Interfacial transfer mass transport

Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydro-dynamic techniques become important, where mass transport is controlled by convection as well as diffusion. 

Electrochemistry in general and the EIS in particular are often used to analyze both bulk sample conduction mechanisms and interfacial processes, where electron transfer, mass transport, and adsorption are often present. EIS analysis has often treated the bulk and interfacial processes separately [4]. The analysis is achieved on the basis of selective responses of bulk and interfacial processes to sampling AC frequencies. The features appearing in the impedance AC frequency spectmm can be described according to the theory of impedance relaxations. Again, as in the case of any other spectroscopy method, the subject of the EIS analysis is the detection and interpretation of these spectrum features. 

Requirements regarding laboratory liquid-liquid reactors are very similar to those for gas-liquid reactors. To interpret laboratory data properly, knowledge of the interfacial area, mass-transfer coefficients, effect of contaminants on mass-transport processes, ionic characteristics of the system, etc. is needed. Commonly used liquid-liquid reactors have been discussed by Doraiswamy and Sharma (1984). 

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

The majority of RDC studies have concentrated on the measurement of solute transfer resistances, in particular, focusing on their relevance as model systems for drug transfer across skin [14,39-41]. In these studies, isopropyl myristate is commonly used as a solvent, since it is considered to serve as a model compound for skin lipids. However, it has since been reported that the true interfacial kinetics cannot be resolved with the RDC due to the severe mass transport limitations inherent in the technique [15]. The RDC has also been used to study more complicated interfacial processes such as kinetics in a microemulsion system [42], where one of the compartments contains an emulsion. 

The moving-drop method [2] employs a column of one liquid phase through which drops of a second liquid either rise or fall. The drops are produced at a nozzle situated at one end of the column and collected at the other end. The contact time and size of the drop are measurable. Three regimes of mass transport need to be considered drop formation, free rise (or fall) and drop coalescence. The solution in the liquid column phase or drop phase (after contact) may be analyzed to determine the total mass transferred, which may be related to the interfacial reaction only after mass transfer rates have been determined. 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

The transfer reaction of redox electrons at a metallic electrode accompanies a mass transport of hydrated redox particles through an interfacial difiusion layer to and from the electrode interface as shown in Fig. 8-8. If the rate of mass transport of hydrated redox particles is great, the reaction current is determined... 

The term on the left side of the equation is the accumulation term, which accounts for the change in the total amount of species iheld in phase /c within a differential control volume. This term is assumed to be zero for all of the sandwich models discussed in this section because they are at steady state. The first term on the right side of the equation keeps track of the material that enters or leaves the control volume by mass transport. The remaining three terms account for material that is gained or lost due to chemical reactions. The first summation includes all electron-transfer reactions that occur at the interface between phase k and the electronically conducting phase (denoted as phase 1). The second summation accounts for all other interfacial reactions that do not include electron transfer, and the final term accounts for homogeneous reactions in phase k. 

It must be emphasized that the above considerations were made in the absence of reaction. Interfacial mass transfer followed by reaction requires further consideration. The Hatta regimes classify transfer-reaction situations into infinitely slow transport compared to reaction (Hatta category A) to infinitely fast transport compared to reaction (Hatta category H) [42]. In the first case all reaction occurs at the interface and in the second all reaction occurs in the bulk fluid. Homogenous catalytic hydrogenations, carbonylations etc. require consideration of this issue. An extreme example of the severity of mass transport effects on reactivity and selectivity in hydroformylation has been provided by Chaudari [43]. Further general discussions for homogeneous catalysis can be found elsewhere [39[. 

It is possible that the pores of wetted catalyst particles eire filled with liquid. Hence, by virtue of the low values of liquid diffusivities (ca. 10 cm s" ), the effectiveness factor will almost certainly be less than unity. A criterion for assessing the importance of mass transfer in the trickling liquid film has been suggested by Satterfield [40] who argued that if liquid film mass transport were important, the rate of reaction could be equated to the rate of mass transfer across the liquid film. For a spherical catalyst particle with diameter dp, the volume of the enveloping liquid fim is 7rdp /6 and the corresponding interfacial area for mass transfer is TTdn. Hence... 

Mass transfer rates are increased in the presence of eruptions because the interfacial fluid is transported away from the interface by the jets. For mass transfer from drops with the controlling resistance in the continuous phase, the maximum increase in the transfer rate is of the order of three to four times (S8), not greatly different from the estimate of Eq. (10-4) for cellular convection. This may indicate that equilibrium is attained in thin layers adjacent to the interface during the spreading and contraction. When the dispersed-phase resistance controls, on the other hand, interfacial turbulence may increase the mass transfer rate by more than an order of magnitude above the expected value. This is almost certainly due to vigorous mixing caused by eruptions within the drop. 

In the previous section, the velocity and concentration distributions have been established and two transfer functions were considered. The explicit form of the third function which relates the fluctuating interfacial concentration or concentration gradient to the potential or the current at the interface, requires to make clear the kinetic mechanism composed of elementary steps with at least one of them being in part or wholly mass transport controlled. 

Figure 3.9 illustrates the electrochemical and mass transport events that can occur at an electrode modified with a interfacial supramolecular assembly [9]. For monolayers in contact with a supporting electrolyte, the principal process is heterogeneous electron transfer across the electrode/monolayer interface. However, as discussed later in Chapter 5, thin films of polymers [10] represent an important class of interfacial supramolecular assembly (ISA) in which the properties of the redox center are affected by the physico-chemical properties of the polymer backbone. To address the properties of these thin films, mass transfer and reaction kinetics have to be considered. In this section, the properties of an ideally responding ISA are considered. 

In the first part, Chapters 2-6, some fundamentals of electrode processes and of electrochemical and charge transfer phenomena are described. Thermodynamics of electrochemical cells and ion transport through solution and through membrane phases are discussed in Chapter 2. In Chapter 3 the thermodynamics and properties of the interfacial region at electrodes are addressed, together with electrical properties of colloids. Chapters 4-6 treat the rates of electrode processes, Chapter 4 looking at fundamentals of kinetics, Chapter 5 at mass transport in solution, and Chapter 6 at their combined effect in leading to the observed rate of electrode processes. 

Mass transport processes - diffusion, migration, and - convection are the three possible mass transport processes accompanying an - electrode reaction. Diffusion should always be considered because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the electrode and the bulk solution arise, which will induce diffusion processes. Reactant species move in the direction of the electrode surface and product molecules leave the interfacial region (- interface, -> interphase) [i-v]. The - Nernst-Planck equation provides a general description of the mass transport processes. Mass transport is frequently called mass transfer however, it is better to reserve that term for the case that mass is transferred from one phase to another phase. 

From the above outline, the mass-transport problem is seen to consist of coupled boundary value problems (in gas and aqueous phase) with an interfacial boundary condition. Cloud droplets are sufficiently sparse (typical separation is of order 100 drop radii) that drops may be treated as independent. For cloud droplets (diameter 5 ym to 40 pm) both gas- and aqueous-phase mass-transport are dominated by molecular diffusion. The flux across the interface is given by the molecular collision rate times an accommodation coefficient (a 1) that represents the fraction of collisions leading to transfer of material across the interface. Magnitudes of mass-accommodation coefficients are not well known generally and this holds especially in the case of solute gases upon aqueous solutions. For this reason a is treated as an adjustable parameter, and we examine the values of a for which interfacial mass-transport limitation is significant. Values of a in the range 10 6 to 1 have been assumed in recent studies (e.g.,... 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

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