Current density logarithm

The arc radius grows as a square root of the discharge current 7(7 (xrl) therefore, an increase of current leaves the current density logarithmically fixed similarly to plasma temperature. The chaimel model always includes current in combination with the discharge tube radius R (the similarity parameter I/R). 

The relationship of anode current density with electrode potential for mild steel in dilute aqueous soil electrolytes has been studied by Hoar and Farrer. The study shows that in conditions simulating the corrosion of mild steel buried in soil the logarithm of the anode current density is related approximately rectilinearly to anode potential, and the increase of potential for a ten-fold increase of current density in the range 10 to 10 A/cm is between 40 and 65 mV in most conditions. Thus a positive potential change of 20 mV produces a two- to three-fold increase in corrosion rate in the various electrolyte and soil solutions used for the experiments. 

Polarisation Curve A plot of the current density flowing from an electrode against the electrode potential, often presented on a logarithmic current density axis. 

Because of the logarithmic relation, polarization depends more strongly on parameter a than on parameter b. The parameter a, which is the value of polarization at the unit current density (1 mA/cm ), assumes values which for different electrodes and reactions range from 0.03 to 2-3 V. Parameter b, which is called the Tafel slope, changes within much narrower limits in many cases, at room temperature b 0.05 V and 0.115 V (or roughly 0.12 V). 

In the region of low polarization (low current densities), where two terms in the series expansion of the logarithms are sufficient, it follows from this equation that... 

Thus, the recombination theory provided the first theoretical interpretation of the linear relation between polarization and the logarithm of current density that had been established experimentally. It is true, though, that the preexponential factor in Eq. (15.12) [2303(RTI2FI) 0.03 V] is four times smaller than the experimental values of slope b but it has been shown in later work that factors closer to the experimental values can be obtained when an inhomogeneous surface is assumed. 

One of the many published correlations between the logarithms of exchange current density of the hydrogen reaction at different metals and the values of hydrogen-bond energy on the same metals is reported in Fig. 28.3. Considering all the points mentioned, one can certainly conclude that a certain bell shape does exist in this plot, but it would not be justified to draw any quantitative conclusions going beyond this assertion (Petrii and Tsirlina, 1994). 

Plotting the overpotential against the decadic logarithm of the absolute value of the current density yields the Tafel plot (see Fig. 5.3). Both branches of the resultant curve approach the asymptotes for r RT/F. When this condition is fulfilled, either the first or second exponential term on the right-hand side of Eq. (5.2.28) can be neglected. The electrode reaction then becomes irreversible (cf. page 257) and the polarization curve is given by the Tafel equation... 

At current densities well below the limiting value, j can be neglected against yd in the numerator of the expression after the logarithm in Eq. (5.4.26) rearrangement then yields... 

Fig. 9. Logarithmic plot of apparent limiting-current density as a function of current increase rate at a rotating-disk electrode i — apparent limiting current density i, = true steady-state limiting current density di/dt = current increase rate (A cm-2 sec-1) (u = rotation rate (rad sec-1). [From Selman and Tobias (S10).]...

It was experimentally found that the polarization curves of the investigated air gas-diffusion electrodes in a semi-logarithmic scale at low current densities (below 10 mA/cm2) are straight lines, which can be treated as Tafel plots. At these low current densities the transport hindrances in the air electrode are negligible so that activation hindrances only are available. 

Figure 4. Logarithm current density at -0.1 V vs. the temperature ofpyrolysis for trinuclear complexes on the surface of AG-3 carbon.

In the right upper panel the distribution for the current density P(j) is shown together with the theoretical prediction for the case (jx) = 0. Lower panels show the computed distributions for the x— and y—components of j on a logarithmic scale together with the analytic expression (20) (straight solid lines). 

Let us now consider the charge state of the electrode. The emitter is positively biased. A p-type silicon electrode is therefore under forward conditions. If the logarithm of the current for a forward biased Schottky diode is plotted against the applied potential (Tafel plot) a linear dependency with 59 meV per current decade is observed for moderately doped Si. The same dependency of 1EB on VEB is observed at a silicon electrode in HF for current densities between OCP and the first current peak at JPS, as shown in Fig. 3.3 [Gal, Otl]. Note that the slope in Fig. 3.3 becomes less steep for highly doped substrates, which is also observed for highly doped Schottky diodes. This, and the fact that no electrons are detected at the collector, indicates that the emitter-base interface is under depletion. This interpretation is sup-... 

Both increase in a logarithmic fashion with current density. i ... 

Zone III the E vs ln(l — j/ji ) logarithmic curve corresponds to concentration polarization, which results from the limiting value ji of the mass transfer limiting current density for the reactive species and reaction products to and/or from the electrode active sites an increase inji from 1.4 to 2.2 Acm leads to a further... 

Surfaces of cadmium with various morphological properties were electro-formed on the Cd electrode from sulfate solutions by varying current densities, temperature, and pulse electrolysis conditions [218]. The surface properties were defined by the values of slopes of quasi-steady state E versus logarithm current density dependencies and exchange current densities in 0.5 M CdS04 + 0.15 M H2SO4 solution. The dependence of the slope values on surface properties was explained in terms of the influence of crystallization overpotential. 

Quantitative treatment of overpotential and related phenomena goes back to 1905, when Tafel showed empirically that, for an electrochemical half-cell from which a net electrical current I is being drawn, an excess potential AE away from the equilibrium potential will inevitably exist, and AE will be a linear function of the logarithm of the current density i (i = I/area of interface) ... 

Consider first the polarization curve (i.e., Tafel plot) for the anodic halfreaction occurring in corrosion of stainless steels (Fig. 16.8). The diagram for the active region is much the same as has been seen for other anodes (Figs. 15.4 to 15.7). As Eh is increased to a certain specific value, however, a sudden and dramatic drop in the anodic current density i occurs, corresponding to formation of an oxide film. At higher Eh, i remains constant at a very low level (the horizontal scale in Fig. 16.8 is logarithmic), and the metal has become passive, that is, effectively immune from corrosion. 

Fig. 14.31. Logarithm of the anodic current density-potential curves of the Q/QH2 redox couple on gold electrode covered by (x) three layers of DPPC + gramicidin,(a) five layers of DPPC + gramicidin. (Reprinted from A. Rejou-Michel, M. A. Habib, and J. O M. Bockris, Electron Transfer at Biological Interfaces, in Electrical Double Layers in Biology, M. Blank, ed., Fig. 9, p. 175, Plenum, 1986.)...

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