Branched and crosslinked polymers

When ethylene (ethene) is copolymerised with small proportions of higher alkenes (olefins), the resulting short-chain branches modify the polymer crystallinity (Section 3.4.1). Long-chain branched molecules (Fig. 2.8) can occur as a result of a side reaction for example when a propagating polyethylene molecule abstracts a H atom from a dead polyethylene molecule 

In graft copolymers the polymer backbone consists of one monomer and the branches of another. For example, polybutadiene contains carbon-carbon double bonds that can be attacked by a free radical initiator 

If styrene is available, polystyrene branches can be grafted on to the polybutadiene backbone. The grafting efficiency is not high, as separate polystyrene molecules will also be formed. Once the polystyrene concentration reaches 2%, phase separation occurs, with spheres of polystyrene 

When the density of branch points is increased in a polymer, there is a progression, from a collection of branched molecules, through a single infinite tree molecule containing no closed rings (Fig. 2.9a), to a three-dimensional network molecule (Fig. 2.9b). When a single tree molecule forms, the gel point occurs if a solvent is added the majority of the polymer forms a swollen gel, rather than dissolving. Both thermosets and rubbers are 

Polyester thermosets are based on partly unsaturated linear polyester from the step-growth polymerisation of propylene glycol, phthalic anhydride and maleic anhydride. 

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The discussions until this point have been concerned with the polymerization of bifunctional monomers to form linear polymers. When one or more monomers with more than two functional groups per molecule are present the resulting polymer will be branched instead of linear. With certain monomers crosslinking will also take place with the formation of network structures in which a branch or branches from one polymer molecule become attached to other molecules. The structures of linear, branched, and crosslinked polymers are compared in Fig. 1-2. 

Macromolecules having identical constitutional repeating units can nevertheless differ as a result of isomerism. For example, linear, branched, and crosslinked polymers of the same monomer are considered as structural isomers. Another type of structural isomerism occurs in the chain polymerization of vinyl or vinylidene monomers. Here, there are two possible orientations of the monomers when they add to the growing chain end. Therefore, two possible arrangements of the constitutional repeating units may occur ... 

For carbohydrates to meet these requirements, diversity is needed on both the molecular and the size-level. Only large carbohydrate molecules, polysaccharides, can provide the wide spectrum of storage, structural, and gel-forming abilities required by nature. Meeting these requirements has made it necessary for plants to produce polysaccharides that can be classified as linear, branched, and crosslinked polymers, as well as homo- and heteropolymers in accordance with terminology in common use in the polymer community (O Fig. 1) [26]. Nature has found need to adopt all different kinds of macromolecular architectures in pursuit of the three different functions of carbohydrates. 

The physical and mechanical properties of polyanhydrides can be altered by modification of the polymer structure with a minor change in the polymer composition. Several such modifications include the formation of polymer blends, branched and crosslinked polymers, partial hydrogenation and reaction with epoxides. 

The rearrangement of more than one inner site in a flexible or semi-flexible chain molecule can be conveniently performed if the geometric constraints that guarantee chain closure are taken into account every time a site is repositioned [50] (see Fig. 1). Performance can be enhanced by favoring low-energy trial positions for each growing site (extended continuum configurational bias, or ECCB method). Since this method can be applied to inner sites of arbitrary functionality, it has been used to study linear, branched, and crosslinked polymers [50-52]. 

Mechanical equilibrium between two phases or between a system and an external reservoir can be achieved by allowing the volume of the system to fluctuate. Conventional volume moves [46], although expensive for molecular systems, are easy to implement. Specialized variants have been proposed to speed up the equilibration in systems of flexible polymers, including branched and crosslinked polymers [51,52]. 

The molecular weights of the polymers decrease when the ring sizes of the ketone components increase. Excess diisocyanate yields branched and crosslinked polymers. The enamine units in the polymers can be hydrolyzed with formic acid to the corresponding ketones. ... 

Figure 1.5. Branched and crosslinked polymer molecules. While a branched polymer molecule retains finite size and an identifiable molecular weight, the crosslinked polymer forms a three-dimensional network of macroscopic proportions. (A rubber band is essentially one molecule, since any two atoms are connected ultimately by covalent bonds.)...

Bifunctional monomers, such as A-A, B-B and A-B, yield linear polymers. Branched and crosslinked polymers are obtained from polyfunctional monomers. For example, polymerization of formaldehyde with phenol may lead to complex architectures. Formaldehyde is commercialized as an aqueous solution in which it is present as methylene glycol, which may react with the trifunctional phenol (reactive at its two ortho and one para positions). The type of polymer architecture depends on the reaction conditions. Polymerization imder basic conditions (pH = 9-11) and with an excess of formaldehyde yields a highly branched polymer (resols. Figure 1.8). In this case, the polymerization is stopped when the polymer is still liquid or soluble. The formation of the final network (curing) is achieved during application (e.g., in foundry as binders to make cores or molds for castings of steel, iron and non-ferrous metals). Under acidic conditions (pH = 2-3) and with an excess of phenol, linear polymers with httle branching are produced (novolacs). 

Figure T.6 Linear, branched, and crosslinked polymer structures. (Ref Baker, A.M.M., and Mead, J., Thermoplastics , Modem Plastics Handbook, C.A. Harper, ed., McGraw-Hill, New York, 2000)...

Branched and Crosslinked Polymers. A branched homopolymer may be written... 

Tobita, H., Hamashima, N. Monte Carlo simulation of size exclusion chromatography for randonnly branched and crosslinked polymers. J. Polym. Sd. B Polym Phys. (2000) 38, pp. 2009-2018... 

R and R in these reactions may be a part of the polymer or oligomer. Also, the functionality in the polymers or oligomers may vary, and thus the network structure of the cured polymers can be varied. For example, difunctional reactants give linear polymers, whereas branched and crosslinked polymers are obtained when the functionality of the reactants is raised to more than two. 

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