# Supercapacitor and Instant Charging

## Teen's Science Project

 Fig. 1: Charging a Capacitor.

18-year-old California student Eesha Khare won the 2013 Intel Foundation Young Scientist Award and \$50,000 for creating a supercapacitor that could recharge a cellphone battery in 30 seconds. [1] He performed the work as a high school student during a 2012 summer internship under Prof. Y. Li in the Department of Chemistry and Biochemistry at the University of California, Santa Cruz. Although Mr. Khare's accomplishment must be contextualized with similar work being performed in industrial laboratories, he did demonstrate that a solid-state device can light an LED after only a short charging time. We will give a brief introduction here about supercapacitors, their advantages and disadvantages as an energy storage technology.

## Capacitors and Instant Charging

A capacitor consists of two conductors separated by a non-conductive region, usually a dielectric. [2] Ideally, the ratio of charge ±Q on each conductor to the voltage U between them is a constant C, the capacitance.

U = Q/C

Fig. 1 shows how a capacitor is charged. Let dQ/dt be the charging current.

U = Qmax/C = R dQ/dt + Q/C

where Qmax is the maximum charge that can be reached and R is the resistance in the circuit. This ODE can be easily solved, yielding the charging time.

Q = Qmax (1 - e-t/RC)

If the circuit is perfectly conducting, charging would be instantly done. More realistically, let us assume that R= 1mΩ and C = 200 mF/cm2 for the supercapacitor designed by Khare. [3] It then takes 2RC = 0.4ms to 85% charge a capacitor of 1cm2.

Conventional chemical batteries need long charge times for the reactions to happen. The good thing of capacitors is that they can store charge instantly. With no chemical reactions involved in the electrodes, capacitors should also have an infinite life time. For the same reason, the power density, defined as the amount of power (time rate of energy transfer) per unit volume, is about 10 times higher in supercapacitors than conventional batteries. [4]

There is nothing either good or bad. One primary disadvantage of supercapacitors is their low energy density when used as electrical energy storage technology, as shown in Fig. 2. The electrostatic energy stored in capacitors can be evaluated as follows.

E = ½QU = ½CU2

The dielectric between two conductors must not take up too much space. The voltage U is thus limited to avoid electrical breakdown. To increase the energy density of capacitors, one need to push C as high as possible and this is exactly what Khare is trying to do. [1] Unfortunately, the best capacitance we have currently corresponds an energy density which is 30 times lower than chemical batteries. [3] This is exactly why an LED, not a real cellphone, was used in the demonstration.

## What is a "Super" Capacitor?

 Fig. 2: Supercapacitor Electrode.

In the preceding text, we confused supercapacitors with capacitors to keep our discussion within the context of high school physics. In this subsection, we will show that two energy storage mechanism, double-layer capacitance and pseudocapacitance, both contribute to the total capacitance of a supercapacitor making it possible to sustain big energy densities. Fig. 2 shows a Helmholtz double layer supercapacitor. A phase boundary originates when we bring an electrode in contact with a solid or electrolyte. Charged electrodes immersed in electrolytic solutions repel the co-ions (1) of the charge while attracting counter-ions (2) to the interface. [4] These two diffusive layers give exponentially decreasing electric potential Φ away from the surface. These arrangement of charged molecules will cause the double layer capacitance. [3] Normally, the very closest spots to the electrode are always occupied by solvent molecules (3). However, some "specifically adsorbed ions" can lose their solvent shell and have direct contact with the electrode. [5] Further,The specific adsorption of the ions could also have electrochemical reaction (redox reaction) when attached to the surface, involving a partial charge transfer between the ion and the electrode (4). [6] This is how the Pseudocapacitance can be originated. Combined with the double-layer and pseudo capacities, supercapacitors can have the energy density higher than normal capacitors and researchers are still trying to get the number even higher to match chemical batteries.

© Yuan Shen. 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.

## References

[1] A. Kooser, "Teen's Science Project Could Charge Phones in 20 Seconds," CNET NEWS, 20 May 20 13

[2] R. A. Serway and C. Vuille, College Physics, 9th Ed., Vol. 4 (Cengage Learning, 2011).

[3] A. Yu, V. Chabot and J. Zhang, Electrochemical Supercapacitors for Energy Storage and Delivery: Fundamentals and Applications, (CRC Press, 2013).

[4] H. Helmholtz, "Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche, Annalen der Physik, Vol 165, 6 211 (1853).

[5] D. C. Grahame, "The Electrical Double Layer and the Theory of Electrocapillarity," Chem. Rev., 41 441 (1947).

[6] S. Trasatti and G. Buzzanca, "Ruthenium Dioxide: a New Interesting Electrode Material: Solid State Structure and Electrochemical Behavior," J. Electroanalyt. Chem. 29 A1 (1971).