Possible Modes of Propagation

There are two possible points of attachment on monosubstituted (X = H) or 1,1-disubstituted monomers for a propagating radical—on either carbon 1 

If each successive addition of monomer molecules to the propagating radical occurs in the same manner as Eq. 3-9 or Eq. 3-8, the final polymer product will have an arrangement of monomer units in which the substituents are on alternate carbon atoms  

This type of arrangement (III) is usually referred to as a head-to-tail (H-T) or 1,3-placement of monomer units. An inversion of this mode of addition by the polymer chain propagating alternately via Eqs. 3-9 and 3-8 would lead to a polymer structure with a 1,2-placement of substituents at one or more places in the final polymer chain. 1,2-Placement is usually 

3-2 STRUCTURAL ARRANGEMENT OF MONOMER UNITS 3-2a Possible Modes of Propagation 

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The propagation stage involves growth of the polymer chain by rapid sequential addition of molecules of monomer to the active centre. The time required for each monomer addition typically is of the order of a millisecond and so several thousand additions can take place within a few seconds. As with the second step of initiation, there are two possible modes of propagation ... 

This involves growth of the polymer chain by rapid sequential addition of monomer to the active centre. As with the second step of initiation, there are two possible modes of propagation... 

Different molecular microstructures arise from there being several possible modes of propagation. The possibility of head-to-tail and head-to-head placements of the repeat units has been encountered already, with the observation that for both steric and energetics reasons the placement is almost exclusively head-to-tail for most polymers. Therefore in the subsequent sections dealing with the stereochemistry of propagation only head-to-tail placements will be considered. 

In the future, it is expected to be possible to make more routine use of additional wave types, specifically shear or S waves (polarised to horizontal and vertical components) which have a transverse mode of propagation, and are sensitive to a different set of rock properties than P waves. The potential then exists for increasing the number of independent attributes measured in reflection surveys and increasing the resolution of the subsurface image. 

Evidence provided by Blout and Karlson 49) and by Bamford and Block 18) implies, therefore, that there are at least two modes oi propagation even in a polymerisation initiated by primary or secondary amines. The evidence for other modes of propagation is apparent from studies of polymerisations initiated by tertiary amines and other aprotic initiators. We shall therefore review these reactions first, and then continue the discussion of possible mechanisms of these most intriguing polymerisations. 

The active center involved in the propagation reaction may be a free-radical, ion, or metal-carbon bond (see Chapters 6-10). A propagating species will be more stable if the unpaired electron or ionic charge at the end of the chain can be delocalized across either or both substituents X and Y. Such resonance stabilization is possible in (VII) but not in (Vm). Moreover when X and/or Y is bulky there will be more steric hindrance in reaction of Eq. (P2.7.2) than in the reaction of Eq. (P2.7.1). So, in general, head-to-tail addition as in Eq. (P2.7.1) is considered to be the predominant mode of propagation in all polymerizations. 

Scheme 11.3 The four possible modes of addition of norbomene (M) to a chiral propagating species (P/ or P ). P denotes a chain containing n monomer units. The four unspecified ligands may be the same or different.

The objective of this paper is to examine the roles of the Zeldovich number Z and the nondimensional sample size R on the different modes of propagation possible in SHS. In particular, we expand on results in [6] for surface modes on a cylinder of radius R as well as chaotic modes occurring in planar SHS combustion. The characteristics of the resulting combustion wave depend significantly on the mode of propagation and impact on the nature of the product synthesized and indeed the ability of the combustion wave to propagate in large samples. 

Figure 14.3 illustrates microscopic flame propagation [14], showing the possible modes of flame propagation between neighboring droplets in a plot of local... 

Analyses of polymers to determine stereosequence distributions and understand the propagation mechanism can be carried out with NMR spectroscopy aided by statistical propagation models [222, 402, 403]. A detailed discussion of the subject is beyond this book. The following is a brief explanation of the concepts. The Bernoulli, Markov, Colman-Fox, models describe propagation reactions with chain end control over monomer placement. The Bernoulli model assumes that the last monomer unit in the propagating chain end determines the stereochemistry of the polymer. No consideration is given to the penultimate unit or other units further back. In such an event, two modes of propagation are possible, meso and racemic ... 

It has been pointed out (8) that not only plane wave but also radial mode propagation is possible in the cavity and this explains the satellite peaks which can under certain circumstances interfere with the main mode of propagation above 7 MHz (7,8). In practice it is found that the simple theory outlined above is valid for a wide variety of systems... 

Because the video failed on the rocket flight, it was not possible to determine if the periodic structure resulted from a periodic mode of propagation or because of a thermodynamically-driven aggregation after the front. The... 

When the heat transfer is less than the maximum, there are two possible modes of steady state flame propagation—one corresponds to a low value of the flame velocity and the other to a high value. Spalding has studied these modes experimentally and discussed them from a quasi-theoretical point of view. 

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