Entropy penalty

These are, without doubt, somewhat artifieial systems. For real systems, one could not tell if anything happened, unless isotopie labeling could be arranged. An even greater problem would oeeur in the gas phase, sinee the entropy penalty required for these peeuliar geometries would be expected to make them very improbable. 

Fig. 2 Schematic diagram of the NN approach to the calculation of free energy of hybridization of a DNA sequence. The free energy is obtained as the sum of the free energies associated to each quartet along the sequence, plus an initiation entropy penalty...

Adamantane (47), however, only offers weak van der Waals interactions to the inner concave surface of the host assembly. This interaction, together with the enthalpic gains provided by the formation of 16 hydrogen bonds, is enough to overcome the entropy penalty for bringing together four monomers and one guest. 

This however complicates the optimization procedure. The problem can be alleviated by using an entropy penalty function P8, which serves to properly apportion the total condenser costs to the reboiler and column. The entropy penalty function, which Evans describes as "negentropy" (12-13), can also be viewed as the commodity or product which the condenser sells to the tower and reboller. The entropy penalty function leaving the condenser Is given by (9, 13-14)... 

The entropy penalty function attributable to the reboller Is given by (9)... 

Thus by requiring the reboller and column to purchase P8 r r and p8 coi from the condenser, the condenser costs are properly included In the optimization procedure. However, the money balances will need to include the money flows associated with the entropy penalty function transactions. 

The last component to be optimized is the condenser. The condenser area is fixed once the process stream temperature, T > and the exit cooling water temperature, T, are fixed. However, the process stream temperature is fixed by the column pressure and the product purities. Thus the condenser is optimized by minimizing the unit cost of the entropy penalty function, As, with respect to T3. 

The free energy is defined as a sum over all atom types i and j of molecules A and B, being a j an effective binding parameter and A j the mutual surface jointly buried by the atom types i and j in the complex.(3 is a constant for the entropy-penalty for the association of two molecules ... 

In this cycle, the main feature is that template T can bind to itself by complementary supramolecular binding units, thus autocatalytically increasing its concentration during the course of the reaction. In a first step, T reversibly binds its constituents A and B to yield a termolecular complex M. This complex pays the entropy penalty that brings the two precursors into close proximity, which facilitates the formation of a covalent bond between them, whether or not this one is assisted by an enzyme [34]. In a second step, termolecular complex M is... 

Surprisingly, the low solubility of small-sized particles does not stem from a weak interaction of particles with their surrounding water environment (77). For example, the heat of solvation of methane in water at ambient temperature is of similar magnitude as the heat of vaporization of pure liquid methane (80). The positive solvation free energy of small apolar particles at low temperatures is the consequence of negative solvation entropy, which overcompensates for the negative solvation enthalpy. It is widely believed that this entropy penalty is caused by the orientation order introduced to the hydration-shell water molecules as they try to maintain an intact hydrogen bond network (77). Parallel to the entropy decrease observed for low... 

Haymet ADJ, Silverstein KAT, Dill KA. Hydrophobicity reinterpreted as minimisation of the entropy penalty of solvation . 

In 1993 Blokzijl and Engberts published an important review article on hydrophobic effects. In 1992, Smith, Zhang and Haymet showed that hydrophobic association of uncharged solutes in water is almost entirely an entropy effect. Haymet went on to point out that experimental data show that methane likes water about as well as it likes any other solvent from the point of view of enthalpy. This view is underlined by the experimentally high solubility of water in cryogenic solvents such as liquid methane. Hydrophobicity in fact arises from the entropy penalty incurred by the water. The methane is not hydrophobic the water is methophobic . 

The conformational analysis of the deprotected analog 212, performed by using NMR and molecular mechanics, indicates a drastic difference from the major conformation found with the natural compound present in solution, especially around the and a> angles [99]. The low energy barriers for conformer interconversion might nevertheless allow easy access to other conformers that can bind to natural receptors without major entropy penalties. 

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