Page 346 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Naturally Occurring Polymers—Plants 309

(a)

(b)

FIGURE 9.6 Ball-and-stick models of “soft” hevea rubber (cis-1,4-polyisoprene) (a) and “hard” gutta per-
cha (trans-1,4-polyisoprene) (b).

When a strip of NR or SR is stretched at a constant rate, the tensile strength required for stretch-
ing (stress, s) increases slowly until elongation (strain) of several hundred percent is observed. This
initial process is associated with an uncoiling of the polymer chains in the uncross-linked regions.
Considerably more stress is required for greater elongation to about 800%. This rapid increase in
modulus (G) is associated with better alignment of the polymer chains along the axis of elongation,
crystallization, and decrease in entropy (∆S). The work done in the stretching process (W ) is equal
l
to the product of the retractile force (F) and the change in length (dl). Therefore, the force is equal to
the work per change in length.

W 1
W 1 = f dl or f = (9.42)
dl
W is equal to the change in Gibbs free energy (dG), which under the conditions of constant pres-
l
sure is equal to the change in internal energy (dE) minus the product of the change in entropy and
the Kelvin temperature as follows:

W 1 dG dE  dS 
f = = = − T  
dl dl dl  dl 
(9.43)
The first term (dE/dl) in Equation 9.43 is important in the initial low-modulus stretching process,

and the second term [T(dS/dl)] predominates in the second high modulus stretching process. For an
ideal rubber, only the second term is involved.

As observed by Gough in 1805 and verified by Joule in 1859, the temperature of rubber increases
as it is stretched, and the stretched sample cools as it snaps back to its original condition. (This can
be easily confirmed by you by rapidly stretching a rubber band and placing it to your lips, noting

that heating has occurred, and then rapidly releasing the tension and again placing the rubber band
to your lips.) This effect was expressed mathematically by Kelvin and Clausius in the 1850s. The
ratio of the rate of change of the retractive force (df) to the change in Kelvin temperature (dT) in an
adiabatic process is equal to the specific heat of the elastomer (C ) per degree temperature (T) times

p
the change in temperature (dT) times the change in length (dl).
df  C p   dT 
=     (9.44)

dT  T   dl

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