Polarization steady-state

Transient measurements have often been used in electrochemical studies as a means of obtaining deeper insight into reaction mechanisms and estimating quantitatively kinetic parameters. Transient measurements have been obtained by applying a rectangular pulse or sinusoidal polarization to the electrode, which has previously reached a certain open-circuit or polarization steady state. The response of the system to these perturbations, recorded oscillographically, may then be analyzed and interpreted. 

At anodic polarization steady-state, denoted by the index s, we have... 

Figure Bl.16.9. Background-free, pseudo-steady-state CIDNP spectra observed in the photoreaction of triethylamine with different sensitizers ((a), antliraquinone (b), xanthone, CIDNP net effect (c), xanthone, CIDNP multiplet effect, amplitudes multiplied by 1.75 relative to the centre trace) in acetonitrile-d3. The stmctiiral formulae of the most important products bearing polarizations (1, regenerated starting material 2, N,N-diethylvinylamine 3, combination product of amine and sensitizer) are given at the top R denotes the sensitizer moiety. The polarized resonances of these products are assigned in the spectra. Reprinted from [21].

Using a procedure similar to the derivation of Equation (4.13) the working equations of the U-V-P scheme for steady-state Stokes flow in a polar (r, 6) coordinate system are obtained on the basis of Equations (4.5) and (4.6) as... 

Working equations of the streamline upwind (SU) scheme for the steady-state energy equation in Cartesian, polar and axisymmetric coordinate systems... 

In a polar coordinate system the steady-state energy equation is written as... 

Fluorescence. The fluorescence detection technique is often used in clinical chemistry analyzers for analyte concentrations that are too low for the simpler absorbance method to be appHed. Fluorescence measurements can be categorized into steady-state and dynamic techniques. Included in the former are the conventional simultaneous excitation-emission method and fluorescence polarization. 

Anode Polarization-the difference between the potential of an anode passing current and the steady-state or equilibrium potential of the electrode with the same electrode reaction. 

For DC polarization studies, the ratio of steady-state to initial current is not the transport number but determines the limiting current fraction , the maximum fraction of the initial current which may be maintained at steady-state (in the absence of interfractional resistances). Variations... 

The concentration of the remaining oxidation centered on the relaxed film at any oxidation time is defined by the difference between the density of charge stored in the point at which the film attains an oxidation steady state at the working potential and large polarization times and the charge density stored after a given polarization time [< j(0]-So the diffusion flow of ions is given by... 

D.Y. Wang, and A.S. Nowick, Cathodic and anodic polarization phenomena at platinum electrodes with doped Ce02 as electrolyte. I. Steady-state overpotential, J. Electrochem. Soc. 126(7), 1155-1165 (1979). 

The predictions of simple rules such as Kaptein s and Muller s can be distorted by relaxation effects. These are particularly noticeable in photochemical experiments. In the pre-steady state (e.g., immediately after irradiation has begun), when build-up of the polarized signals is occurring, relaxation effects in the final product are relatively unimportant and observed spectra accord with the simple theory. Con-... 

Once the model was complete, it was adjusted to a steady state condition and tested using historic carbon isotope data from the atmosphere, oceans and polar ice. Several important parameters were calculated and chosen at this stage. Sensitivity analysis indicated that results dispersal of the missing carbon - were significantly influenced by the size of the vegetation carbon pool, its assimilation rate, the concentration of preindustrial atmospheric carbon used, and the CO2 fertilization factor. The model was also sensitive to several factors related to fluxes between ocean reservoirs. 

Molecular Rotational Diffusion. Rotational diffusion is the dominant intrinsic cause of depolarization under conditions of low solution viscosity and low fluorophore concentration. Polarization measurements are accurate indicators of molecular size. Two types of measurements are used steady-state depolarization and time-dependent (dynamic) depolarization. 

Steady-State Fluorescence Depolarization Spectroscopy. For steady state depolarization measurements, the sample is excited with linearly polarized lig t of constant intensity. Observed values of P depend on the angle between the absorption and emission dipole moment vectors. In equation 2 (9), Po is the limiting value of polarization for a dilute solution of fluorophores randomly oriented in a rigid medium that permits no rotation and no energy transfer to other fluorophores ... 

In spite of the potentialities of reversed micelles entrapping nonaqueous highly polar solvents [34], very few investigations on the solubilization in such systems are reported in the literature. An example is the study of the solubilization of zinc-tetraphenylporphyrin (ZnTPP) in ethylene glycol/AOT/hydrocarbon systems by steady-state and transient... 

To further investigate the role of the liver in brevetoxin metabolism, PbTx-3 was studied in the isolated perfused rat liver model (27, 28). Radiolabeled PbTx-3 was added to the reservoir of a recirculating system and allowed to mix thoroughly with the perfusate. Steady-state conditions were reached within 20 min. At steady-state, 55-65% of the delivered PbTx-3 was metabolized and/or extracted by the liver 26% remained in the effluent perfusate. Under a constant liver perfusion rate of 4 ml/min, the measured clearance rate was 0.11 ml/min/g liver. The calculated extraction ratio of 0.55 was in excellent agreement with the in vivo data. Radioactivity in the bile accounted for 7% of the total radiolabel perfused through the liver. PbTx-3 was metabolized and eliminated into bile as parent toxin plus four more-polar metabolites (Figure 3). Preliminary results of samples stained with 4-(p-nitrobenzyl)-pyridine (29) indicated the most polar metabolite was an epoxide. 

Steady-state measurements of polarization characteristics can be made when all transitory processes associated with changes in current or potential have ended. Here... 

It is basically irrelevant in steady-state measurements in which direction the polarization curves are recorded that is, whether the potential is moved in the direction of more positive (anodic scan) or more negative (cathodic scan) values. But sometimes the shape of the curves is seen to depend on scan direction that is, the curve recorded in the anodic direction does not coincide with that recorded in the cathodic direction (Eig. 12.3). This is due to changes occurring during the measurements in the properties of the electrode surface (e.g., surface oxidation at anodic potentials) and producing changes in the kinetic parameters. 

Steady-state measurements can be made under both galvanostatic and potentiostatic conditions. It is irrelevant for the results of the measurements whether the current or the potential was set first. But in certain cases in which the polarization (/ vs. E) curve is nonmonotonic and includes a falling section (BC in Fig. 12.4), the potentiostatic method has important advantages, since it allows the potential to be set to any point along the curve and the corresponding current measured. But when the galvanostatic method is used, an increase in current beyond point B causes a jump in potential to point D (i.e., the potential changes discontinuously from the value Eg to the value Eg,) and the entire intermediate part of the curve is inaccessible. 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

FIGURE 12.7 Polarization curves (1) steady state, (2) without concentration polarization,... 

Each of the intermediate electrochemical or chemical steps is a reaction of its own (i.e., it has its own kinetic pecnliarities and rules. Despite the fact that all steps occur with the same rate in the steady state, it is true that some steps occur readily, without kinetic limitations, and others, to the contrary, occur with limitations. Kinetic limitations that are present in electrochemical steps show up in the form of appreciable electrode polarization. It is a very important task of electrochemical kinetics to establish the nature and kinetic parameters of the intermediate steps as well as the way in which the kinetic parameters of the individual steps correlate with those of the overall reaction. 

When a gas bubble has tom away, usually the small nucleus of a new bubble is left behind in its place. Therefore, in gas evolution an appreciable supersaturation is needed only for creating an initial set of nuclei, and subsequent processes require less supersaturation. Hence, in a galvanostatic transient the electrode s polarization will initially be higher but will then fall to a lower, steady-state value (Fig. 14.10). Such a time dependence of polarization is typical for many processes involving formation of a new phase. 

Voltammetry, which determines the steady-state or transient polarization characteristics of electrodes in reactions involving the substance being examined... 

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