of 8
Systematic Computational and Experimental Investigation
of Lithium-Ion Transport Mechanisms in Polyester-Based
Polymer Electrolytes
Michael A. Webb,
Yukyung Jung,
Danielle M. Pesko,
Brett M. Savoie,
Umi Yamamoto,
Geo
ff
rey W. Coates,
Nitash P. Balsara,
,
§
,
Zhen-Gang Wang,
and Thomas F. Miller III
*
,
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
§
Materials Science Division and
Environmental Energy Technology Division, Lawrence Berkeley National Laboratory, Berkeley,
California 94720, United States
*
S
Supporting Information
ABSTRACT:
Understanding the mechanisms of lithium-ion
transport in polymers is crucial for the design of polymer
electrolytes. We combine modular synthesis, electrochemical
characterization, and molecular si
mulation to investigate lithium-
ion transport in a new family of polyester-based polymers and in
poly(ethylene oxide) (PEO). Theoretical predictions of glass-
transition temperatures and ionic conductivities in the polymers
agree well with experimental measurements. Interestingly, both
the experiments and simulations indicate that the ionic conduc-
tivity of PEO, relative to the polyesters, is far higher than would
be expected from its relative glass-transition temperature. The
simulations reveal that di
ff
usion of the lithium cations in the
polyesters proceeds via a di
ff
erent mechanism than in PEO, and
analysis of the distribution of available cation solvation sites in t
he various polymers provides a novel and intuitive way to explain the
experimentally observed ionic conductivities. This work provides a platform for the evaluation and prediction of ionic conductivities in
polymer electrolyte materials.
INTRODUCTION
Solvent-free, solid polymeric electrolytes (SPEs)
1
are of interest
for the development of safe, stable, and cost-e
ff
ective battery
technologies. Candidate SPEs typically require both a strong
coordinating a
ffi
nity for the conducting cation and a suitable
distance between coordinating centers.
2
,
3
Consequently, poly-
(ethylene oxide) (PEO) and PEO-based polymers have been
extensively characterized, although ambient temperature ionic
conductivities in such polymers are not satisfactory for many
practical applications.
4
,
5
Signi
fi
cant theoretical evidence suggests that ion transport
in polymers is intrinsically coupled to polymer motion.
6
15
In particular, numerous theoretical studies of ion transport in
PEO-based SPEs have shown that lithium cations are typically
coordinated by 4
7 oxygen atoms (from one or two independent
chains) and di
ff
use via three principal mechanisms: interchain
hopping, intrachain hopping, and codi
ff
usion with short polymer
chains (<10 000 g/mol). E
ff
orts to improve lithium-ion conduc-
tivity in PEO-based polymers have thus mainly focused on dis-
rupting polymer crystallinity an
d lowering the glass-transition
temperature
T
g
, such as through the use of
plasticizing additives,
16
,
17
cross-linked, comb, or graft polymer architectures,
18
22
incorpo-
ration of comonomers into the PEO backbone,
23
30
and polymer
blends.
31
,
32
Despite these e
ff
orts, ionic conductivities in state-of-the-
art, PEO-based SPEs remain lim
ited at ambient temperatures.
21
Non-PEO-based polymer architectures provide new opportu-
nities for enhancing ionic conductivity by altering ion
polymer and
polymer
polymer interactions and are thus of interest for the
design of next-generation SPEs. Io
nic conductivity characteristics
have been experimentally investigated in several novel polymers that
include polyesters, polyphosphaz
enes, polyamines, polysilanes,
polysiloxanes, and
polycarbonates.
33
40
However, few theoretical
studies on the mechanisms of ion transport in such polymers have
been performed, and it is not known to what extent the transport
mechanisms present in PEO are shared in other polymer archi-
tectures. The design of new SPEs requires an improved under-
standing of the mechanisms that facilitate lithium-ion transport in
polymers and the identi
fi
cation of new polymer architectures that
e
ffi
ciently realize these mechanisms.
Received:
May 21, 2015
Published:
July 10, 2015
Research Article
http://pubs.acs.org/journal/acscii
© 2015 American Chemical Society
198
DOI: 10.1021/acscentsci.5b00195
ACS Cent. Sci.
2015, 1, 198
205
This is an open access article published under an ACS AuthorChoice License, which permits
copying and redistribution of the article or any adaptations for non-commercial purposes.
Here, experimental synthesis and electrochemical character-
ization are combined with long
-timescale molecular dynam-
ics (MD) simulations to investigate lithium-ion transport
in six new SPEs. Figure
1
illustrates a schematic overview
of this approach. Modular synthesis produces six polyesters
that have either of two backbone motifs and one of three side
chains (Figure
1
, top). These polymers are then charac-
terized using both simulation and experiment (Figure
1
,
middle), which demonstrates the e
ff
ect of polymer
composition and architecture on ionic conductivity (Figure
1
,
bottom). By comparing experimental observables with the
corresponding quantities from simulation, we identify the
primary trends regarding polymer architecture and con-
ductivity. Agreement between simulation and experiment
then provides a connection between macroscopic properties
and molecular-level processes, which enables a detailed
theoretical analysis of the mole
cular processes that give rise
to the observed trends. This complementary approach provides
a better understanding of ion transport in novel polymer
electrolytes than would be obtained from either an independent
experimental or theoretical study.
POLYMER STRUCTURES
Six aliphatic polyesters with two di
ff
erent backbone motifs and
three di
ff
erent side chains are studied (Figure
2
). The repeat
unit for each is an ester with a pendant side chain. For ease of
reference, the polymers are in
dexed by number according to the
side chain and by letter according
to the backbone motif. Polymers
are indexed as type-1 for a methyl si
de chain, type-2 for an allyl side
chain, and type-3 for an et
hylene-oxide oligomer (
n
=2)sidechain.
The backbone motifs are indexed as type-a for polymers with
a methylene between the two carbonyl groups and type-b for
polymers with an oxygen between the two carbonyl groups.
Comparison between type-a and type-b polymers probes the
e
ff
ect of adding a binding site for the lithium cation in the
backbone. Similarly, comparison of type-1, -2, and -3 polymers
probes the e
ff
ect of including additional binding sites in the side
chain.
METHODS
Synthesis.
The polyesters are synthesized using the transition
metal-catalyzed alternating c
opolymerization of epoxides and
cyclic anhydrides.
41
43
See
Supporting Information
(SI) for
details. The polyester backbone structure is varied by copolymer-
izing glutaric anhydride (type-a) or diglycolic anhydride (type-b)
with
S
-propylene oxide (type-1), allyl glycidyl ether (type-2), or
2-((2-(2-methoxyethoxy) ethoxy) methyl) oxirane (type-3) as
shown in Figure
1
(top). Table
1
provides the number-averaged
molecular weight
M
n
and polydispersity index (PDI) for each
polymer; the polymers in this study exhibit molecular weights
that are su
ffi
ciently high to expect that variation in
M
n
among
the considered samples leads to only minor e
ff
ects on conduc-
tivity and
T
g
.
44
,
45
Simulation.
All MD simulations employ a united-atom
force
fi
eld, with bonding parameters taken from CHARMM
46
and all other parameters taken from the TraPPE-UA force
fi
eld;
47
50
compatible lithium-ion parameters are obtained from
previous simulation studies.
51
All simulations are performed using
the LAMMPS simulation package
52
with GPU acceleration.
53
,
54
The equations of motion are evolved using the velocity-Verlet
integrator with a 1 fs time step. Particle
particle
mesh Ewald
summation is used to compute all nonbonded interactions beyond
a14Åcuto
ff
.TheNose
́
Hoover thermostat (100 fs relaxation) is
used for all NVT simulations, and the Nose
́
Hoover barostat
(1000 fs relaxation) is used for all NPT simulations. Results in the
dilute-ion limit are obtained from simulations of a single lithium
cation di
ff
using in the polymer. Additional details of the simulation
protocols and all force-
fi
eld parameters are provided in the
SI
.
Figure 1.
A schematic overview of the study.
Figure 2.
Repeat units for polyesters. Oxygen atoms are colored
according to type: double-bonded carbonyl oxygens are green, ester
oxygens are orange, ether oxygens in the backbone are purple, and
ether oxygens in side chains are blue.
Table 1. Polymer Properties for Simulation and Experiment
simulation
experiment
M
n
(kDa)
N
c
a
T
g
(
°
C)
r
b
M
n
(kDa) PDI
T
g
(
°
C)
1a
2.54
11
35
0.0062
8.8
1.90
29
1b
2.57
11
47
0.0062
8.0
1.72
12
2a
2.45
12
37
0.0077
10.4
2.00
44
2b
2.47
12
49
0.0077
8.9
1.45
15
3a
2.57
11
39
0.0103
4.2
1.30
48
3b
2.59
11
41
0.0103
6.1
1.77
26
PEO
2.38
12
2
0.0139
5
c
n/a
60
a
Number of polymer chains.
b
Number of lithium cations per nine
polymer backbone atoms.
c
The measurements for
T
g
and conductivity
in PEO employ molecular masses of 4.6 kDa and 5.0 kDa, respectively.
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DOI: 10.1021/acscentsci.5b00195
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2015, 1, 198
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199
Characterization.
For each polymer,
T
g
measurements of
theneatpolymeraremadeusingdi
ff
erential scanning calorimetry.
Polymer electrolytes are then prepared by mixing neat polymer
sample with lithium bis(tri
fl
uoromethanesulfonyl) imide (LiTFSI)
salt and anhydrous
N
-methyl-2-pyrrolidone (NMP) in an argon
glovebox until dissolution at 90
°
C and drying under a vacuum at
90
°
C to remove excess NMP. Ionic conductivities of the polymer
electrolytes are determined fr
om ac impedance spectroscopy.
Additional details for both the
T
g
and conductivity measurements
are provided in the
SI
.
IONIC CONDUCTIVITY RESULTS
Using both simulation and experiment, we examine the ionic
conductivities of each polymer in the dilute-ion limit, which
minimizes complications associated with ion pairing and
aggregation.
Figure
3
a
c presents MD simulation results for the mean
square-displacement (MSD) of the lithium cation at 363 K.
The slopes of the MSDs on a log
log scale are less than unity
(
Table S5
), indicating that the transport is not yet in the fully
di
ff
usive regime even after 150 ns. Comparison of polymers 1a
and 1b (Figure
3
a) reveals that lithium-ion di
ff
usion is slowed
by the presence of the ether oxygen on the backbone. However,
this e
ff
ect is largely mitigated by the presence of side chains
with oxygen atoms, as seen by comparing polymers 2a and 2b
(Figure
3
b), and likewise for polymers 3a and 3b (Figure
3
c).
Comparison of polymers 3a and 1b shows that the di
ff
erences
in polymer architecture considered here at most a
ff
ect the
lithium-ion di
ff
usion by a factor of about 3.75. In contrast, the rate
of lithium-ion transport is at least
an order-of-magnitude faster in
PEO than in any of the polyesters. In particular, the relative span
of the subdi
ff
usive regime, which is the near-plateau region in
the MSD plots, reveals that the lithium cation is restricted to its
local solvation environment for substantially longer times in the
polyesters compared to PEO.
For comparison with experiment, the MSD results in
Figure
3
a
c are used to compute approximate lithium-ion
conductivities using the Nernst
Einstein equation
55
and the
apparent lithium-ion di
ff
usivity
6
evaluated at 150 ns (
Table S5
and Figure S21
). Figure
3
d compares these results with
experimental dilute ionic conductivities (see
SI
, section 7) at the
same temperature and e
ff
ective concentration as the simulations
(Table
1
).
Figure
3
d reveals good agreement between dilute-ion
conductivities obtained from experiment and those obtained
from MD simulations. This correlation for the relative ordering
of conductivities suggests that the lithium-ion dynamics are
mechanistically similar between simulation and experiment.
However, the dilute-ion conductivities obtained from simulation are
systematically lower than the corresponding experimental measure-
ments; for example, the conductivity for PEO obtained from
simulation is (9
±
4)
×
10
6
compared to (2
±
1)
×
10
4
S/cm.
This is possibly because the MD conductivity results re
fl
ect only
contributions from the lithium cation, whereas the experimental
measurements include both cation and anion contributions; of
course, it is also possibly due to inaccuracies of the employed MD
force
fi
eld. Furthermore, the molecular weights of the polymer
chains are smaller in the simulations than in the experimental
samples, though we do not expect this di
ff
erence to have a
substantial e
ff
ect on conductivity based on our knowledge of the
molecular weight-dependence on polymer electrolyte conductiv-
ity.
44
,
45
Polymer 1b is the only qualitative outlier in the correlation
between experimental and simulation results. This is likely because
polymer 1b is notably more solid in experiment, whereas this is not
the case for the MD simulations. Even so, the experimental con-
ductivities are all within a factor of 3 and an order-of-magnitude
smaller than PEO. Thus, both experimental and simulation results
indicate that the e
ff
ect of varying polymer architecture in the
polyesters is somewhat minor compared to the mechanistic
advantage that apparently exists for PEO. In the next section, we
investigate how di
ff
erences in
T
g
a
ff
ect the conductivity in these
polymers.
CORRELATING
T
g
WITH CONDUCTIVITY
Figure
4
a and Table
1
provide both experimental and simulated
values of
T
g
, which is often used as a proxy for the segmental
mobility of polymer chains.
2
,
56
Figure
4
a illustrates that the
experimental and simulation data are qualitatively similar by
plotting the data relative to the glass-transition temperature for
PEO,
T
g,PEO
. Consistently,
T
g
is lower for type-a polymers
relative to type-b polymers, which suggests that adding a polar
Figure 3.
Ion transport properties in the dilute-ion limit at 363 K.
Lithium-ion mean square-displacement (MSD) from MD simulations
in PEO and the (a) type-1 polymers, (b) type-2 polymers, and (c)
type-3 polymers. The data for PEO are reproduced in each panel. (d)
A comparison of experimental and simulated ionic conductivities; both
sets of data are normalized by the corresponding conductivity in PEO.
The error bars in (a
c) report the standard error of the mean
obtained from block-averaging four 500 ns trajectories for each
polymer; error bars in (d) report the sample standard deviation.
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200
ether oxygen between the two carbonyls decreases segmental
mobility. The experimental data also show a weak but con-
sistent side-chain dependence. Namely, increasing side-chain
length (type-1 < type-2 < type-3) leads to a slight reduction in
T
g
, possibly due to a plasticizing e
ff
ect by the side chains or
simply because the
fl
exible side chains constitute a larger volume
fraction of the polymer;
2
,
21
,
57
this particular trend is not as evident
in the simulated
T
g
data.
For the experimental data, Figure
4
b reveals the degree of
correlation between ionic conductivity and
T
g
by plotting the
dilute-ion conductivities (on a logarithmic scale) against
1000(
T
T
g
)
1
. This analysis is similar to a typical Vogel
Fulcher
Tammann ionic conductivity plot,
2
,
58
except that a range
of polymers (and thus a range of
T
g
)isexaminedata
fi
xed
temperature rather than the conductivity of a given polymer over a
range of temperatures. The dashed line is the linear
fi
tofthedata
for the polyesters only. Although there is an overall tendency for
polymers with lower
T
g
to have higher ionic conductivities, the
correlation is not well-characterized by a single line. In particular,
the
fi
gure shows strikingly that PEO
exhibits anomalously high
conductivity among this set of polymers when only the e
ff
ects
associated with changes in
T
g
(i.e., polymer segmental mobility)
are considered. We emphasize th
at the corresponding analysis
performed using the simulation data yields identical conclusions
(
Figure S25
). In the following section, we demonstrate that this
apparent anomaly in the conductivity of PEO can be understood
if the connectivity of lithium-ion solvation sites is additionally
considered.
LITHIUM-ION COORDINATION DYNAMICS
Using the results from the MD simulations, we now investigate
the mechanistic features of lithium-ion solvation and di
ff
usion
in the various polymer electrolytes to better understand the
anomalously high conductivity of PEO.
Figure
5
presents an analysis of the lithium-ion coordina-
tion environments that are observed in the MD simulations.
Representative MD snapshots of common lithium-ion coordi-
nation environments are shown in Figure
5
a for each polymer.
It is well-known from previous MD studies that lithium cations
are coordinated by one or two contiguous chain segments in
PEO;
6
,
7
examples of both of these binding motifs are shown at
the top of Figure
5
a. Interestingly, PEO is the only polymer
among those studied here for which the lithium cation is
frequently solvated by a single contiguous chain segment. This is
surprising, given that the backbone composition for the type-b
polymers is similar to PEO. Figure
5
a also reveals that the ester
oxygens on the backbone are not typically present in the lithium-
ion solvation shell for any of the polyesters. Comparison of the
type-1, -2, and -3 polymers reveals that the side chain can
drastically alter how the lithium cation is solvated by the polymer
chain. For type-1 polymers, the side chain has no a
ffi
nity for
the lithium cation, and the cation predominantly coordinates
with carbonyl oxygens on the polymer backbone. For type-2 and -3
polymers, oxygen atoms on the side chain do interact with the
lithium cation. In fact, type-3 polymers coordinate lithium cations
entirely with the PEO-like side chains.
To provide a more quantitative view of the lithium-ion
solvation environments, Figure
5
b shows the average com-
position of the lithium-ion coordination environment in each
polymer. Interestingly, the statistics for the type-3 polymers are
nearly identical to each other and similar to those of PEO.
There is also marked similarity between the PEO snapshot with
two coordinating chains and the snapshots for the type-3
polymers in Figure
5
a. Whereas PEO coordinates the lithium
cation with one or two chains, two to four polymer chains typically
coordinate the lithium cation in the polyesters. Compared to the
other polyesters, the type-3 polymers require fewer chains to
coordinate the lithium cation, likely due to the coordinating ability
of the PEO-like side chains. Additionally, a comparison of polymer
1a with 1b, and likewise for polymer 2a with 2b, indicates that
fewer chains participate in lithium-ion coordination when polymers
have an additional oxygen atom in the backbone. It is worth noting
that the only ether contribution for the type-a polymers is due to
the terminal groups of the polymer chain (see
SI
, sections 4 and 8).
However, additional simulations reveal that this is a minor e
ff
ect
(
Figure S24
).
To elucidate the compositional di
ff
erences in the lithium-ion
coordination environment for each polymer, Figure
5
c presents
the frequency with which di
ff
erent lithium-ion binding motifs
are observed in the simulations. The binding motifs are identi
fi
ed
by the number of each type of oxygen in the lithium-ion solvation
shell and by the number of chains that participate in lithium-ion
coordination. An array of binding motifs is observed in the type-1
and -2 polymers. In contrast, only one or two binding motifs are
observed for polymers 3a, 3b, and also PEO. These results reveal
a trend in which lithium cations that coordinate with more
polymer chains also have more diversity in the observed binding
motifs. It is interesting that the major binding motif for both the
type-3 polymers and PEO is 006-2, or six ether oxygen atoms
from two di
ff
erent polymer chains, even though PEO exhibits
substantially higher conductivity. These results indicate that the
composition of the
fi
rst lithium-ion solvation shell does not fully
explain the trends in Figure
3
d.
To characterize the lithium-ion solvation environment beyond
the
fi
rst lithium-ion solvation shell, Figure
5
d presents pair radial
distribution functions (RDFs) for the lithium cation and each
type of oxygen atom in the type-a polymers and in PEO; the
Figure 4.
(a)
T
g
obtained via experiment using DSC (open symbols)
and via MD using simulated dilatometry (
fi
lled symbols). (b)
Correlation between dilute-ion conductivity and the inverse temper-
ature di
ff
erence from
T
g
at
T
= 363 K (experimental measurements).
The dashed line indicates the linear
fi
t of the data for the polyesters.
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201
corresponding RDFs for the type-b polymers are shown in
Figure S26
. Figure
5
d reveals that the types of oxygen atoms
that are present in the
fi
rst peak, which is the lithium-ion solvation
shell as discussed for Figure
5
a
c, are absent or depleted in the
second peak. For the type-1 and -2 polymers, the
fi
rst peak, which
occurs at approximately 2 Å, has only backbone contributions
from carbonyl and ether oxygens; the second peak, which occurs
at 4
4.5 Å, is mostly comprised of ester oxygens. For type-3
polymers, side-chain ether oxygens are found in the
fi
rst peak but
not in the second. This di
ff
erence in composition between the
fi
rst and second solvation shells suggests one reason for the faster
lithium-ion di
ff
usion in PEO. Namely, di
ff
usion events in which
the lithium cation escapes from its existing coordination environ-
ment to a neighboring environment are more likely to occur in
PEO because the composition of atoms in the second solvation
shell is similar to the
fi
rst. Consequently, a binding motif com-
prised of atoms in the
fi
rst solvation shell is roughly equal in free
energy to a binding motif that has some atoms in the
fi
rst solva-
tion shell exchanged for atoms in the second. In contrast, for the
polyesters, atoms in the second peak are not typically represented
in the binding motifs enumerated in Figure
5
c, which indicates
that binding motifs with those atoms are energetically less
favorable.
To understand how these di
ff
erences in lithium-ion solvation
a
ff
ect the conductivity, Figure
6
illustrates the displacement
and coordination environment of the lithium cation in a long
MD simulation for PEO and for polymer 3b. Figure
6
a,b
illustrates changes in lithium-ion coordination environment by
tracking the indices of oxygen atoms that are within 3.25 Å of
the lithium cation. In particular, each oxygen atom in the
system is labeled sequentially, starting at one end of a polymer
chain and continuing to the end of that chain before proceeding
to the next; the oxygen atoms are consecutively labeled from
1 to 648 for PEO and from 1 to 759 for polymer 3b. What appear
as solid lines in the
fi
gure are actually formed from the markers of
contiguous oxygen indices, as seen in the inset; thicker lines
typically consist of
fi
ve or six markers, and thinner lines typically
consist of three markers. Figure
7
c,d shows changes in the
Figure 5.
Analysis of lithium-ion coordination data from MD simulations at 363 K. (a) Representative snapshots of lithium-ion binding motifs
observed in the MD simulations. The lithium cation is shown in silver, carbon atoms are black, and the oxygen atoms are colored according to the
scheme in Figures
2
and
5
b. (b) The average number of oxygen atoms (left
y
-axis) and polymer chains (right
y
-axis) in the
fi
rst solvation shell of the
lithium cation. Vertical bars report the number of di
ff
erent oxygen types; markers report the number of coordinating chains in the solvation shell.
Note that backbone ether contributions to the type-a polymers arise due to interactions with the terminal groups of the polymer chains. (c)
Frequency of occurrence for lithium-ion binding motifs, where the binding motifs are de
fi
ned according to the number of each oxygen type and the
number of coordinating chains. The
fi
rst three numbers refer to the number of carbonyl, ester, and ether oxygen atoms, respectively; the number
following the dash refers to the number of di
ff
erent contiguous polymer chain segments (i.e., 402-2 indicates a motif with four carbonyl oxygens,
zero ester oxygens, and two ether oxygens from two di
ff
erent chains). Only binding motifs that constitute more than 5% of the ensemble are
explicitly listed; the remainder are included in
other
. (d) Cation-oxygen radial distribution functions
g
Li+,o
(
r
) for di
ff
erent oxygen types in the type-a
polymers and in PEO. The
g
Li+,o
(
r
) for each oxygen type is normalized with respect to the total oxygen number density in the polymer. Following the
data set for polymer 1a, each subsequent data set is shifted vertically (by 5 units) and horizontally (by 1 Å) for clarity. All statistical properties a
re
calculated from snapshots taken at 100 ps intervals during the MD trajectory. A threshold distance of 3.25 Å from the lithium cation is used to
identify constituents of the
fi
rst lithium-ion solvation shell.
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202
lithium-ion position by tracking the net displacement of the
lithium cation from its initial position.
From Figure
6
a,b, it is clear that one characteristic of PEO is
that the lines
fl
uctuate and drift during the simulation, whereas
the lines for polymer 3b are comparatively static. This drift in
oxygen indices is a signature of intrachain hopping of the lithium
cation to adjacent monomers along the polymer backbone.
Notably, PEO is the only polymer studied that illustrates this
behavior. Intrachain hopping events are not observed in the type-
3 polymers because the lithium cation is localized to the side
chains (
Figure S27
). Similarly, the lithium cation is localized
between the two carbonyl groups on the backbone for the type-1
and -2 polymers, which also do not exhibit signi
fi
cant intrachain
hopping events (
Figure S28
).
Because intrachain hopping is not a viable mechanism in the
polyesters, lithium cations are limited to di
ff
usion via interchain
hopping events and codi
ff
usion with the polymer chains. Changes
in coordination that correspond t
o interchain hopping events are
highlighted by the vertical, red dashed lines in Figure
6
. Figure
6
c,d
illustrates that signi
fi
cant lithium-ion displacements often
coincide with these events. However, the lithium cation in
polymer 3b is limited to local
fl
uctuations during time intervals
between interchain hopping events. It is evident that interchain
hopping is a rare event that occurs on the 100 ns timescale,
even in PEO. Thus, the presence of intrachain hopping in PEO is
the primary reason for the faster lithium-ion di
ff
usion compared
to the polyesters.
To illustrate why these mechanistic di
ff
erences arise, Figure
7
a
shows viable cation solvation sites in polymer 3a, 3b, and PEO,
which are obtained from snapshots of the corresponding MD
simulations for each polymer. Here, viable solvation sites are
considered to be arrangements of atoms in the polymer that
are consistent with common binding motifs found in Figure
5
c; for
the polymers in Figure
7
a, sites are de
fi
ned as the centroid of a set
of
fi
ve or more ether oxygen atoms if each oxygen is also within
3.7 Å of that centroid. Sites are connected in the
fi
gure if they
are closer than 3 Å to provide a qualitative understanding of avail-
able hopping events. It is clear that far fewer viable solvation sites
are identi
fi
ed in the type-3 polymers than for PEO; similarly sparse
networks characterize the type-1 and -2 polymers (
Figure S29
).
In contrast to the isolated clusters in the polyesters, PEO features a
well-connected network of viable solvation sites by virtue of the
compositional overlap between
fi
rst and second solvation shells for
the lithium cation (Figure
5
d).
To quantify the degree to which the various polymers exhibit
connected networks of solvation sites, Figure
7
b provides the
density of 3 Å connections between solvation sites, termed the
connectivity, for each polymer. It is evident that the connec-
tivity for PEO is an order-of-mag
nitude greater than any of the
polyesters. The similarity between Figure
7
bandFigure
3
dis
striking, indicating a strong rela
tionship between connectivity and
lithium-ion conductivity. The concept of connectivity provides an
intuitive and potentially powerful explanation for the e
ffi
ciency of
the intrachain hopping mechanism in PEO. In an intrachain
hopping event, the lithium cation e
ff
ectively migrates up or down
one polymer chain by exchangin
g a small number of solvating
oxygen atoms. Here, this process is represented as a transition
along an edge in the solvation-site network. Unlike the polymer
architecture of the polyesters, th
e topology of PEO facilitates these
transitions among solvation sites.
CONCLUSIONS
This study combines experimental and theoretical approaches
to investigate the mechanisms of lithium-ion transport in six
new polyester-based polymer electrolytes, as well as PEO.
The modi
fi
cations to polymer architecture considered are
shown to signi
fi
cantly alter the lithium-ion solvation environment
Figure 6.
Analysis of changes in lithium-ion coordination with changes
in lithium-ion position. Lithium-ion coordination environment for
(a) PEO and (b) polymer 3b (markers denote coordination with
oxygen for at least half of a 100 ps interval). The horizontal gray lines
demarcate separate polymer chains. The inset in (a) illustrates the
coordination over a 40 ns segment in the trajectory. Lithium-ion
displacement from initial position in (c) PEO and (d) polymer 3b.
The gray curve indicates the instantaneous displacement from the
initial position, and the black curve indicates the rolling average over
100 ps intervals. Vertical, red lines highlight interchain hopping events.
Figure 7.
Analysis of lithium-ion solvation sites. (a) Viable solvation sites (green spheres) in representative con
fi
gurations of polymer 3a, polymer 3b,
and PEO. Sites connected by lines if they are within 3 Å to illustrate the relative connectivity. The polymer con
fi
guration is shown in the transparent
representation. (b) The connectivity density of lithium-ion solvation-site networks for each polymer. Reported data are obtained from averaging o
ver
16 MD trajectory snapshots.
ACS Central Science
Research Article
DOI: 10.1021/acscentsci.5b00195
ACS Cent. Sci.
2015, 1, 198
205
203
and e
ff
ectively change whether the lithium-ion transport is
side-chain- or backbone-mediated. These changes a
ff
ect the
ionic conductivity by a factor of 3. In contrast, the ionic con-
ductivities of the polyesters are about an order of magnitude
lower than in PEO (Figure
3
d). Because the glass-transition
temperature of PEO is only modestly lower than that of some
of the polyesters, the observed trends with ionic conductivity
are not adequately explained on the basis of polymer segmental
mobility (Figure
4
b).
To understand the anomalous di
ff
usivity of PEO, the MD
simulations are employed to perform an extensive analysis of
the lithium-ion solvation and di
ff
usion mechanisms in the various
polymers. We
fi
nd that PEO is the only polymer studied that
frequently coordinates a lithium cation with a single chain or
exhibits signi
fi
cant intrachain hopping of the lithium cations. This
is primarily because the
fi
rst and second lithium-ion solvation
shells di
ff
er signi
fi
cantly in composition for all of the polyesters
(Figure
5
d). Lithium-ion di
ff
usion in the polyesters thus relies
upon interchain hopping events, which occur infrequently on
the 100 ns timescale, and codi
ff
usion with the polymer chains,
which is intrinsically slow (Figure
6
).
This analysis reveals that the anomalously high conductivity
of PEO (Figure
3
d) can be easily understood in terms of a
description of lithium-ion di
ff
usion based on the density and
proximity of viable solvation sites (Figure
7
a). Whereas PEO fea-
tures a well-connected network of viable solvation sites, the
polyesters have isolated cl
usters of sites that hinder e
ffi
cient lithium-
ion conduction. A simple metric of connectivity predicts an order-
of-magnitude higher conductivity for PEO than the polyesters
(Figure
7
b). Knowledge of the solvation structure, including attri-
butes of the second solvation shell, the connectivity between solva-
tion sites, and the number of chains involved in the coordination
appears to provide a powerful tool for the design of future SPEs.
ASSOCIATED CONTENT
*
S
Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website
at DOI:
10.1021/acscentsci.5b00195
.
Synthesis details; simulation protocol details; electro-
chemical characterization details; description of terminal
groups in MD simulations; force-
fi
eld parameters for MD
simulations; apparent di
ff
usivities in simulations; dilute-ion
conductivity measurement details; discussion of terminal
group interactions with lithium cation in type-a polymers;
correlation between
T
g
and conductivity for MD simulations;
lithium cation-oxygen radial pair distribution functions for
all polymers; coordination plots showing the localization
of lithium cation in type-1, -2, and -3 polymers; snapshots
of solvation-site networks in all polymers (
PDF
)
AUTHOR INFORMATION
Corresponding Author
*
E-mail:
tfm@caltech.edu
.
Notes
The authors declare no competing
fi
nancial interest.
ACKNOWLEDGMENTS
This research was supported by the National Science Foundation
under DMREF Award Number NSF-CHE-1335486. M.A.W. also
acknowledges support from the Resnick Sustainability Institute.
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