  A significant problem associated with batteries is the rapid reduction of
charge-storage capacity with increasing charge/discharge rate. For example,
improving this rate-performance is required for fast-charging of car batteries.
Rate-performance is related to the timescales associated with charge or ionic
motion in both electrode and electrolyte. However, no quantitative model exists
which can be used to fit experimental data to give insights into the dominant
rate-limiting processes in a given electrode-electrolyte system. Here we
develop an equation which can be used to fit capacity versus rate data,
outputting three parameters which fully describe rate-performance. Most
important is the characteristic time associated with charge/discharge which can
be expressed by a simple equation with terms describing each rate-limiting
process, thus linking rate-performance to measurable physical parameters. We
have fitted these equations to ~200 data sets from ~50 papers, finding
exceptional agreement, and allowing parameters such as diffusion coefficients
or electrolyte conductivities to be extracted. By estimating relevant physical
parameters, it is possible to show which rate-limiting processes are dominant
in a given situation, facilitating rational design and cell optimization. In
addition, this model predicts the upper speed limit for Li/Na ion batteries, in
agreement with the fastest electrodes in the literature.
