Initiation step/initiator

Initial Step. Initial electron transfer has not been distinguished from initial halogcn-aioiu transfer (Section 7.2.21). 

The constants kj and k, are the rate constants for initiator dissociation and monomer addition, respectively. Since initiator dissociation (ecp. 7.10) is much slower than monomer addition (ecp. 7.11), the first step of the initiation step (initiator dissociation) is the rate-limiting step. Some of the initiator radicals may undergo side (secondary) reactions, such as combination with another radical, that preclude monomer addition. Therefore only a fraction, f (an efficiency factor), of the initial initiator concentration is effective in the polymerization process. Also, decomposition of each initiator molecule produces a pair of free radicals, either or both of which can initiate polymerization. Based on these observations, the rate expression for initiation may be written as ... 

End-functionalized polymers include macromonomers, tele-chelics, and polymers having functional groups pending to the main chain, for example, employed for click chemistry. End-functional groups can be introduced at the initiating step ( initiator method ), at the terminating step ( terminator method ), or during the polymerization like the copolymerization. 

Such step-limiting is often helpful because the direction of correction provided by the Newton-Raphson procedure, that is, the relative magnitudes of the elements of the vector J G, is very frequently more reliable than the magnitude of the correction (Naphtali, 1964). In application, t is initially set to 1, and remains at this value as long as the Newton-Raphson correotions serve to decrease the norm (magnitude) of G, that is, for... 

Polymerization reactions. There are two broad types of polymerization reactions, those which involve a termination step and those which do not. An example that involves a termination step is free-radical polymerization of an alkene molecule. The polymerization requires a free radical from an initiator compound such as a peroxide. The initiator breaks down to form a free radical (e.g., CH3 or OH), which attaches to a molecule of alkene and in so doing generates another free radical. Consider the polymerization of vinyl chloride from a free-radical initiator R. An initiation step first occurs ... 

The secondary reactions are parallel with respect to ethylene oxide but series with respect to monoethanolamine. Monoethanolamine is more valuable than both the di- and triethanolamine. As a first step in the flowsheet synthesis, make an initial choice of reactor which will maximize the production of monoethanolamine relative to di- and triethanolamine. 

The initial step in the pathway is the condensation of erythrose-4-phosphale with phosphoenolpyruvate, yielding dehydroquinic acid, which by elimination of the elements of water affords dehydroshikimic acid reduction of the 3-keto group to hydroxyl gives shikimic acid. 

Having defined and gathered data adequate for an initial reserves estimation, the next step is to look at the various options to develop the field. The objective of the feasibility study is to document various technical options, of which at least one should be economically viable. The study will contain the subsurface development options, the process design, equipment sizes, the proposed locations (e.g. offshore platforms), and the crude evacuation and export system. The cases considered will be accompanied by a cost estimate and planning schedule. Such a document gives a complete overview of all the requirements, opportunities, risks and constraints. 

The time taken to complete a base line study and EIA should not be underestimated. The baseline study describes and inventorises the natural initial flora, fauna, the aquatic life, land and seabed conditions prior to any activity. In seasonal climates, the baseline study may need to cover the whole year. The duration of an EIA depends upon the size and type of area under study, and the previous work done in the area, but may typically take six months. The EIA is often an essential step in project development and should not be omitted from the planning schedule. 

Some discontinuities may be identified by a conventional two-dimensional ultrasonic technique, from which the well-known C-scan image is the most popular. The C-scan technique is relatively easy to implement and the results from several NDE studies have been very encouraging [1]. In the case of cylindrical specimens, a circular C-scan image is convenient to show discontinuity information. The circular C-scan image shows the peak amplitude of a back-scattered pulse received in the circular array. The axial scan direction is shown as a function of transducer position in the circular array. The circular C-scan image serves also as an initial step for choosing circular B-scan profiles. The latter provides a mapping between distance to the discontinuity and transducer position in the circular array. 

Fig. XVIII-22. Schematic illustration of the steps that may be involved in a surface-mediated reaction initial adsorption, subsequent thermalization, diffusion and surface reaction, and desorption. (From Ref. 199 copyright 1984 by the AAAS.)...

A DIET process involves tliree steps (1) an initial electronic excitation, (2) an electronic rearrangement to fonn a repulsive state and (3) emission of a particle from the surface. The first step can be a direct excitation to an antibondmg state, but more frequently it is simply the removal of a bound electron. In the second step, the surface electronic structure rearranges itself to fonn a repulsive state. This rearrangement could be, for example, the decay of a valence band electron to fill a hole created in step (1). The repulsive state must have a sufficiently long lifetime that the products can desorb from the surface before the state decays. Finally, during the emission step, the particle can interact with the surface in ways that perturb its trajectory. 

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

A particular path from a given initial state to a given final state is the reversible process, one in which after each infinitesimal step the system is in equilibrium with its surroundings, and one in which an infinitesimal change in the conditions (constraints) would reverse the direction of the change. 

For an ideal gas and a diathemiic piston, the condition of constant energy means constant temperature. The reverse change can then be carried out simply by relaxing the adiabatic constraint on the external walls and innnersing the system in a themiostatic bath. More generally tlie initial state and the final state may be at different temperatures so that one may have to have a series of temperature baths to ensure that the entire series of steps is reversible. 

Thus, the spontaneous proeess involves the release of a eonstraint while the driven reverse proeess involves the imposition of a eonstraint. The details of the reverse proeess are irrelevant any series of reversible steps by whieh one ean go from the final state baek to the initial state will do to measure AS. 

Here the initially fonned excited species (C2Hg) is sufficiently long lived that the deactivation step (equation (A3.4.35)) is not essential and one writes... 

The initial step in alkane hydrogenolysis is the dissoeiative adsorption, or reaetive stieking of the alkane. One might suspeet that this first step may be the key to the stnieture sensitivity of this reaetion over Ni surfaees. Indeed, the reaetive stieking of alkanes has been shown to depend markedly on surfaee stnieture... 

Vibrational motion is thus an important primary step in a general reaction mechanism and detailed investigation of this motion is of utmost relevance for our understanding of the dynamics of chemical reactions. In classical mechanics, vibrational motion is described by the time evolution and l t) of general internal position and momentum coordinates. These time dependent fiinctions are solutions of the classical equations of motion, e.g. Newton s equations for given initial conditions and I Iq) = Pq. 

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

Bromide ion acts as an inliibitor through step (9) which competes for HBr02 with the rate detennining step for the autocatalytic process described previously, step (4) and step (5). Step (8) and Step (9) constitute a pseudo-first-order removal of Br with HBr02 maintained in a low steady-state concentration. Only once [Br ] < [Br ] = /fo[Br07]//r2 does step (3) become effective, initiating the autocatalytic growth and oxidation. 

After defining the input parameters, the calculation of the trajectories of an incident ion begins with a randomly chosen initial entrance point on the surface. The next step is to find the first collision partner. 

Pick s second law of difflision enables predictions of concentration changes of electroactive material close to the electrode surface and solutions, with initial and boundary conditions appropriate to a particular experiment, provide the basis of the theory of instrumental methods such as, for example, potential-step and cyclic voltanunetry. 

Potential-step teclmiques can be used to study a variety of types of coupled chemical reactions. In these cases the experiment is perfomied under diffrision control, and each system is solved with the appropriate initial and boundary conditions. 

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