Mechanisms of Lithium Transport in Polymer Electrolytes

1
Mechanisms of Lithium Transport in Polymer
Electrolytes

• Yuhua Duan
• School of Physics Astronomy
• University of Minnesota
• Coworkers
• J. Woods Halley, Bin Lin, B. Nieson(UMN)
• L.A. Curtiss, M.-L. Saboungi, A. Baboul(ANL)
• Supported by DOE and MSI

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Outline

• Introduction of Polymer Electrolytes
• Theoretical Model Simulation Methods
• PolymerizationBuild simulation systems
• Ion Pairing in amorphous PEO
• Li Transport in amorphous PEO
• Conclusions

3
Polymer Electrolytes

• Ionically conducting solid materials display many
  advantages over their liquid counterparts
• Solid state material electrolyte and electrode
  are the new generation of devices to replace the
  conventional liquid electrolyte Power sources,
  Displays Sensor, etc.
• Polymer Electrolyte is a new type of solid state
  electrolytes. It is already used as battery(e.g.
  in computer), but can not use for automobile
  since its too heavy.

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Polymer Electrolyte Systems

• Lithium battery
• Li metal as anode has high energy and could be
  used to build high energy battery.
• Problem Li burn in water.
• Polymer Electrolyte can substitute for water
• True solid crystal and amorphous
• Local relaxations provide liquid-like degrees of
  freedom
• Compare with solid oxide electrolyte, it is not
  brittle and easy to make any kind of shape

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What Material can be Polymer Electrolytes?

• As electrochemical point of view, electrolyte
  satisfy
• Conductivity 10-2 10-3 S/cm
• Electrochemical stability at least as wide as
  the voltage window defined by electrode
  reactions
• Compatibility chemically and electrochemically
  compatible with electrode materials
• Thermal and Mechanical stability
• Availability easy to obtain raw materials at low
  cost.
• Except for the first criterion, polymer is a good
  candidate

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Polymer Electrolytes

• Drawback ionic conductivity is of the order of
  100 to 1000 times lower than other kinds of
  materials
• This drawback could be compensated by some
  factors
• Form thin films of large surface area giving high
  power levels(gt100W/dm3).
• Raise the temperature
• Add nano-particles, like TiO2
• It could be improved by investigating the
  mechanism of conductivity. Thats why this field
  is very important and useful.

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Conductivity of Polymer Electrolyte

• Conductivity at room temperature is lower of
  order of 100 to 1000
• Log(1/s) 1/T not linear, means not just one
  hopping mechanism ? System is very complicated

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Polymer Electrolytes

• Homopolymer hosts
• Polypropylene oxide(PPO) --(CH2CHCH3)O--n
• Polyethyline oxide(PEO) --(CH2)mO--n, m2
• Polyethylene iminie(PEI), Thia-alkanes
• Structure of pure PEO
• Tmp66?C, Tg?-60?C, soluble in H2O, CHCl3
• Chain-size from Experimental synthesis is very
  long. Can not relax long range, always get the
  amorphous structure.

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Radial Distribution Function of Amorphous PEO
Long range disorder
Chain Structure
Local order
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What Are We Interested In?

• Ion pairingthe act of anions during Li ion
  transport
• The mechanism of Li transport in the amorphous
  PEO
• Our research results could provide some advices
  for synthesis chemists to synthesize better
  electrolyte
• Using molecular dynamics(MD) simulation

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MD Method and Parameter Fitting

• MD method
• Motion equation d2ri(t)/dt2Fi(r)/mi
• Force calculation Fi(r)-dV(ri)/dri
• Particle motionVerlet algorithm
• ri(th)2ri(t)-ri(t-h)h2Firi(t)/mi
• v(t)(r(th)-r(t-h))/2h
• Thermostat to fix temperature
• (NPE), (NVE)
• Force field parameter fitting
• V(ri)VbondVangleVtorsionVNBVelectrostatic

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Force-field Parameter Fitting

• For PEO
• Choose certain length polymer, for different
  conformation, calculate potential energy with ab
  initio method by our cooperators at ANL.
• United model is used for CH2 CH3 groups
• Fit to analytic formula, get the parameter
• Compare with experimental results
• Ions with PEO
• Approach the ions to PEO with all different
  possible paths, calculate potential energy curve
• Fit to a analytic formula.

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Example of Fitting LiCl Interaction Potential

• Here just shown one result for fitting LiCl
  interaction potential

Vij(r)Ae-Br-C/r4-D/r6
E/r12QiQj/r
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Our Simulation Systems

• Build a little small amorphous system model
• As mentioned this kind of system is a
  non-equilibrium system and in amorphous
  experimentally
• Polymerization from Dimethyl Ether(CH3OCH3)
  liquid to build PEO system
• Imitate the experimental synthesis process
• Compare results with neutron scattering
  experimental results to test our model
• Adjust our model by control parameter in our
  algorithms until close to experimental results.

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PEO Simulation Model
.Using 216 DME to build this system . of Chain
23 .Longest chain size is 29 .shortest is 2
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Structure of PEO Model

• Here g(r) is weighted sum all of gij(r ) together
  
• Our results from our model(JCP,115(2001)3957)
  agree with the experimental results well?our
  model is reasonable.

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LiClO4 pairing in amorphous PEO

• Get the modelPut LiClO4 pair into our PEO Model
  randomly
• Potential of Mean Force Calculations
• Wmf-kBTln gLi-Cl(r)
• Problem only can get gLi-Cl(r) around local
  equilibrium, the sample region can not reach the
  short distance between Li and Cl.
• Fix LiCl separation, directly calculation the
  Wmf -----expensive way

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Ion-pair in PEO Model
Include 20 LiClO4 pairs
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Potential of Mean Force PEO216(LiClO4)
Two minimum 3.5Å 6.5Å
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Potential of Mean Force PEO216(LiClO4) by Radial
Distribution Function g
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Potential of Mean Force PEO216(LiClO4)5 by g(r)
Calculations
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Radial Distribution Function of PEO216(LiClO4)
--gLi-Cl(r) two peak-?two bound
states --gLi-O(r) coordinated O around Li is
about 6
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Radial Distribution Function of PEO216(LiClO4)5
--gLi-Cl(r) Compare with 1 pair case, the first
peak around 3.5Å is very small --gLi-O(r) the
coordinated O around Li is about 6. Each ClO4-
has 2 Li around it, for chain-like structure
Li--ClO4---Li
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Ion-pairing Conclusions(JCP,111(1999)3302)

• Two bound-states of LiClO4 in amorphous PEO
• From g(r) of PEO(LiClO4), Li has 6 Oxygen
  coordinates, one from ClO4-. In PEO(LiCl4)5, each
  ClO4- has about 2 Li near it
• Entropic contributions to the binding are
  significant for the first pair state(3.5?) at
  higher ionic densities, but not in the dilute
  simulations
• Li partial paired during transport, this could
  be one of the reason for the low conductivity
  since the net current is reduced during pairing
• To deal with this problem, we need to investigate
  other anions in our system since experimental can
  put other kinds of anions.

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Li Transport in Amorphous PEO

• We found ions transport in PEO bounce around
  during long time run, after that it has big jump
  (gt1.5?) within a short time.
• VoterPRB, 57(1998)R13985 Parallel Replica
  method
• Infrequent-event system can be exploited in a
  different way to develop an efficient parallel
  approach to the dynamics
• For a system in which successive transitions are
  uncorrelated, running a number of independent
  trajectories in parallel gives the exact
  dynamical evolution from state to state.

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Distribution of Times Between Rare Events

• We use this method to investigate the nature of
  Li move in the different conformation
• According to the assumption of Voters method,
  if this method is applicable, the of events vs.
  simulation time is exponential.

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Simulation Scheme

• Replica Initiate N copies of the simulation
  cell same position, but has different initial
  velocities
• Do ordinary MD for M steps(in out case, M1000)
• quench of N copies relax to local equilibrium
  at T0 K (our time-step is 0.42fs).
• Determine sum of changes(?) of all Li position
• If one of ? lt ?0, (?0 is fixed critical value,
  1.5Å), continue MD and quench
• If ? gt?0, an event found. Run this sample at
  finite temperature for a relaxation time. Then
  replica this sample to find another event

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Simulation Schemerare events
Start
No
Meet the criteria
Replica N sets of Data
Stop all Jobs Collect events
Parallel run MD
yes
Calculate more?
Replica new set of data
Yes
Stop
No
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Snap-shot of Li Moving
0
1
2
3
5
4
6
7
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Snap-shot of Li Moving_continue
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8
11
10
12
13
14
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Li Move Along Whole Simulation Time Scale

• This figure shows the Li movements along the
  long range(ns) and short range(ps)
• Sum of Li path movement ?(?rLi)2 is 138.69Å2
  long run 352.63Å2 short run

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Coordination of Li
The of O around Li within the radius of 2.4?
for 102 events
From this we can learn The O exchange events is
more reasonable for Li transport. Without O
exchange, Li could move back along with polymer
rearrangement.
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Li Diffusion Constant Calculations
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Simulation SchemePotential of mean Force Of Rare
Events

• Free energy surface of these hopping events can
  help to understand the Li transport.
• Potential of mean force(PMF) calculating scheme
• Along MD trajectory of the giving event, between
  the two quench fix Li at a succession of
  positions, let others move, record force on Li
  from it we can get PMF
• Move back before event found, move Li along same
  trajectory, do force calculation
• Also get PMF change(?) among them.

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Scheme of Potential of Mean Force Calculations
potential
some degrees of freedom
Event start
?
?
true trajectory
Li position
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Potential of Mean Force of Rare Events
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Conclusion for Li Transport

• The Lithium Motions Associated with Diffusion
  Occurred with the Order of ps Separated by long
  Rearrangement in the order of ns.
• The Calculated Diffusion Constant is Roughly
  Agreement with Experimental Results
• Primary Results shows the conductivity could be
  increased by Decreasing the Torsion Barrier.

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Further Work

• To investigate relations between torsion barrier
  and conductivity will get more info about Li
  transport
• To study the act of anions during Li transport
  by introducing more pairs and other kinds of
  anions(triflate, TFSI, etc.)
• Improve the algorism to study big system with
  long chain-size.