Theory quantitative models

Flory-Huggins Theory. The simplest quantitative model foi that iacludes the most essential elements needed foi polymer blends is... 

Price (Ref 39) compares the three principal quantitative models of ignition and concludes that there are serious deficiencies in the existing models, so much so that no one theory appears adequate to represent the complexity of ignition of composite solid proplnts. In the gas-phase model (Refs 22 36) the hot oxidizing environ-... 

Models and theories have been developed by scientists that allow a good description of the double layers at each side of the surface either at equilibrium, under steady-state conditions, or under transition conditions. Only the surface has remained out of reach of the science developed, which cannot provide a quantitative model that describes the surface and surface variations during electrochemical reactions. For this reason electrochemistry, in the form of heterogeneous catalysis or heterogeneous catalysis has remained an empirical part of physical chemistry. However, advances in experimental methods during the past decade, which allow the observation... 

We now have enough information to turn our qualitative ideas about a gas into a quantitative model that can be used to make numerical predictions. The kinetic model ( kinetic molecular theory, KMT) of a gas is based on four assumptions (Fig. 4.23) ... 

The preceding set of characteristics and properties of the estimators makes our type of mapping procedures, /, particularly appealing for the kinds of systems that we are especially interested to study, i.e., manufacturing systems where considerable amounts of data records are available, with poorly understood behavior, and for which neither accurate first-principles quantitative models exist nor adequate functional form choices for empirical models can be made a priori. In other situations and application contexts that are substantially different from the above, while much can still be gained by adopting the same problem statements, solution formats and performance criteria, other mapping and search procedures (statistical, optimization theory) may be more efficient. 

The greatest need in model performance testing and validation is clearly the use of quantitative measures to describe comparisons of observed and predicted values. As noted above, although a rigorous statistical theory for model performance assessments has yet to be developed, a variety of statistical measures has been used in various combinations and the frequency of use has been increasing in recent years. The FAT workshop (3.) identified three general types of comparisons that are often made in model performance testing ... 

This extension in the laboratory can be seen as the fantastic hypothesis testing application of molecular modeling. It is rare to find a chemical problem where there are not at least a few theories of the molecular mechanism involved. How many times has each of us heard steric affect or hydrogen bonding invoked as the explanation of a variety of experimental observations made at the bench level How useful would it be to be able to actually build accurate, quantitative models to investigate such ideas ... 

In the second half of the nineteenth century the structural theory of organic chemistry was developed. It led to the concept that chemical, physical and biological properties of all kinds must vary with structural change. The earliest structure-property relationships (SPR) were qualitative. With the development of methods of quantitative measurement of these properties data accumulated. Attempts were then made to develop quantitative models of the structural dependence of these properties. These methods for the quantitative description of structural effects will now be described. 

Yan, L.S. 1985. Study of the carcinogenic mechanism for polycyclic aromatic hydrocarbons — extended bay region theory and its quantitative model. Carcinogenesis 6 1-6. 

Orbital interaction theory forms a comprehensive model for examining the structures and kinetic and thermodynamic stabilities of molecules. It is not intended to be, nor can it be, a quantitative model. However, it can function effectively in aiding understanding of the fundamental processes in chemistry, and it can be applied in most instances without the use of a computer. The variation known as perturbative molecular orbital (PMO) theory was originally developed from the point of view of weak interactions [4, 5]. However, the interaction of orbitals is more transparently developed, and the relationship to quantitative MO theories is more easily seen by straightforward solution of the Hiickel (independent electron) equations. From this point of view, the theoretical foundations lie in Hartree-Fock theory, described verbally and pictorially in Chapter 2 [57] and more rigorously in Appendix A. 

An engineer or scientist is frequently challenged with the task of developing a simulation to explain an observed physical phenomena or to assist the design and optimization of a system or process. Certainly the task is facilitated significantly by a capability to predict, quantitatively, the outcome of a contemplated alternative. Our objective in this text is to present theory and modeling approaches that facilitate accomplishing this task. The required predictive capability is comprised of several essential elements ... 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

Widdas s quantitative model of the simple carrier was able to explain a number of earlier observations and to make predictions about what would be observed in more complex experiments on membrane transport. Thus it was a highly productive scientific insight. One of the earlier, apparently anomalous, results that the theory explained was the dramatic fall of membrane permeability found for solutes which were rapidly transported as solute concentration was increased. For example, in the human red blood cell, Wilbrandt and colleagues had previously measured a permeability constant for glucose which was 1000 times higher in dilute solutions of glucose than it was in a concentrated solution. This phenomenon, subsequently called saturation kinetics, is formally equivalent to the fall, as substrate concentration increases, in the proportion of substrate converted to product by a limited amount of an enzyme. 

Most of the more previous attempts to correlate carcinogenic potency with structural features of benzenoid hydrocarbons are related to the mechanism outlined above. The different quantitative models that have been developed can be distinguished with regard to the number of independent variables. One-variable theories (e.g. the so-called bay-region theory [94]) are normally inferior compared to two- [95] and three-variable theories which refer more explicitely to the different and partly competing metabolic reaction pathways. A particularely efficient model has been developed by v. Szentpaly [96]. In his so-called MCS model three important influences on carcinogenic potency are taken into account M, the initial epoxidation... 

A quantitative model for repulsion and dispersion interactions has been derived by Amovilli and Mennucci [21] based on the theory of weak interactions [22], Cavitation is strictly empirical in this context since it does not depend on the molecule but only on the cavity shape and on the environment it will have an indirect effect on properties only by contributing to the determination of the preferred molecule-interface orientation. 

Re-examination of the first quantitative model of the atom, proposed by Bohr, reveals that this theory was abandoned before it had received the attention it deserved. It provided a natural explanation of the Balmer formula that firmly established number as a fundamental parameter in science, rationalized the interaction between radiation and matter, defined the unit of electronic magnetism and produced the fine-structure constant. These are not accidental achievements and in reworking the model it is shown, after all, to be compatible with the theory of angular momentum, on the basis of which it was first rejected with unbecoming haste. 

The conjugated-circuits model is one of the simplest quantitative models that has been reasonably well studied. As already mentioned this model may be motivated from classical chemical bonding theory (extended a la Clar s classical empiricist argument) or from Simpson s existential quantum-theoretic argument [ 121 ], or from a quantum chemical derivation indicated in our hierarchy of section 3.2. But beyond derivation of the model there is the question of its solution, such as we now seek to address. 

A simple quantitative model, with no adjustable parameters, is developed for the finite size effect of ferroelectric particles on the Curie transition temperature. As the size of ferroelectric particles decreases, the Curie temperature decreases. Based on our model for lattice contraction and the Landau-Ginsburg-Devonshire (LGD) phenomenological theory, size effects on Curie temperature of lead zirconate titanate PbZri. Ti Oj (PZT, x > 0.6) are considered. It is shown that Curie temperature of PZT (x > 0,6) decreases with decreasing particle size. The predictions of our equation are in agreement with the experimental results. 

Recently, a quantitative model for the size-dependent Curie temperature has been established based on mechanic and thermodynamic considerations using the Landau-Ginsburg-Devonshire (LGD) phenomenological theory by equalizing free energies of the ferroelectrics and paraelectrics phases [1-4],... 

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