Resistance phase boundary

The potential dependence of the velocity of an electrochemical phase boundary reaction is represented by a current-potential curve I(U). It is convenient to relate such curves to the geometric electrode surface area S, i.e., to present them as current-density-potential curves J(U). The determination of such curves is represented schematically in Fig. 2-3. A current is conducted to the counterelectrode Ej in the electrolyte by means of an external circuit (voltage source Uq, ammeter, resistances R and R") and via the electrode E, to be measured, back to the external circuit. In the diagram, the current indicated (0) is positive. The potential of E, is measured with a high-resistance voltmeter as the voltage difference of electrodes El and E2. To accomplish this, the reference electrode, E2, must be equipped with a Haber-Luggin capillary whose probe end must be brought as close as possible to... 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

Each of these processes is characterised by a transference of material across an interface. Because no material accumulates there, the rate of transfer on each side of the interface must be the same, and therefore the concentration gradients automatically adjust themselves so that they are proportional to the resistance to transfer in the particular phase. In addition, if there is no resistance to transfer at the interface, the concentrations on each side will be related to each other by the phase equilibrium relationship. Whilst the existence or otherwise of a resistance to transfer at the phase boundary is the subject of conflicting views"8 , it appears likely that any resistance is not high, except in the case of crystallisation, and in the following discussion equilibrium between the phases will be assumed to exist at the interface. Interfacial resistance may occur, however, if a surfactant is present as it may accumulate at the interface (Section 10.5.5). 

Due to polarisation processes in the electrode/mobile phase boundary layer and potential drop (IR-drop) caused by electrical resistance of the mobile phase (in case of poorly conducting mobile phases) the potential applied on the auxiliary electrode versus the working electrode may differ substantially from the potential of the mobile phase versus the working electrode. Moreover, polarisation and electrical resistance are strongly influenced by mobile phase composition while IR-drop is also dependent on the current between the auxiliary and working electrodes. 

The process of mass transfer across a phase boundary is discussed in Volume 1, Chapter 10. A resistance to mass transfer exists within the fluid on each side of the interface, and the overall transfer rate of a component in a mixture depends on the sum of these resistances and the total driving force. 

Important hints on the reaction site can be gained by the Hatta numbers (Ha) of mass transport at the G/L- and L/L-phase boundaries. These numbers are also essential in order to estimate mass transport rates and concentration profiles within the boundary layer. Since the main resistance of mass transport is in the aqueous phase, mass transport coefficients and Ha numbers mentioned in the text are related to the aqueous phase. 

There are several theories concerned with mass transfer across a phase boundary. One of the most widely used is Whitman s two-film theory in which the resistance to transfer in each phase is regarded as being located in two thin films, one on each side of the interface. The concentration gradients are assumed to be linear in each of these layers and zero elsewhere while at the interface itself, equilibrium conditions exist (Fig. 5). Other important theories are Higbie s penetration theory and the theory of surface renewal due to Danckwerts. All lead to the conclusion that, in... 

The resistance in each phase is made up of two parts the diffusional resistance in the laminar film and the resistance in the bulk fluid. All current theories on mass transfer, i. e. film, penetration, and surface renewal assume that the resistance in the bulk fluid is negligible and the major resistance occurs in the laminar films on either side of the interface (Figure 3-2). Fick s law of diffusion forms the basis for these theories proposed to describe mass transfer through this laminar film to the phase boundary. 

The two-film theory is one of the mechanisms suggested to represent the conditions in the region of the phase boundary. This model suggested that the resistance to transfer in each phase could be regarded as lying in a thin laminar film close to the interface (Figure 6.1-2). 

Other contributions to the polarization are activation polarizations (nact) caused by inhibition of the passage of ions through the phase boundary which may arise in the discharge mechanism. Films on the electrode may also contribute (e.g. oxide, metal already deposited, impurity) by offering a resistance to current flow differing from the bath resistance (ohmic polarization, Tlohm)- Hence the observed overvoltage is given by... 

Transports of HTO vapour and H20 vapour to and from surfaces are controlled similarly by eddy diffusion in the free air and molecular diffusion across the viscous boundary layer near the surface. There is also a liquid phase boundary layer, and diffusion through this is a limiting resistance to the transport of sparingly soluble gases such as H2 or HT. For HTO, the liquid film resistance is negligible (Slinn et al., 1978). When the concentration gradients are in opposite directions, transport of HTO to a water surface can proceed simultaneously with evaporation of H20. 

Fifth, fig. 36 shows the temperature dependence of the resistivity p(T) as a function of pressure for the y = 0.75 sample, which is just on the O side of the O -O phase boundary (t < tc) at atmospheric pressure, and fig. 37 shows the change in a(T) with pressure for the same sample (Zhou et al., 1996). A resistivity maximum occurs at Tc where a long-... 

In most common separation processes, the main mass transfer is across an interface between a gas and a liquid or between two liquid phases. At fluid-fluid interfaces, turbulence may persist to the interface. A simple theoretical model for turbulent mass transfer to or from a fluid-phase boundary was suggested in 1904 by Nernst, who postulated that the entire resistance to mass transfer in a given turbulent phase lies in a thin, stagnant region of that phase at the interface, called a him, hence the name film theory.2 4,5 Other, more detailed, theories for describing the mass transfer through a fluid-fluid interface exist, such as the penetration theory.1,4... 

In practice ceramics are usually multiphase, consisting of crystalline phases, glasses and porosity. The overall behaviour depends on the distribution as well as the properties of these constituents. A minor phase that forms a layer round each crystallite of the major phases, and therefore results in a 3-0 connectivity system (see Section 2.7.4), can have a major effect. If the minor phase is conductive it can greatly reduce the resistivity of the composite or, if insulating, it can reduce its conductivity. Also, an abrupt change in the mode of conduction at the main phase-intercrystalline phase boundary may introduce barriers to conduction that dominate the overall electrical behaviour. In contrast, minor phases present as small discrete particles, or porosity present as empty cavities, can only modify properties to a minor extent as indicated by one of the mixture relations such as Lichtenecker s rule (see Section 2.7.4). 

---