Liquid + gas critical phase transition

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. 

Depending on the chain stiffness the liquid-gas critical point can be either observable or buried in the two-phase region of the isotropic-nematic transition (see Fig. 8). One can have a coexistence between dilute/isotropic and dense/nematic in the simplest case, but also three phase coexistence regions are possible between isotropic gas, isotropic liquid and nematic liquid or isotropic gas, nematic semidilute liquid and nematic dense liquid. 

Figure 1. Schematic phase diagram commonly used for polymorphic liquids. LDL and HDL are separated by a first-order phase transition line that ends in a (liquid-liquirj CTiti-cal point, C. Included is the liquid-gas first-order phase transition line this line ends in the liquid-gas critical point, C. The liquid-liquid phase transition extends to low temperatures where the liquid may transform into glass (see Fig. 4).

In the next section, we review a number of lattice gas models for which the addition of directional interactions not only allows for polyamorphism and two liquid phases but also introduces the possibility of a richer phase diagram, in which a critical line following the liquid-liquid first-order phase transition substitutes the critical point. Even though not explored in the literature, this picture is not inconsistent with known experimental results for water and other tetrahedral liquids [38]. 

The understanding of continuous phase transitions and critical phenomena has been one of the important breakthrough in condensed matter physics in the early seventies. The concepts of scaling behavior and universality introduced by Kadanoff and Wi-dom and the calculation of non-gaussian exponents by Wilson and Fisher are undeniably brilliant successes of statistical physics in the study of low temperature phase transitions (normal to superconductor, normal to superfluid helium) and liquid-gas critical points. 

A line of first order phase transitions between two phases with the same symmetry may end at a critical point where fluctuations are expected to dominate. The classic example of this is the liquid-gas critical point. 

M. Gordon suggested some time ago that the behavior of gels at the sol-gel phase transition should be investigated more closely. And indeed shortly thereafter theoretical predictions were published according to which the critical exponents for these phase transitions should differ drastically from those of the widely accepted classical theories These speculations were based on the analogy with other phase transitions like the liquid-gas critical point, and in particular with the percolation problem and its recent advances. 

None of the problems with asymptopia is new since they occur also in thermal phase transitions like the liquid-gas critical point or the magnetic Curie point mentioned above. 

Let us take an example from thermal phase transitions At a liquid-gas critical point the density difference A between liquid and vapor on the coexistence curve, normalized by the density at the critical point, approaches zero continuously, similar to the gelfi-action G near the gel point. For temperatures slightly below that critical temperature, we may write... 

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

Fig. 3. PF diagram for a pure fluid (not to scale) point c is the gas—liquid critical state, is the constant pressure at which phase transition occurs at...

We are all familiar with the gas-liquid phase transition undergone by water. In such a transition, a plot of density versus temperature shows a distinct discontinuity at the critical temperature marking the transition point. There are many other common examples of similar phase transitions. 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

The explosive phenomena produced by contact of liquefied gases with water were studied. Chlorodifluoromethane produced explosions when the liquid-water temperature differential exceeded 92°C, and propene did so at differentials of 96-109°C. Liquid propane did, but ethylene did not, produce explosions under the conditions studied [1], The previous literature on superheated vapour explosions has been critically reviewed, and new experimental work shows the phenomenon to be more widespread than had been thought previously. The explosions may be quite violent, and mixtures of liquefied gases may produce overpressures above 7 bar [2], Alternative explanations involve detonation driven by phase changes [3,4] and do not involve chemical reactions. Explosive phase transitions from superheated liquid to vapour have also been induced in chlorodifluoromethane by 1.0 J pulsed ruby laser irradiation. Metastable superheated states (of 25°C) achieved lasted some 50 ms, the expected detonation pressure being 4-5 bar [5], See LIQUEFIED NATURAL GAS, SUPERHEATED LIQUIDS, VAPOUR EXPLOSIONS... 

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).

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. 

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