Bulk Thermodynamic Properties

Recent work has shown 103) that for alkali halides the Debye characteristic temperature is not very sensitive to volume changes produced by thermal expansion. This probably indicates that, in general, volume changes of an adsorbent will not markedly affect its bulk thermodynamic properties. 

Diakonov, G.G. (1998) Thermodynamic properties ofiron oxides and hydroxides. II. Estimation of the surface and bulk thermodynamic properties of ordered and disordered arrangements (y-Fe203). Eur. J. Min. 10 17-29... 

Diakonov, I. Khodakovsky I. Schott, J. Sergeeva, E. (1994) Thermodynamic properties of iron oxides and hydroxides. I. Surface and bulk thermodynamic properties of goethite (a-FeOOH) up to 500 K. Fur. J. Min. 6 967-983... 

Hygroscopic behavior has been well characterized in laboratory studies for a variety of materials, for example, ammonium sulfate (Figure 14), an important atmospheric material. When an initially dry particle is exposed to increasing RH it rapidly accretes water at the deliquescence point. If the RH increases further the particle continues to accrete water, consistent with the vapor pressure of water in equilibrium with the solution. The behavior of the solution at RH above the deliquescence point is consistent with the bulk thermodynamic properties of the solution. However, when the RH is lowered below the deliquescence point, rather than crystallize as would a bulk solution, the material in the particle remains as a supersaturated solution to RH well below the deliquescence point. The particle may or may not undergo a phase transition (efflorescence) to give up some or all of the water that has been taken up. For instance, crystalline ammonium sulfate deliquesces at 79.5% RH at 298 K, but it effloresces at a much lower RH, 35% (Tang and Munkelwitz, 1977). This behavior is termed a hysteresis effect, and it can be repeated over many cycles. 

The properties of slags are dependent not only upon chemical composition, but upon other factors also. The most pronounced deviations from additivity rules based on composition arise in the estimation of those properties which involve ionic transport eg. electrical conductivity. However surface tension values estimated from additivity rules are frequently in error as bulk thermodynamic properties do not apply at surfaces. Furthermore, virtually all the physical properties of slags are, to some extent, dependent upon the structure of the slag (viz. the length of silicate chains, degree of crystallinity etc.) thus estimation procedures have to accommodate these structural factors, where possible. 

Statistical thermodynamics uses statistical arguments to develop a connection between the properties of individual molecules in a system and its bulk thermodynamic properties. For instance, consider a mole of water molecules at 25° C and standard pressure (1 bar). The thermodynamic state of the system has been defined on the basis of the number of molecules, the temperature, and the pressure. In order to relate the macroscopic thermodynamic properties such as U, G, H and A to the properties of the individual molecules, one would have to solve the Schrodinger wave equation (SWE) for a system composed of 6 x 10 interacting water molecules. This is an impossible task at present but if it were possible, one would obtain a wave function, I y, and an energy, 6)-, for the system. Moreover,... 

Lattice defects may influence the rates of mineral dissolution in two ways (1) by changing the bulk thermodynamic properties and (2) by creating sites of accelerated dissolution on the solid surface. Strain and core energies associated with dislocations contribute insignificantly to the total energy of minerals. For instance, even with the extremely high dislocations density of 1011 cm"2, the free energy of calcite is increased by only 80 J mol", which corresponds to a 25°C activity of 1.04. The same features are observed for quartz and silicate minerals. 

The classical theory of homogeneous nucleation dates back to pioneering work by Volmer and Weber (1926), Farkas (1927), Becker and Doring (1935), Frenkel (1955), and Zeldovich (1942). The expression for the constrained equilibrium concentration of clusters (11.57) dates back to Frenkel. The classical theory is based on a blend of statistical and thermodynamic arguments and can be approached from a kinetic viewpoint (Section 11.1) or that of constrained equilibrium cluster distributions (Section 11.2). In either case, the defining crux of the classical thoery is reliance on the capillarity approximation wherein bulk thermodynamic properties are used for clusters of all sizes. 

Basic questions of the equilibrium theory of fluids are concerned with (1) an adequately detailed description of the emergence of a fluid phase from a solid or the transition between a hquid and its vapor, the phase transition problem, and (2) the prediction from first principles of the bulk thermodynamic properties of a fluid over the whole existence region of the fluid. We will consider primarily the second of these questions. All bulk thermodynamic properties of monatomic fluids follow from a knowledge of the equation of state. This chapter will review certain recent developments in the approximate elucidation of the equation of state of a particularly simple fluid, the classical hard sphere fluid. This fluid is composed of identical particles or molecules, obeying classical mechanical laws, which are rigid spheres of diameter a. Two such molecules interact with one another only when they collide elastically. 

At high enough temperatures the micropores of the high-surface-area catalyst may collapse by sintering or melting. It is therefore essential that the materials chemistry be understood and that compounds with the proper surface and bulk thermodynamic properties be chosen to maintain their thermal stability under diverse (oxidizing or reducing) reaction conditions. 

In this chapter, we apply some of the general principles developed heretofore to a study of the bulk thermodynamic properties of nonelectrolyte solutions. In Sec. 11-1 we discuss conventions for the description of chemical potentials in nonelectrolyte solutions and introduce the concept of an ideal component. In Sec. 11-2, we demonstrate how the concept of solution molecular weight can be introduced into thermodynamics in a natural fashion. Section 11-3 is devoted to a study of the properties of ideal solutions. In Sec. 11-4, we discuss the properties of solutions that can be considered to be ideal when they are dilute but are not necessarily ideal when they are more concentrated. In Sec. 11-5, regular solutions are defined and some of their properties are derived. Section 11-6 is devoted to a study of some of the approximations that prove useful in the derivation of the properties of real solutions. Finally, in Sec. 11-7, some of the experimental techniques utilized for the measurement of chemical potentials and activity coefficients of components in solution are described. 

Boltzmann made many other significant contributions to science, particularly in the area oi statistical mechanics, which is the derivation of bulk thermodynamic properties for large collections of atoms or molecules by using the laws of probability. For example, the molecular speed distributions shown in Figure 10.19 are derived by using statistical mechanics such plots are known as Maxu eU—Boltzmann distributions. 

If the system is not uniform but separated into two fluid phases then the convention of repeating coordinates is adequate for the calculation of bulk thermodynamic properties but not for the study of the interface which would be of irregular, ever-changing, and unidentifiable shape. A simple change of the boundary conditions leads to a much more useful configuration repetition of the coordinates is retained in the x and y directions, but the cell is bounded by reflecting walls at z = 0 and z = L. If now the simulation is started with a flat liquid surface in the x, y (or horizontal) plane, then the repetition of these coordinates tends to maintain its position. Other constraints can be added to enhance the stability. 

Of course, the use of the periodic boxmdary conditions adds additional unphysical constraints to the system which affect the frequency spectrum. An analysis of Lcdcrmann has demonstrated that only a layer extending from the boundary to the bulk is affected by the unphysical constraint the thickness of this layer is of the same order as the interaction length [13]. Therefore, the effect of the periodic boxmdary conditions on the bulk thermodynamic properties of the system disappears in the limit for V +oo, provided that the shape of S is regular (i.e., provided that the area of 9S increases with V as... 

Illustration of relative vapor pressure, Py/p , of water over concave liquid-vapor interface, calculated from Eq. 10 using K , = 18 cmVg, y v = 0.072 J/w and = 0, so K = - Va relative vapor pressure versus radius of pore (a) and magnitude of capillary pressure, / . (b). Dashed curves forpv/p < 0,7 indicate probable limit of applicability of bulk thermodynamic properties. 

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