Polymerization conversion curves

Stoicescu and Dimonie103 studied the polymerization of 2-vinylfuran with iodine in methylene chloride between 20 and 50 °C. The time-conversion curves were not analysed for internal orders but external orders with respect to catalyst and monomer were both unity. Together with an overall activation energy of 2.5 kcal/mole for the polymerization process, these were the only data obtained. Observations about the low DP s of the products, their dark colour, their lack of bound iodine and the presence of furan rings in the oligomers, inferred by infrared spectra (not reported), completed the experimental evidence. The authors proposed a linear, vinylic structure for the polymer, and a true cationic mechanism for its formation and discussed the occurrence of an initial charge-transfer complex on the... 

The initial rate of polymerization was determined from the initial slopes of time-conversion curves (Fig. 1) using f-BuX/Me3 Al/MeCl systems at -40 °C. This... 

Fig. 7. Calculated time/conversion curves and experimental data points in the anionic polymerization of MMA (C0 = 0.1 mol/1) initiated by methyl-a-lithioisobutyate (C0 = 0.05 mol/1) at 25 °C in THF (Products higher than the tetramer are omitted) (A. H. E. Muller, L. Lochmann, J. Trekoval, Ref.S0))...

Fig. 7. Time-conversion curves of thermally initiated emulsion polymerization of 1,4-DVB at 0.1 (I) 0.65 (II) and 0.85 (III) M SDS concentrations. Polymerization temperature = 90 °C water/monomer volume ratio = 12.5. [Reproduced from Ref.84 with permission,Hiithig Wepf Publ., Zug, Switzerland].

It is necessary now to find out whether my theoretical conclusion is supported by experimental evidence in fact, there are many results for bulk polymerizations that indicate a first-order growth reaction. The experimental support that I seek would be found in the shape of the curves relating the conversion, Y, to the total received dose of radiation or to the time at a constant dose-rate. If the polymerizations are of zero order with respect to m, the conversion curves will be rectilinear instead of concave to the dose (or time) axis. Rectilinear conversion curves are actually much more common than first-order type curves, and some instances of this behaviour are listed in Table 1. In example 8 of Table 1 the experimental points are actually on a straight line, but a curve has been drawn past them. 

Poly(acrylic acid) is not soluble in its monomer and in the course of the bulk polymerization of acrylic acid the polymer separates as a fine powder. The conversion curves exhibit an initial auto-acceleration followed by a long pseudo-stationary process ( 3). This behaviour is very similar to that observed earlier in the bulk polymerization of acrylonitrile. The non-ideal kinetic relationships determined experimentally in the polymerization of these two monomers are summarized in Table I. It clearly appears that the kinetic features observed in both systems are strikingly similar. In addition, the poly(acrylic acid) formed in bulk over a fairly broad range of temperatures (20 to 76°C) exhibits a high degree of syndiotacticity and can be crystallized readily (3). 

A detailed investigation of the polymerization of this monomer in a series of solvents has shown, however, that the auto-accelerated character of the reaction is not related to the precipitation of the polymer. Thus, linear conversion curves and atactic polymers are obtained if the monomer is diluted in such nonassociating solvents as toluene, n-hexane, carbon tetrachloride and chloroform, in spite of the precipitation of the polymer, whereas, both auto-acceleration and syndiotacticity persist for fairly high dilutions in water, methanol and dioxane even under conditions where the reaction medium turns homogeneous (4). 

Figure 1. Conversion curves of the polymerization of acrylic acid in toluene solutions (4). Monomer concentrations (volume per cent) (1) 100% (2) 95% (3) 90% (4) 85% (5) 80% (6) 65% (7) 50% (8) 27%. The polymer precipitates as a fine powder at all concentrations. Initiation by gamma-rays at 20°C and...

Methacrylic acid also polymerizes in bulk under precipitating conditions. It forms molecular associations very similar to those of acrylic acid. However, the conversion curves were found to be linear under a variety of experimental conditions temperatures of 16.5 to 60°C and broad ranges of initiation rates and monomer concentration in numerous solvents (7). It was assumed that structures of type III do arise but owing to steric hindrance and to the rigidity of the poly(methacrylic acid) molecule the monomer cannot align to form a "pre-oriented" complex as in the case of acrylic acid and propagation is not favored. 

Further experiments were therefore carried out with polar solvents which do not dissolve the polymer. Most striking results were obtained with trichloroacetic acid. The polymerization of acrylonitrile in this solvent was found to proceed under precipitating conditions at all concentrations. In spite of this, the conversion curves were perfectly linear in solutions containing 60 volume per cent monomer or less (18). Moreover, these systems exhibit marked post-polymerization showing the presence of long-lived radicals. 

From the results presented above it can be concluded that the auto-accelerated conversion curves observed in the polymerization of acrylic acid, methacrylic acid and acrylonitrile are not caused by non-steady conditions arising as a result of the occlusion of growing chains in the precipitated polymer. This occlusion which is responsible for the post-polymerization observed in these systems only contributes to a limited extent to the over-all rates. 

Figure 3. Time-conversion curves in the bulk polymerization of DAP using 0.1 mol/L of BPO at 80°C (O ) total polymer, ( ) gel polymer.

Figure 11.2. Time-conversion curve for polymerization of multiacrylate in dioxane (o) at 75°C, and ( ) at 85°C. Reprinted from R. Jantas, J. Szumilewicz, G. Strobin, and S. Polowinski, J. Polym.

Fig. 33. Polymerization of 1,2-epoxypropane (PO) by the (Me4DBTAA)AlCl (12)-methylalu-minum bis(2,6-di-tert-butyl-4-methylphenolate) (3e) system, [P0]o/[3e]o/[12]o=200/1.0/ 1.0, [12]o=71.4 mM, without solvent, rt. Time-conversion curve...

At 273 and s 9.02 the polymerization followed first order kinetics. At 225 (Figure 4) the conversion curve was indistinguishable from a zero-order plot up to 40 percent conversion but if the whole curve was examined the internal order was seen to lie between zero and one. At 250 the internal order also lay between zero and one but the fit was nearer to the first-order plot in monomer. The kinetics are consistent with a Bateup-Yerusalimskii mechanism. At low temperatures the limiting condition of Equation 3 is approached. As the temperature rises the stationary state concentration of the complex decreases and the mechanism shifts to its other limit... 

Although an appreciable amount of termination is found at elevated temperatures, rate constants can be calculated from the initial slope of the first-order time-conversion curve. The concentration of living ends is calculated from the linear plot of the number-average degree of polymerization vs. conversion.which still remains linear when termination occurs, since the total number of chains remains unaltered., provided nor intermolecular termination (grafting) nor transfer occurs. 

Fig. 7. Conversion curve (arbitrary unit) for polymerization of methyl methacrylate in toluene solution on the presence of triethylaluminum at 256° K in darkness and illuminated with 100 W tungsten light (Aixen and Casey [43))...

In view of the almost ideal behaviour of this copolymerization, the polymerization process could be continued to complete conversion without any inhomogenity in the composition of the products. The time conversion curve for the copolymerization is shown in Fig. 3.4. 

The conversion-time curves appear to be very similar to the shape typical of emulsion polymerization, i.e., an S-shaped curve is attributed to the autoacceleration caused by the gel effect (Smith-Ewart 3 kinetics, n>>l). The rate of polymerization-conversion dependence is described by a curve with two rate maxima. The decrease in the rate after passing through the first maximum is ascribed to the decrease of the monomer concentration in particles. Particle nucleation ends between 40 and 60% conversion, beyond the second rate maximum. This is explained by the presence of coemulsifier which stabilizes the monomer droplets against diffusive degradation. 

High conversions (close to 100%) can be obtained by the dispersion copolymerization of PEO-MA with butyl acrylate initiated by a water-soluble initiator (VA) [80]. The conversion curves have a shape similar to that for the dispersion copolymerization of PEO-MA with styrene. In runs with AIBN the final conversion was around 90% and/or the polymerization was very slow at high conversion. 

Figure 7. Conversion profiles for MM A seed latex polymerization. Solid curves are theoretical predictions and data points are experimental results ((O) a0 = 0.35 ...

This work has shown that by monitoring conversion curves by a computer, emulsifier metering can be varied to produce a desired particle size distribution of smalls in a seeded PVC emulsion polymerization. 

Figure 1. Time-conversion curve for DOL polymerization with EtsOBFh at 30°C.

The sequence accounts satisfactorily for the production of polymer from low oligomers and for the shape of the DP-conversion curve in the oxidation of 2,6-xylenol. Formation of quinone ketals similar to III is, furthermore, a known reaction of hindered aryloxy radicals (I, 14). The major objection to this proposal is the great number of steps required to produce a monomer radical from two polymeric radicals of a high degree of polymerization. 

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