Metastable equilibrium: definition

In the last chapter we have used the word order without giving it any precise meaning. Most definitions of order involve thermodynamic concepts. Thus, for example, one might say that the most ordered state of a system is the one to which the system tends as the temperature tends to absolute zero. This definition would, however, be of little service in the present context. Most of the systems which we will discuss are remote from thermodynamic equilibrium. This is true both of the films during their preparation and also of the final prepared films. However, these prepared films are in states of metastable equilibrium which are likely to survive for periods long compared with the time taken to carry out experiments on them and, very often, for periods so long as to be, from a human point of view, infinite. 

Although, as we have seen, each system has a minimum number of independent variables that must be specified or fixed for the system to be at stable equilibrium, systems frequently have more than this number of variables fixed, and they can then be said to be in metastable equilibrium states. In fact our definition of a metastable state can be restated as one that has more than the minimum number of constraints necessary to fix the equilibrium state. To illustrate what we mean by a metastable state, and the wide-ranging nature of the definition, we consider next three examples. 

We have just defined reversible processes in terms of the stable equilibrium surface, but completely analogous processes are also possible on metastable equilibrium surfaces, and the definition can be extended to include these. In fact, however, most discussions of reversible processes refer to stable equilibrium states and surfaces. 

The unit operation of erystallization is governed by some very complex interacting variables. It is a simultaneous heat and mass transfer process with a strong dependence on fluid and particle mechanics. It takes place in a multiphase, multicomponent system. It is concerned with particulate solids whose size and size distribution, both incapable of unique definition, vary with time. The solids are suspended in a solution which can fluctuate between a so-called metastable equilibrium and a labile state, and the solution composition can also vary with time. The nucleation and growth kinetics, the governing processes in this operation, can often be profoundly influenced by mere traces of impurity in the system a few parts per million may alter the crystalline product beyond all recognition. 

In thermodynamics, a metastable equilibrium state has at least three constraints. Two of these constraints apply to a stable equilibrium state, and the third prevents the system from achieving that state. On releasing the third constraint the system experiences a spontaneous process and achieves the stable equilibrium state. We have seen two examples so far, in Figures 4.1 and 4.6. These examples were chosen to follow from our definition of entropy, and show spontaneous processes having no overall energy change in the system. They show entropy acting as a thermodynamic potential. 

Crystallization, by definition, implies that the initial structure be a glass, followed by the nucleation and growth of a crystalline phase, be it the equilibrium one or a metastable phase. The process is a first-order transformation and involves atomic diffusion, or at least atomic shuttles. Types of crystallization reactions that occur include polymorphous crystallization, which is a composition invariant transformation such as that in Fe-B, and eutectic crystallization, T, in FeNiPB glass, where line lamellae of iron-nickel austenite and mclastable (FeNiJj PB phases grow cooperatively. 

Supersaturated homogeneous solutions are thus metastable, and the metastability decreases with increasing supersaturation. In other words, nucleation starts after the solute concentration has exceeded a definite value, and then solute molecules form aggregates or clusters. If, however, the crystals are placed in a supersaturated solution, the solution eventually attains equilibrium after the growth of the crystals upon crystallization. 

In the original definition of disjoining pressure by Deryaguin [11, 12], only the first two terms on the right-hand side of Equation (16.6) were considered. At low electrolyte concentrations, double layer repulsion predominates and can compensate the capillary pressure that is = P. This results in the formation of an equilibrium-free film which is usually referred to as the thick common film CF ( 50nm thickness). This equihbrium-metastable film persists until thermal or mechanical fluctuations cause mpture. The stability of the CF can be described in... 

Since AG is a maximum, as opposed to a minimum, at Rp = Rp, the equilibrium at this point is metastable. Equation (10.84) relates the equilibrium radius of a droplet of a pure substance to the physical properties of the substance, a and vh and to the saturation ratio S of its environment. Equation (10.84) can be rearranged recalling the definition of the saturation ratio as... 

In position (b), it is possible to imagine the ball balanced and unmoving, so that the first part of the definition would be fulfilled, and this is sometimes referred to as a third type of equilibrium, admittedly a trivial case, called unstable equilibrium. However, it does not survive the second part of the definition, so we are left with only two types of equilibrium, stable and metastable. 

What does it mean to say that our physical properties must be single-valued It means that our thermodynamic functions (such as equation (3.1)) can deal only with systems at equilibrium where, according to our definition, the properties of the system do not change with time. This equilibrium state may be stable or metastable, but generally speaking for systems more complex than a single component (e.g. a pure mineral) stable equilibrium states are almost always referred to." ... 

Look up the definitions of equilibrium, stable, metastable, reversible and quasistatic in any textbooks on thermodynamics or physical chemistry you have at hand, and reflect on the differences between them and the definitions in this text. 

The surfaces in Figure 5.4 must not be confused with the stable equilibrium surface. Only the locus of points at maximum S or minimum U such as A are at stable equilibrium and this locus forms a contour on the stable equilibrium surface as shown in Figure 5.5. All the other points on the surfaces in Figure 5.4 are metastable according to our definitions and would appear at higher U and lower S values having the same total volume V, such as point B in Figure 5.5. 

It would certainly be desirable to see some definitive work establishing the validity of Equation 25 in at least a few systems. The above two examples suggest, furthermore, that it may be entirely possible to have metastable films at one or the other solid interface-for example, if the liquid-film transition involves a structural phase change [11], so that nucleation may be required to produce an equilibrium film. 

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