Fractional Electrode Area

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

So far we have discussed only the reversible case. The equivalence of the net Faradaic current at the NEE and at a macroelectrode of the same geometric area (Fig. 7) means that the flux at the individual elements of the NEE are many orders of magnitude larger than the flux at the macroelectrode. Indeed, the experimentally determined fractional electrode areas (Table 1) indicate that, for the reversible case, the flux at the elements of a... 

Because the fractional electrode area at the lONEE is lower than at the 30NEE (Table 1), the transition to quasireversible behavior would be expected to occur at even lower scan rates at the lONEE. Voltammograms for RuCNHs) at a lONEE are shown in Eig. 8B. At the lONEE it is impossible to obtain the reversible case, even at a scan rate as low as 5 mV s . The effect of quasireversible electrochemistry is clearly seen in the larger AEp values and in the diminution of the voltammetric peak currents at the lONEE (relative to the 30NEE Fig. 8). This diminution in peak current is characteristic of the quasireversible case at an ensemble of nanoelectrodes [78,81]. These preliminary studies indicate that the response characteristics of the NEEs are in qualitative agreement with theoretical predictions [78,81]. 

Voltammograms for various low concentrations of TMAFc at a lONEE are shown in Fig. 9B. While the voltammograms look nearly identical to those obtained at the macroelectrode, the concentrations are 3 orders of magnitude lower. Using the same criterion for the detection limit, we obtain a detection limit at the lONEE that is 3 orders of magnitude lower (1.6 nM) than at the macroelectrode. This experimentally observed enhancement in detection limit at the NEE is exactly as would be predicted from the fractional electrode area data in Table 1. 

The minimum detection limit in the voltammetric analysis on NEEs should be smaller than the value observed on the macroelectrodes, based on their fractional electrode area. Indeed, detection limits of several nM for analytes such as [(trimethylamino)methyl]ferrocene (TMAfc+) are observed with NEEs while the same species on a macroelectrode could be detected only to a minimum of several pM [71] (figure 20.4). Membranes with Au nanotubules are shown to function as... 

This ratio is larger at the NEE than that at the conventional electrode by a factor that is the reciprocal of the fractional electrode area/. Since typical /values for NEEs are between 10" and 10, ip/ic ratios at NEEs can be 2-3 orders of magnitude higher than the ratios at conventional electrodes of the same geometric area. Thus, detection limits at NEEs are 2-3 orders of magnimde lower than that at regular electrodes (5, 68, 69). 

Because the fractional electrode area at the lONEE is lower than at the 30NEE (Table 1), the transition to quasireversible behavior would be expected to occur at even lower scan rates at the lONEE. Voltammograms for at a lONEE are shown in Fig. 8B. At the lONEE it is... 

The ratio between the active and the geometric area defines a key parameter named fractional electrode area (/) ... 

Current Flow Corona discharge is accompanied by a relatively small flow of electric current, typically 0.1 to 0.5 mA/m" of collecting-electrode area (projected, rather than actual area). Sparking usually involves a considerably larger flow of current which cannot be tolerated except for occasional periods of a fraction of a second duration, and then only when smtable electrical controls are provided to hmit the current. However, when suitable controls are provided, precipitators have been operated continuously with a small amount of sparking... 

The relationship between the fractional surface coverage 9 and the double-layer capacitance C may be better understood in terms of the following model. The doublelayer capacitance at the electrode in the presence of adsorption can be viewed as consisting of two capacitors connected in parallel. One capacitor corresponds to the electrode areas that are unoccupied (free) and the other to the electrode areas that are occupied (covered) with adsorbate (13-15). These two condenser-capacitors have different dielectrics and thus different capacitances. The capacitance of a parallel combination of capacitors is equal to the sum of the individual capacitances. 

The proportionality constant A, which represents the fraction of the solute removed per unit of time at any instant of the electrolysis, can be shown to be given by A = AmlV, where A = electrode area, V = volume, and m = mass-transport constant [Equation (14-3)]. The value of A depends on the particular cell geometry (A/V) and the stirring rate. If the initial current is and the proportionality holds throughout the electrolysis, after integration we have... 

It is useful to define an active-area density a as the local fraction of the cathode area that is electroactive (i.e., the fraction that is not blocked by resist). This concept is illustrated in Fig. 2. In places where a large fraction of the electrode surface is blocked, a is low. Further, it is useful to define two different measures of current density. Let the active current density / act represent the current per unit of electroactive area (remembering that some fraction of the electrode area is blocked by resist). Let the superficial current density /gup represent the current per unit superficial area (including both the resist-covered and the electroactive portions). The relationship between /act and /gup is illustrated in Fig. 3. The physical basis for... 

The current measured by an amperometric electrode is directly proportional to the flux described in Eq. 7.11, with proportionality constants n (electrons in the stoichiometric electrochemical reaction), F (Faraday s constant, 96,487 C/mol), A (electrode area) and B (fractional collection efficiency) ... 

At each voltage level of interest, the probability of failure p (i.e., the fraction of specimens with a value of breakdown voltage below this level, corrected if necessary for the number of specimens) is calculated, the electrode area being rq. To calculate the probability of failure p2 at the same voltage, with a different area the following equation is used ... 

Given that the density of electrodeposited nontemplated vanadia is 2.87 g cm , the average density of double-gyroid structured vanadia with a volume fraction of 37.9 % is1.09 g cm, illustrating the porous nature of the DG structure [16]. Thus, the specific surface area of DG-structured V2O5 is 1.48 m g . Furthermore, the mass m of vanadia electrodes was calculated using these densities, the electrode area and thickness. The V2O5 film thickness was determined by cross-sectional SEM or with a surface profilometer. 

Fig. 17 Cyclic voltammograms for the reductive desorption of various SAMs in 0.5 M KOH solution (a) original phase-separated binary SAM of MPA and HDT where the surface mole fraction of MPA is 0.49 (b) SAM after the selective desorption of MPA (c) regenerated binary SAM of MPA and HDT (d) binary SAM of MUAand HDT after the selective replacement of M PA with MUA. Initial potential, —0.2 V scan rate, 20 mV s electrode area,...

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