Supporting Information
Globally Suppressed Dynamics in Ion-doped Polymers
Michael A. Webb, Umi Yamamoto, Brett M. Savoie, Zhen-Gang Wang, and
Thomas F. Miller III
∗
Division of Chemistry and Chemical Engineering, California Institute of Technology,
Pasadena, California 91125, USA
E-mail: tfm@caltech.edu
Contents
1 Simulation Details
SI-1
2 Ion-polymer Dynamics During Constant Coordination
SI-2
3 Rouse-mode Analysis Details
SI-5
4 Internal Mean-squared Distance Between Monomers
SI-7
5 Comparison to Experiment
SI-8
References
SI-10
1 Simulation Details
All simulations were performed using the LAMMPS simulation package
1
with GPU accel-
eration,
2,3
a velocity Verlet integrator with a 1 fs timestep, and a Nose-Hoover thermostat
SI-1
and barostat to control the temperature and pressure. The employed force field for PEO
4,5
and Li
+ 6
is the same as that described in previous studies
6–9
with additional parameters
for PF
−
6
taken from a validated force field for ionic liquids.
10,11
Here, the use of PF
−
6
as the
anion and a fixed-charge force field is motivated by simplicity rather than practicality, since
we are generically interested in the behavior of a polymer electrolyte with a dissociating salt.
Here, the LiPF
6
is almost entirely disassociated with the employed force field, and there are
no salt-rich/pure-polymer domains that may lead to dynamic heterogeneities.
12,13
Future
quantitative work may utilize polarizable force fields or more commercially relevant anions,
like TFSI
−
.
System preparation begins with constructing sixteen independent copies of a simulation
cell, each consisting of a single PEO chain of 640 monomers (
M
n
≈
28,000 g/mol) with
an initial conformation generated according to the RIS approximation.
14
The use of a long
chain suppresses global chain diffusivity, which is not expected to contribute significantly to
Li
+
diffusion for polymer electrolyte applications. Following minimization and condensation
using a previous protocol,
8
the sixteen simulation cells are replicated for each concentration
(to make a total of 5
×
16 = 80 simulation cells). Except for sixteen cells used to study
the neat polymer, Li
+
and PF
−
6
are randomly inserted into the remaining simulation cells to
obtain sixteen replicas at each Li
+
to oxygen ratio; in the case of the “dilute” simulations, a
single Li
+
is inserted into the simulation cell, and the system is neutralized with a uniform
background charge.
15
Each of the simulation cells are annealed for 25 ns at 500 K and
equilibrated for 25 ns at 400 K before production runs of 100 ns at 400 K.
2 Ion-polymer Dynamics During Constant Coordina-
tion
The results from Fig. 1 of the main text are obtained directly from unbiased molecular
dynamics (MD) simulations. Consequently, even at timescales less than the characteristic
SI-2
hopping time (Fig. 1c of main text), the Li
+
mean-squared displacement (MSD) contains
small contributions from Li
+
hopping that could affect the observed power-law scaling. More-
over, the data also is obtained from a mixture of Li
+
coordination structures, namely whether
the Li
+
is complexed by one or two contiguous polymer chain segments, and the impact of
coordination structure on Li
+
MSD and associated power-law scaling has not been previ-
ously studied. To explicitly investigate the ion-polymer dynamics without conflation from
ion-hopping or different coordination structures, we enforce either intra-chain or inter-chain
coordination of the Li
+
(Fig. S1a ); both coordination types are observed in unbiased MD
simulations. The coordination structures are achieved with the use of weak harmonic re-
straints on the distance between oxygen atoms at the center of the polymer chain with a
specific Li
+
; all other atoms in the system are left unconstrained. Fig. S1b characterizes the
ion-polymer co-diffusion for both types of coordination. A clear trend is that inter-chain co-
ordination results in slower diffusion across all concentration regimes. This may have general
implications for ion transport, since coordination by separate units is less favorable from the
standpoint of rafting contributions to the Li
+
diffusivity. On the other hand, the differences
between intra- and inter-chain coordination become less pronounced at higher concentrations,
suggesting that other factors govern the ion-polymer co-diffusion. The power-law scalings
(Fig. S1c) are qualitatively similar to those observed in Fig. 1b of the main text, confirming
key observations. Namely, the power-law scaling for the Li
+
MSD in the dilute regime is
greater than the expected
t
0
.
6
Rouse-like behavior, and a Rouse-like scaling is approached as
the salt concentration increases, albeit at later times compared to the neat polymer. These
results combine to show that the major trends identified with respect to the Li
+
MSD and
its power-law scaling are signatures of coupled ion-polymer motion.
SI-3
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