Energetic Kinetic Theory

The assumption of the Energetic Kinetic Theory (EKT) is that under nonisothermal conditions the total free energy remains that of the equilibrium at the corresponding temperature (i.e., RT In ( 2/ 7) in this example), and that there is a transfer of populations between the/and b types of bonds to render this constraint feasible. The kinetic duality between the b and/units within a closed but split statistical ensemble is the reason for the nomenclature "Split Dual Kinetics," but since the free energy remains as the driving force to determine the tme kinetic expression, we favor the expression "Energetic Kinetic Theory" to describe our new model. It will become apparent shordy that the latter expression has a more general sense. The set of equations for the new statistics... 

We have introduced so far a novel nonequilibrium statistical theory, [eq. (6)]. Although this subject might appear quite different from the objective of this paper on the possible interrelationship between the Tg, and T transitions, it is very pertinent. We will now apply the principle of the Energetic Kinetic Theory, presented above to determine the structure of the dual split, to another situation. We assume that the free energy still remains equal to the equilibrium value at the same temperature (EKT principle), but it is allowed to subdivide into (t) identical systems to render the energetic constraint feasible. Hence the total number of units, Bg, can be divided into (t) systems of (Bp/fV ) units each. We define = Bq/N, and numerically solve the following system of differential equations on a computer. 

Fig. 16. Morphological interpretation of the Energetic Kinetic Theory from the author s thesis. The l>b-balls and the bundles determine the stability of the Energetic Kinetic Systems.

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

Study, the students are taught the basic concepts of chemistry such as the kinetic theory of matter, atomic stmcture, chemical bonding, stoichiometry and chemical calculations, kinetics, energetics, oxidation-reduction, electrochemistry, as well as introductory inorgarric and organic chemistry. They also acquire basic laboratory skills as they carry out simple experiments on rates of reaction and heat of reaction, as well as volrrmetric analysis and qualitative analysis in their laboratory sessions. 

Thus, because of lack of knowledge about a, the kinetic problem of calculating the nucleation rate has been transformed to the thermodynamic problem of evaluating the equilibrium droplet distribution (the discussion of purely kinetic theories that avoid a thermodynamic formulation is beyond the scope of this article the interested reader should consult [5], and the interesting papers by Ruckenstein and coworkers [19-24]). Returning now to Equation (7), the calculation of the nucleation rate requires knowledge of the energetics of embryo formation, which we now address. 

The role of adhesion and surface energetics on polymer friction has been critically examined by Lee. The application of molecular kinetic theory to adhesion and friction of elastomers has been carried out by Lavrentev , and molecular interaction for solids at contact have been reviewed . 

Among other kinetic theories, one should notice the Volkenstein-Ptizyn (51) and the Gotlib-Ptizyn theories (52). In accordance with the former, the relaxation process in the vitrescent substances is considered as an activation process occurring via transition of the kinetic units from one energetic state to another by... 

Although the bond-valence theory (BVT) is primarily meant to rationalize and predict molecular structures in solids, chemists naturally try to extend structural models to rationalize and predict reactivity. If a model helps us understand why particular equilibrium structures are preferred, for instance, perhaps quantifying the principles underlying the model can help us predict energetic differences between structural states, which are the bases for both thermodynamic and kinetic theory. The BVT is an excellent vehicle for exploring structure-energy relationships, because it is in some respects quantitatively predictive, and boils down complex, multi-body interactions into a single parameter, the bond-valence sum. 

In chemical kinetics, it is often important to know the proportion of particles with a velocity that exceeds a selected velocity v. According to collision theories of chemical kinetics, particles with a speed in excess of v are energetic enough to react and those with a speed less than v are not. The probability of finding a particle with a speed from 0 to v is the integral of the distribution function over that interval... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

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