Transition pressure-composition diagram

The four possible stereomers of a chiral surfactant with two asymmetric centers within the polar head group have been synthesized and their absolute configuration determined by X-ray diffraction. One of the diastereomers exhibits a chiral discrimination when spread on water interface the monolayer racemic film undergoes a phase transition from a liquid-expanded towards a liquid-condensed phase upon compression, while the pure enantiomers only have a liquid-expanded phase, as revealed by the measured pressure-area isotherms. The transition pressure-composition diagram indicates that heterochiral interactions are favored. Our results are compared to predictions of Andelman and de Gennes based upon a statistical model. 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

The bulk phase diagrams of pure hydrocarbons and mixtures are well known from the experiments. In the work by Sage et al. [3], the bubble point pressures of methane + n-butane mixtures are determined experimentally from the discontinuity of isothermal compressibility of constant-composition mixture at the point of phase transition. The composition of vapor phase is determined in that work from the residual specific volume of gas. Later experiments employ phase recirculation techniques [4] to achieve vapor-Uquid equilibrium [5, 6], and the phase compositions are analyzed by more advanced methods such as gas chromatography. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

The science dealing with phase transitions is thermodynamics. Using thermodynamics, we may discuss which phase will eventually be formed when a material (of composition c and phase p) is maintained under the same conditions for an infinite time, and the phase reaches the minimum energy state (equilibrium state) under given thermodynamic conditions (temperature and pressure). Experimentally, a phase diagram (equilibrium phase diagram) is prepared, and we may use the data... 

Neutron diffraction studies under pressure [84] on the 70/30 composition have revealed that transitions in this copolymer are displaced towards higher temperature with increasing pressure, as can be seen in the phase diagram of Fig. 11. In addition, it is worth noting the non-linear increase of the Curie temperature with pressure. By considering the Clausius-Clapeyron relation dTc/dP = TCAVC/Ahc, this effect can be related to a decrease in the volume... 

The specified variables are the final temperature and pressure, T2 and P2- The dependent variables are the vapor fraction, t /, the liquid and vapor compositions, X, and the total enthalpy of the two phases, /Z2 + H, and the heat duty, Q. The term isothermal should not be interpreted to imply that the transition from initial conditions to final conditions is at constant temperature is, in general, different from T. It simply means that within the flash drum the temperature, as well as the pressure, is fixed. The heat duty required to bring about the final conditions is equal to the enthalpy change, Q = (Hj + 2) - i> where is the enthalpy at and P,. Isothermal flash conditions may be represented by a point ( 2, P2) on tbs phase envelope diagram. It is clearly possible that this point may fall either within the phase envelope or outside it, in which case the system would be all vapor or all liquid (or dense phase). A flash drum operating at such conditions would have a single product and no phase separation would take place. In a single-phase situation, the dependent variables are the properties of the vapor or liquid product. The liquid or vapor composition is, of course, identical to the feed or overall composition, Z,. Note that any set of temperature and pressure specifications is feasible. 

The computer-aided procedure, unless automated by the program, requires running a series of liquid-liquid equilibrium calculations (the equivalent of vapor-hquid flash calculations) at constant temperature and pressure. The composition is varied around the equilibrium curve, and the transition points from one phase to two, or vice versa, are noted. As many points as needed are obtained this way to generate the entire equilibrium curve. Also, each time an equilibrium calculation is done in the two-phase region, the compositions of the two phases are recorded. Each pair of data points thus obtained defines a tie line. The data obtained at one temperature and pressure generate one triangular diagram. If so desired, the procedure is repeated at other temperatures and pressures to determine the effect of these variables. 

Boey, F., Lee. T. H., and Sullivan-Lee, P High pressure autoclave curing of composites effect of high pressure on glass transition temperature, J. Mater. Sci., 29, 5985-5989 (1994). Gilham, J. K., Time temperature transformation (TTT) state diagram and cure, in The Role of the Polymeric Matrix in the Structural Properties of Composite Materials (J. C. Seferis and L. Nicolais, eds.). Plenum Press, New York, 1983, pp. 1127 145. 

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