Formation free energy

Figure 4.2 (A) Effect of pressure on free energy formation of an oxide produced with an increase in the...

Figure 2, Temperature dependence of free energy formation, AG of actinide intermetallics.

Apart from a few general rules, the alloying behaviour of metals is rather empirical. The classical rules of Hume-Rothery [220] explain this behaviour reasonably well. Such factors as size, electronegativity, valency, electron concentration, free energy, formation of intermediate phases and isomorphism are found to influence the alloying tendency of metals. However, size and electronegativity are the two most important factors, and they profoundly influence the solubility of the solute atoms and greatly affect the crystal structures of the alloys. 

To relate AG of the reactions, we need to know the free energy of formation for the substances involved in the reaction. Free-energy formation for a substance is defined as the free energy released or used to form one mole of the substance in its standard state and is denoted as G°, where f stands for formation, and additional subscripts such as T and t can be used to indicate whether temperature is in Kelvin or °C, respectively. By convention Gf is for stable configuration of elements in then-standard states. For example, Gf for C, HjO, Nj, and O2 is set at zero. Examples of free energies of formation for selected compounds involved in biogeochemical cycles of elements in wetlands (G°, kJ mok are shown in Table 2.1 (Lindsay, 1979 Madigan and Martinko, 2006). 

Table 2-5 summarizes standard enthalpy and Gibbs free energy formation data for some higher rare earth oxide phases. 

Results from the data compilation of Yaws and c -workers (44,46) were selected for Gibb s free energy of formi on of ideal gas. Data for Gibb s free energy formation of the ideal gas is a series expansion m temperature. Equation (1-12). Correlation results are in favorable agreement with data. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

For the steady-state case, Z should also give the forward rate of formation or flux of critical nuclei, except that the positive free energy of their formation amounts to a free energy of activation. If one correspondingly modifies the rate Z by the term an approximate value for I results ... 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

Referring to Section V-2, the double-layer system associated with a surface whose potential is some value j/o requires for its formation a free energy per unit area or a t of... 

A2.1.6.7 STANDARD STATES AND STANDARD FREE ENERGIES OF FORMATION... 

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

The Cyc conformer represents the structure adopted by the linear peptide prior to disulfide bond formation, while the two /3-turns are representative stable structures of linear DPDPE. The free energy differences of 4.0 kcal/mol between pc and Cyc, and 6.3 kcal/mol between pE and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S-S bond formation to proceed. 

Y. Wang and K. Kuczera. Conformational free energy surface of the linear DPDPE peptide Cost of pre-organization for disulfide bond formation. J. Am. Chem. Soc., submitted, 1997. 

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