Branching regular

DichTOMOUsly Branched Regularly divided by pairs from bottom to top. 

When linear a-olefins are polymerised, the polymer contains only methyl branches, regularly distributed along the chain with a separation corresponding to the size of the alkyl substituent in the monomer. It may be interesting that the structure of the polymer formed from 1-pentene, poly[2,5-(l-... 

Figure 1 Macromolecular architectures linear macromolecular chains (homopolymer, block-copolymer and statistical copolymer [14]), brushed-polymer (= linear chains attached to a polymer-chain brush-polymer, brush-copolymers [14]), star polymer [4], mikto-star-polymer [16], arborescent graft polymer (=repeated grafting of linear chains on a macromolecule [17,18]), dendrimer (= maximally branched, regular polymer [15])...

Low density polyethylene is branched, and it is more easily processed than the linear high density polyethylene. This is caused by the special kind of branching short branches regularly spaced along the chain backbone act as an internal plasticizer. 

Regular comb-branches Regular star-branched... 

Chemically, starch is a combination of two polymeric polysaccharides called amylose and amylopectin in which glucose monomers are joined to one another head-to-tail by a- 1 4) linkages. Linearly combined units constitute amylose, while branched imits constitute the amylopectin (see Figure 10.7). Structurally, the starch forms clusters of linked linear polymers, where the o -(1 4) linked chains form columns of glucose units which branch regularly at the a-(1 6) links (Figure 10.7). 

The best fit to data on branched polymers can be made by choice of values of (1/3-X2)- Figure 6 shows such a fit to (1/3—X2) = 0.045 for a series of four and six-branched regular star polymers. Semi-quantitative agreement is achieved although the 0 depression disappears m< e rspidly as molecular weight is increased than is predicted. The effect of solvent on deviations of 0. 2 has been investigated for... 

Beginning with the work of Thomalia [17] in 1986, starburst molecules (dendrimers) have achieved enormous interest within the last years. Dendrimers are highly branched regular molecules, which are usually prepared by stepwise reactions. In many cases the behaviour of dendritic macromolecules are different from that of linear polymers, e. g. the former... 

HI Nearly vertical and parallel adsorption and desorption branches Regular even pores without interconnecting channels... 

Figure 2. Reciprocal scattering factors 1/P(q) versus q 8g for monodisperse systems of the models indicated. Rg is nO /6 (linear Gaussian coil) 5nb /48 (J-branch regular star) nb /M (flexible ring) L /M (thin rod) CP/8 (disk) 3D /20 (sphere).

Table 2 3 lists the heats of combustion of several alkanes Unbranched alkanes have slightly higher heats of combustion than their 2 methyl branched isomers but the most important factor is the number of carbons The unbranched alkanes and the 2 methyl branched alkanes constitute two separate homologous senes (see Section 2 9) m which there is a regular increase of about 653 kJ/mol (156 kcal/mol) m the heat of combustion for each additional CH2 group... 

Fluorinated ether-containing dicarboxyhc acids have been prepared by direct fluorination of the corresponding hydrocarbon (17), photooxidation of tetrafluoroethylene, or by fluoride ion-cataly2ed reaction of a diacid fluoride such as oxalyl or tetrafluorosuccinyl fluorides with hexafluoropropylene oxide (46,47). Equation 8 shows the reaction of oxalyl fluoride with HEPO. A difunctional ether-containing acid fluoride derived from HEPO contains regular repeat units of perfluoroisopropoxy group and is terminated by two alpha-branched carboxylates. 

The ultraphosphates are situated between P O q and the metaphosphates. These comparatively Htde-known, highly cross-linked polymers contain at least some of the phosphoms atoms as triply coimected branching points. This stmctural feature is quite unstable toward hydrolysis. Ultraphosphates undergo rapid decomposition upon dissolution. In amorphous ultraphosphates, the cross-linking is presumably scattered randomly throughout the stmctural matrix in contrast, crystalline ultraphosphates have a regular pattern. 

If a polymer molecule has a sufficiently regular structure it may be capable of some degree of crystallisation. The factors affecting regularity will be discussed in the next chapter but it may be said that crystallisation is limited to certain linear or slightly branched polymers with a high structural regularity. Well-known examples of crystalline polymers are polyethylene, acetal resins and polytetrafluoroethylene. 

Both polymers are linear with a flexible chain backbone and are thus both thermoplastic. Both the structures shown Figure 19.4) are regular and since there is no question of tacticity arising both polymers are capable of crystallisation. In the case of both materials polymerisation conditions may lead to structures which slightly impede crystallisation with the polyethylenes this is due to a branching mechanism, whilst with the polyacetals this may be due to copolymerisation. 

Lest I leave the erroneous impression here that colloid science, in spite of the impossibility of defining it, is not a vigorous branch of research, I shall conclude by explaining that in the last few years, an entire subspeciality has sprung up around the topic of colloidal (pseudo-) crystals. These are regular arrays that are formed when a suspension (sol) of polymeric (e.g., latex) spheres around half a micrometre in diameter is allowed to settle out under gravity. The suspension can include spheres of one size only, or there may be two populations of different sizes, and the radius ratio as well as the quantity proportions of the two sizes are both controllable variables. Crystals such as AB2, AB4 and AB13 can form (Bartlett et al. 1992, Bartlett and van... 

Since the left-hand side of (4.24) is regular in the disk x < p its zeros cannot have a point of accumulation, and in the neighborhood of a zero the branch of the function which becomes singular remains bounded and thus continuous. 

The synthesis of comb-like polymers with regular branching (in contrast to random branching) has been performed in the following way 91) A linear polystyrene precursor fitted with carbanionic sites at both ends is reacted first with 1,1-diphenylethylene (to decrease the nucleophilicity of the sites) and then with a calculated amount of triallyloxytriazine to get chain extension. Each triazine residue still carries one allyloxy... 

This group includes a set of anionic polysaccharides secreted by unrelated bacteria. The common theme, however, is that their main chains have the same tetrasaccharide repeat. Although (high acyl) native gellan (42) and (deacylated) gellan (40,41) are linear polymers, welan (43) is a branched polymer in which a monosaccharide side chain is regularly attached to each repeat. Other members of this family, such as S-657 and rhamsan, are also branched, like welan."0... 

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