Active centre concentrations

When the active centre concentrations change during propagation, the whole polymerization is non-stationary. Kinetically the process becomes more complicated and often even experimental control of the process becomes more difficult. On the other hand, a non-stationary condition can be utilized in studies of the elementary polymerization steps. To this end, the non-stationary phases of radical polymerizations are suitable, where outside these phases the process is essentially stationary [23-25]. Hayes and Pepper [26] called attention to the existence and solution of a simple non-stationary case caused by slower decay of rapidly generated cationic centres. In more complicated cases, exact analysis of the causes of a non-stationary condition is often beyond present possibilities. Information from the process kinetics is often not conclusive. It should be mentioned that, even when the condition d[Ac]/dt = 0 is strictly valid, polymerizations may be non-stationary, particularly in those cases when during propagation the more active form of the centres is slowly transformed to the less active form or vice versa. 

An exact solution of scheme (114) would require the knowledge of various active centre concentrations, [ —M, — M2, and — M3], These data are unknown even for the simplest systems. Therefore use must again be made of the stationary state assumption+ yielding... 

Fig. 11. Dependence of active centre concentration on time during THF polymerization. Temperature 273 K., initiator Et3Al/H20 (2 1) with chloromethyloxirane as co-initiator.

At low active centre concentrations encountered, initiation is slow - termination rapid, ion pair free ion equilibria are thought to be essentially intramolecular. As chain length increases, falling entropy will favour the free ion. Since free ion propagation is believed to be much faster than propagation on cyclic contact ion pairs, the authors suggest that kp depends on the length of the zwitterion. 

The kinetic equations so far derived permit determination of ratios of rate constants but not their individual values. The polymerization has an induction period which the authors attribute to a non-stationary active centre concentration. The following equation was derived to fit this phase of die polymerization... 

At low temperatures reaction (5) is thought to be very slow. Assuming monomolecu-lar termination and a steady state in active centre concentration at the start of polymerization... 

The other alkali metals have been less extensively studied. The propagation rates of polystyrylsodium, -potassium, -rubidium and -cesium have been measured in benzene and cyclohexane [72, 73]. The sodium compound still shows half order kinetics in active centre concentration and is presumably associated to dimers. The rates for the rubidium and cesium compounds are directly proportional to the concentrations of the active chains which are presumably unassociated in solution. Absolute kp values can be determined from the propagation rate in this case. Poly-styrylpotassium shows intermediate behaviour (Fig. 11), the reaction order being close to unity at a concentration of the potassium compound near 5 x 10 M and close to one half at concentrations around 10" M. It could be shown by viscosity measurements that association was absent in the low concentration range. In this system both K2 and kp can be measured. The results are summarized in Table 2. The half order reactions show a large increase in kpK between lithium and potassium which... 

For an active centre concentration [P ] at any time, t, the net loss of monomer is given by... 

Unfortunately, there is no information on the concentrations of active centres in the early st es of reaction with these types of catalyst. Indeed, the question of active centre concentrations in heterogeneous catalysts is beset with difficulties, estimates vary greatly and the methods are sometimes of dubious reliability. Before quoting published values some account of the methods used may be desirable. 

Direct measurements of active centre concentrations have been made by terminating the polymerization with some reagent such as iodine [86], carbon dioxide [115] or an alcohol [116], labelled with an isotope which introduces radioactivity into the polymer e.g. 

There is, in addition, the possibility of calculating active centre concentrations from measurements of polymerization rate and polymer molecular weight. 

An assessment of the methods for determining active centre concentrations has been made by Schnecko and Kern [213], and they conclude that radioactive assay is more reliable than indirect kinetic methods. Propene and butene-1 polymerized by TiClj/AlEtjCl on termination with iodine or BuO H gave comparable extrapolated values of ca. 0.5% for catalyst efficiency. This is lower than earlier estimates but higher than the very low values (0.1%) obtained by Coover and Guillet [121], although the shapes of the curves obtained by the two groups were very similar. 

This catalyst [111] gives several polymer molecules per titanium atom, and there are similar findings for Cr(acac)3/AlEt3 for butadiene and Cr(acac)3/AlEt2 Cl or AlEtCl2 for ethylene [139]. It appears reasonable to assume, therefore, that all the transition metal participates in the reaction. With Cr(acac)3/AlEt2Cl the average number of polymer molecules approximates to one per Cr atom which additionally would indicate the absence of a transfer reaction. This point needs to be confirmed, however, with separate measurements of active centre concentrations and chain transfer, since two soluble nickel catalysts [68, 124] have been reported to have low catalyst efficiencies. 

The results of a number of determinations of active centre concentrations are given in Table 5. With the exception of the soluble catalyst for ethylene, the results for which are not corrected for the known transfer reaction, and the surprisingly high values for the Cr(acac)3/AlEt3 sys-... 

If the effect of the transfer reactions and subsequent re-initiation of growing chains on monomer consumption and active centre concentration are taken into account the polymerization rate is given by [227]... 

Active centre concentrations in butadiene polymerization by Ti(OBu)4/AlEt3 and Ti(acac)3/AlEt3 [124,154]... 

For a concentration of VCI3 = 18.9 x 10" mole 1 , Al/V = 2 and [M] = 2.0 mole 1" the rate in benzene at 30°C was 5.56 x 10 mole min, corresponding to an apparent rate coefficient of 2.45 x 10 1 mole sec , substantially slower than the reaction of propene. From active centre concentrations and rate data the propagation rate coefficient was calculated [238]. This was reported as... 

Monomer was polymerized by a first order reaction but it interferes with the formation of the active catalyst, and the active centre concentration falls inversely with increase in initial monomer concentration. Polymer molecular weights increase with initial monomer concentration and the monomer transfer coefficient (fetr.M/ p) is small (8x10 ). Catalyst efficiency is low (ca. 0.05), in agreement with the observations of Dawes and Winkler [146] for the polymerization of butadiene using the same catalyst. 

To prove these assertions, the rate of disappearance of isoprene had to be shown to be first order with respect to isoprene at a given active centre concentration. For this purpose, the concentration of isoprene was measured dilatometrically at a series of times following its addition to a solution of active centres a series of such experiments were carried out, some to test the reproducibility of the data and some at different initial concentrations of isoprene. These data were analysed on the basis of eqn. (36), the rate coefficients being obtained from the particular form of the general rate expression... 

Most recently the polymerization of methyl methacrylate with Ba counterion has been reported. In THF at —70 °C the rate constant for propagation is independent of the active centre concentration and growth seems to occur via ion pair species only. The kinetic data obtained compare favourably with those for polymethylmethacryl sodium and caesium.As before, active centres are terminated by side-reactions involving the ester group. 

For the use of the diffusion layer model are ne ed parameters of active centre concentration and acidity constants Kp and Kd on the mineral s surface and also equilibrium constants of all specific complexation reactions. This model was successfully used at analysis of adsorption of such ions as Na+, SO or Cl poorly adsorbed on the surface of iron oxide type minerals. 

A specific equation has been developed for a particular case, i.e., when the rate constants of the chain propagation and active centre elimination reaction do not depend on temperature, the kinetic chart of polymerisation favours fast initiation, the reaction is first-order by monomer and active centre concentration in their elimination reaction [84], then ... 

These kinetic features parallel very closely those already proposed by Tait and co-workers. The Yermakov scheme is based on evidence - arising from kinetics and active centre concentration determinations ( CO tagging with PHj addition to prevent copolymerization). These investigations demonstrated that the value of the rate constant for propagation did not depend on either the nature of the alkylaluminium compound (cf. ref. SO) or on the composition of the TiClj sample. Also, the effective activation energy, Eett, of the overall polymerization process in the presence of TiClj was higher than that of the propagation reaction, Ep, such that... 

It is of interest that the kinetic theories of Tait and co-workers, Yermakov et al., and Bohm all involve a two-stage propagation reaction and reversible adsorption of alkylaluminium compounds on the active centres the active centre concentrations being determined by tritium quenching, CO tagging and molecular weight data, respectively. 

Studies on the Polymerization of Propylene Using Highly Active Magnesium Chloride Supported Ziegler-Natta Catalysts Effects of Alkyl Concentration on the Polymerization Rate and on the Active Centre Concentration... 

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