Solid thermodynamic

In the preceding Sect. I have tried to illustrate the problems and developments of polymer stereochemistry from both the historical and logical points of view. A clear connection exists between synthetic and stmctural aspects For the solution of problems yet unsolved an interdisciplinary approach is required involving not only polymer chemistry but also spectroscopy, crystallography, statistical thermodynamics, solid state physics, and so on. 

In Fig. 11.3, we made a comparison between the binodals obtained from dynamic Monte Carlo simulations (data points) and from mean-field statistical thermodynamics (solid lines). First, one can see that even with zero mixing interactions B = 0, due to the contribution of Ep, the binodal curve is still located above the liquid-solid coexistence curve (dashed lines). This result implies that the phase separation of polymer blends occurs prior to the crystallization on cooUng. This is exactly the component-selective crystallizability-driven phase separation, as discussed above. Second, one can see that, far away from the liquid-solid coexistence curves (dashed lines), the simulated binodals (data points) are well consistent... 

Solid Oxide Fuel Cells, Thermodynamics Solid State Electrochemistry, Electrochemistry Using Solid Electrolytes... 

If above relatiOTi can not be determined, it is sometimes possible to deduce activity coefficient values for components in solid phase based on thermodynamic solid solutimi model. For example, if symmetrical solvus (Fig. 1.2) exists for a binary system, regular solution model could be applicable to the estimation of activity coefficients and other thermodynamic parameters values of solid solution... 

Many compounds have the ability to crystallize with different crystal structures, a phenomenon called polymorphism. Each polymorph is in fact a different thermodynamic solid state and crystal polymorphs of the same compound exhibit different physical properties, such as dissolution rate, shape (angles between facets and facet growth rates), melting point, etc. For this reason, polymorphism is of major importance in industrial manufacture of crystalline products. 

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

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. 

The equations of electrocapillarity become complicated in the case of the solid metal-electrolyte interface. The problem is that the work spent in a differential stretching of the interface is not equal to that in forming an infinitesimal amount of new surface, if the surface is under elastic strain. Couchman and co-workers [142, 143] and Mobliner and Beck [144] have, among others, discussed the thermodynamics of the situation, including some of the problems of terminology. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

Density functional theory from statistical mechanics is a means to describe the thermodynamics of the solid phase with information about the fluid [17-19]. In density functional theory, one makes an ansatz about the structure of the solid, usually describing the particle positions by Gaussian distributions around their lattice sites. The free... 

It turns out to be considerably easier to obtain fairly precise measurements of a change in the surface free energy of a solid than it is to get an absolute experimental value. The procedures and methods may now be clear-cut, and the calculation has a thermodynamic basis, but there remain some questions about the physical meaning of the change. This point is discussed further in the following material and in Section X-6. 

Equations X-12 and X-13 thus provide a thermodynamic evaluation of the change in interfacial free energy accompanying adsorption. As discussed further in Section X-5C, typical values of v for adsorbed films on solids range up to 100 ergs/cm. ... 

Koopal and co-workers [186] have extended this thermodynamic analysis to investigate the competitive wetting of a solid by two relatively immiscible liquids. They illustrate the tendency of silica to be preferentially wet by water over octane, a phenomenon of importance in oil reservoirs. 

While a thermodynamic treatment can be developed entirely in terms of f(P,T), to apply adsorption models, it is highly desirable to know on a per square centimeter basis rather than a per gram basis or, alternatively, to know B, the fraction of surface covered. In both the physical chemistry and the applied chemistry of the solid-gas interface, the specific surface area is thus of extreme importance. 

The situation is more complex for rigid media (solids and glasses) and more complex fluids that is, for most materials. These materials have finite yield strengths, support shears and may be anisotropic. As samples, they usually do not relax to hydrostatic equilibrium during an experiment, even when surrounded by a hydrostatic pressure medium. For these materials, P should be replaced by a stress tensor, <3-j, and the appropriate thermodynamic equations are more complex. 

Grzegory I, Jun J, Bockowski M, Krukowski S, Wroblewski M, Lucznik B and Porowski S 1995 lll-V nitrides-thermodynamics and crystal growth at high N2 pressure J. Phys. Chem. Solids 56 639... 

Fig. 6. Free energies of hydration calculated, for a series of polar and non-polar solute molecules by extrapolating using (3) from a 1.6 ns trajectory of a softcore cavity in water plotted against values obtained using Thermodynamic Integration. The solid line indicates an ideal one-to-one correspondence. The broken line is a line of best fit through the calculated points.

The solvation thermodynamics have been interpreted in a classical study by Frank and Evans in terms of the iceberg model . This model states that the water molecules around an nonpolar solute show an increased quasi-solid structuring. This pattern would account for the strongly negative... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

It has long been known that the adsorption of a gas on a solid surface is always accompanied by the evolution of heat. Various attempts have been made to arrive at a satisfactory thermodynamic analysis of heat of adsorption data, and within the past few years broad agreement has been achieved in setting up a general system of adsorption thermodynamics. Here we are not concerned with the derivation of the various thermodynamic functions but only with the more relevant definitions and the principles involved in the thermodynamic analysis of adsorption data. For more detailed treatments, appropriate texts should be consulted. " ... 

To provide a rational framework in terms of which the student can become familiar with these concepts, we shall organize our discussion of the crystal-liquid transition in terms of thermodynamic, kinetic, and structural perspectives. Likewise, we shall discuss the glass-liquid transition in terms of thermodynamic and mechanistic principles. Every now and then, however, to impart a little flavor of the real world, we shall make reference to such complications as the prior history of the sample, which can also play a role in the solid behavior of a polymer. 

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

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