Propagation steps defined

The first-order Markov model In the first-over Markov model, the probability of monomer addition depends upon the identity of the preceding monomer unit. Hence, for an A/B copolymer, there are four possible propagation steps defined by four monomer addition probabilities ... 

In Chap. 5, p was defined as the fraction (or probability) of functional groups that had reacted at a certain point in the polymerization. According to the current definition provided by Eq. (6.66), p is the fraction (or probability) of propagation steps among the combined total of propagation and termination steps. The quantity 1 - p is therefore the fraction (or... 

Photopolymerization, in general, can be defined as the process whereby light is used to induce the conversion of monomer molecules to a polymer chain. One can distinguish between true photopolymerization and photoinitiation of polymerization processes. In the former, each chain propagation step involves a photochemical process [1,2] (i.e., photochemical chain lengthening process in which the absorption of light is indispensable for... 

During the propagation step, depending on the nature of the active ionic species, a limited control on the tacticity of the final polymer is possible. Ion pairs can, indeed, require the insertion of the monomer under a defined orientation, while free ions are unable to orient the insertion. 

First-order behavior (as normally defined) at any pressure can be rationalized if the first propagation step is made reversible. This is not unreasonable because the step in the forward direction is strongly endothermic (+159 kJ mol 1), so its reverse should make itself felt long before the reverse of the overall reaction becomes noticeable. The rate of this reverse step is proportional to a product, so that the retardation it exerts increases with progressing conversion. This translates into a higher apparent reaction order. Quantitatively, the mechanism 9.38 with termination 9.39 and reversible first step gives a rate equation of the form... 

If the bichromophoric system is suitably chosen to eliminate intramolecular processes and to ensure the possibility of inter-molecular reaction, a polymer can be formed. Where previously the term photopolymerization was used to Indicate photoinltiated chain processes (161), the present discussion of nonconjugated blchromophores is from a different point of view. The term "photopolymerization" as defined here, is a polymerization process in which every chain-propagating step Involves the absorption of a photon (162,163). This definition Implies that photopolymerization is a stepwise reaction, in contrast to photoinltiated polymerization, which Is a chain process. A sensitized photopolymerization is a photopol ymerlzation in which the reacting... 

Autocatalysis is defined as a process where a catalyst catalyzes its own formation. This process has been proposed as one of possibilities for the propagation of optical activity on earth [63]. A problem, not solved by the autocatalysis, is how to amplify a small initial enantiomeric excess to a large value, before using autocatalysis in the propagation step. Frank proposed in 1953 a kinetic model which combines amplification of ee and increase of the amount of product (propagation) [64]. It is based on the reaction A-i-B k+S, where R and S are enantiomeric products. The reaction towards R is catalyzed by R, while formation of S is catalyzed by S. A second reaction was considered R+S R. This uncatalyzed reaction gives an inert product P which does not participate in the re-... 

Other workers have reported the homopolymerization of certain substituted bismaleimides in solution by successive 2+2 cycloaddition reactions, and they have appropriately defined this type of process as a true photopolymerization i.e. a polymerization in which every chain-propagating step involves a photochemical reaction. Another such example is the solid-phase 2+2 cyclopolymerization of divinyl monomers.— By contrast, the polymers described above result from a combination of photocycloadditions and Diels-Alder cycloadditions. 

The CO/NO, reaction mechanism is a chain reaction with OH as the chain carrier. The chain length L, of such a reaction is defined as the number of propagation steps occurring for each termination step. 

Removing the Cl and Cl lj that appear on both sides of the equation leaves just the molecules of the overall process. What about the initiation and termination steps and their AW° s They are. separate. Ti.eir AW values are not a part of the enthalpy change as it is defined for the stoichiometric reaction. When we measure the heal of a radical reacl.ion experimentally, the value we obtain will not be precisely equal to AW" fur the propagation steps alone initiation and termination steps arc ocairring, too. and their AW" s will introduce an error. This deviation will usually he small, however, hccau.se initiation and temiination steps (Kcur only infrequently relative to the propagations, and because the AW s for the endothermic initiation is for the most part canceled out by that of the exothermic termination procc.s.ses. 

It is obvious that all three reactions (initiation, propagation and termination) are vital for the polymerization process, but the propagation step determines both the rate of the polymerization process and the chain length (as defined later). The rate of propagation (actually representing the rate of polymerization), tp, depends on the rate constant kp and on the concentration of reactants. It is, in principle, identical to the rate of disappearance of the monomer. 

The chain reactions treated in Section 3.4 consist of straight chains. There is an initiation step taking place at a rate r,-. The propagation steps do not produce nor do they destroy active centers. This is so because in each step of the closed sequence, the active centers change only in kind, not in number. Therefore, there exists a steady state defined by the condition that the rate of initiation is equal to the rate of termination. 

Polyinsertions are defined as polymerizations in which the monomer is added between the growing chain and the initiator moiety (see Section 16.5.1). A coordination of the monomer with the initiator frequently precedes the true insertion step, and so this type of polymerization is also termed a coordination polymerization. However, there are cases in which the monomer is coordinated with the initiator, but no real polyinsertion reaction occurs. Ethylene, for example, forms a coordination compound with silver nitrate, but the subsequent polymerization is a free radical polymerization. For this reason, the name polyinsertion appears to be more appropriate than coordinative polymerization because it emphasizes the propagation step, which is decisive in polymerizations, and not on the complex formation that precedes this step. 

First-order Markov processes are therefore defined by two independent addition probabilities. Although the propagation steps shown above depict free radical polymerisation, the statistical models are equally applicable to other types of chain growth as found, for example, in ionic and Ziegler-Natta polymers (see section 2.3.4). 

In general, during copolymerisation, the two reacting monomers are not incorporated into the polymer chain in the same proportion as in the initial comonomer mixture. The reason for this is that the two monomers generally have different reactivities towards the growing chain ends. In the terminal model, it is assumed that the nature of the monomer at the growing chain end determines relative comonomer reactivity. In other words, there are four types of propagating step, each defined by a different rate constant ... 

Define and provide a specific example of each of the following terms propagation step initiation step bond homolysis limiting reagent... 

The processes of Schemes 1-7 can be catalytic in the oxidation-reduction couple. The true mechanisms are often more complicated than the reaction schemes indicate, and the formation of various complexes involving the metal ion must be considered as well as the possible intervention of ligand transfer processes either within a cage or in noncage reactions. In Schemes 1-7 the initiation step is also one of the propagation steps and a clearly defined sequence of separate initiation, propagation and termination steps does not exist. 

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