Phase transitions triple point

Figure 18 (a) Binodals of a symmetric, binary polymer blend confined into a film of thickness D= 2.6/ e as obtained by self-consistent field calculations. The strength of preference at one surface is kept constant. The surface interactions at the opposite surface vary, and the ratio of the surface interactions is indicated in the key. +1.0 corresponds to a strictly symmetric film, and -1.0 marks the interface localization-delocalization transition that occurs in an antisymmetric film. The dashed curve shows the location of the critical points. Filled circles mark critical points and open circles/dashed horizontal lines denote the three-phase coexistence (triple point) for - 0.735 and -1.0. The inset presents part of the phase boundary for antisymmetric boundaries, (b) Schematic temperature dependence for antisymmetric boundaries. The three profiles correspond to the situations (u), (m), and (I) in the inset of (a), (c) Coexistence curves in the// /-A/y plane. The ratio of surface interactions varies according to the key. The analogs of the prewetting lines for A//pw< 0 and ratios of the surface interactions, -0.735 and -1.0, are indistinguishable, because they are associated with the prewetting behavior of the surface with interaction, which attracts the A-component. Reproduced from Muller, M. Binder, K. Albano, E. V. Europhys. Lett. 2000, 50, 724-730, with authorization of http //epljournal.edpsciences.org/... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

Helium Purification and Liquefaction. HeHum, which is the lowest-boiling gas, has only 1 degree K difference between its normal boiling point (4.2 K) and its critical temperature (5.2 K), and has no classical triple point (26,27). It exhibits a phase transition at its lambda line (miming from 2.18 K at 5.03 kPa (0.73 psia) to 1.76 K at 3.01 MPa (437 psia)) below which it exhibits superfluid properties (27). 

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

The triple point divides each of the curves of transition passing through it into two parts, one of which corresponds with a stable system, and the other with an unstable system. The discrimination between these is effected by means of two theorems due to Roozeboom (1887), which are analogous to the theorems of Moutier and of Robin, for two-phase systems ( 105). 

Fig. 7 Magnetic phase diagram of compound [Cr(Cp )2][Pt(tds)2] M(T) (filled diamonds), M(H) (filled triangles), y (T) (open circles) y (ll) (open squares) Tt is the triple point I denotes the first-order SF transition II and III denote second-order transitions (SF—PM and AF—PM phase boundaries). From [45]...

The triple point is the location at which all three phases boundaries intersect. At the triple point (and only at the triple point), all three phases (solid, liquid, and gas) coexist in dynamic equilibrium. Below the triple point, the solid and gas phases are next-door neighbors, and the solid-to-gas phase transition occurs directly. 

The temperature at which a phase transition occurs is dependent on pressure (Figure 7). At atmospheric pressure (1 atm) the solid-to-liquid phase transition occurs at 0 °C and the liquid-to-gas phase transition occurs at 100 °C. If we increase the pressure, say to 100 atm, the solid-to-liquid phase transition occurs at a temperature slightly less than 0°C (—0.74°C) however, the liquid-to-gas phase transition occurs at a much greater temperature (312°C). If we decrease the pressure, say to 0.1 atm, the solid-to-liquid phase transition occurs at a temperature slightly greater than 0°C (0.004 °C) and the liquid-to-gas phase transition occurs at a lower temperature (46 °C). If we decrease the pressure further to below the triple point, there is no solid-to-liquid phase transition rather, the solid-to-gas phase transition occurs directly. At a pressure of 0.001 atm, the sublimation temperature is — 20.16°C. 

Figure 3.10. Phase diagrams of attractive monodisperse dispersions. Uc is the contact pair potential and (j) is the particle volume fraction. For udk T = 0, the only accessible one-phase transition is the hard sphere transition. If Uc/hgT 0, two distinct scenarios are possible according to the value of the ratio (range of the pair potential over particle radius). For < 0.3 (a), only fluid-solid equilibrium is predicted. For % > 0.3 (b), in addition to fluid-solid equilibrium, a fluid-fluid (liquid-gas) coexistence is predicted with a critical point (C) and a triple point (T).

By combining the various observations obtained from the G-T diagrams in different P conditions, we can build up a P-P diagram plotting the stability fields of the various polymorphs, as shown in figure 2.5. The solid dots in figures 2.4 and 2.5 mark the phase transition limits and the triple point, and conform to the experimental results of Richardson et al. (1969) (A, R, B, C ) and Holdaway (1971) (A, H, B, C). The dashed zone defines the uncertainty field in the... 

Look back at the large phase diagram (Figure 7-1) and notice the intersection of the three lines at 0.01° and 6 X 10 atm. Only at this triple point can the solid, liquid, and vapor states of FljO all coexist. Now find the point at 374° C and 218 atm where the liquid/gas boundary terminates. This critical point is the highest temperature and highest pressure at which there is a difference between liquid and gas states. At either a temperature or a pressure over the critical point, only a single fluid state exists, and there is a smooth transition from a dense, liquid-like fluid to a tenuous, gas-like fluid. 

Marx and Dole and Miyake have presented descriptive models for the 19° C transition in terms of order-disorder theories. Studies of transitions at high pressure in polytetrafluoroethylene have been reported by Bridgman, Weir (1953), and Beecroft and Swenson. The phase diagram in Fig. 7 shows that in addition to the two crystalline phases which are separated by the 19° transition at atmospheric pressure there is a third modification at high pressures. The triple point has been... 

Other features of interest in the phase diagram of 4He include triple points between various liquid and solid phases of the element. At point c in Figure 13.11, liquid I, liquid II and a body-centered cubic (bcc) solid phase are in equilibrium. The bcc solid exists over a narrow range of pressure and temperature. It converts by way of a first-order transition to a hexagonal close packed (hep) solid, or to liquid I or liquid II. At point d, liquid I and the two solids (bcc and hep) are in equilibrium liquid II and the two solids are in equilibrium at point e. 

The lines represent phase equilibrium boundaries. Crossing one of these lines by changing pressure or temperature results in a phase transition (or a change of state). Temperature and pressure combinations that lie on one of these lines allow for two phases to coexist in equilibrium with each other. The triple point of the substance is the single temperature and pressure combination where all three... 

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