Mixed potential, steady-state

Mixed Potential, When a catalytic surface S is introduced into an aqueous solution containing ions and a reducing agent, the partial reaction of reduction [Eq. (8.4)] and the partial reaction of oxidation [Eq. (8.5)] occur simultaneously. Each of these partial reactions strives to establish its own equilibrium, The result of these processes is the creation of a steady state with a compromised potential called the steady-state mixed potential, E mp- The result of this mixed potential is that the potential of the redox couple Red/Ox [Eq. (8.5)] is raised anodically from the reversible value E eq,Red (Tig- 8.3), and the potential of the metal electrode M/M [Eq. (8.4)] is... 

Thus, the basic four characteristics of the steady-state mixed potential are ... 

A system at the steady-state mixed potential is not in equilibrium since a net overall reaction does occur, and therefore the free energy change is not zero, which is the requirement for thermod5mamic equilibrium. 

Induction Period. The induction period is defined as the time necessary to reach the mixed potential at which steady-state metal deposition occurs. It is determined in a simple experiment in which a piece of metal is immersed in a solution for electroless deposition of a metal and the potential of the metal is recorded from the time of immersion (or the time of addition of the reducing agent, i.e., time zero) until the steady-state mixed potential is established. A typical recorded curve for the electroless deposition of copper on copper substrate is shown in Figure 8.11. 

The local electrochemical reaction on the Pt surface creates a Pt-0 surface coverage of 30%, and the remaining 70% remains as pure Pt. At steady-state mixed potential, a complete layer of Pt-0 can never be achieved in order to keep the reaction of Pt to Pt-0 continued due to the diffusion of Pt-O into the bulk metal. The reported mixed cathode potential is around 1.06 V (vs. SHE) at standard conditions (25 °C, 1 atm) with an O2 partial pressure dependence of 15 mV atm [124, 125]. 

El = 1.229 V (vs. NHE)), and the Pt/PtO anode reaction potential (Pt + H2O PtO + 2YC + 2e", E°p p,o = 0.88 V (vs. NHE)). The local electrochemical reaction on the Pt surface could create a PtO surface coverage of 30%, with 70% of the surface remaining as pure Pt. At steady-state mixed potential, a complete layer of Pt-0 can never be achieved in order to keep the reaction of Pt to PtO continuous, due to the diffusion of Pt-0 into the bulk metal. The reported mixed cathode potential is around 1.06 V (vs. NHE) at standard conditions [20, 21] with an O2 partial pressure dependence of 15 mV-atm Furthermore, the H2 that has crossed over through the membrane from anode to cathode can form a local half-cell electrochemical reaction on the cathode, such as H2 2H + 2e, resulting in a mixed cathode potential similar to that of the half-cell reaction (Pt -1- H2O PtO -1-2H + 2e ). The mixed potentials are the dominant sources of voltage losses at open circuits [13]. 

Thus, in the presence of O2, the Pt surface is a mixture of Pt and PtO. Therefore, a steady-state open circuit potential (OOP) of 1.23 V is rarely observed, due to the formation of PtO. Rather, the steady-state rest potential of a Pt electrode in O2 saturate 1 M H2SO4 is 1.06 V, a mixed value of the thermodynamic potential of O2/H2O and of Pt/PtO, because two reactions occur Pt oxidation and O2 reduction [46]. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

It is worthwhile mentioning that the interfacial potential created at the liquid-liquid interface is governed by single ionic or redox equilibrium only in the simple cases. The presence of various, often two, interfacial processes is a source of the steady-state potential, named also the mixed or the rest potential. Its value is situated between the two equilibrium potentials, near that one which corresponds to the higher exchange current... 

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). 

Pt on TiC and TiN has also been reported to show good cycle stability (to 1.2 V), especially when mixed with uncatalyzed carbon.i° Steady-state corrosion tests of Pt/TiC at 1.2 and 1.4 V showed gradual oxidation to Ti02, although this was not dependent on potential. TiC has also been used by 3M as a support for a series of non-PM catalysts and has showed very stable performance over 1,000 h at 0.6 V. However, the overall activity was four times lower than that of an equivalent catalyst on carbon. 

Figure 52. Passivation of A1 substrate in LiBOB-based electrolytes Time-decaying current observed on an A1 electrode at various potentials containing 1.0 M LiBOB in EC/EMC. Inset the dependence of steady-state current density at t= 10 s) on applied potential as obtained on an A1 electrode in electrolytes based on various salts in the same mixed solvent. (Reproduced with permission from ref 155 (Eigure 1). Copyright 2002 The Electrochemical Society.)...

Steady-state electroless metal deposition at mixed potential is preceded by a non-steady-state period, called the induction period. 

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

The potential participation of an alternative route, involving a binuclear elimination reaction between a metal-acyl and a metal-hydride has also been probed [73]. In Rh-catalysed cydohexene hydroformylation, both [Rh4(CO)i2] and [Rh(C(0)R)(C0)4] are observed by HP IR at steady state, the duster species being a potential source of [HRh(CO)4] by reaction with syn-gas. The kinetic data for aldehyde formation indicated no statistically significant contribution from binudear elimination, with hydrogenolysis of the acyl complex dominant. For a mixed Rh-Mn system. 

By contrast, the gas transfer estimates utilizing Rn measurements assumes steady state between Rn production from radioactive decay of nonvolatile Rd and gas transfer with the atmosphere. This assumption is possible because Rn has a half-life of only 3.8 days, so accumulation and lateral ocean fluxes of Rn is assumed to be minimal. Again, a potential problem is the active, versus inactive layer of the ocean in this case, the mixed layer depth that may change during an experiment. 

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