Polymer geometry and Li+ conduction in poly(ethylene oxide)

Abstract

We study the effect of molecular shape on Li + conduction in dilute and concentrated polymer electrolytes (LiI : P (EO) n (3 ≤ n ≤ 100)). We model the migration-diffusion of interacting Li + ions in the helical PEO molecule as Brownian motion in a field of electrical force. Our model demonstrates that ionic conductivity of the amorphous PE structure is increased by mechanical stretching due to the unraveling of loops in the polymer molecule and to increased order. The enhancement of the ionic conductivity in the stretch direction, observed in our Brownian simulations, is in agreement with experimental results. We find an up to 40-fold increase in the LiIP (EO) 7 conductivity, which is also in agreement with experimental results. The good agreement with experiment lends much credibility to our physical model of conductivity.

Stochastic model of lithium ion conduction in poly(ethylene oxide)

“…The analysis of this scenario can explain the dramatic changes in conductivity observed in the simulations of [2]. The exponential dependence of the activation rate on the loop radius can lead to the 40-fold increase in conductivity of the stretched polymer.…”

“…To show that this is a valid approximation, we write the potential created in a loop of radius R in a plane perpendicular to the electrodes at arclength s on the axis of the narrow helix by the PEO charges as [2] …”

“…In [1] and [2] we developed a model of lithium ion conduction in dilute and concentrated polymer electrolytes (LiI : P (EO) n (3 ≤ n ≤ 100)), based on an analogy between protein channels of biological membranes that conduct N a + , K + , and other ions [6], and the PEO helical chain that conducts Li + ions. There are, however, significant differences between them: while protein channels are embedded in the cell membrane and their nearly rectilinear pores are aligned, the PEO molecules contain loops and their directions are random (see Figure 1.1).…”

“…Unfolding the loops by mechanical stretching can, therefore, affect the conductivity of a PEO electrolyte in a decisive fashion. While [2] presents simulations of PEO loops with various degrees of stretching, our purpose in this paper is to elucidate, both analytically and numerically, the effect of stretching and concentration on PEO conductivity.…”

“…To make this paper self-contained, we recall some basic facts from [2]. In our model the PEO chains adopt a helical conformation with all C − O bonds trans and C − C bonds either gauche or gauche minus [5].…”