Transcript Seminar

L. Gitelman
MODELS AND SIMULATIONS OF
LITHIUM ION CONDUCTION IN
POLY(ETHYLENE OXIDE)
This thesis was done under the supervision of
Prof. Moshe Israeli
Prof. Moshe Israeli passed away on February 18, 2007.
This thesis is dedicated to his memory.
Prof. Amir Averbuch
Prof. Zeev Schuss
Prof. Amy Novick-Cohen
Applications
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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
media for micro-batteries
Polymer electrolytes are solid ion conductors,
such as poly (ethylene oxide),
which Is portrayed schematically
Polymer electrolytes are solid ion conductors
formed by the dissolution of inorganic salts in
polymer solutions
The structure of PEO3:LiCF3SO3. (Left)
A single PEO chain with associated ions. (Right)
(Left) The structure of PEO6:LiAsF6 viewed along the
polymer chains.
(Right) View of the structure showing the relative
position of the chains and their conformation.
The effect of stretching the polymer electrolyte
on its conductivity is dramatic,
resulting in up to a 40-fold increase.
Schematic presentation of polymer electrolyte
texture before (a) and after (b) stretching.
Unidirectionally oriented fibrous micro phases
are clearly distinguished in the Scanning
electron microscopy SEM .
unstretched LiI : P(EO)n
stretched
Atomic force microscopy AFM shows that
stretching results in the formation of an ordered
LiI : P(EO)40 polymer electrolyte structure.
The directions of the PEO molecules are
random and they contain loops.
(A)
Disorganized
(B)
organized
models
of a polymer
electrolyte
The helix (molecule) and
the 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
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
Brownian model
The Coulombic potential created on the x-axis
by the PEO charges is given by
The Coulombic potential of the inter-ionic forces acting
on the nth lithium ion at xn is given by
The polymer chain is covered by N boxes.
Each box contains 21 units of CH2 and O.
The origin is in the middle of the central domain.
It coincides with the fourth particle O.
The potential and the corresponding forces are periodic.
The random motion of the ions in the channel
is described by the overdamped Langevin equations

x  FLi x, y  
Li

I
2  kT
y  FI x, y  
Li
m
Li
2  kT
I
m
,
ω
υ .
I
The components of the electric forces (per unit mass) on the
n-th lithium ions
( n)
Li
F
( x, y )   q Li 
Li  ( x , x, y )
x
x  xn
We simulate the system by discretizing
time and moving the ions according to
the Euler scheme
x ( t  t )  x ( t ) 
FLi  x t , y t 
y ( t  t )  y ( t ) 
FI  x t , y t 
 Li
I
2kT
t 
 t ,
 Li m Li
2kT
t 
 t ,
 I mI
The total charge Q(t) absorbed in the graphite by time t
produces the noisy battery current
dQ t 
I t  
dt
Simulation/experimental conductivity ratios
for different n. It shows the effect of stretching
on the conductivity.
Simulation/experimental conductivity ratios
for different n showing the effect of the
temperature for unstretched LiI:P(EO)n
We refine our molecular model of
lithium ion conduction in LiI : P(EO)n
• 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 polymer (part of the molecule)
containing circular loop
Left panel: The helical loop, Right panel: Closeup of the loop
The Coulombic potential, created in a loop
of radius R in a plane perpendicular
to the electrodes at arclength s on the axis
of the helix by the PEO charges,
The potential of the electric field acting on the n-th
lithium ion at sn in the loop
The potential Φ(s) + ΨE(s) in an unstretched
(top) and for stretched (bottom)
The random motion of the ions in the channel
is described by the overdamped Langevin equations

Li

I
s  FLi s, s' 
s'  FI s, s' 
2
Li
m
kT
Li
2  kT
I
m
 s,
ω
υ s .
I
The components of the electric forces (per unit mass)
on the n-th lithium ions
( n)
Li
F
( s, s' )   q Li 
Li  ( s, s' )
sn
.
We simulate the system by discretizing
time and moving the ions according to
the Euler scheme
s ( t  t )  s ( t ) 
FLi st , s' t 
s' ( t  t )  s' ( t ) 
 Li
2kT
t 
 s t ,
 Li m Li
FI st , s' t 
I
2kT
t 
 s t ,
 I mI
The total charge Q(t) absorbed in the graphite by
time t produces the noisy battery current
dQt 
I t  
dt
Simulation/experimental conductivity
ratios for different n as function of n.
Simulation/experimental conductivity ratios for
different n as function of n. It shows
the effect of the temperature on the
conductivity of the unstretched LiI:P(EO)n
Loops in the structure of the tube give
rise to electrical potential barriers.
The polymer folded into a helix containing
a circular loop.
R

L
Energy of one lithium in the loop
  x, y    E  x , y 
U  x, y  
V
 

 

   cos  x    cos  y    
2
2 

 

10
6
x y
2
2
2
 sin
   x  y   CH
2
2
,
Loops in the structure of the tube give rise to
electrical potential barriers.
Mechanical stretching lowers
the barriers and causes an exponential
rise in the output conductivity.
Conductivity (S/cm2) vs stretching
for LiI : P(EO)7 - LiI : P(EO)100.
Conductivity (S/cm2) vs stretching
for LiI : P(EO)7
Conductivity (S/cm2) vs stretching
New insights into structural and
electrochemical properties
of 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
paramagnetic fillers to the MF-cast PEs affords
chemistries the opportunity to develop solid
polymer electrolytes
of 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
applied magnetic field enhances both intraand inter-chain ion mobility by about one
order of magnitude in the direction
perpendicular to the film plane.
Planar SEM images of polymer
electrolytes: typically cast (a) and cast
under a gradient magnetic field (b).
• As can be seen from the plane SEM images
of neat PEO and PEs, the morphology of the
films cast under no field and under MF are
significantly different.
• It seems likely that the response of these
diamagnetic materials to an external
magnetic field occurs by the growth of the
grains.
• The grains, in addition, appear as convex
upward domains.