Lowest free energy

Fermentation is an anaerobic cataboHc process that uses organics as electron receptors. Since fermentation produces organic products that have lower free energy than their precursors, it is usefijl in remediation. The lowest free energy form of carbon produced is methane [74-82-8]. 

The reason for the formation of a lattice can be the isotropic repulsive force between the atoms in some simple models for the crystalhzation of metals, where the densely packed structure has the lowest free energy. Alternatively, directed bonds often arise in organic materials or semiconductors, allowing for more complicated lattice structures. Ultimately, quantum-mechanical effects are responsible for the arrangements of atoms in the regular arrays of a crystal. 

In the course of a reaction the nuclei and electrons assume positions that at each point correspond to the lowest free energies possible. If the reaction is reversible, these positions must be the same in the reverse process too. This means that the... 

The intrinsic aqueous solubility S of a drug X is related to the Gibbs free energy AGs i of the transfer of the drug X from its lowest free energy crystalline form to a saturated solution of the neutral form of X in water by the simple equation ... 

Unger, R. and Moult, J. (1993) Finding the lowest free energy conformation of a protein is a NP-hard problem proof and implications, Bull. Math. Biol., 55, 1183-1198. 

Which crystalline form of polypropylene exhibits the lowest free energy of crystallization Which form exhibits the highest ... 

Our model predicts destabilization of colloidal dispersions at low polymer concentration and restabilisation in (very) concentrated polymer solutions. This restabilisation is not a kinetic effect, but is governed by equilibrium thermodynamics, the dispersed phase being the situation of lowest free energy at high polymer concentration. Restabilisation is a consequence of the fact that the depletion thickness is, in concentrated polymer solutions, (much) lower than the radius of gyration, leading to a weaker attraction. 

Although the tautomeric ratios of the 4 species have not been measured directly, it is known that in aqueous solution the keto-N2H form dominates, while the keto-NlH form is only detectable in non-polar solvents. An analysis of experimental data concluded that in aqueous solution the stability (lowest free energy) is in the order keto-N2H > imino-N2H > enol-NlH > keto-NIH. In the gas phase, calculations predict that the keto-N2H form is the least stable. While solvation is found to favour this species, which is the most polar, this stabilisation is not enough to reverse the order of stability. It is thus clearly predicted that the keto-NIH tautomer is the most stable in... 

Here, the concept of linkage implies only that each intermolecular noncovalent bond is sufficiently large compared with kTto withstand ambient thermal collisions. Thus, for near-standard-state conditions (where kT 0.6kcal mol-1), even weak noncovalent interactions of 1-2 kcal mol-1 may be adequate to yield supramolecular complexes with stable equilibrium populations, thereby becoming true constituent units of the phase of lowest free energy. 

Obviously the lowest free energy is given by the most stable state for a system at constant pressure and, therefore, in due course an emulsion shall break spontaneously to the two-layered system. However, the breaking of an emulsion could be relatively a rather slow phenomenon. There are a number of factors which may be responsible for the slow-coalescence of an emulsion, namely ... 

This shows, in accordance with thermodynamics, that the state having lowest free energy is preferred. For example, (8) is large compared with unity if Aa is small compared with Ab. 

The sitnation shown in Fignre 2.3c is a little more complex. Here, the sohd phase has the lowest free energy at A-rich compositions (Xb < Xs), and the liquid phase has the lowest free energy at B-rich compositions (Xb > Xl). In between the two minima of the solid and liqnid free energy cnrves, Xg < Xb < X, both the liquid and sohd phases can coexist. Why is this Recall that the stability criteria are as follows for a two-phase system ... 

A vety important question now arises. Does this arrangement of hydrated ions in contact with a hydrated electrode always correspond to the configuration of lowest free energy Are some ions capable of divesting themselves (at least partly) of their primary waters, making their way through the hydration sheet of the electrode, and coming into contact with it ... 

In the course of a reaction the nuclei and electrons assume positions that at each point correspond to the lowest free energies possible. If the reaction is reversible, these positions must be the same in the reverse process, too. This means that the forward and reverse reactions (run under the same conditions) must proceed by the same mechanism. This is called the principle of microscopic reversibility. For example, if in a reaction A — B there is an intermediate C, then C must also be an intermediate in the reaction B — A, This is a useful principle since it enables us to know the mechanism of reactions in which the equilibrium lies far over to one side. Reversible photochemical reactions are an exception, since a molecule that has been excited photochemically does not have to lose its energy in the same way (Chapter 7). 

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