Equilibrium state metastable

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

The a — 0 transformation has a large hysteresis in hydrogenated titanium alloys, and different thermal treatments change their phase content. Various degrees of metastability due to hysteresis are implicit for the alloys after different thermal treatments. Metastable phases undergo transformation to a more equilibrium state during deformation, which can effect the flow of the alloy. Below we consider the effect of the thermal pre-strain treatment on ductility on the strength of the Ti-6A1-2Zr-1.5V-lMo-rH alloys. ... 

Fig-1 Stable equilibrium state (left) given by molecules vibrating about their mean position in a free energy well in an unstressed solid. Metastable equilibrium state (right) given by molecules vibrating in an elevated free energy well in a stressed solid (above the stable minimum for an unstressed solid). 

Geochemical models can be conceptualized in terms of certain false equilibrium states (Barton et al., 1963 Helgeson, 1968). A system is in metastable equilibrium when one or more reactions proceed toward equilibrium at rates that are vanishingly small on the time scale of interest. Metastable equilibria commonly figure in geochemical models. In calculating the equilibrium state of a natural water from a reliable chemical analysis, for example, we may find that the water is supersaturated with respect to one or more minerals. The calculation predicts that the water exists in a metastable state because the reactions to precipitate these minerals have not progressed to equilibrium. 

Sometimes the calculation predicts that the fluid as initially constrained is supersaturated with respect to one or more minerals, and hence, is in a metastable equilibrium. If the supersaturated minerals are not suppressed, the model proceeds to calculate the equilibrium state, which it needs to find if it is to follow a reaction path. By allowing supersaturated minerals to precipitate, accounting for any minerals that dissolve as others precipitate, the model determines the stable mineral assemblage and corresponding fluid composition. The model output contains the calculated results for the supersaturated system as well as those for the system at equilibrium. 

Stable, metastable and unstable states a simple analogy. A simple mechanical model is shown in Fig. 2.37 a block on a stand may be in different equilibrium states. In A and C the centre of gravity (G) of the block is lower than... 

Figure 2.37. A simple mechanical system and its equilibrium states. Different positions of a block on a stand and the corresponding values of the gravitation potential energy are shown. Point G is the centre of gravity of the block. In A there is stable equilibrium, in C metastable, in B unstable.

To the best of our knowledge, the supercoil conformation of the monoden-dron jacketed polystyrene is one of the first observations of a defined tertiary structure in synthetic polymers. The plectoneme conformation could be caused by underwinding or overwinding of a backbone from its equilibrium state [168]. Quick evaporation of the solvent certainly can cause a residual torsion in the molecule as it contracted in itself. Unlike macroconformations of biomolecules, where the tertiary structures are often stabilized by specific interactions between side groups, the supercoil of the monodendron jacketed polymers is metastable. Eventually, annealing offered a path for the stress relaxation and allowed the structural defects to heal [86]. 

An unstable equilibrium state (or configuration) that is at maximal potential energy. A metastable state is at equilibrium, and its potential energy [written here as U(x)] is such that any displacement (dx) from Xequiiibnum will result in the loss of potential energy. 

The origin of the deep localized states in the mobility gap that control the dark decay has been attributed to structural native thermodynamic defects [12]. Thermal cycling experiments show that the response of the depletion time to temperature steps is retarded, as would be expected when the structure relaxes toward its metastable liquid-like equilibrium state. As the structure relaxes toward the equilibrium state, t(j decreases further until the structure has reached equilibrium. The only possible inference is that must be controlled by structure-related thermodynamic defects. The generation of such defects is, therefore, thermally activated. We should note that because the depletion discharge mechanism involves the thermal emission of carriers... 

Figure 13.8 Schematic operation of a two-station rotaxane as a controllable molecular shuttle, and idealized representation of the potential energy of the system as a function of the position of the ring relative to the axle upon switching off and on station A. The number of dots in each position reflects the relative population of the corresponding coconformation in a statistically significant ensemble. Structures (a) and (c) correspond to equilibrium states, whereas (b) and (d) are metastable states. An alternative approach would be to modify station through an external stimulus in order to make it a stronger recognition site compared to station A.

Fig. la, h. The elastic part (ne) and the negative of the mixing part (— Jtm) of the osmotic pressure as functions of polymer concentration < >. The intercepts of ae and — nm correspond to the equilibrium state of neutral gels. Numbers besides each curve of — represent Xi> which increases with temperature, (a) x2 = 0. Only one root at all temperatures, (b) Xi = 0.56. Three roots appear in the intermediate temperature range (around Xi = 0.465), which correspond to stable, unstable, and metastable states, respectively. (Reproduced with permission from Ref. 20)... 

The phase coexistence observed around the first-order transition in NIPA gels cannot be interpreted by the Flory-Rehner theory because this theory tacitly assumes that the equilibrium state of a gel is always a homogeneous one. Heterogeneous structures such as two-phase coexistence are ruled out from the outset in this theory. Of course, if the observed phase coexistence is a transient phenomenon, it is beyond the thermodynamical theory. However, as will be described below, the result of the detailed experiment strongly indicates that the coexistence of phases is not a transient but rather a stable or metastable equilibrium phenomenon. At any rate, we will focus our attention in this article only on static equilibrium phenomena. 

When comparisons are made between calculations for an equilibrium redox state and concentrations in the dynamic aquatic environment, the implicit assumptions are that the biological mediations are operating essentially in a reversible manner at each stage of the ongoing processes or that there is a metastable steady-state that approximates the partial equilibrium state for the system under consideration. 

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