Free energy environment

Typical plots of the variation of the surface tension with the logarithmic concentration difference of a surfactant, a saturated hydrocarbon alcohol and an inorganic salt in an aqueous solution are shown in Figure 5.4. Surfactant molecules find a lower free-energy environment at the interface of an aqueous solution than they have in the bulk solution and prefer to concentrate at the surface. The adsorption isotherm of most surfactants shows a sharp decrease initially with the increase in the solute concentration until a plateau appears, due to the formation of micelles following the critical micelle concentration (CMC), where all the solution surface is covered with surfactant molecules. Any further addition of surfactant does not decrease the surface tension of the solution because it is directly consumed in the micelle formation process (see also Section 5.7). Saturated hydrocarbon alcohols also show a decrease in surface tension with increases in their aqueous solution concentration because they do not like to stay in the bulk solution and prefer to enrich on... 

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

In the present case, each endpoint involves—in addition to the fully interacting solute—an intact side chain fragment without any interactions with its environment. This fragment is equivalent to a molecule in the gas phase (acetamide or acetate) and contributes an additional term to the overall free energy that is easily calculated from ideal gas statistical mechanics [18]. This contribution is similar but not identical at the two endpoints. However, the corresponding contributions are the same for the transfonnation in solution and in complex with the protein therefore, they cancel exactly when the upper and lower legs of the thermodynamic cycle are subtracted (Fig. 3a). 

Although moulded polycarbonate parts are substantially amorphous, crystallisation will develop in environments which enable the molecules to move into an ordered pattern. Thus a liquid that is capable of dissolving amorphous polymer may provide a solution from which polymer may precipitate out in a crystalline form because of the favourable free energy conditions. 

FIGURE 3.16 The pH dependence of the free energy of hydrolysis of ATP. Because pH varies only slightly in biological environments, the effect on AG is nsnally small. 

Several different kinds of noncovalent interactions are of vital importance in protein structure. Hydrogen bonds, hydrophobic interactions, electrostatic bonds, and van der Waals forces are all noncovalent in nature, yet are extremely important influences on protein conformations. The stabilization free energies afforded by each of these interactions may be highly dependent on the local environment within the protein, but certain generalizations can still be made. 

In its general corrosion behaviour, beryllium exhibits characteristics very similar to those of aluminium. Like aluminium, the film-free metal is highly active and readily attacked in many environments. Beryllium oxide, however, like alumina, is, a very stable compound (standard free energy of formation = —579kJ/mol), with a bulk density of 3-025g/cm as compared with 1 -85 g/cm for the pure metal, and with a high electronic resistivity of about 10 flcm at 0°C. In fact, when formed, the oxide confers the same type of spurious nobility on beryllium as is found, for example, with aluminium, titanium and zirconium. 

For many years the corrosion of uranium has been of major interest in atomic energy programmes. The environments of importance are mainly those which could come into contact with the metal at high temperatures during the malfunction of reactors, viz. water, carbon dioxide, carbon monoxide, air and steam. In all instances the corrosion is favoured by large free energy and heat terms for the formation of uranium oxides. The major use of the metal in reactors cooled by carbon dioxide has resulted in considerable emphasis on the behaviour in this gas and to a lesser extent in carbon monoxide and air. 

Solute retention can also be explained on a thermodynamic basis where the change in free energy is considered when the solute is moved from the environment of one phase to that of the other. 

The steric environment of the atoms in the vicinity of the reaction centre will change in the course of a chemical reaction, and consequently the potential energy due to non-bonded interactions will in general also change and contribute to the free energy of activation. The effect is mainly on the vibrational energy levels, and since they are usually widely spaced, the contribution is to the enthalpy rather than the entropy. When low vibrational frequencies or internal rotations are involved, however, effects on entropy might of course also be expected. In any case, the rather universal non-bonded effects will affect the rates of essentially all chemical reactions, and not only the rates of reactions that are subject to obvious steric effects in the classical sense. 

It follows from the second law of thermodynamics that the optimal free energy of a hydrocarbon-water mixture is a function of both maximal enthalpy (from hydrogen bonding) and minimum entropy (maximum degrees of freedom). Thus, nonpolar molecules tend to form droplets with minimal exposed surface area, reducing the number of water molecules affected. For the same reason, in the aqueous environment of the hving cell the hydrophobic portions of biopolymers tend to be buried inside the structure of the molecule, or within a lipid bilayer, minimizing contact with water. 

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