Electrolyte materials double-layer capacitance

High double-layer capacitance. The capacitance C of a capacitor is proportional to the capacitance of an electrode, which is dependent on the type of electrolyte material chosen. An electrolyte material showing a high double-layer capacitance Cd for a given electrode is desired. 

High r factors are, however, not without some other complications since they imply porosity of materials. Porosity can lead to the following difficulties (a) impediment to disengagement of evolved gases or of diffusion of elec-trochemically consumable gases (as in fuel-cell electrodes 7i2) (b) expulsion of electrolyte from pores on gas evolution and (c) internal current distribution effects associated with pore resistance or interparticle resistance effects that can lead to anomalously high Tafel slopes (132, 477) and (d) difficulties in the use of impedance measurements for characterizing adsorption and the double-layer capacitance behavior of such materials. On the other hand, it is possible that finely porous materials, such as Raney nickels, can develop special catalytic properties associated with small atomic metal cluster structures, as known from the unusual catalytic activities of such synthetically produced polyatomic metal clusters (133). 

A model predicting electrode response with time must therefore consider the following (1) the double-layer capacitance, (2) the concentration of electroactive species at the electrode surface (which in turn is affected by the diffusion coefficients), (3) the values of the formal potentials (E ), (4) the heterogeneous rate constants of the redox species (with respect to the electrode material and electrolyte composition), and (5) the electrical potential of the electrode itself. 

Double-layer properties of porous carbon materials have been widely investigated in relation to the development of the electrochemical capacitors. For detailed information the reader should consult specialized literature. For porous carbons materials, the double-layer capacitance depends on their specific snrface area [82,83], pore stmcture (notably, the pore size distribntion) [84-87], and their crystalline stmctnre and snrface chemistry [83,88,89], Shi [84] measnred the dc capacitance of varions carbons in a KOH electrolyte and noticed that the overall capacitance may reasonably be described as a sum of the capacitance of micro- and mesopores. Assuming that the electrical double layer propagates into micropores accessible for N2 adsorption, the author estimated the differential donble-layer capacitance per unit of micropore surface area as 15 to 20 p,F/cm. Lower values were reported by Vilinskaya... 

We see that the detailed behaviour varies with the electrolyte concentration but there is always a minimum in the relationship which occurs at a potential characteristic of the electrode material Solvent interface. This is the potential of zero charge (F/ zc)- The potential of zero charge is the potential at which the sign of the charge on the electrode changes. For the Hg/H O interface Epjc is about —0.5 V (SCE). For the Hg/HzO interface the double layer capacitance, CoLi is about 20-25 p cm . ... 

The contribution of faradaic and double-layer capacitances in the response of DG-structured V2O5 can be estimated by comparing the CV curves of devices that use RTIL electrolyte with and without lithium salt, shown in Fig. 5.14b. Since V2O5 does not react with either of the ions of pure RTIL, the lithium-free experiment tests the EDLC response. With lithium salt added, the significant increase in capacitive current and the appearance of peak pairs indicates that redox reactions are taking place. These faradaic processes are kinetically facile and thus considered pseudocapacitive, but phase transitions may occur. Although it is difficult to distinguish between redox and intercalation pseudocapacitance, the latter is likely to be present in DG bicontinuous materials. 

The EDLCs store charge electrostatically by using reversible adsorption of ions of the electrolyte on to high specific surface area materials, usually activated carbons. The charge separation occurs on polarisation at the electrode-electrolyte interface, which was first described by Helmholtz in 1853 as double layer capacitance. This is mathematically defined as ... 

Electrode impedance is an important parameter while fabricating the microelecffode array. Lower impedance is generally favoured for the stimulation material which enables high charge transfer capabilities. Looking closer to the elecffode-electrolyte interface the electrode impedance is dominated by the double-layer capacitance (Cd) as explained earlier, which is in series with the resistance of the electrolyte (Rg) [43], This acts like a high-pass filter with a cut-off frequency at ... 

A simple electrical model of the solution as seen by the electrodes is shown in Fig. 3. Resistances are primarily determined by the ionic content of the electrolyte solution, which is typically in the 0.01-0.10 M range. When the electrodes are placed in an electrolyte solution, a charge separation or double layer forms spontaneously at the electrode-solution interface. This produces a capacitance, commonly referred to as the double-layer capacitance, Cdl- The size of this capacitance is a function of electrode area, electrode-to-solution potential, electrode material, and the ion concentration in solution. The potentiostat compensates only for capacitance, impedance, and resistance (Cdla, Rc, Zfa) within its control loop and allows these to be largely ignored experimentally. Therefore, the uncompensated resistor, R , which is outside the loop, causes an error in the working electrode potential, as a result. However, given the very small amplitude currents usually involved... 

The semicircle at the high frequency region and the spike at the low frequency region are attributed to the bulk material and double layer capacitance at the electrolyte-electrode interface, respectively. The semicircle was found to diminish with temperature increment. On the other hand, the spike becomes more prominent as the temperature rises. This may be due to the ions moving to the electrolyte-electrode interface as temperature increases. 

The first attempts to achieve such a device were made in the 1970s. The cell had a non-symmetric Ag/RbAg4l5/C structure with a double-layer capacitance at the carbon electrode in the range of 10-40 nF cm" interface area However, due to the redox reaction, the working voltage was too low (<0.7 V) for the electronic devices of the time. Furthermore, the reversibility of the Ag electrode was poor and it was difficult to use fully the surface area of the ultrafine carbon. More recently, double-layer capacitors using acidic solution (H2SO4) as liquid electrolyte were developed by NEC (Nippon Electric Co. Ltd). A liquid electrolyte allows most of the surface area of the carbon electrode to be used. The electrical characteristics of the devices can be classified in relation to the properties of each material as follows. 

The actuation model obtained in Section 5.3.1 is an infinite-dimensional transfer function. All parameters in the model are already fundamental material parameters and actuator dimensions except the double-layer capacitance C and the resistance R. Scaling laws for C and R can be further derived to obtain a fully scalable model. In particular, G is proportional to the area A of polymer/electrolyte interface. The resistance R can be obtained as a function of material resistivity and dimensions using a transmission line model [Fang et al. (2008d)]. Fig. 5.5 shows the experimental verification of the scaling laws for C and R, respectively. 

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