Amplitude of the anomaly in the mass density near a liquid-liquid critical point.

Abstract

We address two questions with respect to the amplitude of the critical anomaly in the mass density (or the thermal expansion) as a function of temperature in the one-phase region near a liquid-liquid critical point. First, is this amplitude proportional to the difference in density between the two pure liquid components of the mixture? A consideration of data from the literature on 11 liquid-liquid systems shows no such correlation, nor is any such correlation expected from theory. Second, is this amplitude, as directly measured, thermodynamically consistent with measurements of the heat capacity at constant pressure and composition ${\mathit{C}}_{\mathit{P},\mathit{x}}$ on the same system? Data from the literature on 5 systems show that, in relating the critical coefficient of the density anomaly to the critical coefficient of ${\mathit{C}}_{\mathit{P},\mathit{x}}$, we cannot make a direct calculation of one from the other. If we try to test the consistency among the critical behaviors of the thermal expansion ${\mathit{C}}_{\mathit{P},\mathit{x}}$ and ${\mathit{C}}_{\mathit{V},\mathit{x}}$, then the required data are available for only one system and are not consistent. We attribute these problems to the behavior of ${\mathit{C}}_{\mathit{V},\mathit{x}}$ and also to the importance of terms other than the critical terms. We caution that the interpretation of the amplitudes of small critical anomalies, such as in the density, must be done with care. \textcopyright{} 1996 The American Physical Society.