Ohmic solution resistance

UMEs of 10 pm in diameter and voltammetric instruments for use with such UMEs are commercially available. Electrodes of smaller dimensions can be prepared in the laboratory, although this requires considerable skill [74], In order to use UMEs successfully for high-speed voltammetry in highly resistive solutions, care must be taken concerning the effects of the ohmic drop and the capacitance of the cell system [65 b, 74, 75]. Moreover, two types of voltammograms, i.e. curves (a) and (b) in Fig. 5.23, should be used appropriately, according to the ob-... 

Because of the very small total currents at microelectrodes, it is possible to work in highly resistive solutions that would develop large ohmic (iR) drops... 

In the case of microelectrodes where currents are sufficiently small so that the reference electrode can serve simultaneously as auxiliary electrode (see above) the solution ohmic potential drop (product of current and solution resistance) is also small. This means that measurements can be made in highly resistive media without the addition of supporting electrolyte, a fact that can be very useful. 

Table 2 Solution Ohmic Resistance Versus Reference Electrode Distance...

Solution Ohmic Resistance Kinetic Resistance Mass-Transfer Resistance... 

The sums of the currents resulting from the oxidation and from the reduction reactions are also shown in Fig. 4.13 as a function of potential. The steady-state corrosion condition of ZI0X = ZIred corresponds to the intersection of the XIox and XIred lines, which identifies the corrosion potential, Ecorr. The solution ohmic resistance is assumed to be very small for the present interpretation. 

Miniaturization of enzyme electrodes (H) has always been relevant for in vivo applications. A new generation of microelectrodes has already been employed (14.) for in vivo electroanalysis. The diminished surface area of a microelectrode results in reduced capacitance, reduced ohmic losses as a consequence of the smaller current and increased rates of mass transport to and from the electrode resulting in a steady state response. This has led (1 ) to investigations of electrochemistry in highly-resistive solutions, studies of fast reactions with electron transfer rates greater than... 

Usually the impedance is measured as a ftmction of the frequency, and its variation is characteristic of the electrical circuit (where the circuit consists of passive and active circuit elements). An electrochemical cell can be described by an equivalent circuit. Under appropriate conditions, i.e., at well-selected cell geometry, working and auxihary electrodes, etc., the impedance response will be related to the properties of the working electrode and the solution (ohmic) resistance. 

When a direct current, i, is applied to the cell, both the anode and the cathode are polarized. E in Fig. 4.3.3 illustrates the polarization potential of the working electrode under study, which is the sum of the static potential E and the overvoltage t]. However, the measured potential difference between the working electrode and the reference electrode contains the solution ohmic drop, ipx, since the Luggin tip is located far from the electrode surface by the distance x. p refers to the specific resistivity of the electrolytic... 

The screening of bulk electric fields by the addition of supporting electrolyte is useful since it prevents migration due to electrostatic attractions from influencing the voltammetric current and allows the use of a simpler diffusion-only theory based on Fick s laws (see Chapter 3). What is more, passing current through a resistive solution generates a potential difference known as ohmic drop , since its value can be understood from Ohm s law ... 

The ionic conductivities of the polybromide complexes are considerable, approaching the values of ordinary aqueous salt solutions, due to their fused-salt nature. This property means an additional advantage since the electrolyte resistivity, the ohmic voltage drop, and polarization effects remain low. 

The position of the electrodes in the reactor can be optimized as a function of hydrodynamic parameters and current density (j). Complementary rules should include the influences of electrode gap (e) and operating conditions on voltage U (and consequently on energy consumption). The measured potential is the sum of three contributions, namely the kinetic overpotential, the mass transfer overpotential and the overpotential caused by solution ohmic resistance. Kinetic and mass transfer overpotentials increase with current density, but mass transfer is mainly related to mixing conditions if mixing is rapid enough, mass transfer overpotential should be negligible. In this case, the model described by Chen et al., (2004) is often recommended for non-passivated electrodes ... 

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

Because some substances may preferentially adsorb onto the surface of the electrode, the composition near the iaterface differs from that ia the bulk solution. If the cell current is 2ero, there is no potential drop from ohmic resistance ia the electrolyte or the electrodes. Yet from the thermodynamic analysis it is seen that there is a measurable cell potential. The question from where this potential arises can be answered by considering the iaterface. 

With eveiy change in ion concentration, there is an electrical effect generated by an electrochemical cell. The anion membrane shown in the middle has three cells associated with it, two caused by the concentration differences in the boundaiy layers, and one resulting from the concentration difference across the membrane. In addition, there are ohmic resistances for each step, resulting from the E/I resistance through the solution, boundary layers, and the membrane. In solution, current is carried by ions, and their movement produces a fric tion effect manifested as a resistance. In practical applications, I R losses are more important than the power required to move ions to a compartment wim a higher concentration. 

Another parameter essential for quantitative applications of micropipettes is the internal ohmic resistance, R. It is largely determined by the solution resistance inside the narrow shaft of the pipette, and can be minimized by producing short (patch-type) pipettes. The micropipette resistance has been evaluated from AC impedance measurements. Beattie et al. measured the resistance of micropipettes filled with aqueous KCl solutions (0.01, 0.1, and 1 M) [18b]. The value obtained for a 3.5/am-radius pipette was within the range from 10 to 10 As expected, the tip resistance was inversely proportional to the concentration of KCl in the filling solution. In ref. 18b, the effect of pipette radius on the tip resistance was evaluated using a constant concentration of KCl. The pipette resistance varied inversely with the tip radius. The iR drop was found to be 4.5-8 mV for the pipette radii of 0.6 to 19/rm when 10 mM KCl was used. 

With application of positive current, the entire potential shifted to much more negative values and with positive current, to more negative values. These shifts should be the result of ohmic drop induced by electrical resistance of the octanol solution. 

In addition, the emf to be applied must overcome the ohmic resistance of the solution and the cathode counter potential, which are respectively,... 

This impedance response, in general, is similar to that elicited from an Armstrong electrical circuit, shown in Figure 3, which we represent by Rfl+Cd/(Rt+Ca/Ra). Rfl is identified with the ohmic resistance of the solution, leads, etc. Cj with the double-layer capacitance of the solution/metal interface Rfc with its resistance to charge transfer and Ca and Ra with the capacitance and resistance... 

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). 

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