Kinetics of Chain Polymerisation

Mathematical expressions can be derived to describe the kinetics of chain processes building on the ideas already discussed that such reactions take place in the well defined stages of initiation, propagation, and termination. 

Initiation occurs as a molecule of intiator decomposes to free radicals (Reaction 2.9), where is the rate constant for the reaction. These newly generated free radicals can then interact with monomer molecules preserving the free radical centre (Reaction 2.10). These two processes may be considered to form part of the initiation stage, the first of them being rate determining. 

Following initiation conies the series of propagation steps, which can be generalised as in Reaction 2.11. A single rate constant, is assumed to apply to these steps since radical reactivity is effectively independent of the size of the growing polymer molecule. 

Termination may be the result of either combination (Reaction 2.12) or disproportionation (Reaction 2.13). However, it is rarely necessary to distinguish between these two termination mechanisms, and so the rate constants are generally combined into a single rate constant, k.  

The rates of the three steps may be written in terms of the concentrations of the chemical species involved and these rate constants. The rate of initiation then is given by  

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Types of chain polymerisations and polymers synthesized — keypoints of mechanisms, kinetics... 

On the basis of the kinetic characteristics of chain polymerisation reactions, it is possible to predict the final microstructures available by a so-called random process from a simple mixture of two comonomers. Indeed, the global mechanism of copolymerisation can be illustrated as presented in Figure 30. 

The kinetics of the polymerising system styrene-perchloric acid-methylene dichloride have been studied in the temperature range +19 °C to -19 °C, by a calorimetric technique. The propagation is pseudocationic, its rate constant at 19 °C is kp = 10.6 1 mole 1 s 1, and Ep = 11.6 kcal mole1. The elementary reactions are interpreted in detail by a mechanism involving an ester as chain carrier. 

Gandini and cdlaborators have carried out a detailed investigation of the ptrifluoroacetic acid in methylene chloride. Important side reactions accompanied the normal vinylic prop tion and introduced serious complications for the study of the more fundamental aspects of these processes. Only indirect evidence could therefore be obtained concerning the initiation mechanism and the nature of the chain carriers. Alkenylfurans are considerably more nuclec hilic than styrene and rather resemble p-melhoxystyrene in their behaviour towards Br<6nsted acids. The kinetics of these polymerisations showed that initiation requires two molecules of trifluoroacetic acid ... 

Plesch et al. have studied the kinetics of acenaphthylene polymerisation by EtCO SbFi and EtCO PF6 and calculated a propagation rate constant of 23 M s in nitrobenzene at 25°C with both initiators, which suggests that free ions are the main chain carriers. 

The kinetic equations obtained for stationary and non-stationary (so-called post polymerisation) processes [25, 26] qualitatively explain all the main features of block 3-dimensional polymerisation at high degrees of conversion. This feature has also been quantitatively proven on a wide range of experimental materials connected with the kinetics of photoinitiated polymerisation of dimethacrylates. This allows for the first time a numeric estimate of the rate constants for linear chain termination to be made [29]. 

Lachinov and co-workers [52] have performed a more detailed study of the kinetics of block radical polymerisation of perfluoroalkylmethacrylates (FMA) in the solid state. The main method of investigation of the kinetics of FMA polymerisation was isothermic calorimetry [58]. Due to the absence of data on the heat effects of their polymerisation in the reference literature, these values were measured [52]. The values of AQ and glass transition point (T ) of polymers formed are shown in Table 8.3. Obviously heat of polymerisation of monomers of the fluoroacrylate sequence is quite close to heat of polymerisation of non-substituted monomers of the AMA sequence [59], and a significant influence of the length of the fluoroalkyl radical on this parameter is absent [52]. In accordance with the Polyani-Semenov rule, the present result makes it possible to consider that chain propagation constant of FMA with the accuracy of the pre-exponential multiplicand being equal to each other [57]. 

Fig. 9.10. Sulphur, glasses and polymers turn into viscous liquids at high temperature. The atoms in the liquid ore arranged in long polymerised chains. The liquids ore viscous because it is difficult to get these bulky chains to slide over one another. It is also hard to get the atoms to regroup themselves into crystals, and the kinetics of crystallisation are very slow. The liquid can easily be cooled past the nose of the C-curve to give a metastable supercooled liquid which can survive for long times at room temperature.

This system was slightly modified by R J. Flory, who placed the emphasis on the mechanisms of the polymerisation reactions. He reclassified polymerisations as step reactions or chain reactions corresponding approximately to condensation or addition in Carother s scheme, but not completely. A notable exception occurs with the synthesis of polyurethanes, which are formed by reaction of isocyanates with hydroxy compounds and follow step kinetics, but without the elimination of a small molecule from the respective units (Reaction 1.3). 

As outlined in Chapter 1, polymerisation reactions can be classified as either condensation or addihon processes, the basis of the classification suggested by W. H. Carothers in 1929. More useful, however, is the classification based on reaction kinetics, in which polymerisation reactions are divided into step and chain processes. These latter categories approximate to Carothers condensation and addition reactions but are not completely synonymous with them. 

Kinetics of radical chain polymerisation. Kinetics calculations on radical chain polymerisation are based on the three steps mechanism with notations as shown in Figure 19. 

Figure 19 Mechanisms of radical chain polymerisation with kinetic notations.

Equation (4) clearly shows that the number average degree of polymerisation Xn is inversely proportional to the reaction rate Rp, meaning that, in radical chain polymerisation high reaction rates are linked to low molecular masses and vice versa. One way to avoid this dilemma is to use emulsion polymerisation where the lifetime of a radical (i.e., the "kinetic" chain length) is independent of... 

Yet, during the last decade, considerable advances have been made towards a quantitative understanding of the structural and energetic factors controlling chain cyclisation. Thanks to the application of modern technology there has been a substantial accumulation of reliable data in the form of accurate kinetic or equilibrium measurements of cyclisation reactions of bifunctional chains, as well as of careful analyses of ring-chain polymerisation equilibria. These will be dealt with in the remaining part of this section. 

Once a compound has been shown to polymerise, the most interesting question for me is What is stopping the chains from growing When that question has been answered we must know much about the kinetics of the system and at least a little about its chemistry. Before entering into an account of the reactions which stop chains from growing, it is important to make once again a clear distinction between termination and transfer reactions. There is no reason for not adhering to the radical chemist s definition of termination a reaction in which the chain-carrier is destroyed. In cationic polymerizations there are two main types of termination reaction ... 

The present paper is an attempt to unravel a rather confused aspect of cationoid polymerisations. This concerns the phenomenon comprised in the term monomer complexation of the growing cation . The idea seems to have occurred for the first time in the work of Fontana and Kidder on the polymerisation of propene by AlBr3 and HBr in w-butane [3]. The kinetics indicated a reaction of zero order with respect to monomer, M to explain this, it was assumed that the growing end of the chain, written as a carbenium ion, Pn+, is complexed with M and that the rate-determining growth step is an isomerisation of this complex ... 

Kinetically, the situation during the later part of the polymerisations by both initiator systems therefore resembles very closely the irregularly alternating propagation by unpaired and paired cations contributing to the formation of any one chain in a solvent of intermediate polarity. 

The mechanistic issues to be discussed are the initiation modes of the reaction, the propagation mechanism, the perfect alternation of the polymerisation reaction, chain termination reactions, and the combined result of initiation and termination as a process of chain transfer. Where appropriate, the regio- and stereoselectivity should be discussed as well. A complete mechanistic picture cannot be given without a detailed study of the kinetics. The material published so far on the kinetics comprises only work carried out at temperatures of -82 to 25 °C, which is well below the temperature of the catalytic process. 

More recently, Landis et al. studied the polymerisation kinetics of 1-hexene with (EBI)ZrMe( t-Me)B(C5F5)3 64 as catalyst in toluene [EBI = rac-C2H4(Ind)2]. Catalyst initiation was defined as the first insertion of monomer into the Zr-Me bond, 65 (Scheme 8.30). Deuterium quenching with MeOD was used to determine the number of catalytically active sites by NMR. The time dependence of the deuterium label in the polymer was taken as a measure of the rate of catalyst initiation. This method also provides information of the type of bonding of the growing polymer chain to zirconium, as n-or sec-alkyl, allyl etc. Hexene polymerisation is comparatively slow, with high regio- and stereoselectivity there was no accumulation of secondary zirconium alkyls as dormant states [96]. 

The determination of the microstructure of vinyl polymers is not merely a characterisation tool. Each polymer molecule is unique, and each polymer chain is a record of the history of its formation, including mis-insertions, rearrangements, the incorporation of co-monomers, and the mode of its termination. NMR analysis of polymers can therefore be used to provide detailed mechanistic and kinetic information. This approach has been applied particularly successfully to the microstructure, i. e. the sequence distribution of monomer insertions, of polypropylene, giving rise to a wealth of studies far too numerous to cover here. Progress in this area has recently been summarised in two excellent and very comprehensive review articles [122, 123[. Here we will cover only the most fundamental aspects of stereoselective polymerisations. 

In many real polymerisation reactions, the kinetic scheme given above will be inadequate. Other reaction steps may have to be included amd the results of chain transfer to polymer are not always easy to describe. There is clear evidence which suggests that the chain termination rate coefficient is reduced in value when the concentration of polymer is high [43, 44]. The quantitative assessment for such changes is still a subject of much research [45, 46]. At very high concentrations, the value of kp may also be reduced [47]. Other physical events may also be important, particularly when the reaction becomes heterogeneous. 

The reaction model assumed is one in which free-radical polymerisation is compartmentalised within a fixed number of reaction loci, all of which have similar volumes. As has been pointed out above, new radicals are generated in the external phase only. No nucleation of new reaction loci occurs as polymerisation proceeds, and the number of loci is not reduced by processes such as particle agglomeration. Radicals enter reaction loci from the external phase at a constant rate (which in certain cases may be zero), and thus the rate of acquisition of radicals by a single locus is kinetic-ally of zero order with respect to the concentration of radicals within the locus. Once a radical enters a reaction locus, it initiates a chain polymerisation reaction which continues until the activity of the radical within the locus is lost. Polymerisation is assumed to occur almost exclusively within the reaction loci, because the solubility of the monomer in the external phase is assumed to be low. The volumes of the reaction loci are presumed not to increase greatly as a consequence of polymerisation. Two classes of mechanism are in general available whereby the activity of radicals can be lost from reaction loci ... 

The propagation reaction consists in repetitive interaction of the cycloolefin double bond with a metal alkylidene species formed via the initiation reaction, and differs from this reaction only in the rate constant value. The rate of the propagation reaction should be first order with respect to the monomer concentration. However, the kinetics of polymerisation of cycloolefins is complicated by the fact that any active catalytic species in the polymerisation system will be able not only to coordinate the monomer double bond to lead to a propagation step but also to coordinate a C=C bond from the polymer chain. If the coordination of the latter C=C bond proceeds intramolecularly, then a new... 

The fourth major parameter which defines a system after the monomer, the initiator(s) and the solvent, is the temperature at which the polymerisation is conducted. The effect of temperature upon the position of the propagation-depropa tion equilibrium (ceiling temperature) is not directly relevant and too well-known to be discus here. We are obviously more interested in discussing the specific role of temperature in the reactions leading to the formation of chain carriers. The following considerations are pertinent to the kinetics of such interactions and to the thermodynamics of the reailting equflibria. 

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