Thermodynamic equilibrium force limitations

When the pressure of C02 in a carbonate-oxide system is equal to the equilibrium pressure pe, no net reaction occurs. When p < pe, the thermodynamic driving force favors oxide formation conversely, when p > pe, carbonate formation is favored. In the actual system the favored reaction may not occur, however, because kinetic factors prevent it. Particularly when p is not far from pe, the reaction may not proceed because some rate-limiting process, such as nucleus formation, is proceeding too slowly. The resulting spurious equilibria15 give rise to hysteresis effects, i.e., decomposition stops for some p < pe, recombination stops for some p > pe. It is for this reason that this work relies largely on thermodynamic methods for the calculation of equilibrium pressures. 

For all of the general techniques of Figure 2, the separations are achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase. The driving force and direction of mass transfer by diffusion is governed by thermodynamics, with the usual limitations of equilibrium. Thus, both transport and thermodynamic considerations are crucial in separation operations. The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamic equilibrium. Fluid mechanics also plays an important role, and applicable principles are included in other chapters. 

The primary isomer distribution, which is the result of the disproportionation reaction, may deviate significantly from the thermodynamic equilibrium composition, for two reasons. First, the reaction may be controlled by the kinetics rather than the thermodynamics, i.e. mechanistic reasons may exist which cause the reaction to proceed along a certain path. Second, in the case that the reaction obeys a bimolecular mechanism, it may pass through a transition state which would presumably favor the (taller) para isomer. Hence, it is possible that the primary product contains an enhanced fraction of the para isomer. The departure from the equilibrium composition then gives the driving force for the subsequent (monomolecular) isomerization reaction. This will reduce the fraction of the para isomer, provided the formation of the bulky ortho and meta isomers are not inhibited by sterical effects, i.e. when the micropore diameter is sufficiently large or there is a chance for the isomerization reaction to take place at the outer surface of the crystallites. Thus, the secondary isomer distribution may approach the thermodynamic equilibrium composition, as a limiting case. 

Myriad polydentate aza-macrocycles have been reported 41. The extent of the subject forces limitation of this discussion to only macrocycles containing a pyridine or dipyridine subunit. Most of these coronands have been synthesized by a SchifF base condensation of an aldehyde or ketone with a hfc-primary amine in the presence of a metal ion. The metal ion acts as a template, resulting in dramatic increases in yield of the desired cyclic product over linear polymerization products42 46. Lindoy and Busch45 have described this effect in two ways, kinetic and thermodynamic. If the metal ion controls the steric course of a series of stepwise reactions, the template effect is considered to be kinetic. If the metal ion influences an equilibrium in an organic reaction sequence by coordination with one of the reactants, the template effect is termed thermodynamic. It is the kinetic effect that is believed to be operative in most metal ion-assisted (in situ) syntheses of... 

Intrapellet transport restrictions can limit the rate of removal of products, lead to concentration gradients within pellets, and prevent equilibrium between the intrapellet liquid and the interpellet gas phase. Transport restrictions increase the intrapellet fugacity of hydrocarbon products and provide a greater chemical potential driving force for secondary reactions. The rate of secondary reactions cannot be enhanced by a liquid phase that merely increases the solubility and the local concentration of a reacting molecule. Olefin fugacities are identical in any phases present in thermodynamic equilibrium thus, a liquid phase can only increase the rate of a secondary reaction if it imposes a transport restriction on the removal of reacting species involved in such a reaction (4,5,44). Intrapellet transport rates and residence times depend on molecular size, just as convective transport and bed residence time depend on space velocity. As a result, bed residence time and molecular size affect chain termination probability and paraffin content in a similar manner. 

Abstract The Gibbs phase rule relating the number of degrees of freedom / of a system to the number of components c and the number of coexisting phases p is a central, universally used relation, expressed by what is probably the simplest formula in the natural sciences,/ = c — p + 2. Research into the behavior of small systems, notably atomic clusters, has shown in recent years that the phase rule is not as all-encompassing as is often assumed. Small systems can show coexistence of two or more phases in thermodynamic equilibrium over bands of temperature and pressure (with no other forces acting on them). The basis of this apparent violation of the phase rule, seeming almost like violation of a scientific law, is in reality entirely understandable, consistent with the laws of thermodynamics, and even allows one to estimate the upper size limit of any particular system for which such apparent violation could be observed. 

Because of these factors, typical reactions occur in a limit of strong thermodynamic disequilibrium exactly opposite to the near thermodynamic equilibrium limit of the slow variable models. Consequently, forces acting... 

In general, the rotational and vibrational motions are limited in the amorphous glassy state. In the rubbery state, on the other hand, large-scale molecular motion, such as translational motion, is possible (Ubbink and Schoonman, 2003). Therefore, the encapsulated flavors or oils exist stably in the amorphous glassy state, but in the rubbery state some deterioration may take place. Since an amorphous state is not an equilibrium state, a thermodynamic driving force tends to shift the amorphous state to a more stable crystal state, resulting in a time-dependent crystallization, solidification of powders, and caking. 

The book is divided into four parts. Part One, which consists of six chapters, deals with basic principles and concepts of non-equilibrium thermodynamics along with discussion of experimental studies related to test and limitation of formalism. Chapter 2 deals with theoretical foundations involving theoretical estimation of entropy production for open system, identification of fluxes and forces and development of steady-state relations using Onsager reciprocity relation. Steady state in the linear range is characterized by minimum entropy production. Under these circumstances, fluctuations regress exactly as in thermodynamics equilibrium. 

In the first problem class mentioned above (hereinafter called class A), a collection of particles (atoms and/or molecules) is taken to represent a small region of a macroscopic system. In the MD approach, the computer simulation of a laboratory experiment is performed in which the "exact" dynamics of the system is followed as the particles interact according to the laws of classical mechanics. Used extensively to study the bulk physical properties of classical fluids, such MD simulations can yield information about transport processes and the approach to equilibrium (See Ref. 9 for a review) in addition to the equation of state and other properties of the system at thermodynamic equilibrium (2., for example). Current activities in this class of microscopic simulations is well documented in the program of this Symposium. Indeed, the state-of-the-art in theoretical model-building, algorithm development, and computer hardware is reflected in applications to relatively complex systems of atomic, molecular, and even macromolecular constituents. From the practical point of view, simulations of this type are limited to small numbers of particles (hundreds or thousands) with not-too-complicated inter-particle force laws (spherical syrmetry and pairwise additivity are typically invoked) for short times (of order lO" to 10 second in liquids and dense gases). 

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