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Multiscale Materials Modeling

Lecture 05

Proton Transport in Aqueous SystemsProton Transport in Aqueous Systems

Fundamentals of Sustainable Technology These notes created by David Keffer, University of Tennessee, Knoxville, 2012.

Outline

Proton Transport in Aqueous Systems

I I t d tiI. IntroductionII. Levels of Modeling

II.A. Quantum MechanicsII.B. Reactive Molecular DynamicsII.C. Confined Random Walk TheoryII D Percolation TheoryII.D. Percolation Theory

III. Conclusions

Fundamentals of Sustainable Technology

Moving toward fuel cell-powered vehicles

understanding starts at the

quantum level

H2-powered autos

leads to high-fidelity coarse-grained models

become a reality

impacts fuelimpacts fuelcell performance


improved nanoscale design of membrane/electrodeassembly

how fuel cells work: conceptual level

inputsH2 O2

H+

proton exchange membrane

H+Pt alloycatalyst Pt catalyst

H H+

cathodeanode

e- e-

H2O

e

electrical work

e

outputs


H2Oelectrical workoutputs

proton exchange membranes are polymer electrolytes

industry standard: Nafion (DuPont)perfluorosulfonic acid

sulfonic acid at end of side chainprovides protons

monomer backbone contains CF

perfluorosulfonic acid provides protons

monomer backbone contains CF2.

side chainside chain


CF2 = gray, O = red, S = orange, cation not shown.

Proton Transport in Bulk Water and PEMExperimental Measurements

Robison, R. A.; Stokes, R. H. Electrolyte Solutions; 1959.

Nafion (EW=1100) Kreuer, K. D. Solid State Ionics 1997.


Even at saturation, the self-diffusivity of charge in Nafion is 22% of that in bulk water.

morphology of bulk hydrated membrane

legend:

Nafion

EW = 1144 legend:O of H2O = redH= whiteO of H3O+ = greenS = orange

i d f

EW 1144= 6 H2O/HSO3T = 300 K

Snapshots of the remainder of polymer electrolyte not shown

aqueous nanophase

PEM morphology ismorphology is a function of water content.


low water ( = 6) small aqueous channels

high water ( = 22) large aqueous channels

Proton Transport – Two Mechanisms

Vehicular diffusion: change in position of center of mass of hydronium ion (H3O+)

H

O of H3O+

translation

Structural diffusion (proton shuttling): passing of protons from water molecule to the next (a chemical reaction involving the breaking of a covalent bond)covalent bond)

O of H2O

proton

1 2 1 23 3


phops

In bulk water, structural diffusivity is about 70% of total diffusivity.

Outline




III. Conclusions


Role of Quantum Mechanics

Understanding of fundamental mechanism of structural diffusion

Hydronium ions exist as hydrated ionHydronium ions exist as hydrated ion complexes like

Zundel ions (H5O2+)

and Eigen ions (H9O4+)

t t l diff istructural diffusion orProton hoppinginvolves a reaction in which the ground


gstate is likely an Eigen ion and the transition state is a Zundel ion.

Ojamäe, Shavitt, SingerJ. Chem. Phys. 1998

Zundel & Eigen Ions

Quantum Mechanics

Zundel ion

Molecular Dynamics

MD at = 4.4

Huang, Braams, Bowman,J. Chem. Phys. 2005

Eigen ion

MD at = 4.4

Ojamäe, Shavitt, SingerJ Chem Phys 1998


J. Chem. Phys. 1998

MD simulations will only approximate the structures from Quantum Mechanics.

Outline




III. Conclusions


Reactive Molecular Dynamics (RMD)

Quantum MacroscopicEquivalent Descriptions pComparison of

equilibrium state and transition state

Evaluation of reactant and product concentrations and

temperature as

q p

Small systems,short time scales

temperature as functions of time

Reactive Molecular Dynamics

Macroscales

1 Mechanism

Molecular Dynamics

Simulation of coupled reaction and 1 Ground state 1. Mechanism

(stoichiometry)2. Activation energy3. Heat of reaction4 Reaction rate

transport1. Ground state structure

2. Transition state structure

3 Geometric reaction


4. Reaction rate constant

3. Geometric reaction path

Variety of Approaches of Simulation of Structural Diffusion

Author Year Method Features System

R. Car & Car– • Computationally expensive • Excess H+ in H2O [2]M. Parinello [1] 1985 Parrinello

MD

Computationally expensive• Restricted to small systems • Nonaqueous hydrogen

bonded media

A. Warshel [3] 1980Empirical Valence

• Charge transfer theory of hydrogen bonded complexes

• Used to develop MS EVB SCI MS EVB

• Excess H+ in H2O [4,5]• Enzymes

Bond • Used to develop MS-EVB, SCI-MS-EVB, MS-EVB3

R.G. Schmidt & J. Brickmann [6]

1997 Mixed MD and MC

• Proton hopping between titratable sites• Criteria - Distance between donor and

acceptor

• Excess H+ in H2O• Proton in amino acid

M.A. Lill & V. Helms [7]

2001 Q-HOP MD• Proton hopping between titratable sites• Criteria - Distance and environmental

effect of the surrounding group

• Excess H+ in H2O• Aspartic acid in H2O• Imidazole ring in H2O

[1] R. Car and M. Parrinello, Phys.Rev.Lett., 55, 2471 (1985).

[2] M. Tuckerman, et al., J.Chem.Phys., 103, 150 (1995).

[3] A. Warshel and R.M. Weiss, J. Am. Chem. Soc., 102, 6218 (1980).

[4] J. Lobaugh and G.A. Voth, J. Chem. Phys., 104, 2056 (1996).

[5] D.E. Sagnella and M.E. Tuckerman, J. Chem. Phys., 108, 2073 (1998).

[6] R G S h idt d J B i k B B Ph Ch 101 1816 (1997)


[6] R.G. Schmidt and J. Brickmann., Ber. Bunsenges. Phys. Chem., 101, 1816 (1997).

[7] M.A. Lill and V. Helms, J. Chem. Phys., 115, 7993 (2001).

RMD Algorithm – Step 1

OHOHOHOH 324

232OH

At each step of conventional MD simulation, check if reactant (H3O+) is in a reactive configuration.

Step 1. Satisfy triggers (6 geometric and 1 energetic)

g

≈ 105° 180°rOO,Zundel ≤ rOO,Zundel,max rOH,Zundel ≥ rOH,eqlbmHOH ≈ 105°OHO ≈ 180°


rOO, Eigen ≤ rOO,Eigen,max rOO, hydration ≤ rOO,hydration,max Energetic Trigger


Step 2. Instantaneous Reaction

O of H3O+ = green O of H2O = red H hitH = white

rOH rHO rOHrHOrHOrOH

Exchange identities of H3O+ and H2O molecules

Move proton over to the newly formed hydronium ion so that rOH of the hydronium


Move proton over to the newly formed hydronium ion so that rOH of the hydronium before and after reaction are the same


Step 3. Local Equilibration• There is an increase in the potential energy of the system and disturbance of

structure

)85.1(3)6.1(2)85.1(2)6.1(3 OHOHOHOH 2OnH

)61(3)851(2)851(2)61(3 OHOHOHOH 2OnH

After reaction

During Local Equilibration

• Helps in restoring system structurally and maintaining the correct heat of reaction

Objective Function O of H3O+ = greenO of H O = red

)6.1(3)85.1(2)85.1(2)6.1(3 g q

j

RMS2

RMS1 )(rgwUwFobj

energetic term structural termO of H2O = redH = white

2

RMS

Before

BeforeAfter

UUU

U

Ni 2target


pairsNi

i ij

ijij

pairs rrr

Nrg

1target

targetRMS 1)(

Snapshot representing the complex hydrogen bonding network

m.

Proton Transport in Bulk Water

reaction: H3O+ + H2O H2O + H3O+

rate law: rate = k [H3O+][H2O]

from

S

. J. A

m. C

hem

RTEkk a

o exp

● Adjust triggers to fit erim

enta

l dat

a , Z

.; M

eibo

om,

c., 1

964.

j ggexperimental rate. ● Predict transport properties.

RMD rate constant within 6% of experiment.

Ch lf diff i it di ti

exp

Luz

Soc

Charge self-diffusivity prediction● semi-quantitative agreement with experiment● decomposition into structural and

hi l tvehicular components● structural is 60-70% of total● correct temperature dependence● structural and vehicular

t l t d


components are uncorrelated

d

rrrrD structvehstructveh

tot 2

2lim

22

Acidity and Confinement Effects on Proton Mobility

confinementci

dity

bulk water water in carbon nanotubes

a


bulk hydrochloric acid water in PFSA membranes

Water and Proton Transport in Nafion (Method 1)

Introducing structural diffusion into the simulation via the same RMD algorithm that was used for bulk water HCl solutions and water in carbon nanotubeswas used for bulk water, HCl solutions and water in carbon nanotubes● provided a correct quantitative trend ● but the total charge diffusivity was too large● the vehicular component significantly increased relative to nonreactive MD


The presence of reaction disturbs the local hydrogen-bonding network , resulting in higher mobility of protons (and water (not shown)).

Method 2: Attempt to better maintain hydrogen-bonding network after reaction

Include more water molecules in local equilibration after instantaneous reaction


Include more water molecules in local equilibration after instantaneous reaction.

Water and Proton Transport in Nafion (Method 2)

Method 1

Introducing a more stable hydrogen-bonding network after reaction ● provided a correct quantitative trend ● significantly improved quantiative agreement.

th hi l t i il t ti MD


● the vehicular component now similar to nonreactive MD

Still observed higher water diffusivity.

Correlations in Proton Transport

Fundamentals of Sustainable Technology The correlation term is zero in bulk water, HCl solutions and in carbon nanotubes.

Outline




III. Conclusions


morphology of bulk hydrated membrane

Nafion

EW = 1144= 6 H2O/HSO3 6 H2O/HSO3T = 300 K

Snapshots of the aqueousthe aqueous nanophase show a tortuous path.

legend:legend:O of H2O = redH= whiteO of H3O+ = greenS = orange


S = orangeremainder of polymer electrolyte not shown

PEM morphology is a function of water content

N fi (EW 1144) 6 H O/HSO N fi (EW 1144) 22 H O/HSONafion (EW = 1144) = 6 H2O/HSO3small aqueous channels

Nafion (EW = 1144) = 22 H2O/HSO3much larger aqueous channels

As the membrane becomes better hydrated, the channels in the aqueous domain become larger and better connected resulting in higher conductivity


become larger and better connected, resulting in higher conductivity.(The challenge to finding high-temperature membranes is to find one that can retain moisture at elevated temperatures.)

Determination of Diffusivities from MD Simulation

trtrMSDDii

lili2

Einstein Relation – long time slope of mean square displacement to observation time

position of particle i at

ddD

2lim

2lim

400) l bd 3

particle i at time t

Einstein Relation works well for bulk systems.

250

300

350pa

cem

ent

(Å2 ) lambda = 3

lambda = 6lambda = 9lambda = 15lambda = 22

. C20

10.

But for simulation in PEMs, we can’t reach the long-time limit

i d b Ei t i 100

150

200

n Sq

uare

Dis

p

J. P

hys.

Che

m

required by Einstein relation.

MD simulations alone0

50

00

0.0E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05 1.0E+06

Mea

n

Liu,

J. e

t al.

J


are not long enough.MSDs don’t reach the long-time (linear) regime.

time (fs)

Confined Random Walk Simulation

Mesoscale Model● non-interacting point particles (no energies, no forces)● sample velocities from a Maxwell-Boltzmann distribution M

., K

effe

r, 20

11 a

rticl

e

● sample velocities from a Maxwell Boltzmann distribution● two parameters○ cage size○ cage-to-cage hopping probability

t fit t MSD f M l l D i Si l ti Xion

g, R

., O

jha,

. Rev

. E, 8

3(1)

● parameters fit to MSD from Molecular Dynamics Simulation● runs on a laptop in a few minutes

ai S

elva

n, M

., X

gam

i, T”

, Phy

s.ño

z, E

.M.,

Esa

olso

n, D

.M.,

EgC

alvo

-Mu

D.J

., N

ich

# 01

1120

.


unsuccessful move successful move

Couple MD with Confined Random Walk (CRW) Theory

350

400lambda = 3lambda = 6l bd 9 M

., K

effe

r, 20

11 a

rticl

e

250

300

A2 )

lambda = 9lambda = 15lambda = 22

Random walk Model

Xion

g, R

., O

jha,

. Rev

. E, 8

3(1)

100

150

200

MSD

(A

ai S

elva

n, M

., X

gam

i, T”

, Phy

s.

0

50

100

ñoz,

E.M

., E

saol

son,

D.M

., Eg

00.0E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05 1.0E+06

time (fs)

● Fit MD results (1 ns) to Confined Random Walk (CRW) Theory

Cal

vo-M

uD

.J.,

Nic

h#

0111

20.


● Fit MD results (1 ns) to Confined Random Walk (CRW) Theory.● Extend Mean Square Displacement to long-time limit (100 ns).● Extract water diffusivity.

Comparison of MD/CRW Simulation with Experiment

1 0E+00

1.2E+00experiment

MD/CRW simulation

//

ns; 1

959.

cs19

97.

, J. P

hys.

8.0E-01

1.0E+00di

ffusi

vity

troly

te S

olut

ion

Sol

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tate

Ioni

c

wat

er

M.,

Kef

fer,

D.J

.50

04 ,

2011

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4.0E-01

6.0E-01

redu

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R. H

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// son,

R. A

.; S

tok

on (E

W=1

100,

)

self-

diffu

Selv

an, M

., C

am

. B,d

x.do

i.org

0 5 10 15 20 25 30water conent (water molecules/excess proton)

bulk

Rob

isN

afio

● Excellent agreement between simulation and experiment for water diff i it f ti f t t t

Esa

i SC

hem


diffusivity as a function of water content● Can we predict the self-diffusivity of water without computationally expensive simulations?

Outline




III. Conclusions


Three Factors: Acidity, Confinement & Connectivity

bulk water water in PFSA membranes

(Nafion EW=1144)

acid

ity

● H3O+ concentration is dilute H3O+ concentration● =3 H2O/HSO3, pH ≈ -0.59 (minimally hydrated)=5.6·108 H2O/H+ (pH=7)

ent

a ( y y )● =22, pH≈-0.22 (saturated)

interfacial surface area

conf

inem

e

● interfacial surface area is zero

● 163 Å2/H2O or 2460 m2/g (=3)● 23 Å2/H2O or 1950 m2/g (=22)(=22)

nect

ivity

● no connectivity issues

● connectivity of aqueous domain deteriorates as water


conn

● no connectivity issuescontent decreases

Acidity and Confinement Effects on Proton Mobility

confinementac

idity bulk water water in carbon nanotubes

a


bulk hydrochloric acid water in PFSA membranes

Water Mobility in Bulk HCl solutions – Effect of Acidity

1.1

3-9.

fusi

vity

0.9

1.0 experimentexponential fit

onic

s19

91, 4

6,

educ

ed s

elf-d

iff

0.7

0.8

. Sol

id S

tate

Io

re

0.5

0.6

T.; K

reue

r, K

. D

ckcDcD 1exp0

● In bulk systems the diffusivity of water decreases as the concentration

molarity (mol/l)

0 2 4 6 8 10

Dip

pel,

T


● In bulk systems, the diffusivity of water decreases as the concentration of HCl increases.● The behavior is well fit by an exponential fit.

Water Mobility in Nanotubes – Effect of Confinement

J. M

olec

.

1.8

Pad

diso

n, S

. J

usiv

ity

1.4

1.6 MD simulationexponential fit

, D. J

.; C

ui, S

.;

educ

ed s

elf-d

iffu

1.0

1.2

van,

M.;

Kef

fer,

10.

ckcDcD 1exp0

re

0 6

0.8 SAkSADSAD 2exp0

● In carbon nanotubes the diffusivity of water decreases as the radius of

Esai

Sel

vS

im.2

01

surface area (Å2/water molecule)

20 30 40 50 60 700.6


● In carbon nanotubes, the diffusivity of water decreases as the radius of the nanotube decreases.● The behavior is fit by an exponential fit.

Water Mobility in Bulk Systems – Effect of Connectivity

Invoke Percolation Theory to account for connectivity of aqueous domain within PEMand obtain effective diffusivity.

0)(1

20

dDDgDDz

DD

eff

eff

oEMAbEMA DDpDDpDg 1)(

Percolation theory relates the effective diffusivity to the fraction of bondsPercolation theory relates the effective diffusivity to the fraction of bonds that are blocked to diffusion.


no blocked bondsD = Dopen

some blocked bonds0 < D < Dopen

beyond thresholdD = 0

Structure-Based Analytical Prediction of Self-diffusivity

● Acidity – characterized by concentration of H3O+ in aqueous domain(exponential fit of HCl data)

● Confinement – characterized by interfacial surface area( ti l fit f b t b d t )(exponential fit of carbon nanotube data)

● Connectivity – characterized by percolation theory(fit theory to MD/CRW water diffusivity in PEMs)

. Phy

s.

1.0E+00

1.2E+00experiment

MD/CRW simulation

model - intrinsic D from HCl/CNT simulations

// Excellent agreement of theory with both simulation and experiment K

effe

r, D

.J.,

J.1.

6.0E-01

8.0E-01

uced

sel

f-diff

usiv

ity

experiment.

Theory uses only structural information to

o-M

uñoz

, E.M

.,1

pp 3

052–

3061

2.0E-01

4.0E-01redu predict transport property.

Water is solved!What about chargeel

van,

M.,

Cal

voB

115(

12) 2

011


0.0E+000 5 10 15 20 25 30

water content (water molecules/excess proton)bulk

//What about charge transport?

Esai

Se

Che

m. B

What about Proton Transport?

We have shown thus far that we can model the transport of water fairly accurately using either

1. detailed MD/CRW simulation (months on a supercomputer)2. analytical model based on acidity, confinement & connectivity

(minutes on a laptop computer)

We now want to repeat this process for protons. After all, it is the transport of protons that completes the electrical circuit in a fuel cell.

Why did we start with water?

Diffusion of water is easier to describeDiffusion of water is easier to describe.

Water is transported only via vehicular diffusion (changes in the center of mass of the water molecules).


There are two mechanisms for proton transport.

Proton Transport – Two Mechanisms

Vehicular diffusion: change in position of center of mass of hydronium ion (H3O+)

H

O of H3O+

translation

Structural diffusion (proton shuttling): passing of protons from water molecule to the next (a chemical reaction involving the breaking of a covalent bond)covalent bond)

O of H2O

proton

1 2 1 23 3


phops

In bulk water, structural diffusivity is about 70% of total diffusivity.

em.

Proton Transport in Bulk Water

reaction: H3O+ + H2O H2O + H3O+

rate law: rate = k [H3O+][H2O]

E a fro

m

m, S

. J. A

m. C

he

RTEkk a

o exp

● Adjust triggers to fit i t l t pe

rimen

tal d

ata

z, Z

.; M

eibo

omoc

., 19

64.

experimental rate. ● Predict transport properties.

RMD rate constant within 6% of experiment.

Charge self-diffusivity prediction

exp

Lu So

Charge self-diffusivity prediction● semi-quantitative agreement with experiment● decomposition into structural and vehicular componentsvehicular components● structural is 60-70% of total● correct temperature dependence● structural and vehicular components are uncorrelated


components are uncorrelated

d

rrrrD structvehstructveh

tot 2

2lim

22

RMD In Water

Proton Diffusion in Bulk Water

Non Reactive System R ti S tNon - Reactive System Reactive System


Vehicular Diffusion Structural and Vehicular Diffusion

Bulk HCl Solution: Effect of High Acidity

simulation snapshot periodic system15 H+

15 Cl-15 Cl1875 H2O= 125conc = 0.44 MpH = 0 36pH = 0.36

LegendO of H2O – redO of H O+ – green


O of H3O – greenH – whiteCl- – blue

Bulk HCl Solution: Effect of High Acidity

J.

data

from

. .;

Spe

edy,

R.

m.,

1984

, 88,

xper

imen

tal d

Cor

nish

, B. D

.. P

hys.

Che

m88

8.

• Total charge diffusivity follows the same trend as experimental value but is a bit

ex C J. 1

• Total charge diffusivity follows the same trend as experimental value but is a bit steeper

• Vehicular component of the charge diffusion is almost constant irrespective of the concentration


• Structural diffusion decreases with increases in HCl concentration and plays a major role in determining the dependence of charge diffusion on the concentration

Bulk HCl Solution: Effect of Acidity in an Analytical Fit

1 0E-08

1.2E-08

total self-diffusivity (expt) em.,

1984

.cs

, 199

1.

J., J

. Phy

s.

8.0E-09

1.0E-08

ty (m

2 /s)

y ( p )structural componentvehicular componenttotal self-diffusivity (model)structural component (model)vehicular component (model)

J. P

hys.

Che

id S

tate

Ioni

c

.M.,

Kef

fer,

D.J

1500

4 , 2

011.

4.0E-09

6.0E-09

self-

diffu

sivi

t

a fro

m.

peed

y, R

. J.

er, K

.D.,

Sol

i

alvo

-Muñ

oz, E

rg/1

0.10

21/jp

11

0.0E+00

2.0E-09

erim

enta

l dat

ani

sh, B

. D.;

Spe

l, Th

.; K

reu

i Sel

van,

M.,

Cem

. B,d

x.do

i.or

0 2 4 6 8 10molarity (mol/l)

• Experimental data for total value• Two assumptions (validated by RMD) for structural and vehicular components

expe

Cor

nD

ipp

Esa

Che


Two assumptions (validated by RMD) for structural and vehicular components• Decline in diffusivity due to pH is in the structural component• Structural and diffusive components remain uncorrelated

Proton Transport in Nanotubes: Effect of Confinement

Nominal radii from 5.42 to 10.85 Å.

Infinitely dilute simulations (1 excess H+)

Results averaged over 144 independent simulations.

Snapshots show H3O+

at pore wall with O atom extended

t doutward.


Esai Selvan, M. et al. Mol. Simul., 2010.


Density distribution of H3O+.

H3O+ is preferentially located at

0.008

0.0105.42 Å6.78 Å8.14 Å 3 p y

pore wall.

nsity

(g/c

m3 )

0.004

0.006

0.0089.49 Å10.85 Å

0 2 4 6 8 10 12

de

0.000

0.002

radial distance (Å)

orientation distribution of H3O+.

outw

ard

H3O+ is preferentially oriented with oxygen at the pore wall, so as to maximize hydrogen bonding network with 3 hydrogen O in

war

d

O p

aral

lel O o


network with 3 hydrogen. O


Mol

ec.

45%

percent of bulk value

n, S

.J.,

36(7

-8),

45%100%

i, S

., P

addi

son

12% Keffe

r, D

.J.,

Cu

8.ai

Sel

van,

M.,

Km

.pp.

568

–578


Confinement dramatically reduces structural diffusion.

Esa

Sim

Nanotubes: Effect of Confinement in an Analytical Fit

7.0E-09

8.0E-09total self-diffusivity (RMD)structural component (RMD)vehicular component (RMD) J. P

hys.

5.0E-09

6.0E-09

(m2 /s

)

vehicular component (RMD)total self-diffusivity (model)structural component (model)vehicular component (model)

M.,

Kef

fer,

D.J

., 50

04 ,

2011

.

3.0E-09

4.0E-09

self-

diffu

sivi

ty

vo-M

uñoz

, E.M

10.1

021/

jp11

15

0 0E+00

1.0E-09

2.0E-09

Selv

an, M

., C

alv

. B,d

x.do

i.org

/

• Two assumptions (validated by RMD) for structural and vehicular componentsD li i diff i i d fi i i h l

0.0E+000 10 20 30 40 50 60 70

surface area (Å2/water molecule) Esa

i SC

hem


• Decline in diffusivity due to confinement is in the structural component• Structural and diffusive components remain uncorrelated

Structure-Based Analytical Prediction of Self-diffusivity

● Acidity – characterized by concentration of H3O+ in aqueous domain(exponential fit of HCl data)

● Confinement – characterized by interfacial surface area( ti l fit f b t b d t )(exponential fit of carbon nanotube data)

● Connectivity – characterized by percolation theory(fit theory to MD/CRW water diffusivity in PEMs)

J. P

hys.

Good agreement of theory with experiment.

Theory uses only1.0E+00

1.2E+00experiment

model - intrinsic D from HCl/CNT simulations

//

., K

effe

r, D

.J.,

J50

04 ,

2011

.

Theory uses only structural information to predict transport property.6.0E-01

8.0E-01

ced

self-

diffu

sivi

ty

vo-M

uñoz

, E.M

10.1

021/

jp11

15

Proton transport is well-described by this simple model.2.0E-01

4.0E-01redu

elva

n, M

., C

alv

B,d

x.do

i.org

/1


0.0E+000 5 10 15 20 25 30

water content (water molecules/excess proton)bulk

//

Esai

SC

hem

.

Conclusions

Quantum Mechanics calculations provide understanding of structure of ground state and transition state for structural diffusion, activation energy and rate constant

Reactive MD simulations provide molecular-level understanding of coupling of reaction and diffusion in aqueous systems, carbon

t b d t h b id h t tinanotubes and proton exchange membranes, provides short time mean-square-displacements (MSDs)

Confined Random Walk theory extends MSDs from MD and yieldConfined Random Walk theory extends MSDs from MD and yield water self-diffusivities in excellent agreement with expt.

An analytical model incorporatingAn analytical model incorporating● acidity (concentration of H3O+ in aqueous domain)● confinement (interfacial surface area per H2O)● connectivity (percolation theory based on H2O transport)


y (p y 2 p )is capable of quantitatively capturing the self-diffusivity of both water and charge as a function of water content

Acknowledgments:

This work is supported by the United States Department of Energy Office of BasicThis work is supported by the United States Department of Energy Office of Basic Energy Science through grant number DE-FG02-05ER15723.

Access to the massively parallel machines at Oak Ridge National Laboratory through the UT Computational Science Initiative.


Myvizhi Esai SelvanPhD, 2010Reactive MD

Junwu Liu, PhD, 2009MD in Nafion

Nethika SuraweeraPhD, 2012Vol & Area Analysis

Elisa Calvo-MunozundergraduateConfined Random Walks

Relevant Publications 2007-2011

1. Esai Selvan, M., Calvo-Muñoz, E.M., Keffer, D.J., “Toward a Predictive Understanding of Water and Charge Transport in Proton Exchange Membranes”, J. Phys. Chem. B, dx.doi.org/10.1021/jp1115004 2011.2. Calvo-Muñoz, E.M., Esai Selvan, M., Xiong, R., Ojha, M., Keffer, D.J., Nicholson, D.M., Egami, T., “Applications of a General Random Walk Theory for Confined Diffusion”, Phys. Rev. E, 83(1) 2011 article # 011120.3 S ff C S S “ C f C3. Esai Selvan, M., Keffer, D.J., Cui, S., Paddison, S.J., “Proton Transport in Water Confined in Carbon Nanotubes: A Reactive Molecular Dynamics Study”, 36(7-8), Molec. Sim. pp. 568–578.†4. Esai Selvan, M., Keffer, D.J., Cui, S., Paddison, S.J., “A Reactive Molecular Dynamics Algorithm for Proton Transport in Aqueous Systems”, J. Phys. Chem. C 114(27) 2010 pp. 11965–11976.5. Liu, J., Suraweera, N., Keffer, D.J., Cui, S., Paddison, S.J., “On the Relationship Between Polymer Electrolyte Structure and Hydrated Morphology of Perfluorosulfonic Acid Membranes” J Phys Chem C 114(25) 2010 ppStructure and Hydrated Morphology of Perfluorosulfonic Acid Membranes , J. Phys. Chem. C 114(25) 2010 pp 11279–11292.6. Esai Selvan, M., Keffer, D.J., “Molecular-Level Modeling of the Structure and Proton Transport within the Membrane Electrode Assembly of Hydrogen Proton Exchange Membrane Fuel Cells”, in “Modern Aspects of Electrochemistry, Number 46: Advances in Electrocatalysis”, Eds. P. Balbuena and V. Subramanian, Springer, New York, 2010.†,7. Liu, J., Cui, S., Keffer, D.J., “Molecular-level Investigation of Critical Gap Size between Catalyst Particles and Electrolyte in Hydrogen Proton Exchange Membrane Fuel Cells”, Fuel Cells 6 2008 pp.422-428.8. Cui, S., Liu, J., Esai Selvan, M., Paddison, S.J., Keffer, D.J., Edwards, B.J., “Comparison of the Hydration and Diffusion of Protons in Perfluorosulfonic Acid Membranes with Molecular Dynamics Simulations”, J. Phys. Chem. B112(42) 2008 pp. 13273–13284.9 Li J E i S l M C i S Ed d B J K ff D J St l W V “M l l L l M d li f th9. Liu, J., Esai Selvan, M., Cui, S., Edwards, B.J., Keffer, D.J., Steele, W.V., “Molecular-Level Modeling of the Structure and Wetting of Electrode/Electrolyte Interfaces in Hydrogen Fuel Cells” J. Phys. Chem. C 112(6) 2008 pp. 1985-1993.10. Esai Selvan, M., Liu, J., Keffer, D.J., Cui, S., Edwards, B.J., Steele, W.V., “Molecular Dynamics Study of Structure and Transport of Water and Hydronium Ions at the Membrane/Vapor Interface of Nafion”, J. Phys. Chem. C 112(6) 2008 pp 1975-1984


C 112(6) 2008 pp. 1975-1984.11. Cui, S.T., Liu, J., Esai Selvan, M., Keffer, D.J., Edwards, B.J., Steele, W.V., “A Molecular Dynamics Study of a Nafion Polyelectrolyte Membrane and the Aqueous Phase Structure for Proton Transport”, J. Phys. Chem. B 111(9) 2007 p. 2208-2218.

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