OPEN-CIRCUIT CONDITION

Under both short-circuit and open-circuit conditions, a solar cell produces no electric power, the power is consumed internally in the cell and is dissipated as heat. When a resistive load is connected to a cell in sunlight, a photogenerated voltage, F, is induced across the load and a current flows through it. The existence of requites that the flow of majority carriers be reduced from that in the open-circuit condition there must be a higher battier potential than in the open-circuit case (Fig. 2d). This higher barrier potential (V6 — ) indicates a smaller reduction from Since the photogenerated... 

Approx, impedance of the excitation circuit, (b) Under energized but open circuit condition. CT circuit referred to the Secondary side. 

The corrosion rate is greatest close to the reversible Pb02/PbS04 potential as a result of a solid state reaction between PbOj and the underlying lead surface". This corresponds to the rest or open circuit condition. 

In more recent work embrittlement in water vapour-saturated air and in various aqueous solutions has been systematically examined together with the influence of strain rate, alloy composition and loading mode, all in conjunction with various metallographic techniques. The general conclusion is that stress-corrosion crack propagation in aluminium alloys under open circuit conditions is mainly caused by hydrogen embrittlement, but that there is a component of the fracture process that is caused by dissolution. The relative importance of these two processes may well vary between alloys of different composition or even between specimens of an alloy that have been heat treated differently. 

We start from equation (3.7) which under open-circuit conditions is at equilibrium at the three-phase-boundaries (tpb) metal (M)-gas-YSZ ... 

Since electrochemical promotion (NEMCA) studies involve the use of porous metal films which act simultaneously both as a normal catalyst and as a working electrode, it is important to characterize these catalyst-electrodes both from a catalytic and from an electrocatalytic viewpoint. In the former case one would like to know the gas-exposed catalyst surface area A0 (in m2 or in metal mols, for which we use the symbol NG throughout this book) and the value, r0, of the catalytic rate, r, under open-circuit conditions. 

Figure 4.36. Effect of catalyst potential UWR and work function on the activation energy E (squares) and preexponential factor r° (circles) of C2H4 oxidation on Rh/YSZ. open symbols open-circuit conditions. Te is the isokinetic temperature 372°C and r is the open-circuit preexponential factor. Conditions po2=l.3 kPa, pc2n =7.4 kPa.50 Reprinted with permission from Academic Press.

The backspillover O species on the Pt surface have an O Is binding energy 1.1 eV lower than on the same surface under open-circuit conditions. The Pt catalyst-electrode is surrounded by isoenergetic oxygen species both at the Pt/YSZ and at the Pt/vacuum interfaces.67... 

Figure 5.44. In situ SERS spectra69 of oxygen adsorbed on Ag/YSZ at 300°C under (a) open circuit conditions and with die cell operating in the potentiostatic mode with (b) UWR = -2 V and (c) Uwr = +2 V. Spectra (b) and (c) were obtained after the system had reached steady state, w = 200 mW, photon counter time constant, x = 2 s, ssw = 2 cm l. Reprinted with permission from WILEY-VCH.

It is important to note that equation (7.11), and thus (7.12) is valid as long as the effective double layer is present at the metal/gas interfaces. Therefore equation (7.11) is valid not only under open-circuit conditions (which is the case for the Nernst equation) but also under closed-circuit conditions, provided, of course, that the working electrode effective double layer is not destroyed. Consequently the importance of equation (7.11) is by no means trivial. 

M and M both covered by backspillover O ions and exposed to two different p02 values under open-circuit conditions. How do p,02> P02- and p (=Ep) vary across the cell And how do they relate to the conduction level Ec and valence level Ev of YSZ ... 

It turns out1,5 that varying Uwr and O cause dramatic (up to sixty-fold) increases in k but have practically no effect on kad. Thus NEMCA is much more pronounced on the fuel-lean side, i.e. when equation (8.7) is valid. This was shown in Fig. 4.24 which depicts the effect of the po2/pc2H4 ratio in the well-mixed reactor (CSTR) on the rate under open-circuit conditions and when Uwr is set at +1 V. There is a sixtyfold increase in the rate for high po2/pc2H4 values. 

Figure 8.2. Plot of the effect of gaseous composition and of n=( )/kbT during C2H4 oxidation on two Pt catalyst films, labeled R1 and R2, showing that the rate expression given by (Eq. 8.1) is valid both under open-circuit conditions (open symbols) and also under NEMCA conditions (filled symbols).1 Reprinted with permission from Academic Press.

Figure 8.6. Effect of applied current (left) and corresponding catalyst potential Uw (right) on the rate of C2H4 oxidation on a Rh surface which is reduced under open-circuit conditions.13 Pq2 1.3 kPa, pc2H4=7.4 kPa. O, T=320°C, r0= 1.74x1 O 7 mol/s , T=350°C, ro=6.5x]0 7 mol/s A, T=370°C, r0=8.4xlO 7 mol/s Filled symbols open-circuit conditions. Reprinted with permission from Academic Press.

Figure 8.26. Reaction rate dependence on pCH4 at constant po2 -2 kPa (a) and p02 at constant Pch4=2 kPa (b) for open circuit conditions (circles), UWr=+500 mV (squares) and Uwr=+1000 mV (triangles) during CH4 oxidation on Pd/YSZ, T=400°C Reprinted with permission from Elsevier Science.

Figure 8.28. Steady-state effect of catalyst potential and work function on the rate of CO oxidation on Pt. Open symbols correspond to open-circuit conditions , T=485°C> ro=0.5xl0 7 mol/s , T=505°C, r0=f. 0xl0 7mol/s, , T=535°C, ro=1.5xl0 7 mol/s. pco=0.25xl0"2bar, Po2-l 1.3x1 O 2 bar.34 Reprinted with permission from Trans Tech Publications.

The opposite effect is depicted on Fig. 8.32 where the catalyst under open-circuit conditions exhibits stable limit cycle behaviour with a period of 184 s. Imposition of a negative current of -400 pA leads to a steady state. Upon current interruption the catalyst returns to its initial oscillatory state. Application of positive currents leads to higher frequency oscillatory states. 

A striking feature of the effect of current on the CO oxidation oscillations is shown in Fig. 8.33. It can be seen that the frequency of oscillations is a linear function of the applied current. This holds not only for intrinsically oscillatory states but also for those which do not exhibit oscillations under open-circuit conditions, such as the ones shown on Fig. 8.31. This behaviour is consistent with earlier models developed to describe the oscillatory behaviour of Pt-catalyzed oxidations under atmospheric pressure conditions which are due to surface Pt02 formation35 as analyzed in detail elsewhere.33... 

As shown on Fig. 8.49 one can influence dramatically both the total CH4 conversion as well as product selectivity by varying the Ag catalyst potential. Thus under open-circuit conditions (Uwr=U r ) the CH4 conversion is near 0.02 with a C2 selectivity (methane molecules reacting to form C2H4 and C2H6 per total reacting CH4 molecules) near 0.5. Increasing Uwr increases the methane conversion to 0.3 and decreases the selectivity to 0.23, while decreasing Uwr decreases the conversion to 0.01 and increases the... 

It was found that both the catalytic rates and the selectivity to the various products can be altered significantly (rate changes up to 250% were observed) and reversibly under NEMCA conditions. Depending on the product, electrophobic or electrophilic behaviour is observed as shown in Fig. 8.57. In addition to the selectivity modification due to the different effect on the rate of formation of each product, acetaldehyde, which is not produced under open circuit conditions is formed at negative overpotentials (Fig. 8.58). Enhancement factor A values up to 10 were observed in this complex system.59... 

Figure 8.58. Transient effect of applied negative current on the rate of CH3CHO formation during CO hydrogenation on Pt.5,59 Acetaldehyde does not form under open-circuit conditions, thus p is nominally infinite P=12.5 bar, T=350°C. pH2/pco=l-8, flowrate 85 cm3 STP/min.5,59...

This is a truly exciting electrochemical promotion system which can serve as an excellent example for illustrating the two local and three of the four global promotional rules described in Chapter 6. The reason is that under open-circuit conditions the reaction is positive order in both reactants, as can be seen in subsequent figures. 

It follows from Eq. 9.14 that when 1=0, then re,2=-re,i. Therefore the open-circuit conditions U°hc is a mixed potential bounded between the H2 and 02 evolution potentials. 

Figure 9.26 shows the steady state effect of applied current I on the induced changes, ArH2(=rH2 -r 2) and Ar0(=ro-io )> in the rates of consumption of H2 and O respectively, where the superscript o always denotes open-circuit conditions. The dashed lines in Fig. 9.26 are constant Faradaic efficiency, A, lines. The maximum measured A values are near 40 at low current densities. This value is in excellent qualitative agreement with the following approximate expression which can predict the magnitude of A in NEMCA studies ... 

Figure 9.28 shows the dependence of the catalytic rate of oxygen consumption, r0, on the oxygen partial pressure P02 at fixed pH2 under open-circuit conditions and for a potentiostatically fixed catalyst potential Urhe (=UWr). As also shown in Fig. 9.28, the open-circuit potential UrhE increases from 0.33 to 0.8 V as the Po Ph2 ratio increases from 0.2 to 3.6. 

Figure 9.28. Effect of P02 on the rate of O consumption (u.) and corresponding catalyst potential ( ), U°ile, under open-circuit conditions and on the rate of O consumption (A) and corresponding A0 value under closed-circuit conditions at fixed catalyst potential Urhe-1.05 V total molar flowrate fm=l.7 l0 4 mol/s.35 Reproduced by permission of The Electrochemical Society.

Under open-circuit conditions the catalyst potential UwR=Urhe takes values of the order 0.4-0.85 V, that is -0.35 to +0.1 V on the standard hydrogen electrode scale (she), depending on the hydrogen to oxygen ratio. 

Figure 11.4. Effect of the mole fraction, XIro2, of Ir02 in the Ir02-Ti02 catalyst film on the rate of C2H4 oxidation under open-circuit conditions (open circles) and under electrochemical promotion conditions (filled circles) via application of 1=200 pA T=380°C, Pc2h4=015 kPa, Po2=20 kPa. Triangles indicate the corresponding electrochemical promotion rate enhancement ratio p values.22,29...

Figure 11.7 confirms that electrochemically induced and controlled O2 backspillover from the support to the metal film surface is the promoting mechanism both in the case of YSZ (Fig. 11.7a) and in Ti02 (Fig. 11.7b). These figures show the Ols spectrum of the Pt film deposited on YSZ and on TiC>2, first under open-circuit conditions (Fig. 11.7aC, 11.7bA) and then under positive current and potential application (Fig. 11.7aB, 11.7bB). Figures 11.7aC and 11.7bC show the difference spectra. In both cases, XPS clearly shows the presence of the O2 double layer, even under open-circuit conditions (Figs. 11.7aA, 11.7bA) and also clearly confirms the electrochemically controlled backspillover of O2 from the YSZ orTi02 support onto the catalyst surface. Note that the binding energy of the backspillover O species is in both cases near 529 eV, which confirms its strongly anionic (probably O2 ) state.31,32...

Besides mass transfer limitations, it is very important in electrochemical promotion experiments to compute the maximum mass-balance allowable rate enhancement. This is intimately related to the conversion of the limiting reactant under open circuit conditions, as the conversion of the latter cannot exceed 100%. In this respect keeping the open circuit conversion as low as possible (normally by using a small amount of catalyst) allows the system to exhibit a pronounced rate enhancement ratio. 

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