Rate Enhancement Ratio

The rate enhancement ratio, p, is defined as the ratio of the promoted, r, and unpromoted, r0, catalytic rate  

From a catalytic viewpoint this is the most important phenomenological parameter for quantifying the promoting or poisoning effect of a given coadsorbed species i (e.g. 02 F, Na+, H+) on the rate of a catalytic reaction. Similarly to the case of classical promotion (eq. 2.19), it is defined from  

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Another useful parameter for quantifying the promotional action is the promotional rate enhancement ratio, pp, which can be defined from ... 

Promotional rate enhancement ratio, pp, values of the order 10-100 are rather common as one can see already from Figure 2.3. 

Figure 4.28. Electrophobic behaviour Effect of catalyst work function on the activation energy E and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt p02 4.8 kPa, Pc2H4 0.4 kPa (a) and CH4 oxidation on Pt p02 =2.0 kPa, Pch4 =2.0 kPa (b)."4 Reprinted with permission from Elsevier Science.

Figure 4.35. Effect of catalyst work function on the activation energy EA, preexponential factor k° and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt/YSZ 4 p02=4.8 kPa, Pc2H4=0-4 kPa,4,54 kg is the open-circuit preexponential factor, T is the mean temperature of the kinetic investigation, 375°C.4 T0 is the (experimentally inaccessible) isokinetic temperature, 886°C.4 25,50...

Figure 6.3. Examples for the four types of global electrochemical promotion behaviour (a) electrophobic, (b) electrophilic, (c) volcano-type, (d) inverted volcano-type, (a) Effect of catalyst potential and work function change (vs I = 0) for high (20 1) and (40 1) CH4 to 02 feed ratios, Pt/YSZH (b) Effect of catalyst potential on the rate enhancement ratio for the rate of NO reduction by C2H4 consumption on Pt/YSZ15 (c) NEMCA generated volcano plots during CO oxidation on Pt/YSZ16 (d) Effect of dimensionless catalyst potential on the rate constant of H2CO formation, Pt/YSZ.17 n=FUWR/RT (=A(D/kbT).

Effect of partial electron transfer parameter Figure 6.23 depicts the effect of the value of the partial charge transfer parameter A,d for fixed XA(= 0.15) on the rate enhancement ratio p(=r/r0) for the four main types of promotional behaviour, i.e., electrophobic, electrophilic, volcano and inverted volcano. The main feature of the Figure is that it confirms in general the global mle... 

Figure 8.12. Effect of Ir02 mol fraction in the Ir02-Ti02 catalyst on the open-circuit catalytic rate, r0 of C2H4 oxidation (O), on the electrochemically promoted (1=200 pA) catalytic rate, r, ( ) and on the corresponding rate enhancement ratio p (A).19 (T=380°C, pO2=20 kPa, Pc2h4=0.15 kPa).

Figure 8.21. (a) Effect of the rate, I/2F, of electrochemical oxygen ion removal (I<0) on the induced increase in the rate of propylene oxidation on Pt/YSZ.28 (b) Effect of catalyst potential and work function change on the rate enhancement ratio p (=r/r0) at a fixed gaseous composition. Reprinted with permission from Academic Press. 

Figure 8.35. Effect of catalyst potential and work function on the rate enhancement ratio during CO oxidation on Ag. p02=3 kPa, pCo=5 kPa, , T=363°C, ro=2.7xl0"9 mol O/s A, T=390°C, r0 3.4xlO 9mol O/s , T=410°C, r0=5.5xlO 9mol O/s, A, T=390°C, r0=3.4xlO 9 mol O/s.38 Reprinted with permission from Trans Tech Publications.

Methanol oxidation on Ag polycrystalline films interfaced with YSZ at 500°C has been in investigated by Hong et al.52 The kinetic data in open and closed circuit conditions showed significant enhancement in the rate of C02 production under cathodic polarization of the silver catalyst-electrode. Similarly to CH3OH oxidation on Pt,50 the reaction exhibits electrophilic behavior for negative potentials. However, no enhancement of HCHO production rate was observed (Figure 8.48). The rate enhancement ratio of C02 production was up to 2.1, while the faradaic efficiencies for the reaction products defined from... 

Figure 9.12. Effect of Na coverage on the rate of NO reduction by C2H4 on Pt/p"-Al203. The rate enhancement ratio p is nominally infinite pc2H4=3 kPa, PnO=0.65 kPa, 480°C.6 Reprinted with permission from Academic Press.

A very pronounced, 10-fold, increase in catalytic rate is obtained for high P02/PH2 values (Fig. 9.28). The rate enhancement ratio po defined from ... 

Figure 9.30. Steady-state effect of catalyst potential, Urhe, on the rate enhancement ratios, Ph2 = fH2 / r 2 and po = ro /Iq and on the corresponding consumption rates of hydrogen and oxygen. Conditions as in Fig. 9.26.35 Reproduced by permission of The Electrochemical Society.

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...

For typical experimental parameter values (a =0.5, NM-1019 atom/m2, P,=l D=3.3-10 30 C-m, T=673) the dimensionless parameter IT equals 32 which implies, in view of equation (11.12), dramatic rate enhancement ratio p values (e.g. p =120) even for moderate (-15%) changes in the coverage 0j of the promoting backspillover species, as experimentally observed. 

For a given catalytic reaction does the rate enhancement ratio p depend only on UWr or does it also depend on the nature of solid electrolyte (YSZ, P"-A1203, Ti02, Ce02) ... 

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. 

The magnitude of the NEMCA effect for a given catalytic system is commonly described by two parameters, the rate enhancement ratio, p, (= r/r0, where r and rQ are the electropromoted and unpromoted reaction rate values) and the faradaic efficiency, A, (= (r - r0)/(I/nF)), where I is the current, F is the Faraday constant, and n is the charge of the promoting ion. The magnitude of A can be predicted from the parameter 2Fro/I0, where I0 is the exchange current of the catalyst-support interface [v]. 

The rate enhancement ratio, p, which, similar to the case of classical promotion [Eq. (3)], is defined from... 

The extent of metal-support interactions for a given catalytic system can again be quantified by defining a metal-support interactions rate enhancement ratio, Pmsi, from... 

Figure 4 (top) Effect of po on the rate (TOE) of C2H4 oxidation on Rh supported on five supports of increasing fi). Catalyst loading 0.5 wt. % [137,152], (bottom) Effect of po on the metal-support interactions rate enhancement ratio, Pmsi- (Reprinted with permission from Elsevier Science.)... 

Solution of Eq. (57) with boundary conditions (58) and (59) leads to the following expressions for the rate enhancement ratio p in terms of the dimensionless dipole moment, 11, of the promoting species ... 

As noted above, Vwr values >0.2 V correspond to a Na-free Pt surface. Decreasing Vwr (thus supplying Na to the Pt sur ce) causes a dramatic enhancement in CO2, N2 and N2O rates by factors of 7,10 and 3 respectively at Vwr -0-3V. The rate enhancement ratios pco2, Pn2 and pN2o defined as ... 

Fig. 32. Cell voltage vs rate enhancement ratio (p = r/r0) (a) effect of temperature with SCY electrolyte (b) effect of electrolyte at 1023 K. With permission from Chiang et al. (1993).

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