Branch distribution

Eig. 1. Melting curves (dsc) of two ethylene—1-hexene copolymers produced in a gas-phase process one with a uniform branching distribution (1-hexene content 2.5 mol %) and another with a nonuniform branching distribution (1-hexene content 2.8 mol %). 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

Countries produciug commodity LLDPE and their capacities, as well as production volumes of some U.S. companies, are Hsted iu Table 5. Iu most cases, an accurate estimate of the total LLDPE production capacity is compHcated by the fact that a large number of plants are used, iu turn, for the manufacture of either HDPE or LLDPE iu the same reactors. VLDPE and LLDPE resius with a uniform branching distribution were initially produced in the United States by Exxon Chemical Company and Dow Chemical Company. However, since several other companies around the world have also aimounced their entry into this market, the worldwide capacity of uniformly branched LLDPE resins in 1995 is expected to reach a million tons. Special grades of LLDPE resins with broad MWD are produced by Phillips Petroleum Co. under the trade name Low Density Linear Polyethylenes or LDLPE. 

Figure 2 Short chain branching distribution in polyethylenes. Source Ref. 31.

The method outlined above for characterizing branched polymers will hereafter be referred to as the molecular weight and branching distribution (MWBD) method. In the following sections, its application to the long chain branching in polyvinyl acetate and high pressure low density polyethylene will be demonstrated. 

The MWBD method, when coupled with high speed SEC techni-gues, is more rapid for long chain branching measurements than NMR. In addition, the branching distribution information that it provides, once epsilon has been determined, can not be obtained by other branching characterization methods unless the polymer is fractionated. 

The general structure of linear low density polyethylene is shown in Fig. 18.2 c). Linear low density resins are copolymers of ethylene and 1-alkenes principally 1-butene, 1-hexene, and 1-octene. Comonomer levels range from approximately 2 to 8 mole %. This family of polyethylene is widely known as LLDPE. Linear low density polyethylenes are polydisperse with regard to molecular weight and branch distribution. 

Fig. 21. Comparison of the distributions of randomly branched (full lines) and hyper-branched macromolecules (dashed lines) for f=3 at Jc =25,100, and 1000. The dotted lines represent fits of the distributions to power laws with exponents (l-i)=-1.5 (randomly branched) and -0.5 (hyperbranched), respectively. The intermediate region of the hyper-branched distributions can be described by Eq. (55 )...

Polyethylenes, PE, have been characterized by SEC since the mid-sixties and frequent problems with polystyrene gel columns have been reported ( ). The low density PE, LDPE, because of complexity of the molecular weight and branching distributions,... 

Two classes of LLDPE resins are on the market. One has a predominantly uniform compositional distribution (uniform branching distribution) that is, all copolymer molecules in these resins have approxnnately the same composition. Most commercially produced LLDPE resins, in contrast, have pronounced nonuniform branching distributions there are significant differences in copolymer compositions among different macromolecules in a given resin. 

Optical properties of LLDPE resins also depend on the degree of branching uniformity, Resins with a uniform branching distribution make highly transparent film with haze as low as 3-4%. In contrast, film manufactured from compositionally nonunifonn copolymers is much more opaque, with haze of over 10-15% this is due to the presence of large crystalline lamellae consisting of nearly nonbranched PE chants. 

Due to their multi-sited nature, Ziegler-Natta and chromium catalysts produce structurally heterogeneous ethylene homo- and copolymers. This means that the polymers have broad MWD and broad composition (short-chain branching) distribution (Fig. 9). Catalyst active sites that produce lower molecular weights also have a tendency to incorporate more comonomer... 

Iedema, P.D. and Hoefsloot, H.C.J. (2001) Synthesis of branched polymer architectures from molecular weight and branching distributions for radical polymerisation with long-chain branching, accounting for topology-controlled random scission. Macromol. Theor. Simul., 10, 855. 

Muller et al. [53] prepared similar PMMA-g-PMMA by radical copolymerization of MMA with methacrylate-terminated PMMA macromonomer, 29, and characterized the samples by SEC-multiangle laser fight scattering (MALLS). The power law exponent, a, in the equation, 1/2°cMa, was found to be 0.36. In remarkable contrast to the result of Ward et al. [51], the shrinking factor decreased with increase of MW. This may imply that the difference in graft copolymerization method, anionic or radical, results in the graft copolymers with very different branch distribution. 

At present time, river water runoff at the delta head divides between the Don branch and the right small Mertvy Donets branch (Fig. 13) in the proportion about 97 and 3% of the total river water runoff. Downstream water runoff of the Don branch distributes between the Stary Don (left) and BoPshaya Kalancha (right) branches as 27 and 70% of the total river water runoff. Then water runoff of the Stary Don branch is divided between the Peschany (17% of the total river water runoff) and Merinovo (10%) branches. BoPshaya Kalan-... 

The range of molecular sizes in a polymer material is always a key parameter in determining the balance of its processing and performance properties, but these characteristics may also be affected by other structural features of the polymer. This is particularly the case with crystallizable polymers, such as polyethylene (1-3), where branching impedes crystallization and affects the stiffness and impact resistance of the final articles. Further mention of branching distributions is made in Section 3.4.6. 

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