Cross-links and Networks

The reaction stage referred to as the sol-gel transition (1-3) is called the gel point. At the gel point the viscosity of the system becomes infinite, and the 

Introduction to Physical Polymer Science, by L.H. Sperling ISBN 0-471-70606-X Copyright 2006 by John Wiley Sons, Inc. 

Step polymerization reactions, where little molecules such as epoxies (oxiranes) react with amines, or isocyanates react with polyols with functionality greater than two to form short, branched chains, eventually condensing it into epoxies or polyurethanes, respectively. Schematically 

Chain polymerization, with multifunctional molecules present. An example is styrene polymerized with divinyl benzene. 

Postpolymerization reactions, where a linear (or branched) polymer is cross-linked after synthesis is complete. An example is the vulcanization of rubber with sulfur, which will be considered further below. 

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It is possible to classify polymers by their structure as linear, branched, cross-linked, and network polymers. In some polymers, called homopolymers, merely one monomer (a) is used for the formation of the chains, while in others two or more diverse monomers (a,p,y,...) can be combined to get different structures forming copolymers of linear, branched, cross-linked, and network polymeric molecular structures. Besides, on the basis of their properties, polymers are categorized as thermoplastics, elastomers, and thermosets. Thermoplastics are the majority of the polymers in use. They are linear or branched polymers characterized by the fact that they soften or melt, reversibly, when heated. Elastomers are cross-linked polymers that are highly elastic, that is, they can be lengthened or compressed to a considerable extent reversibly. Finally, thermosets are network polymers that are normally rigid and when heated do not soften or melt reversibly. 

The compatibility of polymer blends has been a snbject of mnch interest. Polymer blends are systems with two (or more) polymers, most of which are incompatible (immiscible). Finding compatible polymer pairs is an important task in the design of snch advanced materials. Moreover, several new polymeric materials with interesting properties involve novel structures, which go beyond the well-known ones (linear, branched, cross-linked, and network). Such novel strnctnres, e.g., starlike polymer and dendrimers may require new concepts for selecting proper solvents and generally for nnderstanding their solnbility behavior. "... 

The function of sulfur derivatives in flame retardancy is not exactly understood. It was suggested that the sulfur derivative appears to be a more effective catalyst for the dehydration, cross-linking, and char formation than ammonium polyphosphate alone [390]. The sulfation and desulfation occur more rapidly than phosphorylation and dephosphorylation. The char is formed both by the sulfation and the phosphorylation routes, but the char obtained appears to be a more effective, more compact, and less penetrable surface barrier. The sulfur compounds may act as synergists of the ammonium polyphosphate, similar to the effect of antimony trioxide in the case of halogen-based additives. It was further noted that the sulfations of nylon-6 and dephosphorylation occur simultaneously and produce cross-links and networks. 

The macromolecnles may form linear, branched, cross-linked, and network-like structures (see Figure 1). Usually, a chain is seen as linear, if it comprises per 1000 C atoms in the backbone less than 10 branches whereas a branched... 

Most of these features were considered in the discussion in Chapter 5 although the subject of cross-linking and network structures will be left to Chapter 8. The copolymers have the added but important complications of two additional variables monomer ratio and monomer sequence distribution. The mere existence of a copolymer system tends to ensure that the polymers are amorphous except in those special cases where the structural units can isomorphously replace each other. Another special case is provided by alternating copolymers. Providing questions of tacticity do not arise (which they usually do ) such systems may have sufficient regularity to be able to crystallize. 

Cross-links and networks of various sizes are formed by cohesion. Elasticity and viscosity are expressed as functions of size of link. 

Figure C2.1.2. Polymers witli linear and nonlinear chain architectures. The nonlinear polymers can have branched chains. Short chains of oligomers can be grafted to tire main chain. The chains may fonn a. stor-like stmcture. The chains can be cross-linked and fonn a network.

Polymers with the mechanical and chemical properties we have discussed in this section are called elastomers. In the next couple of sections we shall examine the thermodynamic basis for elasticity and then apply these ideas to cross-linked polymer networks. 

Bulk Polymerization. The bulk polymerization of acryUc monomers is characterized by a rapid acceleration in the rate and the formation of a cross-linked insoluble network polymer at low conversion (90,91). Such network polymers are thought to form by a chain-transfer mechanism involving abstraction of the hydrogen alpha to the ester carbonyl in a polymer chain followed by growth of a branch radical. Ultimately, two of these branch radicals combine (91). Commercially, the bulk polymerization of acryUc monomers is of limited importance. 

Fibers. The principal type of phenoHc fiber is the novoloid fiber (98). The term novoloid designates a content of at least 85 wt % of a cross-linked novolak. Novoloid fibers are sold under the trademark Kynol, and Nippon Kynol and American Kynol are exclusive Hcensees. Novoloid fibers are made by acid-cataly2ed cross-linking of melt-spun novolak resin to form a fuUy cross-linked amorphous network. The fibers are infusible and insoluble, and possess physical and chemical properties that distinguish them from other fibers. AppHcations include a variety of flame- and chemical-resistant textiles and papers as weU as composites, gaskets, and friction materials. In addition, they are precursors for carbon fibers. 

As the length and frequency of branches increase, they may ultimately reach from chain to chain. If all the chains are coimected together, a cross-linked or network polymer is formed. Cross-links may be built in during the polymerisation reaction by incorporation of sufficient tri- or higher functional monomers, or may be created chemically or by radiation between previously formed linear or branched molecules (curing or vulcanisation). Eor example, a Hquid epoxy (Table 1) oligomer (low molecular weight polymer) with a 6-8 is cured to a cross-linked soHd by reaction of the hydroxyl and... 

Thermoplastics are the largest class of engineering polymer. They have linear molecules they are not cross-linked, and for that reason they soften when heated, allowing them to be formed (ways of doing this are described in Chapter 24). Monomers which form linear chains have two active bonds (they are bifunctional). A molecule with only one active bond can act as a chain terminator, but it cannot form a link in a chain. Monomers with three or more active sites (polyfunctional monomers) form networks they are the basis of thermosetting polymers, or resins. 

Not only are these reactions of importance in the development of the cross-linked polyurethane networks which are involved in the manufacture of most polyurethane products but many are now also being used to produce modified isocycuiates. For example, modified TDI types containing allophanate, urethane and urea groups are now being used in flexible foam manufacture. For flexible integral foams and for reaction injection moulding, modified MDIs and carbodi-imide MDI modifications cU"e employed. 

J 8 Explain the role of chain length, crystallinity, network formation, cross-linking, and intermolecular forces in determining the physical properties of polymers (Section 19.12). 

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

Elasticity and Structure of Cross-linked Polymers2 Networks with Comblike Cross-links... 

Networks with tri- and tetra-functional cross-links produced by end-linking of short strands give moduli which are more in accord with the new theory if quantitative reaction can be assumed (3...13) However, the data on polydimethylsiloxane networks, may equally well be analyzed in terms of modulus contributions from chemical cross-links and chain entangling, both, if imperfect reaction is taken into account (J 4). Absence of a modulus contribution from chain entangling has therefore not been demonstrated by end-linked networks. 

After introduction of cross-links in the strained state, the composite network retracts, upon release, to a stress-free state-of-ease (J9 ) The amount of retraction is determined by the degree of strain during cross-linking and by the ratio >i/v2. The elastic properties relative to the state-of-ease are isotropic for a Gaussian composite network ( 8, 1 9,20). 

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