The Propagation Steps

Once chain initiation is complete, the monomer consumption rate is determined only by the chain propagation step. With the less efficient lithium alkyl initiators in hexane or cyclohexane, rather large amounts of monomer are needed to complete chain initiation. The appearance of a first order decay in monomer concentration, invariably obtained in these experiments, is not a very sensitive indication of the complete absence of initiator. Analysis of trial samples for hydrolysis products of lithium alkyls or spectroscopic determination that the polymer anion concentration has reached a plateau are preferable. A seeding technique is often used [32, 59] where the real initiator is a pre-formed active polymer 

The propagation rate can also be determined for the other alkali metals. In this case it is preferable to produce a polymer of low DP by the reaction of a monomer solution with an alkali metal film. The oligomeric active polymer, which is soluble in hydrocarbons, can be filtered-off and used as initiator. The simple alkyls or aryls of the higher alkali metals are almost insoluble in these solvents and are not easy to produce in a high state of purity. 

With butadiene and isoprene, the orders in lithium alkenyl are near one quarter (or perhaps even one sixth for butadiene [52, 63]). Data exists where the reported order is nearer one half [59, 66], characterized by rates which are close to those given in Fig. 10 at initiator concentrations near 10 M, but which become much lower as the concentration is decreased. In one case, later work has indicated that this is caused by increased initiator destruction at low concentrations and it seems reasonable to suppose that this explanation is valid for the whole group of experiments. Comparison of kinetic order with degree of association is hindered by the fact that there is no agreement as to the association number of polybutadienyl or polyisoprenyllithium, it being variously described as two [32, 60] or near four [33, 61]. The association phenomenon, however, undoubtedly plays a role in the observed kinetics. 

For all three monomers, the observed rate is not a simple measure of the rate of the propagation step (6). Attempts have been made to measure the actual rate coefficient, kp, either by measurement of the dissociation constant of the aggregates, or by decreasing the active polymer concentration to the point at which association no longer exists. Concentrated solution viscosities (which are extremely sensitive to the apparent molecular weight, Tj have been used [67—69] to determine association 

The propagation coefficient for polyisoprenyllithium in heptane has been estimated [65] by working at concentrations as low as 5 x 10 M. The reaction order was found to increase below 10 M (see Fig. 10) and became first in polyisoprenyllithium at about 5 x 10 M. Assuming this corresponds to complete dissociation of the aggregates, a value of 0.65 

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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... 

Termination steps are m general less likely to occur than the propagation steps Each of the termination steps requires two free radicals to encounter each other m a medium that contains far greater quantities of other materials (methane and chlorine mol ecules) with which they can react Although some chloromethane undoubtedly arises via direct combination of methyl radicals with chlorine atoms most of it is formed by the propagation sequence shown m Figure 4 21... 

These two products arise because m one of the propagation steps a chlorine atom may abstract a hydrogen atom from either a methyl or a methylene group of butane... 

The propagation steps in the formation of benzyl chloride involve benzyl radical as an intermediate... 

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. 

Under these conditions, a component with a low rate constant for propagation for peroxy radicals may be cooxidized at a higher relative rate because a larger fraction of the propagation steps is carried out by the more reactive (less selective) alkoxy and hydroxy radicals produced in reaction 4. 

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. 

A typical example of a nonpolymeric chain-propagating radical reaction is the anti-Markovnikov addition of hydrogen sulfide to a terminal olefin. The mechanism involves alternating abstraction and addition reactions in the propagating steps ... 

The degree of polymerization is controlled by the rate of addition of the initiator. Reaction in the presence of an initiator proceeds in two steps. First, the rate-determining decomposition of initiator to free radicals. Secondly, the addition of a monomer unit to form a chain radical, the propagation step (Fig. 2) (9). Such regeneration of the radical is characteristic of chain reactions. Some of the mote common initiators and their half-life values are Hsted in Table 3 (10). 

Halophenols without 2,6-disubstitution do not polymerize under oxidative displacement conditions. Oxidative side reactions at the ortho position may consume the initiator or intermpt the propagation step of the chain process. To prepare poly(phenylene oxide)s from unsubstituted 4-halophenols, it is necessary to employ the more drastic conditions of the Ullmaim ether synthesis. A cuprous chloride—pyridine complex in 1,4-dimethoxybenzene at 200°C converts the sodium salt of 4-bromophenol to poly(phenylene oxide) (1) ... 

The ratio describes the relative reactivity of polymer chain M toward monomer M and monomer M2. Likewise, describes the relative reactivity of polymer chain M2 toward M2 and M. With a steady-state assumption, the copolymerisation equation can be derived from the propagation steps in equations 3—6. 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

It is assumed that for each initiation there are many propagation cycles before termination. The main reaction is therefore given by the addition of the propagation steps alone, which gives the correct stoichiometric equation. A small amount of ethane, C2Hg, is expected due to the termination reaction. 

Wawzonek et al. first investigated the mechanism of the cyclization of A-haloamines and correctly proposed the free radical chain reaction pathway that was substantiated by experimental data. "" Subsequently, Corey and Hertler examined the stereochemistry, hydrogen isotope effect, initiation, catalysis, intermediates, and selectivity of hydrogen transfer. Their results pointed conclusively to a free radical chain mechanism involving intramolecular hydrogen transfer as one of the propagation steps. Accordingly, the... 

Figure 10.1 Mechanism of the radical chlorination of methane. Initiation step Three kinds of steps are required initiation, propagation, and termination. The propagation steps are a repeating cycle, with Cl- a reactant in step 1 and a product in...

Propagation step (Section 5.3) The step or series of steps in a radical chain reaction that carry on the chain. The propagation steps must yield both product and a reactive intermediate. 

The propagation step of polymerization involves an addition of monomeric units to the growing centers followed by regeneration of these centers. A series of consecutive propagation steps yields eventually a long polymeric molecule. 

A radical polymerization involves free radical ends which of course do not associate and which interact only weakly with solvents. Consequently, the early investigators assumed that the course of propagation of radical polymerization is independent of the environment (see, for example, the recent monograph by Walling60). Actually, more recent studies, notably by Russell,36 showed that the nature of the solvent sometimes might considerably affect even the course of radical reactions. Therefore, unusual behavior of the propagation step might be expected in certain solvents. 

The number of active centers determined by the quenching technique was dependent on the polymerization temperature (98) that was the reason for the difference between the overall activation energy and the activation energy of the propagation step. 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

Pulsed laser photolysis (PLP) has emerged as the most reliable method for extracting absolute rate constants for the propagation step of radical polymerizations,343 The method can be traced to the work of Aleksandrov el al.370 PLP in its present form owes its existence to the extensive work of Olaj and eoworkers 71 and the efforts of an 1UPAC working party/45"351 The method has now been successfully applied to establish rate constants, /rp(overall), for many polymerizations and copolymerizations. 

Solvent effects on radical polymerization have been reviewed by Coote and Davis,59 Coote et. Barton and Borsig,71 Gromov,72 and Kamachi" 1 A summary of kinetic data is also included in Beuennann and Buback s review.74 Most literature on solvent effects on the propagation step of radical polymerization deals with influences of the medium on rate of polymerization. 

Since a can be separated from the propagation step only because it is independent of temperature, additional influences which may exist remain undiscovered as far as they are connected with a gain or a loss of enthalpy (forces between the single chains and interactions with solvent). A possibly appearing effect of enthalpy, which occurs only during nucleation is then distributed among the propagation steps. 

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