D. T. Jacobs

Coexistence curve of a binary mixture

Abstract We report precise measurements of the refractive index as a function of temperature in the one- and two-phase region near the consolute point in the binary mixture methanol—cyclohexane. By measuring forty-four data points over four decades in ϵ = ( T c - T )/ T c , 6 × 10 −6 −2 , we were able to determine the coexistence curve and fo critical exponent β to be 0.326 ± 0.003 by using a properly weighted least squares fit to the data. The uncertainty is three times the standard deviation. Our data is consistent with other refractive index data of the same binary fluids although a different value for the critical exponent was found. We do not find a need for the Wegner type correction terms reported by others recently, nor do we see an anomaly in the rectilinear diameter.

Critical point shifts in binary fluid mixtures

An empirical observation is made of an apparent universal shift in the consolute point (Xc=critical composition, Tc=critical temperature) of binary fluid mixtures when the system identity is perturbed. The shift in a ‘‘pure’’ system’s critical point (Xco, Tco) when perturbed becomes (Xc,Tc) which seems to obey (Tc−Tco)/Tco= (Xc−Xco)/Xco. This relation has been observed to hold in a wide range of systems including closed‐loop coexistence curves (guaiacol–glycerol–water, or tertiary butyl alcohol in secondary butyl alcohol and water), deuterated systems (methanol–cyclohexane, or isobutyric acid–water), impurities added to methanol–cyclohexane, the molecular weight dependence in polystyrene–methylcyclohexane, and the pressure dependence of methanol–cyclohexane.

Heat capacity anomaly near the lower critical consolute point of triethylamine–water

The heat capacity of the binary liquid mixture triethylamine–water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent α was determined to be 0.107±0.006, consistent with theoretical predictions. When α was fixed at 0.11 to determine various amplitudes consistently, our values of A + and A− agreed with a previous heat capacity measurement, but the value of A+ was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A+/A −=0.56±0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid‐vapor systems. The correction to scaling amplitude ratio D+/D −=0.5±0.1 was half o...

Acetone impurity effects on the binary fluid mixture methanol–cyclohexane

Measurements on the coexistence curves of the binary fluid mixture methanol–cyclohexane with increasing amounts of acetone impurity showed essentially linear changes in the critical temperature and critical concentration with impurity. Adding 1.0% acetone impurity caused the critical temperature to decrease by 3.4 K, the effective critical exponent β to increase and the critical concentration, as measured by volume fraction methanol, to decrease by 0.005.

Testing the Lorentz–Lorenz relation in the near‐critical binary fluid mixture isobutyric acid and water

The refractive index in each phase of the binary fluid mixture isobutyric acid and water was measured at temperatures below the system’s upper consolute point. This data was combined with existing density data to test the Lorentz–Lorenz relation in a near‐critical binary fluid mixture. The Lorentz–Lorenz relation is verified within experimental error (0.5%) when the volume change on mixing the components is taken into account. The density coexistence curve data is reanalyzed to determine the critical exponent  β and amplitude B. By allowing the order parameter to be a definition of the volume fraction that includes volume loss on mixing, a very symmetric coexistence curve is obtained which can be described by simple scaling with  β=0.326±0.003 and B=1.565±0.021. This exponent agrees with theoretical predictions while the amplitude, when combined with existing turbidity data, confirms two‐scale‐factor universality. The amplitude obtained by analyzing the coexistence curve when the refractive index is the order parameter also combines with turbidity data to confirm two‐scale‐factor universality, but does not require knowledge of the volume loss on mixing or the composition dependence of the refractive index.

Heat capacity anomaly near the critical point of aniline-cyclohexane

The heat capacity of the liquid–liquid mixture aniline-cyclohexane has been measured for the first time near its upper critical consolute point using an adiabatic calorimeter. Two data runs provide heat capacity data that are fitted by equations with background terms and a critical term. The critical exponent α was determined to be 0.104±0.011, consistent with theoretical predictions. When α was fixed at its theoretical value of 0.11 to determine the critical amplitudes A+ and A−, our value for the amplitude ratio A+/A−=0.59±0.03 was consistent with most experimental determinations in liquid–liquid mixtures, but was slightly larger than either theoretical predictions or recent experimental values in liquid–vapor systems. The two-scale-factor universality ratio X, now consistent among experiments and theories with a value between 0.019 and 0.020, is consistent in this system using one published value for the correlation length, but not with another.

Studying chaotic systems using microcomputer simulations and Lyapunov exponents

The study of nonlinear systems in an undergraduate setting has become important, and this article describes the use of an interactive simulation in introducing students to the new techniques used to characterize deterministic chaos. Lyapunov exponents are introduced with emphasis on their physical significance. The results of numerical experiments on the driven, damped, Duffing two‐well oscillator are reported and the global behavior of the Lyapunov exponent spectra is presented. The results confirm an important sum rule satisfied by the Lyapunov exponent spectra. Interesting, structured behavior of the Lyapunov exponent spectra is observed as the Duffing oscillator system follows the period‐doubling route to chaos.

Heat capacity of the liquid-liquid mixture nitrobenzene and dodecane near the critical point

The heat capacity of the liquid-liquid mixture nitrobenzene-dodecane has been measured for the first time near its upper critical consolute point using an adiabatic calorimeter. The theoretical expression for the heat capacity near the critical point was applied to our combined data runs. The critical exponent alpha was determined to be 0.124+/-0.006, which was consistent with theoretical predictions. When alpha was fixed at its theoretical value of 0.11, our value for the amplitude ratio A(+)A(-)=0.58+/-0.02 was consistent with experimental determinations and theoretical predictions. However, the two-scale-factor universality ratio X, now consistent among experiments and theories with a value between 0.019 and 0.020, was violated in this system when using a previously published value for the correlation length.

Thermal expansion of methanol + cyclohexane near the critical solution point☆

Abstract We report precise measurement of volume changes as function of temperature in the one phase region of methanol + cyclohexane near the critical solution point. We find a value for the critical exponent α of 0.11 ± 0.07 in the region 11 Mk 1 8 . For temperatures closer to Tc we observe a stronger divergence. In addition we observe unusual behavior over a small region of temperature centered at T – Tc = 15 mK.

Turbidity of the liquid–liquid mixture perfluoroheptane and 2,2,4-trimethylpentane near the critical point

The heat capacity of the liquid–liquid mixture perfluoroheptane and 2,2,4-trimethylpentane (also known as iso-octane) has been measured for the first time near its upper critical consolute point using an adiabatic calorimeter. The theoretical expression for the heat capacity near the critical point was applied to our combined data runs. The critical exponent α was determined to be 0.106±0.026, which agreed with theoretical predictions. When α was fixed at its theoretical value of 0.11, our value for the amplitude ratio A+/A−=0.59±0.05 was consistent with experimental determinations and theoretical predictions. However, the two-scale-factor universality ratio X, now consistent among experiments and theories with a value between 0.019 and 0.020, was violated in this system when using the published value for the correlation length.