Fundamental parameters governing ion conductivity in polymer electrolytes
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]:Here 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]]:Here 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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