Transport overvoltage

Mass transport overvoltage, 12 207-209 Master agreements, evaluation of,... 

When the transport current of electrons or holes in semiconductor electrodes more or less influences the interfacial electron transfer current, the overvoltage T) consists of an overvoltage of space charge layer iisc, an overvoltage of compact layer t]h, and a transport overvoltage tit in semiconductors as expressed in Eqn. 8-68 ... 

As the polarization (the overvoltage t) ) increases of a redox reaction that requires the transport of minority charge carriers towards the electrode interface (anodic hole transfer at n-type and cathodic electron transfer at p-type electrodes), the transport overvoltage, t)t, increases from zero at low reaction currents to infinity at high reaction current at this condition the reaction current is controlled by the limiting diffusion current (iu.)tm or ip.um) of minority charge carriers as shown in Fig. 8-25. 

Over-the-Counter Drug Review, 18 685 Over/under scales, 26 252 Overvoltage, 12 206-207, 214 mass transport (concentration),... 

As the resistance of mass transport increases, a diffusion overvoltage becomes significant and the total overvoltage t) is distributed to both interfadal ovmvoltage i1h and difiusion overvoltage T)di r as stressed in Eqn. 8-31 ... 

The transfer of anodic holes is associated with the following three processes the generation and transport of holes in the electrode the hole transfer across the compact layer and the diffusion of redox particles in aqueous solution. The total overvoltage, T], is the sum of the three overvoltages np sc for the generation and transport of holes in the electrode, ria for the transfer of holes across the electrode interface, and ii4ur for the diffusion of redox particles in the solution as defined in Eqn. 10-27 ... 

The overvoltage for ihe generation and transport of holes, ii p, ac, is the difTerence between the quasi-Fermi level of interfacial holes and the Fermi level enso of electrons in the electrode interior as defined in Eqn. 10-29 ... 

For p-type electrodes in the dark and in the photoexdted state, the concentration of majority charge carriers (holes) is sufficiently great that the Fermi level eptso of the electrode interior nearly equals the quasi-Fermi level of interfacial holes hence, the overvoltage Up sc for the generation and transport of holes in the space charge layer is zero even as the transfer of anodic holes progresses as expressed in Eqn. 10-30 ... 

Fig. 10-22. Overvoltages in an anodic hole transfer (a) at a photoexcited n-type electrode and (b) at a p-type electrode of the same semiconductor iih = overvoltage for hole transfer across an interface = inverse overvoltage due to generation and transport of photoexcited holes in an n>type electrode.

Since the overvoltage iip,sc for the generation and transport of holes is a negative quantity, the total overvoltage becomes negative when the magnitude of Ti p, sc exceeds t) h the condition usually occims with photoexcited n-type electrodes. This provides the basis for the fact that the potential for the onset of anodic hole transfer at photoexcited n-type electrodes is more cathodic (n ative) than the potential for the onset of anodic hole transfer at p-type electrodes of the same semiconductor or at metal electrodes. 

Fig. 10-28. Polarization curves for cell reactions of photoelectrolytic decomposition of water at a photoezcited n-type anode and at a metal cathode solid curve M = cathodic polarization curve of hydrogen evolution at metal cathode solid curve n-SC = anodic polarization curve of oxygen evolution at photoezcited n-type anode (Fermi level versus current curve) dashed curve p-SC = quasi-Fermi level of interfadal holes as a ftmction of anodic reaction current at photoezcited n-type anode (anodic polarization curve r re-sented by interfacial hole level) = electrode potential of two operating electrodes in a photoelectrolytic cell p. sc = inverse overvoltage of generation and transport ofphotoezcited holes in an n-type anode.

As shown in Eqn. 10-46, the difference in the polarized potential at constant anodic current, between the photoexcited n-type and the dark p-type anodes of the same semiconductor, represents the inverse overvoltage iip sc for the generation and transport of photo-excited holes. 

In the case of mass transport by pure diffusion, the concentrations of electroactive species at an electrode surface can often be calculated for simple systems by solving Fick s equations with appropriate boundary conditions. A well known example is for the overvoltage at a planar electrode under an imposed constant current and conditions of semi-infinite linear diffusion. The relationships between concentration, distance from the electrode surface, x, and time, f, are determined by solution of Fick s second law, so that expressions can be written for [Ox]Q and [Red]0 as functions of time. Thus, for... 

---