Capacitance and ESR as a function of the temperature
In the high frequency range (f > 10Hz), the series resistance variation with temperature can be neglected. In the low frequency range, the equivalent series resistance increases when the temperature decreases [i]. This is due to the fact that the electrolyte ionic resistance RT is strongly influenced by the temperature. Above 0C RT varies slowly with the temperature. Below 0C the temperature dependence is more important, especially for the series resistance. It is due to the rapid electrolyte viscosity increase in the low temperatures range [ii].
A relationship between RT and the temperature has been established from experimental results.
It's given by the expression :
where R20 is the resistance at 20C, T the ambient temperature and kT the temperature coefficient.
At very low frequencies (f < 0.1Hz), the capacitance is almost constant according to the temperature. It means that the ions penetrate in the depth of the pores of the electrodes regardless of the temperature and there is therefore the same contribution to the capacitance of the double layer for the low temperatures as for higher temperatures. The capacitance is influenced by the temperature mainly in the frequency range between 0.1 and 10 Hz, which corresponds to the domain of operation.
Increasing the temperature will have the main effect to reduce the electrolyte viscosity and to improve the accessibility of the surface for the ions. The ions, thanks to their higher mobility in the warm solvent, will be able to reach deeper carbon area in a shorter time. The increased path area is resulting in a reduced supercapacitor series resistance and in an increased capacitance with the temperature. Figures 1 and 2 show the measured and simulated frequency spectra of the BCAP0010 supercapacitor capacitance and series resistance for different temperatures.
[i] Kötz R, Hahn M, Gallay R. Temperature behaviour and impedance fundamentals of supercapacitors. J Power Sources 2006;154:550-5.
[ii] Gualous H, Bouquain D, Berthon A, Kauffmann JM. Experimental study of supercapacitor serial resistance and capacitance variations with temperature. J Power Sources 2003;123:86-93.