Reactivity ratios characterization

NMR spectroscopy has made possible the characterization of copolymers in terms of their monomer sequence distribution. The area has been reviewed by Randall,100 Bovey,139 Tonelli,101 Hatada140 and others. Information on monomer sequence distribution is substantially more powerful than simple composition data with respect to model discrimination,25,49 Although many authors have used the distribution of triad fractions to confirm the adequacy or otherwise of various models, only a few25 58,141 have used dyad or triad fractions to calculate reactivity ratios directly. 

Since the reactivity ratios of ethylene-polar monomer pairs are quite different, the preparation of copolymers with precisely the same comonomer composition can be a challenging endeavor. Earlier in this chapter, we described the synthesis and characterization of precisely placed methyl groups on a polyethylene... 

Nagy, A., Qrszagh, I., and Kennedy, J.P. Living carbocationic copolymerizations. II. Reactivity ratios and microstructures of isobutylene/p-methylstyrene copolymers, J. Phys. Org. Chem., 8, 273, 1995. Puskas, J.E. and Paulo, C. Synthesis and Characterization of Hyperbranched Polyisobutylenes. Proceedings of the World Polymer Congress (lUPAC Macro 2000), 384, 2000. 

Each monomer is characterized by two monomer reactivity ratios. One monomer reactivity ratio represents the propagating species in which the penultimate and terminal monomer units are the same. The other represents the propagating species in which the penultimate and terminal units differ. The latter monomer reactivity ratios are signified by the prime notations. Each radical reactivity ratio is the ratio of the propagation rate constant for reaction of a radical in which the penultimate unit differs from the terminal unit compared to the rate constant where the penultimate and terminal units are the same. 

The HBA/HNA system provides a more suitable system for study, since it is prepared by melt polymerization of the two monomers and is far more stable at elevated temperatures compared to the PHBA/PET. The HBA/HNA copolymers are soluble in pentafluorophenol permitting use of NMR techniques to characterize diad sequences. In Fig. 13b,c the 13CNMR spectrum of the carboxyl carbon region of the HBA/HNA copolyesters of the 73/27 and 48/52 systems is shown [34]. Also shown in Fig. 13a,d are the spectra of 13C enriched HBA and HNA containing copolymers permitting unique identification of the diad sequences. As a result of this technique it was possible to determine the reactivity ratios of the two monomers by analyzing the 50/50 copolymer after polymerization to a molar mass value of 2000 [35]. Examination of the copolymer by 13C NMR showed the same ratio of monomers as in the starting... 

Harwood (17) has described a technique using run number theory to calculate reactivity ratios based on sequence distribution. The run number, R, which characterizes a particular copolymer may be calculated as follows ... 

As long ago as 1960, Tarasov et al. [121] presented some examples of the concrete three-component systems for which the existence of the azeotropic composition had already been predicted theoretically. The list of such systems was widened substantially after publication of the important paper [125], where a set of the known tabulated values of 653 pairs of reactivity ratios for a computer search of the possible multicomponent azeotropes was employed. For this aim one should, at first, reveal all the completely characterized multicomponent systems for which the values of reactivity ratios of all monomer pairs are tabulated. This problem can be formalized by reducing it to the search on the graph with 653 lines of a... 

Hence, within the framework of the traditional kinetic model (2.8) there is a mathematically rigorous solution of the problem of the calculations of the azeotropic composition x under the copolymerization of any number of monomer types knowing their reactivity ratios, i.e. the elements of matrix ay. However, since the values of au can be estimated from the experiment with certain errors Say, the calculated location of azeotrope x is also determined with an accuracy, the degree of which is characterized by vector 8x with components 8xj (k = 1,2,..., m) and modulus 8X ... 

As it follows from the present review, a rather complete and experimentally well-grounded quantitative theory of radical copolymerization of an arbitrary number of monomers has been developed. This theory allows one to calculate various statistical copolymers characteristics using the known values of reactivity ratios. The modern stage of the development of this theory is characterized by new approaches applying, for example, the apparatus of graph theory and theory of the dynamic systems which permit to widen the area of theoretical consideration involving the multicomponent copolymerization at high conversions. 

The same model has been used lt6) to explain the copolymerization of ethylene and propylene with TiCl+/EB/MgCl2—AlEt3, with various amounts of EB added to the cocatalyst. The triad sequence distribution calculated for the copolymer obtained without EB was in disagreement with reactivity ratios, while the values obtained with high concentrations of EB did agree. Thus, the two active species mentioned, having two and one vacancies respectively, would be characterized by... 

Table 1 is a compilation of relatively large scale copolymerization experiments carried out to collect material sufficient for characterization and jdiysical property studies. Results of experiments conducted to elucidate the effects of reaction variables on reactivity ratios i.e., small scale runs ( 20 ml), are listed separately later. 

Errors in variables methods are particularly suited for parameter estimation of copolymerization models not only because they provide a better estimation in general but also, because it is relatively easy to incorporate error structures due to the different techniques used in measuring copolymer properties (i.e. spectroscopy, chromatography, calorimetry etc.). The error structure for a variety of characterization techniques has already been identified and used in conjunction with EVM for the estimation of the reactivity ratios for styrene acrylonitrile copolymers (12). 

Solution NMR is widely used in polymer processing for the qualitative and quantitative analyses of tacti-city, end-groups, degradation products, chain defects, and monomer sequence distribution.A typical application is in the characterization of monomer sequence distribution by quantitative NMR spec-troscopy. For example. Fig. 7 shows a typical NMR spectrum of ethylene-co-l-butene. From the relative peak areas, it is possible to determine the fractions of the two monomers, their reactivity ratios, the triad distribution, and the blockiness or randomness of the monomer distributions. All of these structure factors play an important role in the polymer s physical and mechanical properties. 

Graft copolymers were obtained by the ordinary copolymerization with suitable comonomers, and characterized mainly by GPC and NMR. The monomer reactivity ratios were estimated by Equation 1 under the condition [B] [A]. 

The probabilities of the regiosequence pentads for commercial PVF and urea PVF are shown in Table III. For the former sample it is apparent simply by inspection that the regiosequence distribution is not Bernoullian, since Pobs(C5) and Pobs (D5) are different (2). The distributions conform to first-order Markov statistics, characterized by two reactivity ratios r0 and r 5 where r0 = k /lq, and rj — ku/k10 (kjj is the rate constant for monomer addition to terminal radical i which generates the new terminal radical j). The present pentad data is insufficient to check the validity of this model, but it is unlikely that there is any deviation, as the same model has been tested and found adequate to describe the regiosequence distribution in PVF2 (2). 

We use the term constitution to describe the way in which the monomeric units, or constitutional units, are linked together. A knowledge of copolymer constitution thus requires a study of the distribution of the constitutional sequences (more briefly, sequences) of both monomers. As a general rule, the constitution is quantitatively characterized by the product of the reactivity ratios, the parameter of the terminal copolymerization model. The presence of non-ideal constitutional units is not accounted for by this model small numbers of inversions of C3 units or steric effects must be regarded as a perturbation in this approximation. 

---