Porous effect, electrodes relating

As a matter of fact, for porous carbon electrode it is still a troublesome issue to relate the determined surface fractal dimension dFss with the CPE exponent a. The effect of the surface inhomogeneity on the ion penetration into the pores during doublelayer charging/discharging will be discussed in detail in the following Section V.3. 

As mentioned earlier, thin films can be considered 2-D nanostructures. In the recent past, thin film-based technologies have been responsible for the design of an enormous variety of thin film-based electrochemical devices. 2-D nanostructures [91] composed of 0-D or 1-D materials are those that are associated with the interfacial properties of electrodes. In electrochemistry they are known as porous electrodes, and they sometimes possess an effective surface more than 1,000 times greater than the geometric area expected for a compact and homogeneous 2-D structured electrode, e.g., porous thin film-related electrodes [92-96]. 

The porous electrode theory was developed by several authors for dc conditions [185-188], bnt the theory is usually applied in the ac regime [92,100,101,189-199], where mainly small signal frequency-resolved techniques are used, the best example of which are ac theory and impedance spectra representation, introdnced in the previons section. The porous theory was first described by de Levi [92], who assumed that the interfacial impedance is independent of the distance within the pores to obtain an analytical solution. Becanse the dc potential decreases as a fnnction of depth, this corresponds to the assnmption that the faradaic impedance is independent of potential or that the porons model may only be applied in the absence of dc cnrrent. In snch a context, the effect of the transport and reaction phenomena and the capacitance effects on the pores of nanostructured electrodes are equally important, i.e., the effects associated with the capacitance of the ionic donble layer at the electrode/electrolyte-solntion interface. For instance, with regard to energy storage devices, the desirable specifications for energy density and power density, etc., are related to capacitance effects. It is a known fact that energy density decreases as the power density increases. This is true for EDLC or supercapacitors as well as for secondary batteries and fnel cells, particnlarly due to the distributed nature of the pores... 

The models that consider this approach are largely based on the assumption of effectively homogeneous local relaxation processes related to transport in each of the phases and electrical charge exchange between them. Thus, the complex problem of an uneven distribution of electrical current and potential inside the electrode can be described analytically, and impedances can be calculated. Furthermore the models may be conveniently pictured as a double-channel transmission line (Fig. 3.5). In several papers, the theory of the impedance of porous electrodes has been extended to cover those cases in which a complex frequency response arises in the transport processes [100] or at the inner surface [194,203]. 

There is an optimal concentration of HCIO4 which allows formation of the honeycomb-like stmctures with the maximal surface area [39]. The decrease of number of holes and the increase of their diameter observed after the optimal concentration of this acid are due to coalescence of neighboring hydrogen bubbles. The effect of the different parameters of electrolysis was comparable with those observed in the case of Cu. The mean diameter of the pores increased as the Pb concentration increased. As the current density increased, the porous Pb films became uniform while, at the same time, the pore size, wall thickness, and wire diameter became smaller. The pore size of the deposited porous film was closely related to the size of the hydrogen bubbles that departed from the electrode. A high current density facilitates the departure of the H2 bubbles with a smaller bubble size. 

The pear-shaped pores predict the formation of a semicircle on the complex plane plots that might be confused with a semicircle related to the coupling of the charge transfer resistance and double-layer capacitance. Such effects were observed experimentally for hydrogen evolution on porous electrodes [415, 416, 419, 420]. This suggests that at some electrodes, pores of a pearlike shape are present... 

Novel types of synthesis of modem electrocatalysts revealed that the properties of electrode materials can be affected by the controlled formation of nano-sized, finely dispersed, electrocatalyst particles. In the case of DSA, already the traditional preparation procedure involves the thermal decompositiOTi of the corresponding chlorides after dissolution in an appropriate solvent (usually a solvent of low viscosity, e.g., 2-propanol) [3], Recently, sol-gel synthesis was introduced for DSA preparatirMi, with the main effect being related to the increase in the real surface area of the anode [9,10], The effect is recognized as the geometric factor of increased electrocatalytic ability in addition to an electronic factor related to the chemical structure of electrocatalyst [2,4], which is essential for step (6). The geometric factor is important since the measure for the reaction rate is the current density, i.e., the current per surface area of the electrode available for the reaction. Thus, the reaction rate can be considerably increased by the application of nano-3D electrodes, which are porous systems with an extended real surface area. The polarization curves for the CER on... 

A related system involves thin (one or few monolayers) of surface species either covalently bonded or adsorbed onto the solid substrate. Since the effective surface concentration (Cs) is quite smaller than for thicker films, the PBD signal can be too weak to measure. One way to overcome this problem involves increasing the active area of the electrode while maintaining the geometrical area, by using porous electrodes. In that way, the adsorption of redox intermediates (e.g., CO) of methanol fuel cells on mesoporous metal electrodes have been studied successfully... 

Equation 4.32 shows that the oxidation current depends on the anode surface coverage by HCOOH and CO, Ohcooh and 0co, respectively, and it relates therefore, to the oscillatory phenomena discussed earlier. Experimentally, Lovic et al. determined a Tafel slope of 150 mV dec on Pt/C in both H2SO4 and HCIO4 up to an anode potential of 200 mV vs. SCE (i.e., 440 mV vs. SHE), with further increase (almost doubling) at higher potentials [144]. It was shown that various Oco values could simulate to some extent the measured experimental current densities [144]. Furthermore, the porous nature of the electrode with mass transfer and ionic conductivity related limitations effects also the apparent Tafel slope, inducing what is referred to as multiple Tafel slope behavior [146]. 

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