Cross-linking elastic modulus

Regardless of the method of cross-linking, mechanical properties of a cross-linked elastomer depend on cross-link density. Modulus and hardness increase monotonically with cross-link density, and at the same time, the network becomes more elastic. Fracture properties, i.e., tensile and tear strength, pass through a maximum as the cross-link density increases (see Figure 5.4). 

Because of very low stiffness, the rubber dispersed in the rigid matrix causes a decrease of the modulus and the yield strength of the blend. An extent of reduction depends, however, on the concentration of the rubber, rather than on its type or elastic properties (provided rubber is not highly cross-linked), since modulus of practically all elastomers above their glass transition is very much lower than modulus of the rigid matrix. 

Figure 1.1 describes the general regions of viscoelastic behavior for amorphous polymers where mechanochemistry may be conducted. The tensile and shear moduli for crystalline and amorphous polymers in the solid state are generally in the range of 10 dyn/cm. For the rubbery state, the value is about 10 dyn/cm, and it varies with the density of entanglements and chemical cross-links. The modulus can be calculated from the theory of rubber elasticity, and the short-time viscoelastic properties in the rubbery state are not unlike those of a common rubber band. 

At still longer times a more or less pronounced plateau is encountered. The value of the plateau modulus is on the order of 10 N m", comparable to the effect predicted for cross-linked elastomers in Sec. 3.4. This region is called the rubbery plateau and the sample appears elastic when observed in this time frame. 

Permanent set and low hysteresis properties depend on minimizing the viscous or plastic component of modulus. Because cross-linking increases elasticity, a high state of cure typically provides the best compression set and heat buildup properties. 

The modulus of elasticity can also influence the adhesion lifetime. Some sealants may harden with age as a result of plasticizer loss or continued cross-linking. As a sealant hardens, the modulus increases and more stress is placed on the substrate—sealant adhesive bond. If modulus forces become too high, the bond may faH adhesively or the substrate may faH cohesively, such as in concrete or asphalt. In either case the result is a faHed joint that wHl leak. 

Desirable properties of elastomers include elasticity, abrasion resistance, tensile strength, elongation, modulus, and processibiUty. These properties are related to and dependent on the average molecular weight and mol wt distribution, polymer macro- and microstmcture, branching, gel (cross-linking), and... 

Mechanical properties, such as elastic modulus and yield point, that depend on crystallinity per se are not seriously affected by low to moderate doses of ionizing radiation. On the other hand, those mechanical properties that are sensitive to interlamellar activity are most dramatically affected by the low to moderate radiation doses. This is seen in the ultimate tensile strength and elongation at failure of the polyolefins. It is also reflected in the large change in melt index between 0 and 18 Mrad, which indicates formation of cross-links that increase with increasing... 

We therefore have qualitative evidence for the dependence of the dewetting speed on the elastic properties of the substrate. Dependence of wetting on the elastic modulus was previously suggested in the case of thin substrates [31], It may be conjectured that cross-linking affects the surface properties of the elastomer and, therefore, wettability. However,... 

Other properties such as solubility, viscosity (above Tg and T ), modulus of elasticity, and strength are highly dependent on the polymer architecture, or pattern of the interconnections between units. In other words, these properties vary to a marked degree with changes in the molecular weight and in the degree of cross-linking. 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

A8. The Helmholtz elastic free energy relation of the composite network contains a separate term for each of the two networks as in eq. 5. However, the precise mathematical form of the strain dependence is not critical at small deformations. Although all the assumptions seem to be reasonably fulfilled, a simpler method, which would require fewer assumptions, would obviously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling in the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method is described in Part 3. 

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

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