Quantitative kinetic molecular model

Appendix 1 Mathematical Procedures A1 Al.l Exponential Notation A1 A1.2 Logarithms A4 A1.3 Graphing Functions A6 A1.4 Solving Quadratic Equations A7 A1.5 Uncertainties in Measurements AlO Appendix 2 The Quantitative Kinetic Molecular Model A13... 

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) ... 

In Section 4.4, we used a molecular model of a gas to explain qualitatively why the pressure of a gas rises as the temperature is increased as a gas is heated, its molecules move faster and strike the walls of their container more often. The kinetic model of a gas allows us to derive the quantitative relation between pressure and the speeds of the molecules. 

We have chosen the PVC diad and triad compounds 2,4-dichloropentane (DCP) and 2,4,6-trichloroheptane(TCH) as subjects for our attempt to obtain quantitative kinetic data characterizing their (n-Bu)3SnH reduction in the hope that they will serve as useful models tor the reduction of PVC to E-V copolymers. Unlike the polymers (PVC and E-V), DCP and TCH are low molecular weight liquids whose high resolution 13C NMR spectra can be recorded from their concentrated solutions in a matter of minutes. Thus, it is possible to monitor their (n-Bu)3SnH reduction directly in the NMR tube and follow the kinetics of their dechlorination. 

It is impossible to understand all the complicated kinetic paths and to determine the elementary reaction rate constants without a detailed quantitative investigation of all the donor-acceptor interactions in the reaction system. Strictly speaking, at present there are no data on the elementary reaction rate constants even in low-molecular model systems. 

The true benefit from molecular models is that they permit the quantitative structural description of complex feeds. As noted above, this allows for easy extrapolation to unstudied systems and also permits product quality and properties issues to be addressed. The kinetics, while formulated at the molecular level, are nevertheless still implicitly tied to the mechanism. The CPU demands, however, are relatively small compared to those of mechanistic models. 

Equation (85) represents a general relationship between the Kerr constant K and the dipolar and optical properties of a kinetically rigid particle. To establish the quantitative dependence of K on the conformation and structure of a rigid-chain polymer molecule, the molecular model describing its electro-optical properties should be specified. For this purpose, we use a kinetically rigid worm-like chain, just as for the study of the FB problem. 

Using kinetic data on recombination macroradicals in freezed water solutions of lysozyme, superslow molecular motions of the biopolymer have been studied. Recombination of macroradicals is observed at 160-240 K and it has a stepwise character. The kinetic data are described quantitatively by the model,... 

Part of the power of molecular modeling lies in its ability to isolate aspects of a phenomenon in ways that are simply not possible by experiment. The effects of bond energy on the dissolution or surface diffusion allows one to turn off surface diffusion, for example, to quantitatively determine what effect it has on the dissolution rate and the resulting nanostructure. This example is one of many in which the dependence of critical parameters on the atomistic and molecular composition, as well as the local structure, including defects, can be determined. The insights that such calculations can provide into the overall thermodynamic, mechanical, and kinetic properties of a system are substantial. 

We have just seen how each of the gas laws conceptually follows from kinetic molecular theory. We can also derive the ideal gas law from the postulates of kinetic molecular theory. In other words, the kinetic molecular theory is a quantitative model that implies PV = nRT. Let s now explore this derivation. 

Kinetic molecular theory is a quantitative model for gases. The theory has three main assumptions (1) the gas partieles are negligibly small, (2) the average kinetic energy of a gas particle is proportional to the temperature in kelvins, and (3) the collision of one gas particle with another is completely elastic (the particles do not stick together). The gas laws all follow from the kinetic molecular theory. 

Photo-oxidation of some aaylic-urethane thermoset networks was induced by chromophoric impurities that absorb UV light and produce radicals, initiating a radical oxidation of the polymer [145]. The authors introduced a quantitative kinetic model based on the identified mechanisms and a multi-scale approach from the molecular to the macroscopic level. 

Calculations of the above type have not yet been applied to reactive systems" and there is clearly a perceived need for both quantitative kinetic measurements and complementary molecular mechanics/dynamics simulations for model intrazeolite reactions. In what follows, we describe the first experiments designed to fill this void. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

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