I came to know with increasing C-rate the battery capacity will decrease, whereas for decreasing the C-rate the Capacity increases. I read that with higher C-rate the resistance will increase thus capacity will decrease. Kindly explain more details on how the resistance increase in terms of chemical/electrical perspective?
Omitting details, the basic idea is the following. Battery voltage includes mainly 3 contributions: difference between chemical potentials of the electrodes (well-known equation ΔG=-zFE) and two electrical potentials of the double layers at the surface of each electrode. The potential of the double layer includes the equilibrium part and the part caused be the finite rate of the transfer of the ions between electrodes and electrolyte (so-called overpotential). Battery capacity is the amount of the transferred ions, so it is directly related to the chemical composition of the electrodes and their chemical potentials.
If we charge the battery to the same voltage at two different rates, the overpotential will be higher for the battery charged at the higher rate. Correspondingly, the difference between the chemical potentials will be lower (we fix only the sum of all contributions to voltage!) and amount of the transferred ions will be lower, meaning that the capacity will be lower.
As for resistance, the charge transfer through the double layers constitutes a big part of it. And the battery with high resistance will have slower rate of the ion transfer, which means higher overpotentials at the same charging rate. As a result, the capacity will be lower again.
Omitting details, the basic idea is the following. Battery voltage includes mainly 3 contributions: difference between chemical potentials of the electrodes (well-known equation ΔG=-zFE) and two electrical potentials of the double layers at the surface of each electrode. The potential of the double layer includes the equilibrium part and the part caused be the finite rate of the transfer of the ions between electrodes and electrolyte (so-called overpotential). Battery capacity is the amount of the transferred ions, so it is directly related to the chemical composition of the electrodes and their chemical potentials.
If we charge the battery to the same voltage at two different rates, the overpotential will be higher for the battery charged at the higher rate. Correspondingly, the difference between the chemical potentials will be lower (we fix only the sum of all contributions to voltage!) and amount of the transferred ions will be lower, meaning that the capacity will be lower.
As for resistance, the charge transfer through the double layers constitutes a big part of it. And the battery with high resistance will have slower rate of the ion transfer, which means higher overpotentials at the same charging rate. As a result, the capacity will be lower again.
Dear Bibek,
Our colleague Alexander gave a nice explanation from an electro-chemical perspective.
On the other hand, from a pure electrical perspective, empirical studies on electrochemical batteries demonstrate a non-linear power relationship between the discharge current (or C-rate if normalized to some base rated current) and delivered capacity. This is the well know Peukert's effect and it is formulated through the so called Peukert's law. It should be noted that the aforementioned Peukert's effect is more evident for Lead Acid batteries than for Li-ion batteries. For the latter, it could be even neglected in some cases.
Moreover, extensive experimental investigation of the impedance characteristics of electro-chemical batteries at various conditions (current, temperature and SoC) and aging states can be found in the literature, based on pulse characterization of frequency response measurement techniques (EIS).
It is difficult to summarize in a few lines the contents of these studies. In general, it should be noted that the battery internal resistance may defined in different ways depending on the measurement technique. Moreover, it should be also noted that, in general, the value of the so called internal resistance decreases with the current. However, this dependency could be neglected for example for certain Li-ion batteries at certain temperatures and ageing states. More specifically, newer (least aged) Li-ion batteries operated at higher temperatures tend to show lower dependency, since the average value of the internal resistance is lower under these conditions.
Last but not least, please also note that, even though the internal resistance value may decrease with the current, the delta voltage value measured on battery terminals caused by the charging or discharging current would always increase with the current.
Good luck with your research! :)
Cheers
Thank you Dr. for your long and clear comments. Really appreciate your time .
Dr. Jorge has brought out the key point to be noted. The relationship between temperature and the internal resistance needs to be considered. Internal resistance is a function of both temperature and the state of charge of the battery. it decreases with increase in temperature and it varies across states of charge (may not be linear). At higher current(C) rates, although the overpotential is high and the corresponding internal resistance might seem to increase, the cell temperature would rise at such higher C rates which will eventually lead to decrease in internal resistance. As a result the average internal resistance recorded during a charge or discharge cycle will be lesser at a higher current.
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