RATE OF POLYMERISATION

2 Rate of polymerisation and development of molecular mass distribution 

We are interested in the rate of polymerisation and the produced molecular mass of the polymer (Section 2.2.2), when the radical polymerisation reaction proceeds (usually after a so-called induction period, see Section 2.2.4). 

In determining the rate of polymerisation we usually look at the rate of consumption of the monomer. There are two reactions that consume the monomer the initiation reaction and the propagation reaction. For the rate of polymerisation (l poi) the following equation holds  

In a normal polymerisation reaction, high molecular mass material would be formed, therefore, Rp Ry. each initiation reaction forms a new growing chain, each propagation reaction extends the chain with one more monomeric unit, so the ratio Rp over Ri is 

Since [M ] cannot be measured easily, it is impractical to use. However, we know that the free radical concentration will increase initially and will attain a constant value as soon as the termination reactions quicks in. In other words, a steady state for free radicals is assumed (both in R and M ). This is frequently done in the case when highly reactive species is present in low concentrations. What is actually done is to set the rate of formation (Ri) and the rate of disappearance (Rt) of a radical to be equal, which means that the actual rate of change of the radical concentration (the sum of the rate of production and rate of disappearance) equals zero (steady state). For M this leads to  

The rates of polymerisation (or polymerisation kinetics (176,196,221,265)) are of significant interest because they are directly related to the chemical and mechanical properties of the product, as well as the batch cycle time. The rate of polymerisation is maximised in industrial applications to produce the shortest possible cycle time and the greatest product output. 

Polymerisation rates have been estimated from conversion (jc) versus time (t) data obtained through densitometry and dilatometry. By taking the derivative (dx/dt), the instantaneous rate of polymerisation may be approximated. However, the accuracy of this method is limited by the number of conversion versus time data points and the scatter in this data. 

A more accurate method of directly obtaining the reaction rate is through the use of reaction calorimetry. There are several commercial reaction calorimeters available for measuring the rate of emulsion polymerisation. One such instrument is the Mettler-Toledo RCl Reaction Calorimeter. Continuous (one 

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Na" > > Cs". The amount of unsaturation also iacreases with number-average molecular weight (M ) suggesting that the rate of polymerisation... 

Commercially available VP is usually over 99% pure but does contain several methyl-substituted homologues and 2-pyrrohdinone. Even at this high level of purity, further purification is required if rehable kinetic data concerning rates of polymerisation are desired. This can be accompHshed only by recrystallisation, because distillation will not separate methyl-substituted isomers (7). 

The propagation rate is governed by the concentrations of growing chains [M—] and of monomers [M]. Since this is in effect the rate of monomer consumption it also becomes the overall rate of polymerisation... 

Figure 2.18. Rate of polymerisation of methyl methacrylate with azobisisobutyronitrile at 60°C as measured by various workers. (Copyright 1955 by the American Chemical Society and reprinted by permission of the copyright owner)...

Nowadays, the injection moulder can be supplied with uniform quality granules which consist of partially polymerised resin, fillers and additives. The formulation of the material is such that it will flow easily in the barrel with a slow rate of polymerisation. The curing is then completed rapidly in the mould. 

The explanation for autoacceleration is as follows. As polymerisation proceeds there is an increase in the viscosity of the reaction mixture which reduces the mobility of the reacting species. Growing polymer molecules are more affected by this than either the molecules of monomer or the fragments arising from decomposition of the initiator. Hence termination reactions slow down and eventually stop, while initiation and propagation reactions still continue. Such a decrease in the rate of the termination steps thus leads to the observed increase in the overall rate of polymerisation. 

Furthermore, should free radicals be present, the vinyl groups would much more rapidly polymerise depleting the emulsion droplets of monomer, providing the control required for a particular particle size. The composition of the solution thus determines not only the phase behaviour, but the rate of polymerisation and the particle size. If, the organism has in its genetic code, the abihty to synthesise the monomer, it presumably has... 

Fig. 4.15), are active for ATRP of both styrene and methylmethacrylate (MMA) [46]. Polymerisation was well controlled with polydispersities ranging from 1.05 to 1.47. The rates of polymerisation 1 x 10 s ) showed the complexes to be more active than phosphine and amine ligated Fe complexes, and were said to rival Cu-based ATRP systems. It was quite recent that Cu(I) complexes of NHCs were tested as ATRP catalysts [47]. In this work, tetrahydropyrimidine-based carbenes were employed to yield mono-carbene and di-carbene complexes 42 and 43 (Fig. 4.15), which were tested for MMA polymerisation. The mono-carbene complex 42 gave relatively high polydispersities (1.4-1.8) and a low initiation efficiency (0.5), both indicative of poor catalyst control. The di-carbene complex 43 led to nncontrolled radical polymerisation, which was ascribed to the insolubility of the complex. 

Using these two hypotheses, the overall rate of polymerisation is simply the rate of chain propagation (Rp). 

Rate of polymerisation is zero initially, rises to a maximum as active centres are formed from the initiator, and then remains constant, before falling off when the monomer is consumed... 

Rate of polymerisation is a maximum at the start and decreases continuously as the concentration of the functional groups decreases... 

In all cases, glycine oligomers were obtained, from the dimer up to the decamer yields were pressure dependent. The rate of polymerisation increased during the first 8 days and then remained constant until the 31st day. The authors conclude from their experimental results that abiotic polymerisation reactions during diagenesis were more likely to have occurred in deep-lying sediments than in the primeval ocean (Ohara et al 2007). 

The over all rate of polymerisation and the size of the molecules formed are dependent upon the rate of these separate process. 

Phenols, quinones and aromatic amines reduce the rate of polymerisation by reacting with polymer radical. They lose a hydrogen readily but resultant radicals are not initiators. Inhibitors are added to monomers to prevent polymerisation during storage. Hydroquinone and t-butylcatechol in 0.001 to 0.1 per cent concentration act as inhibitors. 

Retarders are the substances that reduce the rate of polymerisation the retarders reacts with the free radical and forms product which are incapable of adding monomer. A very effective retarder may act as inhibitor. Thus the distinction between retarder and inhibitor is merely of degree. Both retarder and inhibitor reduce the concentration of free radicals and shorten their average life and the length of the Polymer chain. 

Copolymerisation is the process in which a mixture of two or more monomers gets polymerised to yield a product. The product obtained is known as a copolymer. A copolymer product contains some units of each type of monomer and is different from a physical mixture of individual polymer molecules formed by different monomers. It is not always possible to make a copolymer with any two or more monomers. When two monomers A and B are copolymerised the rate of polymerisation is determined by concentration of monomers. Four different propagation reaction can occur for copolymerisation of A and B. AA, AB, BB, BA". 

In some examples of cationic polymerisation, the degree and the rate of polymerisation increase as the temperature decreases. This can be explained as follows. 

Between 0° and -30° the initial rate of polymerisation gave a linear Arrhenius plot, with an Er = 7.0 kcal/mole. The most peculiar and interesting feature of the Wichterle catalyst is that the DP of the polymers is very much greater than that obtained with any other catalytic system, at the same temperature (see Figure 1). 

The rate of polymerisation. It was found that at [isobutene] = 3.2 mole/l and [SnCl4] = 0.185 mole/l the dependence of the rate of polymerisation on the concentration of water varied with the degree of purification of the isobutene and of the ethyl chloride. When both had been subjected to two Podbielniak distillations (the usual procedure for most of the experiments) the rate varied rectilinearly with [H20], but when both monomer and solvent had been subjected to six such distillations, the rate followed the curve shown in Figure 8. Under these conditions the rate at zero added water corresponds to a concentration of the residual water of 5 x 10 4 mole/l. The authors concluded that the reaction would not go without a co-catalyst such as water. 

Figure 8 The initial rate of polymerisation as a function of the concentration of water [3]. Temperature -78°. Solvent C2H5C1. [i-C4H8] = 20 mole% 3.2 mole/l. [SnClJ = 1.15 mole% 0.185 mole/l. [H20] = 0.6 mole% corresponds to 0.1 mole/l. o - Experimental points. Full line calculated from equation xv...

With the reasonable assumptions that c is proportional to the nominal concentration of water and that, as assumed earlier, the rate of polymerisation is given by equation i, we obtain the relation (xv), in which Kt, K2, and K3 are composite, but constant, quantities. 

Co-catalysts other than water. Trichloro- and monochloro-acetic acids, when used as cocatalysts, induced instantaneous polymerisation at -140°. With the following co-catalysts the rate of polymerisation at -78° decreased in the order acetic acid > nitroethane > nitromethane > phenol > water [75a]. Since this is also the sequence of the acid dissociation constants of these substances in water, it appears that the catalytic activity , as shown by the rate of polymerisation, is correlated with the acidity of the cocatalyst in aqueous solution. Flowever, there are two reasons for questioning the validity of this correlation. 

H20, temperature -30 °C to -95 °C) the initial rate of polymerisation of isobutene is proportional to the concentration of monomer, that of styrene proportional to the square of the monomer concentration [13], so that the same mechanism cannot apply to both monomers. Further, in the very system in which the Gantmakher and Medvedev mechanism would be most plausible styrene + SnCl4 + nitrobenzene [10] - the polymerisation is found to be of first order in monomer and not, as Gantmakher and Medvedev predict, of second order, and moreover depended on the presence of water. 

We can now begin to see some of the implications of the theory and in which directions its applicability can be tested. In the course of these considerations one must always keep in mind that the rate of the ionogenic reaction (iii) ( left to right rate-constant k() is very small in comparison with the rates of polymerisation and of complex formation (reaction (ii)) and that the equilibrium concentration of ions is very small (see Table 1). 

The formation of a complex between the propagating end and one or more molecules of monomer can have two extreme consequences. If the incorporation of a monomer molecule from the solvation shell of the cation is the growth-rate determining step, the propagation becomes a unimolecular reaction and the rate of polymerisation becomes of zero order with respect to monomer concentration. Such a model was developed by... 

In chain reactions of the type considered here, the rate of polymerisation is the rate of consumption of monomer. This can be determined directly by measuring the concentration of the residual... 

After what has been explained in the earlier sections, it must be clear that most of the attempts at measuring kp have been misdirected. All but a few investigators assumed that at most two propagating species, P+n and P+nA", were involved in their systems. Therefore we will need to examine for each report, first what were the most likely chain-carriers, i.e., what was the probable principal component of Pn, and to what extent our assessment agrees with the opinion of the original workers and then we need to examine how adequate were the measurements of [Pn ] and of the rate of polymerisation. 

The impact which was made by the writer s revival of the old ester mechanism in the context of polymerisations is attested by the number of polymer chemists who set about examining the validity of the theory experimentally. For example, Bywater in Canada confirmed that during the progress of a polymerisation of styrene by perchloric acid the acid could not be distilled out of the reaction mixture, but after exhaustion of the monomer it could be. This regeneration of the initiating acid after the consumption of the monomer is an often attested characteristic of pseudocationic polymerisations with many different protonic acids it is most simply explained by the decomposition of the ester to an alkene and the acid, i.e., a reversal of the initiation, when the monomer has been consumed. Enikolopian in the USSR found that the effect of pressure on the rate of polymerisation in the same system was not compatible with the propagation step involving an ion, and... 

Water present in the monomer solution before the addition of perchloric acid did not affect the rate of polymerisation (Experiment SGP6, Table 1), but if water was added to the catalyst solution before the polymerisation, with consequent formation of HC104, H20, which is insoluble in methylene dichloride, only the anhydrous acid was found to be an active catalyst (Experiment SGP7, Table 1). 

The observation that traces of water do not influence the rate of polymerisation if the water is present in the reaction medium before the acid is added (Experiment SGP6, Table 2), indicated that (a) The reaction leading to the formation of an ester is much faster than the addition of water to HC104 (b) the ester is fairly insensitive to quantities of water up to about 10 times its concentration [3], i.e., hydrolysis under these conditions is negligible. On the other hand, if H30+C104 is already present when the polymerisation is started, this is found to have no catalytic activity, most probably because it is insoluble in methylene dichloride (Experiment SGP7, Table 2). The destructive effect of water upon the carbonium ions formed at the end of the polymerisations will be discussed in a future paper. 

Our evidence concerning the effect of water on carbonium ions shows convincingly that, since the rate of polymerisation is not affected by relatively large quantities of water [22], it is most improbable that carbonium ions present during the polymerisation, at concentrations too low to be detected by our spectroscopic technique, could be responsible for the propagation. If that had been so, no polymerisation would have been obtained with... 

Explanation The ester polystyryl perchlorate is stabilised by M, but it decomposes slowly to Pn4. In the moderately pure system the [Pn+] are consumed by impurities, mainly water, and only when depletion of M leads to fast decomposition of E are enough Pn+ formed to give colour and conductivity. In the very pure system the scavenging of water, etc., by the ions is completed before all the M has been consumed, so that the Pn+ formed thereafter contribute to the rate. At the end of a typical polymerisation of this type the [Pn+] is ca. 10"7 mol l"1. If [H20] > [HClO4]0, the k1 is unaffected because the rate of reaction of E with H20 in CH2C12 is much smaller than the rate of polymerisation, but the Pn+ and/or the HC104 are hydrated so that no colour or conductivity appears. The visible and conducting ions are not polystyryl carbenium ions, but a cocktail of others in which the substituted indanyl ion is the most abundant [28]. 

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