Boundary phase transition

The phase transition boundaries (phase envelope) of adamantane need to be investigated and constmcted. Predictable and diverse geometries are important features for molecular self-assembly and pharmacophore-based dmg design. Incorporation of higher diamondoids in solid-state systems and polymers should provide high-temperature stability, a property already found in polymers synthesized from lower diamondoids. 

Fig. 12 Morphology diagram of PEP-6-PLA. ODTs determined by rheology A, , 0, x ordered microstrue lures directly observed by SAXS A S C 0 G x L. Solid lines ordered range of xN as determined by rheological measurements dashed lines approximate phase-transition boundaries using experimental data and mean-field theory predictions. From [63]. Copyright 2002 Wiley...

Similarly, when rhombic red a-sulfur is heated above 100°C, it usually fails to exhibit the expected thermodynamic conversion to yellow /3-sulfur at 96°C. Instead, it persists as a superheated metastable phase up to 114°C (dashed line), where it exhibits an apparently normal melting point to the liquid form (unless extreme patience or a nucleating seed crystal of /3-sulfur is employed). The dashed lines in Fig. 7.5 therefore mark out metastable phase transition boundaries between forms of sulfur that are not true Gibbs free energy minima at the cited temperature and pressure (e.g., superheated a-sulfur and supercooled liquid sulfur at 114°C, 1 atm). The metastable phase domains can overlap stable phase domains in a quite complex and confusing manner. A kinetically facile metastable phase boundary will often appear more real and relevant to actual chemical phenomena than will the idealized boundary between (kinetically inaccessible) phases of lowest Gibbs free energy. 

The following phase diagram shows part of the liquid/vapor phase-transition boundaries for pure ether and a solution of a nonvolatile solute in ether. 

Figure 5. The frequency-field (squares) and linewidth-field (circles) dependencies of the ESR excitations in CuGe03 at T= 4.2 K. The data are shown for ascending fields, B a. The dash line is a frequency-field dependence of magnetic excitations with g=2.15. The solid lines are guides for eyes. The dot line denotes the dimerized-incommensurate phase transition boundary.

Section II describes the model used for deriving the expressions for the interparticle potential. A brief account of the statistical mechanical approach to locate the phase transition boundaries is given in Section III and the results of the calculation are presented in Section IV. 

The procedure to locate the phase transition boundaries from a dilute disordered (fluid) phase to a concentrated ordered (solid) phase involves the determination of the chemical potential of the particles in both phases. The condition of the equality of the pressures and of the chemical potentials of the phases locates the phase transition boundaries. The chemical potential of the particles in each phase is obtained using the following expression, separately for each phase ... 

Differential scarming calorimetry (DSC) (22) is based on measuring changes in heat capacity because the temperature of a system is varied monotonically. As heat capacity is a thermodynamic response function, it is expected to exhibit critical behavior close to a phase transition boundary, which in turn can be detected by DSC. Consequently, DSC is a common way to detect phase behavior. 

Hirose K., Fei Y., Ono S., Yagi T., and Funakoshi K.-I. (2000) In situ measurements of the phase transition boundary in Mg3Al2Si30i2 implications for the nature of the seismic discontinuities in the Earth s mantle. Earth Planet. Sci. Lett. 5705, 1-7. 

Thus the effect of applying pressure is expected to be two-fold. First, the transition temperature is changed hyIXPlaK. Therefore the slope of the phase transition boundary 5T,/8P is 2 XjaK, and Equation (2) can be re-written ... 

Several published equations of state for H2O were available when the first HDAC was made. Of these, Haar et al. [10] and Saul and Wagner [11] were considered to be the most comprehensive and accurate. One of the first applications of the HDAC [5] was undertaken to compare EOS data of water with the published a-P phase transition boundary in quartz... 

While the heat capacities at constant pressme are useful for calciflation of various thermodynamic quantities, related to Gibbs free energy for aqueous species, and chemical equilibria involving aqueous species, the isochoric heat capacity measurements are useftil in developing equations of state (EOS) because they yield valuable information about the second derivative of the pressure and of the Helmholtz energy with respect to temperature. Detailed comparisons of experimental Cv data with available EOS are needed to establish their accuracy. Cv experiments contain direct information on the curvature behavior of the p-T isochores, which are extremely important in the development of a reliable EOS. Furthermore, the temperature dependence of Cv at fixed density serves as a sensitive indicator of the phase transition boundary. Thus C measurements provide a tool for investigation of temperatures T and densities d on the coexistence ciuve, especially near the critical point. 

Two different analytical methods and two different t3 es of munerical methods for solving problems with discontinuities are used. In the first method discontinuities are segregated and continuous regions are described by the Eqs. (1) or (2). Some boundary conditions derived from Eqs. (1) and (2) are put in areas of discontinuity. The phase transition boundary conditions are the following [8, 13] ... 

The point d, where the adsorption curve M meets the phase transition boundary, may be found firom the vector equahty... 

The hypothetical sequence of phases shown in Fig. 4.26 is never observed in its entirety and phase transition boundaries are rarely vertical. However, the predominant dependence of phase structure on concentration and the order with which phases are stable upon increasing... 

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