Intramolecular branch distribution

Figure 3.2 PE branch distributions, intermolecular branch distribution (top and middle), and intramolecular branch distribution (bottom).

Fig. 18.5 Inter- and intramolecular branching distribution of tailored LLDPEs two side views and surface contours of the averaged 3D bivariate (MW-1-hexene content) distribution from SEC and TREE corresponding to M and T effects. The profile on the right corresponds to 180° rotation over the vertical axis of the teyi-hand-side profile (Vadiamudi et ai. 2009)...

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. 

These synthetic linear and branched molecules may be important as type polymers, particularly if the interconversion of amylose to amylopectin is intramolecular, in which case the initial molecular weight and molecular-weight distribution would be retained. There is the possibility that the in vitro synthesis may even result in a truly three-dimensional structure, as distinct from that of the natural component. 

As mentioned previously, the behavior of systems containing bifunctional as well as trifunctional reactants is also governed by the equations developed above. The variation of wx for the polymerization of bifunctional monomers, where the branching coefficient a is varied by using appropriate amounts of a trifunctional monomer, is similar to that observed for the polymerization of trifunctional reactants alone. The distribution broadens with increasing extent of reaction. The effect of unequal reactivity of functional groups and intramolecular... 

Stockmayer 25 subsequently developed equations relating to branched-chain polymer size distributions and gel formation, whereby branch connectors were of unspecified length and branch functionality was undefined. An equation was derived for the determination of the extent of reaction where a three-dimensional, network ( gel ) forms this relation was similar to Flory s, although it was derived using another procedure. Stockmayer likened gel formation to that of a phase transition and noted the need to consider (a) intramolecular reactions, and (b) unequal reactivity of differing functional groups. This work substantially corroborated Flory s earlier studies. 

Precrosslinked" or "intramolecularly crosslinked" particles are micronetworks [1]. They represent structures intermediate between branched and macroscopically crosslinked systems. Their overall dimensions are still comparable with those of high molecular weight linear polymers, the internal structure of micronetworks (p-gels), however, resembles a typical network [2]. Synthesis is performed either in dilute solution or in a restricted reaction volume, e.g., in the micelles of an emulsion. Particle size and particle size distribution can be controlled by reaction conditions. Functional groups can be... 

One consequence of the intramolecular incorporation of macromer is that each site incorporates only macromer that it produced itself. That is, cross-insertion by one site of macromer produced on another site should happen rarely or not at all. Evidence from experiments with metallocene catalysts [533] in slurry polymerizations failed to produce any evidence of "cross-insertion" between sites. This finding means that LCB can be concentrated within any region of the MW distribution. Another expected result is that sites producing long backbone chains should also produce long branches, and short backbones should contain short branches, so called "Y-shaped" molecules. 

At present, a number of questions remain open. There is the specific question on the structure of the often branched side chains and the more general question on whether structural features are intra- or intermolecular phenomena. Do the molecules of a pectin preparation have smooth and hairy regions or is there a mixture of pure galac-turonan molecules and galacturonan molecules with many side chains How is the inter- and intramolecular distribution of methoxylated and free carboxyl groups ... 

A decrease in the size, R, of a PE star as a function of polymer concentration is most pronounced for polyions with a relatively small number of branches p. As discussed above, in this case the counterions are distributed most uniformly between intra- and intermolecular space. Therefore, an increase in the average concentration of counterions in the solution leads to a proportional increase in their concentration in the intramolecular volume of these branched polyions. In contrast to this, stars that have many arms have a modest response to an increase in the PE concentration. This is because at any (arbitrarily small) solution concentration, only a small fraction of the counterions is found in the intermolecular space. This behavior of PE stars should be contrasted with that of neutral star polymers. In the latter case, screening of the intramolecular excluded-volume repulsion, and the contraction of... 

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