Charging equivalent circuit

The internal resistance /fi for electric vehicle batteries should be evidently as low as possible. The charging equivalent circuit of a battery is shown in Fig. 5.12. 

Figure Bl.28.8. Equivalent circuit for a tliree-electrode electrochemical cell. WE, CE and RE represent the working, counter and reference electrodes is the solution resistance, the uncompensated resistance, R the charge-transfer resistance, R the resistance of the reference electrode, the double-layer capacitance and the parasitic loss to tire ground.

Figure 13. Schematic presentation of a small segment of polyheteromicrophase SEI (a) and its equivalent circuit (b) A, native oxide film B, LiF or LiCl C, non conducting polymer D, Li2CO, or LiCO, R GB, grain boundary. RA,/ B,RD, ionic resistance of microphase A, B, D. Rc >Rqb charge-transfer resistances at the grain boundary of A to B or A to D, respectively. CA, CB, CD SEI capacitance for each of the particles A to D.

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

FIG. 6 Randles equivalent circuit for the ITIES Zq is the interfacial capacitance, Zy)v are the faradaic impedances of the charge transfer reactions, and is the solution resistance. 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

With respect to the size and charge selectivity of paracellular pathways, equivalent pore theory has been utilized to calculate an effective radius based on the membrane transport of uncharged hydrophilic molecules, while equivalent circuit theory has been used to separate mediated from paracellular membrane transport of small ions. The term equivalent should be emphasized, as selectivity parameters are obtained from membrane transport data, so phenomenological information is used to quantitate the magnitude of aqueous pathways... 

Now an equivalent circuit, which takes into account both the ion transport along the TC and the charge transfer through the carbon electrode material to the current collector, may be represented as in Fig. 2, wherein N = a(c)/4r, Cm and Rm are the total NP capacitance and resistance in a unit electrode volume (defined here as a product of a unit electrode area and the tier thickness), Re is the electrical resistance of an electrode in the same unit... 

Very often, the electrode-solution interface can be represented by an equivalent circuit, as shown in Fig. 5.10, where Rs denotes the ohmic resistance of the electrolyte solution, Cdl, the double layer capacitance, Rct the charge (or electron) transfer resistance that exists if a redox probe is present in the electrolyte solution, and Zw the Warburg impedance arising from the diffusion of redox probe ions from the bulk electrolyte to the electrode interface. Note that both Rs and Zw represent bulk properties and are not expected to be affected by an immunocomplex structure on an electrode surface. On the other hand, Cdl and Rct depend on the dielectric and insulating properties of the electrode-electrolyte solution interface. For example, for an electrode surface immobilized with an immunocomplex, the double layer capacitance would consist of a constant capacitance of the bare electrode (Cbare) and a variable capacitance arising from the immunocomplex structure (Cimmun), expressed as in Eq. (4). 

FIGURE 7.3 Simplified equivalent circuit of an original (unmodified) EIS structure (a) and EIS biosensor functionalized with charged macromolecules (b). Cj, Cx and CML are capacitances of the gate insulator, the space-charge region in the semiconductor, and the molecular layer, respectively / u is the resistance of... 

Fig. 18b.5. (a) The capacitor-like metal solution interface, the double layer, (b) The equivalent circuit with solution resistance and overall double-layer capacitor, (c) Charging current transient resulting from a step-potential at... 

Once the cell resistance, Ru, or the residual resistance ARu, is known, another possible strategy to handling ohmic drop problems consists of introducing ohmic drop and double-layer charging into the theoretical treatment of the cyclic voltammograms.19 The following relationships, obtained from the equivalent circuits in Figure 1.5, may be used for this purpose. 

FIGURE 2.45. Equivalent circuit for the cell and instrument. WE, RE, and CE, working, reference, and counter electrodes, respectively iph, photocurrent ij/, double-layer charging current Q, double-layer differential capacitance Rc, Ru, cell compensated (by the potentiostat) and uncompensated resistances, respectively Rs, sampling resistance RP, potentiostat resistance E, potential difference imposed by the potentiostat between the reference and working electrodes Vpu, photo-potential as measured across the sampling resistor. Adapted from Figure 1 of reference 51, with permission from Elsevier. 

Fig. 5-60. Equivalent circuit for an interfacial electric double layer comprising a space charge layer, a surface state and a compact la3 er at semiconductor electrodes Csc = capacity of a space charge layer C = capacity of a surface state Ch = capacity of a compact layer An = resistance of charging and discharging the surface state.

However, although the WO3 surface is filled , ions still move from the electrolyte reservoir toward the WO3-electrolyte interface. Such a situation results in the accumulation of charge at this interface. In effect, we have a structure which is physically very similar to that of a typical plate capacitor (see Figure 5.3). For this reason, the equivalent circuit (see Figure 8.12(b)) also contains a capacitor Q (where the subscript denotes surface ). 

The impedance response with frequency can be closely simulated by the equivalent circuit shown in Figure 27a, where Re, Ra, Cdi, Rad, and Cad represent the resistance or capacitance for the electrolyte solution, charge-transfer, double layer, and adsorbed layer, respectively. An interesting correlation was found between the passivating ability of various anions and the resistances of the two impedance components R and Rad, which are high for LiPFe-and LiBF4-based electrolytes and low for LiTf- or Lilm-based electrolytes. Using the rationale proposed by the authors, the former component (Ret) is... 

Figure 68. Nyquist plots of a charged lithium ion cell, a lithiated graphite/graphite cell, and a delithiated cathode/ cathode symmetrical cell. The inset is an equivalent circuit used for the interpretation of the impedance spectra. (Reproduced with permission from ref 512 (Figure 3). Copyright 2003 Elsevier.)...

Figure 6.19. Simplified equivalent circuit for single-electrode reaction [e.g., Eq. (6.6)] Qi, double-layer capacitance of test electrode charge-transfer resistance of electrode reaction.

In practice, poor charge mobility, energetic disorder, carrier trapping, and physical aberrations comphcate device characterization. The effects of these nonidealities are often modeled according to an equivalent circuit shown in Fig. 12. Incorporating all specific series resistive elements as R, and all specific parallel resistances as R, one obtains the expression... 

Generally, depending on the bias potential, the EIS leads to RC equivalent circuit loops representing both the space charge and the interface impedance components. The complete set of imaginary versus real impedance data leads to the construction of a semicircle that can be... 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

Find the charge-transfer resistance (/ CT), the double-layer capacitance (CDL), and the solution resistance (Rso]n) from the data listed in Table P.4 by using the simplest equivalent circuit for an electrochemical reaction shown in the figure. If the measurement was carried out at equilibrium potential, what is the exchange current (Kim)... 

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

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