Collective Coordinates and Minimum Reaction Path

Regular 10x10x10 grid of points is generated. Each point represents one configuration of the these three CCs.

At each of these positions a geometry optimization including all remaining degrees of freedom is performed.

The path which contains the minimum configuration energy is identified (as shown).

1 2 3

Frequency Spectrum obtained from AIMD Simulation

Three collective coordinates: hydronium motion r, sidechain rotation and sidechain tilting .

r

Car-Parrinello NVT simulation at T =

300K

Simulation time = 20ps

The frequency spectrum is calculated

as a

Fourier transform of velocity correlation

function:

Frequency of Normal Modes using Morse Potential Fit

Correlations in interfacial layer are strong function of sidechain density.

Transition between upright (“stiff”) and tilted (“flexible”) configurations at

dCC = 6.5Å involves

hydronium motion, sidechain rotation, and sidechain tilting.

Reducing interfacial dynamics to the evolution of 3 collective coordinates

enabled determination of

transition path (activation energy 0.55 eV).

The frequency of normal modes for sidechain rotation and tilting are

calculated using Morse potential

fit and compared with frequency spectrum from AIMD simulation.

2( ) (1 )V D e

• A. Roudgar, S. Narasimachary and M. Eikerling, J. Phys. Chem. B 110, 20469 (2006).• M. Eikerling and A.A. Kornyshev, J. Electroanal. Chem. 502, 1-14 (2001). K.D. Kreuer, J. Membrane Sci. 185, 29- 39 (2001).• C. Chuy, J. Ding, E. Swanson, S. Holdcroft, J. Horsfall, and K.V. Lovell, J. Electrochem. Soc. 150, E271-E279 (2003).• E. Spohr, P. Commer, and A.A. Kornyshev, J. Phys.Chem. B 106, 10560-10569 (2002).• M. Eikerling, A.A. Kornyshev, and U. Stimming, J. Phys.Chem.B 101, 10807-10820 (1997).

References

4. Conclusions

The largest formation energy E = -2.78 eV at dCC = 6.2 Å corresponds to the upright structure.

The tilted structure can be found in 3 different states:

- fully dissociated

- partially dissociated

- non-dissociated

• The fluctuations of sidechain rotation and sidechain tilting are responsible for proton transfer.• There is a weak coupling between collective coordinates and the rest of the degrees of freedom.• Low frequencies ≈ 100cm-1 are responsible for proton transfer.

Barrier energy = 0.55eV

2. Mechanism and Dynamics at Interface

Computational details

Understanding the effect of chemical architecture, phase separation, and random morphology on transport properties and stability of polymer electrolyte membranes (PEM) is vital for the design of advanced proton conductors for polymer electrolyte fuel cells.

Low temperature (T<100˚C), high degree of hydration, proton transfer in bulk, high conductivity

High temperature (T>100˚C), low degree of hydration, proton transfer at interface, conductivity?

Evolution of PEM Morphology and Properties

Car-Parrinello Molecular Dynamics (CPMD) using functional BLYP

Configuration energy as a function of and for couple system

Upright Tilted

Side view Top view

0 01

1( ) ( )

N

i ii

C t v t v t tN

Hydrogen bond breaking occurs