Noncritical interface near a critical end point II

The tension of the interface between a noncritical phase α and a near-critical phase βγ, or between α and the individual β and γ phases into which βγ separates, is discussed. A thermodynamic description of a critical end point is given, earlier theoretical results on the interfacial tensions are reviewed, and the earlier theory is generalized and extended and some of its restrictions are relaxed. The theory is then reformulated, and made to incorporate nonclassical critical-point exponents. The critical isotherm of interfacial tension σα,βγ as a function of composition has a horizontal tangent at the critical point, where it is found to be of degree μβ ≈ 3.9, with μ and β the conventional critical surface-tension and coexistence-curve exponents. The tensions σαβ and σαγ when T<Tc, and the tension σα,βγ at fixed, critical composition when T > Tc, as functions of θ ∼ TTc− 1, all have |θ|γ and |θ|μ as their leading singularities, with γ the conventional critical susceptibility exponent. Numerical results are presented for the realistic case γ ≈ μ. It is remarked that the liquid-vapor interface in 4He at its λ-point is also a noncritical interface at a critical end point.