Multi-State Models. In studies of copolymerization kinetics and polymer microstructure, the use of reaction probability models can provide a convenient framework whereby the experimental data can be organized and interpreted, and can also give insight on reaction mechanisms. (1.,2) The models, however, only apply to polymers containing one polymer component. For polymers with mixtures of different components, the one-state simple models cannot be used directly. Generally multi-state models(11) are needed, viz. [Pg.175]

Among those TDQM studies, exact quantum dynamical calculations were usually limited to the total angular momentum / = 0. For / > 0, most of the authors used a capture model (or L-shift model) [77] to estimate the reaction probability from the / = 0 results. Even the direct calculations of reaction probabilities for / > 0 were performed using the centrifugal sudden (CS) approximation. Carroll [Pg.28]

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. [Pg.540]

Coupled channel methods for colllnear quantum reactive calculations are sufficiently well developed that calculations can be performed routinely. Unfortunately, colllnear calculations cannot provide any Insight Into the angular distribution of reaction products, because the Impact parameter dependence of reaction probabilities Is undefined. On the other hand, the best approximate 3D methods for atom-molecule reactions are computationally very Intensive, and for this reason. It Is Impractical to use most 3D approximate methods to make a systematic study of the effects of potential surfaces on resonances, and therefore the effects of surfaces on reactive angular distributions. For this reason, we have become Interested In an approximate model of reaction dynamics which was proposed many years ago by Child (24), Connor and Child (25), and Wyatt (26). They proposed the Rotating Linear Model (RLM), which Is In some sense a 3D theory of reactions, because the line upon which reaction occurs Is allowed to tumble freely In space. A full three-dimensional theory would treat motion of the six coordinates (In the center of mass) associated with the two [Pg.494]

In contrast to the vibrational effect, the rotational effect on hydrogen dissociation on Cu is much less understood, until very recently. Most 3D quantum calculations have used the plane rotor model, which is not appropriate for studying rotational effects. The studies of Refs. 113, 114, and 117 using the spherical rotor treatment have obtained important results on the effect of rotational orientation and the nuclear symmetry. The rotational orientational effect is clearly shown in Fig. 15, where reaction probabilities for different initial rotational orientation states are plotted as a function of kinetic energy. Significant enhancement of reaction probability is seen for the state with j = m ( helicopter mode) while the m = o ( cartwheel mode) is least effective for dissociation. [Pg.269]

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