Chain kinetics initiation

Fig. 2. Main steps of reaction kinetics, where chain initiation is identical to other vinyl polymerizations.

Monomer molecules, which have a low but finite solubility in water, diffuse through the water and drift into the soap micelles and swell them. The initiator decomposes into free radicals which also find their way into the micelles and activate polymerisation of a chain within the micelle. Chain growth proceeds until a second radical enters the micelle and starts the growth of a second chain. From kinetic considerations it can be shown that two growing radicals can survive in the same micelle for a few thousandths of a second only before mutual termination occurs. The micelles then remain inactive until a third radical enters the micelle, initiating growth of another chain which continues until a fourth radical comes into the micelle. It is thus seen that statistically the micelle is active for half the time, and as a corollary, at any one time half the micelles contain growing chains. 

It Is well known that low values of Tq and [ ]q lead to high DPs. This Is accurately reflected by parameter (v )q, the Initial kinetic chain length (Table XIll), which Is a quotient of feed composition ratio Xq and dimensionless parameter a. Thus,... 

In the absence of an initiator, alcohols are oxidized with self-acceleration [7-9]. As in the oxidation of hydrocarbons, the increase in the reaction rate is due to the formation of peroxides initiating the chains. The kinetics of radical formation from peroxides was studied for the oxidation of isopropyl alcohol [58] and cyclohexanol [59,60]. 

Radical polymerizations have three important reaction steps in common chain initiation, chain propagation, and chain termination. For the termination of chain radicals several mechanisms are possible. Since the lifetime of a radical is usually less than 1 s, radicals are continuously generated and terminated. Each propagating radical can add a finite number of monomers between its initiation and termination. If a divinyl monomer is in the monomer mixture, the reaction kinetics changes drastically. In this case, a dead polymer chain may grow again as a macroradical, when its pendant vinyl groups react with radicals, and the size of the macromolecule increases until it extends over the whole available volume. 

The same phenomenon was found in the polymerization (to dimers and trimers) of trans-stilbene by TiCl4-CCl3COOH in benzene [8]. In this case chain initiation is presumably by protons, and there appears to be no kinetic termination at all. 

Note In many cases, the rate of chain initiation is fast compared with the rate of ehain propagation, so that the number of kinetic-ehain earriers is essentially eonstant throughout the polymerization. 

Consider the polymerization of styrene initiated by di-t-butyl peroxide at 60°C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rates of initiation and polymerization are 4.0 x 10 11 and 1.5 x 10 7 mol L 1 s 1, respectively. Calculate the values of (jkj), the initial kinetic chain length, and the initial degree of polymerization. Indicate how often on the average chain transfer occurs per each initiating radical from the peroxide. What is the breadth of the molecular weight distribution that is expected, that is, what is the value of Xw/Xnl Use the following chain-transfer constants ... 

Nucleophiles such as water, alcohols, esters, acetals, and ethers can also act as transfer agents by reacting with the macrocations, at the same time forming a new cation that initiates the growth of a new chain the kinetic chain thus remains unbroken. 

Oxidative chain reactions of organic compounds are current targets of theoretical and experimental study. The kinetic theory of collisions has influenced research on liquid-phase oxidation. This has led to determining rate constants for chain initiation, branching, extension, and rupture and to establishing the influence of solvent, vessel wall, and other factors in the mechanism of individual reactions. Research on liquid-phase oxidation has led to studies on free radical mechanisms and the role of peroxides in their formation. 

Tetralin hydroperoxide (1,2,3,4-tetrahydro-l-naphthyl hydroperoxide) and 9,10-dihydroanthracyl-9-hydroperoxide were prepared by oxidizing the two hydrocarbons and purified by recrystallization. Commercial cumene hydroperoxide was purified by successive conversions to its sodium salt until it no longer increased the rate of oxidation of cumene at 56°C. All three hydroperoxides were 100% pure by iodometric titration. They all initiated oxidations both thermally (possibly by the bi-molecular reaction, R OOH + RH — R O + H20 + R (33)) and photochemically. The experimental conditions were chosen so that the rate of the thermally initiated reaction was less than 10% of the rate of the photoreaction. The rates of chain initiation were measured with the inhibitors 2,6-di-ter -butyl-4-methylphenol and 2,6-di-fer -butyl-4-meth-oxyphenol. None of the hydroperoxides introduced any kinetically first-order chain termination process into the over-all reaction. 

For the purpose of determining the chain termination type, Figure 5.9 shows the dependence of the methane oxidation rate on the chain initiation rate, which is characterized by the elementary reaction of H202 dissociation (k ) to hydroxyl radicals and described by the following kinetic equation ... 

For example, the formation of living polymers allows the preparation of block polymers by sequential addition of monomers. It also permits the introduction of functional groups on the ends of each chain. From kinetic considerations of live polymer systems, it follows that, in a batch reaction, a fast initiation step relative to the propagation step will result in a very narrow molecular-weight distribution. It also follows that the molecular weight will be directly proportional to the mole ratio of initiator to monomer. 

Hydrocarbon distributions in the Fischer-Tropsch (FT) synthesis on Ru, Co, and Fe catalysts often do not obey simple Flory kinetics. Flory plots are curved and the chain growth parameter a increases with increasing carbon number until it reaches an asymptotic value. a-Olefin/n-paraffin ratios on all three types of catalysts decrease asymptotically to zero as carbon number increases. These data are consistent with diffusion-enhanced readsorption of a-olefins within catalyst particles. Diffusion limitations within liquid-filled catalyst particles slow down the removal of a-olefins. This increases the residence time and the fugacity of a-olefins within catalyst pores, enhances their probability of readsorption and chain initiation, and leads to the formation of heavier and more paraffinic products. Structural catalyst properties, such as pellet size, porosity, and site density, and the kinetics of readsorption, chain termination and growth, determine the extent of a-olefin readsorption within catalyst particles and control FT selectivity. 

A number of transition metals are now known147-156 to form stable dioxygen complexes, and many of these reactions are reversible. In the case of cobalt, numerous complexes have been shown to combine oxygen reversibly.157 158 Since cobalt compounds are also the most common catalysts for autoxidations, cobalt-oxygen complexes have often been implicated in chain initiation of liquid phase autoxidations. However, there is no unequivocal evidence for chain initiation of autoxidations via an oxygen activation mechanism. Theories are based on kinetic evidence alone, and many authors have failed to appreciate that conventional procedures for purifying substrate do not remove the last traces of alkyl hydroperoxides from many hydrocarbons. It is usually these trace amounts of alkyl hydroperoxide that are responsible for chain initiation during catalytic reaction with metal complexes. 

However, a recent kinetic study188 has shown unequivocally that chain initiation proceeds via the usual metal-catalyzed decomposition of the hydroperoxide. Thus, the rate of initiation of the autoxidation of cumene was, within experimental error, equal to the rate of production of radicals in the (Ph3P)4Pd-catalyzed decomposition of tert-butyl hydroperoxide in chlorobenzene at the same temperature and catalyst concentration. Moreover, long induction periods were observed (in the absence of added tert-butyl hydroperoxide), when the cumene was purified by passing it down a column of basic alumina immediately prior to use. Autoxidation of cumene purified by conventional procedures showed only short induction periods. These results further demonstrate the necessity of using highly purified substrates in kinetic studies. 

However, this interpretation has been questioned by Vreugdenhil.631 He showed in a careful kinetic study that the catalytic activity of Ag-on-Si02 is mainly, if not entirely, due to its capacity to decompose hydroperoxides into chain-initiating radicals. (Approximately one-third of the ethylene is burned to carbon dioxide during the silver-catalyzed epoxidation.)... 

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