Polarization curve calculation examples

Photocurrent measurements permit the determination of the hole diffusion length Lp. As was already noted, comparison of measured and calculated polarization curves allows Lp to be determined by a fitting procedure. For example, Butler (1977) and Wilson (1977) obtained for W03 and TiOz the values of Lp equal to 0.5 x 10-4 and 4 x 10-4 cm, respectively. 

An example of solvent-induced solvatochromic shifts (calculated at a characteristic snapshot from the MD trajectory for each solvent) on different electronic excited states is shown in Fig. 5.5. Inspection of this plot reveals that the electronic states with the dipole moments that are larger than the dipoles in the ground state (shown as solid red curves in Fig. 5.5) become increasingly stabilized (red-shifted) in polar solvents. For example, l Ai, l Bi, 2 Bi states, which dipoles are larger than in the ground state dipole (7.7 Debye), demonstrate systematic red shifts upon solvation. The red shift increases in more polar solvents (in the order of c-hexane, dioxane, and water). The most dramatic red shift is experienced by the experimentally observed l Ai charge-transfer state with the (gas-phase) dipole moment of 12.9 D. It is quite intriguing that this state (the lowest red state in Fig. 5.5) is only the third lowest excited state in the gas phase but becomes the lowest excited state in water. On the... 

Ri, the internal resistance, is a critical parameter and it can be calculated from electrical characterization of an MFC. A polarization curve measurement is a popular method to extract / ,. An example of polarization curve is shown in Fig. 3. At low current density, activation resistance dominates, and the voltage across external load drops very fast with the increase of current. When the current density increases to be an intermediate range, the voltage versus current profile becomes approximately linear, indicating ohmic resistance dominates. As the current density further increases, the increase rate slows down and the voltage drops quickly this is because the concentration resistance dominates. 

Similarly, the performance losses are calculated for each current density using the two polarization curves. The cell has passed the accelerated aging test when the acceptance criterion is met, for example, when the cell does not exceed a specified power loss for a number of specified on/off cycles or a specified test duration, or the loss rate in cell voltage remains below a specified value for the applied operating conditions [9]. 

The polarization curve (voltage and power density versus current density) is based on the cell voltage (and power density) averaged for the minimum 5 min period at each current density. In addition, the standard deviation of the voltage (and power density) is calculated. The cell has passed the performance test when the acceptance criterion is met, for example, the cell maintains a specified voltage at a given current density or exhibits a specified power density for the applied operating conditions [10]. 

Example 3.5 Assume that the rates of oxidation of Zn and reduction of if" " are controlled by activation polarization. Use the data given below to a) plot the appropriate polarization curves and determine Eeorr and icon-from the plot. Calculate b) both Eeorr and icorr c) the corrosion rate Cr in mm/y, and the polarization resistance Rp in ohm an . Data ... 

Anodic polarization curves in (NH4)4 EDTA under various conditions of pH, temperature, and [(NH4)4(EDTA)] were run with a RDE. Iron was excluded from the tests. The /crit was determined. Various concentrations of FedIDEDTA wore prepared, and cathodic polarization curves were determined so that Dcould be calculated. Finally, actual passivation tests were run to relate the passivation to pH, temperature, [(NH4)4 EDTA], flow, and [Fe ]. The /um was calculated at passivation and compared to Ian determined from the anodic curves. In addition, the effects of various oxidizers used to generate ferric EDTA were evaluated in short- and long-term tests. For example. 

FIGURE 3-24. Resulting polarization curve and operating point a for the example. It can be calculated ... 

Using (5.14) and the determined value of aabs, we can estimate 8 if ab is known, and vice versa. Two examples of thermal bistability data, fit to a calculated tuning curve based on (5.12), are shown below. Figure 5.7 is for the bare sphere, and Fig. 5.8 is for the PDDA-coated sphere. In the figures, the laser scans slowly across a TM-polarized WGM dip (taking several thermal relaxation times to scan Av), first down in frequency, then reversing at the vertical dashed line, and scanning back up in frequency across the same mode. The continuous smooth lines are the theoretical fits. 

Figures la and lb are typical curves found for the heat of immersion of polar solids in water (and are also foimd for polar and nonpolar solids in organic liquids). An example of Fig. la is found in the immersion of chrysotile asbestos having known and increasing amounts of physically adsorbed water on its surface (S ). The linear relationship between the heat of wetting and the volume adsorbed up to about a monolayer is significant and indicates surface homogeneity since the heat evolved is proportional to the amount of bare surface present. In accord with this finding, the isosteric heat values calculated from adsorption isotherms increased with coverage to a maximum near the monolayer as expected for adsorption on a surface possessing nearly uniform sites.

As an example, calculations examined the fluctuations that occur in the interaction energy of the water dimer as small perturbations are introduced into the basis set. These perturbations included addition of a second set of d-functions on O, minor adjustments in the polarization function exponent, or the number of primitive gaussians in the contraction. The raw interaction energies for the water dimer with R(00) = 3.0 A are illustrated by the broken curves in Fig. 1.3 as the basis set was altered. Note the large fluctuations at the MP2 as well as SCF levels. For example, the MP2 interaction energies vary between —5.5 and —8.5 kcal/mol. After counterpoise correction, on the other hand, the data is much more eon-sistent from one basis set to the next, as illustrated by the solid curves. 

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