Growing chains, number

The electron distribution ciround the carbon atom (meirked with an asterisk in Figure 2.21) of a growing chain may take a number of forms. In Figure 2.21 (a)... 

One of the most striking features of the common fatty adds is that they have an even number of carbon atoms (Table 27.1, p. 1062). This even number results because all fatty acids are derived biosynthelically from acetyl CoA by sequential addition of two-carbon units to a growing chain. The acetyl CoA, in turn, arises primarily from the metabolic breakdown of carbohydrates in the glycolysis pathway that weTl see in Section 29.5. Thus, dietary carbohydrates consumed in excess of immediate energy needs are turned into fats for storage. 

The initiator or iniferter determines the number of growing chains. Several methods of initiation are used. Only three will be considered here. The first involves direct use of a species 1-X (e.g. a dilhiocarbamale ester - Section 9.3.2 or an alkoxyamine - Section 9.3.6) as shown in Scheme 9.4. Ideally, the degree of polymerization is given by eq. I and the molecular weight by eq. 2. 

In ATRP, the initiator (RX) determines the number of growing chains. Ideally, the degree of polymerization is given by eq. 7 and the molecular weight by cq. 8. Note the appearance of the initiator efficiency (/ ) in the numerator of these expressions. In practice, the molecular weight is ofien higher than anticipated because the initiator efficiency is decreased by side reactions. In some cases, these take the form of heterolytic decomposition or elimination reactions. Further redox chemistry of the initially formed radicals is also known. The initiator efficiencies are dependent on the particular catalyst employed. 

Figure 20 shows the plot of the surface tension vs. the logarithm of the concentration (or-lg c-isotherms) of sodium alkanesulfonates C,0-C15 at 45°C. In accordance with the general behavior of surfactants, the interfacial activity increases with growing chain length. The critical micelle concentration (cM) is shifted to lower concentration values. The typical surface tension at cM is between 38 and 33 mN/m. The ammonium alkanesulfonates show similar behavior, though their solubility is much better. The impact of the counterions is twofold First, a more polarizable counterion lowers the cM value (Fig. 21), while the aggregation number of the micelles rises. Second, polarizable and hydrophobic counterions, such as n-propyl- or isopropylammonium and n-butylammonium ions, enhance the interfacial activity as well (Fig. 22). Hydrophilic counterions such as 2-hydroxyethylammonium have the opposite effect. Table 14 summarizes some data for the dodecane 1-sulfonates.

The dynamic chain length is the number average length of the growing chains before termination. The dead polymer will have the same average length as live polymer if termination is by disproportionation and will have twice this length if termination is by combination. 

X indicates a small substituent, which may be an atom such as hydrogen (H) or chlorine (Cl) or it may he a group such as methyl (CH3), cyano (CN), carhoxyl (COOH), carbomethoxy (COOCH3), etc. The growing chain is terminated by collision with another chain or other radical source or by one of several other mechanisms. The number of monomer units in the polymer chain is the degree of polymerization, abbreviated DP. If the degree of polymerization is very low, the product is sometimes referred to as an oligomer. 

Currently this model is one of the most commonly used in the theory of free-radical copolymerization. The formation of a donor-acceptor complex Ma... iVlbetween monomers Ma and in some systems is responsible for a number of peculiarities absent in the case of the ideal model. Such peculiarities are due to the fact that besides the single monomer addition to a propagating radical, a possibility also exists of monomer addition in pairs as a complex. Here the role of kinetically independent elements is played by ultimate units Ma of growing chains as well as by free (M ) and complex-bound (M ) monomers, whose constants of the rate of addition to the macroradical with a-th ultimate unit will be... 

The rate of consumption of PMDS was too fast to follow, however, this was not the case for HMDS, and the disappearance of dichloride was followed with time. The dependence of the reaction on the surface area of sodium is shown in Figure 5. There is an initial period of increasing rate, and this is very dependent on the sodium surface area. This induction period can be associated with an Increase in the number of actively growing chains with comparatively long life-... 

Detailed studies by Patzlaff et al.918 have shown that addition of ethene causes an increased fraction I, of the distribution characterized by a and a small increase of ctj. This indicates that ethene mainly acts as a chain initiator of hydrocarbons formed according to distribution 1, and to a very small extent as a surface intermediate for insertion into a growing chain. Concurrent experimental results were obtained by Schulz and Claeys.19 Distribution 2 and also a2 are not affected by co-feeding of ethene. Figure 11.4 shows that ethene changes the ASF plot only in the range of low carbon numbers. 

Since there is a close correlation between the specific conductivity of the catalytic solutions and the DP of the polymers formed in them, it follows that the electrochemical nature of the solutions must be largely unaffected by the polymerisation. Therefore at most a small fraction of the solute can be involved with the growing chain, and the remainder must be unaffected by the initiation of the polymerisation. This conclusion is strongly supported by the fact that in typical experiments the number of moles of polyisobutene formed was several powers of ten smaller than the number of moles of catalytic complex. 

However, for a variety of reasons it seems extremely unlikely that the same mechanism is applicable to the polymerisation of cyclic formals and acetals. One reason is that these compounds cannot be co-polymerised with cyclic ethers another is that the polymers are predominantly cyclic, with the number of end-groups far smaller than the number of growing chains. One mechanism which has been proposed and which accounts for most of the observations involves formation of an oxonium ion (X) from the initiator and the monomer, and a subsequent propagation by a ring-expansion reaction (see 13). 

As in the case with cationic polymerizations, the number of growing chains is constant so that a steady state exists such as the Ri = R. This is useful because it is difficult to determine the concentration of [M ] so that it can be eliminated as follows ... 

As it is experimentally found that the number of growing chains is constant, there exists a steady state in M so that = Rtd (a similar scenario can be used to develop rate expressions for coupling). 

Since the initiation of polymerization takes place in the aqueous phase, essentially no polymerization occurs in the globules. Thus, they serve primarily as a reservoir of monomer supplied to the micelles to replace monomer converted to polymer. The number of droplets per milliliter of water is on the order of lO k Since there are 10 million times as many micelles as droplets, the chance of initiation of monomer in a droplet is very small and the chance that more than one growing chain occurs within the same droplet is very small. 

When polymerizations become viscous, termination slows allowing an increase in the number of growing chains and rate of polymerization. This is known as the gel of Trommsdorff effect. If such reactions are allowed to continue without cooling, explosions are possible. 

Since it is experimentally observed that the number of growing chains remains approximately constant throughout the duration of most copolymerizations (i.e., a steady state in the number of growing chains), the concentrations of Mj and are constant, and the rate of conversion of Mj to Mj is equal to the conversion of Mj to Mj i.e., i2[Mj][M2] = k2 [Mj][Mi]. Solving for Mj gives... 

It was observed that in some systems even oligomers are not able to complex but polymers with high molecular weight give insoluble, stable polymer-polymer complexes. The number of units in polymer chain sufficient for stable absorption is called critical length. Below the critical length, the growing chain can exist in solution, above the criti-... 

Sr = sum of the rates of chains transfer and termination processes Ct = number of growing chains at time t... 

It can be seen that the kinetic studies on dienes confirm that the propagation reaction has a first-order dependence on the monomer concentration. These observations are to be expected since in the absence of adventitious impurities the number of growing chains should remain constant, only the monomer concentration decreases. 

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