Phase boundary liquid-solid

We call each solid line in this graph a phase boundary. If the values of p and T lie on a phase boundary, then equilibrium between two phases is guaranteed. There are three common phase boundaries liquid-solid, liquid-gas and solid-gas. The line separating the regions labelled solid and liquid , for example, represents values of pressure and temperature at which these two phases coexist - a line sometimes called the melting-point phase boundary . 

Dynamic contact angles are the angles which can be measured if the three-phase boundary (liquid/solid/vapor) is in actual motion. A Wilhelmy plate is used in dynamic contact angle measurements, and this method is also called the tensiometric contact angle method. It has been extensively applied to solid-liquid contact angle determinations in recent years. In practice, a solid substrate is cut as a thin rectangular plate, otherwise a solid material is... 

Figure 7.1 Schematic phase diagram of water (not to scale), showing phase boundaries (heavy solid lines), triple point (triangle), critical point (circle-x), and a representative point (circle, dotted lines) at 25°C on the liquid-vapor coexistence curve.

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

FIGURE 18.6 Supercritical region of a hypothetical compound. The solid lines represent phase boundaries between solid-liquid, liquid-gas, and solid-gas phases. Supercritical region is the region indicated by the dotted line. 

Vapor-pressure lowering of a solution decreases the triple-point temperature, the intersection of the liquid-vapor (vapor pressure) and solid-vapor phase boundaries. The solid-liquid phase boundary originating at the triple point is moved slightly to the left on the phase diagram (the solid-vapor boundary is unchanged). The freezing temperature of the solution is thereby lowered (the freezing-point is depressed). 

Unlike the Laplace equation, which can only be applied to fluid surfaces, the Kelvin equation is valid for any phase boundary, also solid-gas, solid-liquid, and even solid-solid. As for the Laplace equation, Eq. (10.9) can also be modified to accommodate nonspherical curved surfaces then 2/(l/i + l/i 2) should be used instead of r. The values for the solubility should give the thermodynamic activity of the substance involved, for the equation to be generally valid for ideal or ideally dilute solutions, concentrations can be used. Most gases in water show ideal behavior. It should further be noted that Eq. (10.9) applies for one component if a particle contains several components, it should be applied to each of them separately. Finally, there are some conditions that may interfere with the... 

Gradients at the boundary between different phases (gas/liquid/solid) in the reaction medium. 

A phase is a part of a system that is chemically uniform and has a boundary around it. Phases can be solids, liquids and gases, and, on passing from one phase to another, it is necessary to cross a phase boundary. Liquid water, water vapour and ice are the three phases found in the water system. In a mixture of water and ice it is necessary to pass a boundary on going from one phase, say ice, to the other, water. 

The interaction of liquid crystals with neighbor phases (gas, liquid, solid) is a very interesting problem relevant to their electrooptical behavior. The structure of liquid crystalline phases in close proximity to an interface is different from that in the bulk, and this surface structure changes boundary conditions and influences the behavior of a liquid crystal in bulky samples. The nematic phase is especially sensitive to external agents, in particular, to surface forces, and the majority of papers devoted to the surface properties of mesophases have been carried out on nematics. In addition, the nematic phase is of great importance from the point of view of applications in electrooptical devices. Thus, in this chapter, we will concentrate on surface properties of nematics, though the properties of the other phases will not be skipped either. 

The equilibrium phase boundaries between solid and liquid, solid and gas, and liquid and gas for a single component are represented by a line on a pressure-temperature diagram as shown in Fig. 12.1. The state of coexistence of all three phases in equilibrium is represented by the triple point [1]. In Fig. 12.2, one can see a snrface in the three-dimension space of state variables [pressure (P), mass density (p) and temperature (7)] and the projections of the state surface on the planes (P, T) and (P, 1/p). The three usual states of matter are separated by Coexistence Curves. If the values of (P, T) are such that the component s state is located inside a coexistence curve, then the pure component is observed under the form of two coexisting phases. 

Figure 3.1.9 Phase boundaries between solid, liquid, and gas (a) and phase diagram of water (b) (M.Pt. melting point B.Pt. boiling point).

One often wishes to describe a galvanic cell without taking the trouble to draw an actual picture of it. The notation used is a rudimentary diagram of the cell. Phase boundaries (between solid and liquid, liquid and gas, or solid and gas) are indicated by a liquid junction is represented by, a salt bridge by. The cells previously discussed may be represented thus (with spaces for filling in the concentrations) ... 

The strict definition of a phase is any homogeneous and physically distinct region that is separated from another such region by a distinct boundary . For example a glass of water with some ice in it contains one component (the water) exhibiting three phases liquid, solid, and gaseous (the water vapour). The most relevant phases in the oil industry are liquids (water and oil), gases (or vapours), and to a lesser extent, solids. 

In order to describe any electrochemical cell a convention is required for writing down the cells, such as the concentration cell described above. This convention should establish clearly where the boundaries between the different phases exist and, also, what the overall cell reaction is. It is now standard to use vertical lines to delineate phase boundaries, such as those between a solid and a liquid or between two innniscible liquids. The junction between two miscible liquids, which might be maintained by the use of a porous glass frit, is represented by a single vertical dashed line, j, and two dashed lines, jj, are used to indicate two liquid phases... 

DEF. The phase boundary which limits the bottom of the liquid field is called the liquidus line. The other boundary of the two-phase liquid-solid field is called the solidus line. 

Similar results, to the Fe-Zn system were obtained in the Ti,j,-Al(,) and Ti(j)-Al, ) system where, in the solid-liquid couples some of the expected surface layer phases were not formed, whereas in the solid-vapour system it was possible to obtain all the phases and predict from the AG -concen-tration curves the compositions at the different layer phase boundaries. 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

Various methods have been employed for the determination of E of liquid and solid metals. Besides purely electrochemical ones (e.g. measurement of the differential double layer capacity (see also chapter 4.2)) further techniques have been used for the investigation of the surface tension at the solid/electrolyte solution phase boundary. The employed methods can be grouped into several families based on the meas-... 

Closely eonneeted to this aspeet is the proeess of adsorption at eleetrode surfaees, whieh is a eompetetive proeess like at any other solid/liquid surfaee where a solvent moleeule is replaeed by an adsorbate moleeule. Compared to eommon adsorption proeesses at solid/liquid interfaees the strong eleetrie field at eleetroehemieal phase boundaries adds an influenee of utmost importanee. The strength of the interaetion between the eleetrode and the adsorbed speeies ean be expressed by the free enthalpy of adsorption. Employing a variety of methods many data have been reported, they are listed in this volume. 

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