Abstract
• Self-discharge data from litterature fitted to stretched exponential function • Results interpreted as a distribution of decay rate constants • Fast charging gives a wider distribution of rate constants • Changing temperature does not alter the distribution of rate constants Supercapacitors are prone to self-discharging, which is most often measured as a voltage decrease with time under open circuit conditions. It is of substantial interest to find simple and general methods to extract information about the processes going on in the supercapacitor during self-discharge. The current work fits a stretched exponential function to experimental data available in the literature, thus extracting parameters that allows one to probe the internal processes of the supercapacitor. In particular, experimental data related to charge holding time, charging rate before self-discharge and temperature dependence are investigated. It is demonstrated how the fitting data can be understood in terms of a kinetic model exhibiting a distribution of rate constants which are related to the fitting parameters. The current work therefore proposes a method that allows one to quickly map the internal processes of a self-discharging supercapacitors with only two variables, and might therefore become a useful tool.
Highlights
The Leyden jar was probably the first man-made capacitor, invented in 1745 [1]
In 1854, Kolrausch investigated the decay of charge from a Leyden jar, and found that it did not follow a simple exponential decay law on the form exp(− t /τ1) with decay time τ1 as one might expect [2]
The stretched exponential function has been used extensively to explain the behavior of glassy states, luminescence decay and electronic systems in terms of a distribution of relaxation times [5, 6]
Summary
The Leyden jar was probably the first man-made capacitor, invented in 1745 [1]. Its ability to store electrical energy played a crucial role for the development of science and technology the following century. In 1854, Kolrausch investigated the decay of charge from a Leyden jar, and found that it did not follow a simple exponential decay law on the form exp(− t /τ1) with decay time τ1 as one might expect [2] Instead, he introduced a stretched exponential function on the form exp[− (t/τ)β] to explain the observed decay, where 0
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