Thermodynamics, equilibrium

In thermodynamics, a reversible process is one that can be reversed by infinitesimal changes in some property of the system without loss of energy. In chemistry, this normally means a transition (e.g. chemical reaction or phase transformation) from some initial state to some final state. If, after transitioning to the final state, the process is 

PHASE EQUILIBRIA, PHASE DIAGRAMS, AND PHASE MODELING 

In chemical thermodynamics, it is prefered to focus attention on the system rather than the surroundings. Thus, it is convenient to consider the free energy function as the quantity of energy available in a system for producing work. Using this state function, the criterion for spontaneity is a decrease in the system s free energy on moving from the 

fi is known as the chemical potential for the ith component, and X can be any of a number of external forces that causes an external parameter of the system, a, to change by an amount da. Under conditions of constant temperature and constant pressure, the first two terms on the right-hand side of Eq. 11.3 drop out. 

The Gibbs energy change is related to some other important physical quantities, like the equilibrium constant for a chemical reaction and the electromotive force (emf) of an electrochemical cell, by the Nemst and van t Hoff equations  

In this chapter, we first introduce the principles of irreversible or nonequilibrium thermodynamics as opposed to those of equilibrium thermodynamics. Then, we identify important thermodynamic forces X (the cause) and their associated flow rates / (the effect). We show how these factors are responsible for the rate with which the entropy production increases and available work decreases in a process. This gives an excellent insight into the origin of the incurred losses. We pay attention to the relation between flows and forces and the possibility of coupling of processes and its implications. 

Equilibrium thermodynamics is the most important, most tangible result of classical thermodynamics. It is a monumental collection of relations between state properties such as temperature, pressure, composition, volume, internal energy, and so forth. It has impressed, maybe more so overwhelmed, many to the extent that most were left confused and hesitant, if not to say paralyzed, to apply its main results. The most characteristic thing that can be said about equilibrium thermodynamics is that it deals with transitions between well-defined states, equilibrium states, while there is a strict absence of macroscopic flows of energy and mass and of driving forces, potential differences, such as difference in pressure, temperature, or chemical potential. It allows, however, for nonequilibrium situations that are inherently unstable, out of equilibrium, but kinetically inhibited to change. The driving force is there, but the flow is effectively zero. 

The preceding introduction might lead one to believe that this chapter could simply be divided into two basic parts—thermochemical considerations and kinetic considerations—which would cover all the relevant subject matter. However, in the last decade, first-principles (ab initio) computations have become commonplace and their results have often confirmed predictions based on thermochemical approaches, sometimes even surpassing them in accuracy. Hence, there is a need to encompass both thermochemical and ab initio treatments. We group the latter under the heading structural energetics and explore this topic further in Section 2.2. We also talk about the relevant thermodynamic and kinetic factors for specific systems in their respective chapters. For now, we discuss thermodynamics and kinetics in the most general terms. 

This is but one possible expression for the Gibbs free energy. We could write an expression in terms of changes in other state variables, such as temperature and pressure. Furthermore, we must account for the possibility that a component may be distributed among or transported between several phases within the system (e.g., alloys). Alternatively, many reactions of interest to the materials 

The phase rule of Josiah Willard Gibbs (1839-1903) gives the general conditions for chemical equilibrium between phases in a system. At equilibrium, AG = 0, there is no further change with time in any of the system s macroscopic properties. It is assumed that surface, magnetic, and electrical forces may be neglected. In this case, the phase rule can be written as 

Consider the reaction between chemical entities A and B to form a reaction product By. The chemical reaction can be written as 

To illustrate this the solubility constant (Kso) for the dissolution of the mineral gibbsite will be calculated. The dissolution reaction can be written as the dissociation of the mineral, where subscript (s) refers to the solid phase and (aq) to the aqueous state  

The term Al(OH)3(s) is omitted because by definition the activity of a solid phase at standard state is unity, therefore, the solubility constant is given by 

The value of Kso can be calculated by using the tabulated values (Stumm and Morgan, 1981) of Gibbs free energy AG for the following species as follows  

The numerical values, irrespective of the size of the vessel and of what be the reactants, seem intended to help us keep our feet firmly on the ground of empirical science. I cannot help wishing to see some of my classically thermodynamic friends try the experiment with asphalt as one ingredient and nitroglycerin as the other. 

What can this branch of physical chemistry offer materials chemists Thermodynamic considerations can estimate the driving forces for simple chemical processes, which can be useful for those cases where the atoms have a high mobility and reactivity because then the end state can sometimes be described correctly. Driving forces for processes in the solid are discussed below. The equilibrium 

The bonding energies in the compounds determine the phase diagram (T-x) of the system. Demixing occurs if the atoms of the components of the diagram prefer to surround themselves by their own sort while alloys or compounds occur if the atoms have a higher affinity for the other atoms than for their own sort. This is an equilibrium argument. Considered as a description of what will happen under certain circumstances, it assumes that equilibrium will be attained. 

There are existence areas in phase diagrams in which one phase is stable and coexistence areas where two phases are in equilibrium. Line compounds (very narrow existence regions) are phases that have very low solubility for the separate 

3 illustrates the way in which the G T)lx graphs form the binodal in the T/x diagram. It can also be seen that in the spinodal region the mixtures are unstable in the face of any fluctuation in the composition. 

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Fox R F 1969 Contributions to the theory of non-equilibrium thermodynamics PhD Thesis Rockefeller University, New York... 

Fox R F and Uhlenbeck G E 1970 Contributions to non-equilibrium thermodynamics. II. Fluctuation theory for the Boltzmann equation Rhys. Fluids 13 2881... 

CET89, Chemical equilibrium thermodynamics code for evaluating shock parameters in explosive, chemically-reactive systems, NASA 1989. 

R. W. Haywood, Equilibrium Thermodynamics for Engineers and Scientists, Wiley, 1980. 

Product composition may be governed by the equilibrium thermodynamics of the system. When this is true, the product composition is governed by thermodynamic control. Alternatively, product composition may be governed by competing rates of formation of products. This is called kinetic control. 

D. Blankschtein, G. Thurston, G. Benedek. Phenomenological theory of equilibrium thermodynamic properties and phase separation of micellar solutions. J Chem Phys 25 7268-7288, 1986. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

The transition state theory allows us to apply results of equilibrium thermodynamics, and we, therefore, write, for a reactant or transition state species i. 

I. Prigogine (Brussels) non-equilibrium thermodynamics, particularly the theory of dissipative structures. 

The flow behavior of the polymer blends is quite complex, influenced by the equilibrium thermodynamic, dynamics of phase separation, morphology, and flow geometry [2]. The flow properties of a two phase blend of incompatible polymers are determined by the properties of the component, that is the continuous phase while adding a low-viscosity component to a high-viscosity component melt. As long as the latter forms a continuous phase, the viscosity of the blend remains high. As soon as the phase inversion [2] occurs, the viscosity of the blend falls sharply, even with a relatively low content of low-viscosity component. Therefore, the S-shaped concentration dependence of the viscosity of blend of incompatible polymers is an indication of phase inversion. The temperature dependence of the viscosity of blends is determined by the viscous flow of the dispersion medium, which is affected by the presence of a second component. 

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

Note that while the power-law distribution is reminiscent of that observed in equilibrium thermodynamic systems near a second-order phase transition, the mechanism behind it is quite different. Here the critical state is effectively an attractor of the system, and no external fields are involved. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

The mechanism of radiative transfer in flares was found to depend on compn, flare diameter and pressure (Ref 69). The flare efficiency calcn is complicated by the drop-off in intensity at increasing altitudes and at very large diameters owing to the lower reaction temps (Ref 11, p 13) and the narrowing of the spectral emittance band (Ref 35). The prediction of the light output in terms of compn and pressure (ie, altitude) is now possible using a computer program which computes the equilibrium thermodynamic properties and the luminance (Ref 104) Flare Formulations... 

See, for example Jui Sheng Hsieh, Principles of Thermodynamics, Scripta Book Company, Washington, 1975 Kenneth Wark, Thermodynamics. Fourth Edition, McGraw Hill Book Company, New York, 1983 James Coull and Edward B. Stuart, Equilibrium Thermodynamics, John Wiley Sons, Inc., New York, 1964. 

Approximately every twenty years, the international temperature scale is updated to incorporate the most recent measurements of the equilibrium thermodynamic temperature of the fixed points, to revise the interpolation equations, or to change the specifications of the interpolating measuring devices. The latest of these scales is the international temperature scale of 1990 (ITS-90). It supersedes the earlier international practical temperature scale of 1968 (IPTS-68), along with an interim scale (EPT-76). These temperature scales replaced earlier versions (ITS-48 and ITS-27). 

Having briefly discussed the way in which the important features of a single crystal are incorporated into a simple model we next consider what information can be obtained on this single crystal from equilibrium thermodynamics. 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

In order to begin this presentation in a logical manner, we review in the next few paragraphs some of the general features of polymer solution phase equilibrium thermodynamics. Figure 1 shows perhaps the simplest liquid/liquid phase equilibrium situation which can occur in a solvent(l)/polymer(2) phase equilibrium. In Figure 1, we have assumed for simplicity that the polymer involved is monodisperse. We will discuss later the consequences of polymer polydispersity. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... 

Hence, we find a relation between K and the enthalpy of the reaction, instead of the free energy, and the expression for the equilibrium is in conflict with equilibrium thermodynamics, in particular with Eq. (32) of Chapter 2, since the prefactor can not be related to the change of entropy of the system. Hence, collision theory is not in accordance with thermodynamics. 

Observance of a mixed potential of about 1.0 V (instead of the equilibrium thermodynamic reversible potential Ec= 1.23 V vs. SHE) due to the formation of surface oxides at the platinum electrode, according to different electrode reactions ... 

Belouzov-Zhabotinsky reaction [12, 13] This chemical reaction is a classical example of non-equilibrium thermodynamics, forming a nonlinear chemical oscillator [14]. Redox-active metal ions with more than one stable oxidation state (e.g., cerium, ruthenium) are reduced by an organic acid (e.g., malonic acid) and re-oxidized by bromate forming temporal or spatial patterns of metal ion concentration in either oxidation state. This is a self-organized structure, because the reaction is not dominated by equilibrium thermodynamic behavior. The reaction is far from equilibrium and remains so for a significant length of time. Finally,... 

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