Equilibrium, metastable

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

And finally, it should be mentioned that only siderite (at pH < 7) or magnetite (at pH > 7) can occur in equilibrium (metastable) with free... 

The liquid-cluster system appears to have equilibrium metastable or stable heterophase states, in which the volume fraction of solid clusters may vary from negligibly small values up to unity. To find these states, the thermodynamics of the liquid-cluster systems will be considered. 

The conclusion that polynuclear hydroxide complex ions do not constitute a significant part of the solute species of aluminum at equilibrium in the solutions studied here is in accord with the conclusions of Frink and Sawhney (4). The microcrystalline gibbsite itself is metastable in the sense that as crystals grow in size with longer aging time their solubility decreases. Although at equilibrium metastable species can be ignored, it can be so diflBcult to attain an equilibrium condition that the concept has little practical usefulness. 

As the temperature of the liquid is lowered towards that of the glass transition, as noted previously, there will be a temperature at which the liquid cannot attain thermodynamic equilibrium (metastable with respect to the crystal) in the time scale of typical experimental conditions For example, a fluid with a viscosity of 10 poise and shear modulus (G) of 10 dynes/cm has a relaxation time (t) of 10 seconds (i = Gr) and would require experimental times in excess of this to achieve equilibrium. When equilibrium is no longer maintained (with decreasing temperature) the density fluctuations, including those due to excess volume, become irreversibly time dependent, and the formalism becomes very complex. 

For the first-order phase transition, there are multiple solutions that need to be calculated, corresponding to the stable (equilibrium), metastable and unstable branches. Fig. 2(a) shows a representation of these solutions. 

There may be situations when pjquations 7 and 9 are realized while Equations 8 and 10 are not realized, i.c. the system is stable toward infinitely small perturbations while being unstable toward finite ones (a local maximum of entropy or a minimum of internal energy with at least one additional extremum). In such cases it is generally agreed to speak of a metastable equilibrium (metastable state) of the system. Conditions 8 and 10 define a stable equilibrium. When simultaneously breaking conditions 7 10, the system proves to be absolutely unstable. 

To start with, it is sufficient to replace the terms stable ( equilibrium ), metastable , and unstable by the terms stationary , metastationary , and non-stationary . Thus, with the aid of such a primitive glossary, a complete analogy in description of linear and non-linear phenomena may be attained including even the methods of description and the criteria of first- and second-order (in Landau s sense) phase transitions. 

For iron-carbon alloys (i.e., steels), an understanding of microstructures that develop during relatively slow rates of cooling (i.e., pearlite and a proeutectoid phase) is facilitated by the iron-iron carbide phase diagram. Other concepts in this chapter were presented as a prelude to the introduction of this diagram—the concepts of a phase, phase equilibrium, metastability, and the eutectoid reaction. In Chapter 10, we explore other microstructures that form when iron-carbon alloys are cooled from elevated temperatures at more rapid rates. These concepts are summarized in the following concept map ... 

T. Michalowski, Application of GATES and MATLAB for Resolution of Equilibrium, Metastable and Non-Equilibrium Electrolytic Systems, Chapter 1 in Applications of MATLAB in Science and Engineering (ed. by T. Michalowski), InTech - Open Access publisher in the fields of Science, Technology and Medicine, 2011. 

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