Propagation probabilities

An analogous homopolymerisation can be initiated by strong bases, including for example tert-amines. In this case chain propagation probably proceeds through an oxyanion ... 

In a recent study of this system Rozenberg (41) found that the rate of reaction of the dialkyl acyl oxonium ion with THF is less than the rate of propagation, probably as a result of conjugation of the oxonium ion with the carbonyl group. 

Since this brief summary covers most of our present knowledge of the stereospecific polymerizations, it must be very evident that any mechanism now proposed must be based largely on intuition and cannot be detailed. Most authors agree that propagation probably occurs via an anionic reaction between a metal alkoxide and an epoxide,... 

Reduction and chain propagation probably occur in a manner described earlier for unsupported Ziegler catalysts. 

Zip length = Probability of propagation Probability of (transfer + termination)... 

The initiation step depends upon formation of oxonium ions. Because a carbon cation intermediate is indicated, it was suggested that the propagation probably occurs by ether exchange which results from a nucleophilic attack by the monomer on the oxonium ion. 

Therefore, a further automation of the screening process including a systematic calculation of fire propagation probabilities has been developed and tested. In addition, standardized simplified fire simulations by means of a simpler zone model have been included in the screening process to roughly predict parameters critical for the Fire PSA. 

Table 1.8 Tacticity sequence probabilities expressed in terms of propagation probabilities for Bernoullian and first-order Markov statistics the parameters u and v are defined in the text...

Other propagation models are also possible. An example is an adaptation [48,55,65] of the Coleman-Fox [66] mechanism in which the polymerisation is considered to take place at two active sites, each with a different Bernoullian propagation probability (see chapter 2). 

Firstly, we assume that termination is solely by disproportionation and that the propagation probability factor is equal for each chain length. The probability for the occurrence of a polymer chain—hence its distribution function—with the length P is given by the probability of P - 1 propagation steps and the probability of one chain-stopping event (termination or transfer). 

In this section, we introduce the concept of ASRs and the related architectural attributes. These architectural attributes are used to calculate failure propagation probabilities and relate the software architectures to the system reliability. Based on the failure propagation and the reliability quantification, these attributes are then used to derive the architectural design rationale and decisions. 

Digressing for a moment, it should be recognized that the sequence propagation probability, p, in the melt can be related to the comonomer reactivity ratio for addition type copolymerization. Formulating copolymerization kinetics in the classical manner(5), we let Fa represent the fraction of monomer Ma in the increment of copolymer formed at a given stage of the polymerization. Then one can write... 

A major consequence of Eq. (5.26) is the expectation that the melting temperature of a copolymer, where only one type unit is crystallizable, depends only on the sequence propagation probability p and not directly on composition. This result is rather unusual, and is unique to long chain molecules. Considering the major categories of copolymer structure we find in the extremes that... 

---