Epoxy rubbery modulus

Thus, the level of sophistication which one may consider for the application of rubber-like elasticity theory to epoxy networks may depend on the application. For highly crosslinked systems (M < 1,000), a quantitative dependence of the rubbery modulus on network chain length has recently been demonstrated , but the relevance of higher order refinements in elasticity theory is questionable. Less densely crosslinked epoxies, however, are potentially suitable for testing modern elasticity theories because they form via near quantitative stepwise reactions. Detailed investigations of such networks have been reported by Dusek and coworkers in recent studies ... 

A number of workers have treated non-Gaussian networks theoretically in terms of this finite extensibility problem. The surprising conclusion is that the effect on simple statistical theory is not as severe as might be expected. Even for chains as short as 5 statistical random links at strains of up to 0.25, the equilibrium rubbery modulus is increased by no more than 20-30 percent (typical epoxy elastomers rupture at much lower strains). Indeed, hterature reports of highly crosslinked epoxy M, calculated from equilibrium rubbery moduh are consistently reasonable, apparently confirming this mild finite extmsibiUty effect. 

Direct measurement of the cross-link density of thermoset polymers including those from epoxy resins remains one of the most difficult analytical challenges in the field. A far too common approach simply relates the rubbery modulus (Gr), the thermoset modulus above Tg, to the molecular weight between cross-links (Me) using the theory of rubbery elasticity (133,134). Unfortunately thermoset networks have much more complex features than do true elastomers, including non-Gaussian chain behavior, interchain interactions, and entanglements (172). 

Eqs. 7.20 or 7.33 can be used to confirm mathematically the Joule effect or the increase of modulus with temperature in the rubbery range (see problem 7.5). The elastic (or 30 second) modulus for the epoxy of Fig. 7.3 in the rubbery range is shown plotted vs. absolute temperature in Fig. 7.10. Obviously, the rubbery modulus does increase linearly with increasing temperature. Even though the extrapolated data does not go through the origin it does serve as confirmation of the Joule effect mentioned in Chapter 1. 

The molecular weight between crosslinks (Me) was determined for each epoxy/amine ratio of the neat resin from the rubbery plateau region of the modulus curve following the Tg region. This can be seen in Figure 13 for several epoxy/amine ratios. The Me values were calculated from the following equation ... 

It is well known that the elasticity of polymer networks with constrained chains in the rubbery state is proportional to the number of elastically active chains. The statistical (topological) model of epoxy-aromatic amine networks (see Sect. 2) allows to calculate the number of elastically active chains1 and finally the equilibrium modulus of elasticity Eca,c for a network of given topological structure 9 10). The following Equation 9) was used for the calculations of E, c ... 

Experimentally, the glass transition has also manifested itself by a sharp increase in relative rigidity (measured by dynamic-mechanical methods) and a simultaneous drastic decrease in the rate constant of the autocatalytic epoxy-amine reaction The mobility or rigidity of the system is a function of reaction conversion a in the pre-gel region it can be characterized by dynamic viscosity which is proportional to M of the reacting system. Beyond the gel point, still in the rubbery region but not close to the gel point, the dynamic modulus, G, is at low frequencies proportional to " (m a 1)... 

According to a report presented by Fu et al. [180], the influence of POSS-triol on epoxy-amine reaction depends mostly on the magnitude of AT (Tg -Tc) used. Since Tg for epoxy cured with linear aliphatic diamine—2-methyl-1,5-pentadiamine (MPDA)—was higher than the Tg of the same epoxy cured with diamine-terminated polypropylene oxide (PPO), when cured at the same temperature, epoxy-cured MPDA showed a greater improvement in the value of Tg. Moreover, the addition of POSS-triol in tetraglycidyl diamino diphenyl methane (TGDDM) cured with MPDA also increased the rubbery plateau modulus (Fig. 6). 

The use of rubbers (particularly epoxy-terminated butadiene nitrile, ETBN, rubber or carboxy-termi-nated butadiene acrylonitrile, CTBN, rubber) to toughen thermoset polymers is perhaps the most widely explored method and has been applied with some measure of success in epoxy resins. Phase separation of the second rubbery phase occurs during cure and its incorporation in the epoxy matrix can significantly enhance the fracture toughness of the thermoset. Although the rubber has a low shear modulus, its bulk modulus is comparable to the value measured for the epoxy, ensuring that the rubber inclusions introduced... 

The onset of the Tg is near 175°C. This composite, which is 45° carbon-fiber-reinforced, shows a dynamic storage modulus of the epoxy matrix in the glassy-state of ca. 15 GPa. At the onset of the glass-to-rubber transition (see Figure 6), the modulus drops gradually from 15 GPa (175°C) to about 3 GPa (300°C) as the rubbery plateau is reached. 

Based on studies of an homologous, endlihked, epoxy/amine network series, the simple theory of rubber elasticity has proved effective for determining reasonable cross-link densities from equilibria modulus measurements in the rubbery state. 

Demonstration of Dual Cure. To demonstrate thermal cure after UV cure three sets of films were prepared for Dynamic Mechanical Analysis (DMA). In the first set, four formulations were based on AM 1, AH 2, the epoxy acrylate, amd the urethane acrylate. Formulations used the test resin at 65% in TPGDA, and included 3% Darocur 1173 as a source of free radicals. DMA plots for the epoxy acrylate and urethane acrylate are shown in Figure 9. The elastic or storage modulus (E ) in the rubbery region is often used as a measure of crosslink density. The maximum of the tan delta plot, not shown, is... 

The increase in modulus may also often be expressed in terms of the slightly different Mooney (1951) or Guth (1944)-Smallwood (1944) equations. For example, with glass-bead-filled epoxy resins, Lewis and Nielsen (1970) found agreement between predicted and observed values of modulus in the rubbery region using the Mooney (1951) equation ... 

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