Radical chain polymerization kinetics

The steady-state assumption is not unique to polymerization kinetics. It is often used in developing the kinetics of many small-molecule reactions that involve highly reactive intermediates present at very low concentrations—conditions that are present in radical chain polymerizations. The theoretical validity of the steady-state assumption has been discussed [Kondratiev, 1969] and its experimental validity shown in many polymerizations. Typical polymerizations achieve a steady-state after a period, which may be at most a minute. 

The kinetic chain length v of a radical chain polymerization is defined as the average number of monomer molecules consumed (polymerized) per each radical, which initiates a polymer chain. This quantity will obviously be given by the ratio of the polymerization rate to the initiation rate or to the termination rate, since the latter two rates are equal. 

Use of a Reliable Homemade Dilatometer To Study the Kinetics of the Radical Chain Polymerization of PMMA 123... 

Table 6.2 shows the general range of values of the various concentrations, rates, and rate constants pertaining to the above kinetic scheme. These values are typical of radical chain polymerizations. 

Table 6.7 Kinetic Parameters in Radical Chain Polymerization...

The second step of initiation [Eq. (8.83)], being slower than the first [Eq. (8.82)], is rate-determining for initiation (unlike in the case of free-radical chain polymerization) and so though the amide ion produced upon chain transfer to ammonia can initiate polymerization it is but only at a rate controlled by the rate constant, ki, for initiation. Therefore, this chain transfer reaction may be considered as a true kinetic-chain termination step and the application of steady-state condition gives Eq. (8.90). 

Free-Radical Chain Polymerization. In contrast to the typically slow stepwise polymerizations, chain reaction polymerizations are usually rapid with the initiated species rapidly propagating until termination. A kinetic chain reaction usually consists of at least three steps, namely, initiation, propagation, and termination. The initiator may be an anion, cation, free radical, or coordination catalyst. 

Kinetic analysis of this type of system is possible. The basic equations for the kinetics of radical-chain polymerization are derived by assuming a low steady-state concentration of reacting radicals. Under these conditions, the rate of termination equals that of initiation ... 

The ceiling temperature constraint in the homopolymerization of alphamethyl styrene (AMS) can be circumvented by copolymerization with acrylonitrile (AN) to prepare multicomponent random microstructures that offer higher heat resistance than SAN. The feasibility of a thermal initiation of free radical chain polymerization is evaluated by an experimental study of the terpolymerization kinetics of AMS-AN-Sty. Process considerations such as polyrates, molecular weight of polymer formed, sensitivity of molecular weight, molecular weight distribution, and kinetics to temperature were measured. 

The usual equations that are used to describe free radical chain polymerizations are not readily applicable to the polymerization of PTFE because the reaction does not meet the first requirement for application of the usual kinetic scheme, the steady state assumption [41, 42]. The CF2 radical has a very long lifetime, and usual termination reactions (combination and disproportionation] do not seem to occur. The need to have an extremely high molecular weight in order to have adequate physical properties requires a reaction system essentially free of any material that will chain transfer, eliminating that mode of termination. The result is that molecular weight of PTFE increases with time of polymerization, unlike most other radical-chain polymerizations. 

The kinetic chain length, v, of a radical chain polymerization is the average number of monomer molecules consumed for each radical initiating a chain. Thus, at steady state. 

At the high pressures involved, the polymerization step is very rapid. The polymerization process can be described by the classic kinetic description of free radical (chain) polymerization. 

It became apparent fliat file presence of a metal center greatly influenced polymerization kinetic behavior. In several cases, the homopolymerization kinetics were imusual and did not follow flie classic rate law (r = A(M] [I] ) for radical chain polymerization. For example, (Ti -vinylcyclopentadienyl)tricarbonylmanganese, 18, exhibited rate dependencies that were 1.5-order in monomer concentration and halforder in initiator concentration in benzene, benzonilrile, and acetone. This rate... 

Scheme 5.4 Kinetic scheme of free-radical chain polymerization in homogeneous liquid phase. M monomer P polymer.

Termination of free-radical chain polymerization may also take place by disproportionation. The description for chain termination by disproportionation is given in Eq. (9). The kinetic chain length (v) is the number of monomer molecules consumed by each primary radical and is equal to the rate of propagation divided by the rate of initiation for termination by disproportionation. The kinetic equation for the termination by disproportionation is... 

Photoinitiation is not as important as thermal initiation in the overall picture of free-radical chain-growth polymerization. The foregoing discussion reveals, however, that the contrast between the two modes of initiation does provide insight into and confirmation of various aspects of addition polymerization. The most important application of photoinitiated polymerization is in providing a third experimental relationship among the kinetic parameters of the chain mechanism. We shall consider this in the next section. 

Mechanisms. Because of its considerable industrial importance as well as its intrinsic interest, emulsion polymerization of vinyl acetate in the presence of surfactants has been extensively studied (75—77). The Smith-Ewart theory, which describes emulsion polymerization of monomers such as styrene, does not apply to vinyl acetate. Reasons for this are the substantial water solubiUty of vinyl acetate monomer, and the different reactivities of the vinyl acetate and styrene radicals the chain transfer to monomer is much higher for vinyl acetate. The kinetics of the polymerization of vinyl acetate has been studied and mechanisms have been proposed (78—82). 

At the same rate of polymerization, the kinetic chain length for vinyl acetate is over a hundred times that for styrene on account of the greater speed of propagation relative to termination for vinyl acetate. At a convenient rate of 10 moles/liter/sec., for example, each radical chain generated consumes on the average about 5X10 vinyl acetate units under the conditions stated. 

Nair et al. studied the kinetics of the polymerization of MMA at 60-95 °C using N,1SP-diethyl-NjW-di(hydroxyethyl)thiuram disulfide (30a) as the thermal in-iferter [142]. The dependence of the iniferter concentration on the polymerization rate was examined. The chain transfer constant of the propagating radical of MMA to 30a was determined to be 0.23-0.46 at 60-95 °C, resulting in the activation energy of 37.6 kj/mol for the chain transfer. Other derivatives 30b-30d were also prepared and used to derive telechelic polymers with the terminal phosphorus, amino, and other functional aromatic groups [143-145]. Thermal polymerization was also investigated with the end-functional poly(St) and poly(MMA) which were prepared using the iniferter 13 [146]. 

Unlike ionic polymerizations, the termination of the growing free radical chains usually occurs by coupling of two macroradicals. Thus, the kinetic chain length (v) is equal to DP/2. The chemical and kinetic equations for bimolecular termination are shown below (Equations 6.17 and 6.18). 

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