Phase boundary processes

The rate of the addition reaction is determined by a phase boundary process, the contracting area expression [eqn. (7), n = 2] is obeyed and E = 37 kJ mole-1. The value of E for decomposition of the frarcs-chloro isomer (right-hand side of above equation) is 51 kJ mole-1, which is less than that (130 kJ mole-1) for HC1 elimination from the cis-chloro isomer. 

Terjesen S.G., Erga O., Thorsen G. and Ve A. (1961) II. Phase boundary processes as rate determining steps in reactions between solids and liquids. Chem. Engn. Sci. 74, 277-288. 

Steps 1-3 are known to be very fast and are called phase boundary processes. In contrast, in step 4, the rate of diffusion of species through the membrane is a rather slow process and it is controlled by the bulk membrane properties. 

However, it is likely that these authors were dealing with two different phenomena. A satisfactory explanation of Figs. 54-57 may be given in terms of phase-boundary processes both at the ingoing and outgoing surfaces (53). Adopting the nomenclature of p. 170, one may suppose that the transference of an atom from both... 

The universality of this relation must have important implication for the actual phase-boundary processes. This point will be discussed in more detail on pp. 178 seq. 

Among the possible phase-boundary processes one might include the following An adsorbed gas molecule or atom is driven into the solid by molecular bombardment by an activated gas molecule. Smithells and Ransley tested this possibility by introducing argon at 100 atm. into a diffusion system Hg-Ni where the hydrogen pressure on the ingoing side... 

The correct equations for the permeability showed that it always reached a limiting value at infinite pressure. Barrer (82) also showed that the phase-boundary processes could result in very great concentration discontinuities at the surface of a metal, and that under these conditions, even at high pressures, the concentration just within the metal could be a fraction only of the equilibrium value found in the absence of phase-boundary processes. He advanced the view that in the expression... 

Later (53), it was shown that for certain Hg-Pd systems (C — was indeed much less than its equilibrium value. This was indicated by mea suring both the permeability constant and the diffusion constant (Chap. V). When gas flow occurred from a finite pressure through palladium into a vacuum the values of Cl — Cg) were those in Table 43, for palladium samples of low permeability. On the other hand, when a palladium sample was alternately oxidised and reduced the permeabihty was high, and for some measurements of Lombard and his co-workers (69) the values of (C — Cg) approached the equilibrium ones (Table 43). Here the phase-boundary processes have... 

Since the permeability constant depends on the diffusion constant, upon phase boundary processes and upon the solubility it is not possible to interpret these... 

Even when all phase-boundary processes occur much more rapidly than any other processes, the temperature coefficients of the permeability constants are governed by the terms (iii) and (iv) above. But one notes the general correspondence between the differences AE in the temperature coefficients of permeability of metals to hydrogen and deuterium, and... 

When one examines the literature one finds that relatively few measurements have been made of the diffusion constants of gases in solids. One has to be sure that phase-boundary processes do not control the velocities of absorption, but this is not always easy to establish. Again, the mathematical analysis of the data often presents difficulties, and very frequently a number of phases co-exist which render interpretation even more uncertain. One has sometimes to deal with the case when the diffusion constant is a function of the concentration, necessitating the use of Fick s law in the form... 

Fig. 7.25 The voltage development on polarization of an ion-blocking cell corresponding to Fig. 7.23 with a constant current for To t- - ears as a purely ohmic contribution (IR drop) and the phase boundary process becomes apparent. For times of the order of r (3) the phase boundary process is complete (C elements impermeable). At this time resolution the initial jump becomes I(R o + R ). The bulk polarization is stationary when t t (4) and all capacitive elements are blocked U(t = oo) = R- - + Re n [431].

Figure 1 shows the mechanistic picture developed by C. M. Starks (1,2) for Hquid—Hquid PTC in a graphical form. The catalyst cation extracts the more hpholilic anion Y from the aqueous to the nonpolar organic phase where it is present in the form of a poorly solvated ion pair Y ]. This then reacts rapidly with RX, and the newly formed ion pair X ] returns to the aqueous phase for another exchange process X — Y . In practice most catalyst cations used are rather lipophilic and do not extract strongly into the aqueous phase so that the anions are exchanged at the phase boundary. 

Since all these processes listed here can work independently of each other, they can also occur combined in an equation of motion for the phase boundary ... 

In this section we discuss the basic mechanisms of pattern formation in growth processes under the influence of a diffusion field. For simphcity we consider the sohdification of a pure material from the undercooled melt, where the latent heat L is emitted from the solidification front. Since heat diffusion is a slow and rate-limiting process, we may assume that the interface kinetics is fast enough to achieve local equihbrium at the phase boundary. Strictly speaking, we assume an infinitely fast kinetic coefficient. 

Since the catalyst is concentrated and operates in the ionic phase, and also probably at the phase boundary, reaction volumes in the biphasic technology are much lower than in the conventional single-phase Dimersol process, in which the catalyst concentration in the reactor is low. As an example, the Difasol reactor volume can be up to 40 times lower than that classically used in the homogeneous process. 

Because of the financial importance of this process to steel producers (about one-third of all the steel produced in the world is subsequently galvanised) a great deal of research has been carried out throughout the world to establish the true equilibrium phase boundaries in the Fe,, -Zn( system and the critical temperature of stability of the f phase. Since the AG -7 diagrams or the phase stability diagrams could not account for these discrepancies in this system, AG ,-concentration curves were used for... 

This value does not express the actual result since side and/or parallel reactions (e.g., H+ or 02 reduction) are not considered, but it does demonstrate the completeness of the cementation process and the effectiveness of this liquid-liquid extraction. During this extraction no external current flows through the phase boundary Hg (amalgam)/solution thereby establishing a potentiometric condition. The question of the potential difference at the phase boundary can be answered by constructing the experimentally accessible current-voltage curves for the reactions ... 

The explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

The presupposition is that parallel electrochemical reactions (i.e., ion or electron transfer) occur across the phase boundary, if the measured ions and interfering ions are both present in the solution. A redox process in which electrons pass the phase boundary is also considered an interfering electrochemical reaction. 

Some limitations of optical microscopy were apparent in applying [247—249] the technique to supplement kinetic investigations of the low temperature decomposition of ammonium perchlorate (AP), a particularly extensively studied solid phase rate process [59]. The porous residue is opaque. Scanning electron microscopy showed that decomposition was initiated at active sites scattered across surfaces and reaction resulted in the formation of square holes on m-faces and rhombic holes on c-faces. These sites of nucleation were identified [211] as points of intersection of line dislocations with an external boundary face and the kinetic implications of the observed mode of nucleation and growth have been discussed [211]. 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

An unusual variation in kinetics and mechanisms of decomposition with temperature of the compound dioxygencarbonyl chloro-bis(triphenyl-phosphine) iridium(I) has been reported by Ball [1287]. In the lowest temperature range, 379—397 K, a nucleation and growth process was described by the Avrami—Erofe ev equation [eqn. (6), n = 2]. Between 405 and 425 K, data fitted the contracting area expression [eqn. (7), n = 2], indicative of phase boundary control. At higher temperatures, 426— 443 K, diffusion control was indicated by obedience to eqn. (13). The... 

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