Logarithmic rate law

Figure 5.6 Rate laws for formation of oxide films, (a) Parabolic rate law. (b) Effect of film cracking (successive parabolic segments), (c) Limiting case of (6). (d) Logarithmic rate law.

The oxidation of iron by (dry) air at ambient temperature proceeds according to the inverse logarithmic rate law, which may be written... 

It is clearly recognized that on oxide semiconductors various types of chemisorption can and do occur as a result of various types of electron exchange between adsorbent and adsorbate. Slow rates of adsorption may be due to the conditions of this exchange. The logarithmic rate law, however, seems to represent a number of different processes (bulk or surface diffusion, activation or deactivation of catalytic surfaces, chemisorption). It appears futile to explain this empirical relation in terms of a unique mechanism. 

A rate-determining electron supply should be considered as a possibility in interpreting a logarithmic rate law. This can perhaps be discussed in connection with the low temperature oxidation of metals with p-type surface layers, in particular nickel (51). Experimental results by Scheuble (52) are available in this connection (Fig. 13). He observed a logarithmic rate law for the time dependence of oxygen consumption due to NiO-formation ... 

Fig. 13. Logarithmic rate law of the air oxidation of nickel at 200°C (51) according to data from ref. (52).

Theories of oxidation have been developed by Wagner and by Mott ° . In general the logarithmic rate law applies to very thin oxide layers which form protective coatings and the parabolic rate law to thick oxide layers. More recent reviews of the subject have been given by Grimley , Kubaschewski and Hopkins and by Wyn Roberts . ... 

The rate of oxidation and/or oxide formation has been described with Hnear, parabolic, logarithmic, and inverse logarithmic rate laws [1,22,23]. The generally accepted rate of oxidation is given in units of mass per area, the mass of oxide product formed per area of metal, and is denoted as W. The fUm thickness x is proportional to the weight gain. 

The logarithmic rate law has no theoretical basis and is an empirical relationship. The logarithmic rate is given as ... 

Fig. 11.15 Oxide thickness vs. time observed for logarithmic and inverse logarithmic rate laws.

Figure 11.16 clearly indicates the logarithmic rate law is valid only for very thin oxide layers. Nickel oxidation follows the logarithmic law up to 200 °C. At 340 °C, the parabolic rate law better fits the data [26]. The oxidation reaction follows different rate laws at different temperatures. 

On the other hand, if the electronic conductivity of the product layer is high enough, ionic transport in the electrical field of the condenser may become rate-controlling. In this case, an inverse logarithmic rate law results, since the activation energy for the motion of an ion in the product layer decreases when there is a constant electrical potential difference across the layer. The amount by which the activation energy decreases is proportional to the electric... 

Under hydrogen water chemistry (HWC) conditions, the Co deposition was observed to proceed faster than predicted from a logarithmic rate law, suggesting that under such conditions cobalt deposition is not controlled exclusively by the... 

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