Physical Chemistry Third Edition

28.9 Rubber Elasticity 1201

after polymerization. Natural rubber has thecisconfiguration at each of these bonds.

A portion of the structural formula for a rubber molecule is (hydrogens have been

omitted):

C

C

C

C C

C

C

C

C C

C

C

C

C C

C

C

v

C

C

Natural rubber is a sticky, semifluid substance. In 1839, after 10 years of trial-and-error

experimentation in his kitchen, Charles Goodyear inventedvulcanization, a process in

which sulfur is reacted with natural rubber. In this process, sulfur reacts with double

bonds in two adjacent chains, forming short chains of sulfur atoms between the polymer

chains, producing a more nearly solid and elastic product than natural rubber. The extent

of this cross-linking and the presence of various additives such as “carbon black” (finely

powdered carbon) determine the physical properties of the rubber. Vulcanized rubber

can be made in varying degrees of hardness, from flexible rubber like that in inner

tubes, through the less flexible rubber used in tires, to the hard rubber used in combs.

Charles Goodyear,1800–1860,wasan
Americaninventor whose patentwas
widely infringedupon,andwhodiedin
debt.

Before 1955, various synthetic rubbers were invented, but were found to be inferior

to natural rubber. It was possible to make polyisoprene, but the double bonds were in a

random mixture of thecisandtransconfigurations. In 1955, catalysts were developed

that can produce a synthetic rubber that is identical to natural rubber, and automobile

tires made of synthetic rubber are now common.^42

The Thermodynamics of Rubber

A piece of vulcanized rubber is not a simple system in the thermodynamic sense,

because work other than compression work can be done on it. When it is stretched

reversibly, the total work in an infinitesimal displacement is given by

dw−PdV+fdL (28.9-1)

whereLis the length of the piece of rubber andfis thetension force.

It is found experimentally that the stretching of a rubber object approximately obeys

three properties: (1) the volume remains constant; (2) the tension force is proportional

to the absolute temperature; and (3) the energy is independent of the length at constant

temperature. Anideal rubberexactly conforms to these three properties. Since the

volume is constant, the first term on the right-hand side of Eq. (28.9-1) vanishes for an

ideal rubber. For reversible processes in a closed system made of ideal rubber, the first

and second laws of thermodynamics give the relation:

dUdq+dwTdS+fdL (ideal rubber) (28.9-2)

We define an enthalpy-like variable,K

KU−fL (definition) (28.9-3)

(^42) J. Nattaet al.,J. Am. Chem. Soc., 77, 1708 (1955); K. Ziegleret al.,Angew. Chem., 67 , 426 (1955a).
See the Macrogalleria website (http://www.pslc.usm.edu/macrog) to view an animation of this catalytic
action.