Capacitor, charging process

Figure 29. Depiction of the charging process of a symmetric capacitor.

In the second type of supercapacitor, sometimes termed pseudocapacitors, redox capacitors or electrochemical capacitors, the non-Faradaic doublelayer charging process is accompanied by charge transfer. This Faradaic process must be characterized by extremely fast kinetics in order to allow device operation with high current density discharge pulses. 

Note that this capacitance is linked to the electron transfer reaction and therefore has a faradaic origin and is not related to the double-layer charging process (this last capacitance corresponds to a pure capacitor see Sect. 6.4.1.5). In this sense, it has been called pseudo-capacitance [56]. The normalized current i/rCv is a ratio of capacitances since, from Eq. (6.161), y ev = (Icv/v)/(Qf F/RT)) = Ccv/Cf [48, 57],... 

FIGURE 8.32 Typical potential profiles for (a) positive electrode in a conventional asymmetric capacitor built with a non pre-doped Li inter calation carbon for the negative electrode (curve 1), an asymmetric capacitor with a pre-doped Li-ion intercalation carbon material (curve 2), and (b) positive and negative electrodes of an EDLC during the charging process. (From Aida, T., et al., Electrochem. Solid-State Lett., 9, A534, 2006. With permission.)... 

In the fields of capacitors and rechargeable batteries charge capacity defines the capacity that is involved in the charge process of the device and is usually compared to the capacity that is involved in the discharge process (discharge capacity). The losses in the charge process should be minimal in order to obtain good cycleability life of the device. 

The cell time constant, Tceii = RCd expresses the ability of the cell to respond to fast changes in the electrode potential. Part of the current observed initially in a CA experiment in which the potential is changed suddenly is used to charge the doublelayer capacitor and is called the capacitative current, k- Because this charging process passes the resistance in the cell, the current response will be the same as for a RC circuit, that is, an exponential function (Eq. 82). 

The subscripts refer to frequency, a sine wave parameter. Doo is the surface charge density at t = 0+, which is after the step but so early that only apparently instantaneous polarization mechanisms have come to effect (high frequency e.g., electronic polarization). The capacitor charging current value at t = 0 is infinite, so the model has some physical flaws. Do is the charge density after so long time that the new equilibrium has been obtained and the charging current has become zero. With a single Debye dispersion, this low-frequency value is called the static value (see Section 6.2.1). t is the exponential time constant of the relaxation process. 

Now let us introduce passive ion channels in the membrane of a polarized cell (Figure 5.7). The channels are normally closed, but now suddenly opened. Due to the potential difference, cations will immediately start to migrate into the negative cell interior. A current density field is suddenly created both intra- and extracellularly. The extracellular current density vector field J and the potential field are related by Eq. 2.1 V = — J/a. The current is generated by the ionic flow, and it terminates on the membrane capacitor in a discharge/charge process. 

Fig. 14.6 In situ XRD patterns of KS6 cathode in KS6/AC capacitor in the initial charge process (weight ratio of AC/KS6 is 1). Reproduced with the permission from Ref. 6, copyright (2006), Electrochemical Society...

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