Reversibility and equilibrium

Figure 2.8 A schematic illustration of the relationship between osmosis (dialysis), os motic equilibrium and reverse osmosis...

In the 19th century the variational principles of mechanics that allow one to determine the extreme equilibrium (passing through the continuous sequence of equilibrium states) trajectories, as was noted in the introduction, were extended to the description of nonconservative systems (Polak, 1960), i.e., the systems in which irreversibility of the processes occurs. However, the analysis of interrelations between the notions of "equilibrium" and "reversibility," "equilibrium processes" and "reversible processes" started only during the period when the classical equilibrium thermodynamics was created by Clausius, Helmholtz, Maxwell, Boltzmann, and Gibbs. Boltzmann (1878) and Gibbs (1876, 1878, 1902) started to use the terms of equilibria to describe the processes that satisfy the entropy increase principle and follow the "time arrow."... 

In order to clearly explain the possibilities of describing nonequlibrium irreversible processes in terms of equilibrium it is certainly necessary to define quite accurately the notions of equilibrium and reversibility, nonequilibrium and irreversibility. It is clear that their interpretation, as well as the interpretation of other scientific notions, changes with the development of respective theories, models, and methods. Since the work touches upon the issues of interrelations between the competing models in a historical profile it is desirable that the appropriateness of various interpretations of the said notions be assessed in this profile. Making no pretence of the systematic presentation of the issue we will only touch upon some points that are important for understanding the text1 below. 

However, the presented interpretation of equilibrium processes turns out to be unsatisfactory for the analysis of possibility to use equilibrium descriptions for irreversible phenomena. The interpretation of interrelations between equilibrium and reversibility that was given by... 

The above statement on the identity of equilibrium and reversible processes is also consistent to some extent with the Gorban interpretation only in the assumption on the limiting coincidence of nonequilibrium states, located on the trajectories S = const, with equilibrium ones—on the Boltzmann trajectory. In this case the entire set of possible states in Figure 1 is reduced to the curve Sj Smax. 

In this chapter we present a general-purpose transport model of the multireaction type. The model was successfully used to predict the adsorption as well as transport of several heavy metals in soils (Selim, 1992 Hinz and Selim, 1994 Selim and Amacher, 2001). Multireaction models are empirical and include linear and nonlinear equilibrium and reversible and irreversible retention reactions. A major feature of... 

Further discussion of these topics is found in Chapters 10 and 14. We leave these other considerations until later because a full discussion is much easier when other thermodynamic concepts such as activity and fugacity have been introduced. One of these considerations will be found to be that although as defined here phases and components appear to be entities that occur in rocks, minerals, solutions, and other parts of the real world, we will show that they are in fact parts of the thermodynamic model, just as much as are equilibrium and reversible processes. 

Osmosis, osmotic equilibrium, and reverse osmosis are illustrated in Figure 9.1. 

If we can assume association to be an entire equilibrium and reversible, it can be decomposed into intra- and intermolecular association. In intramolecular association, each chain has a conformation carrying several inframolecular flowers along the chain [29]. The hydrophobic cores are regarded as composite associative groups. In intermolecular association, such composite chains are connected with each other by intermolecular association. Thus, the system is modeled as a polymer solution in which polymers carry many associative groups of different sizes that may form junctions of variable multiplicity. The functionality of each chain is not fixed, but is controlled by the thermodynamic requirement. 

To describe the kinetics of this reaction in the gas phase, the equation type is selected to be equilibrium and reversible and the stocheometry of it is selected using standard equations. The equilibrium and rate constants as functions of temperature are given by ... 

Figure 12.26 A study in both equilibrium and reversibility in polymer chains adhering to surfaces. Poly(ethylene oxides) containing C,s hydrocarbon tails on both ends, adhering to polystyrene latex particles in aqueous dispersion. Note that poly(ethylene oxide) is water soluble. Samples of first 100,000 g/mol (Cie-100) and then 17,000 g/mol (0,6-17) were placed on the latex, and the other allowed to diffuse in with partial replacement.

All of the illustrated examples correspond to equilibrium and reversible conditions. The response of the adsorption layer formed at the hydrophobic methylated surfaces to the applied compression is schematically illustrated in Figure 2.17. The layer is displaced from the contact zone as the particles are compressed against each other and returns when the particles are pulled apart. The situation is principally different in the case of polar particles and adsorption from nonpolar media, such as in the case of amines on glass spheres. The chemisorption that takes place leads to the formation of an adsorbed layer that has its own mechanical strength, in which case a critical compressive force, needs to be applied for the adsorption layer to rupture and to be displaced from the contact zone (Figures 2.17b and 2.18). 

Deryagin developed a theory of adhesion in [57] he established that adhesion took place under the influence of surface forces and could be considered as a thermodynamic equilibrium and reversible process, provided that the radius of curvature of both the surfaces greatly exceeded the radius of action of the surface forces. 

The thermodynamic Deryagin theory of adhesion considers adhesion as an equilibrium and reversible process and the adhesive force as a function of the gap separating the contiguous surfaces. When this gap equals zero, the adhesive force is proportional to the dimensions of the bodies in contact [see (1.64)]. 

Guldberg Cato Maxmilian (1836-1902), Norw. chem., developed chemical law of mass action, studied chemical equilibrium and reverse reactions... 

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