Solid-liquid-vapor three-phase

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

Calculation of Three-Phase Solid-Liquid-Vapor Equilibrium Using an Equation of State... 

When one component is present in three phases at equilibrium, the phase rule states that the system is invariant and possesses no degrees of freedom. This implies that such a system at equilibrium can only exist at one definite temperature and one definite pressure, which is termed the triple point. For instance, the solid/liquid/vapor triple point of water is found at a temperature of 273.16K and a pressure of 4.58 torr. 

The sampling techniques depend on whether the sample is In vapor phase, a liquid, or a solid. In these three phases the Intermolecular forces differ significantly and thus it is Imperative that the data obtained be specified for the sampling technique used. 

The phase diagram shows the location of the phase boundaries between the solid, liquid, and gas phases. All three phases are in equilibrium at the triple point. If the temperature and pressure exceed the so-called critical values, the phase boundary between liquid and vapor vanishes. For this supercritical state, a change of pressure and temperature no longer leads to a change of the state of aggregation. The influence of pressure on a phase transition is given by the Clapeyron equation. 

When we plot our experimental data, we arrive at the phase diagram shown in Figure 4.12. In contrast to the phase diagram in Figure 4.10, the two-phase systems, such as vapor/liquid mixtures, correspond to a line, not a region, and likewise for the other two-phase systems, solid/vapor and solid/liquid. The three two-phase borders meet at the triple point, the unique condition at which solid, liquid, and vapor coexist. The triple point is usually at a temperature slightly colder than the melting point at 1 atm, but at a much lower pressure - typically less than 0.01 atm. 

If one component and three phases are present, / = 0 and there is no choice about the temperature, the pressure, or any other intensive variable. This three-phase state is represented by a triple point at which three coexistence curves intersect. The solid-liquid-vapor triplepoint of water occurs at a temperature of273.16 K (this value defines the size of the kelvin) and a pressure of 4.562 torr. 

First-order wetting transition assumes the existence of a prewetting transition, which is located out of the bulk coexistence (dotted line in the left panel of Fig. 8). This is a first-order phase transition between the thin and thick films, adsorbed at the wall. The prewetting transition meets the liquid-vapor coexistence curve at T, which in fact is a triple point (solid circle), where three phases coexist. At the prewetting critical point... 

Equations (3)-(5) are valid only for ideal, smooth, homogeneous, impermeable, and nondeformable surfaces. Because textile fibers do not have such ideal surfaces, their wetting phenomena are more complicated. In addition, the prediction of wetting phenomena (e.g., spreading) from wetting energetics is difficult because a direct method for determining ysv a term found in Eqs. (3), (4), and (6), is not available. It is more convenient to use the forces in balance at a three-phase (solid, liquid, vapor) boundary as an indication of wettability. 

Any given pure substance may exist in three states as a solid, as liquid or as vapor. Under certain conditions, it may exist as a combination of any two phases and changes in conditions may alter the proportions of the two phases. There is also a condition where all three phases may exist at the same time. This is known as the triple point. Water has a triple point at near 32°F and 14.696 psia. Carbon dioxide may exist as a vapor, a liquid and solid simultaneously at about minus 69.6°F and 75 psia. Substances under proper conditions may pass directly from a solid to a vapor phase. This is known as sublimation. 

Point A on a phase diagram is the only one at which all three phases, liquid, solid, and vapor, are in equilibrium with each other. It is called the triple point. For water, the triplepoint temperature is 0.01°C. At this temperature, liquid water and ice have the same vapor pressure, 4.56 mm Hg. 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

Systems in which the saturated vapor pressure curve cuts a three-phase line of liquid + liquid + gas at a second quaternary point (solid + liquid + liquid + gas). Such systems have the first (or normal) quaternary point (solid + solid + liquid + gas) at lower temperatures and pressures (Fig. 13). Examples, ethane +... 

For a pure substance, having three phases in equilibrium results in a triple point that is invariant. When pure solid, liquid, and gaseous water are in equilibrium, the temperature is fixed at a value of 273.16 K, and the pressure of the gas is fixed at the vapor pressure value (0.6105 kPa). 

Intermolecular forces are responsible for the existence of several different phases of matter. A phase is a form of matter that is uniform throughout in both chemical composition and physical state. The phases of matter include the three common physical states, solid, liquid, and gas (or vapor), introduced in Section A. Many substances have more than one solid phase, with different arrangements of their atoms or molecules. For instance, carbon has several solid phases one is the hard, brilliantly transparent diamond we value and treasure and another is the soft, slippery, black graphite we use in common pencil lead. A condensed phase means simply a solid or liquid phase. The temperature at which a gas condenses to a liquid or a solid depends on the strength of the attractive forces between its molecules. 

FIGURE 7.25 The variation of the (molar) Gibbs free energy with temperature for three phases of a substance at a given pressure. The most stable phase is the phase with lowest molar Gibbs free energy. We see that, as the temperature is raised, the solid, liquid, and vapor phases in succession become the most stable. 

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. 

In Fig. 8.8, we see that sulfur can exist in any of four phases two solid phases (rhombic and monoclinic sulfur), one liquid phase, and one vapor phase. There are three triple points in the diagram, where various combinations of these phases, such as monoclinic solid, liquid, and vapor or monoclinic solid, rhombic solid, and liquid, coexist. However, four phases in mutual equilibrium (such as the vapor, liquid, and rhombic and monoclinic solid forms of sulfur, all in mutual equilibrium) in a one-component system has never been observed, and thermodynamics can be used to prove that such a quadruple point cannot exist. 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

Alloys are classified broadly in two categories, single-phase alloys and multiple-phase alloys. A phase is characterized by having a homogeneous composition on a macroscopic scale, a uniform structure, and a distinct interface with any other phase present. The coexistence of ice, liquid water, and water vapor meets the criteria of composition and structure, but distinct boundaries exist between the states, so there are three phases present. When liquid metals are combined, there is usually some limit to the solubility of one metal in another. An exception to this is the liquid mixture of copper and nickel, which forms a solution of any composition between pure copper and pure nickel. The molten metals are completely miscible. When the mixture is cooled, a solid results that has a random distribution of both types of atoms in an fee structure. This single solid phase thus constitutes a solid solution of the two metals, so it meets the criteria for a single-phase alloy. 

Water is the only form of matter occurring abundantly in all three phases (or states) solid, liquid, and gas (or vapor) (Fennema, 1996). Temperature and pressure determine the phase of water, as well as the type(s) and velocity(ies) of water molecule motion. A basic phase diagram (moderate pressure-temperature range) for pure water is shown in Figure 7. Given the... 

The chemistry of soil is contained in the chemistry of these three phases. For the solid phase, the chemistry will depend on the amount and type of surface available for reaction. In the liquid phase, solubility will be the most important characteristic for determining the chemistry occurring. In the gaseous phase, gas solubility and the likelihood that the component can be in the gaseous form (i.e., vapor pressure) will control reactivity. 

---