Overall Extent of Polymerization

It should be noted that Eq. (6.24) represents the instantaneous rate of polymerization corresponding to [M] and [I] values at any given instant. Since these values change with conversion, Eq. (6.24) must be integrated over a period of time to determine the overall extent of polymerization. 

If the initiator decomposes in a unimolecular reaction [cf Eq. (6.3)], the rate of initiator disappearance is first order in initiator, represented by 

Being independent of the initial concentration of the initiator, ti/2 is a convenient criterion for initiator activities. Several common initiators with their half-lives at various temperatures are listed in Table 6.1.] 

Since the extent of monomer conversion, p, is usually defined as [M]o - [M] 

Solvents used a Benzene b toluene c cyclohexene d styrene. 

Source Calculated from Eq. (6.27) using ka data from Brandmp et al. (1999). 

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A moment s reflection reveals that the effect on v of transfer to polymer is different from the effects discussed above inasmuch as the overall degree of polymerization is not decreased by such transfers. Although transfer to polymer is shown in one version of Eq. (6.84), the present discussion suggests that this particular transfer is not pertinent to the effect described. Investigation of chain transfer to polymer is best handled by examining the extent of branching in the product. We shall not pursue the matter of evaluating the transfer constants, but shall consider instead two specific examples of transfer to polymer. 

When the polymerization has proceeded to such an extent that all of the monomer droplets have vanished, which occurs after 60-80% conversion, all of the residual monomer is located in the latex particles. The monomer concentration in the particles now declines as polymerization proceeds further, i.e., in this final period the reaction is first order. At the end of the polymerization, the emulsion consists of polymer particles with a size distribution between 50 and 150 pm, which is larger than the original micelles, but smaller than the original monomer droplets. The changes of surface tension and overall rate of polymerization with conversion are schematically shown in Fig. 2.2. 

Overall rates of polymerization are generally rather insensitive to the presence of diluent. Das, Chatterjee and Palit (50) compared rates at 50 mole percent concentration in a variety of liquids. In the range of their experiments, polymerization rate was nearly independent of the choice of diluent. Bamford, Jenkins and White (22) point out that transfer agents reduce the mean degree of occlusion. Since the termination rate is increased under these conditions, the overall polymerization rate is reduced. The extent of polymer swelling will vary from one liquid to another (32, 130), and this obscures the interpretation to be made from limited data. 

According to Scheme 13 a benzyl derivative of Nd is formed. At a polymerization temperature of 60 °C the benzyl Nd intermediate once formed decomposes rapidly as Nd(benzyl)3 is reported to be stable only below - 15 °C [425,426]. As a consequence of the low thermal stability of the Nd benzyl species proton transfer from toluene is irreversible and the overall rate of polymerization is reduced by the decrease of the amount of the active catalyst species. As TBB lacks benzyl protons it can only act as a 7r-donor. Therefore, TBB reduces the polymerization rate to a lower extent than toluene. Beside the interpretations given, the study also presents detailed investigations on the evolution of the MMDs with monomer conversion in the three solvents n-hexane, TBB, toluene [422]. In the two aromatic solvents a high molar mass fraction is more pronounced than in n-hexane. 

Non-radiative direct energy transfer (DET) is the transfer of the exited state energy from a donor molecule to an acceptor molecule. This transfer occurs without the appearance of a photon, and is primarily a result of dipole-dipole interactions between the donor and acceptor. DET between phenanthrene and anthracene chromophores has been successfully employed to investigate the morphologies of PMMA and PS labelled homopolymer latex particles prepared by seeded emulsion polymerization, as well as PMMA/PS and PS/PMMA composite particles [85]. The results tend to confirm the existence of a core-shell structure of the latex particles, but more important, provide deeper insights into the interfacial structures in the particles. There is a limitation in the quantitative interpretation of the data due to the overall extent of energy transfer which is still small, even when there is substantial mixing nevertheless, trends are apparent. 

The study of PF polymerization is far more difficult than that of methylolation due to the increased complexity of the reactions, the intractability of the material, and a resulting lack of adequate analytical methods. When dealing with methylolation, we saw that every reactive ring position had its own reaction rate with formaldehyde that varied with the extent of prior reaction of the ring. Despite this rate sensitivity and complexity, all reactions kinetics were second-order overall, first-order in phenol reactive sites and first-order in formaldehyde. This is not the case with the condensation reactions. 

These sites can be used to initiate the polymerization of a small amount of di-vinylbenzene (DVB)8-10. The bifunctional monomer will polymerize to small tightly crosslinked nodules each of them is connected with the /chain ends which have participated in its initiation process. The average functionality /of the nodules is not directly accessible. However, it was shown in the case of star-shaped molecules that /increases with the overall concentration of the precursor, and, to a smaller extent, with the amount of DVB added per living end./is almost independent of the precursor chain length11. ... 

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