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5.6 Systems with complex background contributions

Figure 5.25: Acoustical attenuation-per-wavelength spectrum for (i−C4E1/H2O) mix- ture of critical composition at 25 oC. The subdivision follows from nonlinear least-squares regression analysis of the experimental spectrum of terms of Eqs.(5.18) and (3.31).

are required for an adequate analytical representation of the experimental data [110]. In addition to a broad critical contribution Rc(f) Eq.(4.16), a restricted Hill-type R# H(f) Eq.(3.39), and a Debye-type RD(f), Eq.(3.32), relaxations are indicated by relative max- ima in the spectrum, Fig.(5.25). Here the restricted Hill term reflects the micelle formation and decay kinetics [113]. The additional contribution represented by the Debye term ex- ists already in i−C4E1 without water added. It seems to reflect a chemical equilibrium of i−C4E1 molecules, likely a step in the isobutoxyethanol isomerization scheme. Informa- tion about the spectrum has been achieved from broadband measurements at noncritical mixtures with 0.09 ≤Y < 1 in [113]. This complicated spectrum requires a special re- gression analysis. In order to reduce the number of adjustable parameters, ones more, the critical relaxation rate Γ(ε) from light scattering has been used as known parame- ter in the regression analysis of the spectra. Furthermore, in the fitting procedure of the low-frequency measurements (inset of Fig.(5.26)) between 200 kHz and 3 MHz the pa- rameters of the Hill and Debye relaxation terms have been obtained by interpolation and extrapolation from previous data [110]. Therefore, in determining the scaling function F(Ω) (Fig.5.26), the only adjustable parameter in the data evaluation was the critical amplitude SBF. As result, the temperature dependence in SBF, as follows from the fit- ting procedure of the attenuation coefficient data in terms of the Bhattacharjee-Ferrell scaling function, is almost as large as for the (NE-CH) system. According to Eq.(5.15),

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