Chain reaction with termination

Pseudo-Steady-State Assumption (PSSA). This assumption, limited to chain reactions with termination, states that the absolute value of the rate of change of free radicals with time is so small relative to the other terms in the differential equations for free radicals, that it can be set equal to zero. Aris (3) refers to this as an... 

Chain Reaction with Termination. More work has been done on this mechanism, using free radical polymerization as the principle example. As shown in Table IV, batch polymerization has received far more interest within this area than the simpler case of continuous polymerization in a stirred tank, presumably because of commercial laboratory practice. The limited work on tubular reactors is not shown and will be discussed separately later. 

Batch Reactors. One of the classic works in this area is by Gee and Melville (21), based on the PSSA for chain reaction with termination. Realistic mechanisms of termination, disproportionation, and combination, are treated with a variety of initiation kinetics, and analytical solutions are obtained. Liu and Amundson (37) solved the simultaneous differential equations for batch and transient stirred tank reactors by using digital computer without the PSSA. The degree of polymerization was limited to 100 the kinetic constants used were not typical and led to radical lifetimes of hours and to the conclusion that the PSSA is not accurate in the early stages of polymerization. In 1962 Liu and Amundson used the generating function approach and obtained a complex iterated integral which was later termed inconvenient for computation (37). The example treated was monomer termination. 

Reactions (7.2), (7.3) and (7.4) form a series of chain reactions, with reaction (7.3) the rate-determining stage. The chain reaction terminates by the reactions... 

Hydroperoxide is produced in the chain reaction with bimolecular chain termination. The rate of ROOH formation is proportional to (initiation rate)172 and the shorter the chain length higher the initiation rate. With increasing concentration of the catalyst this situation is encountered when the reaction occurs with v = 1. 

This is a chain reaction with many similarities to the chain reactions that occur in free-radical combustion processes in the previous chapter. For the chain reaction A B + C we represented the process as a kinetic chain involving the chain-propagating intermediate R, which was fed and terminated by initiation and termination reactions (Figure 1 1-2). In the preceding reaction sequence AMj is involved in a similar chain, but now each time the chain goes around the molecule is increased in size by one monomer unit We can represent this process in Figure 11-3. This reaction system is a series reaction in AMj,... 

The new Brownsville, Tex., plant for the manufacture of synthetic liquid fuels from natural gas makes use of this reaction to increase the octane number of its product by as much as 20 units. Synthetic naphtha produced over iron catalyst is highly olefinic and contains substantial amounts of straight-chain isomers with terminal double bonds (8). The shifting of these double bonds toward the center of the molecule may be accomplished by vapor-phase treatment employing synthetic cracking catalyst in the fluid state, under mild catalytic cracking conditions. Oxygenated compounds also present are converted under the isomerization conditions to hydrocarbons and water. 

Radiation-induced chlorination of polyisobutene in carbon tetrachloride was studied at various temperatures. The process is a chain reaction with a G value of about 10 to 105, depending on the reaction conditions. At very low dose rates (0.1 to 0.2 rad I sec), the chlorination rate is directly proportional to the dose rate. At higher dose rates, the rate approaches a square-root dependence on the dose rate. The termination reaction and the influence of oxygen are discussed. The reaction is first order with respect to chlorine concentration. An activitation energy of about 4 kcal/mole was obtained. In connection with the chlorination reaction, degradation of the polyisobutene takes place. This degradation was followed by osmometric measurements. The structure of the chlorinated product was briefly investigated by IR spectroscopy. 

However, since the QSSA has been used to elucidate most reaction mechanisms and to determine most rate coefficients of elementary processes, a fundamental answer to the question of the validity of the approximation seems desirable. The true mathematical significance of QSSA was elucidated for the first time by Bowen et al. [163] (see also refs. 164 and 165 for history and other references) by means of the theory of singular perturbations, but only in the case of very simple reaction mechanisms. The singular perturbation theory has been applied by Come to reaction mechanisms of any complexity with isothermal CFSTR [118] and batch or plug flow reactors [148, 149]. The main conclusions arrived at for a free radical straight chain reaction (with only quadratic terminations) carried out in an isothermal reactor can be summarized as follows. 

Equation (8) undoubtedly is identical to corresponding Semenov s equation which describes kinetics of N active sites in branched chain reaction with quadratic law of chain termination and zero order of initiation [5], However the essence of processes is different. 

In cationic ring-opening polymerization the situation is similar to the one observed for polycondensation heteroatoms along the chain may participate in reaction with terminal active species ... 

Lewis and Feitknecht found that HBr reacted rapidly with O3 at room temperature. Above a critical pressure (20-30 torr for equimolar mixtures) explosion occurs, as is typical of a branched-chain reaction with wall termination. 

The chain reaction is terminated by reactions that remove radicals that would otherwise produce more allylic radicals by hydrogen abstraction. Examples are the combination of two hydroperoxy radicals leading to nonradical products and molecular oxygen or reaction with a free-radical scavenger (antioxidant) generating a more stable radical. 

In the simplest cases of open chain epoxides with terminal alkenes,46 reaction is predominantly at the end of the chain and the product is overwhelmingly the T -isomcr. 

The conditions above are necessary, but not sufficient. For example, an exothermic, nonisothermal reaction is stable unless the temperature is so high that its heat generation (with exponential temperature dependence) exceeds the heat loss to the environment or a cooling coil (with linear temperature dependence). A chain reaction with chain branching is stable unless the radical population is so large that acceleration by chain branching (with exponential dependence on the radical population) outruns termination (with quadratic dependence). 

Catechins can trap peroxyl radicals and thus suppress radical chain reactions and terminate lipid peroxidation. Catechins also inhibit metmyoglobin-initiated peroxidation of low-density lipoproteins (LDLs) and the consumption of a-tocopherol. Among tea catechins, EGCG is most effective in reacting with most reactive oxygen... 

When a free radical reacts, it usually snatches an electron from the reactant, turning it into a free radical. This in turn will steal a single electron from another nearby molecule. A chain reaction ensues until two free radicals react together, effectively neutralizing each other, or alternatively, until an unreactive free-radical product is formed. Free radicals are said to be quenched by vitamin C, because the free-radical product — the ascorbyl radical — is so unreactive. As a result, free-radical chain reactions are terminated. Lipid-soluble vitamin E (a-tocopherol) works in the same way, in membranes rather than in solution, often in cooperation with vitamin C at the interface between membranes and the cytosol (the watery ground substance of the cytoplasm that surrounds the intracellular organelles). When vitamin E reacts with a free radical, it too produces a poorly reactive (resonance-stabilized) free-radical product, called the a-tocopheryl radical. Tocopheryl radicals can be reconverted into vitamin E using electrons from vitamin C. 

In the propagation steps, a site-specific radical R is generated from an organic substrate by removal of the Z group. In Scheme 1 the structure [RZMR 3] represents a reactive intermediate or a transition state. The radical R then reacts with the hydride generating the reduced product and fresh R 3M radicals. The chain reactions are terminated by radical combination or disproportionation. 

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