Free radical polymerization combination rate constant

Stereocontrol of free radical polymerization is influenced by monomer constitution, solventy and temperature. Most polymerizations seem to follow at least a Markov first-order one-way mechanism. Ratios of the four possible rate constants ki/iy ki/8, k8/i, and k8/8 can be calculated from the experimentally accessible concentrations of configurational triads and diads. With increasing temperature, more heterotactic triads are formed at a syndiotactic radical whereas the monomer addition at an isotactic radical favors isotactic and not heterotactic triads. Compensation effects exist for the differences of activation enthalpies and activation entropies for each of the six possible combinations of modes of addition. The compensation temperature is independent of the mode of addition whereas the compensation enthalpies are not. 

In treatments of polymerization reactions that concentrated on a single feature, the effect of molecular weight upon the termination rate constant has been deduced, the relative rates of initiation of two monomers in a copolymerization have been assessed, constants for chain transfer to monomer have been obtained in an emulsion copolymerization, the relative amounts of chain termination by combination and disproportionation have been discovered from a molecular weight distribution, and the rate constant for long-chain branch formation in the free-radical polymerization of ethylene has been found by fitting a probalistic model. ... 

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

Now, according to the transition-state theory of chemical reaction rates, the pre-exponential factors are related to the entropy of activation, A5 , of the particular reaction [A = kT ere k and h are the Boltzmann and Planck constants, respectively, and An is the change in the number of molecules when the transition state complex is formed.] Entropies of polymerization are usually negative, since there is a net decrease in disorder when the discrete radical and monomer combine. The range of values for vinyl monomers of major interest in connection with free radical copolymerization is not large (about —100 to —150 JK mol ) and it is not unreasonable to suppose, therefore, that the A values in Eq. (7-73) will be approximately equal. It follows then that... 

When reviewing the published literature on the emulsion polymerization of vinyl acetate, one is struck with seemingly contradictory data presented by many reputable research teams. Some of these results published may not be strictly comparable because of variations in the polymerization recipes used. For example, the effect of the emulsifiers on the rate of polymerization may have a profound effect on the course of the reaction. In a persulfate-initiated system using no other surfactant, it has been postulated that the free radicals formed fixrm the decomposition of the initiator combine with the monomer in solution. As polymer forms, aggregates develop which absorb more monomer and the number of particles increases up to a constant value (at about 5% conversion). Then, while the number of particles remains constant at 1.7 X 10 per ml, the reaction rate increases. Ultimately, as a last stage of the reaction, the rate begins to drop off. The latex formed in this process is said to consist of particles of great uniformity with a diameter of 0.26 fim [137]. 

The constants kj and k, are the rate constants for initiator dissociation and monomer addition, respectively. Since initiator dissociation (ecp. 7.10) is much slower than monomer addition (ecp. 7.11), the first step of the initiation step (initiator dissociation) is the rate-limiting step. Some of the initiator radicals may undergo side (secondary) reactions, such as combination with another radical, that preclude monomer addition. Therefore only a fraction, f (an efficiency factor), of the initial initiator concentration is effective in the polymerization process. Also, decomposition of each initiator molecule produces a pair of free radicals, either or both of which can initiate polymerization. Based on these observations, the rate expression for initiation may be written as ... 

According to Equation (20-53), a combination of the propagation rate constant with rate constants of other elementary reactions is always obtained instead of the rate constant of propagation, alone, from the polymerization kinetics at low conversions. The free radical yield and the initiator decomposition constant are obtained in separate experiments with added inhibitor. The inhibitor reacts with the initiator free radicals, so that the product fk can be calculated from its consumption ... 

The initiator, I-I, is homolyticaUy broken into two free radicals by either absorption of a photon, hv, or by collision with another molecule, B. In either case there must be sufficient energy to break the center bond of the initiator. Once formed, each free radical, written as I, can start a polymerization reaction by adding monomer molecules. The first step leads to the free radical monomer, I-A , also written as Mj. The next step of the reaction produces a free radical called Mj. Each step of the chain reaction has up to this point its own specific rate constant. Addition of further monomers goes, however, substantially with the same rate, so that one can write during the main growth period of the molecule for each step the fourth reaction equation in Fig. 3.23, where x is the degree of polymerization. Ultimately, the reaction may be stopped by a termination reaction of the chain. The example of the termination reaction shown is a combination of two free radicals. The special case for... 

Copolymers generally possess a different composition than that of the initial monomer mixture, provided in each case that the polymerization does not reach 100% conversion. The composition depends on the reactivity (measured as rate constants) and the concentrations of growing ends (e.g., free radicals) and monomers. In copolymerization, the more reactive monomer will polymerize preferentially. The copolymer formed at low yields will therefore contain more of the more reactive monomer. The actual composition depends on the composition of the monomer mixture and the difference in reactivity of the monomers. The consumption of the more reactive monomer, however, means that the remaining monomer mixture will become deficient in this monomer, so that the copolymer that is formed at higher yields must exhibit a different composition than that produced originally. The composition of the copolymer is equal to the initial mixture composition only at a specific combination of reactivities and concentrations (azeotropic copolymerization). 

In this mechanism, P-X is thermally or photochemically dissociated into P and X", where a stable (persistent) radical X is assumed to be stable enough to undergo no reaction other than the combination with P" (and other alkyl radicals, if any present), namely, an ideal stable free radical (SFR) does not react among themselves, does not initiate polymerization, and does not undergo disproportionation with P". The best known examples of SFR are nitroxides such as TEMPO (2,2,6,6- tetra-methylpiperidinyl-l-oxy) (Figure 1), even though they are not perfectly ideal in the mentioned sense. The rate constants of... 

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