Do all solids expand upon heating? To most people's surprise, there is a class of rather common solids, namely rubbery elastic polymers, capable of contracting upon heating1,2 while staying in the same solid phase. This seems contradictory to common sense and the physical theories of thermal behavior of ordinary solids. The physical behavior of elastic polymers continues to amaze physics and chemistry students as well as many scientists, despite the fact that it was experimentally detected in natural rubbers two centuries ago. For the following 125 years this phenomenon remained unexplained. An explanation was finally found only in the 1930s when the new science of “polymer physics” emerged. The goal of this paper is to demonstrate that some elements of polymer physics can be useful in teaching introductory general physics, especially in discussing the thermal properties of solids and for introducing the concept of entropy. Initially, several simple demo/lab experiments manifesting the extraordinary thermal properties of rubbers will be discussed. A brief description of the search for an explanation of the physics underlying this behavior will follow. The discussion will include the macromolecular hypothesis of Staudinger,3 the notion of a conformational state of a macromolecule, and the idea of statistical probabilities for the end-to-end macromolecular distances.1,2,4 The latter leads directly to an explanation of the emergence of the entropic force that is responsible for contraction upon heating. These notions are shown to be easily employable for introducing the idea of entropy to a beginner.

Topics
Entropy, General physics, Thermodynamic states and processes, Polymers, Education, Teaching, Macromolecules
1.
L. R. G. Treloar, The Physics of Rubber Elasticity, 3rd ed. (Clarendon Press, Oxford, 1975).
2.
P. C. Nelson, Biological Physics (W. H. Freeman and Co., New York, 2003), pp. 342–350.
3.
H. Morawetz, Polymers: The Origin and Growth of a Science (Wiley, New York, 1985), pp. 86–99.
4.
P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969).
5.
R. D. Knight, Five Easy Lessons: Strategies for Successful Physics Teaching (Addison-Wesley, San Francisco, 2003), p. 184.
6.
In our experiment the contraction was approximately 2 mm for the rubber band with the initial circular length of 8 cm that was stretched 2.5 times by the load of 0.2 kg; the temperature changed from 20° to 90°C. It should be remembered, though, that the contraction depends strongly on the properties of the particular rubber, especially on its degree of cross-linking.
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A. Y. Grosberg and A. Khokhlov, Giant Molecules: Here, There, and Everywhere (Academic Press, San Diego, 1997), pp. 81–105.
9.
Even after the physical theories have been developed, and when it seems that we should know practically everything about elastomeric polymers, the complexities of the thermal properties of rubbers still manifest themselves, sometimes acutely, as in the first shuttle tragedy of 1986. As we know now, the disaster was caused by the faulty thermal behavior of the rubber O-rings that were supposed to tightly seal two compartments of the rocket booster. Most likely, the problem was compounded by a partial loss of elasticity of the O-rings at a temperature that was lower than usual. Though rubber elasticity is not exactly the subject of this paper, it is closely related to the issue of thermal behavior of rubbers.
10.
A linear polymer molecule in a fully extended configuration is modeled as a straightedge in Fig. 2(a). The length of many lamellar polymer crystals [Fig. 2(b)] is comparable to the length of the macromolecule. It may seem obvious that the axis of the macromolecule should be parallel to the length of the lamellar crystal since this would provide a good fit [Fig. 2(c)]. However, x-ray studies show that the axis of the macromolecule is parallel to the width of the crystal [Fig. 2(d)]. The predicament is that the width of the lamella is orders of magnitude smaller than the length of the macromolecule. The problem is to reconcile these two seemingly incompatible conditions—the small width of the lamellar crystal and the length of the polymer chain, which is many times greater than the width of the lamella—and to fit the molecule into a crystal unit cell. The solution is to allow the polymer molecule to bend on itself many times, as shown in Fig. 2(e), and/or to pass also through other crystal units.
11.
In an undeformed cross-linked rubber sample, polymer chains between the cross-links are random coils in the vicinity of their most probable configurations,1,4 8 and their root-mean-square length of the end-to-end vector is close to the value of r = n 1/2 l. Compression, as well as stretching, changes the value of r and drives the molecular configurations toward less-probable states. The emerging entropic elastic force acts in the direction of returning the chains to the undeformed or high-entropy state. An increase in temperature facilitates the return to the high-entropy state. Under constant loading, this return means contraction for stretched samples and elongation for compressed ones. This answers Question 2 posed at the end of the section “Gough-Joule Effect.”
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© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
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