Condensed Phases —Solids

The connections between molecular level characteristics and the macroscopic properties of materials are not always easy to discern, but current research in materials science and computer modeling are advancing our ability to make them. In this chapter, we will introduce ideas that can be used to infer the molecular scale explanations of why materials behave the way they do. Along the way, we will be able to answer at least some of the questions we have raised about carbon-based materials and the emerging field of nanotechnology. 

The various forms of carbon that we have just described share one important physical property—they are all solids at normal laboratory temperature and pressure. The vast majority of elements are solids under such conditions. What factors contribute to the stability of condensed phases Forces between atoms and molecules certainly play a role in the answer to this question, but the basic structure of condensed phases also contributes to an understanding of their stability. We will begin our treatment from this structural perspective. 

Now let s shift our thinking firom marbles to atoms. The packing efficiency of the atoms will clearly be related to the density of a material because an increase in the packing efficiency will put more atoms into the same volume. Experiments on 

The term condensed phases refers to both solids and liquids. 

Nonspherical molecules can also be packed Into crystals, but we will limit our discussion to spherical atoms for the sake of simplicity. 

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Cartesian space coordinates V, y, z Condensed phase (solid or liquid) cd... 

Assume that at the isothermal temperature of interest the following stable condensed phases (solid or liquid) can be formed M, MO, MS, MSO4. From the Phase Rule it is clear that the maximum number of condensed phases in contact with each other can be three, in addition to the gaseous phase (SO2 and O2). Following the suggestion of Kellog and Basu , the... 

As pointed out by Cook (Ref 2), there is no unequivocal method of computing A for expls that produce appreciable amts of condensed phase (solid) products. Cook suggests the use of an empirical relation... 

The defining equation for fugacity fc in a condensed phase (solid or liquid) is the same as in the gas phase... 

The condensed phase (solid or liquid) is considered as a general phase that will vaporize to a gaseous fuel with a mass fraction TFo, and can possibly form char with properties designated by ()c. The virgin fuel properties are designated without any subscript. 

Compressing ammonia gas under high pressure forces the molecules into close proximity. In a normal gas, the separation between each molecule is generally large - approximately 1000 molecular diameters is a good generalization. By contrast, the separation between the molecules in a condensed phase (solid or liquid) is more likely to be one to two molecular diameters, thereby explaining why the molar volume of a solid or liquid is so much smaller than the molar volume of a gas. 

It is essential that all PSs are multiphase. The easiest case to handle is the biphase system consisting of a condensed phase (solid) and a void inside porous particles or between consolidated ensembles of nonporous or porous particles. The void occupies a part of the volume, s, which is referred to as porosity. The other part of a PS volume is equal to ri=(l -e), and is termed density of packing. It is filled with the condensed phase (see Section 9.4). Generally, PSs can include various condensed phases of different structure, including combinations of solid(s) and liquid(s). 

This part includes a discussion of the main experimental methods that have been used to study the energetics of chemical reactions and the thermodynamic stability of compounds in the condensed phase (solid, liquid, and solution). The only exception is the reference to flame combustion calorimetry in section 7.3. Although this method was designed to measure the enthalpies of combustion of substances in the gaseous phase, it has very strong affinities with the other combustion calorimetric methods presented in the same chapter. 

In general, an electrostatic potential arises between two phases when they are brought into contact. We deal with the electrostatic potential in two condensed phases being in contact. The electrostatic inner potential, of a condensed phase (solid or liquid) is given by the sum of the outer potential, V(o>, associated with the electric charge, a, of the condensed phase and the surface potential, X(dip associated with the surface dipole as shown in Eqn. 4—1 and Fig. 4-5 ... 

Detonation and explosion in condensed phase (solid or liquid as opposed to gas, dust or vapor) explosives were briefly discussed in Vol 3 of our Encycl, p C495-R, under "Condensed Explosives , but the following comments of C.G. Dunkle (Ref 22) may be added. His discussion is based mainly on the information obtained at the lOthSympCombstn (1964) and other Symposiums... 

If the gas phase activity of the host is controlled by the presence of a pure condensed phase, solid or liquid, the equilibrium between host and guest in a stoichiometric clathrate can be described in terms of the gas phase pressure of the guest. This is, in effect, a vapor pressure for the guest. At higher pressures the guest will condense to form clathrate, and at lower pressures the clathrate will decompose. Temperature variation of this pressure will follow the Clapeyron equation which, with the usual assumptions (ideal gas behavior of the vapor and negligible volume of the condensed phase), reduces to the Clausius-Clapeyron equation ... 

For a pure substance in condensed phase (solid or liquid) their vapour pressure is taken to be related to their activities. When we measure equilibrium vapour pressure, the vapour and the solid (or liquid) are at equilibrium and hence the activities of the constituent in both phases are the same. Hence, the activity of the vapour phase would represent the activity of the solid or liquid. 

Surfaces can be broadly described as the boundary between a condensed phase (solid, hquid) of matter and another material (solid, gas, or liquid). Surfaces are encountered in most aspects of life, from the contact of a car s wheel with the pavement (solid-solid interface) to the evaporation of a water droplet (liquid-gas interface). Equally as important, surfaces play a fundamental role in many chemical processes including catalysis, thin film coatings, and electrochemical oxidation and reduction. 

The surface of a condensed phase (solid or liquid) is usually coordinately unsaturated, and this generally leads to adsorption of chemical species coming into contact with it. This process produces an enrichment in concentration of the adsorbed substance compared to its concentration in the adjoining bulk phases. The material capable of being adsorbed is usually called the adsorptive, while the material in the adsorbed state is called the adsorbate. In cases of chemisorption, adsorptive and adsorbate may be chemically different species (e.g., in dissociative adsorption). When adsorption occurs at the interface between a fluid phase and a solid, the solid is usually called the adsorbent. 

In this chapter we shall be concerned with condensed phases (solid or liquid) consisting of a single component solutions will be studied in later chapters. 

Condensed phase in the cell State of condensed phase Solid compounds Temperature range in K Gaseous species Ref./Year ... 

Several points are worth emphasizing. The first point is mass balance. The total amount of each element is conserved in the chemical equilibrium calculations. Thus the abundances of all gases and all condensed phases (solids and/or liquids) sum to the total elemental abundance - no less and no more. The second point is that chemical equilibrium is completely independent of the size, shape, and state of aggregation of condensed phases - a point demonstrated by Willard Gibbs over 130 years ago. Finally, the third point is that chemical equilibrium is path independent. Thus, the results of chemical equilibrium calculations are independent of any particular reaction. A particular chemical reaction does not need to be specified because all possible reactions give the same result at chemical equilibrium. This is completely different than chemical kinetic models where the results of the model are critically dependent on the reactions that are included. However, a chemical equilibrium calculation does not depend on kinetics, is independent of kinetics, and does not need a particular list of reactions. This point may seem obvious, but is often misunderstood. 

Atoms, groups of atoms, ions, molecules, macromolecules, and particles always are subject to forces between them. These interaction forces may cause chemical reactions to occur, i.e., cause the formation of other molecular species, but they are also responsible for the existence of condensed phases (solids and liquids), for adherence of a liquid to a solid surface, or for aggregation of particles in a liquid. In short, all structures form because of interaction forces. Generally, formation of a structure causes a decrease in entropy, and this may counteract the tendency of formation, depending on its magnitude compared to that of the energy involved. 

The integration of the standard free energy of reaction in this equation is best done after breaking it up into separate free energy terms for each of the main types of physical states involved in reactions, i.e., condensed phases (solids and liquids), gases and solutes (usually aqueous in our cases). Thus we can write... 

Condensed phases—solids and liquids—must have surfaces or interfaces. The suit of an astronaut maneuvering in outer space represents a solid-vacuum interface (Fig-... 

Although commonly thought of as a single process, the deposition of thin films by thermal evaporation consists of several distinguishable steps (i) transformation of the condensed phase, solid or liquid, into the gaseous state (ii) vapor molecules traversing the space between the source and the substrate and (iii) condensation of the vapor upon arrival on the substrate. 

Morse potential energy cnrve of a given condensed phase, solid or liqnid [11]. The potential energy of interaction V is plotted against the mean intermolecnlar distance d. (Reprodnced with permission of the copyright owner, Oxford University Press, Oxford, UK.)... 

For reactions in a condensed phase (solid or liquid solution) it is often convenient to. .consider the reactants in the initial and final states at a fixed finite separation, as making small vibrations around the positions of minimum potential energy due to the interactions with the medium. Therefore, the quasiclassical approximation for this motion, assumed to correspond to the reaction coordinate, may be used for the same reason as for a unimolecular gas phase reaction which occurs at high presure. 

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