Compensation behavior temperature-dependent

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

In studying interfacial electrochemical behavior, especially in aqueous electrolytes, a variation of the temperature is not a common means of experimentation. When a temperature dependence is investigated, the temperature range is usually limited to 0-80°C. This corresponds to a temperature variation on the absolute temperature scale of less than 30%, a value that compares poorly with other areas of interfacial studies such as surface science where the temperature can easily be changed by several hundred K. This "deficiency" in electrochemical studies is commonly believed to be compensated by the unique ability of electrochemistry to vary the electrode potential and thus, in case of a charge transfer controlled reaction, to vary the energy barrier at the interface. There exist, however, a number of examples where this situation is obviously not so. 

The theoretical and mechanistic explanations of compensation behavior mentioned above contain common features. The factors to which references are made most frequently in this context are surface heterogeneity, in one form or another, and the occurrence of two or more concurrent reactions. The theoretical implications of these interpretations and the application of such models to particular reaction systems has been discussed fairly fully in the literature. The kinetic consequence of the alternative general model, that there are variations in the temperature dependence of reactant availability (reactant surface concentrations, mobilities, and active areas Section 5) has, however, been much less thoroughly explored. 

It is reasonable to suppose that between the members of a group of related reactions there will be modifications, but not drastic changes, in the positions of surface equilibria and in the temperature dependences of c1 c2, and As. Such variations, when subject to appropriate constraints, are capable of providing an explanation of compensation behavior (Appendix I and Section II, A, 5). From this it follows that the compensation effect appears as a general or at least a widely occurring characteristic feature of surface processes, rather than an exceptional phenomenon that requires an exceptional explanation. 

A more rigorous treatment of adsorption equilibria would include due allowance for the total number of surface sites available, which sets an upper limit on the surface concentrations to be used in the above equations, the variation in the heat of adsorption with coverage, and surface heterogeneity. The significant feature of Eq. (11), relevant to the present discussion of compensation behavior, is that this predicted temperature dependence of variations of c i and c2 results in no deviation from obedience to the Arrhenius equation. If a given set of kinetic results obey Eq. (1) the condition for a fit to Eq. (9) is... 

The possible role of nickel formate as an intermediate in the breakdown of formic acid on nickel has been extensively discussed (3, 232, 240b, 244) this is another catalytic reaction in which there is compensation behavior (Table III, R). While the observed obedience to Eq. (2) does not identify the reaction mechanism, it is probably significant that catalytic activity becomes apparent in the temperature range of onset of salt instability. Again it may be envisaged that the temperature dependence of effective concentration of nickel formate intermediate may vary with reaction conditions. 

The compensation relationships mentioned here for the decomposition of formic acid on metals (Table III, K-R and Figs. 6 and 7) cannot be regarded as established, meaningful kinetic descriptions of the reactions concerned, since the magnitudes of the calculated values of B and e depend on the selection of data to be included in the calculation. While there is evidence of several sympathetic interrelationships between log A and E, the data currently available do not accurately locate a specific line and do not define values of B and e characteristic of each system, or for all such systems taken as a group. The pattern of observations is, however, qualitatively attributable to the existence of a common temperature range within which the adsorbed formate ion becomes unstable. The formation of this active intermediate, metal salt, or surface formate, provides a mechanistic explanation of the observed kinetic behavior, since the temperature dependence of concentration of such a participant may vary with the prevailing reaction conditions. 

Appendix I Compensation Behavior Resulting from Temperature-Dependent Variations in Concentrations of Surface... 

Since b values for simple electron-transfer-controlled processes are approximately of the correct magnitude at 298 K, taking P — 0.5, it is clear that the temperature factor in the experimental behavior must be entering the electrochemical Arrhenius expression in more or less the conventional way, i.e., as a (kT) term. However, since b is often found to be independent of 7, it is clear that there must be another compensating temperature-dependent effect, namely an approximately linear dependence of a or j8 on temperature in the Tafel slope, b = RT/a T)F. The experimental results for a variety of reactions, summarized in Section III, show that this is a general effect. Reduction of C2H5NO2 is an exception while reduction of other nitro compounds takes place with substantial potential dependence of a ... 

Typical behavior for the evolution of the temperature-dependent resistivity (p) as Eg crosses Ec is shown in Figure 15.10 for p-doped germanium as a function of the compensation (carrier density) [89]. For the material with the largest compensation (smallest carrier density), p has the largest magnitude and strongest temperature dependence. As the compensation is decreased (carrier density is increased),... 

The temperature dependence of x(T) discussed above is qualitatively similar to that of a magnetic impurity exhibiting the Kondo effect especially when - 1. For isolated magnetic impurities in metallic systems the problem scales to a strong coupling problem and the local spin is fully compensated by the conduction electrons and the local moment is quenched (see Varma, 1976). A similar situation is envisaged in mixed valent compounds to explain the susceptibility behavior. Varma and Yafet (1976) have taken this view point and have calculated the susceptibility for a two band model (f and d). According to them, for the mixed valent compounds x(T- 0) = where is the effective... 

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