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Seal and Gasket Design 121<br />

within the molecule, with the bonds being stretched beyond their minimum energy<br />

capacity, but a thermal component is also involved. Again, rotation of a molecule<br />

plays a role because, between cross-linked sites, different geometries can occur as<br />

the molecule rotates. The molecular interactions at room temperature store kinetic<br />

energy as oscillations occur. When the structure is strained, this energy is released<br />

in the form of heat and a decrease in entropy occurs. We can see this relation in the<br />

following equation:<br />

S= kBInΩ (8.1)<br />

Here, S is entropy, k B is the Boltzmann constant (1.38066 × 10 –23 ), and Ω is the<br />

number of microstates that the molecule can assume per macrostate. If we consider<br />

entropy as the inability of a system’s energy to do work, we can see that entropy will<br />

decrease as the chain is stretched [6]. Likewise, as the chain is relaxed, entropy will<br />

increase in an endothermic process.<br />

Natural rubber shows a strong dependence on temperature; it has behavioral<br />

characteristics in three regions: glassy region,<br />

transition region, and rubber region [7]. At lower<br />

temperature, the rubber will be crystalline and,<br />

as the rubber’s temperature increases, it enters<br />

the transition phase where it becomes leather-like<br />

[7]. Eventually, the material will enter the rubber<br />

phase with the sheer modulus decreasing in each<br />

phase [7].<br />

As natural rubber is vulcanized, the disulfide<br />

bonds shown in Figure 8.11 shorten the chains of<br />

the rubber and increase the rate at which the chain<br />

will contract. The greater the number of disulfide<br />

bonds, the greater is the hardness of the natural<br />

rubber. Hardness affects the seal’s ability to compress<br />

as well as its performance in thermal cycling events.<br />

As with all rubbers, natural rubber (NR) is greatly affected by the type of filler<br />

utilized, amount of filler, and shape of the filler. The filler content contributes to the<br />

Payne and Mullins effects. The Payne effect is exhibited in seals and gaskets with<br />

carbon black filler. A. R. Payne studied this effect, which is seen during cyclic loading<br />

conditions upon a rubber material [8]. In this effect, as the strain gets larger, the storage<br />

modulus decreases. The effect is seen at approximately 0.1% strain amplitude [8].<br />

That is, at over 0.1% strain amplitude, the ability of a rubber to store energy decreases<br />

rapidly. At 20%, a lower limit comes into play [8]. The Payne effect is not observed<br />

in samples without filler. Likewise, the Mullins effect (named for Leonard Mullins)<br />

is the stress–strain phenomenon that can be considered softening of the stress–strain<br />

behavior when a load is beyond that which has been previously reached.<br />

In 2005, nearly 8.6 million tons of natural rubber were produced. Of this amount,<br />

94% was from Thailand, Malaysia, and Indonesia. The total world consumption of<br />

rubber is around 18 million tons per year with about 20% SBR (styrene butadiene<br />

R<br />

S<br />

FIgure 8.11 Diagram of disulfide<br />

bond.<br />

S<br />

R

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