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
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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
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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
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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
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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.
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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.
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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
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phops
In bulk water, structural diffusivity is about 70% of total diffusivity.
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
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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
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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
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J. Chem. Phys. 1998
MD simulations will only approximate the structures from Quantum Mechanics.
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
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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
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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)
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[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°
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rOO, Eigen ≤ rOO,Eigen,max rOO, hydration ≤ rOO,hydration,max Energetic Trigger
RMD Algorithm – Step 2
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
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Move proton over to the newly formed hydronium ion so that rOH of the hydronium before and after reaction are the same
RMD Algorithm – Step 3
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
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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
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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
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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
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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
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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
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● 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
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
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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
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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
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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
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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
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., X
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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
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3(1)
100
150
200
MSD
(A
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., X
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saol
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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.
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● 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
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, J. P
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.; S
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self-
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., 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
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diffusivity as a function of water content● Can we predict the self-diffusivity of water without computationally expensive simulations?
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
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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
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conn
● no connectivity issuescontent decreases
Acidity and Confinement Effects on Proton Mobility
confinementac
idity bulk water water in carbon nanotubes
a
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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
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elf-d
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0.8
. Sol
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0.5
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T.; K
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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
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● 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
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● 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.
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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
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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).
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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
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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
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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
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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
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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
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• 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)
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.M.,
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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
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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.
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Esai Selvan, M. et al. Mol. Simul., 2010.
Proton Transport in Nanotubes: Effect of Confinement
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
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network with 3 hydrogen. O
Proton Transport in Nanotubes: Effect of Confinement
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
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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
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• 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
Fundamentals of Sustainable Technology
• 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
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ty
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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
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/1
Fundamentals of Sustainable Technology
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)
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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.
Fundamentals of Sustainable Technology
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
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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.