Near-critical systems

The transport properties of a near-critical system contain an enhancement or a reduction due to critical fluctuations in addition to the contributions of molecular transport processes which are strictly a function of the thermodynamic state. Therefore, the transport coefficients in the critical region are usually... 

Debenedetti, P. G. and R. S. Mohamed. 1989. Attractive, weakly attractive and repulsive near-critical systems. Journal of Chemical Physics. 90, 4528. 

The introduction of neutron lifetimes and delayed neutrons attempts to prepare the student for a discussion of the kinetics of near-critical systems. This, however, has been found to be a difficult concept to e.xplain. 

Continue until the multiplication becomes large enough that a direct determination of criticality may be used. This determination will involve both the definition of what is meant by criticality and reactor kinetics for near critical systems with and without a source in the reactor. 

Criticality Precautions. The presence of a critical mass of Pu ia a container can result ia a fission chain reaction. Lethal amounts of gamma and neutron radiation are emitted, and a large amount of heat is produced. The assembly can simmer near critical or can make repeated critical excursions. The generation of heat results eventually ia an explosion which destroys the assembly. The quantity of Pu required for a critical mass depends on several factors the form and concentration of the Pu, the geometry of the system, the presence of moderators (water, hydrogen-rich compounds such as polyethylene, cadmium, etc), the proximity of neutron reflectors, the presence of nuclear poisons, and the potential iateraction with neighboring fissile systems (188). As Httle as 509 g of Pu(N02)4 solution at a concentration Pu of 33 g/L ia a spherical container, reflected by an infinite amount of water, is a critical mass (189,190). Evaluation of criticaUty controls is available (32,190). 

Adrian et al. (2000) have reported a novel high-pressure liquid-liquid extraction process with reference to processing in biotechnology the example of cardiac glycosides (digitoxin and digoxin) is cited. A completely miscible, binary system of water and a hydrophobic organic solvent like ethanol can split into two liquid phases when a near-critical gas (e.g. CO2) is added. The near-critical C02/water/l-propanol system is reported, for which possibilities for industrial exploitation exist. 

Larger system sizes suffer less from this effect and can be used to obtain coexistence densities near critical points. 

The last several decades have seen the growing scientific importance of phenomena near critical points, those conditions of system properties where two coexisting phases, such as liquid and vapor, become identical. This is exemplified by the 1982 Nobel Prize awarded to Kenneth Wilson for his theoretical studies of... 

Phase behavior in complex fluids such as polymer blends and block copolymers has been a rich area of the chemical sciences. Near-critical and other transitional phenomena are frequently prominent. Since molecular movement in viscous systems such as these is comparatively slow, phase transitions can be studied more easily in time, and manipulated by quenching and other external influences. Processes for controlled growth of ordered materials are often readily influenced by diffusion, a variety of external fields, and the influence of interacting boundaries, or flow. 

The benefits from tuning the solvent system can be tremendous. Again, remarkable opportunities exist for the fruitful exploitation of the special properties of supercritical and near-critical fluids as solvents for chemical reactions. Solution properties may be tuned, with thermodynamic conditions or cosolvents, to modify rates, yields, and selectivities, and supercritical fluids offer greatly enhanced mass transfer for heterogeneous reactions. Also, both supercritical fluids and near-critical water can often replace environmentally undesirable solvents or catalysts, or avoid undesirable byproducts. Furthermore, rational design of solvent systems can also modify reactions to facilitate process separations (Eckert and Chandler, 1998). 

Chemical reactions at supercritical conditions are good examples of solvation effects on rate constants. While the most compelling reason to carry out reactions at (near) supercritical conditions is the abihty to tune the solvation conditions of the medium (chemical potentials) and attenuate transport limitations by adjustment of the system pressure and/or temperature, there has been considerable speculation on explanations for the unusual behavior (occasionally referred to as anomalies) in reaction kinetics at near and supercritical conditions. True near-critical anomalies in reaction equilibrium, if any, will only appear within an extremely small neighborhood of the system s critical point, which is unattainable for all practical purposes. This is because the near-critical anomaly in the equilibrium extent of the reaction has the same near-critical behavior as the internal energy. However, it is not as clear that the kinetics of reactions should be free of anomalies in the near-critical region. Therefore, a more accurate description of solvent effect on the kinetic rate constant of reactions conducted in or near supercritical media is desirable (Chialvo et al., 1998). 

This chapter deals with critical phenomena in simple ionic fluids. Prototypical ionic fluids, in the sense considered here, are molten salts and electrolyte solutions. Ionic states occur, however, in many other systems as well we quote, for example, metallic fluids or solutions of complex particles such as charged macromolecules, colloids, or micelles. Although for simple atomic and molecular fluids thermodynamic anomalies near critical points have been extensively studied for a century now [1], for a long time the work on ionic fluids remained scarce [2, 3]. Reviewing the rudimentary information available in 1990, Pitzer [4] noted fundamental differences in critical behavior between ionic and nonionic fluids. 

The results substantiate earlier observations for the liquid-liquid phase transition of Na + NH3. This system shows a transition to metallic states in concentrated solutions but in dilute solutions and near criticality, ionic states prevail [98], and the gross phase behavior seems to be in accordance with a Coulombic transition [37]. Crossover was found at f — 10-2 [46], and it seems to be much more abrupt than in the picrate systems. However, much depends on the subtle details of the data evaluation. Das and Greer [99] could smoothly represent the data by a Wegner series. 

In the literature there have been repeated reports on an apparent mean-field-like critical behavior of such ternary systems. To our knowledge, this has first been noted by Bulavin and Oleinikova in work performed in the former Soviet Union [162], which only more recently became accessible to a greater community [163], The authors measured and analyzed refractive index data along a near-critical isotherm of the system 3-methylpyridine (3-MP) + water -I- NaCl. The shape of the refractive index isotherm is determined by the exponent <5. Bulavin and Oleinikova found the mean-field value <5 = 3 (cf. Table I). Viscosity data for the same system indicate an Ising-like exponent, but a shrinking of the asymptotic range by added NaCl [164],... 

One major problem in determining phase transition lines is associated with the use of finite systems, so that near criticality the correlation length of the fluctuations begins to exceed the size of the simulation box. Finite-size... 

---