Free radical polymerization equilibrium

Generalization of Flory s Theory for Vinyl/Divinyl Copolvmerization Using the Crosslinkinq Density Distribution. Flory s theory of network formation (1,11) consists of the consideration of the most probable combination of the chains, namely, it assumes an equilibrium system. For kinetically controlled systems such as free radical polymerization, modifications to Flory s theory are necessary in order for it to apply to a real system. Using the crosslinking density distribution as a function of the birth conversion of the primary molecule, it is possible to generalize Flory s theory for free radical polymerization. 

While in most of the reports on SIP free radical polymerization is utihzed, the restricted synthetic possibihties and lack of control of the polymerization in terms of the achievable variation of the polymer brush architecture limited its use. The alternatives for the preparation of weU-defined brush systems were hving ionic polymerizations. Recently, controlled radical polymerization techniques has been developed and almost immediately apphed in SIP to prepare stracturally weU-de-fined brush systems. This includes living radical polymerization using nitroxide species such as 2,2,6,6-tetramethyl-4-piperidin-l-oxyl (TEMPO) [285], reversible addition fragmentation chain transfer (RAFT) polymerization mainly utilizing dithio-carbamates as iniferters (iniferter describes a molecule that functions as an initiator, chain transfer agent and terminator during polymerization) [286], as well as atom transfer radical polymerization (ATRP) were the free radical is formed by a reversible reduction-oxidation process of added metal complexes [287]. All techniques rely on the principle to drastically reduce the number of free radicals by the formation of a dormant species in equilibrium to an active free radical. By this the characteristic side reactions of free radicals are effectively suppressed. 

These methods are based on the idea of establishing equilibrium between the active and dormant species in solution phase. In particular, the methods include three major techniques called stable free-radical polymerization (SFRP), atom transfer radical polymerization (ATRP), and the degenerative chain transfer technique (DCTT) [17]. Although such syntheses pose significant technical problems, these difficulties have all been successively overcome in the last few years. Nevertheless, the procedure of preparation of the resulting copolymers remains somewhat complicated. 

Although ATRP behaves differently from conventional free radical polymerization, the fundamental reactions involved are very similar and include initiation, propagation, transfer and termination (see Scheme 6). Since chain termination does not occur in a truly living polymerization, the living character of the chains in ATRP derives from the fact that chain propagation is first order with respect to radical concentration and irreversible bi-molecular termination is second order. As such, the concentration of the radicals is kept very low, the rate of bi-molecular termination is greatly reduced, and typically less than 10% of all of the chains will terminate. Unlike conventional free radical polymerization, where the rate is dictated by a steady state between the initiation and termination rates, the rate and concentration of propagating radicals in ATRP is controlled entirely by the equilibrium between activation and deactivation [255]. 

If reactions 1 to 3 in Scheme 7 are considered, there is no reason to assume that addition of a RAFT agent to a conventional free radical polymerization will have an effect on the polymerization rate, since the equilibrium concentration of propagating radicals will not be affected. However, it has been found that considerable retardation does take place in RAFT polymerization [275-281]. The intermediate radical was postulated to be the reason for the significant retardation of the polymerization rate. Two explanations for retardation have been put forward ... 

It is not practical to conduct free-radical polymerizations under conditions where there is an equilibrium between polymerization and depolymerization processes. The polymer synthesis is effectively irreversible in normal radical polymerizations. The course of the reaction is then determined kinetically, and the molecular weight distribution cannot be predicted statistically as was done for equilibrium step-growth polymerizations described in Chapters. 

There is an important difference between the distributions calculated for equilibrium, bifunctional step-growth polymerization in Chapter 5 and for the free-radical polymerizations with termination by disproportionation or chain transfer that are being considered here. The distribution functions in the step-growth case apply to the whole reaction mixture in the free-radical polymerization this distribution describes only the polymer which has been formed. There is obviously a strong parallel between the probability S of this section and the extent of reaction p used in the step-growth calculations in Chapter 5. Many authors use the same symbol for both parameters. Different notations are used here, however, for clarity. 

A somewhat unique situation has been studied in the free radical polymerization in urea 70) and thiourea (77) clathrates. Several monomers have been found for which all conditions for solid state polymerization to a stereoregular equilibrium crystal outlined above are fulfilled. The radicals are protected from termination by neighboring radicals by the urea or thiourea walls of the canals. The proper approach of the monomer molecules is achieved in thiourea by stacking the monomer... 

The propagation step in ionic polymerizations is considerably more comphcated than in free radical polymerization (5). In addition to monomer structure and temperature, solvent and counter ion type are of importance. The separation between the counter ion and the active polymer chain end is the primary rate determining factor it can be represented schematically as an equilibrium between four species of different level of separation ... 

This discrepancy is partly due to the fact that random copolymers produced by a batch free-radical polymerization synthetic method can have a significant composition drift if the respective reactivity ratios of the monomers are different.2 This means that the value of the parameter/is not homogeneous in the copolymer layer at the interface. In the PS-PVP case discussed above, the random copolymers directly in contact with the PS or the PVP side of the interface at equilibrium would be PS-rich or PVP-rich, respectively. This segregation of copolymer fractions to their preferred interfaces gives rise to a broadening of these interfaces relative to the case of a random copolymer with a narrow distribution of/values. 

Problem 6.41 If a free-radical polymerization of 1.0 M solution of methyl methacrylate was being carried out at 100°C, what would be the maximum possible conversion of the monomer to polymer, that is, till the polymerization-depolymerization equilibrium is reached (Take relevant data from Table 6.13.)... 

Most addition polymerizations involve vinyl or diene monomers. The opening of a double bond can be catalyzed in several ways. Free-radical polymerization is the most common method for styrenic monomers, whereas coordination metal catalysis (Zigler-Natta and metallocene catalysis) is important for olefin polymerizations. The specitic reaction mechanism may generate some catalyst residues, but there are no true coproducts. There are no stoichiometry requirements, and equilibrium limitations are usually unimportant so that quite long chains are formed 7iv > 500 is typical of addition polymers. 

Anionic and later cationic pol3Tnerization gave most of examples of living pol3rmerization systems until recently, when more sophisticated methods of manipulation with free-radical polymerization processes become available. These methods are based on the use of the compounds which reversibly react with propagating radical and convert it to the so-called dormant species . When the equilibrium between the active and dormant species is regulated by special catalysts based on a transition metal, this process is called atom transfer radical polymerization (ATRP). If this equilibrium is provided by stable radicals such as nitroxides, the process is called stable free-radical polymerization (SFRP). In the case when dormant species are formed via a chain transfer rather than reversible termination reactions, this process is referred to as reversible addition fragmentation chain transfer (RAFT) polymerization. All these techniques allow to produce macromolecules of desired architecture and molecular masses. 

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