טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentGitelman Larissa
SubjectModeling and Simulation of Li-Ion Conduction in Poly
(Ethylene Oxide)
DepartmentDepartment of Applied Mathematics
Supervisor Professor Amy Novick-Cohen


Abstract

Polyethylene oxide (PEO) containing a lithium salt serves as a solid polymer electrolyte in thin-film batteries and its ionic conductivity is a key parameter of their performance. We model and simulate Li ion conduction in a single PEO molecule. Our simplified stochastic model of ionic motion is based on an analogy

between protein channels of biological membranes that conduct Na, K, and other ions, and the PEO helical chain that conducts Li ions. In contrast with protein channels and salt solutions, the PEO is both the channel and the solvent for the lithium salt. The mobile ions are treated as charged spherical Brownian particles. We simulate Smoluchowski dynamics in channels with a radius of about 0.1 nm, and study several models of the effects of stretching on ion conductivity. 


We assume that each helix (molecule) forms a random angle with the axis between the electrodes. We model the effects of room-temperature stretching on the structural properties and ionic conductivity in dilute and concentrated

LiI:P(EO)n (3≤n≤100) polymer electrolytes. In our model the mechanical stretching increases the order in the no stretched amorphous PE structure. The helical PEO molecule is represented in terms of loops, inside which Li ion conduction is represented as Brownian motion in a force field.  The computed enhancement of the ionic conductivity in the stretch direction is in good agreement with experimental and recent theoretical and experimental results.


We develop, analyze, and simulate a physical model Li-ion conduction inside polyethylene oxide helical tubes, which act as solvents for LiI salt. The current is due to diffusion and electric interactions with a permanent external field, the PEO charges, and ion-ion interactions. Potential barriers are created in the PEO by structure's loops. We calculate the configuration energy of one or two lithium ions in the loop and derive an explicit expression for the activation energy. We use Kramers' formula to calculate the conductivity as function of mechanical stretching, which lowers the barrier and causes an exponential rise in the conductivity output.