Entropy theory model

B. Relation of Entropy Theory to Elastic Modulus Model of Structural Relaxation... 

One final point with regard to comparing the critical-distance and entropy theories is the following. Words like true and false , correct and incorrect , and valid and invalid have been avoided. Such descriptives have no place in discussions of chemical models that are, above all, fictitious. Models—one must never forget—are to be used, not believed. Thus, I do not claim the spatiotemporal hypothesis represents the truth I merely claim that it is a valuable aid for thinking, especially in cases where entropic arguments fail to help. 

The entropy theory of the glass transition was developed by Gibbs and DiMarzio and by Adams and Gibbs to describe polymeric systems. By mixing the polymer links with holes or missing sites on a lattice to account for thermal expansion as in a lattice gas model, they could determine the entropy of mixing and the configurational entropy of the polymer. They found a second-order transition at a temperature They then pointed... 

Models for polymer chains The early theories of steric stabilization 10.5.1 Loss of configurational entropy theories... 

The entropy theory is the result of a statistical mechanical calculation based on a quasi-lattice model. The configurational entropy (S, ) of a polymeric material was calculated as a function of temperature by a direct evaluation of the partition function (Gibbs and Di Marzio (1958). The results of this calculation are that, (1) there is a thermodynamically second order liquid to glass transformation at a temperature T2, and 2), the configurational entropy in the glass is zero i.e. for T > T2, => 0 as T... 

Taking into account this dual aspect of the glass transition, two main models have been proposed for the theoretical description of the glass transition phenomenon the kinetic based free volume , and the thermodynamic based conformational entropy theory. 

The first developed a mathematical model to relate Young s modulus to polymer chain scission and is based on entropy theory for rubber elasticity. The second was an MD study of the effect of chain scission on Young s modulus in a semi-crystalline polymer. The third study developed a model to relate Young s modulus to polymer chain scission, and is based on atomic-scale simulations for glassy polymers. 

Overall, the order parameter model provides both a simple physical interpretation of thermodynamic changes at Tg and a semiquantitative estimate of their magnitude. It does not, however, explain why segmental motion freezes in and in the absence of knowledge of the two-state parameters 8s and 8, it does not lead to predictions of Tg and therefore cannot explain how Tg will vary with molecular weight, composition, and chemical structure. The free-volume theory and the GM configurational entropy theory are the two most important attempts to explain why molecular motions eventually stop in a supercooled liquid and hence why the glass transition takes place. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

It is clear by comparing the uansition state theory with the collision model that the conesponding entropy of activation can be calculated from the value... 

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