Theory Prigogine

On the other hand, Stecki and Taylor29 study the equation which gives the correlations in the Prigogine theory. The property (44) for the creation operator allows us to develop p 0 (t — t ) about t = 0 in Eq. (48), which gives... 

The authors find lastly that expression (A.25) substituted in formula (A.31) of the Prigogine theory leads to a result equivalent to the one that one obtains if one combines Eqs. (A. 17-23) with the first equation of the hierarchy (6) in the Bogolubov method. 

THE. 13. R. Defay et I. Prigogine, Theorie thermodynamique de la tension superficielle dynamique (Thermodynamic theory of dynamic surface tension), J. Chim. Phys. Physico-chim. Biol. 43, 217-234... 

In any event, the pragmatism of the solubility parameter concept is seldom affected by the extreme conditions predicted by the Prigogine theory. There are, however, special cases where this concept should be kept in mind—for example, in high pressure plastic molding operations. 

Some novel statistical theories of solutions of polymers use the %i parameter, too. They predict the dependence of the %i parameter on temperature and pressure. According to the Prigogine theory of deformable quasi-lattice, a mixture of a polymer with solvents of different chain length is described by the equation ... 

These constants can be calculated from heats of mixing, values of parameter %i, and from swelling ratios. The Prigogine theory was further developed by Patterson, who proposed the following expression "... 

More importantly, the crystalline-solvent phase diagrams, thus solved in the context of the Flory-Huggins theory alone, cannot account for the existence of the solidus line, because the crystal phase always coincides with the pure crystalline polymer axis due to the inherent assumption, adopted from Prigogine theory, of the complete rejection of solvent molecules from the crystaHine phase [66,67]. Thus,... 

Glansdorff P and Prigogine I 1971 Thermodynamio Theory of Structure, Stability and Fluctuations (London Wiley-Interscience)... 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

I. Prigogine (Brussels) non-equilibrium thermodynamics, particularly the theory of dissipative structures. 

I. Prigogine, The Molecular Theory of Solution, North-Holland Publishing Co., Amsterdam, p. 448 (1957). 

Prigogine, I., Bellemans, A., and Mathot, V., The Molecular Theory of Solutions, North Holland, Interscience, New York, 1957. 

A theoretical analysis of the helium-xenon system was reported by Zandbergen and Beenakker (Zl), who based their calculations on the Prigogine-Scott theory of corresponding states for mixtures (PI 5, S2). We cannot here go into the details of their analysis, but will merely indicate the essential elements. Zandbergen and Beenakker use the three-liquid theory to obtain an expression for the volumes of helium-xenon mixtures as a function of temperature, pressure, and composition. This expression is... 

Flory (11) improved the notation and form of Prigogine s expressions, and it is essentially the Flory form of Prigogine s free-volume theory that is of most use for design purposes. The Flory work (11) leads to an equation of state which obeys the corresponding-states principle ... 

To recapitulate, the Flory version of the Prigogine free-volume or corresponding-states polymer solution theory requires three pure-component parameters (p, v, T ) for each component of the solution and one binary parameter (p ) for each pair of components. 

It is often of industrial interest to be able to predict the equilibrium sorption of a gas in a molten polymer (e.g., for devolatilization of polyolefins). Unfortunately, the Prigogine-Flory corresponding-states theory is limited to applications involving relatively dense fluids 3,8). An empirical rule of thumb for the range of applicability is that the solvent should be at a temperature less than 0.85 Tp, where Tp is the absolute temperature reduced by the pure solvent critical temperature. 

The corresponding-states theory of polymer solution thermodynamics, developed principally by Prigogine and Flory, has provided a reliable predictive tool requiring only minimal information. We have seen here several examples of the use of the corresponding-states theory. We have also seen that the corresponding-states theory is a considerable improvement over the older Flory-Huggins theory. 

The flow of matter and energy through an open system allows the system to self-organize, and to transfer entropy to the environment. This is the basis of the theory of dissipative structures, developed by Ilya Prigogine. He noted that self-organization can only occur far away from thermodynamic equilibrium [17]. 

Roos, B. O., Andersson, K., Fiilscher, M. R, Malmqvist, P.-A., Serrano-Andres, L., 1996, Multiconfigurational Perturbation Theory Apphcations in Electronic Spectroscopy in Advances in Chemical PhysicsXCIII, Prigogine,... 

If the approach does not go beyond the ordinary entropy, or if it applies an optimized result to a constrained state, then one can immediately conclude that a quantitative theory for the nonequilibrium state is unlikely to emerge. Regrettably, for phenomenological theories of the type just discussed, the answer to both questions is usually negative. The contribution of Prigogine, in particular, will be critically assessed from these twin perspectives (see Section HE). 

Evans and Baranyai [51, 52] have explored what they describe as a nonlinear generalization of Prigogine s principle of minimum entropy production. In their theory the rate of (first) entropy production is equated to the rate of phase space compression. Since phase space is incompressible under Hamilton s equations of motion, which all real systems obey, the compression of phase space that occurs in nonequilibrium molecular dynamics (NEMD) simulations is purely an artifact of the non-Hamiltonian equations of motion that arise in implementing the Evans-Hoover thermostat [53, 54]. (See Section VIIIC for a critical discussion of the NEMD method.) While the NEMD method is a valid simulation approach in the linear regime, the phase space compression induced by the thermostat awaits physical interpretation even if it does turn out to be related to the rate of first entropy production, then the hurdle posed by Question (3) remains to be surmounted. 

The theory of the thermodynamics of irreversible systems (Prigogine, 1979 Prigogine and Stengers, 1986) shows that the differential quotient of entropy with time (the change of entropy with time) can be expressed as the sum of products, the terms of which contain a force factor and a flow factor. In chemical systems, the... 

Prigogine I (1957) The molecular theory of solution. North-Holland, Amsterdam... 

Another theoretical basis of the superheated liquid-film concept lies on the irreversible thermodynamics developed by Prigogine [43]. According to this theory, irreversible chemical processes would be described (Equation 13.17) by extending the equation of De Donder, provided that simultaneous reactions were coupled in a certain thermodynamic model, as follows ... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

From the quantitative point of view, the success of the cell model of solutions was more limited. For example, a detailed analysis of the excess functions of seven binary mixtures by Prigogine and Bellemans5 only showed a very rough agreement between theory and experiment. One should of course realize here that besides the use of the cell model itself, several supplementary assumptions had to be made in order to obtain numerical estimates of the excess functions. For example, it was assumed that two molecules of species and fi interact following the 6-12 potential of Lennard-Jones ... 

Concerning point (b), a generalized theory was developed independently by Prigogine and his co-workers10 11 and by Scott.18 The main idea was to combine the concept of average potential involved in the cell model with the theorem of corresponding states for pure compounds, in such a way that ... 

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