Entropy stabilization

Turning to polymers giving thermodynamically stable mesophases we must assume that, since we have described bundles as an inherent structural feature of undercooled polymer melts, such structures should occur, at least in principle, also in such systems, to the extent that attractive interchain interactions which account for bundle formation play a significant role. On the other hand, rigorously speaking Class II mesophases are entropy-stabilized and inter-chain... 

The binary systems we have discussed so far have mainly included phases that are solid or liquid solutions of the two components or end members constituting the binary system. Intermediate phases, which generally have a chemical composition corresponding to stoichiometric combinations of the end members of the system, are evidently formed in a large number of real systems. Intermediate phases are in most cases formed due to an enthalpic stabilization with respect to the end members. Here the chemical and physical properties of the components are different, and the new intermediate phases are formed due to the more optimal conditions for bonding found for some specific ratios of the components. The stability of a ternary compound like BaCC>3 from the binary ones (BaO and CC>2(g)) may for example be interpreted in terms of factors related to electron transfer between the two binary oxides see Chapter 7. Entropy-stabilized intermediate phases are also frequently reported, although they are far less common than enthalpy-stabilized phases. Entropy-stabilized phases are only stable above a certain temperature,... 

We note that at the consolute point the conductivity is still metallic, the appearance of an activation energy e2 occurring for somewhat lower concentrations. The reason for this, in our view, is as follows. The consolute point should occur approximately at the same concentration as the kink in the free-energy curve of Fig. 4.2, namely that at which the concentration n of carriers is of order given by n1/3aH 0.2. Above the consolute point there is no sudden disappearance of the electron gas as the concentration decreases its entropy stabilizes it, so metallic behaviour extends to lower concentrations, until Anderson localization sets in. Conduction, then, is due to excited electrons at the mobility edge, as discussed above. 

Thermodynamic studies performed on a number of other guanosine adducts show some examples where binding represents an enthalpic destabilized, but entropy stabilized, process and others that are enthalpically stabilized, but entropically destabilized. The net thermodynamic result, however, appears to be a relatively modest localized free-energy destabilization that could form the basis for some recognition mechanism. 

On the molecular level, an UCEP often occurs when polar molecules are mixed with nonpolar molecules, with energy required to separate the polar molecules when diluted with nonpolar molecules. A LCEP happens when interactions between molecules result in complex formation and a resultant large entropy stabilization. This is not a very common occurrence. The hydrogen bond can cause the formation of such complexes, and a LCEP, when it forms, often involves mixtures of components that can hydrogen bond. 

Enmeshment Enthalpy/Entropy Stabilization Equivalent Spherical Diameter... 

For the formation of acetate complexes, Table 2, the values of AH are still quite positive not only for the hard lanthanoid ions, where a markedly electrostatic bond is certainly expected, but also for Cu2+, Zn2+ and Cd2+ which are all in the border region between hard and soft acceptors. Only for the soft Pb2+, and also for H+, AH is 0. All acetate complexes so far investigated are thus entropy stabilized, i.e. oxygen behaves as a very hard donor atom also in the environment presented by the acetate ion. 

In Chapter 3 we will demonstrate that some of the stabilizers, introduced above, can be treated in terms of probability theory. We mention here, as an example only, a minimum entropy stabilizer, which selects the simplest possible solution required to fit the data ... 

Thus, we can see that minimization of the stabilizing functionals can impose different conditions on the class of model parameters. One case (e.g., maximum smoothness or minimum entropy stabilizers) requires a smooth distribution of the model parameters. Another case (e.g., a minimum gradient support stabilizer, or... 

Temperature dependence of hydrophobicity enthalpy versus entropy stabilizations... 

These three-phase behavior systems have been found to be associated with ultealow interfacial tension and, thus, were the target of the enhanced oil-recovery research in the seventies. Note that the ultralow interfacial tension is perfectly consistent with the possibility of entropy stabilization of microemulsions, because it decreases the interfacial free energy term yAA [50]. 

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