Branch length

Figure 2.15 Log of viscosity enhancement factor versus parameter measuring branch length for polyisoprene, [Data from W. W. Graessley, T. Masuda, J. E. I. Roovers, and N. Hadjichristidis, Afacromo/ecu/ej 9 127 (1976).]...

Alpha-Olefin comonomer Carbon content Branch length... 

The starburst point occurs at a well-defined limit for each dendrimer system, and its occurrence is dependent mainly on (a) the functionality of the core, (b) the multiplicity of the branches and (c) the branch length. However, the volume of the core itself, and the length of the monomer branches also have an influence. The end groups may occupy the outer surface of the dendrimer, or the branches may fold inwards, thus distributing the end-groups within the dendrimer. The factors that control this behaviour of the branches are not fully understood, but include the nature of the solvent and the detailed chemistry of the dendrimer branches. 

The properties of a polymer depend not only on its gross chemical composition but also on its molecular weight distribution, copolymer composition distribution, branch length distribution, and so on. The same monomer(s) can be converted to widely differing polymers depending on the polymerization mechanism and reactor type. This is an example of product by process, and no single product is best for all applications. Thus, there are several commercial varieties each of polyethylene, polystyrene, and polyvinyl chloride that are made by distinctly different processes. 

Recent studies by Liu et al. [82] have expanded the scope of using NMR to detect branch lengths up to 10 carbon atoms. Liu et al. [82] were able to assign chemical shits values to carbon atoms in a branch longer than six carbons by using ultra-high frequency 13C-NMR (188.6 MHz). 

Fig. 1.5. Delineation of Bursaphelenchus species. (A) Maximum parsimony phylogram of an analysis of the aligned ITS1 and ITS2 regions from Bursaphelenchus isolates. Branch lengths are given above each branch, and bootstrap support below. (B) As for (A) but using NJ analysis (logdet/paralinear distance correction). Adapted from Beckenbach etal. (1999).

E. M. V. Johansson, E. Kolomiets, F. Rosenau, K.-E. Jaeger, T. Darbre, and J.-L. Reymond, Combinatorial variation of branching length and multivalency in a large (390, 625 member) glycopeptide dendrimer library Ligands for Fucose-specific lectins, New J. Chem., 31 (2007) 1291-1299. 

The core first method has been applied to prepare four-arm star PMMA. In this case selective degradation of the core allowed unambiguous proof of the star structure. However, the MWD is a little too large to claim that only four-arm star polymers are present [81], Comb PMMAs with randomly placed branches have been prepared by anionic copolymerization of MMA and monodisperse PMMA macromonomers [82], A thorough dilute solution characterization revealed monodisperse samples with 2 to 13 branches. A certain polydispersity of the number of branches has to be expected. This was not detected because the branch length was very short relative to the length of the backbone [83]. Recently, PMMA stars (with 6 and 12 arms) have been prepared from dendritic... 

The arrangement of the sequences and/or internal branches around each node is completely arbitrary. The two branches can be rotated at each node and still have exactly the same branching order and branch lengths. The tree in Fig. 3 is identical to that in Fig. 1 with respect to the implied phylogenetic information. Sometimes the arrangement is used to emphasize a particular point or to make the tree easier to read. Sometimes, however, in a large tree with many nodes and sequences, the branches can be rotated to make some sequences look like they are closely related when, in fact, they are not. 

The tree in Fig. 3 is redrawn without any branch lengths in Fig. 4. Only the branching order in the tree is shown. Some methods of phylogenetic reconstruction cannot easily generate branch lengths, and some people prefer not to use them at all, as they consider the... 

Fig. 4. The tree in Fig. 3 shown with no branch length information.

If there are only two sequences, then, there is only one possible rooted or unrooted tree if branch lengths are ignored and focus is on the tree... 

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