Universal amplitude ratios and the interfacial tension near consolute points of binary liquid mixtures

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Abstract
The densities of the coexisting phases and the capillary length have been measured to obtain the interfacial tension (σ) near the consolute temperatures Tc of the three binary liquid mixtures: triethylamine+water, triethylamine+heavy water, and methanol+cyclohexane. Our data are combined with data from the literature to test predictions for three temperature-independent ‘‘universal’’ ratios: U+1=σ(ξ+)2/(kBTc) and Y(±)=σ(αt2C±s/kB) −2/3/(kBT0). [Here ξ+ is the correlation length, C±s is the singular part of the heat capacity per unit volume, α=0.11 is the exponent characterizing the specific heat divergence, and t≡(T−Tc)/Tc]. Near Tc, the new experimental values of Y(+) range from 5.5–5.8 in agreement with the value 5.6 obtained by Moldover [Phys. Rev. 31, 1022 (1985)] in a review of earlier experiments. However, the experimental values of Y(+) are inconsistent with either the value Y(+)=4.4±0.4 obtained from a recent simulation of the simple-cubic Ising model or the value Y(+)=2.6–3.0 obtained from a one-loop renormalization group calculation. The experimental values Y(−)=3.7 and U+1 =0.39 are also much larger than both the Ising model and the renormalization group values. It is unlikely that the inconsistency between the experimental and the theoretical ratios Y(±) and U+1 can be explained by systematic errors in the measurements of σ, because diverse techniques for measuring σ have yielded consistent results for a wide variety of fluid systems. A table of the relevant amplitudes for 16 fluid systems is included.