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5 Experimental Verification of Dynamic Scaling Theories and Discussions

Figure 5.57: Amplitude of the life time of concentration fluctuations in dependence of X , according to Eq.(5.32): (1) ethanol-dodecane, (2) nitrobenzene-isooctane, (3) nitrobenzene- n-hexane, (4) methanol-cyclohexane, (5) benzonitrile-isooctane, (6) methanol-n-hexane, (7) methanol-n-heptane, (8) nitroethane-3-methylpentane, (9) nitroethane-cyclohexane, (10) n- pentanol-nitromethane, (11) isobutoxyethanol-water, (12) 2,6-dimethylpyridine-water, (13) triethylamine-water.

relaxation rate decreases with increasing surface tension, while group (II) displays an op- posite trend. The third group (III) shows the behavior of binary aqueous solutions, with by far the largest surface tension. However, this kind of qualitative studies give an in- dication that there must exists an additional parameter which interacts additionally with the surface tension. In fact it has been argued by Fisk and Widom and recognized later as an aspect of the tow-scale factor universality that there exists a universal combination of critical amplitudes involving the surface tension amplitude σ0, [153]. According to Br´ezin [154], the simplest way to define the universal combination is to notice that the free interfacial energy per unit area (divided by kBT), multiplied by an area as defined by the correlation length, is both temperature independent and universal in the vicinity of Tc. Owing to this argument, the following expression can be written, [30]:

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