Ohmic Drop Effects Research Articles

Effect of uncompensated ohmic drop in surface linear potential sweep voltammetry Application to the determination of surface rate constants

Effect of uncompensated ohmic drop in surface linear potential sweep voltammetry Application to the determination of surface rate constants

Effect of uncompensated ohmic drop in surface linear potential sweep voltammetry: Application to the determination of surface rate constants

The effect of ohmic drop on linear potential sweep voltammograms is studied theoretically in the case of quasi-reversible surface redox reactions. The uncompensated resistance produces manifestations on reversible peaks (shape, shift of peak potential) which are very similar to those due to a slowness of the electrochemical reaction, so that it is practically impossible to distinguish them on the basis of the experimental data alone. The limitations of the method for the determination of rate constants of surface electrochemical processes are discussed. A comparison is made with the faradaic impedance method.

Deposition and Dissolution on Sinusoidal Electrodes

Deposition and dissolution have been simulated on model sinusoidal electrodes. The effects of variations in kinetic, geometric, and mass transport parameters were studied. Predicted reduction in the amplitude of a profile undergoing anodic dissolution is compared with results obtained from other approximate solutions. Simulated deposits on macroprofiles, where mass transport limitations are important, displayed a characteristic flattening at the peak. The flattening is not manifested on microprofiles, where the diffusion layer is assumed to follow the average surface plane of the sine wave. Simulations at low Wagner numbers predicted that a slight depression should form at the peak of the sine wave during deposition for a specified range of geometric parameters. The phenomenon, which was unexpected from a prioriconsiderations, is shown to result from an interaction between the effects of ohmic drop, surface overpotential, and of electrode curvature. Contours of copper deposits, for comparison with simulated deposit profiles, were obtained on initially sinusoidal mandrels. In order to perform experiments over a range of Wagner numbers, sinusoidal profiles of different initial amplitudes (0.3 and 2 mm) were machined on the mandrels. Based on the deposit thickness (∼1 mm) at each point, deviation between simulated and experimental results is less than 13%.

ChemInform Abstract: STEADY‐STATE POLARIZATION AT POROUS, FLOW‐THROUGH ELECTRODES WITH SMALL PORE DIAMETER. I. REVERSIBLE KINETICS

AbstractEs wird ein Modell für reversible Einelektro‐ nenübertragungsreaktionen an porösen Durchflußelektroden entwickelt und einige Voraussagen experi‐mentell bestätigt.

Steady‐State Polarization at Porous, Flow‐Through Electrodes with Small Pore Diameter: I . Reversible Kinetics

This paper considers the effect of mass transfer and ohmic limitations on the current‐polarization relations for porous flow‐through electrodes with fine pores, for reversible one‐electron transfer reactions. The model includes mass transfer by both axial forced convection and axial diffusion. A new analytical solution is presented which reduces to a previous solution when axial diffusion is negligible. The effects of axial diffusion and ohmic potential drop in the pore electrolyte on the current and concentration distributions inside the electrode are investigated. Experimental confirmation is presented for some of the predictions and a quantitative comparison between theory and experiment is presented. It is concluded that axial diffusion effects are negligible under many experimental conditions, e.g., normal diffusion coefficient, flow rate, electrode length, etc. The results demonstrate the validity of the one‐dimensional model presented here under these conditions.

Linear sweep voltammetry—Bandpass limitations andmaximum usable sweep rate in the study of faradaic processes

Summary The bandpass limitations of the potentiostat and current measurer may affect the shape and characteristics of the LSV polarization curves. This problem is studied in the case of a nernstian faradaic reaction controlled by linear and semi-infinite diffusion. Three independent parameters are in general required to characterize the effects of ohmic drop through the uncompensated resistance, double layer charging and bandpass limitations. Under critical conditions the number of parameters is reduced to two. The solution is given in the form of an integral equation which was numerically computed for various sets of parameter values mainly in the case of critical conditions. The main effects of bandpass limitations on the faradaic peak are a shift in the same direction as that due to ohmic drop and an enhancement of the peak height opposite to the effect of ohmic drop. These effects increase rapidly with the sweep rate. Working curves are given that allow the maximum sweep rate corresponding to a specified permissible error to be computed. With potentiostat and current measurer amplifiers having gain-bandwidth product pulsations of the order of 107 rad s−1, the effect of bandpass limitations in current practice of LSV falls into the range of experimental errors up to about 1000 V s−1. Such amplifiers having moreover high input impedance specifications and 6 db/octave operating gain-frequency characteristics are required anyway in order to ensure the transfer function to be second order with a good accuracy. The theoretical analysis was experimentally verified with respect to peak portion and peak height by introducing purposely an additional resistor in the potentiostat loop. Second order conditions appear to be the most convenient to reach the maximum analogical compensation keeping the possibility of measuring accurately the residual uncompensated resistance and of correcting the residual ohmic drop mathematically. The best operating conditions are shown to involve a slightly overoscillatory double layer response.

Current-sampled polarographic techniques for the measurement of species reduced at more negative potentials than the major component

With conventional d.c. polarography. a particular depolarizer cannot be determined accurately in the presence of a considerable concentration of another species which is reduced at more positive potentials. Current-sampled read-out has been suggested previously to improve the situation; this idea has now been tested experimentally. The read-out of Tast (current-sampled), derivative Tast and pulse polarographic techniques permits determinations of this type to be achieved accurately and conveniently over quite a wide concentration range, provided that a three-electrode potentiostat is used to minimize ohmic iR drop effects. The maximal concentration and the limiting concentration ratio of the two depolarizers were generally fixed more by instrumental than chemical limitations, although at very high concentrations of the major species some evidence of electrochemical interference was found.

Linear sweep voltammetry—compensation of cell resistance and stability: Determination of the residual uncompensated resitance

The problem of cell resitance compensation with a system comprising a potentiostat, a current measurer and a positive feedback device is discussed in relation to stability in the case of linear sweep voltammetry. The part of the cell resistance that remains uncompensated by the action of the potentiostat may be quite significant, particularly in non-aqueous solvents. Reduction of this resitance by means of a positive feedback compensation allows first a better separation of the double layer charging current from the faradaic current. Also the effect of ohmic drop on faradaic polarization curves is minimized. “Unconditional” stability by means of phase shifting devices has not been attempted. On the contrary, the approach was to perform a purely ohmic compensation involving a real positive feedback rate so that a mathematical correction can be effected after measuring of the residual uncompensated resistance. It is shown that these conditions can be met practically for systems characterized by a second order transfer function. A controlling and measuring instrument composed of operational amplifiers is described which fulfils the preceding requirements. General procedures are proposed for the verification of the second order character of a given controlling and measuring system and for the measurement of the residual uncompensated resistance. They are applied experimentally to the particular instrument considered here, with a dummy cell in which no faradaic reaction occurs at the working electrode, and with another one involving a simulation of the faradaic current. Lastly, the question of complex positive feedback is briefly discussed.

Linear sweep voltammetry—compensation of cell resistance and stability Determination of the residual uncompensated resistance

The problem of cell resitance compensation with a system comprising a potentiostat, a current measurer and a positive feedback device is discussed in relation to stability in the case of linear sweep voltammetry. The part of the cell resistance that remains uncompensated by the action of the potentiostat may be quite significant, particularly in non-aqueous solvents. Reduction of this resitance by means of a positive feedback compensation allows first a better separation of the double layer charging current from the faradaic current. Also the effect of ohmic drop on faradaic polarization curves is minimized. “Unconditional” stability by means of phase shifting devices has not been attempted. On the contrary, the approach was to perform a purely ohmic compensation involving a real positive feedback rate so that a mathematical correction can be effected after measuring of the residual uncompensated resistance. It is shown that these conditions can be met practically for systems characterized by a second order transfer function. A controlling and measuring instrument composed of operational amplifiers is described which fulfils the preceding requirements. General procedures are proposed for the verification of the second order character of a given controlling and measuring system and for the measurement of the residual uncompensated resistance. They are applied experimentally to the particular instrument considered here, with a dummy cell in which no faradaic reaction occurs at the working electrode, and with another one involving a simulation of the faradaic current. Lastly, the question of complex positive feedback is briefly discussed.

Linear sweep voltammetry. Effect of uncompensated cell resistance and double layer charging on polarization curves

Summary Ohmic drop in the uncompensated cell resistance influences simultaneously the double layer charging current and the faradic current. Consequently, the effect of the ohmic drop on the polarization curves depends not only on the magnitude of the uncompensated cell resistance, but also on the diffeential capacity of the double layer. Theoretical relations have been derived that related the peak characteristics to these quentities as well as to the other experimental factors (sweep rate, depolarizer concentration, etc.) through two adimensional independent parameters. The theoretical analysis is devoted to the case of a Nernstian charge transfer, kinetic control being by diffusion. The double layer capacity is assumed to be constant and independent of the course of the faradaic process in the potential range considered. It is shown that evaluation of the ohmic drop effect on the peak can be significantly erroeous, especially at high sweep rates, if the influence of the double layer charging is ignored. A series of experiments have been performed with the system fluorenone-fluorenone anion in acetonitrile. The results are used to test the validity of the theoretical analysis and to exemplify the orders of magnitude of the ohmic drop effects in the current practice of linear sweep voltammetry. A simple correction procedure is suggested for small values of the ohmic drop.

Linear potential-sweep voltammetry at a plane mercury- film electrode

A general treatment is given of linear potential-sweep voltammetry with a mercury-film electrode. The current-potential equations for both oxidizing and reducing potential-sweeps are considered. A mathematical approximation, useful for very thin mercury-films, is discussed, while the limiting case of zero film thickness is also considered. The effect of ohmic drop on the current-potential curves is given. The bearing of the results on experiment is pointed out.

Ohmic drop distortion of anodic stripping curves from a thin mercury-film electrode

An exact treatment of the effect of uncompensated ohmic drop on anodic stripping curves from a plane, thin mercury-film electrode is given. The decrease in peak current caused by the ohmic drop can be 2.5–3 times larger than in the corresponding case of semi-infinite linear diffusion (“normal” linear-sweep voltammetry) Practical implications of the results, as well as the case of spherical micro-electrodes, are discussed briefly.

Abrupt junction diode theory

Forward voltage-current characteristics for planar abrupt junction silicon and germanium diodes are presented. These curves, derived directly from the basic current and continuity equations, extend the knowledge of diode behavior from the low injection region continuously to the high injection region. They include the effects of conductivity modulation, ohmic drop, and electric fields in the base, but neglect space charge recombination currents. The presentation includes treatment of both infinite recombination and majority carrier base contacts. Band pictures for several cases are shown and discussed in terms of the various mechanisms influencing them.