Branching and Crosslinking

Often branching and crosslinking are not separately classified and cross-linked polymers are frequently included in the genre of branched polymers. However, it is necessary to separate these two from the standpoint of gel formation. 

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It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

Quentin may have been the first to sulfonate (arylene ether sulfone).168 In this patent, it was demonstrated that the bisphenol A polysulfone could be sulfonated by chlorosulfonic acid to produce a sulfonated polyfarylene ether sulfone), which was used for desalination via reverse osmosis. However, the chlorosulfonic acid may be capable of cleaving the bisphenol A polysulfone partially at the iso-propylidene link or it might induce branching and crosslinking reactions by... 

The topological structure of condensation polymers is predetermined by the functionality of the initial monomers. If all of them are bifunctional then linear polymers are known to form. Branched and crosslinked molecules are prepared only when at least one of the monomers involves three or more functional groups. 

In polymer science and technology, linear, branched and crosslinked structures are usually distinguished. For crosslinked polymers, insolubility and lack of fusibility are considered as characteristic properties. However, insoluble polymers are not necessarily covalently crosslinked because insolubility and infusibility may be also caused by extremely high molecular masses, strong inter-molecular interaction via secondary valency forces or by the lack of suitable solvents. For a long time, insolubility was the major obstacle for characterization of crosslinked polymers because it excluded analytical methods applicable to linear and branched macromolecules. In particular, the most important structural characteristic of crosslinked polymers, the crosslink density, could mostly be determined by indirect metho ds only [ 1 ], or was expressed relatively by the fraction of crosslinking monomers used in the synthesis. 

Statistical methods based on generation of branched and crosslinked structures from units in different reaction states. 

The first moment of the distribution is Pt0T the total, cumulative molar concentration of polymeric material. As the molecular weight of polymeric species increases, branching and crosslinking reactions yield a thermoset resin. Chromatography analysis of epoxy resin extracts confirms the expected population density distribution described by Equation 4, as is shown in Figure 2. Formulations and cure cycles appear in Table II. 

Figure 1. Statistical build-up of branched and crosslinked structure from units.

There exist a number of experimental methods for determination of structure sensitive parameters of a system undergoing branching and crosslinking. However, evaluation of some of the results requires application of a theoretical approach to the phenomenon the measurement is concerned with. Then, we may be testing two theories at once. The equilibrium elasticity is one example, since there exist alternative rubber elasticity theories. However, certain conclusions can always be made. 

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. 

Trimerization of isocyanate groups to form isocyanurates also occurs and serves as an additional source of branching and crosslinking ... 

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 ... 

Essentially two methods can be used for the preparation of branched and crosslinked polyurethanes. 

Hofmeier H, Schubert US. Supramolecular branching and crosslinking of terpyridine-modified copolymers complexation and decomplexation studies in diluted solution. Macromol Chem Phys 2003 204 1391-1397. 

Branching and crosslinking processes can be treated as a combinatorial problem which is not too complicated when the functionalities are equally reactive and unreacted functionalities are considered as the only kind of defects. If loop formation (intra-molecular cyclization) is involved, the complexity increases considerably. The same holds if the monomers contain groups of unequal reactivity or if the reactivity is influenced by substitution effects. 

Dase-catalyzed phenol-formaldehyde resins polymerized with a mole ratio of formaldehyde to phenol greater than one pose an interesting molecular weight characterization problem. This system is a dynamic one with active methylol end groups. Branched and crosslinked structures are formed, and in general, the separation of the resin from the reaction mixture is difficult. Figure 1 illustrates the chemical nature of a resole resin. 

Due to these different primary structures of the main chain, important modifications and a broad variety of systems is realizable. While linear polymers can be essentially characterized by the number of the monomer units, for branched and crosslinked systems e.g. the way of branching and their quantity is of significance for the polymer specific properties. In cases of crosslinked systems the molecular dimension is the macroscopic dimension of the sample. 

A broad variety of l.c. polymers is conceivable because of the wide range of well known mesogenic molecules, e.g. tabulated in the book of Dcmus27), and the different types of polymers. Further variations are possible by copolymers or systems, where each monomer unit carries more than one mesogenic moiety ( en bloc systems28)). Furthermore the synthesis of linear, branched and crosslinked systems has to be mentioned. Because of this broad variety a manifold influence on the phase behavior of the systems via the chemical constitution is feasible. In the following chapter we will discuss some basic considerations on the phase behavior of l.c.-side chain polymers. 

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