Coupling of thermodynamics and kinetics

The aim of this chapter is to introduce the reader to some of the ways in which the CALPHAD approach has been combined with kinetics to predict the formation of phases and/or microstructures under conditions which are not considered to be in equilibrium. Broadly speaking, the combination of thermodynamics and kinetics can be broken down into at least two separate approaches (1) the calculation of metastable equilibria and (2) the direct coupling of thermodynamic and kinetic modelling. 

Such an approach should not be confused with the direct coupling of thermodynamic and kinetic parameters. Broadly speaking, this can achieved either... 

By the direct coupling of thermodynamic and kinetic models in a single software package, where the kinetic model can call the thermodynamic calculation part as a subroutine for the calculation of critical input parameters. 

The general features discussed so far can explain the complexity of these reactions alone. However, thermodynamic and kinetic couplings between the redox steps, the complex equilibria of the metal ion and/or the proton transfer reactions of the substrate(s) lead to further complications and composite concentration dependencies of the reaction rate. The speciation in these systems is determined by the absolute concentrations and the concentration ratios of the reactants as well as by the pH which is often controlled separately using appropriately selected buffers. Perhaps, the most intriguing task is to identify the active form of the catalyst which can be a minor, undetectable species. When the protolytic and complex-formation reactions are relatively fast, they can be handled as rapidly established pre-equilibria (thermodynamic coupling), but in any other case kinetic coupling between the redox reactions and other steps needs to be considered in the interpretation of the kinetics and mechanism of the autoxidation process. This may require the use of comprehensive evaluation techniques. 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

In the last two decades, significant attention has been paid to the study of surface electrode reactions with SWV and various methodologies have been developed for thermodynamic and kinetic characterization of these reactions. In the following chapter, several types of surface electrode processes are addressed, including simple quasireversible surface electrode reaction [76-84], surface reactions involving lateral interactions between immobilized species [85], surface reactions coupled with chemical reactions [86-89], as well as two-step surface reactions [90,91]. 

Transport is a three-phase process, whereas homogeneous chemical and phase-transfer [2.87, 2.88] catalyses are single phase and two-phase respectively. Carrier design is the major feature of the organic chemistry of membrane transport since the carrier determines the nature of the substrate, the physico-chemical features (rate, selectivity) and the type of process (facilitated diffusion, coupling to gradients and flows of other species, active transport). Since they may in principle be modified at will, synthetic carriers offer the possibility to monitor the transport process via the structure of the ligand and to analyse the effect of various structural units on the thermodynamic and kinetic parameters that determine transport rates and selectivity. 

Both the thermodynamics and kinetics of electron transfer reactions (redox potentials and electron transfer rates) have steric contributions, and molecular mechanics calculations have been used to identity them. A large amount of data have been assembled on Co3+/Co2+ couples, and the majority of the molecular mechanics calculations reported so far have dealt with hexaaminecobalt (III/II) complexes. 

In this chapter we try to classify the more important types of reactions encountered in inorganic chemistry, and describe some of their mechanisms. The emphasis is placed upon the principles which determine the stability or instability, existence and nonexistence of inorganic substances from the viewpoint of the ease or otherwise of preparing a compound, and the tendency a compound - once prepared - may have to react spontaneously to give other products. Both thermodynamic and kinetic considerations are obviously involved here. The division of material between this chapter and the next has not been easy, and there is inevitably a good deal of overlap. Coupling reactions, which might have deserved a section in this chapter, are discussed in Sections 10.5 and 10.6. 

Despite the clear importance of RA, its behavior is still not properly understood. This can be attributed to a very complex combination of process thermodynamics and kinetics, with intricate reaction schemes including ionic species, reaction rates varying over a wide range, and complex mass transfer and reaction coupling. As compared to distillation, RA is a fully rate-controlled process, and it dehnitely occurs far from the equilibrium state. Therefore, practitioners and theoreticians are highly interested in establishing a proper rate-based description of this process. 

The members of the hydrogen sulfide family are both thermodynamically and kinetically unstable in oxic seawater. The thermodynamic bias against them can be appreciated in a simple redox couple to sulfate, the predominant form of oceanic sulfur. 

Commercial yeast invertase (Bioinvert ) was immobilized by adsorption on anion-exchange resins, collectively named Dowex (1x8 50-400,1x4 50-400, and 1x2 100-400). Optimal binding was obtained at pH 5.5 and 32°C. Among different polystyrene beads, the complex Dowex-1x4-200/invertase showed a yield coupling and an immobilization coefficient equal to 100%. The thermodynamic and kinetic parameters for sucrose hydrolysis for both soluble and insoluble enzyme were evaluated. The complex Dowex/inver-tase was stable without any desorption of enzyme from the support during the reaction, and it had thermodynamic parameters equal to the soluble form. The stability against pH presented by the soluble invertase was between 4.0 and 5.0, whereas for insoluble enzyme it was between 5.0 and 6.0. In both cases, the optimal pH values were found in the range of the stability interval. The Km and Vmax for the immobilized invertase were 38.2 mM and 0.0489 U/mL, and for the soluble enzyme were 40.3 mM and 0.0320 U/mL. 

In terms of Eq. (1), the driving force is ApA and the resistance, f2 = L/Pa. Although the effective skin thickness L is often not known, the so-called permeance, PA/L can be determined by simply measuring the pressure normalized flux, viz., Pa/L = [flux of A]/A/j>a, so this resistance is known. Since the permeability normalizes the effect of the thickness of the membrane, it is a fundamental property of the polymeric material. Fundamental comparisons of material properties should be done on the basis of permeability, rather than permeance. Since permeation involves a coupling of sorption and diffusion steps, the permeability is a product of a thermodynamic factor, SA, called the solubility coefficient, and a kinetic parameter, DA, called the diffusion coefficient. 

The choice of the redox couple for an accelerated test will depend on factors such as its thermodynamics and kinetics, its compatibility with other accelerating factors (e.g., temperature, aggressive anion concentration), and its ease of use. Rarely is the relevance of the redox couple to the service environment of interest considered. 

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