Scaling kinetic results

The aim of the book is to give practical advice for those who want to generate kinetic results, valid for scale-up, and backed by sensible theory and understandable mathematical explanation. [Pg.280]

Finally, Section X provides a summary of the results and outlines the path toward large-scale kinetic models of metabolism. [Pg.109]

Atoms taking part in diffusive transport perform more or less random thermal motions superposed on a drift resulting from field forces (V//,-, Vrj VT, etc.). Since these forces are small on the atomic length scale, kinetic parameters established under equilibrium conditions (i.e., vanishing forces) can be used to describe the atomic drift and transport, The movements of atomic particles under equilibrium conditions are Brownian motions. We can measure them by mean square displacements of tagged atoms (often radioactive isotopes) which are chemically identical but different in mass. If this difference is relatively small, the kinetic behavior is... [Pg.107]

In many cases, the study of kinetics concerns itself with the paths and rates adopted by systems approaching equilibrium. Thermodynamics provides invaluable information about the final state of a system, thus providing a basic reference state for any kinetic theory. Kinetic processes in a large system are typically rapid over short length scales, so that equilibrium is nearly satisfied locally at the same time, longer-length-scale kinetic processes result in a slower approach to global equilibrium. Therefore, much of the machinery of thermodynamics can be applied locally under an assumption of local equilibrium. It is clear, therefore, that the subject of thermodynamics is closely intertwined with kinetics. [Pg.4]

Most of the kinetic results so far obtained upon oxygen exchange are summarized in Figs. 3 to 6, which also show the kinetics of the equilibration reaction plotted to the same scale. Before attempting an interpretation of these observations, it is desirable to consider first the nature and extent of the oxide surface and the adsorption of oxygen thereon and also to review briefly other experimental evidence regarding the interaction between gas and surface. [Pg.202]

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. [Pg.469]

The search for local minima in the neighborhood of a given local minimum is usually performed by the excitation of the system from this state followed by the relaxation of the system. If the relaxation of the excited system results in a state different from the initial state (and explored earlier), then a new local minimum is found, otherwise the evolution of the excited system is continued. The ways of moving out of the initial state can be different in temperature accelerated dynamics (TAD) by Sorensen and Voter [78], MD is used at high temperatures in the activation-relaxation technique (ART) by Mousseau and Barkema [79] and the local activated Monte Carlo method (LAMC) [80], the system evolves along the direction opposite to the direction of the force in the long-scale kinetic Monte Carlo... [Pg.485]

Our kinetic results of the hydrolysis of NHAS between pH 4 and 5.8 were obtained from the analysis of rapid mixing stopped-flow experiments in the kinetic studies of NO reaction with HSO3. Figure 3 shows the curve of absorption vs. time for a typical stopped-flow experiment at pH 4.6. The flow was stopped at 4 seconds on the scale shown in the figure. The absorbance initially rose due to the continued reaction of NO with HSO3 and As the reactants were... [Pg.171]

Decomposition of Ti(0-iC 3117)4 dissolved in supercritical isopropanol leads to the formation of titanium oxide. The reaction is studied in the temperature range 531 to 568 K under 10 MPa and a mechanism is proposed. The obtained kinetic results are further used to optimize a continuous reactor producing submicronic TiC>2 powder at a laboratory pilot scale. [Pg.133]

Example 15.8 A bench-scale kinetic study was conducted on a particular carbonaceous waste producing the result below. Calculate T IJ-cm, and K,. [Pg.714]

Walas, S. M. Scaling Test Results, In Reaction Kinetics for Chemical... [Pg.133]

Kinetic results. Figure 6 shows the distribution of kinetic measurements for 7 temperature steps between 90.4° and 94.4°C (duration times in logarithmic scale). [Pg.287]

The oxidation of Ti3A1 alloys would not be expected, in light of the above thermodynamic considerations, to form continuous alumina scales. Instead they form mixed rutile-alumina scales [49].The oxidation kinetics of Ti3Al between 600 and 950°C are reported to be essentially those expected for rutile growth [50,51]. These kinetics result from the development of a complex oxide layer which contains continuous paths of Ti02 through which rapid transport occurs. Typical oxide scales are shown schematically in Figure 14. [Pg.29]

Sometimes correlations of kinetic results with Hammett a constants present difficulties. Reactions (a), (d) and (i) of Table 8 give curved plots, all with the concavity upwards, independently of the signs of the average slopes. For reaction (d), however, it has been shown that a linear plot can be obtained using a (T scale, based on ionisation of phenols in various solvents adopting the new abscissa, the p value is lowered to something between 0.2 and 0.3. [Pg.106]

Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...