Mass transport Diffusion, Migration

We will assume for all of the techniques discussed in this chapter that the analyte solution is quiet (that is, still and unstirred) in order to ensure that mass transport by convection is absent. Furthermore, we will also assume that an excess of ionic electrolyte has been added to the solution to ensure that mass transport by migration is also absent. We see that the only form of mass transport remaining is diffusion, and hence the subtitle to this chapter. 

In the previous chapter, we discussed dynamic electroanalytical techniques such as polarography and voltammetry. Each technique in that chapter was similar insofar as the principal mode of mass transport was diffusion. Mass transport by migration was minimized by adding an inert ionic salt to the electroanalysis sample and convection was wholly eliminated by keeping the solution still ( quiescent ). ... 

In the previous chapter we have introduced the case of multiple-electron transfers (multi-E mechanisms). As discussed then, depending on the formal potentials of the different electrochemical steps comproportiona-tion/disproportionation reactions may be thermodynamically favourable and may affect the voltammetry if the electron transfers are not reversible, the diffusion coefficients of the species are different, there is mass transport by migration or other chemical reactions take place. For example, let us consider the case of two consecutive reduction processes (the EE mechanism) where the formal potential of the second step is much more negative than the first one ... 

In certain experimental conditions (see examples below), the electrolyte may have zones where diffusion plays a negligible role compared to the other mass transport modes (migration and convection). These are often called bulk electrolyte. The zone(s) where diffusion cannot be disregarded is (are) then defined as the diffusion layer(s) Defining the diffusion layer volume in quantitative terms, and in particular defining its thickness, wholly depends on how precisely one chooses to observe and define the phenomena . A diffusion layer, which is generally next to an interface, may see migration and convection also occur. 

When mass transport kinetics interferes, the steady-state current-potential curves show a limiting current for the redox process, which brings into play this mass transport. The limiting current is shown on a current-potential curve as a horizontal plateau. It is often also called a limiting diffusion current. It is dependent on the mass transport parameters (migration, diffusion and convection) and is, with a few exceptionsproportional to the concentration of the consumed species, because their mass transport limits the reaction rateand therefore the current flow... 

Under realistic conditions a balance is secured during current flow because of additional mechanisms of mass transport in the electrolyte diffusion and convection. The initial inbalance between the rates of migration and reaction brings about a change in component concentrations next to the electrode surfaces, and thus gives rise to concentration gradients. As a result, a diffusion flux develops for each component. Moreover, in liquid electrolytes, hydrodynamic flows bringing about convective fluxes Ji j of the dissolved reaction components will almost always arise. 

It was shown in Section 1.8 that in addition to ion migration, diffusion and convection fluxes are a substantial part of mass transport during current flow through electrolyte solutions, securing a mass balance in the system. In the present chapter these processes are discussed in more detail. 

Surface diffusion is yet another mechanism that is often invoked to explain mass transport in porous catalysts. An adsorbed species may be transported either by desorption into the gas phase or by migration to an adjacent site on the surface. It is this latter phenomenon that is referred to as surface diffusion. This phenomenon is poorly understood and the rate of mass... 

Mass transport can be by migration, convection or diffusion. As discussed in chapter 1, in the presence of strong electrolyte migration can be neglected, as can convection if the solution is unstirred, at a uniform temperature and the timescale of the experiment is short (i.e. a few seconds). Thus, we can make the first distinction between electrode reactions that are dominated by step 1, diffusion-controlled, and those for which steps 1 and 2 contribute to the overall observed rate. 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

The previous models were developed for Brownian particles, i.e. particles that are smaller than about 1 pm. Since most times particles that are industrially codeposited are larger than this, Fransaer developed a model for the codeposition of non-Brownian particles [38, 50], This model is based on a trajectory analysis of particles, including convective mass transport, geometrical interception, and migration under specific forces, coupled to a surface immobilization reaction. The codeposition process was separated in two sub-processes the reduction of metal ions and the concurrent deposition of particles. The rate of metal deposition was obtained from the diffusion... 

To know that the overall process of mass transport occurs via three mechanisms, namely convection, migration and diffusion. Convection is the physical movement of solution, migration is the movement of charged analyte in response to Coulomb s law and diffusion is an entropy-driven process. In terms of mass transport, the order of effectiveness is as follows convection migration > diffusion. 

Such movement is termed mass transport, and proceeds via three separate mechanisms, namely migration, convection and diffusion. The overall extent of... 

Each one of these three inodes of mass transport, i.e. migration, diffusion and convection, will now be considered in turn. 

If the overall mass control comprises three components - migration, convection and diffusion - which form of mass transport is the most effective ... 

Mass transport comprises three different modes , i.e. convection, migration and diffusion. Convection (stirring) is the most efficient form of mass transport. Migration can be minimized by adding a swamping electrolyte to the solution. Diffusion occurs even in the absence of migration and convection. 

In this case, the first reason for deviation from linearity is that the exponent on the scan rate is not 1/2, but some other fraction. If the exponent is greater than 1/2, then we assume that an additional means of mass transport supplements the diffusion - with either convection or migration also being involved. Conversely, if the exponent is much less than 1/2, then we usually assume that the analyte is adsorbed at the electrode, implying that there is little mass transport of analyte at all. 

Mass transport by diffusion can never be totally eliminated if there are differences in concentration throughout the solution (e.g. as caused by current flow), but convection is such an efficient form of mass transport, when compared with either migration or diffusion, that it is safe to assume that diffusion is quite negligible in comparison. 

Mass transport The means of effecting movement of electroanalyte to an electrode prior to electromodification. The three forms ( modes ) of mass transport are convection, migration and diffusion. 

Narayanan et al. conducted a theoretical analysis on the cell parameters that determined this maximum shuttling current. By assuming that the mass transport of the redox couple [R]/[0] is mainly realized by means of diffusion—which is reasonable because the low concentration of [R]/[0] at the additive level makes the field-assisted migration negligible—they applied the finite linear diffusion... 

There are three kinds of mass transport process relevant to electrode reactions migration, convection and diffusion. The Nernst—Planck equation... 

Since the electrochemical reduction or oxidation of a molecule occurs at the electrode-solution interface, molecules dissolved in solution in an electrochemical cell must be transported to the electrode for this process to occur. Consequently, the transport of molecules from the bulk liquid phase of the cell to the electrode surface is a key aspect of electrochemical techniques. This movement of material in an electrochemical cell is called mass transport. Three modes of mass transport are important in electrochemical techniques hydrodynamics, migration, and diffusion. 

Excluding adsorption, there are three sources of mass transport of reactant from solution to the electrode surface migration, convection, and diffusion. The first... 

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