Branch lengths, short

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... 

Linear low-density polyethylene (LLDPE)440-442 is a copolymer of ethylene and a terminal alkene with improved physical properties as compared to LDPE. The practically most important copolymer is made with propylene, but 1-butene, 4-methyl-1-pentene, 1-hexene, and 1-octene are also employed.440 LLDPE is characterized by linear chains without long-chain branches. Short-chain branches result from the terminal alkene comonomer. Copolymer content and distribution as well as branch length introduced permit to control the properties of the copolymer formed. Improvement of certain physical properties (toughness, tensile strength, melt index, elongation characteristics) directly connected to the type of terminal alkene used can be achieved with copolymerization.442... 

These data allow us to construct an evolutionary tree, with branch lengths approximately proportional to the number of differences between the species (see Fig. 4-10). The human and rabbit show most similarity and therefore are connected by short branches. The silkworm cytochrome c is closer to both mammalian forms than it is to Neurospora, and so should be connected to the mammalian junction. The length of the silkworm branch will be approximately three times the length of the rabbit and human branches. Finally, Neurospora shows approximately the same number of differences with all the animal species, and therefore can be joined to their common branch. 

The data for the three types of star-branched polymers show a decrease in rj on branching, with the exception of the trichain and tetrachain polybutadiene of longer branch length, for which the reverse is true. The data for most of the randomly branched and comb-type poly-vinylacetates nearly all show higher values than the linear polymer, excepting for two samples containing short branches, for which the reverse is true. 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

Similarly there is the substance glycogen, occurring in animal liver, in certain shellfish, and in sweet corn. It is the counterpart of the branched starch fraction, except that the branch length consists of only 10 glucose units instead of 25 to 30. In other words, it is a bushlike molecule instead of a tree. Glycogen will not associate or crystallize under any circumstances—its exterior branches are just too short. 

Proportional to length x(n — 1) Branching in short chains one-time... 

NMR not only yields chemical information, but can also be used to analyze polymer tacticity, sequence lengths, short-chain branching, and crystallinity. 

TREF analysis is still reported quite often on the basis of dissolution temperature scale, but as discussed in the introduction of Sect. 4.1 there is a linear relation between dissolution temperature and comonomer incorporatiOTi, which has been confirmed experimentally [62]. The calibration of temperature to comonomer content can be performed by using narrow composition standards (metallocene-type resins) of the same comonomer type. Boisson et al. [92] recently presented TREF calibration curves for different types of PE copolymers, as shown in Fig. 17. At the same mole percentage of comonomer incorporated, the dissolution temperature (TREF) decreases with increasing branch length. Propylene incorporation in PE with the lowest short chain branch (methyl), results in the highest dissolution temperature indicating that the methyl branch, besides being able to enter into the crystal lattice, has the lowest crystallizability perturbance. Octene and hexene copolymers can use the same calibration curve as shown in Fig. 17. 

Physical Properties. All polyethylene above 0.86 g/cm density is semicrystalline. The basic crystalline structure for most commercial LLDPE is chain-folded lamellae (Fig. 7). The body of the crystal consists of polymer backbone segments, and the surfaces are a collection of chain folds, loose cilia, and tie chains (chains incorporated into more than one crystal). When crystallized isothermally, it has been foimd that 95% of the lamellae in a given sample are within 5% of the same thickness (10). There is some debate over the mechanism of chain folding and of the subsequent fold loops. The most likely model includes adjacent reentry, loose adjacent reentry, and nonadjacent reentry. Short-chain branch length... 

Figure 14.2 Phylogenetic analysis cox I amino acid sequences to determine relationship within the long-looped terebratulides. (A) ML tree with LBPs estimated by ProtML, using the three outgroup short-looped forms. Branch length refers to the estimates number of substitutions per 100 sites. (B) MP consensus tree based on 50% majority-rule. A total of 500 bootstrap replicates were performed.

Figure 14.3 ML tree of long-looped terebratulides including the kraussinid Megerlina sp. and terebratellids Magellania joubini and M. fragiliSy using the three short-looped forms as outgroup. Branch length refers to the estimated number of substitutions per 100 sites.

---