Transport, thermodynamics irreversible transfer

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

In contrast to thermodynamic properties, transport properties are classified as irreversible processes because they are always associated with the creation of entropy. The most classical example concerns thermal conductance. As a consequence of the second principle of thermodynamics, heat spontaneously moves from higher to lower temperatures. Thus the transfer of AH from temperature to T2 creates a positive amount of entropy ... 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

Equations (64 )-(66 ) are equal to those used by other researchers [3-20, 28, 35-37]. These authors obtained Eqs (64 )-(66 ) by considering the basic Stokes-Einstein equation. We obtained the same equations as a particular case from Eq. (6), based on kinetics of irreversible processes (nonequihb-rium thermodynamics). In Table 5.3 are presented examples of individual and overall mass-transfer coefficients, obtained at titanium(IV) ion transport through the BOI ILM system [1]. 

Reverse osmosis is simply the application of pressure on a solution in excess of the osmotic pressure to create a driving force that reverses the direction of osmotic transfer of the solvent, usually water. The transport behavior can be analyzed elegantly by using general theories of irreversible thermodynamics however, a simplified solution-diffusion model accounts quite well for the actual details and mechanism in most reverse osmosis systems. Most successful membranes for this purpose sorb approximately 5 to 15% water at equilibrium. A thermodynamic analysis shows that the application of a pressure difference, Ap, to the water on the two sides of the membrane induces a differential concentration of water within the membrane at its two faces in accordance with the following (31) ... 

Transport in OSN membranes occurs by mechanisms similar to those in membranes used for aqueous separations. Most theoretical analyses rely on either irreversible thermodynamics, the pore-flow model and the extended Nemst-Planck equation, or the solution-diffusion model [135]. To account for coupling between solute and solvent transport (i.e., convective mass transfer effects), the Stefan-Maxwell equations commonly are used. The solution-diffusion model appears to provide a better description of mixed-solvent transport and allow prediction of mixture transport rates from pure component measurements [136]. Experimental transport measurements may depend significantly on membrane preconditioning due to strong solvent-membrane interactions that lead to swelling or solvent phase separation in the membrane pore structure [137]. 

Similar phenomena such as diffusion potential and thermal diffusion potential in systems where ion transport is involved are also of considerable interest. Coupling of flow of ions relative to solvent is involved in the development of diffusion potential, while in the case of thermal diffusion potential, coupling of flow of ions and energy flow is involved. In such situations, the effective transference number as compared to Hittorf transference number is affected. Interesting experimental results have been reported in the context of galvanic cells (thermo-cells), in which the two electrodes are not at the same temperature where results have been interpreted in terms of thermodynamics of irreversible processes [3]. 

The product of thermodynamic forces and fiows yields the rate of entropy production in an irreversible process. The Gouy-Stodola theorem states that the lost available energy (work) is directly proportional to the entropy production in a nonequilibrium phenomenon. Transport phenomena and chemical reactions are nonequilibrium phenomena and are irreversible processes. Thermodynamics, fiuid mechanics, heat and mass transfer, kinetics, material properties, constraints, and geometry are required to establish the relationships... 

In the electrochemical literature it is useful to refer to a reversible interface or interfacial reaction as one whose potential is determined only by the thermodynamic potentials of the various electroactive species at the electrode surface. In other words, it is only necessary to take into account mass transport to and from the interface, and not the inherent heterogeneous kinetics of the interfacial reaction itself, when discussing the rate of the charge transfer reaction. This nomenclature has two principal disadvantages. First, it neglects the fact that mass transport to the interface, whether migration or diffusion, is inherently an irreversible or dissipative... 

My background led me to view chemical kinetics as closely related to transport phenomena. While the relationship of these topics is well known, it is often ignored, except for brief discussions of irreversible thermodynamics. In fact, the physics underlying such apparently dissimilar processes as reaction and energy transfer is not so very different. The intermolecular potential is to transport what the potential-energy surface is to reactivity. 

A quite different response is found for couples O/R where Iq is large (in fact, where Iq > 10" /l or k > 10" cm s ). Then the electron transfer reaction at the surface is rapid enough that under most mass transport conditions obtainable experimentally, the electron transfer couple at the surface appears to be in equilibrium. Then the surface concentrations may, at each potential, be calculated from the Nernst equation, a purely thermodynamic equation, and the current may be calculated, for example, from equation (1.57). The I-E curve has the form shown in Fig. 1.16 the I-E curve crosses the zero current axis steeply and there is no overpotential for oxidation or reduction. Systems with these characteristics are often termed reversible . On the other hand, the limiting current densities do not depend on the kinetics of electron transfer closer to E. Hence the limiting current densities for reversible and irreversible reactions are the same. 

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