Slope decade

Introduction and commercial application Investment opportunities in the exploration and production (E P) sector of oil and gas business are abundant. Despite areas such as the North Sea, Gulf of Mexico and the North Slope in Alaska being mature areas, there are still many new fields under development in those regions, and new areas of business interest are opening up in South America, Africa and South East Asia. Some fields which have a production history of decades are being redeveloped, such as the Pedernales Field in Venezuela. 

The two dashed lines in the upper left hand corner of the Evans diagram represent the electrochemical potential vs electrochemical reaction rate (expressed as current density) for the oxidation and the reduction form of the hydrogen reaction. At point A the two are equal, ie, at equiUbrium, and the potential is therefore the equiUbrium potential, for the specific conditions involved. Note that the reaction kinetics are linear on these axes. The change in potential for each decade of log current density is referred to as the Tafel slope (12). Electrochemical reactions often exhibit this behavior and a common Tafel slope for the analysis of corrosion problems is 100 millivolts per decade of log current (1). A more detailed treatment of Tafel slopes can be found elsewhere (4,13,14). 

First one assumes that the final closed loop compensation network will have a continuous -20dB/decade slope. To achieve a 15 kHz cross-over frequency, the amplifier must add gain to the input signal and push-up the gain curve of the Bode plot. 

To find values of gain and phase at a different frequeneies along a -20dB/decade gain slope and its associated phase curve ... 

The resulting average slope of the closed-loop gain curve should be an average of -20dB/decade. 

As can be seen from equation (6.34), each time the frequency doubles (an increase of one octave) the modulus halves, or falls by 6dB. Or alternatively, each time the frequency increases by a factor of 10 (decade), the modulus falls by 10, or 20 dB. Hence the HF asymptote for a first-order system has a slope which can be expressed as —6 dB per octave, or —20 dB per decade. 

Thus a Tafel slope of -0-118 V/decade could be diagnostic of a discharge-chemical desorption mechanism in which proton discharge is the r.d.s. 

The measured potential is thus a linear function of pH an extremely wide (10-14 decades) linear range is obtained, with calibration plots yielding a slope of 59 mV per pH unit. The overall mechanism of the response is complex. The selective response is attributed to the ion-exchange properties of the glass surface, and in particular the replacement of sodium ions associated with the silicate groups in the glass by protons ... 

Solution Plotting E vs. log[Ca2+] gives a straight line with a slope of 29 mV/ decade and an intercept of 245 mV A calcium concentration of 5 x 10 4M thus yields ... 

The electronic conductivity of a conducting polymer can vary by more than 10 orders of magnitude with changing potential. For lightly p-doped materials, the conductivity generally increases exponentially with increasing potential (see Fig. 11). Slopes of 60-130 mV decade-1 are... 

From an analysis of data for polypyrrole, Albery and Mount concluded that the high-frequency semicircle was indeed due to the electron-transfer resistance.203 We have confirmed this using a polystyrene sulfonate-doped polypyrrole with known ion and electron-transport resistances.145 The charge-transfer resistance was found to decrease exponentially with increasing potential, in parallel with the decreasing electronic resistance. The slope of 60 mV/decade indicates a Nemstian response at low doping levels. 

ELECTRODEjcls Fig. 4.24 The operation of an ion-specific electrode with a slope of 59.16 mV per decade for mono-valent ions (29.58 mV/dec for di-valent ions) is simulated under the assumption that a digital volt meter with a resolution of, say, 0.1 mV is used. The sample volume and the concentration of the metered titration solution are known. Normally, one would add a few milliliters of the concentrated titration solution and do the calculation spelled out in lines 140-150 in Table 4.22 here, because the sample concentration is known, the result can be normalized to it. The operation of short-cuts (volume correction), unknowns (volume bias, deviation of true slope from theoretical), and equipment shortcomings (digitization) can be studied. 

The ORR at Pt metal sites has a rate dependence on potential described by a Tafel slope of 120 mV/decade (as determined for Pt model systems at high cathodic overpotential, where Pt is practically surface oxide-free [Parthasarathy et al., 1992a, b]). 

Is there a way to verify experimentally not only that the measured low Tafel slope of 60mV/decade in the fuel-cell-relevant potential range is fully explainable by an intrinsic slope of 120 mV/decade for ORR at Pt metal, but also that this intrinsic Tafel slope can be experimentally verified within the fuel-cell-relevant potential range In fact, an elegant response to this challenge has recently been provided by impedance spectra measured for the ORR process at Pt/C in a PEFC cathode... 

Finally, we briefly discuss the mechanism of enhanced specific ORR activities (ki p) at the Pt skin layer on the alloys. The Tafel slope in the high current density region at the Pt skin layer was found to be 120mV/decade [Toda et al., 1999 Wakabayashi et al., 2005b], indicating that the enhancement of ORR activities at... 

For /3-FePc, only one Tafel slope could be observed, with a value close to — 63 mV/decade. 

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