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.

The reverse Pluronic triblock copolymer 17R4 is formed from poly(propylene oxide) (PPO) and poly(ethylene oxide) (PEO): PPO(14)-PEO(24)-PPO(14), where the subscripts denote the number of monomers in each block. In water, 17R4 shows both a transition to aggregated micellar species at lower temperatures and a separation into copolymer-rich and copolymer-poor liquid phases at higher temperatures. For 17R4 in H(2)O and in D(2)O, we have determined (1) the phase boundaries corresponding to the micellization line, (2) the cloud point curves marking the onset of phase separation at various compositions, and (3) the coexistence curves for the phase separation (the compositions of coexisting phases). In both H(2)O and in D(2)O, 17R4 exhibits coexistence curves with lower consolute temperatures and compositions that differ from the minima in the cloud point curves; we take this as an indication of the polydispersity of the micellar species. The coexistence curves for compositions near the critical composition are described well by an Ising model. For 17R4 in both H(2)O and D(2)O, the critical composition is 0.22 ± 0.01 in volume fraction. The critical temperatures differ: 44.8 °C in H(2)O and 43.6 °C in D(2)O. The cloud point curve for the 17R4/D(2)O is as much as 9 °C lower than in H(2)O.

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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 a was determined to be critical exponents. These values, for the most part, agree very well with experimental results. _-3 Several universal amplitude ratios have also been predicted and many have also been experimentally tested with mixed results. 5 A particularly powerful observation is that only two critical exponents are linearly independent, and that the leading amplitudes are interrelated using only two scale factors.l-3 Thus the universality of the exponents could be used with two experiments to determine all the leading critical behavior of a given system.The heat capacity provides a delicate probe of the system near a critical point and can determine essential amplitude and exponent values. In particular, a precise measurement of the heat capacity of the binary fluid mixture triethylamine and water will help settle a dispute in the literature about the amplitude in the one-phase region and its effect on the universal ratio X, measure the universal ratio of the amplitudes above and below the critical temperature, andgive the first attempt in binary liquid mixtures at using a new "universal" amplitude relation R_, to reduce the number of fitting parameters while testing theoretical predictions.The heat capacity has a weak divergence near the critical point that is governed by the critical exponent _, has a critical contribution Be to the background heat capacity, and has correction to scaling terms that extend the theoretical description further from the critical point. 3'6 The critical point influences the system properties over a global region. 78 however, this experiment measures behavior near the critical point and we will use the simpler formalism that is appropri-8048

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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.

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.

Self-organized criticality has been proposed to explain complex dynamical systems near their critical points. This experiment examined a monodisperse conical bead pile and how the distribution of avalanches is affected by the pattern of beads glued on a base, by the size or shape of the base, and by the height at which each bead was dropped onto the pile. By measuring the number of avalanches for a given size that occurred during the experiment, the resulting distribution could be compared to a power law description. When the beads were dropped from a small height, all data were consistent with a simple power law of exponent -1.5, which is the mean-field model value. The data showed that neither the bead pattern on the base nor the base size or shape significantly affected the power law behavior. However, when the bead is dropped from different heights, then the power law description breaks down and a power law times an exponential is more appropriate. We found a scaling relationship in the distribution of avalanches for different heights and relate the data to an energy dissipation model. We both confirm self-organized criticality and observe deviations from it.