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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.

Experimental work has provided significant insight into lithium-ion capacitor (LIC) performance [^{−1}) and long cycle life (e.g. 300,000 cycles in laboratory experiments at General Capacitor) but low specific energy (5 - 10 Wh∙kg^{−1}) [

Cao and Zheng have studied how LICs’ internal resistance decreases at high temperatures [

Past LIC modeling studies have focused upon the effects of ambient and operating temperature upon cycle life or upon LIC performance as part of a larger system. Omar et al. [

Concerning LIC cycle life, Uno and Kukita [

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.

As aforementioned, electrolyte breakdown is a primary cause of EDLC degradation. This degradation is conveniently represented by an Arrhenius equation, as follows

k = A r e − E a R T (1)

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 [_{a} is not constant but has been observed in the range 10 - 50 kJ∙mol^{−1} for LICs [

D T = k b (2)

and

A D = A b (3)

wherein D_{T} is the degradation ratio and A_{D} is the degradation constant, Equation (1) above can be rewritten as follows

D T = A D e − E a R T (4)

where 0 ≤ D_{T} ≤ 1 [_{T} can be used to compute the degradation acceleration factor based upon 10˚C of T.

α = ( T − T r e f 10 ) D T D T r e f (5)

where α is the acceleration factor, T is the ambient temperature, D T r e f is a

degradation factor at a given reference ambient temperature, and T r e f is the reference ambient temperature [_{d}) can be computed

C d = 100 − d T r e f α ( T − T r e f 10 ) t (6)

where d T r e f is a degradation rate constant at T r e f and t is the time in number

of cycles [_{T} decreases over time and, consequently, the change in C_{d} decreases as a function of time, creating an Arrhenius curve [

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 [

By contrast, another method computes capacitance degradation from the effects of temperature and voltage upon electrochemical double layer degradation as follows

C d = ( c i − a t 1 + v t c i ) × 100 (7)

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 [

At high temperatures LICs’ internal resistance decreases [

Furthermore, the Butler-Volmer equation predicts an inverse relationship between cycle current and temperature as follows

i d = i 0 ( e α a F n R T η − e − α c F n R T η ) (8)

where i d is current density, i 0 is exchange current density, α a is the specific surface area of the anode electrode, α c 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 [

Because in an LIC the amount of charge stored at the negative electrode is orders of magnitude higher than the cathode [

e − α c F n R T η ≈ 1 (9)

Therefore

i d = i 0 e α a F n R T η − 1 (10)

This assumption has proven accurate in past studies approximating energy storage as a function of constituent component materials, design, and operating conditions [

i d = i a (11)

where i is current and A is the surface area

i ∝ 1 T (12)

The relationships given in Equation (4) and Equation (12) indicate that cells cycled at constant temperature but different cycle currents should also degrade according to an Arrhenius equation taking the basic form

D T = A i e − k i (13)

wherein D_{T} is a degradation ratio, A_{i} is a degradation constant specific to i, and k_{i} is a kinetic constant dependent upon current, wherein

i ∝ k i (14)

However, Moye et al. recently found that although Equation (12) is accurate, temperature change during a charge cycle inside an LIC is small (<1%), and temperature changes are mostly observed in the low current regimes where Faradaic energy storage reactions dominate, similar to a lithium-ion battery [_{d} values in excess of 250 A∙kg^{−1} no temperature increase was observed. Thus elevated current does not necessarily elevate temperature, but, as established by Uno et al. and El Ghossein et al., it does degrade a LIC in a similar manner [

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

General Capacitor has collected cycle life data on its LCA200G1. The LCA200G1 was one of General Capacitor’s established commercial products, so data was easily obtained. Using an established, commercial product eliminated much of the experimental variability often encountered in laboratory-made LICs. Much LCA200G1 evaluation data has been made public in earlier studies [

Parameter | Value |
---|---|

Lithium Source | Foil Strips |

Positive Electrode Active Material | Activated Carbon |

Positive Electrode Active Layer Thickness | 100 µm |

Double-Sided Positive Electrodes | 7 |

Negative Electrode Active Material | Hard Carbon |

Negative Electrode Active Layer Thickness | 90 - 95 µm |

Double-Sided Negative Electrodes | 6 |

Single-Sided Negative Electrodes | 2 |

Negative Electrode Lithium Loading | 8.81% |

Negative Electrode Porosity | 44.16% |

Positive Electrode : Negative Electrode Mass Ratio | 0.678 |

Lithium Source | Foil Strips |

Positive Electrode Active Material | Activated Carbon |

Positive Electrode Active Layer Thickness | 100 µm |

Double-Sided Positive Electrodes | 7 |

Cycle life data was acquired at 4A and 5A for General Capacitor LCA200G1 LICs made in accordance with

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

c i − c f c i = A D e − k t t (15)

where A_{D} is a degradation constant, k t is a kinetic constant encompassing E_{a}, , and T, and t is the cycle number. Although Equation (15) does not use Langmuir adsorption coefficients, like Equation (7) it does depend upon an exponential governed by t. c f is the final capacitance of the LIC after degradation, related to D_{T} by

D T = c i − c f t (16)

where c i is the initial capacitance of the LIC [

c f = c i − t A D e − E a R T (17)

Combining Equation (15) with Equation (17) indicates

A D e − k t t = c i − t A D e − E a R T (18)

At t = 1 cycle Equation (18) simplifies to

A D e − k t = c i − A D e − E a R T (19)

If A_{D} is close in value to c i , then

k t = − ln ( 1 − e − E a R T ) (20)

and

E a = − R T ln ( 1 − e − k t ) (21)

Trend lines were extrapolated from the foiled data, as shown in

c = 0.97 e − 7 × 10 − 7 t (22)

for 4 A cycles, and

c = 0.97 e − 1 × 10 − 6 t (23)

For 5 A cycles. A_{D} is a constant 0.97. k t is 7 × 10^{−}^{7} for 4 A cycles and 1 × 10^{−}^{6} for 5 A cycles. For 5 A cycles, assuming cell failure when c f is 80% of c i , Equation (21) indicates 275,263 cycles. The only changing input variable is cycle current. A_{D} remains a constant, as it should for two identical LICs with identical chemical and physical properties. Thus Equations (15) and (17) are met.

Notice that for both relationships

i ∝ k t (24)

meeting the requirements of Equation (14). Solving Equation (21) for E_{a} using the k value given in Equation (22) and the nearly constant average ambient temperature of 31˚C (304 K) yields E_{a} = 30.4 kJ∙mol^{−}^{1}. Likewise, solving Equation (21) for E_{a} using the k value given in Equation (23) yields E_{a} = 35.8 kJ∙mol^{−}^{1}.

These values agree with 10 - 50 kJ∙mol^{−}^{1} reported by Uno and Tanaka. Thus elevating cycle current decreases E_{a}. In accordance with Equation (1), decreased E_{a} accelerates degradation like increased T does.

Prior to this study, it was well established that elevated temperatures accelerate LIC degradation. During this study, experimental LIC cycle life degradation at different cycle currents but constant ambient temperatures was approximated by Arrhenius equations as a function of the number of cycles. The Butler-Volmer equation indicates elevated cycle current may impact cell temperature and thereby degrade the LIC. However, other studies indicate that current does not induce much temperature increase in LICs. This study sought to understand why elevated current degrades a LIC without appreciably changing its temperature. Results indicate that cycle current decreases activation energy. These effects on activation energy degrade the LIC in the same manner as temperature.

Mathematically, these results agree with other, unrelated studies examing LIC degradation from the perspective of ambient temperature and the electrochemical double layer. Now that this study has demonstrated that dis/charge current affects activation energy as a degradation mechanism, future research should examine reasons for this phenomenon and eventually quantify the relationship between current and activation energy.

This research was performed using the resources of General Capacitor LLC and Moye Consultants LLC.

The authors declare no conflicts of interest regarding the publication of this paper.

Moye, D.G., Moss, P.L., Chen, X.J., Cao, W.J. and Foo, S. (2020) Observations on Arrhenius Degradation of Lithium-Ion Capacitors. Materials Sciences and Applications, 11, 450-461. https://doi.org/10.4236/msa.2020.117031

A Langmuir adsorption coefficient as a function of temperature

A Ampere

A area

A_{D} degradation rate constant

B arbitrary constant

C Celsius

C_{d} per cent capacitance degradation

c_{f} final capacitance

c_{i} initial capacitance

COTS commercial off the shelf

D_{T} rate constant

d T r e f degradation rate constant at T_{ref}

D T r e f degradation factor at a given reference ambient temperature

E_{a} activation energy

ECM equivalent circuit model

EDLC electrochemical double layer capacitor

EIS electrochemical impedance spectroscopy

ESR equivalent series resistance

F Faraday’s constant

g gram

i current

i_{d} current density

i_{o} exchange current density

k kilo

k Chemical reaction rate per cycle

K Kelvin

k_{t} kinetic constant relating E_{a}, R, and T to t

LIB lithium-ion battery

LIC lithium-ion capacitor

mol moles

n number of electrons per ion

R universal gas constant

R_{ct} charge transfer resistance

R_{s} series resistance

R_{W} Warburg resistance

SEI solid electrolyte interphase

t time in numbers of cycles

T cell temperature

T_{ref} reference ambient temperature

v Langmuir adsorption coefficient

Wh watt-hour

α acceleration factor

α a anode specific surface area

α c cathode specific surface area

η activation overpotential