# Two phase asymmetry in the phase diagram of critical binary liquid systems: carbon disulphide+ nitromethane and cyclohexane+ acetic anhydride

Gopal, E. S. R. ; Chandra Sekhar, P. ; Ananthakrishna, G. ; Ramachandra, R. ; Subramanyam, S. V. (1976) Two phase asymmetry in the phase diagram of critical binary liquid systems: carbon disulphide+ nitromethane and cyclohexane+ acetic anhydride Proceedings of the Royal Society of London - Series A: Mathematical and Physical Sciences, 350 (1660). pp. 91-106. ISSN 0080-4630

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Related URL: http://dx.doi.org/10.1098/rspa.1976.0097

## Abstract

The coexistence curves of two binary liquid systems, carbon disulphide+nitromethane and cyclohexane+acetic anhydride, are examined over a temperature range $10^{-6}<-\epsilon$ = $(T_{\text{c}}-T)/T_{\text{c}}<10^{-1}$. The critical index $\beta$ for the two systems are 0.316 and 0.362, which agree with other experiments. The diameters of the coexistence curves for both systems show significant deviations near $T_{\text{c}}$ from the rectilinear diameter law. For $t=T_{\text{c}}-T>10$ K, rectilinear behaviour is shown. For $t<10\text{K}$, the deviation $\Delta x$ from the straight line is described by $\Delta x=Ft^{f}$ exp $(-Gt^{h})$, with $f\approx$ 0.9, showing that the derivative $\partial (\Delta x)/\partial t)$ diverges weakly like the heat capacity as $t\rightarrow$ 0. This is in striking agreement with recent theoretical models. A three-variable scaling theory is formulated to describe the critical behaviour of binary liquid systems. In addition to giving the usual scaling-law equalities, the theory shows that the heat capacity, the compressibility and the thermal expansion of binary liquid systems have the same $\alpha$-divergence at $T_{\text{c}}$. The theory is also capable of accommodating the diameter singularity, in which form it shows that, close to $T_{\text{c}},\Delta x$ behaves as $t^{-\alpha}$ and that the difference between the fluctuations, in composition, in two phases diverges as $t^{\beta -1}$.

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