Simple carrier, analysis

We note that the transition between the forms E, and E2 is between forms which interact with different species of the substrate (S, and S2, respectively). It is to be expected, therefore, that such transitions can be revealed by kinetic analysis at the steady-state level. We will see later that the model of Fig. 6 contains all the kinetic features of the classical carrier model. Thus we define a system which behaves according to the kinetic scheme of Fig. 6 as the simple carrier [2]. 

The fact that the infinite cis and trans experiments can be performed and yield finite values of the respective half-saturation concentration leads, as we have seen, to the rejection of the simple-pore model (and its more complex form). The simple carrier can then temporarily be considered acceptable for such systems as yield finite half-saturation concentrations for these procedures. But the actual value of these parameters may or may not be consistent with the simple carrier and hence one can develop rejection criteria for the simple carrier in terms of the experimentally measurable parameters. The point of such an analysis is the following For a system which behaves as a simple carrier, the unidirectional flux Eqn. 30 is appropriate and will serve to account for all steady-state experiments involving the single substrate S. Yet Eqn. 30 contains only four independently variable parameters—one form in K and three forms in R (since the forms are connected by /Jqo + ee 12 21)-... 

The simple carrier of Fig. 6 is the simplest model which can account for the range of experimental data commonly found for transport systems. Yet surprisingly, it is not the model that is conventionally used in transport studies. The most commonly used model is some or other form of Fig. 7. In contrast to the simple carrier, the model of Fig. 7, the conventional carrier, assumes that there exist two forms of the carrier-substrate complex, ES, and ES2, and that these can interconvert by the transitions with rate constants g, and g2- Now, our experience with the simple- and complex-pore models should lead to an awareness of the problems in making such an assumption. The transition between ES, and ES2 is precisely such a transition as cannot be identified by steady-state experiments, if the carrier can complex with only one species of transportable substrate. Lieb and Stein [2] have worked out the full kinetic analysis of the conventional carrier model. The derived unidirectional flux equation is exactly equivalent to that derived for the simple carrier Eqn. 30, although the experimentally determinable parameters involving K and R terms have different meanings in terms of the rate constants (the b, /, g and k terms). The appropriate values for the K and R terms in terms of the rate constants are listed in column 3 of Table 3. Thus the simple carrier and the conventional carrier behave identically in... 

As mentioned above, the interpretation of CL cannot be unified under a simple law, and one of the fundamental difficulties involved in luminescence analysis is the lack of information on the competing nonradiative processes present in the material. In addition, the influence of defects, the surface, and various external perturbations (such as temperature, electric field, and stress) have to be taken into account in quantitative CL analysis. All these make the quantification of CL intensities difficult. Correlations between dopant concentrations and such band-shape parameters as the peak energy and the half-width of the CL emission currently are more reliable as means for the quantitative analysis of the carrier concentration. 

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

If the sample conductivity is dominated by only one type of carrier, then a simple Hall-effect analysis is sufficient. The appropriate equations for a Hall-... 

Normally, it is also a simple task to estimate recycle flows as a function of the design variables. The recycle flows and feed flows provide the information required to conduct reactor synthesis/analysis studies. The cost of the reactor is usually not very important, but the product distribution and the need for heat carriers and/or diluents have a major impact on the synthesis of the separation system. 

Example 9.14 Nonisothermal facilitated transport An approximate analysis of facilitated transport based on the nonequilibrium thermodynamics approach is reported (Selegny et al., 1997) for the nonisothermal facilitated transport of boric acid by borate ions as carriers in anion exchange membranes within a reasonable range of chemical potential and temperature differences. A simple arrangement consists of a two-compartment system separated by a membrane. The compartments are maintained at different temperatures T] and T2, and the solutions in these compartments contain equal substrate concentrations. The resulting temperature gradient may induce the flow of the substrate besides the heat flow across the membrane. The direction of mass flow is controlled by the temperature gradient. 

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