Propagation steps, chain reactions

The step in which the reactive intermediate, in this case A-, is generated is called the initiation step. In the next four equations in the example above, a sequence of two reactions is repeated this is the propagation phase. Chain reactions are characterized by a chain length, which is the number of propagation steps that take place per initiation step. Finally, there are termination steps, which include any reactions that destroy one of the reactive intermediates necessary for the propagation of the chain. Clearly, the greater the frequency of termination steps, the lower the chain length will be. 

The photoinduced electron transfer (PET) initialed cyclodimerization was first studied with 9-vinylcarbazole as substrate1 and characterized mechanistically as a cation radical chain reaction.2 The overall reaction sequence3-4 consists of a) excitation of an electron acceptor (A), b) electron transfer from the alkene to the excited acceptor (A ) with formation of a radical ion pair, c) addition of the alkene radical cation to a second alkene molecule with formation of a (dimeric) cation radical, and d) reduction of this dimeric cation radical by a third alkene molecule with formation of the cyclobutanc and a new alkene cation radical. Steps c) and d) of the sequence are the chain propagation steps. The reaction sequence is shown below. 

The intermediates are CH3O, CH and CH3OCH. The best way to identify a chain reaction is to look for a cycle of steps where intermediates are regenerated, and identify them. CH and CH3OCH are recycled in steps 2 and 3 and are therefore chain carriers, and steps 2 and 3 are propagation steps. The reaction is a chain. 

This is a reaction in which reactive species, such as radicals, are produced in more than one step. These reactive species, radicals, propagate the chain reaction. 

X is the chain carrier that acts as reactant in the first propagation step.) For reactions wity irreversible propagation steps ... 

An alternative mechanism was also considered in which reaction (4 ) was the chain-propagating step and reaction (2 ) the chain-terminating step, viz. 

The most widely used antioxidants are free radical scavengers that remove reactive radicals formed in the initiation and propagation steps of autoxidation. A number of natural or synthetic phenols can compete, even at low concentrations, with lipid molecules as hydrogen donors to hydroperoxy and alkoxy radicals, producing hydroperoxides and alcohols and an unreactive radical. (3-carotene reacts with per-oxy radicals, producing a less-reactive radical. These stabilized radicals do not initiate or propagate the chain reaction. 

The disproportionation reaction of the free radical chain can generate the monomer as a successive process. There are, however, some other issues regarding the propagation for free radical chain reactions. In addition to the "regular" propagation step, different reactions may occur in a so-called transfer step. In this step, the free radical chain reacts with another molecule and generates a different radical chain and a new polymeric molecule. There are two possible types of transfer reactions. The transfer step can be an intermolecular chain transfer or an intramolecular chain transfer. An example of an intermolecular chain transfer is... 

These two steps remove the intermediates which propagate the chain reaction and stop the chain. Inhibition chemistry is the centerpiece of the application of antioxidant packages in lubricants. 

Polymerizations by a free-radical mechanism are typical free-radical reactions. That is to say, there is an initiation, when the radicals are formed, a propagation, when the products are developed, and a termination, when the radical reactions end. In the polymerizations, the propagations are chain reactions. A series of very rapid repetitive steps follow each single act of initiation, leading to the addition of thousands of monomers. 

In contrast to the free-radical copolymerization, the lack of termination in living ionic copol5mierization enables the direct determination of the rate coefficients of the cross-propagation step. The reaction rate of monomer B with the living chain end a is directly accessible via the concentration decrease of a , which may be traced via a suitable spectroscopic method. Alternatively, the concentration of B can be determined as a function of time with the concentration of a being held constant. The latter experimental technique requires extrapolation of time toward zero, because the cross-propagation step is immediately followed by homopropagation of B. 

The characteristic feature of a chain propagation step is reaction of a radical and a molecule to give a new radical. A chlorine atom, also called a chlorine radical, is consumed in Step 2, but an ethyl radical is produced. Similarly, an ethyl radical is consumed in Step 3, but a chlorine radical is produced. Steps 2 and 3 can repeat thousands of times as long as neither radical is removed by a different reaction. 

Cu(edta)P" and [Zn(trien)] + ions at pH 7.0—10.5. The exchange rate is accelerated by traces of edta or trien, and the chain-propagation steps involve reactions between [Cu(edta)] and trien and between [Zn(trien)f + and edta. ... 

Initiation. The reaction cannot start without the presence of a radical. A radical must be formed to start the process, in a reaction known as an initiation step. Peroxides are good generators of radicals because of the weakness of their oxygen-oxygen bond (Fig. 11.26, Step 1). Once a radical is created in the presence of hydrogen bromide, a second initiation step, abstraction of hydrogen (Fig. 11.26, Step 2), takes place to form a bromine atom, which is the radical that propagates the chain reaction. 

This series of kinetic steps typifies a chain reaction. A chain reaction is a reaction whose mechanism consists of steps whose products are intermediates that react to form other intermediates, usually in an apparently cyclical fashion. Reaction a, which started the chain reaction in this example, is called an initiation reaction (or initiation step). Reactions b and c of this example use one intermediate and produce another intermediate. They are called propagation reactions. The reactions d represent a loss of the intermediates that propagate the chain reaction. They are called termination steps. All steps can be generally characterized by the change in the reactive intermediates over the course of the reaction. Initiation steps form reactive intermediates from reactants, propagation steps use an intermediate but form another (so there is no net change in the amount of reactive intermediate), and... 

In a radical reaction, the steps that propagate the chain reaction compete with the steps that terminate it. Termination steps are always exothermic, because only bond making (and no bond breaking) occurs. Therefore, only when both propagation steps are exothermic can propagation compete successfully with termination. When HCl or HI adds to an alkene in the presence of a peroxide, any chain reaction that is initiated is then terminated rather than propagated because propagation caimot compete successfully with termination. Consequently, the radical chain reaction does not take place, and the only reaction that occurs is ionic addition (H" followed by Cr or F"). 

The chain carriers are the radicals C2H5 and H. The free radical CHj does not propagate the chain reaction, since it is formed in step (1), deactivates in step (2), and is not to be regenerated. The stationary conditions for CH3, C2H5 and H lead to the following set of differential equations ... 

In practice side reactions intervene to reduce the efficiency of the propagation steps The chain sequence is interrupted whenever two odd electron species combine to give an even electron product Reactions of this type are called chain terminating steps Some commonly observed chain terminating steps m the chlorination of methane are shown m the following equations... 

Propagation steps (Section 4 17) Elementary steps that repeat over and over again in a chain reaction Almost all of the products in a chain reaction arise from the propagation steps... 

Carbon-centered radicals generally react very rapidly with oxygen to generate peroxy radicals (eq. 2). The peroxy radicals can abstract hydrogen from a hydrocarbon molecule to yield a hydroperoxide and a new radical (eq. 3). This new radical can participate in reaction 2 and continue the chain. Reactions 2 and 3 are the propagation steps. Except under oxygen starved conditions, reaction 3 is rate limiting. 

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

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