|Fig. 1: Electrolytes are usually flammable organic liquids. (Source: Wikimedia Commons)|
Imagine driving a car in traffic. What would allow the car to move faster? If there were more lanes or a carpool lane to change into then you would certainly be able to go much faster. The same idea applies in battery science. There is a flow of lithium ions that is the driving force behind the modern electronic age - lithium ions flowing from negative to positive electrodes back and forth power our computers and our phones and they are beginning to power our cars and homes (see Fig. 1). The speed and ease at which the lithium ions travel (the conductivity) is a vital piece to improving the performance of a battery.
Currently, the dominating electrolytes are organic liquid solvents, such as LiPF6.  However, replacing liquid electrolytes with a solid-state alternative would improve the safety as well as the thermal, mechanical, and electrochemical stability of the batteries. Organic liquid solvents are flammable and create a large risk for electric vehicles that are powered by lithium ion batteries. While they are more dangerous, liquid electrolytes also have extremely good conductivity. Creating an inorganic solid-state electrolyte with comparable conductivity to liquid electrolytes (above 1mS/cm) has become a great challenge for materials and battery research.
A common lithium ion battery involves LixCoO2 as the positive electrode and lithium metal as the negative electrode. These are their half reactions upon discharging:
|CoO2(s) + Li+ + e-||→||LiCoO2||(positive electrode/cathode)|
|Li(s)||→||Li+ + e-||(negative electrode/anode)|
These reactions are separated by an electrolyte that is usually an organic liquid electrolyte, typically LiPF6 (see Fig 2. to see the basic layout and structure of a lithium ion battery). The speed at which lithium cations travel across the electrolyte plays a large role in how much time it takes to charge and discharge a lithium ion battery. The conductivity of liquid electrolytes is typically above 1 mS/cm; however, until 2010, solid-state electrolytes could only attain practically useful conductivities of 0.1 mS/cm (an order of magnitude lower than organic liquid electrolytes).  Until Li10GeP2S12 was reported by Kamaya et al. to have a new three-dimensional framework structure that had an extremely high lithium ionic conductivity of 12 mS/cm (even higher than liquid organic electrolytes). 
|Fig. 2: The cathode and anode materials are usually layered materials that allow lithium ions to intercalate in and out easily. (Source: Wikimedia Commons)|
During discharge, there are 3 reactants at the positive electrode: CoO2, Li+, and e-. The integrated rate law for a reaction with 3 reactants is Rate = k[A][B][C] for a reaction 
|A + B + C||→||Product|
|CoO2(s) + Li+ + e-||→||LiCoO2|
The concentration of Li+ determines the rate at which LiCoO2 will form. The faster Li+ is transported from the negative electrode to the positive electrode the higher [Li+] will be.
Wang et al. studied several materials with similar properties to Li10GeP2S12 (the first lithium superionic conductor from Kamaya et al.) including Li7P3S11 as well as electrolytes with lower conductivities to find out what separated superionic conductors from subpar ionic conductors.  They found that ionic diffusion is fundamentally the migration of lithium ions between stable sites through a higher energy environment. The highest energetic point that the lithium ion passes on its path is the activation energy for migration between the stable sites. The stable site is usually a tetrahedral or octahedral site connected to another polyhedral site in the structure.
The kinetics of the ionic migration is related to the activation energy. The rate constant k can be found with the Arrhenius Equation: 
|k = A exp(-Ea/kBT)|
|Li(n+) → Li(p+)||(unimolecular system in the electrolyte to transport lithium ions from the negative to positive)|
|Rate = k[Li(n+)]||(for the unimolecular system ignoring the reverse reaction)|
As the activation energy Ea increases, k will decrease. Since the reaction rate is directly proportional to k, the reaction rate will decrease as the activation energy increases. Lithium moving from tetrahedral site to another tetrahedral site has an activation energy of 0.15 eV while movement involving an octahedral site involves barriers of above 0.40 eV. This increase in activation energy translates to a three orders of magnitude decrease in conductivity. 
Simulations and experiments both confirm that Li ions have a relatively uniform energy landscape through connected tetrahedral sites in bcc lattices with an evenly distributed probability density for Li ions. [2,5]
Having relatively flat energy paths for Li ions to travel through is a general guiding principle for developing new solid state superionic conducting electrolytes. Just substituting Si for Ge in Li10GeP2S12 (since Ge is closer to P in energy) lowers its activation energy by 0.01 eV.  However, replacing Ge with Sn (farther in energy from P) increases activation energy by 0.03 eV.  This local cation effect just flattens the pathway for Li ions to drive back and forth from the positive and negative electrodes.
There has been a push for solid-state electrolytes for lithium ion batteries to improve the safety of the batteries that power our world. There is also potential for improvements in the conductivity of lithium ions through solid-state electrolytes that could even surpass traditional flammable liquid electrolytes. The scientific community's understanding of how to better engineer solid-state electrolytes has been improving very recently; there is a lot of hope for the future of solid-state electrolytes for lithium ion batteries.
© Andrew Zhao. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 J. S. Lee et al., "Ionic Liquids as Electrolytes for Li Ion Batteries," J. Ind. Eng. Chem. 10, 1086 (2004).
 N. Kamaya et al., "A Lithium Superionic Conductor," Nat. Mat. 10, 682 (2011).
 S. S. Zumdahl and S. A. Zumdahl Chemistry, 6th Ed. (Brooks Cole, 2002), Ch. 12.
 Y. Wang et al., "Design Principles for Solid-State Lithium Superionic Conductors," Nat. Mater. 14, 1026 (2015).
 Y. Mo, S. P. Ong, and G. Ceder, "First Principles Study of the Li10GeP2S12 Lithium Super Ionic Conductor Material," Chem. Mater. 24, 15 (2012).
 J. M. Whiteley et al., "Empowering the Lithium Metal Battery Through a Silicon-Based Superionic Conductor," J. Electrochem. Soc. 161, A1812 (2014).