Critical point from state transition diagrams

Fig. 35 Phase diagrams AB miktoarm-star copolymers for n = 2, n = 3, n = 4 and n = 5. mean-field critical point through which system can transition from disordered state to Lam phase via continuous, second-order phase transition. All other phase transitions are first-order. From [112]. Copyright 2004 American Chemical Society...

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. 

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

In the preceding discussion, QOtas treated as a uniform substance undergoing a phase transition a from the gas experimental phase diagram in Figure 20.12. The critical point is deLnedfkjyandTc. Above the critical point, that is, fqj > Pc... 

Figure 13. Schematic phase diagram of water s metastable states. Line (1) indicates the upstroke transition LDA —>HDA —>VHDA discussed in Refs. [173, 174], Line (2) indicates the standard preparation procedure of VHDA (annealing of uHDA to 160 K at 1.1 GPa) as discussed in Ref. [152]. Line (3) indicates the reverse downstroke transition VHDA—>HDA LDA as discussed in Ref. [155]. The thick gray line marked Tx represents the crystallization temperature above which rapid crystallization is observed (adapted from Mishima [153]). The metastability fields for LDA and HDA are delineated by a sharp line, which is the possible extension of a first-order liquid-liquid transition ending in a hypothesized second critical point. The metastability fields for HDA and VHDA are delineated by a broad area, which may either become broader (according to the singularity free scenario [202, 203]) or alternatively become more narrow (in case the transition is limited by kinetics) as the temperature is increased. The question marks indicate that the extrapolation of the abrupt LDA<- HDA and the smeared HDA <-> VHDA transitions at 140 K to higher temperatures are speculative. For simplicity, we average out the hysteresis effect observed during upstroke and downstroke transitions as previously done by Mishima [153], which results in a HDA <-> VHDA transition at T=140K and P 0.70 GPa, which is 0.25 GPa broad and a LDA <-> HDA transition at T = 140 K and P 0.20 GPa, which is at most 0.01 GPa broad (i.e., discontinuous) within the experimental resolution.

For higher ab = 0-5, the phase diagram differs qualitatively from the previous one. This can be seen from Fig. 4.14(b) where a bifurcation appears (i.e., at a triple point) for ptr — —2.25 and Tjr 1.075 at which a gas phase coexists simultaneously with both a mixed and a demixed fluid phase. Consequently a critical point exists (peb — -2.25, Tcb — 1.15) at which the line of first-order transitions between mixed liquid and gas states ends. The line of first-order transitions involving mixed and demixed liquid states ends at a higher temperatinre and chemical potential of ptri — —2.00 and Ttri — 118, and the A-line is shifted toward lower temperatures as one can see from the plot in Fig. 4.14(b). This type of phase diagram comports with the one shown in Fig. 1(b) of Wilding et al. [87]. 

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