Length of branches

Fig. 3.12 (a) A pom-pom with three arms at each branch point (q = 3). At short times the polymer chains are confined to the Doi-Edwards tuhe. Sc is the dimensionless length of branch point retraction into the tube X is the stretch ratio where L is the curvilinear length of the crossbar and Lq is the curvilinear equilibrium length, (b) Relaxation process of a long-chain-branched molecule such as LDPE. At a given flow rate e the molecule contains an unrelaxed core of relaxation times t > g 1 connected to an outer fuzz of relaxed material of relaxation t < g 1, behaving as solvent. [Reprinted by permission from N. J. Inkson et al., J. Rheol., 43(4), 873 (1999).]... 

The microstructures of polyolefin materials are most effectively studied by C NMR spectroscopy in solution. In particular C atoms at branching positions and at the ends of chains and branches are easily distinguished from those inside a chain. In this way, the numbers and mean lengths of branches, e.g. in polyethylene chains, can be determined rather reliably. 

Chain branching in low density versions of polyethylene is common. Extent and length of branching stem primarily from the mechanism of polymerization and incorporation of comonomers. Branching is classified as long chain branching (LCB) or short chain branching (SCB). By convention, SCB implies branches of 6 or fewer carbon atoms. LDPE contains extensive LCB and branches can contain hundreds of carbon atoms. Branches on branches are also common in LDPE. 

Molecular branching is a molecule property comprising several structural variables such as number of branching, valence, distances apart, distances from the graph centre and length of branches [Kirby, 1994]. Given this multifaced definition of branching. 

Figure 10 A rooted universal tree of life, showing the three domains of life. The tree is based on sequence comparisons of ribosomal RNA, analysed by Carl Woese and his colleagues. The order and length of branches are proportional to the sequence similarities within and between the domains and the kingdoms of life — in other words, they are directly proportional to the genetic similarities between species. It is humbling to note that the animals, plants and fungi account for just a small comer of the Eucarya domain, and that there is less variation in ribosomal RNA sequences within the entire animal kingdom than there is between different groups of methanogen bacteria.

Type of branches—1-butene comonomer gives ethyl branches, 1-hexene comonomer gives butyl branches, and 1-octene comonomer gives hexyl branches. The length of branches has a small influence, but the number of branches is more important since the branches do not take part in crystallization. 

Let us now examine the dependence of the CE of a vertical separator equipped with centrifugal branch pipes (multicyclones) on various parameters. The dependence on thermobaric conditions (pressure and temperatures), geometrical parameters (diameter of supply pipeline, length of branch pipes), and also on the gas flow rate presents the greatest interest to us. 

A change of temperature has only a small effect on the CE. A change of the supply pipeline diameter produces the same effect as in gravitational separators. An increase in the length of branch pipes will also result in an increased CE of the separator (Fig. 19.7). 

Experimental studies of solutions of PE star polymers are rare, because the synthesis of macromolecules with a controlled number and length of branches still presents a significant challenge. A few recent studies report on various properties... 

The type and amount of branches present in the polyethylenes produced in SCCO2 is not influenced by the total pressure or the temperature. The solvent, however, appears to have a small influence on the total branch content of the polyethylenes. The total amount of branches in the polyethylene produced in SCCO2 is slightly higher. This increase in total branch content cannot be attributed to a certain type or length of branch, but is rather a general increase in the amount of all branches. 

When only one type of repeat unit is found in a polymer chain it is described as a homopolymer. This illustration uses 25 units in every case so that the degree of polymerization (i.e. number of repeat units in the polymer) is the same for each. As can be seen, polymers may be linear, branched, ring- or star-shaped. The length of branches may be the same or different in the branched and star-shaped molecules. 

Under constitution are included the type and arrangement of the chain atoms, the kinds of substituents and end groups, the sequence of monomeric units, type and length of branching, the molecular weight, and the breadth of the molecular-weight distribution. Since molecular weights are almost exclusively evaluated from solution properties, these will be discussed in Part II. 

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