Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Transport equations current flow

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. [Pg.281]

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). [Pg.113]

In electrochemical cells we often find convective transport of reaction components toward (or away from) the electrode surface. In this case the balance equation describing the supply and escape of the components should be written in the general form (1.38). However, this equation needs further explanation. At any current density during current flow, the migration and diffusion fluxes (or field strength and concentration gradients) will spontaneously settle at values such that condition (4.14) is satisfied. The convective flux, on the other hand, depends on the arbitrary values selected for the flow velocity v and for the component concentrations (i.e., is determined by factors independent of the values selected for the current density). Hence, in the balance equation (1.38), it is not the total convective flux that should appear, only the part that corresponds to the true consumption of reactants from the flux or true product release into the flux. This fraction is defined as tfie difference between the fluxes away from and to the electrode ... [Pg.63]

In addition to the transport of charge, the current flow in an electrolyte is also accompanied by mass transport. The migration flux of species / is given by the equation... [Pg.96]

Diffusion. Often, the most important mode of mass transport is diffusion. The rate of diffusion can be defined in terms of Pick s laws. These two laws are framed in terms of flux, that is, the amount of material impinging on the electrode s surface per unit time. Pick s first law states that the flux of electroactive material is in direct proportion to the change in concentration c of species i as a function of the distance x away from the electrode surface. Pick s first law therefore equates the flux of electroanalyte with the steepness of the concentration gradient of electroanalyte around the electrode. Such a concentration gradient will always form in any electrochemical process having a non-zero current it forms because some of the electroactive species is consumed and product is formed at the same time as current flow. [Pg.22]

Fig. 13 Experimental (symbols) and theoretical (lines) data for the current-density as a function of applied voltage for a polymer film of a derivative of PPV under the condition of space-charge-limited current flow. Full curves are the solution of a transport equation that includes DOS filling (see text), dashed lines show the prediction of Child s law for space-charge-limited current flow assuming a constant charge carrier mobility. From [96] with permission. Copyright (2005) by the American Institute of Physics... Fig. 13 Experimental (symbols) and theoretical (lines) data for the current-density as a function of applied voltage for a polymer film of a derivative of PPV under the condition of space-charge-limited current flow. Full curves are the solution of a transport equation that includes DOS filling (see text), dashed lines show the prediction of Child s law for space-charge-limited current flow assuming a constant charge carrier mobility. From [96] with permission. Copyright (2005) by the American Institute of Physics...
OCV represents the open circuit voltage, i.e. the voltage difference between the two current collectors, when no current flows. Under the assumption that no gas crossover from one electrode to the other takes place, and assuming that there is no electronic transport within the electrolyte, the Nemst equation can be employed to calculate the OCV ... [Pg.72]

Extension of the equilibrium model to column or field conditions requires coupling the ion-exchange equations with the transport equations for the 5 aqueous species (Eq. 1). To accomplish this coupling, we have adopted the split-operator approach (e.g., Miller and Rabideau, 1993), which provides considerable flexibility in adjusting the sorption submodel. In addition to the above conceptual model, we are pursuing more complex formulations that couple cation exchange with pore diffusion, surface diffusion, or combined pore/surface diffusion (e.g., Robinson et al., 1994 DePaoli and Perona, 1996 Ma et al., 1996). However, the currently available data are inadequate to parameterize such models, and the need for a kinetic formulation for the low-flow conditions expected for sorbing barriers has not been established. These issues will be addressed in a future publication. [Pg.130]

A mathematical description of an electrochemical system should take into account species fluxes, material conservation, current flow, electroneutrality, hydrodynamic conditions, and electrode kinetics. While rigorous equations governing the system can frequently be identified, the simultaneous solution of all the equations is not generally feasible. To obtain a solution to the governing equations, we must make a number of approximations. In the previous section we considered the mathematical description of electrode kinetics. In this section we shall assume that the system is mass-transport limited and that electrode kinetics can be ignored. [Pg.242]

Neglecting transport due to convection, or the existence of concentration gradients (these are valid assumptions for the bulk of the solution, far from surface boundary layers where concentrations might vary), the equations describing current flow in an electrolyte containing cations and anions reduce to the familiar Ohm s law. Unidirectional current between two parallel plates can be described by (1)... [Pg.182]

To illustrate the use of the transport equations, the following problem is posed. An electrochemical cell containing vertical flat sheets of copper as the anode and cathode is operated with an aqueous CUSO4 electrolyte. The copper plates are connected to a DC power supply so that oxidation and reduction reactions proceed at the anode and cathode (Cu -1- 2e — Cu at the cathode Cu -> Cu -I- 2e at the anode). For the case when there is no forced or natural convection during current flow, we derive a simple expression between the constant applied current density and the steady-state cupric ion concentration profile. The cation flux and current density equations for the flat plate electrode/no convection cell are... [Pg.1756]


See other pages where Transport equations current flow is mentioned: [Pg.188]    [Pg.101]    [Pg.82]    [Pg.32]    [Pg.51]    [Pg.273]    [Pg.41]    [Pg.158]    [Pg.8]    [Pg.214]    [Pg.251]    [Pg.501]    [Pg.44]    [Pg.147]    [Pg.147]    [Pg.284]    [Pg.277]    [Pg.397]    [Pg.176]    [Pg.125]    [Pg.13]    [Pg.70]    [Pg.242]    [Pg.263]    [Pg.412]    [Pg.174]    [Pg.2103]    [Pg.438]    [Pg.536]    [Pg.43]    [Pg.348]    [Pg.1756]    [Pg.1761]    [Pg.14]    [Pg.72]    [Pg.186]    [Pg.187]    [Pg.135]   
See also in sourсe #XX -- [ Pg.50 ]




SEARCH



Current equations

Current flow

Current transport

Flow equations

Transport equation

Transport flows

© 2024 chempedia.info