models and simulations of lithium ion conduction in poly(ethylene oxide) this thesis was done under...

MODELS AND SIMULATIONS MODELS AND SIMULATIONS OF LITHIUM ION OF LITHIUM ION CONDUCTION IN CONDUCTION IN

POLY(ETHYLENE OXIDE)POLY(ETHYLENE OXIDE)This thesis was done under the supervision ofThis thesis was done under the supervision of

Prof. Moshe IsraeliProf. Moshe Israeli

Prof. Amir AverbuchProf. Amir Averbuch

Prof. Zeev SchussProf. Zeev Schuss

Prof. Amy Novick-CohenProf. Amy Novick-Cohen

L. GitelmanL. Gitelman

Prof. Moshe Israeli passed away on February 18, 2007. This thesis is dedicated to his memory ..

Applications• rechargeable batteries• ambient temperature fuel cells• electrochromic devices• modified electrodes/sensors• solid state reference electrode systems• super capacitors• thermoelectric generators• high vacuum electrochemical devices• electrochemical switches• and more

Solid polymer electrolytes are ideal Solid polymer electrolytes are ideal media for micro-batteriesmedia for micro-batteries

Polymer electrolytes are solid ion conductors, Polymer electrolytes are solid ion conductors, such as poly (ethylene oxide), such as poly (ethylene oxide),

which Is portrayed schematicallywhich Is portrayed schematically

Polymer electrolytes are solid ion conductors Polymer electrolytes are solid ion conductors formed by the dissolution of inorganic salts in formed by the dissolution of inorganic salts in

polymer solutionspolymer solutions

The structure of PEOThe structure of PEO33:LiCF:LiCF33SOSO33. (Left) . (Left)

A single PEO chain with associated ions. (Right)A single PEO chain with associated ions. (Right)

(Left) The structure of PEO(Left) The structure of PEO66:LiAsF:LiAsF66 viewed along the viewed along the

polymer chains. polymer chains. (Right) View of the structure showing the relative(Right) View of the structure showing the relative

position of the chains and their conformation.position of the chains and their conformation.

The effect of stretching the polymer electrolyte The effect of stretching the polymer electrolyte on its conductivity is dramatic, on its conductivity is dramatic,

resulting in up to a 40-fold increase.resulting in up to a 40-fold increase.

Schematic presentation of polymer electrolyte Schematic presentation of polymer electrolyte texture before (a) and after (b) stretching.texture before (a) and after (b) stretching.

Unidirectionally oriented fibrous micro phases Unidirectionally oriented fibrous micro phases are clearly distinguished in the Scanning are clearly distinguished in the Scanning

electron microscopy SEM .electron microscopy SEM .

unstretched LiI : P(EO)n stretched

Atomic force microscopy AFM shows thatAtomic force microscopy AFM shows thatstretching results in the formation of an ordered stretching results in the formation of an ordered

LiI : P(EO)LiI : P(EO)4040 polymer electrolyte structure. polymer electrolyte structure.

The directions of the PEO molecules are The directions of the PEO molecules are random and they contain loops.random and they contain loops.

(A) Disorganized

(B) organized models of a polymer electrolyte

The helix (molecule) and The helix (molecule) and the setup of the physical modelthe setup of the physical model

• Each helix (molecule) forms a random angle with an axis, which is perpendicular to the electrodes.

• Upon mechanical stretching,

the inclination of molecules decreases .

The key simplifying assumptions The key simplifying assumptions in this model:in this model:

1. Brownian dynamics of Li+/I ions are simulated in a single molecule.

2. In the present setup, the Li+ and I ions are kept apart from each other by the polymer and

3. The Li+ ions are kept apart by Coulombic repulsion, so the finite size effects (e.g., Lennard-Jones forces) become significant only at high concentrations.

Therefore, finite size effects are not incorporated in the present simulation.

A simplified one-dimensional A simplified one-dimensional Brownian modelBrownian model

The Coulombic potential of the inter-ionic forces actingThe Coulombic potential of the inter-ionic forces actingon the nth lithium ion at xn is given byon the nth lithium ion at xn is given by

The Coulombic potential created on the x-axis The Coulombic potential created on the x-axis by the PEO charges is given byby the PEO charges is given by

The polymer chain is covered by N boxes. The polymer chain is covered by N boxes. Each box contains 21 units of CHEach box contains 21 units of CH22 and O. and O.

The origin is in the middle of the central domain. The origin is in the middle of the central domain. It coincides with the fourth particle O. It coincides with the fourth particle O.

The potential and the corresponding forces are periodic.The potential and the corresponding forces are periodic.

The random motion of the ions in the channel The random motion of the ions in the channel is described by the overdamped Langevin equationsis described by the overdamped Langevin equations

.2

,2

υyx,y

ωyx,x

F

F

m

m

I

III

Li

LiLiLi

kT

kT

The components of the electric forces (per unit mass) on the The components of the electric forces (per unit mass) on the n-th lithium ionsn-th lithium ions

nxx

LiLi

nLi x

xqF

)yx,,()yx,()(

We simulate the system by discretizing We simulate the system by discretizing time and moving the ions according to time and moving the ions according to

the Euler schemethe Euler scheme

,2,)()(

,2,

)()(

tm

kTt

tytxFtytty

tm

kTt

tytxFtxttx

III

I

LiLiLi

Li

The total charge Q(t) absorbed in the graphite by time t The total charge Q(t) absorbed in the graphite by time t produces the noisy battery currentproduces the noisy battery current

dt

tdQtI

Simulation/experimental conductivity ratios Simulation/experimental conductivity ratios for different n. It shows the effect of stretching for different n. It shows the effect of stretching

on the conductivity.on the conductivity.

Simulation/experimental conductivity ratios Simulation/experimental conductivity ratios for different for different nn showing the effect of the showing the effect of the temperature for unstretched LiI:P(EO)temperature for unstretched LiI:P(EO)nn

We refine our molecular model of We refine our molecular model of lithium ion conduction in LiI : P(EO)lithium ion conduction in LiI : P(EO)nn

• Scanning Electron (SEM) and Atomic Force (AFM) microscopy show that stretching orders the structure of LiI : P(EO)n polymer electrolytes

• Unidirectionally oriented fibrous micro phases are clearly distinguishable in the SEM micrographs.

• In the aligned configuration of the helix the oxygen atoms are directed inward, lining the tunnel cavity and thus favoring cation transport. The CH2 groups all face outward.

• Linear segments tend to align in the direction of stretching and the radii of circular loops decrease

The simulation model.The simulation model.The polymer (part of the molecule) The polymer (part of the molecule)

containing circular loopcontaining circular loop

Left panel: The helical loop, Right panel: Closeup of the loopLeft panel: The helical loop, Right panel: Closeup of the loop

The Coulombic potential, created in a loop The Coulombic potential, created in a loop of radius R in a plane perpendicular of radius R in a plane perpendicular

to the electrodes at arclength s on the axis to the electrodes at arclength s on the axis of the helix by the PEO charges,of the helix by the PEO charges,

The potential of the electric field acting on the n-th The potential of the electric field acting on the n-th lithium ion at slithium ion at snn in the loop in the loop

The potential The potential ΦΦ(s) + (s) + ΨΨEE(s) in an unstretched (s) in an unstretched

(top) and for stretched (bottom)(top) and for stretched (bottom)

The random motion of the ions in the channel The random motion of the ions in the channel is described by the overdamped Langevin equationsis described by the overdamped Langevin equations

.υ2

','

,ω2

',

F

F

s

I

III

s

Li

LiLiLi

m

mkT

sss

kTsss

The components of the electric forces (per unit mass) The components of the electric forces (per unit mass) on the n-th lithium ionson the n-th lithium ions

.)',(

)',()(

n

LiLi

nLi s

ssqssF

We simulate the system by discretizing We simulate the system by discretizing time and moving the ions according to time and moving the ions according to

the Euler schemethe Euler scheme

,2',)(')('

,2',

)()(

tm

kTt

tstsFtstts

tm

kTt

tstsFtstts

sIII

I

sLiLiLi

Li

The total charge Q(t) absorbed in the graphite by The total charge Q(t) absorbed in the graphite by time t produces the noisy battery currenttime t produces the noisy battery current

dt

tdQtI

Simulation/experimental conductivity Simulation/experimental conductivity ratios for different n as function of n.ratios for different n as function of n.

Simulation/experimental conductivity ratios for Simulation/experimental conductivity ratios for different n as function of n. It showsdifferent n as function of n. It showsthe effect of the temperature on the the effect of the temperature on the

conductivity of the unstretched LiI:P(EO)conductivity of the unstretched LiI:P(EO)nn

Loops in the structure of the tube give Loops in the structure of the tube give rise to electrical potential barriers.rise to electrical potential barriers.

R

L

The polymer folded into a helix containing The polymer folded into a helix containing a circular loop.a circular loop.

Energy of one lithium in the loopEnergy of one lithium in the loop

6

22 2 2

, ,,

cos cos2 2

10,

sin2

E

CH

x y x yU x y

V

x y

x yx y

Loops in the structure of the tube give rise to Loops in the structure of the tube give rise to electrical potential barriers.electrical potential barriers.

Mechanical stretching lowersMechanical stretching lowersthe barriers and causes an exponential the barriers and causes an exponential

rise in the output conductivity.rise in the output conductivity.

Conductivity (S/cmConductivity (S/cm22) vs stretching ) vs stretching for LiI : P(EO)for LiI : P(EO)7 7 - LiI : P(EO)- LiI : P(EO)100100..

Conductivity (S/cmConductivity (S/cm22) vs stretching ) vs stretching for LiI : P(EO)for LiI : P(EO)77

Conductivity (S/cm2) vs stretching

New insights into structural and New insights into structural and electrochemical propertieselectrochemical properties

of anisotropic polymer electrolytesof anisotropic polymer electrolytes

• Polymer crystals show very anisotropic properties.

• The configuration of a polymer is defined by the polymerisation method.

Typically, solid polymer electrolytes are prepared by casting from solution; this causes – preferential planar (XY) orientation of

PEO helices – much higher longitudinal than

orthogonal conductivity.

Incorporation of nano-size diamagnetic and Incorporation of nano-size diamagnetic and paramagnetic fillers to the MF-cast PEs affords paramagnetic fillers to the MF-cast PEs affords

chemistries the opportunity to develop solid chemistries the opportunity to develop solid polymer electrolytes polymer electrolytes

of improved conductive propertiesof improved conductive properties.

• A first approach is to promote the transition from parallel to perpendicular lamellae of PEO helices and to do so without mechanical means.

• Casting and drying of LiI-based PEs under an Casting and drying of LiI-based PEs under an applied magnetic field enhances both intra- applied magnetic field enhances both intra- and inter-chain ion mobility by about and inter-chain ion mobility by about one one order of magnitudeorder of magnitude in the direction in the direction perpendicular to the film plane.perpendicular to the film plane.

Planar SEM images of polymer Planar SEM images of polymer electrolytes: typically cast (a) and cast electrolytes: typically cast (a) and cast

under a gradient magnetic field (b).under a gradient magnetic field (b).

• As can be seen from the plane SEM images As can be seen from the plane SEM images of neat PEO and PEs, the morphology of the of neat PEO and PEs, the morphology of the films cast under no field and under MF are films cast under no field and under MF are significantly different. significantly different.

• It seems likely that the response of these It seems likely that the response of these diamagnetic materials to an external diamagnetic materials to an external magnetic field occurs by the growth of the magnetic field occurs by the growth of the grains. grains.

• The grains, in addition, appear as convex The grains, in addition, appear as convex upward domains.upward domains.