Kinetics copolymerization

The problem of free-radical copolymerization kinetics is not nearly in such good shape. In addition to the four propagation reactions, there are three possible termination reactions (Fx- H- Fj-, Fx -H Fx-, Pz +- Fj-), each with its own rate constant. A general rate equation has been developed, but because of a lack of 

Calculations of copolymer composition are based on kinetic considerations and procedures. In spite of this, less attention has been paid to the copropagation rate than to other copolymerization problems. Today a single concise theory is available, solving the rate of the simplest radical binary copolymerization. Other cases described have not been generalized so far they treat the kinetic behaviour of specific monomer pairs or triplets in specific polymerization circumstances. 

Melville et al. [222] started from the copolymerization scheme (62), extended to include initiation (141) and termination by mutual combination (142). M, M. is a copolymer chain of r monomeric units with an M (or M ) radical at tne end. A chain containing a number of units different from r is designated by the index s. 

The consumption rate of both monomers is given by the sum of the rates in eqn. (63) and (64) (for long chains, monomer consumption by initiation is negligible) 

For stationary copolymerizations, this can be transformed by means of eqn. (65) and of the copolymerization parameters to the simpler form 

With simplifying assumptions (stationary state and termination by mutual radical combination) the radical concentration [Mf] can be derived. The generation rate of each radical type is equal to its rate of termination 

If the reactor fluid contains two different monomers Mi and M2, both monomers can react with radical sites to form copolymer radicals. If there is no template for the monomer preference to react with the radical site, then the sequence of monomer addition will be based on monomer reactivity rules. Description of copolymerization kinetics differs from that in Fig. 1.3.1 (homopolymerization kinetics) during chain propagation, as shown in Fig. 1.3.4 

Specifically, the copolymer mechanism expressed in Fig. 1.3.4 is the so-called terminal model, because identification and reactivity of copolymer radicals are solely based on which monomeric unit contains the radical site. Based on the rate coefficients shown above the reaction arrows, the following reactivity ratios are defined  

In the first case, radical sites from a particular monomer have the preference of reacting with monomers of the other type that is why the copolymer chain has an alternating sequence between the two monomers. In the second case, radical sites from a particular monomer prefer to react with monomers of the same type. Thus, once a particular monomer is incorporated, the same monomer is added into the copolymer chain in subsequent reactions as long as it is available. One note of caution here is that these copolymerization reactions are also based on statistical rules. For example, if r = 10 and the copolymer radical site comes from monomer 1, then if monomer 2 in the vicinity of the radical site outnumbers monomer 1 by 10 1 there is an equal likelihood for either monomer type to be incorporated in the copolymer chain. 

When we incorporate termination reactions into the analysis of monomer sequence formation in copolymerization kinetics, we note that in general the development of the copolymer sequence can be prematurely stopped. If one monomer sequence is being formed during propagation and the chain is terminated by disproportionation, then the result is more of a homopolymer than a copolymer. If the chain is terminated by recombination of a similar molecule, then the same type of homopolymer is formed. In fact, termination reactions usually prevent the formation of block copolymers when both monomers are present in the reactor fluid. With the radical trapping mechanism of the FRRPP process that will be discussed in the next chapter, formation of certain block copolymers becomes feasible in statistical-based radical copolymerizations. This is an apparent contradiction in terms, but the FRRPP process has been shown to break new ground in polymerization systems. 

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Homogeneous GopolymeriZation. Nearly all acryhc fibers are made from acrylonitrile copolymers containing one or more additional monomers that modify the properties of the fiber. Thus copolymerization kinetics is a key technical area in the acryhc fiber industry. When carried out in a homogeneous solution, the copolymerization of acrylonitrile foUows the normal kinetic rate laws of copolymerization. Comprehensive treatments of this general subject have been pubhshed (35—39). The more specific subject of acrylonitrile copolymerization has been reviewed (40). The general subject of the reactivity of polymer radicals has been treated in depth (41). 

Multi-State Models. In studies of copolymerization kinetics and polymer microstructure, the use of reaction probability models can provide a convenient framework whereby the experimental data can be organized and interpreted, and can also give insight on reaction mechanisms. (1.,2) The models, however, only apply to polymers containing one polymer component. For polymers with mixtures of different components, the one-state simple models cannot be used directly. Generally multi-state models(11) are needed, viz. 

V. Copolvmerization Kinetics. Qassical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon whkh to derive nations which would reflect detector response for a GPC separation based upon properties other than molecular weight. The distributions can then serve as c bration standards analagous to the use of molecular weight standards. 

Polymers produced by chain-reaction polymerization Copolymerization Kinetics... 

Johnson PM, Stansbury JW, Bowman CN (2007) Alkyl chain length effects on copolymerization kinetics of a monoacrylate with hexanediol diacrylate. J Comb Chem 9 1149-1156... 

Attempts to elucidate the polymerization or copolymerization kinetics of ethynyl and maleimide-functionalized monomers have been undertaken via vibrational spectroscopy (137). The thermal polymerization of A-(3-ethynyl-phenyl) maleimide (the structure is given in Fig. 48) was studied via IR and Raman spectroscopy. This model compound is interesting because it carries maleimide and ethynyl groups attached to the same aromatic ring. Kinetic studies indicate that both the acetylene and maleimide group react at the same rate, which strongly suggests the formation of a copolymer rather than a mixture of homopolymers. 

The presence of cross-associated species needs to be considered in the interpretation of copolymerization kinetics. It has been found 269) that the reaction of poly(butadie-nyl)lithium with p-divinylbenzene in benzene solution proceeds at a rate which increases markedly with time. Such a result implies that the poly(butadienyl)lithium aggregate is less reactive than the mixed aggregate formed between the butadienyl-and vinylbenzyllithium active centers. Interestingly, no accelerations with increasing reaction time were found with poly(butadienyl)lithium and m-divinylbenzene nor with poly(isoprenyl)lithium and either the m- or p-divinylbenzenes. This general behavior was subsequently verified 270) by a series of size exclusion chromatography measurements on polydiene stars (linked via divinylbenzene) as a function of conversion. 

Although DADMAC (M and AAM (M2) were first reacted in 1959 [61], publications on the copolymerization kinetics are relatively limited. Figure 12 shows in-... 

An alternative rationale for the unusual RLi (hydrocarbon) copolymerization of butadiene and styrene has been presented by O Driscoll and Kuntz (71). Rather than invoking selective solvation, these workers stated that classical copolymerization kinetics is sufficient to explain this copolymerization. They adapted the copolymer-composition equation, originally derived from steady-state assumptions for free-radical copolymerizations, to the anionic copolymerization of butadiene and styrene. Equation (20) describes the relationship between the instantaneous copolymer composition c/[M,]/rf[M2] with the concentrations of the two monomers in the feed, M, and M2, and the reactivity ratios, rt, r2, of the monomers. The rx and r2 values are measures of the preference of the growing chain ends for like or unlike monomers. 

The polymerization described so far is homo-polymerization based on single monomers. Some polymers used in pharmaceutical applications are copolymers. They have properties that each homo-polymer does not exhibit. For example, the copolymer of hydroxyethyl methacrylate and methyl methacrylate is synthesized in order to obtain a polymer exhibiting a hydrophilic/hydrophobic balance. A variety of copolymers (alternating, block, random) can be formed from two different monomers. Special processes produce alternating and block copolymers, while random copolymers are produced by free-radical copolymerization of two monomers. The polymerization steps, such as initiation, propagation, and termination, are the same as in free-radical homo-polymerization. Copolymerization kinetics are depicted as follows ... 

Iwatsuki and Yamashita (46, 48, 50, 52) have provided evidence for the participation of a charge transfer complex in the formation of alternating copolymers from the free radical copolymerization of p-dioxene or vinyl ethers with maleic anhydride. Terpolymerization of the monomer pairs which form alternating copolymers with a third monomer which had little interaction with either monomer of the pair, indicated that the polymerization was actually a copolymerization of the third monomer with the complex (45, 47, 51, 52). Similarly, copolymerization kinetics have been found to be applicable to the free radical polymerization of ternary mixtures of sulfur dioxide, an electron donor monomer, and an electron acceptor monomer (25, 44, 61, 88), as well as sulfur dioxide and two electron donor monomers (42, 80). 

Another unsolved fundamental problem of this theory concerns the correct description of copolymerization kinetics which obviously requires a well-grounded expression, from the physicochemical viewpoint, for the rate constant of the bimolecular chain termination reaction. This elementary reaction of interaction of two macroradicals proves to be diffusion-controlled beginning from the very initial conversions, and therefore, its rate in the course of the entire process is controlled by physical, rather than chemical factors. Naturally, the consideration of the kinetics of bulk copolymerization requires different approaches ... 

Hoare and McLean [69] developed a kinetic model for the copolymerization of up to four co-monomers to predict both chain and radial distributions of carboxylic groups in PNIPAAm-based microgels. The model can accurately predict the experimentally observed radial distributions of functional monomers with significantly different hydrophobicities, copolymerization kinetics, and reactivities. 

Copolymerization refers to the process by which two monomers (Mj and M2) are simultaneously polymerized. Mayo and Lewis [149] developed the following equation to describe copolymerization kinetics... 

The basic reaction scheme for free-radical bulk/solution styrene homopolymerization is described below. A complete description of copolymerization kinetics involving styrene is not given here however, the homopolymerization kinetic scheme can be easily extended to describe copolymerization using the pseudo-kinetic rate constant method [6]. Such practice has been used by many research groups [7-10] and has been used extensively for modelling of copolymerization involving styrene by Gao and Penlidis [11]. In this section, all rate constants are defined as chemically controlled, i.e. they are only a function of temperature. 

This paper, which is divided into three sections, critically reviews the state-of-the-art of free-radical copolymerization kinetics, characterization, reactor design, operation and control from the view point of their possible implementation to industrial processes. 

So far, we have reviewed the existing copolymerization theory. It is evident at this point, that in order to elucidate the copolymerization kinetics, extensive and systematic experimentation is required to provide data on the initiation, termination... 

It is evident that, in order to elucidate the copolymerization kinetics, extensive and systematic experimentation is required to provide data on the initiation, termination and propagation rates. The major stumbling block in the acquisition of experimental data has been, besides the normal difficulties associated with polymer experimentation, the lack of efficient characterization techniques which can yield reliable quantitative information on the MWD, CCD, and SLD or at least some of their leading moments. Such information is of primary importance in the elucidation of copolymerization kinetics. It is, therefore, felt that a major effort aimed at the study of copolymerization kinetics and at the development of characterization techniques is clearly justified. 

Free-radical copolymerization kinetics and copolymer composition... 

Tertiary amine catalyzed reactions were also studied by Tanaka and Kakiuchi (8), who essentially supported the Fischer mechanism, but disagreed on the kinetic order. The copolymerization kinetic scheme proposed by both Fischer and Tanaka postulate three rates, R, R2, and R, as follows ... 

Karol,F.J., Carrick,W.L. Transition metal catalysts. VII. Identification of the active site in organometallic mixed catalysts by copolymerization kinetic studies. J. Am. Chem. Soc. 83,2654-2658 (1961). 

Gotze T, Valtink M, Nitschke M et al (2008) Cultivation of an immortalized human corneal endothelial cell population and two distinct clonal subpopulations on thermo-responsive carriers. Graefes Arch Clin Exp Ophthalmol 246 1575-1583 Gramm S, Komber H, Schmaljohann D (2005) Copolymerization kinetics of N-isopropylacryla-mide and diethylene glycol monomethylether monomethacrylate determined by online NMR spectroscopy. J Polym Sci Pol Chem 43 142-148 Hatakeyama H, Kikuchi A, Yamato M et al (2006) Bio-functionalized thermoresponsive interfaces facilitating cell adhesion and proliferation. Biomaterials 27 5069-5078... 

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