Linear growth rate, definition

If the necessary conditions for a parabolic growth rate are not fulfilled, then other rate laws will be obeyed. One may find, for example, that the reaction rate is constant (i.e. independent of the instantaneous thickness of the product layer). However, this observation alone does not permit one to decide upon a definite rate-controlling elementary reaction mechanism, since several mechanisms can give rise to an overall linear rate law. 

Figures 3.80(a) and (b) show the behaviour of n, k and the thickness L of a polypyrrole film during its growth on a Pt electrode in aqueous perchlorate solution obtained via in situ ellipsometry. A definite lag can be seen between the change in L and the changes in n and k. Up to c. 1.3 s the thickness of the film increases linearly with time while n and k remain constant. Between 1.3 and 2 s the growth almost tails off before increasing slowly up to 4 s and then more quickly until attaining a steady rate of increase at t > 4 s. Similarly at 1.3 s < t < 4 s both n and k increase, with n attaining a maximum value at 4 s before decreasing, while k increases at a lower rate at t > 4 s than at t < 4 s.

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