Polarization, concentration definition

To determine actual cell performance, three losses must be deducted from the Nernst potential activation polarization, ohmic polarization, and concentration polarization. Definition of the ohmic polarization is simply the product of cell current and cell resistance. Both activation polarization and concentration polarization required additional description for basic understanding. 

The membrane in a broad sense is a thin layer that separates two distinctively different phases, i.e., gas/gas, gas/liquid, or liquid/liquid. No characteristic requirement, such as polymer, solid, etc., applies to the nature of materials that function as a membrane. A liquid or a dynamically formed interface could also function as a membrane. Although the selective transport through a membrane is an important feature of membranes, it is not necessarily included in the broad definition of the membrane. The overall transport characteristics of a membrane depends on both the transport characteristics of the bulk phase of membrane and the interfacial characteristics between the bulk phase and the contacting phase or phases, including the concentration polarization at the interface. The term membrane is preferentially used for high-throughput membranes, and membranes with very low throughput are often expressed by the term barrier. ... 

Polarization (1) In an electrochemical cell, a phenomenon in which the magnitude of the current is limited by the low rate of the electrode reactions (kinetic polarization) or the slowness of transport of reactants to the electrode surface (concentration polarization). (2) The process of causing electromagnetic radiation to vibrate in a definite pattern. 

The terms activation polarization and concentration polarization are also frequently used. This practice is to be discouraged because polarization is an ill-defined and misleading concept, as exemplified by the many different definitions to be found in dictionaries. Indeed, Sir William Grove himself stated, in 1874, that the word is sadly inaccurate . 

In order to provide a quantitative indication of the polarization level, several different concentration polarization coefficients can be found in the literature. The most used definitions are summarized in Table 14.1. The first thing to... 

Wang et alP uses a similar approach to define a concentration polarization coefficient, with the only difference that in their definition the coefficient is close to zero when the polarization is negligible. 

In order to link concentration polarization and membrane selectivity, Zhang et alP used the permeating fluxes in the definition of the coefficient. In the case where only one component is able to permeate through the membrane, this definition is very useful, because it does not depend on the particular permeation mechanism and, thus, is general. However, this approach is valid only for a binary mixture and cannot simply be generalized for a multi-component mixture. Additionally, the overall coefficient varies between zero and infinity, therefore not allowing an immediate perception of the polarization level. 

In faet, in the presenee of concentration polarization, whieh eauses the bulk eonditions to be different from those on the membrane surfaee, the only known quantities are the membrane permeanee and the bulk driving foree. In fact, the former ean be obtained from pure hydrogen tests, whilst the latter is ehosen by the user by setting the external pressure eonditions. Therefore, it would be useful to have these two quantities in the definition of the eoneentration... 

By comparing the expressions in eqn (14.7), this definition can be read in two ways when concentration polarization is negligible, i.e. CPC 0, membrane permeance is, in fact, coincident with that of bulk, or, dually, the permeation driving force between the bulks is the same as that between the membrane surfaces. It should also be noticed that the condition of maximum polarization, i.e. CPC= 1, is an asymptotic conditions where permeating flux tends to zero because the hydrogen partial pressure at membrane surface approaches to zero. This situation is summarized in Table 14.2. 

Definition of Concentration Polarization Coefficient in the Presence of Inhibition... 

The definition of concentration polarization coefficient adopted in the previous section (eqns (14.8) to (14.10)) is general and, thus, can be conveniently applied to different situations. In particular, CPC can be also used in a situation in which permeation is affected by inhibition, as reported in eqn (14.13) in terms of both driving forces and permeances ... 

According to their definitions, CPC and IC provide quantitative measures of the flux decrease due to concentration polarization and inhibition, respectively. However, it is sometimes useful to have an indication of the overall flux... 

For this aim, an overall permeance reduction coelScient , PRCP was introduced, to take into account the permeation reduction owing to both concentration polarization and inhibition at the same time. Its definition, reported in eqn (14.19), arises from the simple consideration that the lowest permeance is evaluated at bulk conditions when both polarization and inhibition affect the membrane system, whereas, on the other hand, the ideal membrane behavior and the maximum permeance can be found under pure hydrogen conditions ... 

According to its definition, the coefficient PRC is able to deal with the possible situations in which a membrane system affected by concentration polarization and inhibition can operate (Table 14.5). 

According to their definition, these coefficients - namely, concentration polarization coefficient CPC), inhibition coefficient IC) and the overall... 

The rejection coefficient when there is no concentration polarization (M = 1) is called the inherent rejection coefficient R°. By manipulating Eqs. fl7-21cl and (17-24a). we can find a relationship between retention R at one set of conditions and R at another set of conditions for well-mixed systems. Often the base case (Case A) condition is an e q)eriment with no concentration polarization (M ase a 1 f ase A = R°). Substitute Eq. fl7-21cl into the definition of R, Eq. ri7-24al. for both Cases A and B. Solve for 1 - R in both equations and then divide the Case B equation by the Case A equation. The ratio is... 

These three parameters (or other equivalent dimensionless groups) must appear in whatever formulation of this type of problem (the esterification reaction in PVRs), possibly together with other parameters which take into account other aspects such as additional phenomena (for example concentration polarization of the membrane), the presence of products in the initial mixture, the concentration of the catalyst and more complex constitutive equations. The dimensionless parameters have a more general validity than the individual dimensional parameters that appear grouped into them and characterize more univocally the behaviour of the system. The adoption of the parameter 5, the ratio of the characteristic rate of permeation to the characteristic rate of reaction, can be extended to any PVR and in general also to any membrane reactor. With this approach the comparison between different studies on PVRs is more direct and meaningful. On the other hand, the less acceptable, though often employed, dimensional parameter A/V, is comprised in the definition of 5. 

Clearly when there is no concentration polarization of 5 or 6 in the film, the modified definitions of the reaction layer thicknesses revert to the original definitions. 

When using literature data for ASR, it is critical to verify the definition of ASR. Some researchers have defined ASR s to include the activation and concentration polarization as well as the ohmic polarization. 

In the electrolytic cell, the cupric ions and sulfate ions both contribute to the conduction mechanisms. But only cupric ions enter into the electrode reaction and pass through the electrode-solution interface. The electrode therefore acts like a semipermeable membrane which is permeable to the Cu ions but impermeable to the 80 ions. Anions accumulate near the anode and become depleted near the cathode, resulting in concentration gradients in the solution near the electrodes of both ions. This is termed as concentration polarization. Let us determine the current-voltage characteristic of the cell, that is, the concentration polarization. To do this, we must calculate the flux of metal ions (cations) arriving at the cathode and depositing on it. We assume that the overall rate of the electrode reaction is determined by this flux. Once the cation distribution is known, the potential drop can be calculated. Note that anions are effectively motionless and do not produce a current. Let us assume that electrodes of the electrolytic cell are infinite planes at the anode (y = 0) and cathode (y = h) (Figure 6.3). The electrolyte velocity is zero. The definition of the current densities is... 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

Trying to determine which column is ideal for a specific analysis can be difficult with over 1000 different columns on the market [74]. A proper choice implies a definition of parameters such as column material, stationary phase (polarity), i.d., film thickness and column length. Guides to column selection are available [74,75]. The most important consideration is the stationary phase. When selecting an i.d., sample concentration and instrumentation must be considered. If the concentration of the sample exceeds the column s capacity, then loss of resolution, poor reproducibility and peak distortion will result. Film thickness has a direct effect on retention and the elution temperature for each sample compound. Longer columns provide more resolving probe, increase analysis times and cost. 

Another pertinent observation is the fact that the reaction proceeded twice as fast in -butyraldehyde (polar) as in benzene (nonpolar), even though the catalyst concentration was reduced to only one-third the comparable level. A graphic illustration of this effect is given in Fig. 9. The rate of gas uptake is plotted as a function of time for a reaction conducted in benzene and again for a second reaction conducted in butyraldehyde. The rate of reaction in the polar solvent was initially fast and decreased with time. The rate in the nonpolar benzene was initially slow, became faster as the solvent became more polar with the presence of product aldehyde, and then subsequently diminished with time. When the data were replotted as the log of unreacted olefin vs. time, the polar medium reaction showed first-order dependence on olefin concentration, whereas the nonpolar solvent reaction showed no definite order, owing to the constantly changing polarity. 

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