Heat capacity anomaly in a self-aggregating system: Triblock copolymer 17R4 in water.

The reverse Pluronic, triblock copolymer 17R4 is formed from poly(propylene oxide) (PPO) and poly(ethylene oxide) (PEO): PPO14 - PEO24 - PPO14, where the number of monomers in each block is denoted by the subscripts. In water, 17R4 has a micellization line marking the transition from a unimer network to self-aggregated spherical micelles which is quite near a cloud point curve above which the system separates into copolymer-rich and copolymer-poor liquid phases. The phase separation has an Ising-like, lower consolute critical point with a well-determined critical temperature and composition. We have measured the heat capacity as a function of temperature using an adiabatic calorimeter for three compositions: (1) the critical composition where the anomaly at the critical point is analyzed, (2) a composition much less than the critical composition with a much smaller spike when the cloud point curve is crossed, and (3) a composition near where the micellization line intersects the cloud point curve that only shows micellization. For the critical composition, the heat capacity anomaly very near the critical point is observed for the first time in a Pluronic/water system and is described well as a second-order phase transition resulting from the copolymer-water interaction. For all compositions, the onset of micellization is clear, but the formation of micelles occurs over a broad range of temperatures and never becomes complete because micelles form differently in each phase above the cloud point curve. The integrated heat capacity gives an enthalpy that is smaller than the standard state enthalpy of micellization given by a van't Hoff plot, a typical result for Pluronic systems.

Self-organized criticality in a bead pile.

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.

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.

Universality in eight-arm star polystyrene and methylcyclohexane mixtures near the critical point.

Measurements of the coexistence curve and turbidity were made on different molecular mass samples of the branched polymer-solvent system eight-arm star polystyrene in methylcyclohexane near its critical point. We confirmed that these systems belong in the Ising universality class. The location of the critical temperature and composition as well as the correlation length, susceptibility, and coexistence curve amplitudes were found to depend on molecular mass and the degree of branching. The coexistence curve diameter had an asymmetry that followed a "complete scaling" approach. All the coexistence curve data could be scaled onto a common curve with one adjustable parameter. We found the coexistence curve amplitude to be about 12% larger for branched than linear polystyrenes of the same molecular mass in either solvent cyclohexane or methylcyclohexane. The two-scale-factor universality ratio R was found to be independent of molecular mass or degree of branching.

Turbidity determination of the critical exponent eta in the liquid-liquid mixture methanol and cyclohexane.

The turbidity of the liquid-liquid mixture methanol-cyclohexane has been measured very near its critical point and used to test competing theoretical predictions and to determine the critical correlation-correction exponent eta. By measuring the ratio of the transmitted to incident light intensities over five decades in reduced temperature, we are able to determine that Ferrell's theoretical prediction for the turbidity explains the data with the correlation length amplitude xi0=0.330+/-0.003 nm and critical exponents eta=0.041+/-0.005 and nu=0.632+/-0.002. These values are consistent with the values measured before for xi0 in this system and with the exponents predicted by theory. The data allow five different theoretical expressions to be tested and to select two as being equivalent when very close to the critical point.