Simple Mixture Model Research Articles

The sound velocity in metastable liquid water under atmospheric pressure

Ultrasonic sound velocity data in supercooled water are analyzed in the light of present theories. Preliminary evidence for a minimum in the sound speed versus temperature curve is shown to be consistent with available data for other thermodynamic properties. A simple two-state mixture model combined with experimental data may be used to yield similar evidence. Sound speed data in superheated water are used to determine other thermodynamic parameters in the 100 to 170 °C temperature range under atmospheric pressure.

The iron˗magnesium partitioning between naturally occurring coexisting olivine and Ca˗rich clinopyroxene : an application of the simple mixture model to olivine solid solution

Le partage de Fe et Mg entre olivine et clinopyroxène calcique a été interprété en appliquant des modèles de simple mélange pour l'olivine et de solution idéale pour le clinopyroxène. La relation entre le coefficient de partage, K et le coefficient de partage apparent, K' s'écrit : ln K = ln K' + (1—2X) W[ol]/RT où W[ol] est un paraètre thermodynamique dépendant de la température et de la pression, et X est le rapport Fe/(Fe + Mg) dans l'olivine. En utilisant les données expérimentales publiées sur W[ol] [, sa dépendance] avec la température a été examinée. Bien que la signification physique du terme W[ol] ne soit pas bien comprise, le coefficient de partage apparent entre olivine et clinopyroxène est sensible à la température à cause d'une grande dépendance de W[ol] de la température, et donc, ce coefficient de partage est un géothermomètre utile, spécialement à basse température.

Thermochemical parameters of minerals from oxygen-buffered hydrothermal equilibrium data: Method, application to annite and almandine

Reversed univariant hydrothermal phase-equilibrium reactions, in which a redox reaction occurs and is controlled by oxygen buffers, can be used to extract thermochemical data on minerals. The dominant gaseous species present, even for relatively oxidizing buffers such as the QFM buffer, are H2O and H2; the main problem is to calculate the chemical potentials of these components in a binary mixture. The mixing of these two species in the gas phase was assumed by Eugster and Wones (1962) to be ideal; this assumption allows calculation of the chemical potentials of the two components in a binary gas mixture, using data in the literature. A simple-mixture model of nonideal mixing, such as that proposed by Shaw (1967), can also be combined with the equations of state for oxygen buffers to permit derivation of the chemical potentials of the two components. The two mixing models yield closely comparable results for the more oxidizing buffers such as the QFM buffer. For reducing buffers such as IQF, the nonideal-mixing correction can be significant and the Shaw model is better. The procedure of calculation of mineralogical thermochemical data, in reactions where hydrogen and H2O simultaneously appear, is applied to the experimental data on annite, given by Wones et al. (1971), and on almandine, given by Hsu (1968). For annite the results are: Standard entropy of formation from the elements, S f 0 (298, 1)=−283.35±2.2 gb/gf, S 0 (298, 1) =+92.5 gb/gf. G f 0 (298, 1)=−1148.2±6 kcal, and H f 0 (298, 1)=−1232.7±7 kcal. For almandine, the calculation takes into account the mutual solution of FeAl2O4 (Hc) in magnetite and of Fe3O4 (Mt) in hercynite and the temperature dependence of this solid solution, as given by Turnock and Eugster (1962); the calculations assume a regular-solution model for this binary spinel system. The standard entropy of formation of almandine, S f,A 0 (298, 1) is −272.33±3 gb/gf. The third law entropy, S 0 (298, 1) is +68.3±3 gb/gf, a value much less than the oxide-sum estimate but the deviation is nearly the same as that of grossularite, referring to a comparable set of oxide standard states. The Gibbs free energy G f,A 0 (298, 1) is −1192.36±4 kcal, and the enthalpy H f,A 0 (298, 1) is −1273.56±5 kcal.

結晶性高分子のレオロジー

The rheological properties of crystalline high polymers are discussed in contrast with those of amorphous polymers.The mixture of hard particles and amorphous polymer gives the simplest model of crystalline polymers. Some considerations in changes of structure of mixing state, gives a good interpretation for the change of Young's modulus with increasing crystallinity by this simple mixture model. Although this approach can not give the interpretations of time-dependent phenomena, the author believes that this simple model has still some possibility of progresses.The time dependent mechanical properties of high polymers must be expressed as a function of time and temperature. The most elabolate method, which measures the dynamical properties as a function of both time and temperature is developed by Fitzgerald. Very recently, it is revealed by Fitzgerald's transducer, that the crystalline polymers show some resonance-type dispersions at audio frequencies. This phenomenon has an important meaning which connects the polymer rheology with dislocation theory of crystal plasticity.Relations between mechanical loss factor and temperature under nearly constant frequency for various crystalline polymers are obtained by Schmieder and many other researchers.On the contrary, the measurement under constant temperature and variable frequencies need a high technique. Fujino and Kawai, and Tokita have measured the mechanical responses of several crystalline polymers covering six decade of frequencies by the use of several different apparatus.The time-temperature reduction method, which has played an important role in the progress of rheology of amorphous polymers, is found to be also applicable for crystalline polymers. By the application of reduction method and of its modification by Takemura, the author and his coworkers have succeeded to determine the relaxation time spectra of Nylon-6, Teflon, Kel-F and Polyethylene over a wide range of relaxation time. As is seen in Fig. 3, these spectra for crystalline polymers seem to have some common features. And it is found that these spectra give successful interpretation for many of rheological properties of crystalline polymers.The investigations of non-linear behavior, and mechanical properties of anisotropic polymers, which are most interesting for crystalline polymer, will need more accumulations of systematic experimental works not only by rheological methods but also by colaboration of structure analysis, dielectric and NMR measurements.