Chain initiation definition

Similarly, a recent study141 of the homogeneous oxidation of cyclohexene by various low-valent phosphine complexes of Group VIII transition metals yielded no definite proof for initiation by oxygen activation. Results were consistent with reactions involving chain initiation via the usual redox reactions of the metal complexes with traces of hydroperoxides. Long induction periods were observed with peroxide-free hydrocarbons. 

The basic elements of Markov-chain theory are the state space, the one-step transition probability matrix or the policy-making matrix and the initial state vector termed also the initial probability function In order to develop in the following a portion of the theory of Markov chains, some definitions are made and basic probability concepts are mentioned. 

Now in polymerization it is probably not so much the monomer rate, but the product polymer rate and the properties of the product polymer that are of interest. The product polymer rate follows directly from equation (1-123) since, to the extent that the pssh is valid, the initiation and termination rates must be equal. The kinetic analysis also leads to some characterization norms for the product that are useful. The number-average degree of polymerization, P , is the average number of monomer units in the polymer product. This is defined in a manner analogous to the chain length definition of equation (1-113) and is... 

The chain reaction is a complicated process consisting of diverse elementary reactions (stages) these stages are related to one another in a definite way. They are classified as stages of chain initiation, propagation, and termination. 

An initial definition of supply chain risk is encompassed by Zsidisin (2005 p. 3) as the potential occitrrence of an incident or failrrre to seize opportunities with inboimd supply in which its outcomes resrrlt in a financial loss for the [purchasing]... 

After ouflining the topic of interest and the objectives of die work at hand. Chapter 2 attends to the theoretical backdrop of the research conducted, which, in essence, comprises a definitional and a contentual part. As the presentation of the objectives in Chapter 1 indicates, two terms are central, supply chain initiative and value, the understanding of which is clarified in Chapters 2.1 and 2.2. In terms of content, relevant research fields are identified (Chapter 2.3) that establish the basis for an overview of the state of the art in the value determination of SCIs (Chapter 2.4). The chapter closes with a short summary in Chapter 2.5. 

Probably the most important development of the past decade was the introduction by Brown and co-workers of a set of substituent constants,ct+, derived from the solvolysis of cumyl chlorides and presumably applicable to reaction series in which a delocalization of a positive charge from the reaction site into the aromatic nucleus is important in the transition state or, in other words, where the importance of resonance structures placing a positive charge on the substituent - -M effect) changes substantially between the initial and transition (or final) states. These ct+-values have found wide application, not only in the particular side-chain reactions for which they were designed, but equally in electrophilic nuclear substitution reactions. Although such a scale was first proposed by Pearson et al. under the label of and by Deno et Brown s systematic work made the scale definitive. 

Many emulsion polymerizations can be described by so-called zero-one kinetics. These systems are characterized by particle sizes that are sufficiently small dial entry of a radical into a particle already containing a propagating radical always causes instantaneous termination. Thus, a particle may contain either zero or one propagating radical. The value of n will usually be less than 0.4. In these systems, radical-radical termination is by definition not rate determining. Rates of polymerization are determined by the rates or particle entry and exit rather than by rates of initiation and termination. The main mechanism for exit is thought to be chain transfer to monomer. It follows that radical-radical termination, when it occurs in the particle phase, will usually be between a short species (one that lias just entered) and a long species. 

Kinetic vs. material chain. Kinetically, a chain reaction exists throughout the "life" of the radical, that is, from the initiation of a radical up to its termination by recombination or by disproportionation. The lifetime of a radical determines the so-called kinetic chain length Lp defined as the number of monomers consumed per initiating radical. Lp, by definition, can be calculated from the ratio between the propagation rate Rp to the initiation rate R, or, using steady-state hypothesis (Equation (1)), from the ratio between propagation rate to the termination rate Rt (Equation (3)). 

It is known that the oxidation potentials of diazodiphenylmethane and Cu(I) in acetonitrile are very similar. With CuBr2 however, no radical-chain reaction takes place. Contrary to the copper perchlorates, CuBr2 and CuBr initiate identical reaction pathways involving copper carbenoids. No definite answer to this discrepancy is available 402). 

Considering that for a steady system, the termination and initiation steps must be in balance, the definition of chain length could also be defined as the rate of product formation divided by the rate of termination. Such a chain length expression would not necessarily hold for the arbitrary system of reactions (3.1)—(3.6), but would hold for such systems as that written for the H2—Br2 reaction. When chains are long, the types of products formed are determined by the propagating reactions alone, and one can ignore the initiation and termination steps. 

---