Kinetic Analysis of Styrene Polymerization

Mn = number average molecular weight rp = polymerization rate rt = chain transfer rate kt = termination rate constant  

MAO and TIBA act as chain transfer agents, whereas /J-hydride elimination was not the main reaction for chain transfer with this catalyst system. Murata et al. [39] showed that a living polymerization was observed in low- temperature polymerization using this catalyst system. This result is in agreement with this model. 

Active site formation Chain propagation Chain transfer 

The effect of the catalyst and monomer concentrations on the polymerization was examined. The reaction rate increased proportional to the catalyst concentration and the monomer concentration (Fig. 4.12). 

On the other hand, the decay of the polymerization reaction rate is too fast to explain it as a hrst-order reaction. The time-conversion curves are htted as a second-order reaction, but it does not explain the effects of the catalyst concentration. These results indicate that this polymerization proceeds by a single site catalyst under different morphological conditions and/or under variable monomer concentrations, for example, a polymerization in the crystalline polymer and in the amorphous polymer state. 

From these results, the polymerization reaction can be described by the following equations. 

The polymerization rate constants are measured by an adjustment of the equations above to the experimental polymerization results. 

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Kinetic analyses indicate that DHb is consumed during polymerization about twenty times slower than DHa. The main consumption pathway for DHb appears to be copolymerization. From kinetic analysis of photoinitiated polymerization of styrene [64], they conclude that chain transfer to monomer is negligible and that most of the chain transfer that takes place during spontaneous styrene polymerization is due to DHa (chain transfer constant 100). 

Since the discovery of Fox et al. ( 2) that in the anionic polymerization of MMA the tacticity of the resulting polymer is fully controlled by the experimental conditions, many attempts have been made to elucidate structures of the active species responsible for the tacticities obtained under different conditions. However, this can only be achieved, if a complete analysis of the polymerization process is performed by investigating the kinetics of polymerization in different systems, as has been done for styrene. 

It has been shown [60] in the investigation of styrene polymerization in benzene that the observed rate constant greatly increases upon the introduction of small amounts of tetrahydrofuran but decreases with further addition. A detailed kinetic analysis shows that different particles are present in the system dimers ( S , Li )2, monomers (--S , Li ), monoetherates ("-S , Li , THF), dietherates (- 8 , Li , 2THF), etc. In this case monoetherate is more active than dietherate, although its activity is lower than that of the solvent separated ion pair. 

Kinetic data on olefin polymerization by polymer-immobilized zirconocene are scarce. It is generally accepted that homogeneous metallocene catalysts contain uniform active sites however, if they are immobilized on a polymer support, the MWD polymer production becomes broader compared with a homogeneous catalyst [103]. Kinetic analysis of gas-phase ethylene polymerization catalyzed by (CH3)2[Ind]2ZrCl2 bound at a hydroxylated copolymer of styrene with divinylbenzene and previously activated with MAO (0.17 wt.% Zr) has been carried out [104]. The influence of temperature (333 to 353 K), ethylene partial pressure (2 to 6 atm) and MAO level (molar ratio of MAO to zirconium from 2600 to 10,700) were studied. The activity of the catalyst in the gas-phase process changed from 5 to 32 kg PE (g of Zr atm h)It is possible that there are two types of active site. They are stable to temperature and deactivated by the same mechanism. A first-order reaction takes place. The propagation rate constants of two active sites show a similar dependence on temperature. 

The NIR-Raman spectroscopy was used by Wang et al. [163] to study the kinetics of styrene polymerizations in glass reaction flasks. Wang et al. [164], Ozpozan et al. [165], Al-Khanbashi et al. [166], Urlaub et al. [122], Bauer et al. [167], Van Den Brink et al. [168], McCaffery and Durant [169], and Elizalde et al. [170] performed similar studies forVA, styrene/butyl acrylate, MMA, cyanacrylate, styrene/ butadiene, styrene and butyl acrylate/MMA polymerizations in emulsion and miniemulsion reactions. These studies showed that NIR-Raman spectral data obtained in-line during emulsion polymerizations could be used for kinetic model building and kinetic analysis. 

Lutz and Matyjaszewski [18] have followed the evolution of the bromine end functionality during the bulk ATRP of styrene, in the presence of the CuBr/4,4 -di-(5-nonyl)-2,2 -bipyridine catalyst. The retention of the bromide chain-end functionality was monitored through the withdrawal of aliquots at given times from the polymerization mixture and their analysis by H NMR (600 MHz). A decrease in the functionality with conversion was observed, significant at high monomer conversion (90%). The experimental data allowed, by comparison with a kinetic model of styrene ATRP, better understanding of the side reactions that led to the loss in catalyst functionality and helped in the design of the most suitable reaction conditions in order to optimize the reaction kinetics and end-product properties. 

The effect of media viscosity on polymerization rates and polymer properties is well known. Analysis of kinetic rate data generally is constrained to propagation rate constant invarient of media viscosity. The current research developes an experimental design that allows for the evaluation of viscosity dependence on uncoupled rate constants including initiation, propagation and macromolecular association. The system styrene, toluene n-butyllithium is utilized. 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

The above analysis method measures the propagation rate only when all butyllithium has reacted and the initiation rate when very few polymer chains are present. It is possible that in the intermediate stages mixed associated species are present involving butyllithium and polymer chains. In the polymerization of styrene a value of 2//q can be derived from an approximate treatment of the overall process which is in reasonable agreement with the separately determined values of kt and k2 so that mixed species do not have an important effect on the overall kinetics. This may not be true however in other cases. 

Our kinetic work (10) showed that the small molecule radical produced by chain transfer with monomer had to be a stable radical. This was confirmed in the present paper by analysis of the isotope effect on the bulk polymerization rates. The isotope effect on molecular weights and rates unequivocally showed that almost 100% of the chain transfer involved the vinyl hydrogen. There is some evidence in the literature to support the idea of a stable vinyl radical. Phenyl acetylene acts as a retarder when copolymerized with styrene or methyl methacrylate (25). Thus the phenyl vinyl radical is very stable compared to the growing styryl or methacrylyl radical. 

Equation 11 refers to equilibrium swelling conditions. Now, Flory (24) concludes from theoretical considerations that monomer is easily supplied to the polymer particles at the required rate even in the case of monomers which are little soluble in water, such as styrene. That equilibrium swelling is maintained during emulsion polymerization is supported by a comparison of values of the monomer concentrations determined in equilibrium swelling measurements with those found to prevail during polymerization and determined by analysis of reaction kinetics (see below). The results obtained by both methods are plotted in Figure 10. 

The kinetic analysis here is based on quantitative considerations of the ideal emulsion polymerization systems which have been described qualitatively in the preceding sections. The treatment centers only around stage I and stage II (Fig. 6.18), as no general theory for stage III is available. The treatment applies to styrene-like monomers, meaning those monomers with low water solubility and those in which monomer and polymer are completely miscible over all ranges of composition. 

The situation is less clear-cut for RAFT systems. For a dithiocarbonate-mediated styrene polymerization studied by Goto and co-workers, the steady-state kinetic analysis applied both in the presence and absence of a BPO initiator (Figure 3.10). Similarly, for the solution polymerization of methyl methacrylate, mediated by dithioesters containing a-cyanobenzyl groups in the presence of AIBN initiator, pseudo-first-order plots were obtained although a significant induction period was detected. 

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