Graining Reversed

The assembly models discussed in the preceding sections are presumably the simplest ones that one can set up for co-operative supramolecular polymerization. Their advantage is the relatively small number of adjustable parameters and conceptual simplicity. Disadvantage is the lack of a detailed description of the processes that actually led to the assembly becoming nucleated and that are system specific, that is, that depend on the details of the molecules involved and how precisely they interact. 

In this particular example, estimates for both free energy parameters g and ga of the coarse-grained model are obtainable from more detailed molecular models albeit that strictly speaking they depend not only on the chemical composition and structure of the molecular building blocks but in principle also on the solvent properties. It is important to stress again for it is often ignored, the solvent molecules not only drive the assembly but have been shown to play an active role in structural reorganizations of supramolecular assemblies (Bouteiller et al., 2005 Jonkheijm et al., 2006). Ideally, their influence should not be absorbed in adjustable parameters as is almost always done. 

Much more sophisticated models are needed to explicitly deal with the role of the solvent and presumably the only sensible way to make headway here is by means of detailed, that is, atomistic computer simulations. Unfortunately, detailed computer simulations of the self-assembly of large polymeric objects are often not very practical because they require excessive computer processing times, in particular if the solvent molecules are 

However, proteins are almost always charged (Dello Orco et al., 2005), for otherwise they would drop out of the solution, that is, phase separate macroscopically. Indeed, this is what usually happens near the isoelectric point of the proteins, i.e. their point of zero net charge. If two proteins bind to become part of an assembly, charged patches on them get on average closer together and hence repel each other when of the same sign. In other words, Coulomb repulsion between the proteins 

This gives the following estimate for the protein-protein binding energy in an assembly, 

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Figure A2.1.2. Reversible expansion of a gas witli the removal one-by-one of grains of sand atop a piston.

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

On slow cooling the reverse changes occur. Ferrite precipitates, generally at the grain boundaries of the austenite, which becomes progressively richer in carbon. Just above A, the austenite is substantially of eutectoid composition, 0.76% carbon. 

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