Page 230 - Handbook of Plastics Technologies

ELASTOMERS

4.22 CHAPTER 4

FIGURE 4.12 Entropy as a function of strain.

The statistical theory of rubber elasticity, based on estimates of the changes in entropy
due to deformation gives

ν RT
e
G = ------------- (4.5)
V
where G is the shear modulus (for elastomers 1/3 the value of Young’s modulus) and ν is
e
the numbers of moles effective (supportive) network chains. Equation 4.5 assumes that the
natural log of number of configurations that can be assumed by a flexible segment is pro-
portional to its configurational entropy. Shear stress is proportional to the product of abso-
lute temperature and the derivative of this entropy with respect to shear strain. Equation
4.5 was given by Flory in the early 1930s. The relation is only a good approximation be-
cause of complexities and certain assumptions (e.g., that the chains’ motion is not re-
stricted by the presence of neighboring chains). There has been much controversy and
refinement of the equation; nevertheless, all of this supports the idea of the retraction be-
ing the result of the entropic spring.

4.5 VULCANIZABLE ELASTOMERS

The first rubber to be discovered and used by industry was natural rubber. After quite a
long time, synthetic rubbers were introduced. In this section, we consider natural and syn-
thetic conventional (i.e., vulcanizable) rubbers. There is some emphasis on the science and
technology of natural rubber for two reasons: (1) natural rubber has been the most studied,
and (2) many of the synthetic elastomers are quite similar to natural rubber in many re-
spects.

4.5.1 Vulcanization
Unvulcanized rubber articles are generally not strong, do not regain their shape after large
deformations, and can even be sticky and have the consistency of chewing gum. The first
commercial method for vulcanization has been attributed to Charles Goodyear. His pro-
cess (heating natural rubber with sulfur) was first used in Springfield, Massachusetts, in
1841. Thomas Hancock used essentially the same process about a year later in England. In
addition to natural rubber, many synthetic rubbers have been introduced and, in addition to

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