Successive situations chain

The simplest successive events chain (SEC) is a couple of events parent and offspring event. Parent event represents the cause of possible spreading. For example, such parent event can he a defect in cable-junction box and as an offspring event we can consider a blaze in a control room. Of course, the parent event must not lead to offspring event in any case. SEC can he considered as a Markov process with three possible states the transient parent state and two absorbing states, first of them represents a system collapse due to the offspring event, the second one is the situation when cable-junction box does not cause any consequent event (e. g. it is repaired and no offspring event occurs). 

Fig. 6.4. Four successive situations of a reptating chain, (a) The initial conformation of the primitive chain and the tube which we call the original tube, (b) and (c) As the chain moves right or left, some parts of the chain leave the original tube. The parts of the original tube which have become empty of the chain disappear (dotted line), (d) The conformation at a later time t. The tube segment vanishes when it is reached by either of the chain ends e.g., the tube segment P and Q vanish at the instance (ft) when (t) = Sp and at (c) when t) = SQ-L,...

Free successive situations for a reptating chain (a) the chain is trapped in its original tube (b) the chain moves to the right and a certain portion (I,F) of the original tube disappears (c) the chain moves to the left, and a portion (JuJz) of the original tube disappears. 

All polymer molecules have unique features of one sort or another at the level of individual repeat units. Occasional head-to-head or tail-to-tail orientations, random branching, and the distinctiveness of chain ends are all examples of such details. In this chapter we shall focus attention on two other situations which introduce variation in structure into polymers at the level of the repeat unit the presence of two different monomers or the regulation of configuration of successive repeat units. In the former case copolymers are produced, and in the latter polymers with differences in tacticity. Although the products are quite different materials, their microstructure can be discussed in very similar terms. Hence it is convenient to discuss the two topics in the same chapter. 

Having said this, it was felt therefore that there is a need for a book addressing analysis and characterisation of polymers from the point of view of what we wish to call the primary analytical question. Many excellent textbooks and reference works exist which address one or more individual analytical techniques, see, for example, references [1-10]. These books form the basis of the knowledge of the technique expert. They also contain many excellent and varied examples on successful applications of analytical techniques to polymer analysis and characterisation. There are also books which address the multitude of analytical techniques applied in polymer analysis, see, for example, references [11-24], However, a synthetic chemist may wish to know the constitution of his/her polymer chain, a material scientist may want to find out the reasons why a fabricated sample had failed. What technique is best or optimal to study chain constitution will depend on the situation. Polymer failure may result from morphological features, which needs to be avoided, a contaminant, a surface property degradation, etc. When a sample has been processed, e.g., a film blown, molecular orientation may be the key parameter to be studied. A formulation scientist may wish to know why an additive from a different supplier performs differently. It is from such points of view that polymer analysis and characterisation is addressed in this book. 

Different planning philosophies prevail in industry simultaneous planning approaches and successive planning approaches. While the first one is clearly the best choice in smaller well-defined planning situations, in supply chains often thousands of individual decisions need to be made and coordinated. Due to the high degree of complexity successive planning approaches are therefore often chosen in practice. 

Several workers have attempted to use the common ion technique to depress [Pn+] and thus to achieve a monoeidic Pn+A system, as was done so successfully for anionic systems. However, because generally the solvents used for cationic polymerisations are much more polar, the KD of the chain-carriers and of the common-ion salts are considerably greater than in the anionic systems. Therefore the electro-chemical situation is likely to be complicated by triple ion formation and the effects of ionic strength on the KD and on the rate-constants, so that any results obtained by extrapolations to infinite ionic strength need to be scrutinised most carefully. 

The situation is quite different in chain polymerization where an initiator is used to produce an initiator species R with a reactive center. The reactive center may be either a free radical, cation, or anion. Polymerization occurs by the propagation of the reactive center by the successive additions of large numbers of monomer molecules in a chain reaction. The distinguishing characteristic of chain polymerization is that polymer growth takes place by monomer reacting only with the reactive center. Monomer does not react with monomer and the different-sized species such as dimer, trimer, tetramer, and n-trier do not react with each other. By far the most common example of chain polymerization is that of vinyl monomers. The process can be depicted as... 

Radical chain processes break down whenever the velocity of a termination reaction is comparable to the velocity of the rate-controlling step in a chain reaction. This situation would occur, for example, if one attempted to use EtsSiH as the hydrogen atom donor in the alkyl halide reduction sequence in Figure 4.6 and employed typical tin-hydride reaction conditions because the rate constant for reaction of the silane with an alkyl radical is 4 orders of magnitude smaller than that for reaction of Bu3SnH. Such a slow reaction would not lead to a synthetically useful nonchain sequence, however, because no radical is persistent in this case. In fact, a silane-based radical chain reduction of an alkyl halide could be accomplished successfully if the velocity of the initiation reaction was reduced enough such that it (and, hence, also the velocity of alkyl radical termination... 

Some success has been achieved in the tandem formation of two rings when two double bonds are appropriately situated on an ortho side chain of iodobenzene (equation 27).80... 

Polymer chains are, in general, regularly built-up, but a few variations are possible. We shall, successively, consider arrangement of monomers, situation of side groups, arrangement round a double bond, branching, and copolymer structure. 

Epitaxial crystallization of helical polymers may involve three different features of the polymer chain or lattice. These are (a) the interchain distance (as for stretched out polymers), (b) the chain axis repeat distance, and (c) the interstrand distance - the distance between the exterior paths of two successive turns of the helix. The two former periodicities are normal and parallel to the chain axis direction, and are therefore not usually sensitive to the chirality of the helix (unless the substrate topography is asymmetric and favors a given helical hand). However, the interstrand distance is oblique to the helix axis (it is normal to the orientation of the outer chain path) and therefore has different, symmetric orientations relative to the helix axis for left-handed and right-handed helices (Fig. 2). In other words, epitaxies that involve the interstrand distances are discriminative with respect to helix chirality. This discrimination becomes visible if the crystal structure is based on whole layers of isochiral helices. Such a situation does indeed exist for isotactic poly(l-butene), Form I, that will be considered soon. 

Applications of controlled radical reactions - including oxidation - deal almost exclusively with C=C double bonds. Indeed, a multitude of examples have been reported for the selective transformation of this functional group. Contrasting with this situation, only a very limited number of selective ( stereocontrolled ) radical reactions involving sp3-hybridized C-H bonds are known. Particularly useful functionalizations along these lines include the hydroxylation and the acyloxylation of alkyl chains. The reason for their limited success is of course due to the high stability of the C-H bond compared with that of the olefinic C=C unit most electrophilic reagents which readily add to unsaturated substrates are not able to oxidize a C-H bond. 

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