With the goal of designing an EC for a specific application that requires a high level of energy density or high power density or both, many researchers have made significant progress with respect to both the theoretical and practical development of ECs and have published a large number of research articles and technical reports. The reported results reveal that EC performance is predominantly characterized by the following factors:
● Specific capacitance and equivalent series resistance
As discussed in the previous section, the capacitance (C) is dependent on the mechanism through which electrochemical capacitors store energy. For a typical parallel plate capacitor,
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the capacitance, which is measured in farads (F), is directly proportional to the SSA of the electrode and the relative permittivity of the electrolyte, and inversely proportional to the effective thickness of the double layer as indentified in Eq. (1). The density of the electrode material will also significantly affect capacitor performance; such parameters are usually expressed as gravimetric energy (Wh/kg) and power (W/kg) densities. The most important metric of an electrode material is therefore its specific capacitance parameter, such as the gravimetric (F/g) or volumetric capacitance (F/cc) of the device.
The main indicator of EC power capability is based on the direct current resistance or equivalent series resistance (ESR). A lower ESR can obviously supply peak powers more efficiently, leading to increased overall system efficiency and cycle stability. In practical EC devices, a number of factors contribute to resistance: the electronic resistance of the electrode material, the interfacial resistance between the electrode and the current-collector, the resistance of the ions moving through the separator, and the intrinsic resistance of the electrolyte.
● Energy and power density
Two primary attributes of an EC are its energy and power density. The electrical energy stored in a charged capacitor is established between the plates that accommodate charges +Q and –Q at a voltage difference, V; the stored energy (E) is therefore calculated from
(28) Maximum energy density is achieved when V and C are at maximum levels, but this value is applicable only in the case of ideal EDLCs that have no equivalent series resistance or parallel leakage resistance. This value thus reflects the theoretical maximum energy density
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[17]. In practice, the cell voltage usually falls appreciably with the extent of the charge consumed, and an integral Q·dV is required because V drops during the discharge.
Power (P) generally refers to the rate of energy delivery per unit of time, or it can correspond to a specific rate of discharge into a given load resistance at a particular current. Power density can be defined as the current (I) multiplied by the differential potential (V), but the internal resistance of a capacitor limits its maximum power. The potential normally decreases with increasing I owing to an ohmic IR drop caused by the internal series resistance of the cell (RS) or by the effects of kinetic polarization. However, Miller has shown how maximum power delivery can be calculated with use of a simple series RC circuit [44]. When maximum power delivery as described in Eq. (29) is considered, the maximum discharging current Imax is Vi (initial potential)/2RS so that the maximum potential can then be defined as Vi/2. The maximum power densities can therefore be expressed as
(29) From these equations, it can be seen that V, C and Rs are three important variables that determine EC energy and power densities. Maximum energy density is proportional to its capacitance and operating voltage window, meaning that increasing the capacitance and the EC voltage within the stability of the electrolyte is an effective method of improving energy density. Such an enhancement can be achieved by increasing the specific capacitance of the electrode materials as well as by selecting appropriate electrolytes. Eq. (29) also indicates that the larger the ESR, the lower power density will be. If the goal is to improve EC performance by increasing the power density, the major focus should be reducing the ESR.
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In contrast to their discharged state, charged batteries are in a state characterized by a high level of free energy, which means that a specific thermodynamic force provides a stable voltage in a charged state. Unlike batteries, electrostatically charged ECs have no mechanism that thermodynamically or kinetically stabilize their voltages. As a result, the charge status can be easily disturbed, causing to their self-discharge. To date, very little work has been conducted with the objective of uncovering the self-discharge mechanism in ECs, but it is known that an electrostatically determined potential difference can be easily disturbed by a depolarizing process set up, e.g., from an impurity or from internal redox reactions [45-48]. The self-discharge creates a decline in voltage so that the charge is lost, causing the capacitor to approach malfunctioning condition. EC self-discharge behavior therefore constitutes an unreliability factor in energy storage and makes the self-discharge characteristics of an EC important in evaluating its performance. A study revealed that ECs are characterized by a low duration and by a high self-discharging rate of 10 to 40% per day [49].
● Temperature dependence
The dependence of EC performance on temperature can be of practical significance in the operation of a variety of applications. For example, if their cycle life performance for a wide range of temperature is considered, ECs could function effectively in specific environments such as in vehicles or for cold-starting in northern climates. Typical operating temperatures range from -40 °C to 70 °C. However, under high power operating conditions, internal heat generation raises the temperature of the device, which strongly influences cycle life performance. Capacitance degradations are also influenced by temperature. A practical evaluation of the effects of temperature on power availability, capacitance and degradation of
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materials with respect to cycle life is therefore necessary. These factors will play an important role in technology development and device testing for a variety of applications, in which reliable energy storage is required for the operation of proprietary electronic devices under all temperature conditions.