SOLIDS, AND PHASE TRANSITIONS

In addition to just knowing these phases, you will have to know the different theories and their implications, and how to work with some of the formulas involved. We will review the different kinds of molecular interactions that dictate the phase characteristics of molecules. The phase diagram that is discussed in this chapter is also important from the MCAT point of view. 

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The objective of statistical mechanics is generally to develop predictive tools for computation of properties and local structure of fluids, solids and phase transitions from the knowledge of the nature of molecules comprising the systems as well as intra and intermolecular interactions. 

Fig. 4. DSC-trace of octamethyltetra-siloxane showing the melting transition at 298 K and a solid state phase transition at 262 K. Heating rate lOK/ min. (Ref. 10))...

Vapor Pressure Equations of Adamantane and Diamantane for Eiquid-Vapor and Solid-Vapor Phase Transitions... 

This methodology developed to observe water freeze-thaw in concrete materials, may be used quite generally to observe solid-liquid phase transitions in many different materials of industrial and technological interest. The method could be also applied to other problems involving freezing and thawing of water in confined pores. 

In this second edition the text has been revised and new scientific findings have been taken into consideration. For example, many recently discovered modifications of the elements have been included, most of which occur at high pressures. The treatment of symmetry has been shifted to the third chapter and the aspect of symmetry is given more attention in the following chapters. New sections deal with quasicrystals and other not strictly crystalline solids, with phase transitions and with the electron localization function. There is a new chapter on nanostructures. Nearly all figures have been redrawn. 

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. 

The book covers a variety of questions related to orientational mobility of polar and nonpolar molecules in condensed phases, including orientational states and phase transitions in low-dimensional lattice systems and the theory of molecular vibrations interacting both with each other and with a solid-state heat bath. Special attention is given to simple models which permit analytical solutions and provide a qualitative insight into physical phenomena. 

The variation of the phase transition temperature with pressure can be calculated from the knowledge of the volume and enthalpy change of the transition. Most often both the entropy and volume changes are positive and the transition temperature increases with pressure. In other cases, notably melting of ice, the density of the liquid phase is larger than of the solid, and the transition temperature decreases... 

The preceding paragraphs illustrate that analogies between point defects in a crystal and solute molecules in a solution have been used previously but in a fairly elementary way. However, the implications of the existence of such analogies in the formulation of the statistical mechanics of interacting defects has not been considered in detail apart from an early paper by Mayer,69 who was interested primarily in the relation of defect interactions, to the solid-liquid phase transition in crystals with short-range forces. The... 

Bicyclopropylidene (1) with its melting point of -10.4°C undergoes a solid state phase transition at -40.2°C with AH = 0.038 kcal/mol, and the two polymorphous structures possess different structural parameters (Table 2) [85,86]. A similar behavior was also observed for me50-bis(bicyclopropylidenyl) meso-87 [56]. The structure of meso-S represents essentially a combination of the two bicyclopropylidene units the central bond length h (1.494 A, Table 2) which is practically the same as that in bicyclopropyl (1.492 A) indicates the absence of any strong electronic interaction between the two bicyclopropylidene units in meso-S which should thus react independently of each other. 

Fig. 5 The typical DSC diagram for solid state phase transition with latent heat red plot) or without latent heat blue plot). The scale is not the same in general the curve for a second-order transition blue plot) is associated with smaller changes of heat capacity (and therefore more difficult to detect)...

Mnyukh Yu (2001) Fundamentals of solid state phase transitions, ferromagnetism and ferroelectricity. First Books New York... 

Many phenomena such as dislocations, electronic structures of polyacetylenes and other solids, Josephson junctions, spin dynamics and charge density waves in low-dimensional solids, fast ion conduction and phase transitions are being explained by invoking the concept of solitons. Solitons are exact analytical solutions of non-linear wave equations corresponding to bell-shaped or step-like changes in the variable (Ogurtani, 1983). They can move through a material with constant amplitude and velocity or remain stationary when two of them collide they are unmodified. The soliton concept has been employed in solid state chemistry to explain diverse phenomena. 

In the Chapter 7, formation of monolayers in air-liquid interfaces and the resulting film pressure and phase transitions are discussed. This chapter also includes a brief discussion of adsorption on solid surfaces from solutions. 

On the basis of the calibration by melting points and phase transitions, a number of shift thermometers have been developed for solid-state NMR spectroscopy in various temperature ranges. Wehrle et al. 144), for example, used the line splitting in the N CP/MAS NMR spectrum of the organic dye molecule tetra-methyldibenzotetraaza annulene (TTAA) in the temperature range 123—405 K. A high-temperature shift thermometer for temperatures of up to 790 K was developed by van Moorsel et al. 40) on the basis of Sn MAS NMR spectroscopic... 

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