Epoxy network crosslink density

Shear yielding is well established as the principal deformation mechanism and source of energy dissipation in both uiunodified and rubbo -toughened epoxy resins [2,3,27,83,121]. As molecular mobility in the epoxy resin network chains decreases, the ability of the matrix to deform by shear yielding is reduced. This is the reason why epoxy resins become both more brittle and more difficult to toughen as the epoxy resin crosslink density increases and/or as the network chains increase in rigidity, e.g. by use of highly aromatic epoxy resin monomers (see Section 19.7.1.1). 

The degradation of the matrix in a moist environment strongly dominates the material response properties under temperature, humidity, and stress fatigue tests. The intrinsic moisture sensitivity of the epoxy matrices arises directly from the resin chemical structure, such as the presence of hydrophilic polar and hydrogen grouping, as well as from microscopic defects of the network structure, such as heterogeneous crosslinking densities. 

For imperfect epoxy-amine or polyoxypropylene-urethane networks (Mc=103-10 ), the front factor, A, in the rubber elasticity theories was always higher than the phantom value which may be due to a contribution by trapped entanglements. The crosslinking density of the networks was controlled by excess amine or hydroxyl groups, respectively, or by addition of monoepoxide. The reduced equilibrium moduli (equal to the concentration of elastically active network chains) of epoxy networks were the same in dry and swollen states and fitted equally well the theory with chemical contribution and A 1 or the phantom network value of A and a trapped entanglement contribution due to the similar shape of both contributions. For polyurethane networks from polyoxypro-pylene triol (M=2700), A 2 if only the chemical contribution was considered which could be explained by a trapped entanglement contribution. 

The critical network structural parameters that control the mechanical performance of epoxies are macroscopic heterogeneities in crosslink density and the network topography on the molecular level. 

Due to the approach chosen for controlling the crosslink density and the curing conditions adopted, the considered systems can be viewed as model epoxy networks. 

Chemical clusters can be obtained also with two monomers, when two reaction mechanisms are in competition, favoring formation of regions of higher and lower crosslink densities. This situation is more complex and more difficult to control. It is certainly the case for dicyanodiamide (Dicy)-cured epoxies with this hardener an accelerator is always used and a competition between step (epoxy-amine addition) and chain (epoxy homopolymerization) occurs (Chapter 2), leading to inhomogeneous networks. 

In principle, these relationships open the way to a determination of fg which is found to decrease with crosslink density as well in ideal epoxy networks (Gerard et al., 1991), as in nonideal polyesters (Shibayama and Suzuki, 1965). However, it must be recognized that, in both series of data, it is impossible to have consistent values of, Cf, Cf, a, and fg except if BD varies with the structure, which can be considered as a serious argument against the free volume interpretation of WLF parameters. 

All the above observations seem to justify Porter s approach (Eq. 11.11)), according to which the Poisson s ratio should depend only on the cumulative loss tangent. It was found that the unrelaxed Poisson s ratio determined from ultrasound (5 MHz) propagation rate, for 12 of amine-crosslinked epoxy stoichiometric networks, displays only small variations (Av < 0.01), in spite of the relatively large variations of the cohesive energy density (0.59 < CED <0.66 GPa) and the crosslink density (2.0 5.9 mol kg 1)-... 

There are several ways to modify the crosslink density of ideal networks. The first one is the use of monomers with the same structure but with different molar masses. Many workers have reported on epoxy networks... 

A linear decrease of KIc with an increase in crosslink density was reported for model PU based on triisocyanate and diols of various molar masses (Bos and Nusselder, 1994), and for epoxy networks (Lemay et al., 1984). It was suggested that the dilational stress field at the crack tip may induce an increase in free volume and a devitrification of the material. A linear relationship between GIc and M XJ2 was verified for these systems, although other empiric equations were found in other cases (Urbaczewski-Espuche et al., 1991). 

Epoxy networks were synthesized using mixtures of amines of different functionality to vary Me and the average functionality, fE (Galy et al., 1994 Crawford and Lesser, 1998). In both studies, the increase in crosslink density increased both ay and Tg and produced a corresponding decrease in KIc. A linear relationship between KIc, measured at room temperature, and crosslink density is shown in Fig. 12.11 (Galy et al., 1994). 

Figure 12.11 Evolution o K C at 25°C for ideal epoxy networks based on DGEBA./3DCM/MCHA versus crosslink density. (+), theoretical (o), experimental. (see Table 12.1 for abbreviations). (By permission from Galy et al., 1994, Copyright 2001, ChemTec Publishing.)...

Grillet et al. (1991) studied mechanical properties of epoxy networks with various aromatic hardeners. It is possible to compare experimental results obtained for networks exhibiting similar Tg values (this eliminates the influence of the factor Tg — T). For instance, epoxy networks based on flexible BAPP (2-2 - bis 4,4-aminophenoxy phenyl propane) show similar Tg values ( 170°C) to networks based on 3-3 DDS (diamino diphenyl sulfone). However, fracture energies are nine times larger for the former. These results constitute a clear indication that the network structure does affect the proportionality constant between ay and Tg — T. Although no general conclusions may be obtained, it may be expected that the constant is affected by crosslink density, average functionality of crosslinks and chain... 

For the nonlinear step growth case above, eiTg, the crosslink density must be related to p. A relevant model, based on calculating the probabilities of finite chains being formed, has been published For the reaction of A -1- 2B2 (e.g., tetra-functional amine -b difunctional epoxy), A4 is considered to be an effective cross-linking site if three or more of its arms lead out to the infinite network. The probability of finding an effective crosslink is related to one minus the probability of a randomly chosen A leading to the start of a finite chain, which in turn is related to the extent of reaction. Application of this procedure to the system of Fig. 15 has been presented in detail The more complicated reaction of a tetrafunctional amine with a trifunctional epoxy was also considered. ... 

Epoxy networks may be expected to differ from typical elastomer networks as a consequence of their much higher crosslink density. However, the same microstructural features which influence the properties of elastomers also exist in epoxy networks. These include the number average molecular weight and distribution of network chains, the extent of chain branching, the concentration of trapped entanglements, and the soluble fraction (i.e., molecular species not attached to the network). These parameters are typically difficult to isolate and control in epoxy systems. Recently, however, the development of accurate network formation theories, and the use of unique systems, have resulted in the synthesis of epoxies with specifically controlled microstructures Structure-property studies on these materials are just starting to provide meaningful quantitative information, and some of these will be discussed in this chapter. 

A nodular epoxy network is thought to be a two-phase system in which regions of relatively high crosslink density are dispersed in a less crosslinked interconnecting matrix. If this is true, then the nodules should exhibit properties different from those of the matrix, e.g., a higher Tg, and a different specific volume. It is also reasonable to expect that the size and concentration of nodules should be sensitive to variations in the reactant ratio and cure conditions. 

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