Propagation free-radical polymerization kinetics

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

Free radical polymerization kinetics has received much attention and many aspects of the process are well understood (see Chapter 4). Most academic investigations have been carried out in idealized conditions where the extent of monomer conversion is low. The classical expression for the rate of polymerization (Rp), in a single-phase reaction, is Eq. (13), where kp is the propagation rate coefficient, Cm is monomer concentration, J i is the initiation rate and kt is the termination rate coefficient [63]. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

Later, other authors utilized the differences found in the optical activity of monomer and polymer to carry out kinetic investigations on the free-radical polymerisation (70,72,120) and copolymerization (71), and tried to achieve the steric control of the propagation step of free-radical polymerization and copolymerization (13, 14, 39, 73, 98) using optically active monomers and initiators. 

The molecular weight distribution and the average molecular weight in a free-radical polymerization can be calculated from kinetics. The kinetic chain length v is defined as the average number of monomers consumed per number of chains initiated during the polymerization. It is the ratio of the propagation rate to the initiation rate (or the termination rate with a steady-state approximation) ... 

Radiation-Induced Polymerization. Polymerization induced by irradiation is initiated by free radicals and by ionic species. On very pure vinyl monomers, D. J. Metz demonstrated that ionic polymerization can become the dominating process. In Chapter 12 he postulates a kinetic scheme starting with the formation of ions, followed by a propagation step via carbonium ions and chain transfer to the vinyl monomer. C. Schneider studied the polymerization of styrene and a-methylstyrene by pulse radiolysis in aqueous medium and found results similar to those obtained in conventional free-radical polymerization. She attributes this to a growing polymeric benzyl type radical which is formed partially through electron capture by the styrene molecule, followed by rapid protonation in the side chain and partially by the addition of H and OH to the double vinyl bond. A. S. Chawla and L. E. St. Pierre report on the solid state polymerization of hexamethylcyclotrisiloxane by high energy radiation of the monomer crystals. 

In both cases, free radical polymerization has three major kinetic steps initiation, propagation and termination (35,36). When external initiators are used, in the initiation step they provide free radicals which become active sites of following reactions. At the... 

In many free-radical polymerizations, the molecular weight of the polymer produced is lower than that predicted from Eq. (6-64). This is because the growth of macroradicals in these systems was terminated by transfer of an atom to the macroradical from some other species in the reaction mixture. The donor species itself becomes a radical in the process, and the kinetic chain is not terminated if this new radical can add monomer. Although the rate of monomer consumption may not be altered by this change of radical site, the initial macroradical will have ceased to grow and its size is less than it would have been in the absence of the atom transfer process. These reactions are called chain transfer processes. They can be classified as varieties of propagation reactions (Section 6.3.2). 

In conventional free radical polymerization, the initiation, propagation, and termination are kinetically coupled. Consequently, the increase of initiation rate increases the overall polymerization rate but reduces the degree of polymerization. In contrast to this situation (kinetically coupled initiation, propagation, and termination), the formation of chemically reactive species is not the initiation of a subsequent polymerization. Under such an activation/deactivation decoupled reaction system, the mechanism for how chemically reactive species are created and how these species react to form solid material deposition cannot be viewed in analogy to polymerization. 

The above kinetic expressions illustrate some basic differences between cationic and free radical processes. In the cationic polymerization, the propagation rate is of first order with respect to the initiator concentration, whereas in free radical polymerization it is proportional to the square root of initmtor concentration (Eq. [34]). Furthermore, the molecular weight (or DP) of the polymer synthesized by the cationic process is independent of the concentration of the initiator, regardless of how termination takes place, unlike free radical polymerization where DP is inversely proportional to [I] in the absence of chain transfer (Eq. [35]). 

A limited number of attempts have been made to set up a general mechanistic scheme describing cationic systems in terms of fundamental reactions, in a similar manner to that used in free radical polymerizations, and to derive generally applicable kinetic equations [3—4]. Because of the individuality of each cationic system, however, this approach has met with little success, and there has been a greater tendency towards treating each polymerization in isolation for detailed kinetic analysis. It is possible, however, to postulate at least token schemes which can be used as a guide. After the pre-initiation equilibria, polymerization can be considered in terms of classical initiation, propagation, transfer and termination reactions, i.e. for vinyl monomers... 

Woecht I, Schmidt-Naake G, Beuermann S, et al. Propagation kinetics of free-radical polymerizations in ionic liquids. J. Polym. ScL, Part A Polym. Chem. 2008. 46, 1460-1469. 

Nitroxide mediated SFRP, DPE mediated polymerization, ATRP, RAFT polymerization, etc. achieve polymerization control through the use of kinetic mediators or transfer agents, which protect a propagating free radical from imdesirable transfer and termination reactions. The emulsion block copolymer method is unique in that it does not require the use of any chemical mediators to achieve this control. Polymerization control is achieved by physically trapping radicals by... 

In general, a polymerization process model consists of material balances (component rate equations), energy balances, and additional set of equations to calculate polymer properties (e.g., molecular weight moment equations). The kinetic equations for a typical linear addition polymerization process include initiation or catalytic site activation, chain propagation, chain termination, and chain transfer reactions. The typical reactions that occur in a homogeneous free radical polymerization of vinyl monomers and coordination polymerization of olefins are illustrated in Table 2. 

The kinetics of polymerization with anionic initiation are less well understood than free-radical polymerization, but a simple treatment allows the important results to be drawn from a consideration of the initiation, propagation and termination reactions (Muller, 1989). 

Though ionic polymerization resembles free-radical polymerization in terms of initiation, propagation, transfer, and termination reactions, the kinetics of ionic polymerizations are significantly diflFerent from free-radical polymerizations. In sharp contrast to free-radical polymerizations, the initiation reactions in ionic polymerizations have very low activation energies, chain termination by mutual destruction of growing species is nonexistent, and solvent effects are much more pronounced, as the nature of solvent determines whether the chain centers are ion pairs, free ions, or both. No such solvent role is encountered in free-radical polymerization. The overall result of these features is to make the kinetics of ionic polymerization much more complex than the kinetics of free-radical polymerization. 

The polymerization rate for an anionic polymerization where termination occurs simultaneously with propagation follows in a manner similar to free-radical polymerizations. An example is the potassium amide initiated polymerization in liquid ammonia. This is one of the few anionic systems in which all active centers behave kinetically as free ions. In this system, initiation involves dissociation followed by addition of amide ion to monomer ... 

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