Observations on Arrhenius Degradation of Lithium-Ion Capacitors

Earlier research determined that lithium-ion capacitor (LIC) cycle life degradation can be accelerated by elevated temperature. LIC cycle life degradation can be described by an Arrhenius equation. This study performed cycle life testing at a constant temperature but varied cycle current. The results were described by an Arrhenius equation relying upon the number of cycles and a constant, which was determined by cycle current. Using mathematical derivations and experimental results, the researchers quantified the effects of activation energy and temperature upon this constant. Because cell temperature is nearly constant during cycles, it was deduced that elevated cycle current decreases activation energy. This lower activation energy then accelerates degradation. Thus this research demonstrates that cycle current ages LICs through its effects on their activation energies.

Cao and Zheng have studied how LICs' internal resistance decreases at high temperatures [3]. Solid electrolyte interphase (SEI) is a thin layer that forms on the anode's surface as lithium reacts with the electrolyte or impurities in the cell.
This SEI is essential to performance, as it enables the passage of lithium ions between the electrolyte and the porous carbon material. However, SEI growth can become too thick and impede the intercalation of lithium-ions into the negative electrode. This is a common degradation mechanism, which often leads to  [12]. All of these studies collect data on pre-made, existing COTS LICs but do not consider any variables describing the electrochemistry inside the LICs.
This study seeks to understand cycle current's effects on cycle life degradation in LICs. It will be shown that findings from this study agreed with results from earlier studies, validating the research method employed here, which is described in Section 3.1.

Earlier Research
As aforementioned, electrolyte breakdown is a primary cause of EDLC degrada- where k is the chemical reaction rate per cycle, A r is a rate constant, E a is the activation energy, R is the gas constant, and T is the absolute temperature in Kelvin [13]. E a is not constant but has been observed in the range 10 -50 kJ•mol −1 for LICs [13]. Assuming an arbitrary constant (b) where 0 ≤ D T ≤ 1 [13]. From this equation D T can be used to compute the degradation acceleration factor based upon 10˚C of T.
where α is the acceleration factor, T is the ambient temperature, degradation factor at a given reference ambient temperature, and ref T is the reference ambient temperature [13]. From this relationship the per cent capacitance after degradation (C d ) can be computed [13].
Once A D , E a , and T are known, a LIC's degradation can be predicted. This model relies upon experimentally-determined parameters. However, A D and E a are not the same for all manufacturers [11] and require either a previous test or detailed knowledge of the manufacturing process. An Arrenhius equation that accurately predicts the degradation of one LIC may not be accurate for another.
By contrast, another method computes capacitance degradation from the effects of temperature and voltage upon electrochemical double layer degradation as follows where c i is the initial capacitance, t is the cycle number, a is the Langmuir adsorption coefficient as a function of temperature, and v is the Langmuir adsorption coefficient as a function of voltage [12]. Langmuir adsorption coefficients balance a material's likelihood to enter a carbon material against its propensity to gas. This agrees with earlier studies indicating that dendrite formed by lithium precipitating out of carbon electrodes is a common degradation and failure mechanism in LICs [14]. Using Langmuir coefficients to study cycle life degradation may be a promising approach. In catastrophic failures both gassing and dendrites have been observed [15]. Also, gassing appears to be a sign of de- where d i is current density, 0 i is exchange current density, a α is the specific surface area of the anode electrode, c α is the specific surface area of the cathode electrode, n is the number of electrons per ion (1 for lithium), η is the activation overpotential, F is Faraday's constant, and T is the absolute temperature of the electrochemical cell [1].
Because in an LIC the amount of charge stored at the negative electrode is orders of magnitude higher than the cathode [1], assume [17] where i is current and A is the surface area The relationships given in Equation (4) and Equation (12)  [13].
The main objective of this study was to determine why variations in cycle current degrade a LIC similarly to variations in cell temperature, although current does not appreciably change temperature.

A cycle life evaluation was performed upon a LCA200G1 LIC made by General
Capacitor, shown in Figure 1. General Capacitor has provided the design parameters for this product, as shown in Table 1.
General Capacitor has collected cycle life data on its LCA200G1. The

Experimental Method
Cycle life data was acquired at 4A and 5A for General Capacitor LCA200G1 LICs made in accordance with Table 1. Testing conditions could not be perfectly controlled. The temperature in the testing room averaged 29˚C -33˚C and was subject to variations during several power outages and maintenance on nearby equipment. Recent studies have noted changes in LIC energy storage as a function of temperature [2] [4]. Consequently, the data showed many small perturbations, including diurnal variation.
To correct these perturbations a foil was applied, averaging 9 data points before and 9 data points after each data point of interest, extending each datapoint over a 24 hour period. In order for the relationships identified in Equations (4) and (8) to hold valid under this experimental method, an Arrhenius relationship indicating degradation over subsequent cycles must take the form where A D is a degradation constant, t k is a kinetic constant encompassing E a ,  (16) where i c is the initial capacitance of the LIC [7]. Notice that in order to agree with Equation (4), Equation (15) must obey Equation (12). Combining Equation

Results
Trend lines were extrapolated from the foiled data, as shown in Figure 2. The trendlines revealed the following Arrhenius relationships, which meet the form of Equation (15), where capacitance (c) is expressed as a percentage

Conclusions
Prior