The effect of an impurity on the critical point of a binary liquid system as a surface phenomenon

Abstract

An impurity which is considerably more soluble in one of the components of a binary liquid system than the other raises the temperature of an upper critical (consolute) point. Since the interfacial tension vanishes at the critical temperature, this effect can be described as a surface effect: The impurity raises the interfacial tension and is thus negatively adsorbed at the interface. The amount of impurity in the interface is assumed to be calculable by summing the dissolved amounts at all points of the interface, and can be seen to depend on the second derivative of the solubility as a function of concentration. These phenomena were treated thermodynamically with the help of the Gibbs adsorption equation in earlier papers, before the nature of the singularities at a critical point were well understood. These ideas are now brought up to date by incorporating the more recent developments about critical points, and scaling laws are found for the solubility and the adsorption at the interface. Renormalization of exponents has been considered. Information about the interface thickness can be obtained by applying the theory to experimental data. Application is made to the cyclohexane–aniline system. The thickness has been found to be given as a function of the temperature T and the critical temperature T_c by the formula 2.1 [(T_c−T)/ T_c]^−0.62 Å. This is 4 or 5 times less than the thickness of the interface in the cyclohexane–methanol system determined by optical measurements. Part of the difference might be removed by use of better measurements of the solubility of water in cyclohexane–aniline.