Equilibria phases concerned

In the previous section, non-equilibrium behaviour was discussed, which is observed for particles with a deep minimum in the particle interactions at contact. In this final section, some examples of equilibrium phase behaviour in concentrated colloidal suspensions will be presented. Here we are concerned with purely repulsive particles (hard or soft spheres), or with particles with attractions of moderate strength and range (colloid-polymer and colloid-colloid mixtures). Although we shall focus mainly on equilibrium aspects, a few comments will be made about the associated kinetics as well [69, 70]. 

Low-temperature solid-state synthesis is preferred in most cases, where appropriate, for obvious reasons such as energy and cost economy and process safety or for critical concerns regarding the accessibility of compounds that are stable only at low temperatures or non-equilibrium phases, i.e., compounds thermodynamically unstable with respect to the obtained phase (e.g., a ternary instead of binary phase). The use of low-temperature eutectics as solvents for the reactants, hydrothermal growth... 

Thus, looking at the equilibrium phase diagram and knowing the physical-chemical properties of the elemets A and B and their compounds, it is possible to draw certain conclusions concerning the sequence of compound-layer formation in a multiphase binary system. It must be remembered, however, that any predictions based on the above-mentioned or other criteria hitherto proposed are only weak correlations, rather than the precise rules. As both the researcher and technologist are always interested in knowing the sequence of occurrence of chemical compounds in a particular reaction couple, they can hardly be satisfied even with a correlation valid in 99 out of 100 cases, because it remains unknown whether this couple falls in the range of those 99 or is the only exception. Further theoretical work in this direction is badly needed. 

This chapter focuses mainly on the microstructures encountered in mixtures of oil and water with surfactants (mostly nonionic from the family of ethoxylated alcohols, designated as CjEj or Q(EO) , where i and j are the number of carbon atoms in the alkyl chain and the number of ethylene oxide (EO) groups of the polar head, respectively, of the surfactant molecule) and sometimes in the presence of alcohols. However, a short survey concerning the investigation of the equilibrium phase behavior of these systems seems to be in order. 

The equilibrium phase diagram of RDX has been determined to 7.0 GPa and 573K. Three solid phases, a, p and 7, have been found and their stability fields delineated. The pressure dependence of the melting point has also been defined. The ot and P phases were found to thermally decompose in the P, T regime of concern here. Pressure enhances the rate of decomposition of the a phase and probably reacts through a bimolecular-type mechanism. The activation volume, AV, for the reaction is -5.6 cm /mole and is temperature independent. The... 

Unless other statements have been made by the authors, it is assumed that the phases concerned are homogeneous and in a state of equihbrium. Where the state of equilibrium had not been attained or where metastable, unstable or martensitic phases or heterogeneous substances had been considered, this is referred to in the second last column or in an additional footnote. 

The molecular mechanics calculations discussed so far have been concerned with predictions of the possible equilibrium geometries of molecules in vacuo and at OK. Because of the classical treatment, there is no zero-point energy (which is a pure quantum-mechanical effect), and so the molecules are completely at rest at 0 K. There are therefore two problems that I have carefully avoided. First of all, I have not treated dynamical processes. Neither have I mentioned the effect of temperature, and for that matter, how do molecules know the temperature Secondly, very few scientists are interested in isolated molecules in the gas phase. Chemical reactions usually take place in solution and so we should ask how to tackle the solvent. We will pick up these problems in future chapters. 

The 2nd law is true only statistically and does not apply to individual particles nor to a small number of particles, i.e. thermodynamics is concerned with bulk properties of systems. Thermodynamics thus has many limitations, but is particularly valuable in defining the nature and structure of phases when equilibrium (a state that does not vary with time) has been attained thermodynamics provides no information on the rate at which the reaction proceeds to equilibrium, which belongs to the realm of chemical kinetics. 

The fundamental idea of this procedure is as follows For a system of two fluid phases containing N components, we are concerned with N — 1 independent mole fractions in each phase, as well as with two other intensive variables, temperature T and total pressure P. Let us suppose that the two phases (vapor and liquid) are at equilibrium, and that we are given the total pressure P and the mole fractions of the liquid phase x, x2,. .., xN. We wish to find the equilibrium temperature T and the mole fractions of the vapor phase yu y2,. .., yN-i- The total number of unknowns is N + 2 there are N — 1 unknown mole fractions, one unknown temperature, and two unknown densities corresponding to the two limits of integration in Eq. (6), one for the liquid phase and the other for the vapor phase. To solve for these N +2 unknowns, we require N + 2 equations of equilibrium. For each component i we have an equation of the form... 

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