Critical points phenomena near

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

At low temperatures, rj will be unity because all of the Cu atoms will be localized on A sites. 1 But the degree of disorder increases as the temperature increases until the Cu and Zn atoms are mixed randomly on the two sublattices and 77 = 0. This process, called a positional (order + disorder) transition, is often described as a cooperative phenomenon because it becomes easier to produce additional disorder once some disorder is generated. In the vicinity of a critical temperature, the order parameter rj behaves like the density difference (pi — pg) near the gas-liquid critical point. Thus,... 

There is one more unique feature of supercritical fluid solvents that will be a recurring theme in this chapter. Several studies have demonstrated that near the critical point, the density of the solvent about a solute is enhanced relative to the bulk density (solvent/solute clustering). As such, the mobility of the solute may be impeded to an extent greater than expected on the basis of the bulk viscosity. This phenomenon may also affect reactivity for reactions that are diffusion-controlled or for which cage effects are important, particularly near the critical point (vide infra). 

Precipitation from supercritical fluids is of interest not only in relation to the production of uniform particles. The thermodynamics of dilute mixtures in the vicinity of the solvent s critical point (more specifically, the phenomenon known as retrograde solubility, whereby solubility decreases with temperature near the solvent s critical point) has been cleverly exploited by Chlmowitz and coworkers (12-13) and later by Johnston et al. (14). These researchers implemented an elegant process based on retrograde solubility for the separation of physical solid mixtures which gives rise to high purity materials. 

Generally, the metastability is a phenomenon associated with the persistence of the given phase well below the stability domain, bordered by the first order transition, for instance (/) the glass transition phenomenon, (//) metastable systems studies linked to spinodals - absolute stability limits, with particular attention towards the inherently metastable negative pressure domain (///) metastability near a critical point, (/v) the quest for the liquid - liquid near-critical transition in one component liquid, (v) the issue of liquid crystals where... 

That liquid surfaces scatter light was first predicted by von Smoluchow-ski in 1908. He expected the phenomenon to be visible near the critical point where the surface tension of the liquid is small. A quantitative theory was developed by Mandelstamm, who described the thermal roughness of... 

In fluids Xt s generally a well-behaved function of the thermodynamic state. Near the critical point, however, Xt becomes divergent (arbitrarily large). It follows that the intensity of scattered light increases very strongly as the critical point is approached. In fact there is so much scattering that the critical fluid appears cloudy or opalescent. This phenomenon, as mentioned above, is called critical opalescence. 

Stability, systems are intrinsically stable as one homogeneous phase when the temperature is greater than rcnticai- Hence, rcnticai is consistent with the definition of an upper critical solution temperature. Since Sp/SV)t, w, = 0 at rcriacai. small changes in pressure produce enormous changes in density near the critical point. This phenomenon is exploited by physical chemists, who perform lightscattering studies near Tcriticai-... 

Patterns usually appear due to the instability of a uniform state. However, such an instability does not necessarily lead to pattern formation. Let us consider, e.g., phase separation of a van-der-Waals fluid near the critical point Tc. For T > Tc, there exists only one phase, while for T < Tc, there exist two stable phases, corresponding to gas and liquid, and an unstable phase whose density is intermediate between those of the gas and the liquid. When an initially uniform fluid is cooled below Tc, the unstable phase is destroyed, and in the beginning one observes a mixture of stable-phase domains, i.e. hquid droplets and gas bubbles, which can be considered as a disordered pattern. However, the domain size of each phase grows with time (this phenomenon is called Ostwald ripening or coarsening). Finally, one observes a full separation of phases a liquid layer is formed in the bottom part of the cavity, and a gas layer at the top. Thus, the instabihty of a certain uniform state is not sufficient for getting stable patterns. Below we formulate some mathematical models that describe both phenomena, domain coarsening and pattern formation. 

This suggests that near the critical point a fluid displays unusual behavior. The behavior is unusual because natural fluctuations are not completely suppressed, as they are when Kt- is bounded and positive, but neither are fluctuations able to grow so as to force a phase change, as they can when Kj is negative. Such fluctuations cause the observable phenomenon known as critical opalescence moreover, critical fluctuations are independent of molecular constitution, so that near their critical points all fluids have certain traits in common. Descriptions of critical phenomena are beyond the scope of this book see instead [6]. 

An interesting phenomenon is the behaviour of fluids near the critical point. Approaching the critical state the time required to reach equilibrium increases with an inverse power of the difference between actual and critical temperature. In the experiments of Borisov et al. [7] for instance it took about 20 hours. As a consequence of large scale critical fluctuations the propagation of sound is severely impeded. Soundspeed measurements in the kHz and... 

At the critical point, the size of fluctuations of density or concentration, diverges and the time of their relaxation becomes infinite. The slow relaxation near the critical point is known as critical slowing down and the theory that describes this phenomenon is known as dynamic scaling .The basic idea of dynamic scaling is simple a fluctuation the size of the correlation length has a lifetime proportional to the volume of the fluctuation ... 

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