Entropy theory thermodynamics

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

See Transition-State Theory Transition-State Theory (Thermodynamics) Transition-State Theory in Solutions Entropy of Activation Volume of Activation... 

The Kauzmann temperature plays an important role in the most widely applied phenomenological theories, namely the configurational entropy [100] and the free-volume theories [101,102]. In the entropy theory, the excess entropy ASex obtained from thermodynamic studies is related to the temperature dependence of the structural relaxation time xa. A similar relation is derived in the free-volume theory, connecting xa with the excess free volume AVex. In both cases, the excess quantity becomes zero at a distinguished temperature where, as a consequence, xa(T) diverges. Although consistent data analyses are sometimes possible, the predictive power of these phenomenological theories is limited. In particular, no predictions about the evolution of relaxation spectra are made. Essentially, they are theories for the temperature dependence of x.-jT) and r (T). 

We can describe irreversibility by using the kinetic theory relationships in maximum entropy formalism, and obtain kinetic equations for both dilute and dense fluids. A derivation of the second law, which states that the entropy production must be positive in any irreversible process, appears within the framework of the kinetic theory. This is known as Boltzmann s H-theorem. Both conservation laws and transport coefficient expressions can be obtained via the generalized maximum entropy approach. Thermodynamic and kinetic approaches can be used to determine the values of transport coefficients in mixtures and in the experimental validation of Onsager s reciprocal relations. 

One must be carefiil here because one can prove too much. The entropy theory of glasses, also called the Gibbs-Di Marzio (GD) theory, is a theory of equilibrium thermodynamic quantities only, it is not a theory of the kinetics of glasses. Polymer viscosities do in fact get so large at the glass transition that the relaxation times in the material equal and exceed the time scale of the experiment. At such temperatures one should not expect to have a perfect prediction of the various thermodynamic quantities. It is sensible to suppose that our predictions should not accord perfectly with experiment in these high viscosity regions. 

The "entropy in information theory" is closely related to the "entropy in thermodynamics" C410, 4273. H(A) is a measure of the uncertainty or capacity of the source A. Before experiment A is performed, an uncertainty of H(A) bit exists. After the experiment one knows the result and therefore the uncertainty is zero. On the average, an information of H(A) bit results from this experiment- The amount of information which can be achieved by an experiment depends on the uncertainty (entropy) which exists before the experiment is carried out. 

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 thermodynamic theory considers the glass to be a fourth state of matter, characterized by zero conformational entropy. The thermodynamic theory uses the S—V—T equation of state and the transition to the thermodynamic stable glassy state is characterized by a second-order transition situated at a temperature 72 50 K below the experimentally observed glass temperature, J g [15, 16]. The second-order transition occurs for zero conformational entropy in the S—V—T... 

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. 

Pure thermodynamics is developed, without special reference to the atomic or molecular structure of matter, on the basis of bulk quantities like internal energy, heat, and different types of work, temperature, and entropy. The understanding of the latter two is directly rooted in the laws of thermodynamics— in particular the second law. They relate the above quantities and others derived from them. New quantities are defined in terms of differential relations describing material properties like heat capacity, thermal expansion, compressibility, or different types of conductance. The final result is a consistent set of equations and inequalities. Progress beyond this point requires additional information. This information usually consists in empirical findings like the ideal gas law or its improvements, most notably the van der Waals theory, the laws of Henry, Raoult, and others. Its ultimate power, power in the sense that it explains macroscopic phenomena through microscopic theory, thermodynamics attains as part of Statistical Mechanics or more generally Many-body Theory. 

A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

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 theory predicts high stabilities for hard acid - hard base complexes, mainly resulting from electrostatic interactions and for soft acid - soft base complexes, where covalent bonding is also important Hard acid - soft base and hard base - soft acid complexes usually have low stability. Unfortunately, in a quantitative sense, the predictive value of the HSAB theory is limited. Thermodynamic analysis clearly shows a difference between hard-hard interactions and soft-soft interactions. In water hard-hard interactions are usually endothermic and occur only as a result of a gain in entropy, originating from a liberation of water molecules from the hydration shells of the... 

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. 

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