Constant rate of propagation

Methyl acrylate Methyl methacrylate n-Butyl methacrylate Tert. butyl methacrylate 2-Vinylpyridine 

The determination of the elementary propagation rate constant is connected with considerable difficulties. Measurements can rarely be made in the gaseous phase, and in the condensed phase the consequences of attractive intermolecular forces cannot be excluded. The reaction studied depends on the medium. Therefore the micromechanism of propagation must be known in detail, and suitable kinetic methods must be applied. Even then, the elementarity of the measured constant will not be guaranteed at the present state of the art. 

On the other hand, a certain dose of creative spirit is appropriate. When the requirements of modem research methods are respected, good reproducibility can be achieved, disturbing effects can be limited, and our knowledge can be promoted by a further step. The measured constants, even though only defined for a certain system, form an excellent basis for further discoveries. The values of propagation rate constants for some monomers in radical, ionic and coordination polymerizations are summarized in Table 9. 

Mortimer, Reaction Heats and Bond Strengths, Pergamon Press, London 1962, 

Allen and C. R. Patrick, Kinetics and Mechanisms of Polymerization Reactions, Horwood, Chichester, 1974, pp. 210-220, 230. 

---

Kinetics. Details of the kinetics of polymerization of THF have been reviewed (6,148). There are five main conclusions. (/) Macroions are the principal propagating species in all systems. (2) With stable complex anions, such as PF , SbF , and AsF , the polymerization is living under normal polymerization conditions. When initia tion is fast, kinetics of polymerizations in bulk can be closely approximated by equation 2, where/ is the specific rate constant of propagation /is time [I q is the initiator concentration at t = 0 and [M q, [M and [M are the monomer concentrations at t = 0, at equiHbrium, and at time /, respectively. 

In this equation, Mp is the monomer concentration within forming particles, pa is the adsorption rate of oligomeric radicals by the forming particles, Vp is the volume fraction of forming particles within the system, and kp and k, are the rate constants of propagation and termination, respectively. 

Table 2. Rate constants of propagation for ionic polymerization...

The latter seem to be the only species contributing to propagation, and hence the apparent rate constant of propagation is given by... 

An interesting approach to studies of the effects of coordination on the reactivity of lithium polydienes in hydrocarbon solvents was developed by Erussalimski and his colleagues 151 154 The polymerization of lithium polyisoprene in hexane is accelerated by the addition of TMEDA152), the rate levels off at a value of R = [TMEDA]/[li-thium polyisoprene] of 8, its final value giving the absolute rate constant of propagation of the polyisoprene coordinated with TMEDA, namely 0.17 M7l s at 20 °C. 

The reason is that these alleged kp values are mostly composite, comprising the rate constants of propagation of uncomplexed Pn+, paired Pn+ (Pn+A ), and Pn+ complexed with monomer or polymer or both, without or with an associated A" [17]. Even when we will eventually have genuine kp values for solvents other than PhN02, it will not be possible to draw many (or any ) very firm conclusions because the only theoretical treatments of the variation of rate constants with solvent polarity for (ion + molecule) reactions are concerned with spherically symmetrical ions, and the charge distribution in the cations of concern to us is anything but spherically symmetrical. 

In the second part of the paper 6.10 [143] this writer generalises his new kinetic treatment of living polymerisations [134], By applying it to data from the literature, he shows how this treatment can reveal which one of the components of a binary syncatalytic system (e.g. I2 and organic iodide) determines the concentration of the propagating species and, much more important, how the rate-constant of propagation can be calculated from readily available data. There remains here a rich mine of information to be exploited by others. 

By means of a simple kinetic analysis of living polymerisations it is shown how both the concentration of growing ends and the rate-constant of propagation can be determined, provided that both the yield and the degree of polymerisation are given as functions of time. 

The values of absolute rate constants of propagation given in Table I have been obtained by using these formulas. 

The typical emulsion polymerization of styrene was confirmed to proceed in Case 2. According to Eq. (I), the rate constant of propagation can be calculated by measuring the rate of polymerization (Rp) and the number of particles (N) and substituting 0.5 for n. 

Molar Cyclization Equilibrium Constant (Kx) and the Rate Constant of Propagation (kp x) and Depropagation (kj x) for Cyclic x-mer at 0eC with LiO-t-Bu (4.5xl0-3M)... 

Thus, in the present paper we review the available data, pertinent to the kinetics and mechanism of anionic polymerization of lactones and discuss the recent data of our own, giving eventually an access to the rate constants of propagation on macroions and macroion--pairs. 

In all but one of these studies the apparent rate constants of propagation were determined. The observed apparent propagation rate constant (kSPP) is a summ of products of rate constants on various forms of active centers (e.g. free ions, ion-pairs, aggregates) and their fractions in the polymerizing mixture... 

Figure 9 gives the apparent rate constants of propagation (kp) as a function of the inverse square root of the living end concentration with and without an electric field for styrene with Li+ gegenions in binary... 

If this three-state polymerization mechanism is accepted, we have for the apparent rate constant of propagation kp,... 

Besides the field influence on the monomer reactivity ratio mentioned in the previous sections, living anionic systems present strong evidence against the electroinitiated polymerization mechanism. First of all, the experimental fact, that the apparent rate constant of propagation was increased by the presence of an electric field, rules out a possibility that the observed field-accelerating effect resulted only from the initiation reaction enhanced by the field. The finding that the field had no influence on the dependences of the polymerization rate on monomer and initiater concentrations, but did influence the rate constant, implies that the reaction mechanism was unaltered by the application of the field. These results confirm our very low opinion of the electroinitiated polymerization mechanism. 

Because the rate constant of propagation is independent of the identity of... 

Conversion of a randomly-coiled growing polymer into a helix affects the surroundings of its active end and, therefore, such a transformation is expected to modify the rate constant of propagation. This most interesting situation was visualised by Doty and Lundberg (36), and a model, taken from a paper by Weingarten (33) and shown in Fig. 16, illustrates how a helical structure might influence the monomer addition. 

With the experimental techniques available at present, rate constants of diad formation cannot be determined directly. There is however a way to calculate the rate constants from the experimentally determined triad, diad, etc. fractions if the rate constant of propagation and the statistical model are known (e.g., a one-way mechanism, a two-way mechanism, enantiomorphic site model) (9, JO). Very few rate constants of propagation are available, however. 

XY, F2C = CRR, k , kpl, kTe and ktr represent the telogen, the monomer, the rate-constant of initiation, the rate-constants of propagation, of termination and of transfer, respectively. 

---