Near-critical systems, equilibrium phase

Note that while the power-law distribution is reminiscent of that observed in equilibrium thermodynamic systems near a second-order phase transition, the mechanism behind it is quite different. Here the critical state is effectively an attractor of the system, and no external fields are involved. 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

In this paper we use dynamic light scattering (DLS) methods to examine micelle size and clustering in (1) supercritical xenon, (2) near-critical and supercritical ethane, (3) near-critical propane as well as (4) the larger liquid alkanes. Reverse micelle or microemulsion phases formed in a continuous phase of nonatomic molecules (xenon) are particularly significant from a fundamental viewpoint since both theoretical and certain spectroscopic studies of such systems should be more readily tractable. Diffusion coefficients obtained by DLS for AOT microemulsions for alkanes from ethane up to decane are presented and discussed. It is shown that micelle phases exist in equilibrium with an aqueous-rich liquid phase, and that the apparent hydrodynamic size, in such systems is highly pressure dependent. 

These findings indicate that the control of phase behavior is one of the keys to controlling chemical reactions in near-critical fluids. Phase equilibrium plays an important role in dense fluid reaction systems, because the number of phases in equilibrium and their composition can be changed easily by pressure and temperature, and also as a consequence of the conversion of materials by chemical reactions. 

The invitations to participants suggested that the written papers concern Fast Adiabatic Phase Changes in Fluids and Related Phenomena. Particular topics suggested were Liquefaction shockwaves and Shock splitting Evaporation waves Condensation in Laval nozzles and turbines Stability in multiphase shocks Non-equilibrium and near-critical phenomena Nucleation in dynamic systems Structure of transition layers Acoustic phenomena in two-phase systems and Cavitation waves. All of these topics should have been treated with emphasis on physical results, new phenomena and theoretical models. Participants from fourteen nations took part in the Symposium and presented papers which were within the range of suggested topics. 

For multicomponent systems, experiments with synthetic methods yield less information than with analytical methods, because the tie lines cannot be determined without additional experiments. A common synthetic method for polymer solutions is the (P-T-m ) experiment. An equilibrium cell is charged with a known amount of polymer, evacuated and thermostated to the measuring temperature. Then flie low-molecular mass components (gas, fluid, solvent) are added and the pressure inereases. These eomponents dissolve into the (amorphous or molten) polymer and the pressure in the equilibrium eell deereases. Therefore, this method is sometimes called pressure-decay method. Pressure and temperature are registered after equilibration. No samples are taken. The composition of the liquid phase is often obtained by weighing and using the material balance. The synthetic method is particularly suitable for measurements near critical states. Simultaneous determination of PVT data is possible. Details of experimental equipment can be found in the original papers compiled for this book and will not be presented here. 

These diagrams can take various forms depending on the properties of the solute and solvent molecules. A very thorough study of the possibilities has been made by van Konynenburg and Scott [15] who identified six principal types of fluid/fluid equilibrium behaviour in binary systems. For a complete discussion, reference should be made to the above study and also to the works of Rowlinson [16] and other authors [17-19]. In the discussion below a simplified classification is used to describe typical forms of fluid/fluid phase behaviour in the near-critical region. (Some readers may find it helpful to read... 

Use of equations of state and other methods for collating phase equilibrium data for systems with a near-critical component (the solvent)... 

The technique to study phase coexistence via MD by simulating phase separation kinetics in the MVT ensemble until equilibrium is established [234] becomes cumbersome near critical points, and in any case it requires the simulation of very large systems over a large simulation time. In addition, this method is hardly feasible when the model systems contains long polymers - their diffusion simply is too slow [5, 6, 8, 9, 31]. Experience with the simulation of spinodal decomposition in lattice models of polymer mixtures [9, 180, 241] shows that only the early stages of phase separation are accessible, meaning that the method is unsuitable for studying the equilibrium states of well phase-separated systems. 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

We note that even short-range interactions may, however, allow a mean-field scenario, if the system has a tricritical point, where three phases are in equilibrium. A well-known example is the 3He-4He system, where a line of critical points of the fluid-superfluid transition meets the coexistence curve of the 3He-4He liquid-liquid transition at its critical point [33]. In D = 3, tricriticality implies that mean-field theory is exact [11], independently from the range of interactions. Such a mechanism is quite natural in ternary systems. For one or two components it would require a further line of hidden phase transitions that meets the coexistence curve at or near its critical point. 

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