Gibbs specific function

The value AG (Gibbs specific function of local, for example, supra-molecular structures formation) is given for nonequilibrium phase transition supercooled liquid —> solid body [11]. From the Eq. (1.14) it follows, that the condition AG = 0 is achieved atd =3, that is, atd =dand at transition to Euclidean behavior. In other words, a fractal structures are formed only in nonequilibrium processes course, which is noted earlier [12]. 

The Gibbs specific function notion for nonequilibrium phase transition overcooled liquid —> solid body is connected closely to local order notion (and, hence, fractality notion, see chapter one), since within the ffamewoiks of the cluster model the indicated transition is equivalent to cluster formation start. In Fig. 1.1, the dependence of clusters relative fraction (p, on the... 

Figure 1.6 The dependence of the Gibbs specific function of non-equilibrium phase...

Figure 1.7 The dependence of the Gibbs specific function of non-equilibrium phase transition AG on AT = T - 293 K for (1) 15 semi-crystalline (2) amorphous glassy and (3) crosslinked polymers. The value of AG is given in cal/g [50]. The straight line is plotted according to data [46]...

It is commonplace to assume a form of the Gibbs energy function which excludes the pressure variable for solid-state phase transformations, as the magnitude of the PAV term is small at atmospheric pressures. This is of course not the case in geological systems, or if laboratory experiments are deliberately geared to high-pressure environments. Klement and Jayaraman (1966) provide a good review of the data available at the time when some of the earliest CALPHAD-type calculations were made (Kaufman and Bernstein 1970, Kaufman 1974). Much work was also carried out on specific alloy systems such as Fe-C (Hilliard 1963) and the Tl-In system (Meyerhoff and Smith 1963). 

We saw in Chapter 2 that an important thermodynamic quantity is the Gibbs free energy, AG. The specific functional relationship we use to describe the free energy will depend on whether we are studying a physical or a chemical transformation. For physical processes, such as phase transformations, the most useful form of the Gibbs free energy is its definition given in Chapter 2 ... 

Based upon experimentally observed spectroscopic data, statistical thermodynamic calculations provide thermodynamic data which would not be obtained readily from direct experimental measurements for the species and temperature of interest to rocket propulsion. If the results of the calculations are summarized in terms of specific heat as a function of temperature, the other required properties for a particular specie, for example, enthalpy, entropy, the Gibb s function, and equilibrium constant may be obtained in relation to an arbitrary reference state, usually a pressure of one atmosphere and a temperature of 298.15°K. Or alternately these quantities may be calculated directly. Significant inaccuracies in the thermochemical data are not associated generaUy with the results of such calculations for a particular species, but arise in establishing a valid basis for comparison of different species. 

To characterize the thermodynamic behavior of the components in a solution, it is necessary to use the concept of partial molar or partial specific functions. The partial molar quantities most commonly encountered in the thermodynamics of polymer solutions are partial molar volume Vi and partial molar Gibbs free energy Gi. The latter quantity is of special significance since it is identical to the quantity called chemical potential, pi, defined by... 

The results above for the activity coefficients and fugacities are not general, but are specific to the very simple excess Gibbs energy function we have used,... 

Membrane phenomena cover an extremely broad field. Membranes are organized structures especially designed to perform several specific functions. They act as a barrier in living organisms to separate two regions, and they must be able to control the transport of matter. Moreover, alteration in transmembrane potentials can have a profound effect on key physiological processes such as muscle contraction and neuronal activity. In 1875, Gibbs stated the thermodynamic relations that form the basis of membrane equilibria. The theory of ionic membrane equilibrium was developed later by Donnan (1911). From theoretical considerations, Donnan obtained an expression for the electric potential difference, commonly known as the membrane potential between two phases. 

Up to now, the discussion has been about thermodynamic properties of gaseous and liquid Freon-22. The thermodynamic functions of condensed-phase Freon-22, including the solid, are tabulated in Ref. [3.55] at T = 15-232 K (Table 31). This table also includes the values for entropy, enthalpy, and Gibb s function in the vapor phase at Tnbp- Specifically, - //q)g = 9482.8 cal/ mol at Tnbp- On the other hand, data in [3.41, 3.63] show that =... 

A further point worth emphasizing is related to the last one, and has already been touched on in the last section, namely that the values of the potentials p, T, and in which enter into the arguments abcrve are those of the bulk phases. We do not have to ask if they have the same value at the surface as they have in the bulk. The question does not arise in Gibbs s treatment it does arise and must be answered, if a third phase is introduced. It is true that Gibbs specifically states that in has the same value at the surface as in the bulk, but he neither uses this result nor provides an operational definition of in at the surface. This and similar questions about local thermodynamic functions are best answered by using the methods of statistical ffiermodynamtcs ( 4.10). 

The values of these functions change when thermodynamic processes take place. Processes in which the Gibbs energy decreases (i.e., for which AG<0), will take place spontaneously without specific external action. The Gibbs energy is minimal in the state of equilibrium, and the condition for equilibrium are given as... 

With tables of ion entropies available, it is possible to estimate a Gibbs function change without the necessity of carrying out an experiment or seeking specific experimental data. For example, without seeking data for the potential of calcium electrodes, it is possible to calculate the calcium electrode potential or the Gibbs function change in the reaction... 

The quantity A i (( )) is the solvation Gibbs (or Helmholtz) energy for the molecule with occupation number i (i = 0, 1,2) and specific angle (j). Although we believe some specific solvent effects might contribute significantly to the correlation function (see also Chapter 9), we did not include solvent effects in the present calculations (apart from the dielectric constants and Dj, as indicated above). 

The excess term should allow the total Gibbs energy to be fitted to match that of Eq. (6.3) while at the same time incorporating a return to the inclusion of f 6) and f i) in the lattice stabilities. With the increased potential for calculating metastable Debye temperatures and electronic specific heats from first principles (Haglund et al. 1993), a further step forward would be to also replace Eq. (6.5) by some function of Eq. (6.8). 

This relationship identifies the surface energy as the increment of the Gibbs free energy per unit change in area at constant temperature, pressure, and number of moles. The path-dependent variable dWs in Eq. (2.60) has been replaced by a state variable, namely, the Gibbs free energy. The energy interpretation of y has been carried to the point where it has been identified with a specific thermodynamic function. As a result, many of the relationships that apply to G also apply to y ... 

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