Gibbs theory

Tolman, R.C., Consideration of the Gibbs theory of surface tension, J. Chem. Phys. 1948,16, 758-774... 

There is another important law that follows from the classical theory of capillarity. This law was formulated by J. Thomson [16], and was based on a Clausius-Clapeyron equation and Gibbs theory, formulating the dependence of the melting point of solids on their size. The first known analytical equation by Rie [17], and Batchelor and Foster [18] (cited according to Refs. [19,20]) is... 

Using the specific entropy determined in the simulations, one can test this theoretical approach by fitting this expression to the temperature dependence of D observed in the simulations. It has been concluded that the Adam-Gibbs theory cannot predict the temperature dependence of the dynamics from the thermodynamic information contained in the temperature dependence of the... 

Van der Waals acknowledges the unexpected difficulty in extending his equation to binary mixtures, and the key role of Gibbs theory of free energy minimization in handling both binary mixtures and association complexes. 

The central focus of Gibbs theory is the equilibrium state S, a quiescent limiting condition of a sufficiently large ( macroscopic ) physical system that exhibits characteristically simple responses to attempted changes of the control variables that specify the state. 

Observed dispersions e1 for four sized fractions with average molecular weights M from 0.44 to 1.85 x 106 Dalton at concentrations C 8 to 9 x 10 5 are shown in Figure 1(b). Within experimental Error, the values of Ae /C, where Ac is the increment of static permittivity for added solute, were independent of concentration but increased linearly with molecular weight, as predicted by the McTague-Gibbs theory for molecular weights below about 106 Dalton. 

These principles, necessary consequence of Gibbs theories, have been brought out for the most part by Roozboom and his pupils. 

At equilibrium. Tf = T, and the equilibrium version of the Adam-Gibbs theory, discussed earlier, is recovered. For a glass that is not able to relax, T/ is constant, and then follows an Arrhenius temperature-dependence, which accords well with experimental measurements on deeply quenched glasses. 

Figure 4.26 The log of the average relaxation time versus Adam-Gibbs exponent U jlTS for the facilitated Ising model on the square lattice. The points are from Monte Carlo simulations and the straight line through the points is the prediction of the Adam-Gibbs theory. (From Fredrickson 1988, with permission from the Annual Review of Physical Chemistry, Volume 39, 1988, by Annual Reviews, Inc.)...

Theberge SM, Luther GW, Rozan TF, Rickard DT (2000) Evidence for aqueous clusters as intermediates during copper sulfide formation. Abstr Am Chem Soc 220 353 Thompson DN, Sayer RL, Noah KS (2000) Sawdust-supported passive bioremediation of western United States acid rock drainage in engineered wetland systems. Minerals Metall Process 17 96-104 Tolman RC (1966) Consideration of Gibbs theory of surface tension. J Chem Phys 16 758-774 Tolman RC (1949) The effect of droplet size on surface tension. J Chem Phys 17 333-337 Tomino H, Kusaka I, Nishioka K, Takai T (1991) Interfacial tension for small nuclei in binary nucleatioa J Crystal Growth 113 633-636... 

According to Gibbs theory, adsorption is a three-phase system consisting of the stationary phase (adsorbent), the mobile phase and the adsorbed phase (adsorbt) (Fig. 2.1). The adsorbt is viewed as a 2-dimensional boundary layer between the other phases. It is also assumed that the activated surface of the adsorbent is identical for all components and does not change its properties. This reduces the adsorption to a two-phase system with an interaction between the adsorbt and the mobile phase. 

Thus, the main problem with the various inferences drawn from Adam-Gibbs theory seems to emanate from the fact that the evaluation of the configurational entropy on the basis of ACp values is erroneous. This... 

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