Networks with fixed crosslinks

The classical models of rubber elasticity reduce the elastic properties to a study of entropic springs. In the phantom model the EV interaction only gives the volume conservation, while in the affine deformation model it also is responsible for the affine position transformation of the crosslinks. Otherwise the entropic forces and the excluded volume interactions and consequently the entanglements, as they are a result of the EV interaction, completely decouple from the chain elasticity. The elasticity is entirely determined by the strand entropy. It is obvious that this is a 

N = 10. or/a=1.0 Randomly oriented melt, X=2.0 o Total stress Covalent Noncovalent 

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The last two models have been investigated extensively by Flory He considered networks forming part of a larger network with fixed jimctions outside the network under consideration. The crosslinking points of the inner network were assumed to fluctuate freely, or to have fixed positions in space. In both cases, the inner network can be considered as localized by boundary conditions. In particular, Flory considered a network formed in two hypothetical steps. First, a giant acyclic molecule is formed by joining all chains via the available multifunctional junctions such a tree-like molecule can be characterized by v -H 1 v junctions plus chain ends (i.e. number of labelled points). Figure 3 shows an example of the network after the first step. In the second step additional connections are formed by the reaction of 2 unreacted functionalities, which reduces the number of labelled points to approximately The number is called the cycle rank, which can be defined... 

Thus, to improve upon the physical and mechanical properties of the polymer material, one must not only consider the materials used, but also the conditions under which the polymer was formed. These reaction conditions, along with the type of monomer system chosen, will completely control the conversion of functional groups in the system. More importantly, the conversion will ultimately determine the mechanical, physical, and wear properties of the material. Since most dental materials are crosslinked polymers, characterizing the polymerization reaction becomes even more important since the physical nature of a crosslinked polymer is fixed upon completion of the polymerization. For example, not only is the microstructure (i.e. the degree of crosslinking) largely unalterable after polymerization, but the system is insoluble and fixed macroscopically. Clearly, to produce crosslinked networks with the desired material properties, one must ascertain the appropriate reaction conditions and the effects of the reaction conditions on the network structure. 

In order to deal with the four non-crystalline forms in a unified way, we define a network chain in a crosslinked system, as the section of network between neighbouring crosslinks (Fig. 3.6). The shape of both a network chain in a rubber, and a molecule in a polymer melt, can be changed dramatically by stress, and both can respond elastically. However, when the polymer is cooled below Tg, the elastic strains are limited to a few per cent (unless a glassy polymer yields), so the molecular shape is effectively fixed. If the melt or rubber was under stress when cooled, the molecular shape in the glass is non-equilibrium. This molecular orientation may be deliberate, as in biaxially stretched polymethylmethacrylate used in aircraft windows, or a by-product of processing, as the oriented skin on a polystyrene injection moulding. Details are discussed in Chapter 5. 

Allyl esters, unsaturated polyesters, as well as some of what are known as vinyl or acrylic esters are cured by free radical addition polymerization. In the case of allyl esters, the monomers, themselves, are cross-linked. On the other hand, unsaturated polyesters are copolymerized with monomers such as styrene or methyl methacrylate. Since the unsaturated polyesters have many main-chain double bonds and the structure of a cross-linked network is fixed after quite low conversions, only a few double bonds actually react. These unconverted double bonds can then react later with atmospheric agents, and so produce poor weathering properties of the crosslinked networks. In addition, the polymerization produces many free chain ends that contribute nothing or even disadvantageously to the mechanical properties. The newly developed vinyl or acrylic esters avoid both of these problems in that the monomers capable of cross-linking only have unsaturated double bonds at the molecular ends (see also Section 26.4. S). 

In order to answer these questions, the kinetic and network structure models were used in conjunction with a nonlinear least squares optimization program (SIMPLEX) to determine cure response in "optimized ovens ". Ovens were optimized in two different ways. In the first the bake time was fixed and oven air temperatures were adjusted so that the crosslink densities were as close as possible to the optimum value. In the second, oven air temperatures were varied to minimize the bake time subject to the constraint that all parts of the car be acceptably cured. Air temperatures were optimized for each of the different paints as a function of different sets of minimum and maximum heating rate constants. 

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

Microgels are distinguished from linear and branched macromolecules by their fixed shape which limits the number of conformations of their network chains like in crosslinked polymers of macroscopic dimensions. The feature of microgels common with linear and branched macromolecules is their ability to form colloidal solutions. This property opens up a number of methods to analyze microgels such as viscometry and determination of molar mass which are not applicable to the characterization of other crosslinked polymers. 

Network formation was generated on the lattice (hexagonal, tetragonal and cubic) with the total number of crosslinks amounting to 2-4 x 102. Tetrafunctional amine molecules were fixed in the lattice knots. This lattice was immersed in uniform liquid of diepoxide molecules which could penetrate the lattice freely. The network appeared as a result of an addition reaction between diepoxides and amine groups of crosslinks. 

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