Diffusional concentration polarization

The standard rate constant kP characterizes the rates of both the forward and reverse processes. Its value is independent of the reference electrode selected, in contrast to what holds true for the values of k and and it is also independent of the component concentrations, in contrast to what holds true for the exchange CD. Therefore, this constant is an unambiguous characteristic of the kinetic properties exhibited by a given electrode reaction. 

3 DIFFUSIONAL CONCENTRATION POLARIZATION 6.3.1 Solutions with Excess Foreign Electrolyte 

Under the effect of pure concentration polarization, when activation polarization is absent, the electrode potential retains an equilibrium value, but this is a value tied to the variable nonequilibrium values of surface concentrations 

It follows that concentration polarization is defined by the expression 

The surface concentrations that are attained as a result of balance between the electrode reaction rates and the rates of supply or escape of components by diffusion and migration are given by Eqs. (4.11) and (4.12). Hence, the overall expression for concentration polarization becomes 

---

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

In an electrochemical system, gas supersaturation of the solution layer next to the electrode will produce a shift of equilibrium potential (as in diffusional concentration polarization). In the cathodic evolution of hydrogen, the shift is in the negative direction, in the anodic evolution of chlorine it is in the positive direction. When this step is rate determining and other causes of polarization do not exist, the value of electrode polarization will be related to solution supersaturation by... 

An -> ideal nonpolarizable electrode is one whose potential does not change as current flows in the cell. Much more useful in electrochemistry are the electrodes that change their potential in a wide potential window (in the absence of a - depolarizer) without the passage of significant current. They are called -> ideally polarized electrodes. Current-potential curves, particularly those obtained under steady-state conditions (see -> Tafel plot) are often called polarization curves. In the -> corrosion measurements the ratio of AE/AI in the polarization curve is called the polarization resistance. If during the -> electrode processes the overpotential is related to the -> diffusional transport of the depolarizer we talk about the concentration polarization. If the electrode process requires an -> activation energy, the appropriate overpotential and activation polarization appear. 

The water flux, J, which is normally expressed as kg (or L) m h is proportional to the water vapor pressure gradient, Apm, between the feed-membrane and strip-membrane interfaces, and the membrane mass transfer co-efficient K, [Eq. (3)]. The vapor pressure gradient between the two interfaces depends on the water activity, a, in the bulk feed and strip streams, and the extent to which concentration polarization reduces that activity at each interface. Whilst can be estimated using established diffusional transport equations, it is more difficult to estimate values for the water vapor pressure at the membrane wall for use in Eq. (3). However, an overall approach using the vapor pressures of the bulk solutions and semi-empirical correlations that take account of the different conditions near the membrane wall can be used to estimate J. 

These relations can be used as rough estimates of steric rejection, if the solute and membrane pore dimensions are known. The derivation is based on a strictly model situation (see Figure 1) and a long list of necessary assumptions can be written. Apart from the simplified geometry (hard sphere in a cylindrical pore), it was also assumed that the solute travels at the same velocity as the surrounding liquid, that the solute concentration in the accessible parts of the pore is uniform and equal to the concentration in the feed, that the flow pattern is laminar, the liquid is Newtonian, diffusional contribution to solute transport is negligible (pore Peclet number is sufficiently high), concentration polarization and membrane-solute interactions are absent, etc. 

The potential difference can be seen to be made up of two terms. The first term represents the ohmic potential drop due to the flow of current through a medium of given electrical conductance. The second term, called the diffusion potential drop, is associated with a region in which there is a concentration gradient (concentration polarization region). This term does not disappear in the absence of a current and is due to unequal rates of diffusion of the charged particles, thus giving rise to a diffusional electric field. 

For the electrodeposition of laminar metal coatings, two conditions must be fulfilled (1) The reversible potentials for metals A and B must be sufficiently different so that at a given current density, the less noble one (B) virtually does not electrodeposit during the electrodeposition of the more noble one (A) until complete concentration polarization with respect to ions of metal A takes place (2) within the duration of the current density pulse, Send s equation [15] for diffusional polarization is obeyed with respect to concentration change, resulting in transition from electrodeposition of metal A to electrodeposition of metal B after well-defined transition time. 

In the case where s" Km and layer thickness is large, the current is independent of layer thickness and linearly dependent on substrate concentration. It also varies as the square root of the catalyst loading. In this case there is a thin reaction layer, and reaction kinetics at the particle surface are much more rapid than the diffusional transport of the substrate through the film. Therefore the reaction is diffusion-controlled, and there is considerable concentration polarization of substrate through the film. This fact is clearly indicated in the concentration profiles illustrated in Fig. 2.31. 

Now, consider flow along the surface of a membrane. The same boxmdary layer forms as with flow through a pipe. However, with a membrane system, because there is a net flow out through the membrane, there is convective flow to the membrane, but only diffusional flow away from the membrane. Since diffusion is slower than convection, solutes rejected by the membrane tend to build up on the surface and in the boxmdary layer. Thus, the concentration of solutes at the membrane sxtrface is higher than in the bulk solution. This boxmdary layer is called concentration polarization. The phenomenon is shown in Figure 3.4. 

Beta is not a property of the membrane it is an artifact of the system design that is selected. Specifically, Beta is a function of how quickly the influent stream is dewatered through the RO system. If water is removed too quickly from the influent stream. Beta will increase, as a relatively high volume of dissolved soHds is left behind on the membrane because of the high volume of water that permeates out through the membrane. Concentration polarization further exacerbates the problem because of the diffusional-only flow away from the membrane surface. See Chapter 9.6 for more information about Beta and its relationship with water flux and salt passage. 

For a voltammetric sensor, the current or potential peak shift that may relate to the concentration of the sensing species is an important measurement. In a dynamic situation in which polarization characteristics are obtained, it is essential that the mass transfer characteristics are reproducible for both calibration and actual measurements. In the case of a stationary planar sensor, stagnant solution or steady flow conditions in a flow cell provides good reproducibility. Or in another case, a sufficiently high concentration of an electrolyte is used to maintain a constant ohmic drop in the cell, regardless of the concentration of the pertinent sensing component. Under these conditions, the mass transfer can be purely diffusional and adequately described by Pick s law of diffusion. 

Studies of diffusional phenomena have direct relevance to detergency processes. Experiments are reported which investigate the effects of changes in temperature on the dynamic phenomena, which occur when aqueous solutions of pure non-ionic surfactants contact hydrocarbons such as tetradecane and hexadecane. These oils can be considered to be models of non-polar soils such as lubricating oils. The dynamic contacting phenomena, at least immediately after contact, are representative of those which occur when a cleaner solution contacts an oily soil on a polymer surface. With Ci2E5 as non-ionic surfactant at a concentration of 1 wt.% in water, quite different phenomena were observed below, above, and well above the cloud point when tetradecane or hexadecane was carefully layered on top of the aqueous solution. Below the cloud point temperature of 31°C very slow solubilisation of oil into the one-phase micellar solution occurred. At 35°C, which is just... 

---