Solid-vapor systems

All the liquid freezes and some vapor remains (i.e., a solid-vapor system at equilibrium). The energy released (heat of fusion) would then go to heat the system—Since 335 J/g are released, and Cp 4.22 J/g°C, too much energy is released for only the solid and vapor to be present. 

This report is concerned with contact angle hysteresis and with a closely related quantity referred to as "critical line force (CLF)." More particularly, it is concerned with the relationship between contact angle hysteresis and the magnitude of the contact angle itself. Two sets of liquid-solid-vapor systems have been investigated to provide the experimental data. One set consists of Teflon [poly(tetrafluoroethylene), Du Pont] and a series of liquids forming various contact angles at the Teflon-air interface. The second set consists of polyethylene and a similar series of liquids. In neither case was the ratio of air to test liquid vapor at the boundary line controlled, but it can be assumed that the ambient vapor phase operative in all the systems was close to an equilibrium mixture. 

The power of the phase rule is immediately evident in that the solid/liquid/vapor system is characterized by the same amount of variance as was the solid/vapor system. As a result, the arguments made regarding the pressure-temperature curves of the former system can be extended to apply to the latter system, except that the liquid phase takes the place of the anhydrate phase. 

The thermodynamic analysis of the CO2-N2 solid-vapor system has been reported previously and compared with the experimental data for this system to 100 atm pressure P]. Consequently, the equations and methods of solution will not be discussed in detail here. 

In Section 6.3.1, we cover external forces, specifically gravitational, electrical and centrifugal forces inertial force is also included here. In Section 6.3.2, chemical potential gradient driven equilibrium separation processes involving vapor-liquid, liquid-liquid, solid-melt and solid-vapor systems are considered the processes are flash vaporization, flash devolatilization, batch distillation, liquid-liquid extraction, zone melting, normal freezing and drying. Section 6.3.3 illustrates a number of membrane separation processes in the so-called dead-end filtration mode achieved when the feed bulk flow is parallel to the... 

We consider here the role of bulk flow parallel to the direction of the chemical potential gradient based force in phetse-equilibrium based open two-phase systems. Vapor-liquid systems of flash vaporization, flash devolatilization and batch distillation are considered first, followed by a liquid-liquid system for extraction. Solid-liquid systems for zone melting and normal freezing are studied thereafter to explore how bulk flow parallel to the force direction is essential to considerable purifleation of solid systems followed by solid-vapor systems as in drying. 

Young and Crowell [16] have listed the molecular areas of many adsorbates. In practice, for consistency, the areas are corrected on the basis of the area occupied by a nitrogen molecule at liquid nitrogen temperature. However, the area occupied by a molecule may depend upon the nature of the surface and calibration for that particular solid-vapor system may be necessary [183]. 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

Some solids inlet systems are also suitable for liquids (solutions) if the sample is first evaporated at low temperatures to leave a residual solid analyte, which must then be vaporized at higher temperatures. 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

In pharmaceutical systems, both heat and mass transfer are involved whenever a phase change occurs. Lyophilization (freeze-drying) depends on the solid-vapor phase transition of water induced by the addition of thermal energy to a frozen sample in a controlled manner. Lyophilization is described in detail in Chapter 16. Similarly, the adsorption of water vapor by pharmaceutical solids liberates the heat of condensation, as discussed in Chapter 17. 

A number of new approaches to the way in which precursors are delivered to a substrate have been developed in which the precursor is dispersed into the gas phase without having to be volatile. These new systems each have their own advantages for a particular precursor depending on its physical state. Most of the delivery systems in use can be classified as one of the following a liquid injection system (LIS), where a precursor is vaporized directly from a neat liquid or solution containing the precursors a solid delivery system (SDS), where the precursor is vaporized... 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

The result obtained here is considered very valuable foi optimizing the gas-solid photocatalytic system for the purification of the airstream polluted with benzene the performance can be improved by the additior of water vapor to the airstream. 

When we consider a one-component, two-phase system, of constant mass, we find similar relations. Such two-phase systems are those in which a solid-solid, solid-liquid, solid-vapor, or liquid-vapor equilibrium exists. These systems are all univariant. Thus, the temperature is a function of the pressure, or the pressure is a function of the temperature. As a specific example, consider a vapor-liquid equilibrium at some fixed temperature and in a state in which most of the material is in the liquid state and only an insignificant amount in the vapor state. The pressure is fixed, and thus the volume is fixed from a knowledge of an equation of state. If we now add heat to the system under the condition that the temperature (and hence the pressure) is kept constant, the liquid will evaporate but the volume must increase as the number of moles in the vapor phase increases. Similarly, if the volume is increased, heat must be added to the system in order to keep the temperature constant. The change of state that takes place is simply a transfer of matter from one phase to another under conditions of constant temperature and pressure. We also see that only one extensive variable—the entropy, the energy, or the volume—is necessary to define completely the state of the system. 

The thermodynamic approach applied here considers the adsorbent plus the adsorbed gas, or vapor, as a solid solution (system aA). Applying this description, it is feasible to get the fundamental thermodynamic equation for the aA system [2,15,16,25]... 

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