Phase transition solid - liquid equilibria

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

The triple point is the location at which all three phases boundaries intersect. At the triple point (and only at the triple point), all three phases (solid, liquid, and gas) coexist in dynamic equilibrium. Below the triple point, the solid and gas phases are next-door neighbors, and the solid-to-gas phase transition occurs directly. 

We can now distinguish three stages in the development of thermodynamics. First, there is the equilibrium stage in which the forces and the consequent flows vanish. It is under those conditions that we have equilibrium phase transitions such as solid to liquid and liquid to vapor. The structures that arise in such phenomenon, as for instance in a crystal, can be understood in terms of the minimization of the well-known free energy F. We have... 

Alternatively, thermodynamic phase equilibrium in a model system can be evaluated by beginning the simulation with two (or more) phases in the same simulation volume, in direct physical contact (i.e., with a solid-fluid interface). This approach has succeeded [79], but its application can be problematic. Some of the issues have been reviewed by Frenkel and McTague [80]. Certainly the system must be large (recent studies [79,81,82] have employed from 1000 up to 65,000 particles) to permit the bulk nature of both phases to be represented. This is not as difficult for solid-liquid equilibrium as it is for vapor-liquid, because the solid and liquid densities are much more alike (it is a weaker first-order transition) and the interfacial free energy is smaller. However, the weakness of the transition also implies that a system out of equilibrium experiences a smaller driving force to the equilibrium condition. Consequently, equilibration of the system, particularly at the interface, may be slow. 

The adsorption of QBr on the solid surface of SeK2 plays an insignificant role in the kinetic description. The solid-liquid equilibrium of KBr between its soluble parts and solid parts is still existed. Wu [217] reported that the kinetic data for S-shape curves were found in this system, as shown in Fig. 8 for different amounts of potassium sebacate used. This revealed that the catalytic transition complex [R-Br-Q-Br] in the organic phase would lead to a long induction period for the reaction of SeK2 with TC. 

The appearance of two stable steady states X, X3 allows the system to exist in two phases with different densities X and X3 of the species X. It may even happen that these two phases coexist in the same system separated by a phase boundary. The whole situation is very similar to the phenomenon of phase transitions in equilibrium systems such as gas-liquid or liquid-solid systems. According to this similarity, the phenomenon of different phases in a nonequilibrium system is called a nonequilibrium phase transition or a "dissipative structure". Clearly, the inclusion of coexistence between X and X3 and of phase boundaries into our theory requires the introduction of additional diffusion terms into the equation of motion (6.5) in order to account for spatial variations of X. The analogies between our autocatalytic system (for v = 2) and equilibrium phase transitions have been worked out by F. SCHLOGL (1972) on a phenomenological and by JANSSEN (1974) on a stochastic level. 

The closer the external temperature is to the equilibrium temperature, the smaller are the temperature gradients and the closer are the states of the system to equilibrium states. In the limit as the temperature difference approaches zero, the system passes through a sequence of equilibrium states in which the temperature is uniform and constant, energy is transferred into the system by heat, and the substance is transformed from solid to liquid. This idealized process is an equilibrium phase transition, and it is a reversible process. 

Confinement in pores affects all phase transitions of fluids, including the liquid-solid phase transitions (see Ref. [276, 277] for review) and liquid-vapor phase transitions (see Refs. [28, 278] for review). Below we consider the main theoretical expectations and experimental results concerning the effect of confinement on the liquid-vapor transition. Two typical situations for confined fluids may be distinguished fluids in open pores and fluids in closed pores. In an open pore, a confined fluid is in equilibrium with a bulk fluid, so it has the same temperature and chemical potential. Being in equilibrium with a bulk fluid, fluid in open pore may exist in a vapor or in a liquid one-phase state, depending on the fluid-wall interaction and pore size. For example, it may be a liquid when the bulk fluid is a vapor (capillary condensation) or it may be a vapor when the bulk fluid is a liquid (capillary evaporation). Only one particular value of the chemical potential of bulk fluid provides a two-phase state of confined fluid. We consider phase transions of water in open pores in Section 4.3. 

In equilibrium, this describes the coexistence of two different phases (solid and liquid), just as in the case of the Ising model ( hising) with the up and down magnetization phases. When h 0, one of these two phases has a priority. Therefore, a sign change of h -h induces a first-order phase transition. (Note that for modeling reasons h(T) may be assumed to depend on temperature.)... 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

In the CO2 phase diagram of Figure 8.1, we considered only (solid + liquid), (vapor + solid) and (vapor + liquid) equilibria. A (solid + solid) phase transition has not been observed in C(>,m but many substances do have one or more. Equilibrium can exist between the different solid phases I, II, III, etc., so that... 

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Where applications to industrial combustion systems involve a relatively limited set of fuels, fire seeks anything that can bum. With the exception of industrial incineration, the fuels for fire are nearly boundless. Let us first consider fire as combustion in the gas phase, excluding surface oxidation in the following. For liquids, we must first require evaporation to the gas phase and for solids we must have a similar phase transition. In the former, pure evaporation is the change of phase of the substance without changing its composition. Evaporation follows local thermodynamics equilibrium between the gas... 

We can predict whether an ice cube will melt just by looking carefully at the phase diagram. As an example, suppose we take an ice cube from a freezer at — 5 °C and put it straightaway in our mouth at a temperature of 37 °C (see the inset to Figure 5.1). The temperature of the ice cube is initially cooler than that of the mouth. The ice cube, therefore, will warm up as a consequence of the zeroth law of thermodynamics (see p. 8) until it reaches the temperature of the mouth. Only then will it attain equilibrium. But, as the temperature of the ice cube rises, it crosses the phase boundary, as represented by the bold horizontal arrow, and undergoes a phase transition from solid to liquid. 

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