Breaking phenomena structure

One is purely formal, it concerns the departure from symmetry of an approximate solution of the Schrodinger equation for the electrons (ie within the Bom-Oppenheimer approximation). The most famous case is the symmetry-breaking of the solutions of the Hartree-Fock equations [1-4]. The other symmetry-breaking concerns the appearance of non symmetrical conformations of minimum potential energy. This phenomenon of deviation of the molecular structure from symmetry is so familiar, confirmed by a huge amount of physical evidences, of which chirality (i.e. the existence of optical isomers) was the oldest one, that it is well accepted. However, there are many problems where the Hartree-Fock symmetry breaking of the wave function for a symmetrical nuclear conformation and the deformation of the nuclear skeleton are internally related, obeying the same laws. And it is one purpose of the present review to stress on that internal link. 

The break in curve 3 in Figure 7.14 is characteristic of this type of plot for soluble amphipathic molecules. Note that it appears in the experimental curves of Figure 7.15 also. The break is understood to indicate the threshold of micelle formation (see Chapter 1, Section 1.3a), known as the critical micelle concentration (see Chapter 8). We do not discuss this phenomenon any further since the next chapter is devoted entirely to micelles and related structures. 

The first interesting phenomenon we observe is the breaking of the smooth invariant circle picture when the node-periodic points on the circle become foci [Figs. 8(a) and 8(b)]. The basic structure of the trajectories remains the same, but the object we are now studying is no longer a well-defined circle ... 

As mentioned above, an area in which the concepts and techniques of statistical physics of disordered media have found useful application is the phenomenon of catalyst deactivation. Deactivation is typically caused by a chemical species, which adsorbs on and poisons the catalyst s surface and frequently blocks its porous structure. One finds that often reactants, products and reaction intermediates, as well as various reactant stream impurities, also serve as poisons and/or poison precursors. In addition to the above mode of deactivation, usually called chemical deactivation (2 3.), catalyst particles also deactivate due to thermal and mechanical causes. Thermal deactivation (sintering), in particular, and particle attrition and break-up due to thermal and mechanical causes, are amenable to modeling using the concepts of statistical physics of disordered media, but as already mentioned above the subject will not be dealt with in this paper. 

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