Griffiths-Wheeler geometrical picture of critical phenomena: experimental testing for liquid-liquid critical points.

An experimental approach to the verification of specific relations between thermodynamic properties as predicted from the Griffiths-Wheeler theory of critical phenomena in multicomponent systems is developed for the particular case of ordinary liquid-liquid critical points of binary mixtures. Densities rho(T) , isobaric heat capacities per unit volume C(p)(T) , and previously reported values of the slope of the critical line (dT/dp)c for five critical mixtures are used to check the thermodynamic consistency of C(p) and rho near the critical point. An appropriate treatment of rho (T) data is found to provide the key solution to this issue. In addition, various alternative treatments for C(p)(T) data provide values for both the critical exponent alpha and the ratio between the critical amplitudes of the heat capacity A+/A- that are in agreement with their widely accepted counterparts, whereas two-scale-factor universality is successfully verified in one of the systems studied.

[1]  J. Sengers,et al.  Critical fluctuations and the equation of state of Van der Waals , 2004 .

[2]  J. Troncoso,et al.  Heat capacity and thermal expansion anomalies in the nitromethane-1-butanol mixture near its upper critical point. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Vesna Najdanovic-Visak,et al.  Two ways of looking at Prigogine and Defay's equation , 2002 .

[4]  U. Kaatze,et al.  Concentration Fluctuations in Ethanol/Dodecane Mixtures. A Light-Scattering and Ultrasonic Spectroscopy Study , 2000 .

[5]  J. Troncoso,et al.  Systematic determination of densities and speeds of sound of nitroethane + isomers of butanol in the range (283.15-308.15) K , 2000 .

[6]  E. Carballo,et al.  Highly precise determination of the heat capacity of liquids by DSC: calibration and measurement , 2000 .

[7]  A. Pelissetto,et al.  Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  A. Milewska,et al.  Deuterium Isotope Effects on Miscibility Curves of Nitromethane + Pentanol and Nitromethane + Isobutanol , 1999 .

[9]  P. Butera,et al.  Renormalized couplings and scaling correction amplitudes in the N -vector spin models on the sc and the bcc lattices , 1998, hep-lat/9805025.

[10]  J. Zinn-Justin,et al.  Critical exponents of the N-vector model , 1998, cond-mat/9803240.

[11]  Jacobs,et al.  Amplitude of the anomaly in the mass density near a liquid-liquid critical point. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Bose,et al.  Specific heat capacity singularity and related weak anomalies in the nitroethane-cyclohexane critical binary mixture. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Anisimov,et al.  Crossover between vapor-liquid and consolute critical phenomena. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  K. Orzechowski.  Electrical properties of an ethanol–dodecane mixture near the upper critical solution point , 1994 .

[15]  J. González,et al.  Thermodynamics of binary mixtures containing organic carbonates. 4. Liquid-liquid equilibria of dimethyl carbonate + selected n-alkanes , 1991 .

[16]  G. Schneider,et al.  (Liquid + liquid) phase equilibria and critical curves of (ethanol + dodecane or tetradecane or hexadecane or 2,2,4,4,6,8,8-heptamethylnonane) from 0.1 MPa to 120.0 MPa , 1989 .

[17]  D. T. Jacobs.  Critical point shifts in binary fluid mixtures , 1989 .

[18]  H. R. Krishnamurthy,et al.  Equilibrium Critical Phenomena in Binary Liquid Mixtures , 1983 .

[19]  C. Godrèche,et al.  Universal combination of critical amplitudes from field theory , 1980 .

[20]  D. T. Jacobs,et al.  Thermal expansion of methanol + cyclohexane near the critical solution point , 1978 .

[21]  E. Gopal,et al.  The heat capacity of liquid carbon disulfide + acetonitrile, especially near the upper critical solution temperature , 1973 .

[22]  B. Allen,et al.  Phase studies of some nitroalkane hydrocarbon mixtures , 1972 .

[23]  J. Wheeler,et al.  Critical Points in Multicomponent Systems , 1970 .