Elsevier

Electrochimica Acta

Volume 299, 10 March 2019, Pages 191-196
Electrochimica Acta

Fundamental parameters governing ion conductivity in polymer electrolytes

https://doi.org/10.1016/j.electacta.2018.12.143Get rights and content

Highlights

  • Electrostatic and elastic forces control decoupled ion conductivity.

  • Increase in shear modulus increases energy barrier for ion conductivity.

  • Ion-ion correlations decrease conductivity in polymer electrolytes by ∼10 times.

Abstract

We analyze conductivity of polymerized ionic liquids with focus on fundamental limitations hindering faster charge transport in polymer electrolytes. We emphasize that to achieve the required ionic conductivity ∼10−3 S/cm in dry polymer electrolytes, a decoupling of ion transport from segmental dynamics is required. We demonstrate that two competing mechanisms control decoupling of ion transport: electrostatic interactions that dominates for small ions such Li, and elastic force that dominates for large ions. Our experimental results indeed confirm significant contribution of the elastic force to the energy barrier controlling transport of large ions. We also emphasize importance of ion-ion correlations that strongly affect charge transport (conductivity) even at the same ion diffusivity. Our analysis suggests that these correlations suppress ion conductivity in polymer electrolytes by about ten times. At the end, we formulate some ideas on design of polymer electrolytes with high ion conductivity.

Introduction

It is widely recognized that use of polymer electrolytes instead of traditional liquid electrolytes will significantly improve performance and safety of current batteries [[1], [2], [3], [4]]. Among polymer electrolytes, polymerized ionic liquids (PolyILs), where one ion remains mobile while the counter ion is attached to the polymer chain, attract significant attention due to their single-ion conductivity [5,6]. PolyILs do not require any addition of salts for conductivity because they have intrinsic ions. Single ion conductance is beneficial for many applications, including flow and conventional batteries. It also simplifies data analysis and theoretical treatment of PolyILs, and make them ideal model systems to study microscopic parameters controlling conductivity.

In this contribution we discuss the fundamental parameters controlling conductivity in polymer electrolytes. We emphasize that decoupling of ion transport from segmental (structural) relaxation is critical for achieving high ionic conductivity in dry polymer electrolytes. There are two contributions, electrostatic and elastic forces, controlling the decoupled ion transport. We demonstrate that reduction in elastic force contribution indeed decreases the energy barrier for ion conductivity in glassy PolyILs. In addition ion-ion correlations significantly affect charge diffusion and thus the conductivity. This effect is not actively discussed in literature, but according to our analysis it reduces ionic conductivity in PolyILs by almost 10 times.

Section snippets

What controls ionic conductivity in polymer electrolytes

We start with the analysis of ionic conductivity σ using classical Nernst-Einstein equation [7,8]:σ=nq2DkT=nq2kTλ26τiHere n is the conducting ion concentration, q is their charge, D is their diffusion coefficient presented as a random-walk terms with the length of the ion jumps λ divided by the time between ion jumps τi (inverse ion jumps rate) and by 6, which accounts for dimensionality [8]. Mobile ions concentration in PolyILs is usually in the range 2–5 nm−3 [9]. Ion jump length in condensed

Mechanisms controlling decoupling of ion transport from segmental dynamics

For simplicity we will start with the analysis of ionic conductivity in PolyILs at temperatures below Tg, i.e. in their glassy state. In this case segmental relaxation is essentially frozen and ions moves by over-barrier jumps. Indeed polymer electrolytes show an Arrhenius temperature dependence of conductivity at T < Tg, σ = σ0·exp(-Eσ/kBT) [16,35,36] (Fig. 1). Thus, studies of ionic conductivity in polymer electrolytes at T < Tg might reveal microscopic details controlling decoupling and the

Role of ion-ion correlations

An important point often overlooked in studies of ionic conductivity in polymers is that conductivity is defined by a charge diffusion and not directly by the ion diffusion [[44], [45], [46]]. The ion conductivity is defined by the velocity-velocity correlation of ions [[44], [45], [46]]:σ=q23VkT0i=1N[sgn(qi)vi(0)]j=1N[sgn(qj)vj(t)]dtHere V is the volume of the system, sgn(qi) and vi(t) are the sign and velocity of an ion i. Thus conductivity is defined by velocity-velocity correlations

Conclusions

Presented analysis demonstrates importance of two mechanisms of ionic conductivity in polymer electrolytes, a liquid-like when ion motion is coupled to segmental dynamics, and a quasi-solid-like when ion can jump over energy barriers in a frozen or slow moving environment. However, to achieve the required by many applications conductivity σ∼10−3S/cm, the first mechanism requires extremely fast segmental dynamics that is not feasible in dry polymer electrolytes. Thus, employment of the second

Notice

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will

Acknowledgments

Authors thank K. D. Kreuer and C. A. Angell for helpful discussions and suggestions. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division.

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