Branched polymers, comparison

The preceding equations will, of course, be somewhat in error owing to the neglect of intramolecular condensations. Very large species will be suppressed relatively more on this account. All conceivable errors can do no more, however, than to effect a distortion of the quantitative features of the predictions, which will be small in comparison with the vast difference between the branched polymer distribution and that usually prevailing in linear polymers. From this point of view, the statistical theory given offers a useful description of the state of affairs. 

A simple algorithm [17] makes it possible to find the probability of any fragment of macromolecules of Gordonian polymers. Comparison of these probabilities with the data obtained by NMR spectroscopy provides the possibility to evaluate the adequacy of a chosen kinetic model of a synthesis process of a particular polymer specimen. The above-mentioned probabilities are also involved in the expressions for the glass transition temperature and some structure-additive properties of branched polymers [18,19]. 

Table 11.2 Comparison of different dendritically branched polymer types, see Figure 11.7...

The link between the long-chain branch structure and the properties of the polymer has to be established experimentally by means of model branched polymers. This link can also be derived theoretically or through computer modehng. As a result, a large sub-field of study has emerged. The methods and results of this theoretical work are systematically reviewed by J. Freire. Where available, comparisons with experimental results are made. 

These equations are general and apply equally for multifunctional reactions such as that of Af with B, or that of Ay with A—A and B B. Depending on which of these reactant combinations is involved, the value of a will be appropriately determined by the parameters r,f, p, and p. For convenience the size distributions in the reaction of equivalent amounts of trifunctional reactants alone, that is, where a p, will be considered. A comparison of Eqs. 2-89 and 2-166 shows that the weight distribution of branched polymers is broader than that of linear polymers at equivalent extents of reaction. Furthermore, the distribution for the branched polymers becomes increasingly broader as the functionality of the multifunctional reactant increases. The distributions also broaden with increasing values of a. This is seen in Fig. 2-17, which shows the weight fraction of x-mers as a function of a for the polymerization involving only trifunctional reactants. 

The reaction temperature was also found to influence the efficiency of the linking reaction. As summarized in Table I, the increase in reaction temperature from 25°C to 45°C resulted in an increase in star-branch polymer formation. Qualitatively, it was also observed that the formation of vinylbenzylanion occurred more rapidly at the elevated temperatures. Apparently, the increased reaction temperatures render the intermolecular attack on the pendant vinyl groups by the polydienyllithium anions more favorable in comparison to the intramolecular intra-nodule alkylbenzyl anion-vinyl group reaction (Table I on the following page). 

In the 1960 s, several groups of workers recognised that by modification of the Szwarc living polymer procedure of anionic polymerization it would be possible to synthesize polymers of fairly definitely known branched structure, which could be used to test existing theories of the effects of LBC on polymer properties, and a considerable amount of work has been published, which is summarised in Section 8. It may be said that the theories do not come very well out of comparison with experiment, and this work shows up the inadequacy of present understanding of the properties of branched polymers. 

Pereira, M. S., Mulloy, B., and Mourao, P. A. (1999). Structure and anticoagulant activity of sulfated fucans. Comparison between the regular, repetitive, and linear fucans from echinoderms with the more heterogeneous and branched polymers from brown algae. ]. Biol. Chem. 274, 7656-7667. 

Figure 11 shows the coexistence curves of branched polymers L, B2, and D with r2 = 65 and different architectures. The predictions from this model agree very well with MC data (Arya and Panagiotopoulos, 2005), particularly at high-polymer volume fractions. Figure 12 illustrates the comparisons between calculated binodal curves by the RFT (Chen et ah, 2005), this work (Xin et ah, 2008b), and corresponding simulation data (Chen et ah, 2000 Chen et ah, 2005) for random... 

The effect of branching on the solution properties is usually discussed in terms of the comparison with those of corresponding linear polymers. The mean-square radius of gyration of branched polymers, b, is characterized using a dimensionless parameter, the shrinking factor, g, which is defined as... 

The increase in HLMI exceeds that usually expected from the elimination of (3-hydride from the tertiary carbon atom of an inserted branch, as is evident by the fact that the polymer density barely changed with addition of 1-hexene. As expected, vinylidene appeared in the polymer upon addition of 1-hexene to the reactor with any of these three catalysts, because of (3-hydride elimination from the tertiary carbon atom. However, Cr/AlP04 produced nearly three times more vinylidene than Cr/silica, although it incorporated only a fourth as much 1-hexene branching. This comparison indicates that Cr/A1P04 has a strong tendency to terminate immediately after 1-hexene incorporation (Scheme 34A). This tendency, which may result from the phosphate acidity, can drive up the MI without affecting the resin density, because a terminal branch has little influence on the polymer crystallinity. 

The considered effect is very similar to the received one at the comparison of polyarylates, S5mthesized by equilibrium and nonequilibrium (interphase) polycondensation [5], So, for polyarylate F-2, received by the first from the indicated methods, estimation according to the Eq. (4), gives D=. ll and by the second one—D=. 55. This distinction was explained by the polyarylates structure distinction, received by the indicated above methods. Hard conditions of equilibrium poly condensation (high temperature, large process duration) can cause the appearance of branched reaction products owing to lacton cycle rupture in phenolphthaleine residues then the exponent in Mark-Kuhn-Houwink equation should be reduced, since its value is less for a branched polymer, than for a linear one [5], If it is like that, then Devalue should be increased respectively according to the Eq. (4). 

The new regularly branched polymers on the basis of PS were synthesized recently [227]. Each repeated link of these polymers maeromol-eeules contains the Dendron s of Frechett5 e as a side ladieal. The study of this modified by Dendron s PS solutions has shown, that the generation number increase from 1 up to 4 results in hydro dynamical sizes and macromolecules equilibriiun rigidity enhancement in comparison with the initial PS (see Table 24). The similar results were obtained for other polymers as well, modified by Dendron s. These studies were performed within the framework of classical experimental methods, which are distinguished by both high complexity and united theoretical basis absence, taking into account macromolecule structure in solution. Therefore, the authors [240] performed the theoretical description within the framework... 

M. Strobel, V. Jones, C.S. Lyons, M. Ulsh, M.J. Kushner, R. Dorai, M.C. Branch, A comparison of corona-treated and flame-treated polypropylene films. Plasmas Polym. 8, 61-95 (2003)... 

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