Slow surface diffusion

The rate determining step need not always be, as in this case, one of the reduction steps. Thus at low overpotential, slow surface diffusion was rate determining for the deposition of copper.7... 

The kinetics of physical adsorption were reviewed by Brunauer in 1943 (5). A 1 careful literature survey (6) reveals that the present status of the subject is substantially unchanged. Elementary considerations indicate that the process of physical adsorption should proceed very rapidly and be practically complete within the order of magnitude of one minute, and indeed, experiment usually confirms this. Deviations from this behavior have been accounted for by the time required to dissipate the heat of adsorption or by a very slow surface diffusion into a microporous structure. 

SAMs of TDT and MPOH at three total concentrations of TDT and MPOH in ethanol. The variation of the mutual solubility with X poH i probably due to the slow surface diffusion of adsorbed thiolates. The slope of X h orption of MPOH-rich domains increases with the increase in the total concentration of the thiols in the bathing solution the smaller the domain, the larger the slope is. The slope and its concentration dependence are much smaller for the reduction of TDT-rich domains. 

In all cases, careful attention should be paid to the usual conditions of Knudsen experiments. In particular, problems such as surface depletion of the volatile component in the specimen must be investigated, especially with solid materials where diffusion rates may be relatively slow. Surface diffusion of the eflfusate round the edges of the orifice, which may be particularly marked for knife-edge orifices, can make an additional contribution to the measured pressure, and non-obedience to the cosine law by the effusing vapour can also lead to incorrect vapour pressure values. All of these problems have been discussed in detail by Ward in a recent series of publications. 

Models with a slow surface diffusion This case is quite rare. 

The assumption of slow surface diffusion[118] in the case of mercury cathodes also seems to be improbable, since it is usually connected with the presence of different types of adsorption centers at the metal surface. 

Antoniou and Wetmore[143] considered the slow stage as the surface diffusion of the adsorbed atoms. They rejected the assumption about a slow discharge on the basis of the value v = 1 for the stoichiometric number. It has been shown in [150] that this contention is completely unsubstantiated since the value v = 1 can actually correspond to a slow discharge. Moreover, the assumption about a slow surface diffusion, coupled with the requirement that a first-order reaction take place for the adsorbed hydrogen atoms (otherwise, we do not get the value b = 60 mV), leads to the value v = 2[150]. Hence, the value v = 1 actually refutes the slow surface diffusion mechanism. 

The sequence of events in a surface-catalyzed reaction comprises (1) diffusion of reactants to the surface (usually considered to be fast) (2) adsorption of the reactants on the surface (slow if activated) (3) surface diffusion of reactants to active sites (if the adsorption is mobile) (4) reaction of the adsorbed species (often rate-determining) (5) desorption of the reaction products (often slow) and (6) diffusion of the products away from the surface. Processes 1 and 6 may be rate-determining where one is dealing with a porous catalyst [197]. The situation is illustrated in Fig. XVIII-22 (see also Ref. 198 notice in the figure the variety of processes that may be present). 

The kinetics of ion backspillover on the other hand will depend on two factors On the rate, I/nF, of their formation at the tpb and on their surface diffusivity, Ds, on the metal surface. As will be shown in Chapters 4 and 5 the rate of electrochemically controlled ion backspillover is normally limited by I/nF, i.e. the slow step is their transfer at the tpb. Surface diffusion is usually fast. Thus, as shown in Chapter 5, for the case of Pt electrodes where reliable surface O diffusivity data exist, obtained by Gomer and Lewis several years ago,76 Ds is at least 4.-10 11 cm2/s at 400°C and thus an O2 ion can move at least 1 pm per s on a Pt(lll) or Pt(110) surface. Therefore ion backspillover from solid electrolytes onto electrode surface is not only thermodynamically feasible, but can also be quite fast on the electrode surface. But does it really take place This we will see in the next Chapter. 

Thermal-Gradient Infiltration. The principle of thermal-gradient infiltration is illustrated in Fig. 5.15b. The porous structure is heated on one side only. The gaseous reactants diffuse from the cold side and deposition occurs only in the hot zone. Infiltration then proceeds from the hot surface toward the cold surface. There is no need to machine any skin and densification can be almost complete. Although the process is slow since diffusion is the controlling factor, it has been used extensively for the fabrication of carbon-carbon composites, including large reentry nose cones. 

In order to assess the role of the platinum surface structure and of CO surface mobility on the oxidation kinetics of adsorbed CO, we carried out chronoamperometry experiments on a series of stepped platinum electrodes of [n(l 11) x (110)] orientation [Lebedeva et al., 2002c]. If the (110) steps act as active sites for CO oxidation because they adsorb OH at a lower potential than the (111) terrace sites, one would expect that for sufficiently wide terraces and sufficiently slow CO diffusion, the chronoamperometric transient would display a CottreU-hke tailing for longer times owing to slow diffusion of CO from the terrace to the active step site. The mathematical treatment supporting this conclusion was given in Koper et al. [2002]. 

The reaction is carried out in close-loop reactor connected to a mass spectrometer for 1S02, 180160 and 1602 analyses as a function of time [38], The gases should be in equilibrium with the metallic surface (fast adsorption/desorption steps 1 and f ) If the bulk diffusion is slow (step 6) and the direct exchange (step 5) does occur at a negligible rate, coefficients of surface diffusion Ds can be calculated from the simple relationship between the number of exchanged atoms Ne and given by the model of circular sources developed by Kramer and Andre [41] ... 

When surface diffusion is the only process of exchange, ag tends to an equilibrium value a at t - oo. In most cases, after a rapid step of surface diffusion, it can be observed that a% continues slowly decreasing. This phenomenon corresponds to a slow step of bulk diffusion (coefficient l)h). A model of bulk diffusion in spherical grains was developed by Kakioka et al. which led to the following equation [43] ... 

They found that the hydrolysis products of 4-AP and 1-naphthol produced well-defined anodic responses at low potentials at a bare SPCE. However, the presence of antibody immobilized on the electrode surface slowed the diffusion of 4-AP towards the electrode surface. In addition, 4-AP may interact with polyphenols on the electrode surface, thus reducing the electroactive working area of the electrode by fouling. In contrast, diffusion of 1-naphthol to the electrode surface was not hindered by immobilized antibody. This feature, along with its low cost, ease of availability, and high solubility, resulted in 1-NP being the preferred AP substrate in their work. 

As seen in Fig. 4.8, the adsorption of lauric acid (C12) is slow because of slow transport (diffusion) at concentrations smaller than 10 6 M. In case of Na+-caprylate (Cs) the attainment of equilibrium is delayed most probably by structural rearrangement at the surface. In case of anions, such association reactions are slower than with free acids. 

The cell potential is simply the work that can be accomplished by the electrons produced in the SOFC, and this potential decreases from the equilibrium value due to losses in the electrodes and the electrolyte. For YSZ electrolytes, the losses are purely ohmic and are equal to the product of the current and the electrolyte resistance. Within the electrodes, the losses are more complex. While there can be an ohmic component, most of the losses are associated with diffusion (both of gas-phase molecules to the TPB and of ions within the electrode) and slow surface kinetics. For example, concentration gradients for either O2 (in the cathode) or H2 (in the anode) can change the concentrations at the electrolyte interface,which in turn establish the cell potential. Similarly, slow surface kinetics could result in the surface at the electrolyte interface not being in equilibrium with the gas phase. 

We begin our discussion with the diffusion of a Si adatom over a flat terrace. This problem has previously been addressed with ab initio calculations for the case of symmetric dimers. The main result is that diffusion is highly anisotropic on the surface, with fast diffusion taking place over the top of the dimers with a saddle point energy of about 0.60 eV. Slow adatom diffusion is predicted to take place across the dimer rows with a barrier of 1.0 eV. Experiments based on a number counting of the island density are in agreement with these results. ... 

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