MODELS AND SIMULATIONS OF LITHIUM ION CONDUCTION IN POLY(ETHYLENE OXIDE) This thesis was done under the supervision of Prof. Moshe Israeli Prof. Amir Averbuch Prof. Zeev Schuss Prof. Amy Novick-Cohen L. Gitelman Prof. Moshe Israeli passed away on February 18, 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 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 PEO 3 :LiCF 3 SO 3. (Left) A single PEO chain with associated ions. (Right)

The structure of PEO 4 :KSCN. (Left) A single PEO chain with associated ions. (Right) View of the structure along the bre axis.

The structure of PEO:KCF 3 SO 3.

(Left) The structure of PEO 6 :LiAsF 6 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 of the inter-ionic forces acting on the nth lithium ion at xn is given by The Coulombic potential created on the x-axis by the PEO charges is given by

The polymer chain is covered by N boxes. Each box contains 21 units of CH 2 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 The components of the electric forces (per unit mass) on the n-th lithium ions

We simulate the system by discretizing time and moving the ions according to the Euler scheme The total charge Q(t) absorbed in the graphite by time t produces the noisy battery current

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 CH 2 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 s n in the loop

The potential Φ(s) + Ψ E (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 The components of the electric forces (per unit mass) on the n-th lithium ions

We simulate the system by discretizing time and moving the ions according to the Euler scheme The total charge Q(t) absorbed in the graphite by time t produces the noisy battery current

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.

Energy of one lithium in the loop

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/cm 2 ) vs stretching for LiI : P(EO) 7 - LiI : P(EO) 100.

Conductivity (S/cm 2 ) vs stretching for LiI : P(EO) 7

Conductivity (S/cm 2 ) 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 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 intra- and inter-chain ion mobility by about one order of magnitude in the direction perpendicular to the film plane.Casting and drying of LiI-based PEs under an applied magnetic field enhances both intra- and 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.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.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.The grains, in addition, appear as convex upward domains.