Thermodynamic systems, stability

The thermodynamic phase stability diagrams appear to be preferred by corrosion scientists and technologists for the evaluation of gas-metal systems where the chemical composition of the gaseous phase consisting of a single gas or mixture of gases has a critical influence on the formation of surface reaction products which, in turn, may either stifle or accelerate the rate of corrosion. Also, they are used to analyse or predict the reason for the sequence of formation of the phases in a multi-layered surface reaction product on a metal or alloy. 

A detailed explanation of the construction of thermodynamic phase stability diagrams may be found in References 22-25. In this section the basic principles of construction and interpretation for the specific situation of gas-metal equilibria will be addressed using a hypothetical system. 

Fig. 7.79 Five possible reaction paths on a schematic thermodynamic phase stability diagram, and the corresponding distribution of phases in the reaction systems (after Stringer...

Fig. 7.80 A schematic thermodynamic phase stability diagram for the A-C-O system, showing three reaction paths. Paths 2 and 3 are only possible if gaseous diffusion in pores in the oxide product results in a carbon activity increase through the scale, as shown in Fig. 7.81 (after...

The two main assumptions underlying the derivation of Eq. (5) are (1) thermodynamic equilibrium and (2) conditions of constant temperature and pressure. These assumptions, especially assumption number 1, however, are often violated in food systems. Most foods are nonequilibrium systems. The complex nature of food systems (i.e., multicomponent and multiphase) lends itself readily to conditions of nonequilibrium. Many food systems, such as baked products, are not in equilibrium because they experience various physical, chemical, and microbiological changes over time. Other food products, such as butter (a water-in-oil emulsion) and mayonnaise (an oil-in-water emulsion), are produced as nonequilibrium systems, stabilized by the use of emulsifying agents. Some food products violate the assumption of equilibrium because they exhibit hysteresis (the final c/w value is dependent on the path taken, e.g., desorption or adsorption) or delayed crystallization (i.e., lactose crystallization in ice cream and powdered milk). In the case of hysteresis, the final c/w value should be independent of the path taken and should only be dependent on temperature, pressure, and composition (i.e.,... 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and /Cred of a complex in different oxidation states with experimentally measurable redox potentials EH and EHa. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if Kted is known or vice versa. 

In an attempt to impart selectivity and greater thermodynamic cation stability to these types of calixarenediquinone systems, a calixarenediquinone-crown ether [57] (Fig. 29) was synthesized (Beer et al., 1994a). 

Thermodynamic system, which is a state of equilibrinm where environmental parameters, snch as pressure and temperature, are imposed on the bulk composition of the system. This approach is nsed to predict the system stability and the impact of changing environmental conditions. 

When dealing with general thermodynamic systems, the fact that entropy tends to a maximum in the trend toward equilibrium of a natural process generalizes the above mechanical consideration with respect to stability. An equilibrium state can be characterized as a stable equilibrium when the entropy is a maximum neutral equilibrium when displacement from one equilibrium state lo another does not involve changing entropy and unstable equilibrium when entropy is a minimum. Any slight disturbance from an unstable equilibrium state or a system will lead to transition to another state of equilibrium. 

In order to extract the maximal energy out of the available foodstuff oxidative phosphorylation should operate at the state of optimal efficiency in vivo. Since a zero as well as an infinite load conductance both lead to a zero efficiency state, obviously there must be a finite value of the load conductance permitting the operation of the energy converter at optimal efficiency. For linear thermodynamic systems like the one given in equations (1) and (2) the theorem of minimal entropy production at steady state constitutes a general evolution criterion as well as a stability criterion.3 Therefore, the value of the load conductance permitting optimal efficiency of oxidative phosphorylation can be calculated by minimizing the entropy production of the system (oxidative phosphorylation with an attached load)... 

The completely reliable computational technique that we have developed is based on interval analysis. The interval Newton/generalized bisection technique can guarantee the identification of a global optimum of a nonlinear objective function, or can identify all solutions to a set of nonlinear equations. Since the phase equilibrium problem (i.e., particularly the phase stability problem) can be formulated in either fashion, we can guarantee the correct solution to the high-pressure flash calculation. A detailed description of the interval Newton/generalized bisection technique and its application to thermodynamic systems described by cubic equations of state can be found... 

The entire thermodynamic system of the membrane and TM protein must be considered to understand how the protein and bilayer achieve their native state. We have summarized four of the mechanisms, hydrophobic matching, tilt angles, and specific protein/lipid and protein/protein interactions that are important in determining the stability (Fig. 5). Other important factors, such as the stability of lipid/lipid interactions, have been left out of our protein-centric view. We describe a hydrophobic mismatch as an unfavorable interaction that can be relieved by the other three processes, but we would expect all these properties of the system to interact. We could easily describe the same equilibria by saying that a strain in curvature is relieved by a hydrophobic mismatch or that strong protein/protein packing interactions might help relieve the hydrophobic mismatch or curvature stress. The complex interplay between all these interactions is at the heart of what determines membrane protein stability and will no doubt be difficult to quantify. 

Thermodynamic Analysis of the System Stability The rate of energy dissipation in this system is written as... 

Microemulsions are fluid, transparent, thermodynamically stable oil and water systems, stabilized by a surfactant usually in conjunction with a cosurfactant that may be a short-chain alcohol, amine, or other weakly amphiphilic molecule. An interesting characteristic of microemulsions is that the diameter of the droplets is in the range of 100-1000 A, whereas the diameter of droplets in a kinetically stable macroemulsion is 5000 A. The small droplet size allows the microemulsion to act as carriers for drugs that are poorly soluble in water. The suggested method of preparation of microemulsions is as follows the surfactant, oil, and water are mixed to form a milky emulsion and titrated with a fourth component, the cosurfactant,... 

These inequalities are important in the study of the stability of thermodynamic systems. 

This book is the first volume of a Treatise on Thermodynamics based on the methods of Gibbs and De Donder. It deals with the following topics fundamental theorems, homogeneous systems, heterogeneous systems, stability and moderation, equilibrium displacements and equilibrium transformations, solutions, azeotropy, and indifferent states. The second volume deals with surface tension and adsorption while the third and last will be concerned with irreversible phenomena. 

Stable A term describing a system in a state of equilibrium corresponding to a local minimum of the appropriate thermodynamic potential for the specified constraints on the system. Stability cannot be defined in an absolute sense, but if several states are in principle accessible to the system under given conditions, that with the lowest potential is called the stable state, while the other states are described as metastable. Unstable states are not at a local minimum. Transitions between metastable and stable states occur at rates that depend on the magnitude of the appropriate activation energy barriers that separate them. 

A simple determination of resonance stabilization in benzene is shown in Fig. 2. Suppose we take three moles of cyclohexene and one mole of benzene as two different thermodynamic systems, each having three... 

The free energy of mixing of a system describes the thermodynamic state of the system and thus provides information about the system stability. If a system is unstable and separates in two coexisting phases, transport of individual components has to take place. The transport processes are determined by thermodynamic parameters, which are expressed by driving forces, and by kinetic parameters, which are determined by diffusivities, i.e., the diffusion coefficient. Fick s law relates the diffusion coefficient to concentration gradients. However, the actual driving forces for any mass transport are gradients in the chemical po-... 

McHale JM, Auroux A, Perrotta AJ, Navrotsky A (1997) Surface energies and thermodynamic phase stability in nanocrystalline aluminas. Science 277 788-791 McKeown DA, Waychunas GA, Brown GE Jr (1985a) EXAFS study of the coordination environment of aluminum in a series of silica-rich glasses and selected minerals within the sodium aluminosilicate system. J Non-Crystal Solids 74 349-371... 

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