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Cluster-continuum model study to guide the
choice of anions for Li+-conducting ionomers
Huai-Suen Shiau,1 Wenjuan Liu,2 Michael J. Janik,1
Ralph H. Colby2
1 - Department of Chemical Engineering
2 – Department of Materials Science and Engineering
Pennsylvania State University
Ion-containing polymers (ionomers) can offer “single-ion conduction”
Polymer-salt mixtures
Ionomers
+
 Advantage
of ionomers : avoid anion concentration polarization1
 Disadvantage of ionomers: the conductivity of ionomers is lower than that of
polymer/electrolyte mixtures2
(v3)
1) D. R. Sadoway et al. J. Power Sources 97-98 (2001) 621-623
2) Klein et al. Macromolecules 40 (2007) 3990
2
Computational method as a tool to aid in ionomer design
Overall objective: design ionomers for enhanced Li-ion conduction
Approach: Experimental synthesis and
characterization (Dr. Colby and collaborators),
quantum chemical calculations (Dr. Janik)
Question:
+ ionomers
find
the
anions
for
Li
side chain=?
A-=?
with high conducting ion fraction
scompositions
≈ emLiare
pLiextensive!
The choices for Li ionomer
+
– Side chains – Interact with Li to free? Solvate anion?
– Anion – weaken Li+ interaction? Avoid clustering?
(v3)
3
Model of ion states:
Four major ion states in ionomers
Free Ion
Ion Pair
Triple Ion
Quadrupole
(v3)
4
Four state model used to represent Li+ ion states in ionomers
Solvent separated pairs
observed in PEO-salt systems4
MD simulation1 sees ion clusters
SAXS data consistent with quadrupoles2
Charge carried by “interstitial pair”3
Four state model:
A-
Li+
Li+ AIon clusters
(quadrupoles)
Li+
A-
Li+ A-
or
Li+ A- Li+
A-
Ion pairs
Li+ +
A-
Separated ions
(free)
Charged ion clusters
(triple ions)
1) K. –J. Lin, J. Maranas. Unpublished
2) W. Wang et al. Macromolecules 43 (2010) 4223
3) M. Duclot et al. Solid State Ionics 136 –137 (2000) 1153
(v3)
5
Cluster-Continuum Model (CCM) can accurately capture local
and long-range solute-solvent interactions
Parameter: dielectric constant (εof diethyl ether used here).
dielectric continuum solvent
(long-range interaction)
 of diethyl ether used
Solvation free energies in DMSO at 298 K (kcal/mol)1
Cation
Expt
DFT/CCM
Li+
-132.5
-133.9
Na+
-106.2
-106.6
atomistic solvent, DME
(local interaction)
Cluster continuum model produces
solvation free energies in agreement
with experiment1-2
1) Tissandier et al, J. Phys. Chem. A 102 (1988) 7787
(v3) 2)
Bryantsev et al., J. Phys. Chem. B 112 (2008) 9709; Pliego Jr. and Riveros, J. Phys. Chem. A 105 (2001) 7241
6
Dimethyl Ether (DME) used as a model for PEO
length scale of QM: 150-200 atoms
Full representation of polymers is prohibitive
Modeling choices:
How many DME to include in cluster portion?
reduce PEO into
DMEn
cut
cut
cut
(v3)
7
Strongly bound DME identified and included in the explicit
cluster region
LiA + N DME  LiA(DME)N
N
PCM
PCM
PCM
Esolvation ( N )   ( E pair
 ( n 1) DME  EDME  E pair  nDME )
n 1
N=0
3
(eV)
2.5
state
2
E
1.5
1
0.5
PCM
(v3)
0
1
2
3
4
5
6
7
number of DME
8
9
10
8
Strongly bound DME identified and included in the explicit
cluster region
LiA + N DME  LiA(DME)N
N
PCM
PCM
PCM
Esolvation ( N )   ( E pair
 ( n 1) DME  EDME  E pair  nDME )
n 1
N=1
3
(eV)
2.5
state
2
E
1.5
1
0.5
PCM
(v3)
0
1
2
3
4
5
6
7
number of DME
8
9
10
9
Strongly bound DME identified and included in the explicit
cluster region
LiA + N DME  LiA(DME)N
N
PCM
PCM
PCM
Esolvation ( N )   ( E pair
 ( n 1) DME  EDME  E pair  nDME )
n 1
N=2
3
(eV)
2.5
state
2
E
1.5
1
0.5
PCM
(v3)
0
1
2
3
4
5
6
7
number of DME
8
9
10
10
Strongly bound DME identified and included in the explicit
cluster region
LiA + N DME  LiA(DME)N
N
PCM
PCM
PCM
Esolvation ( N )   ( E pair
 ( n 1) DME  EDME  E pair  nDME )
n 1
N=3
3
(eV)
2.5
state
2
E
1.5
1
0.5
PCM
(v3)
0
1
2
3
4
5
6
7
number of DME
8
9
10
11
Strongly bound DME identified and included in the explicit
cluster region: Example – Pair State
LiA + N DME  LiA(DME)N
N
PCM
PCM
PCM
Esolvation ( N )   ( E pair
 ( n 1) DME  EDME  E pair  nDME )
n 1
N=4
3
(eV)
2.5
N=3 sufficient
state
2
E
1.5
1
0.5
PCM
(v3)
0
1
2
3
4
5
6
7
number of DME
8
9
10
12
Strongly bound DME identified and included in the explicit
cluster region
LixAy + N DME  LixAy(DME)N
LiALi+:
N=6
3.5
Li+: N=4
N=4
LiALi+: N=6
3
E
LiALiA: N=4
state
(eV)
2.5
Li+: N=4
2
LiALiA: N=4
1.5
LiA: N=3
1
0.5
PCM
(v3)
0
ALiA-: N=2
1
2
3
4
5
6
7
number of DME
8
9
10
13
Solvated state energies can be used to determine the equilibrium
distribution among states
4DME
Separated ions
Li+ +
Li+ AIon pairs
3DME
A-
A-
Li+
A-
Li+ A-
Li+ Aquadrupoles
4DME
Negative triple ions
2DME
Li+ A- Li+
Positive triple ions
6DME
(v3)
14
TFSI-
FSI-
fraction of locally charged Li ion states
CCM model is necessary to get reasonable locally charged ion
concentrations, but not necessary for ranking of anions
0.01
TFSI- FSI-
PF6- BF4C6F5SO3 - CH3SO3CF3SO3C6H5SO3FCF3SO3-
10
-12
10
-22
s ≈ emLipLi
C6F5SO3 -
10
-32
Cluster continuum model
Gas phase, no solvation
10
-42
anion identity
Solvation necessary to predict charged ion fractions on order of magnitude of experiment
Solvation does not change the ordering of anions for maximizing charged Li+ concentration
(v3)
15
s ≈ emLipLi
Question:
what is the activation barrier to
Li+ hopping for conduction?
(v3)
16
Positive triple ion is also a conducting ion?!
Hypothesis: An interstitial cationic pair (called positive triple ion) is formed by dissociation
of an ion pair, followed by interstitial pair migration with the polymer motion.
1
1. M. Duclot et al., Solid State Ionics 136 –137 (2000) 1153 –1160
2. P. G. Bruce et al., J. Chem. Soc. Faraday Trans., 1993, 89(17), 3187-3203
3. Daniel Fragiadakis et al., JCP 130, 064907 (2009)
(v3)
Increase in molar conductance with salt content
was attributed to triple ion formation2, but also
A significantly
higher
ion mobility
was
possibly
to the increase
in dielectric
constant.
found in the higher ion content ionomers.3
(with a lower exponent n)
17
Li+ hopping between contact ion pairs
fixed 11 Angstrom S – S distance
Daniel Fragiadakis et al., JCP 130, 064907 (2009)
(v3)
18
Hopping potential energy surface
Li+A- Li+ A-Li+
3.5
CCM_3DME
PCM without DME
LiALi+: N=6
3
75
state
(eV)
2.5
55
E
Energy relative to contact triple ions (kJ/mol)
95
35
15
Li+A-Li+
2
LiALiA: N=4
1.5
LiA: N=3
1
0.5
Li+A-
A-Li+
3
4
5
6
7
Distance between S and Li (angstrom)
8
ALiA-: N=2
Li+A-Li+
0
-5 2
Li+: N=4
9
1
2
3
4
5
6
7
8
number of DME
0.6 eV = 58 kJ/mol
1. Specific solvation by 3 DME in the case of CCM_3DME can stabilize the transition
state by 39 kJ/mol, compared with the case of PCM without DME.
2. What if we add a fourth DME to the cluster?
Lower transition state by another 0.6 eV = 58 kJ/mol
and make separated triple ion more stable than contact triple ion!
(v3)
19
Hopping potential energy surface in the presence of 4DME
Li+ between two benzene sulfonate - Li+ ion pairs
Energy relative to separated pair (kJ/mol)
14
distance between two S is 11 angstrom
12
10
effective activation barrier
= 8.7 kJ/mol
~ 3.5 kT
8
6
4
2
0
3
(v3)
3.5
4
4.5
5
5.5
6
6.5
Distance between S and Li (angstrom)
7
7.5
8
20
Summary
Cluster-continuum model mimics solvation of
ionic states in PEO-based ionomers.
N=3
LiALiA: N=4
LiALi+: N=6
Energy relative to separated pair (kJ/mol)
14
distance between two S is 11 angstrom
12
Solvent-separated pairs are more stable
than contact ion pairs. The effective
activation barrier for S-S=11 angstrom
is about 3.5 kT.
10
8
6
4
2
0
3
(v3)
3.5
4
4.5
5
5.5
6
6.5
Distance between S and Li (angstrom)
7
7.5
8
21
Acknowledgments
Iman
Dr. Colby and his group
Dr. Janik and his group
All participants in the DOE project
Computational Support:
High Performance Computing Group at PSU
Penn State Materials Simulation Center
Funding:
National Science Foundation: CBET Energy for
Sustainability (CBET-0933391)
Hopping potential energy surface
Li+A- Li+ A-Li+
3.5
CCM_3DME
PCM without DME
LiALi+: N=6
3
75
state
(eV)
2.5
55
E
Energy relative to contact triple ions (kJ/mol)
95
35
15
Li+A-Li+
2
LiALiA: N=4
1.5
LiA: N=3
1
0.5
Li+A-
A-Li+
3
4
5
6
7
Distance between S and Li (angstrom)
8
ALiA-: N=2
Li+A-Li+
0
-5 2
Li+: N=4
9
1
2
3
4
5
6
7
number of DME
0.4 eV = 39 kJ/mol
0.6 eV = 58 kJ/mol
What if we add a fourth DME to the cluster?
Lower transition state by another 0.6 eV = 58 kJ/mole
and make separated triple ion more stable than contact triple ion!
8
Li-ion conductivity is affected by distribution of ions among various
states
s ≈ emLipLi
Relative energy
σ: conductivity
μLi: Li ion mobiliy
p Li : mobile Li ion concentration
Neutral Ion
Clusters
A- Li+
Li+ A-
Charged Ion Clusters
Li+-(O)n or AIon pairs
+
+
Li A Li
or
A-Li+
“Free” ions
A-Li+ADielectric spectroscopy modeling:
<0.004% of Li+ are mobile1
Hypothesis: Increasing the concentration of “locally charged” species will
increase conduction.
Assume concentration impact on conductivity is separable from mobility
Li+ states in ionomer
1) Klein et al., J. Chem. Phys. 124 (2006) 144903
Solvated state energies can be used to determine the equilibrium
distribution among states
[ACAC] =
q
[AC] =
ACAC ----> AC + AC
ACAC ----> CAC + A
ACAC ----> ACA + C
AC
----> A + C
p
[ACA] =
t2
[CAC] =
t1
[A] = f1 [C] =
f2
p2
2Epair  Equad
 exp(
)
q
RT
t1 f1
Epositvetriple  Equad
 exp(
)
q
RT
t2 f 2
Enegativetriple  Equad
 exp(
)
q
RT
f1 f 2
 Epair
 exp(
)
p
RT
t  f t  f
1
2
2
1
Charge balance
2q  2t1  t2  f 2  p  1
Mass balance (cation conservation)
Assumptions: Limited to the 4 states considered, ZPVE corrected 0K energy used
to consider equilibrium – no entropic considerations
(v3)
25
Li+
m
s = emp+
100% : Tg=240K
<49% : Tg=230K
electrode polarization (ionic polarization)
slowest mechanism
occur at lowest frequency
polymer relaxation (dipolar relaxation)
contribute to ion conduction
along polymer chains
faster mechanism
occur at higher frequency
1. If scale factor goes to infinity, the molecule is placed as if in vacuum even though
PCM is used.
2. The larger scale factor is, the weaker the interaction between solute and continuum
solvent is.
space between red
and blue circle is
vacuum
hypothetical atom radius
scale factor = 1.3
real atom radius
The scale factor is justified by considering that the first solvation layer does not
have the same dielectric properties as the bulk of the solvent.*
* Vincenzo Barone, J. Chem. Phys., Vol. 107, No. 8, 22 August 1997
Quadrupole/pair equilibrium dominates
smaller anion (d decreases)
increases
Quadrupole increases
Pair decreases
Locally positively charged states have small populations
Li+ A-
0.01
Li+ A10
-4
10
-6
10
-8
+
+
fraction of Li ions in state
1
Li+
+
Li+
10
-10
10
-12
fraction of Li ions in state
A-
1.2
1.6
2
2.4
1000/T
A-
2.8
3.2
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
2
Li+ A- Li+
Li+ +
2.2
2.4
2.6
A-
2.8
3
3.2
3.4
1000/T
>95% of ions are in aggregates at physically relevant temperatures
Fraction of charged species is 2x10-8 at room temperature
Triple ions are more populous than “free ions”
(v3)
32
Li+ vs Na+ with benzene sulfonate: ab initio model compared to
experiment
anion: C6H5SO3-
log[conducting ion fraction]
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
-4
Li
Na
y = -1.7405x
-5
-6
y = -2.3555x
-7
-8
1000/T (10 3K-1)
Ea (kJ/mol) C6H5SO3- (exp.) C6H5SO3- (model) C6F5SO3- (model) CH3SO3- (model) F - (model)
Li+
25.2 ± 0.5
45.1
40.5
48.8
67.8
Na+
23.4 ± 0.5
33.3
28.5
40.9
58.7
Li+ vs Na+: ab initio model matches dielectric spectroscopy model for Na+ vs Li+ (EaNa+ < EaLi+)
Discrepancy in slope of charged ion concentration versus 1000/T is 20 kJ/mol
(v3)
Expt data: The Journal of Chemical Physics 124, 144903
(2006)
33