Simple carrier, analysis model

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... 

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)-... 

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. 

The gas chromatograph also used to determine dry analysis yields was Perkin Elmer Fractometer Model 154. A simple device was constructed of Tygon tubing and brass connectors to permit breakage again of the irradiated capillaries directly in the carrier stream. 

We now follow an analysis by Allen et al. (1979) to show the fallacy of a possible scattering model as explanation of the low-temperature resistivity increase. Then for a metallic number of carriers kp is approximately Kla with a the interatomic separation which is equivalent to L (the mean distance between scatterers) a. One simple estimate... 

The simple Drude model assumes that the sole relaxation channel of the carriers arises from elastic scattering, and hence ignores correlation and inelastic scattering effects. In an analysis of the optical response of strongly correlated materials, the latter can be incorporated by considering an extended Drude model [45] in which the frequency-dependence of the... 

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