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4 Critical Contribution, Dynamic Scaling and Crossover Theory

Consequently, one can get the frequency dependence of Cp at Γ = 0, by using the mode- coupling formalism. It follows:

with a constant a. The attenuation coefficient α introduced in Chapter (3), is proportional to:

The plot of α/ f 2 versus f −1.057 represents a straight line as is shown by the example of the n-pentanol-nitromethane mixture of critical composition in Fig.(4.1).

Up to now, the temperature dependence of the amplitude has not be considered. Bhat- tacharjee and Ferrell give an expression for the amplitude of critical contribution:

with:

SBF : the temperature dependent Bhattacharjee-Ferrell amplitude FBF : the Bhattacharjee-Ferrell scaling function Γ : relaxation rate of concentration fluctuations Ω= ω/Γ : reduced frequency cs : sound velocity.

According to Eq.(4.16), where ˜α0/Z0˜ν = 0.057, the amplitude parameter A is related to

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