DEGREE OF BRANCHING

In a perfectly branched dendrimer, only one type of repeat unit can be distinguished, apart from the terminal units carrying the chain ends (Fig. 4). A more 

The second method, based on the degradation of the hyperbranched backbone, was presented by Hawker and Kambouris [56]. The chain ends are chemically modified and the hyperbranched skeleton is fully degraded by hydrolysis. The degradation products are identified using capillary chromatography. Two chemical requirements have to be fulfilled to use this technique successfully. First, degradation must not affect chain ends, and second, the conversion into elementary subunits must be complete. 

In agreement with Flory s predictions, hyperbranched polymers based on A,jB monomers reported in the literature exhibit a broad molecular weight distribution (typically 2-5 or more). The polydispersity of a hyperbranched polymer is due to the statistical growth process. A strategy to overcome this disadvantage is to add a By-functional core molecule, or a chain terminator, which Hmits the polydispersity and also provides a tool to control the molecular weight of the final polymer. The concept of copolymerizing an A2B monomer with a B3 functional core molecule was first introduced by Hult et al. [62] and more recently also utilized by Feast and Stainton [63] and Moore and Bharathi [64]. 

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The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has v branches, it has v 2 chain ends if the branching is relatively low. Branched molecules are sometimes described as either combs or... 

EinaHy, in 1976, Kaminsky and Sinn in Germany discovered a new family of catalysts for ethylene polymerization. These catalysts (ie, Kaminsky catalysts) contain two components a metallocene complex, usually a zkconocene, and an organoaluminum compound, methylaluminoxane (8,9). These catalysts and thek various later modifications enable the synthesis of ethylene copolymers with a high degree of branching uniformity. Formally classified as MDPE, LLDPE, or VLDPE, the resins thus produced have a number of properties that set them apart from common PE resins in terms of performance... 

Mechanical Properties. The principal mechanical properties are Hsted in Table 1. The features of HDPE that have the strongest influence on its mechanical behavior are molecular weight, MWD, orientation, morphology, and the degree of branching, which determines resin crystallinity and density. 

Paraffin alkylation as discussed here refers to the addition reaction of an isoparaffin and an olefin. The desired product is a higher molecular weight paraffin that exhibits a greater degree of branching than either of the reactants. 

Mixtures of isomeric amyl alcohols (1-pentanol and 2-methyl-1-butanol) are often preferred because the different degree of branching imparts a more desirable combination of properties they are also less expensive to produce commercially. One such mixture is a commercial product sold under the name Primary Amyl Alcohol by Union Carbide Chemicals and Plastics Company Inc. 

For commercial grades of unfractionated PVP prepared by similar means (presumed to exhibit similar molecular weight distribution (MWD) and degree of branching), the following regression formula can be employed (71) ... 

Polychloroprene polymers also vary in the degree of branching in the polymer. Polychloroprenes with little or no branching are called sol polymers, whereas those with considerable branching are referred to as gel polymers. Sol polymers are soluble in aromatic solvents. All of the solvent-grade polychloroprene polymers (except Neoprene AG) are sol polymers. The gel content in the polychloroprene affects the cohesive strength, resilience, elongation, open tack time, resistance to permanent set, and oil swell. 

The properties of the solvent-bome CR adhesives depend on the molecular weight, degree of branching and rate of crystallization of the polymer. The ability of polychloroprene adhesives to crystallize is unique as compared to other elastomers. The higher the crystallization rate, the faster the adhesive strength development. 

The ease with which a polymer will form into crystalline regions depends on the structure of the molecular chain. It can be seen, for example, that if the polyethylene molecule has a high degree of branching then it makes it difficult to form into the ordered fashion shown in Fig. A.9. Also, if the side... 

Operational sequence diagrams are flcw-charting techniques that represent any sequence of control movements and information collection activities that are executed in order to perform a task. Various activities in the diagram are represented with a symbolic notation, supported where necessary by a text description. For the majority of simple applications, OSDs assume a linear flow drawn from top to bottom with a limited degree of branching and looping. The symbols used are usually tailored to fit the type of task being studied and its level of analysis. 

Other substituted cyclohexanes are similar- to methylcyclohexane. Two chair confonnations exist in rapid equilibrium, and the one in which the substituent is equatorial is more stable. The relative fflnounts of the two confor-rnations depend on the effective size of the substituent. The size of a substituent, in the context of cyclohexane confor-rnations, is related to the degree of branching at the atom connected to the ring. A single... 

Table 3.1-5 provides data for a series of ionic liquids in which the only difference is the degree of branching within the allcyl chain at the imidazolium ring 3-position [24, 47]. 

Table 3.1-5 Melting points and heats of fusion for isomeric [BMIM][PFg] and [PMIM][PFs] ionic liquids, showing melting point and crystal stability increasing with the degree of branching in the alkyl substituent.

One of the benefits of catalytic cracking is that the primary and secondary ions tend to rearrange to form a tertiary ion (a carbon with three other carbon bonds attached). As will be discussed later, the increased stability of tertiary ions accounts for the high degree of branching associated with cat cracking. 

Note that, apart from the filler particle shape and size, the molecular mass of the base polymer may also have a marked effect on the viscosity of molten composites [182,183]. The higher the MM of the matrix the less apparent are the variations of relative viscosity with varying filler content. In Fig. 2, borrowed from [183], one can see that the effect of the matrix MM on the viscosity of filled systems decreases with the increasing filler activity. In the quoted reference it has also been shown that the lg r 0 — lg (MM)W relationships for filled and unfilled systems may intersect. The more branches the polymer has, the stronger is the filler effect on its viscosity. The data for filled high- (HDPE) and low-density polyethylene (LDPE) [164,182] may serve as an example the decrease of the molecular mass of LDPE causes a more rapid increase of the relative viscosity of filled systems than in case of HDPE. When the values (MM)W and (MM)W (MM) 1 are close, the increased degree of branching results in increase of the relative viscosity of filled system [184]. 

The degree of branching in PVAc is strongly dependent on the polymerization conditions. Differences in the degree of branching are thought to be one of the main factors responsible for substantial differences in properties between various commercial samples of PVAc or PVA.203"205... 

Additional parameters should be taken into account for polyester networks and hyperbranched polyesters, for example, crosslink density and degree of branching. 

Hyperbranched polymers are characterized by their degree of branching (DB). Hie DB of polymers obtained by the step-growth polymerization of AB2-type monomers is defined by Eq. (2.1) in which dendritic units have two reacted B-groups, linear units have one reacted B-group, and terminal units have two unreacted B-groups191 ... 

Note Kricheldorf et al.268 synthesized the same polyester by a similar procedure using Ti(OPr)4 as polymerization catalyst. The characteristics of the resulting polymer were inherent viscosity 0.22 dL/g (determined at 20°C in 4/1 CH2C12-trifluoroacetic acid at a concentration of 0.2 g/dL). DSC Tg = 164°C. Degree of branching (DB) 0.48 (determined by H NMR). 

AB2 reacts selectively with only one antagonist function of a second polyfunctional molecule, the other ones being protected81 (Fig. 5.16). The perfect hyperbranched molecules obtained according to that step-by-step process are called dendrimers. The degree of branching characterizes the structure of a hyperbranched polymer and has been defined by Hawker et al.82 as... 

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