Chains propagation

The polymeric chain propagation consists of the growth of M through the successive additions of large numbers of monomer molecules (Reaction 11.5). Each addition unit creates a new radical that has the same identity as the one previously, except that it is larger by one monomer unit. The successive additions can be represented by 

Termination can be the result of either combination (Reaction 11.6) or disproportionation (Reaction 11.7). However, it is rarely necessary to distinguish between these two termination mechanisms, and so the rate constants are generally combined into a single rate constant, k.  

The termination mode of poly(alkyl methacrylate) radicals has also been the subject of much research.[9] Model compound studies of the bimolecular reactions of l-methoxycarbonyH-methylethyl radicals and the higher esters ethyl and butyl have resulted in for MMA, 0.72 for EMA, and 1.17 for nBMA.[9,10]. A k /k =4.37 was obtained by means of Matrix-assisted laser desorption/ionisation-time of flight mass spectrometry (MALDI-TOF MS) to the end-group analysis of low MW PMMA.[11] The use of fluorinated derivatives of BPO in combination with F NMR analysis of PMMA also indicated that the termination occurred mainly due to the disproportionation in this system.[12] 

The reaction of ketones with oxygen is a chain process in which the chain propagates by the alternating steps 

When the oxygen pressure is sufficiently high ( 100 torr), chains are terminated by the interaction of peroxy radicals, and the rate-limiting propagation step is R02 + RH. The rate of initiated oxidation of ketones is expressed as 

Values of kp for some ketones are given in Table 8. It can be seen that oxidation of the methyl group of acetone is slow, that of the ketones with a CH2 group is faster, and still more rapid is that of methyl i-propyl ketone with a tertiary C H bond. However, partial kps for one attacked C—H bond of ketone must be calculated for correct comparison of different C—H bond reactivities. Values of ftPtC H 316 given in Table 9. 

Rate coefficients, kp, for ketones and corresponding Arrhenius parameters 

The following relation between Ea and DCH of the attacked bond was established [150,151], viz. 

Initiation is followed by chain propagation, in which the growth of RM, often represented as Mi, takes place by successive addition of a large number of monomer molecules, according to Eqs. (6.5). The monomer addition takes place in the same way as shown in Eq. (6.8). Following each addition reaction, the chain size increases by one monomer unit, while the radical center is transferred to the end monomer unit. 

In writing the sequence of equations (6.5), it was assumed that the radical reactivity is independent of chain length so that all successive propagation steps are characterized by the same rate constant kp and may thus be represented by the general equation (6.6). The overall rate of propagation is therefore given by 

In the kinetically controlled regime, the chain propagation reaction is predominant and a high molecular-weight polymer (P ) is formed (Equation 12.1). The monomer-polymer equiUbrium (Equation 12.2) is characterized by the equilibrium constant (K) which is approximately equal to the inverse equilibrium monomer concentration ([M]e) (Equation 12.3). Equation 12.4 relates the equilibrium monomer concentration and the free enthalpy of polymerization (AG°). For standard conditions ([M]o = 1 mol L ) and above a critical temperature, no polymer is obtained. The critical temperature is defined as ceihng temperature (Tc) when both AH° and AS° are negative (Equation 12.5). 

In the thermodynamically controlled regime, back-biting reactions occur to form a low-molecular-weight fraction of cyclic oligomers (M ) (Equation 12.6) a ring chain equilibrium is then established where IQ is the equilibrium constant. 

Within the thermodynamically controlled regime, further intermolecular transesterification reactions occur, and from a starting Poisson distribution a Schulz-Flory distribution of the molecular weight is approached. The ratios k /ki and kp/feie, where kp is the rate constant of propagation, kt the rate constant of backbiting and kte the rate constant of the transesterification reaction, determine the selectivity of the reaction on the one hand and the microstmcture of the polymer (in the case of copolymerization) on the other hand. The rate constants are determined by the monomer used and the nature of the active site. 

The barrier height for the reaction to proceed can be expanded into a power series 

The increase of AE with chain length must originate from the difference between the monomer lattice constant and the length of oligomer/polymer repeat unit. Anticipating proportionality between 5AE/5n and lattice mismatch as suggested by studies under pressure (see 5.2), the variation of AE with n can be calculated for arbitrary conversion X from the low conversion value (8AE/8n)x=o  

Here b and bp are the lattice constants of monomer along b and the length of the oligomer/polymer repeat unit, respectively, and b(X) is the average b-axis dimension at arbitrary conversion X. 

(7) can be used to calculate the number of repeat units n contained in the polymer as a function of conversion. In the low conversion range, n is given by the number 

The rate constant for the i-th reaction step, kj, depends upon i according to  

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The free-radical polymerization of acrylic monomers follows a classical chain mechanism in which the chain-propagation step entails the head-to-tail growth of the polymeric free radical by attack on the double bond of the monomer. 

Chemical Interaction. Halogens and some phosphoms flame retardants act by chemical interaction. The flame retardant dissociates into radical species that compete with chain propagating and branching steps in the combustion process. 

Radicals are employed widely in the polymer industry, where their chain-propagating behavior transforms vinyl monomers into polymers and copolymers. The mechanism of addition polymeri2ation involves all three types of reactions discussed above, ie, initiation, propagation by addition to carbon—carbon double bonds, and termination ... 

I- is the initiating radical, P is the chain-propagating polymer radical that subsequendy abstracts a hydrogen atom from another polymer molecule,... 

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 ... 

Chemistry. Free-radical nitrations consist of rather compHcated nitration and oxidation reactions (31). When nitric acid is used in vapor-phase nitrations, the reaction of equation 5 is the main initiating step where NO2 is a free radical, either -N02 or -ON02. Temperatures of >ca 350° are required to obtain a significant amount of initiation, and equation 5 is the rate-controlling step for the overall reaction. Reactions 6 and 7 are chain-propagating steps. 

As the quinone stabilizer is consumed, the peroxy radicals initiate the addition chain propagation reactions through the formation of styryl radicals. In dilute solutions, the reaction between styrene and fumarate ester foUows an alternating sequence. However, in concentrated resin solutions, the alternating addition reaction is impeded at the onset of the physical gel. The Hquid resin forms an intractable gel when only 2% of the fumarate unsaturation is cross-linked with styrene. The gel is initiated through small micelles (12) that form the nuclei for the expansion of the cross-linked network. 

The and e values of the aHyl group in DAP have been estimated as 0.029 and 0.04, respectively, suggesting that DAP acts as a fairly typical unconjugated, bifunctional monomer (42). Cyclization affects copolymerization, since cyclized radicals are less reactive in chain propagation. Thus DAP is less reactive in copolymerization than DAIP or DATP where cyclization is stericaHy hindered. Particular comonomers affect cyclization, chain transfer, and residual unsaturation in the copolymer products. DiaHyl tetrachloro- and tetrabromophthalates are low in reactivity. 

Eor antioxidant activity, the reaction of aminyl radicals with peroxy radicals is very beneficial. The nitroxyl radicals formed in this reaction are extremely effective oxidation inhibitors. Nitroxides function by trapping chain-propagating alkyl radicals to give hydroxylamine ethers. These ethers, in turn, quench chain propagating peroxy radicals and in the process regenerate the original nitroxides. The cycHc nature of this process accounts for the superlative antioxidant activity of nitroxides (see Antioxidants). Thus, antioxidant activity improves with an increase in stabiUty of the aminyl and nitroxyl radicals. Consequendy, commercial DPA antioxidants are alkylated in the ortho and para positions to prevent undesirable coupling reactions. 

Copolymers with butadiene, ie, those containing at least 60 wt % butadiene, are an important family of mbbers. In addition to synthetic mbber, these compositions have extensive uses as paper coatings, water-based paints, and carpet backing. Because of unfavorable reaction kinetics in a mass system, these copolymers are made in an emulsion polymerization system, which favors chain propagation but not termination (199). The result is economically acceptable rates with desirable chain lengths. Usually such processes are mn batchwise in order to achieve satisfactory particle size distribution. 

Chain transfer to monomer is the main reaction controlling molecular weight and molecular weight distribution. The chain-transfer constant to monomer, C, is the ratio of the rate coefficient for transfer to monomer to that of chain propagation. This constant has a value of 6.25 x lO " at 30°C and 2.38 x 10 at 70°C and a general expression of 5.78 30°C, chain transfer to monomer happens once in every 1600 monomer... 

Although the main uses for benzoic acid are as a chemical raw material, it also has numerous direct uses. Benzoic acid is used in substantial quantities to improve the properties of various alkyd resin coating formulations, where it tends to improve gloss, adhesion, hardness, and chemical resistance. Benzoic acid terminates chain propagation in alkyd resins (qv) and promotes crystallinity in the final product. 

Epichlorohydrin Elastomers without AGE. Polymerization on a commercial scale is done as either a solution or slurry process at 40—130°C in an aromatic, ahphatic, or ether solvent. Typical solvents are toluene, benzene, heptane, and diethyl ether. Trialkylaluniinum-water and triaLkylaluminum—water—acetylacetone catalysts are employed. A cationic, coordination mechanism is proposed for chain propagation. The product is isolated by steam coagulation. Polymerization is done as a continuous process in which the solvent, catalyst, and monomer are fed to a back-mixed reactor. Pinal product composition of ECH—EO is determined by careful control of the unreacted, or background, monomer in the reactor. In the manufacture of copolymers, the relative reactivity ratios must be considered. The reactivity ratio of EO to ECH has been estimated to be approximately 7 (35—37). 

Effects of compounds observable at lower concentrations ai e probably connected with the effect on the initiation/termination stages (transition metals in TMB-0, reaction with photoinitiation, UDMH in the same reaction with chemical initiation), while the compounds influencing only at higher concentrations may affect chain propagation stages. 

For all of these reactions, the reagents and reaction conditions must be chosen to meet the fundamental requirement for successful chain reactions. Each step in the sequence must be exothermic to permit chain propagation. ... 

FIGURE 11.11 Chain propagation in polymerization of styrene. The growing polymer chain has a free-radical site at the benzylic carbon. It adds to a molecule of styrene to extend the chain by one styrene unit. The new polymer chain is also a benzylic radical it attacks another molecule of styrene and the process repeats over and over again. 

Much of the CI2O manufactured industrially is used to make hypochlorites, particularly Ca(OCl)2, and it is an effective bleach for wood-pulp and textiles. CI2O is also used to prepare chloroisocyanurates (p. 324) and chlorinated solvents (via mixed chain reactions in which Cl and OCl are the chain-propagating species).Its reactions with inorganic reagents are summarized in the scheme opposite. 

Oxaziranes derived from isobutyraldehyde react with ferrous salts to give only substituted formamides fEq. (23)], The chain propagating radical 30 thus suffers fission with elimination of the isopropyl group. An H-transfer would lead to substituted butyramides, which are not found. Here is seen a parallel to the fragmentation of alkoxyl radicals, where the elimination of an alkyl group is also favored over hydrogen. The formulation of the oxazirane fission by a radical mechanism is thus supported. 

The chain propagation step consists of a reaction of allylic radical 3 with a bromine molecule to give the allylic bromide 2 and a bromine radical. The intermediate allylic radical 3 is stabilized by delocalization of the unpaired electron due to resonance (see below). A similar stabilizing effect due to resonance is also possible for benzylic radicals a benzylic bromination of appropriately substituted aromatic substrates is therefore possible, and proceeds in good yields. 

The low concentration of elemental bromine required for the chain propagation step is generated from NBS 4 by reaction with the hydrogen bromide that has been formed in the first step ... 

Photopolymerization, in general, can be defined as the process whereby light is used to induce the conversion of monomer molecules to a polymer chain. One can distinguish between true photopolymerization and photoinitiation of polymerization processes. In the former, each chain propagation step involves a photochemical process [1,2] (i.e., photochemical chain lengthening process in which the absorption of light is indispensable for... 

In conclusion, furan and 2-alkylfurans can be polymerized only by acidic initiators or by y-radiation because the other standard methods of polyaddition fail to induce a chain-propagation reaction. 

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