Theoretical HighPerformance Approach to the Study of Mechanisms of Lithium Transport in Polymer Elec

1
Theoretical High-Performance Approach to the
Study of Mechanisms of Lithium Transport in
Polymer Electrolytes

• Yuhua Duan
• Department of Chemical Engineering and Materials
  Science
• University of Minnesota

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Outline

• Introduction to Polymer Electrolytes
• Theoretical Model Simulation Methods
• Force Field Parameterization
• Build Amorphous PEO Simulation System
• Ion Pairing in Amorphous PEO
• Li Transport in Amorphous PEO

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Battery
Chemical energy
Electrical energy
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Battery Structure
Cathode
Anode
separator
electrolytes
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Lithium ion battery

• Li metal as anode has high energy density and
  could be used to build high energy battery.

• Problem Li burns in water.
• To solve this problem, Use solid materials as
  electrolytes.

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Lithium Ion Polymer Battery

• Conducting electrolytes practical quantities of
  very ionic lithium salts (LiClO4, LiBF4, LiPF6,
  LiCF3SO3, etc) dissolved in polymer. No
  traditional separator needed.
• Anode Li insert into graphite LiC6
• Li?Lie-
• Cathode non-aqueous LiCoO2 , TiS2, LiMn2O4
• xe-xLiTiS2?LixTiS2 or xe-xLiLiMn2O4?Li
  1xMn2O2

1mm
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Solid Electrolytes

• Ionically conducting solid materials display many
  advantages over their liquid counterparts
• Virtually unlimited shelf life
• Wide operating temperature range
• High energy density and voltage density
• No gassing, corrosion or leakage
• Leakproof design and safety

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Polymer Electrolytes

• Polymer Electrolyte is a new type of solid state
  electrolytes. It is already used in battery, but
  such battery can not use for driving automobile
• Properties of polymer Electrolytes
• True solid crystal and amorphous
• Local relaxations provide liquid-like degrees of
  freedom
• Compare with solid oxide electrolyte, polymer
  electrolyte is easy to make different shape

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What Material can be Polymer Electrolytes?

• As electrochemical point of view, electrolyte
  should 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, Polyethylene
  oxide(PEO) and related polymers are good
  candidates

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PEO Related 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 some by some
  factors, but still not meet the required level
• Form thin films of large surface area giving high
  power levels (gt100W/dm3).
• Raise the temperature.

• It could be improved by investigating mechanism
  of conductivity. Thats why this field is very
  important and useful.

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Polyethylene Oxide (PEO)

• Structure formula --CH2CH2O--n,
• Tmp66?C, Tg?-60?C, soluble in H2O, CHCl3
• Chain-size from experimental synthesis is very
  long. Always get amorphous structure at room
  temperature.
• NMR experimental established that Li moves
  through the amorphous portions of the polymer.

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Computational Goals and Approach

• To understand Li transport and ion pairing
  mechanisms in amorphous PEO in order to guide
  synthetic chemists in the search for better
  materials.
• To treat the non-thermo-equilibrium system and
  face the long time scale simulations
• Our approach is to build molecular dynamics (MD)
  model of the amorphous regions of the PEO for
  simulation by ab initio parameterization of the
  force field
• Studying system PEO with Li ClO4-

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Molecular Dynamics(MD) Method

• MD method
• Newtons 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
• (NPE), (NVE) periodic boundary condition applied
• The force field of the model system
• VVintraVinter

• Coding Serial and Parallel with MPI.

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Intra-molecular Potential for PEO and ClO4-
Force-field Parameter Fitting

• Calculate the vibrational frequencies for
  isolated dimethyl ether(DME) and ClO4- with ab
  initio method (Gaussian94 98 package).
• Using the analytical formula to fit the
  frequencies by changing the parameters.

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Fitting Procedure

• With the analytical potential form and trial
  parameters, to form the 3Nx3N Hessian matrix
  which is the second partial derivatives of the
  potential V with respect to displacement of the
  atoms.
• Diagonalize this matrix.
• A set of 3N eigenvectorsnormal modes
• 3N eigenvalues? frequencies square
• Compare with ab initio results, adjust the
  parameters, until these two results are very
  close to each other.

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Geometry and vibrational frequencies of DME
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Bond length and frequencies for ClO4-
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Inter-molecular Force Field

• PEO chainPEO Chain
• United model is used for CH2 CH3 groups
• Most force parameters are taken from other work
• Li or ClO4- PEO Li or ClO4- Li or ClO4-
• Approach the ions to PEO with different possible
  paths, calculate potential energy curve
• Fit to an analytical form.

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Example C of PEO with Cl of ClO4-
16 approach configurations
ClO4-
DME
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PEOClO4- Parameterization
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Fitted Inter-molecular Potential Parameters
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Building Simulation Systems

• The system is in a meta-stable non-equilibrium
  amorphous state at room temperature. We can not
  get structure from crystal.
• We use a computational polymerization method to
  simulate the polymer configuration starting from
  Dimethyl Ether(CH3OCH3) liquid
• Imitate the experimental synthesis process
• Compare results with neutron scattering
  experimental results to test our model
• Adjust our model by a control parameter in our
  algorithms until close to experimental results.

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Polymerization Procedure

• Step 1 Put certain of DME into system, pick a
  CH3 center from the end of a chain at random
• Step 2 Explore a sphere(gtCH2-CH2 bond length)
  around this center. If no chain end found within
  the sphere, go back to step 1.
• Step 3 Change the inter-molecular force to
  intra-molecular. Change mass of CH3 to CH2
• Step 4 Run MD to quasi-equilibrium for giving
  annealing time ta to produce amorphous
  structures, ta is our control parameter to get
  characteristically different structure
• Go back to step 1 until no more bonds can be
  formed. Count and list the chains formed
• Compare with experimental to adjust ta.

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PEO Simulation Models

• Using 216 DME to build this system
• of Chains 23
• Longest chain size is 29
• shortest is 2
• Total atoms 1080

• 1728 DME
• of Chains 165
• Longest Chain-size 46
• Total atoms 8640

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Structure of PEO Model

• Here g(r) is weighted sum all of gij(r ) together
  

• The results from our model(JCP,115(2001)3957)
  agree with the experimental results well? our
  model is reasonable

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Ion Pairing in the Polymer

• Ion pairing can significantly reduce the lithium
  ion conductivity. Even if the Li-anion pair is
  mobile, no net charge may be conducted
• Experimentally the degree of pairing depends on
  the identity of the anion but no principles guide
  the choice of what anion
• To explore if Li and ClO4- are paired in PEO
• Get the modelPut LiClO4 pair into our PEO Model
  randomly, run MD to local equilibrium state

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LiClO4 pairing in amorphous PEO

• Potential of Mean Force Calculations
• Wmf-kBT ln 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.
• For one pair case, we can fix the LiCl
  separation, directly calculation the Wmf
  -----expensive way since extensive sampling is
  needed.

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Radial Distribution Function of PEO(LiClO4)

• gLi-Cl(r) two peak?two bound states
• gLi-O(r) coordinated O around Li is about 6

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Potential of Mean Force PEO(LiClO4)
Calculated from g(r) T280K
Direct calculated

• Simulate at 5 different temperatures
• For g(r) calculation, we take average about 15
  different configurations, for direct calculation,
  we take average more than 50 different
  configurations
• Two bound states are found from both calculations
• No obvious entropy contribution in these two
  bound states

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Radial Distribution Function of PEO(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, at least one from ClO4-
• Each ClO4- has 2 Li around it, form chain-like
  structure Li--ClO4---Li

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Potential of Mean Force PEO(LiClO4)5 by g(r)
Calculations
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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
  neighbors. In PEO(LiCl4)5, each ClO4- has about 2
  Li near it
• 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 to help
  experimentalists choose right cathode materials

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Li Transport in Amorphous PEO

• The Mechanism of Li conductivity in PEO at room
  temperature is not fully understood
• Li move mainly through the amorphous region
• Li conductivity doesnt arise from a simple
  process of statistically independent Li hops
  through a static polymer matrix, but dynamics of
  polymer matrix are essential to the transport
• Li bound to O of polymer very strong, Li
  hopping events have a high barrier and expected
  to be rare
• Up to 100ps MD, no Li hopping found
• Some attempts could find such hopping, but off
  the battery technology interest
• Raising above melting point, studying short chain
  system, reducing interactions.

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Li Transport in Amorphous PEO

• We want to catch these rare events efficiently
  since MD simulation time is very long.

• Voter(PRB, 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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Time Distribution 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 box
  same position, but different initial velocity
  distributions
• Do ordinary MD for M steps(in our 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 ? lt ?0, (?0 is fixed critical value, 1.5Å),
  continue MD and quench
• If one of ? 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 Scheme
Start
No
Replica N sets of Data
Parallel run MD, quench
Meet the criteria
Stop all Jobs Collect events
yes
Calculate more?
Relaxation before replica
Yes
Stop
No
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Parallel Performance
Normal Parallel MD
Parallel Replica

• Speedup goes down if more than 20 processors are
  used, due to heavy data transfer and
  communication among processors.

• The speedup is almost linear with the number of
  processor since only a broadcast communication
  are involved among the processors.

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Snap-shot Movie of Li Moving
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Coordination Oxygen around Li
The of O around Li within the radius of 2.4Å
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
Experimental D (2.20.3)x10-14 m2/s We get D1
(2.250.31)x10-13 m2/s include all events
D2 (4.733.01)x10-14 m2/s only O
exchange events
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Li Diffusion vs Torsion barrier of PEO

• Reduce the torsion force in PEO chain, the Li
  diffusion constant will be increased. Torsion
  barrier domain the chain relaxation
• This could help synthetic chemist to choose
  better polymer which torsion barrier is lower
  than PEO

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Conclusion for Li Transport (JCP,122(2005)4702)

• This is the first time the parallel replica
  method has been used into polymer system
• The Li Motions associated with diffusion
  occurred with the order of ps separated by long
  rearrangement in the order of ns
• Results shows the conductivity could be increased
  by decreasing the torsion barrier. This will help
  synthetic chemists to choose right polymer
  electrolyte materials.

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Further Work

• To investigate relations between torsion barrier
  and conductivity will get more information about
  Li transport
• To study the act of anions during Li transport
  by introducing other kinds of anions (such as
  triflate, TFSI, etc.)
• Improve the algorithm to speedup the simulation
  by treating low-frequency modes differently

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My Related Publications

• Y. Duan, J. W. Halley, L. Curtiss and P. Redfern,
  Mechanisms of Lithium Transport in Amorphous
  Polyethylence Oxide, J. Chem. Phys.,
  122(2005)054702
• J. W. Halley, Y. Duan, K. Lidke, A. Wynveen and
  M. Zhuang, Multiscale Modeling of Many Body
  Systems, Condensed Matter Theories Vol. 17
  Superconductivity, Superfluidity and Quantum Hall
  systems, M. P. Das and F. Green ed., Page
  257-278, Nova Science Pub Inc, New York, 2003
• J. W. Halley, Y. Duan, Role of Atomic Level
  Simulation in Development of Batteries, J. Power
  Sources, 110(2002)383-388
• J. W. Halley, Y. Duan, B. Nielsen, L. Curtiss and
  P. Redfern, Simulation of Polyethylene Oxide
  Improved Structure Using Better Models for
  Hydrogen and Flexible Walls, J. Chem. Phys.,
  115(2001)3957-3966
• J. W. Halley, Y. Duan, Mechanisms of Lithium
  Conductance in PEO from Molecular Simulation,
  Proceedings of Electrochemistry Society Vol.
  2000-36, A. Landgrebe, R. J. Klingler ed., page
  317-325, 2000
• J. W. Halley, P. Schelling and Y. Duan,
  Simulation Methods for Chemically Specific
  Modeling of Electrochemical Interfaces,
  Electrochimica Acta, 46(2000)239-245
• J. W. Halley, Y. Duan, Simulation of Battery
  Components and Interfaces on the Atomic Scale
  Ion Pairing as an Example of What We Can Learn,
  J. Power Sources, 89(2000)139-142
• J. W. Halley, Y. Duan, B. Nielsen, L. Curtiss and
  A. G. Baboul, Lithium perclorate ion pairing
  transport in a model of amorphous polyethylene
  oxide, J. Chem. Phys., 11(1999)3302-3308

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Acknowledgements

• Co-workers
• J. Woods Halley, Bin Lin, B. Nielson (UMN)
• L.A. Curtiss, A. Baboul, P. Redfern, M.-L.
  Saboungi (ANL)

• Supported by
• Department of Energy(DOE)
• Minnesota Supercomputing Institute(MSI)

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Thank You!