Three-phase boundaries

Roll-up. The principal means by which oily soil is removed is probably roU-up. The appHcable theory is simply the theory of wetting. In briefest outline, a droplet of oily soil attached to the substrate forms at equiUbrium a definite contact angle at the oil-sohd-air boundary line. This contact angle (Fig. 4) is the result of the interaction of interfacial forces in the three phase boundaries of the system. These interfacial forces, expressed in mN/m(= dyn/cm), or interfacial free energy values expressed in mj/m (erg/cm s) are conveniently designated 1SA iSlj subscripts relate to the Hquid-air,... 

The experimental setup is depicted schematically in Figure 1.2. Upon varying the potential of the catalyst/working electrode the cell current, I, is also varied. The latter is related to the electrocatalytic (net-charge transfer) reaction rate re via re=I/nF, as well known from Faraday s law. The electrocatalytic reactions taking place at the catalyst/solid electrolyte/gas three-phase-boundaries (tpb), are ... 

As shown schematically in Figure 1.4, ions arriving under the influence of the applied current or potential at the three-phase boundaries catalyst/solid electrolyte/gas form there adsorbed species (0(a), Na(a)) which have only three possibilities ... 

Figure 1.4. Possible pathways of 0(a) and Na(a) adsorbed species created at the three-phase boundaries via application of electric current (a) Desorption (b) Reaction (c) Backspillover.

Although several metals, such as Pt and Ag, can also act as electrocatalysts for reaction (3.7) the most efficient electrocatalysts known so far are perovskites such as Lai-xSrxMn03. These materials are mixed conductors, i.e., they exhibit both anionic (O2 ) and electronic conductivity. This, in principle, can extend the electrocatalytically active zone to include not only the three-phase-boundaries but also the entire gas-exposed electrode surface. 

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

We then note that the equilibrium condition for reaction (3.7) now taking place not only at the tpb (three phase boundaries), but over the entire gas exposed Pt electrode surface is very similar to Eq. (3.28), i.e. 

Figure 3.6. Spatial variation of the electrochemical potential, jl02-, of O2 in YSZ and on a metal electrode surface under conditions of spillover (broken lines A and B) and when equilibrium has been established. In case (A) surface diffusion on the metal surface is rate limiting while in case (B) the backspillover process is controlled by the rate, I/nF, of generation of the backspillover species at the three-phase-boundaries. This is the case most frequently encountered in electrochemical promotion (NEMCA) experiments as shown in Chapter 4.

As discussed below, the porosity and surface area of the catalyst film is controllable to a large extent by the sintering temperature during catalyst preparation. This, however, affects not only the catalytically active surface area AG but also the length, t, of the three-phase-boundaries between the solid electrolyte, the catalyst film and the gas phase (Fig. 4.7). 

Electrocatalytic reactions, such as the transformation of O2 from the zirconia lattice to oxygen adsorbed on the film at or near the three-phase-boundaries, which we denote by 0(a), have been found to take place primarily at these three phase boundaries.5 8 This electrocatalytic reaction will be denoted by ... 

This electrochemical reaction contains the elementary step (4.1) and under conditions of backspillover can be considered to take place over the entire metal/gas interface including the tpb.1,15 18 This is usual referred to as extension of the electrochemical reaction zone over the entire metal/gas interface. But even under these conditions it must be noted that the elementary charge transfer step 4.1 is taking place at the three-phase-boundaries (tpb). 

In the latter case one would like to know the length Apb of the metal-solid electrolyte-gas three-phase-boundaries (tpb) (in m or in metal mols, for which we use the symbol Ntpb throughout this book) and the value of the exchange current I0, where (W2F) expresses the value of the (equal and opposite under open-circuit conditions) forward and reverse rates of the charge-transfer reaction 4.1. 

This observation immediately rules out the possibility that NEMCA is an electrocatalytic phenomenon causing only a local acceleration of the catalytic rate at the three-phase-boundaries (tpb) metal-solid electrolyte-gas. In such a case the rate increase would obviously be instantaneous during a galvanostatic transient. 

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

We start by considering a schematic representation of a porous metal film deposited on a solid electrolyte, e.g., on Y203-stabilized-Zr02 (Fig. 5.17). The catalyst surface is divided in two distinct parts One part, with a surface area AE is in contact with the electrolyte. The other with a surface area Aq is not in contact with the electrolyte. It constitutes the gas-exposed, i.e., catalytically active film surface area. Catalytic reactions take place on this surface only. In the subsequent discussion we will use the subscripts E (for electrolyte) and G (for gas), respectively, to denote these two distinct parts of the catalyst film surface. Regions E and G are separated by the three-phase-boundaries (tpb) where electrocatalytic reactions take place. Since, as previously discussed, electrocatalytic reactions can also take place to, usually,a minor extent on region E, one may consider the tpb to be part of region E as well. It will become apparent below that the essence of NEMCA is the following One uses electrochemistry (i.e. a slow electrocatalytic reaction) to alter the electronic properties of the metal-solid electrolyte interface E. 

If only the three-phase-boundaries (tpb) were electrocatalytically active one would expect Cd values of the order of 10 pF/cm2. The thus measured high Cd values also provide evidence that the charge transfer zone is extended over the entire gas-exposed electrode surface, i.e. that an effective double layer is formed over the entire gas exposed electrode surface. 

For the experiments shown in Fig. 5.30 the ratio Cdi2/Cdi] is on the average 2500, very close to the ratio NG/Ntpb ( 3570)54 where N0 is the gas-exposed electrode surface area and Ntpb is the surface area of the three phase boundaries. These quantities were measured via surface titration and via SEM and the techniques described in section 5.7.2, respectively. Thus once N0 has been measured, AC Impedance spectroscopy allows for an estimation of the three-phase-boundary (tpb) length via ... 

In summary AC impedance spectroscopy provides concrete evidence for the formation of an effective electrochemical double layer over the entire gas-exposed electrode surface. The capacitance of this metal/gas double layer is of the order of 100-300 pF/cm2, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore it permits estimation of the three-phase-boundary length via Eq. 5.62 once the gas exposed electrode surface area NG is known. 

Several approaches have been proposed to measure the three phase boundary (tpb) length, Ntpb in solid state electrochemistry. The parameter Ntpb expresses the mol of metal electrode in contact both with the solid electrolyte and with the gas phase. More commonly one is interested in the tpb length normalized with respect to the surface area, A, of the electrolyte. This normalized tpb length, denoted by Ntpb,n equals Ntpt/A. 

In the case of electrochemically promoted (NEMCA) catalysts we concentrate on the adsorption on the gas-exposed electrode surface and not at the three-phase-boundaries (tpb). The surface area, Ntpb, of the three-phase-boundaries is usually at least a factor of 100 smaller than the gas-exposed catalyst-electrode surface area Nq. Adsorption at the tpb plays an important role in the electrocatalysis at the tpb, which can affect indirectly the NEMCA behaviour of the electrode. But it contributes little directly to the measured catalytic rate and thus can be neglected. Its effect is built in UWr and [Pg.306]

This equation is always valid at steady state and has been originally derived for the case of NEMCA in alkaline solutions.37 In the present case of the acidic environment in the Nafion electrolyte the following two electrocatalytic (net charge transfer) reactions take place at the Pt working electrode, presumably at the three-phase-boundaries (tpb) Pt-Nafion-gas ... 

In all these cases the support has a dramatic effect on the activity and selectivity of the active phase. In classical terminology all these are Schwab effects of the second kind where an oxide affects the properties of a metal. Schwab effects of the first kind , where a metal affects the catalytic properties of a catalytic oxide, are less common although in the case of the Au/Sn02 oxidation catalysts9,10 it appears that most of the catalytic action takes place at the metal-oxide-gas three phase boundaries. 

We consider the porous metal catalyst film shown in Figure 11.12 which is interfaced with an O2" conductor. When a positive current, I, is applied between the catalyst and a counter electrode, oxide ions O2 are supplied from the solid electrolyte to the three phase boundaries (tpb) solid electrolyte-metal-gas at a rate I/2F. Some of these O2 will form 02 at the tpb and desorb ... 

As shown in Figure 12.4 this finely dispersed Pt catalyst can be electrochemically promoted with p values on the order of 3 and A values on the order of 103. The implication is that oxide ions, O2", generated or consumed via polarization at the Au/YSZ/gas three-phase-boundaries migrate (backspillover or spillover) on the gas exposed Au electrode surface and reach the finely dispersed Pt catalyst thereby promoting its catalytic activity. 

The reason is that the backspillover ions desorb to the gas phase directly from the three-phase-boundaries or react directly at the three-phase-boundaries (electrocatalysis, A=l) before they can migrate on the gas-exposed electrode surface and promote the catalytic reaction. The limits of NEMCA are set by the limits of stability of the effective double layer at the metal/gas interface. 

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