Quadratic driving force approximation

A quadratic-driving-force approximation has been developed by Vermeulen (V3). For r = 0 this fits Eq. (81) closely over the entire range of x. This can be extended to the general form ... 

The breakdown of the linear rate approximation for nonlinear systems was noted by Vermuelen who developed modified lumped parameter approximations which represent the diffusion models more accurately than the simple linear rate expression. For solid diffusion (model 2a or 2b) a quadratic driving force approximation is recommended ... 

In contrast with the Butler-Volmer approximation, the activation-driving force relationships [equations (1.32)] are quadratic rather than linear. This... 

We examine next the cyclic voltammetric responses expected with nonlinear activation-driving force laws, such as the quasi-quadratic law deriving from the MHL model, and address the following issues (1) under which conditions linearization can lead to an acceptable approximation, and (2) how the cyclic voltammograms can be analyzed so as to derive the activation-driving force law and to evidence its nonlinear character, with no a priori assumptions about the form of the law. 

In a strict sense, one should model the solution at least as a regular one, but the formation enthalpy of the regular solution is much less than the driving force to form the intermetallic compound. Thus, neglecting the mixing enthalpy in the parent phase wiU not lead to any substantial error. For the intermetallic phase AI9C02, we use the quadratic approximation of the Gibbs potential... 

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