Non-equilibrium structures

Phase diagrams are important. Whenever materials engineers have to report on the properties of a metallic alloy, or a ceramic, the first thing they do is reach for the phase diagram. It tells them what, at equilibrium, the structure of the alloy or ceramic is. The real structure may not be the equilibrium one, but equilibrium structure gives a base line from which other (non-equilibrium) structures can be inferred. 

These problems have of course different weights for the different metals. The high reactivity of the elements on the left-side of the Periodic Table is well-known. On this subject, relevant examples based on rare earth metals and their alloys and compounds are given in a paper by Gschneidner (1993) Metals, alloys and compounds high purities do make a difference The influence of impurity atoms, especially the interstitial elements, on some of the properties of pure rare earth metals and the stabilization of non-equilibrium structures of the metals are there discussed. The effects of impurities on intermetallic and non-metallic R compounds are also considered, including the composition and structure of line compounds, the nominal vs. true composition of a sample and/or of an intermediate phase, the stabilization of non-existent binary phases which correspond to real new ternary phases, etc. A few examples taken from the above-mentioned paper and reported here are especially relevant. They may be useful to highlight typical problems met in preparative intermetallic chemistry. 

The temporally and spatially resolved transient structures elucidated by UED include structures in radiationless transitions, structures in non-concerted organic reactions, structures in non-concerted organometallic reactions, structures of carbene intermediates, dynamic pseudorotary structures, non-equilibrium structures and conformational structures on complex energy landscapes, transient structures of surfaces and bulk crystals, and solid-to-... 

The surface of bulk block copolymer samples has been studied using TEM by Turturro et al. (1995). They report that non-equilibrium structures with lamellar and cylindrical microdomains oriented normal to the free surface can result from solvent casting, with a high evaporation rate. However, slower evaporation of solvent from their PS-PB diblocks resulted in the equilibrium conformation with domains parallel to the free surface. Perpendicular orientation of PS-PB lamellae at the free surface was observed earlier by Henkee et al. (1988) who studied thin films prepared by solvent casting. They observed that a reduction of this orientation occurs in favour of the parallel one on annealing the sample. 

The presence of both terminations might be explained by the nonequilibrium growth conditions the growing surface necessarily passes through non-equilibrium structures in order to fill the incomplete lower layers. A perfect Ni-terminated octopolar domain can be transformed to O-termination via incorporation of a half-monolayer of nickel and a half-monolayer of oxygen atoms. 

There is an important connection. Life developed under non-equilibrium conditions. Consider first an example. Far from equilibrium, you have chemical oscillations in which millions of millions of molecules change their color simultaneously. This type of coherence is possible only if there are long-range correlations. They occur only far from equilibrium. Similarly, biomolecules, with their complex structures, would be impossible to build in equilibrium conditions. They would have a negligible probability. This is no more so in far-from-equilibrium conditions. However, the detailed mechanism by which biomolecules appeared is still a controversial problem. But surely, biomolecules are non-equilibrium structures maintained from one generation to the next by self-replication. 

In addition to the equilibrium phase structures mentioned above, non-equilibrium surfactant phase structures exist thatare also finding applications in drug delivery. Vesicular forms of surfactants are generally formed by dispersing lamellar phases in an excess of water (or non-aqueous polar solvents such as ethylene glycol or dimethylformamide) or, in the case of reversed vesicles, in an excess of oil. With most surfactants, vesicles are non-equilibrium structures that will eventually re-equilibrate back into the lamellar phases from which they originated. Vesicles are structural analogs of liposomes (discussed later) they are approximately spherical structures and have the ability... 

BAM has been widely used for studying the formation and morphological features of condensed domains in the LE-LC coexistence region and to observe and analyze the phase diagrams of Langmuir monolayers ). Upon rapid compression of a monolayer across a phase transition, non-equilibrium structures like dense-... 

Crystallization in or from solution brings another variable, solvent selectivity, into play. If the solvent is selective for the crystalline block, it can swell the crystalline lamellae (Tm is obviously also reduced). In contrast, if the solvent is selective for the non-crystalline block, it can precipitate out of solution in a non-equilibrium structure. 

Mezzenga, R. 2007. Equilibrium and non-equilibrium structures in complex food systems. Food Hydrocolloids 21 674—682. 

These long relaxation times are responsible for non-equilibrium structures, generated by the... 

Efficient drug delivery systems based on liposomes need to possess a large number of special qualities. First, good colloidal, chemical, and biological stability is required. The fact that liposomes are non-equilibrium structures does not necessarily mean that they are unsuitable for drug delivery. On the contrary, a colloidally stable non-equilibrium structure is less sensitive to external changes than equilibrium structures, such as micelles. Hence, colloidally stable liposomes often work well in pharmaceutical applications. 

Related to the generation of nanocapsules discussed above, is the appearance of rings or particles with single holes in hybrid system consisting of hydrophobic iron oxide, organic solvent, and polymer, probably in combination with KPS as initiator (see anchoring effect, Sect. 3.2). The emergence of these non-equilibrium structures is attributed to a delicate interplay of phase separation, viscosity, and solvent evaporation [191,192]. 

Monte Carlo simulation results for the non-equilibrium and equilibrium d3oiamics of a glassy polymer melt are presented. When the melt is rapidly quenched into the supercooled state, it freezes on the time scale of the simulation in a non-equilibrium structure that ages physically in a fashion similar to experiments during subsequent relaxation. At moderately low temperatures these non-equilibrium effects can be removed completely. The structural relaxation of the resulting equilibrated supercooled melt is strongly stretched on all (polymeric) length scales and provides evidence for the time-temperature superposition property. 

Combining the results of all techniques involved in the analysis of the phase transitions which were observed in the blends, the diagram shown in Figure 9.25 was obtained. It also contains non-equilibrium structures, and the lines were drawn in these cases during a closely controlled thermal history (Figure 9.25 Table 9.2). 

The strain that hinders the motion in the amorphous phases is transmitted by the polymer molecules that traverse large parts of the sample and set up a global, non-equilibrium structure. If these strained molecules were immobilised during mechanical drawing of the sample, as is necessary in the production of films or fibres, the amorphous areas become oriented and reduce the entropy (degree of disorder). Because melting is governed by the entropy of fusion AS = AHIT and the heat of fusion, AH, is... 

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