Chemical Education Today
Letters “Disorder” in Unstretched Rubber Bands? In the February 2002 issue of the Journal, Warren Hirsch described the classic rubber band experiment and its oft-used thermodynamic implications in JCE Classroom Activity #42 (1). It is an amusing coincidence, but perhaps confusing to many, that my article showing “disorder” to be a misleading concept happened to appear in the same issue (2). Explication of the behavior of a rubber band has long been thought to be a prime example of the value of “disorder”! However, when “disorder” is discarded, the rubber band experiment can be more fundamentally understood. First, energy spreading out in molecular motion is what entropy measures. The more such dispersal of energy occurs or can occur (as a function of temperature), the greater the entropy (3). Second, the process of stretching a rubber band (and its retraction) involves two modes of energy spreading out (4). The major way in which energy is spread out in the long twisted molecules in rubber is in the rotating portions of the molecules or in equally fast bending of the links per molecule. This is favored in the conformations of unstretched rubber where parts of the molecules are relatively free to move, as in a liquid. Therefore in the unstretched rubber, energy is much spread out—as is indicated by its high entropy. In contrast, when a rubber band is pulled, its enormous number of lengthy molecules are stretched out and there is less opportunity for free rotation or bending in these conformations. There are fewer ways for energy to be distributed among the molecules and thus a stretched band has lower entropy than one unstretched. When the tension on the band is released, because its energy can be more spread out in the unstretched form, the band spontaneously snaps to that form and its entropy increases. The thermal effects fit well with the foregoing description of molecular behavior. A rubber band when stretched becomes warm from the work of stretching it plus the energy that can no longer be spread out in the more mobile molecular conformations of the unstretched rubber. After reaching room temperature, the stretched band has much less entropy than the unstretched band. When the band is rapidly released, it becomes cool because energy is spread out from the vibrational to the now-available conformational modes of motion and the temperature drops. Eventually, energy from the surroundings is spread out within the band to bring its temperature to ambient. It is probably best in most classes to emphasize only the predominant path of energy dispersal: more ways to spread out in the more freely rotating segments of the molecules in the unstretched rubber (higher entropy), fewer ways in the less freely moving portions in stretched rubber (lower entropy). The minor pathway of energy dispersal involves weak bond formation or breaking (van der Waals interaction between molecules or parts) that are analogous to phase change from a “liquid” unstretched rubber (5) to a “solid” stretched rubber band. When the band is stretched, the warmth is due
to the work done plus the energy released analogous to a true liquid changing to a solid. (A liquid has more ways of spreading energy among its freely rotating molecules than in the more restricted molecular movement in a solid.) Conversely, when the “solid” stretched band is released, it cools because energy must be transferred from the surroundings to be spread out in the increased number of rotations and movement in the “liquid” unstretched rubber. The “disordered” sketch, atop page 200B (right) in Activity #42 (1), actually represents a liquid polymer because of the presence of relatively free rotating and bending of the many links in unstretched poly(isoprene) (5), a state characterized by increased entropy compared to the solid form shown (in a too precise pattern) at its left. (Note that it is not correct to apply the Gibbs equation where the pressure on the system is difficult to define; the ∆A = ∆U – T∆S of Helmholtz is proper because the volume is essentially constant) (4). Literature Cited 1. 2. 3. 4. 5.
Hirsch, W. J. Chem. Educ. 2002, 79, 200A–200B. Lambert, F. L. J. Chem. Educ. 2002, 79, 187–192. Lambert, F. L. J. Chem. Educ. 2002, 79, 1241–1246. Byrne, J. P. J. Chem. Educ. 1994, 71, 531–533. Nash, L. K. J. Chem. Educ. 1979, 56, 363–368. Frank L. Lambert Department of Chemistry Occidental College (Emeritus) Los Angeles, CA 90041 Present address: 2834 Lewis Drive, La Verne, CA 91750
[email protected] The author replies: Dr. Lambert has presented an interesting, alternative way of teaching the concept of entropy in his article “Disorder— A Cracked Crutch for Entropy Discussions” (1). However, in my view, he has not succeeded in “showing”, as he contends, that molecular disorder should be rejected as a viable model. Furthermore, the disorder model is not at all confusing to students, if presented properly. For example, Richard Feynman clearly and simply says, “We measure disorder by the number of ways that the insides can be arranged, so that from the outside it looks the same…entropy measures the disorder” (2). In a slightly more mathematical manner, Ilya Prigogine says, “Boltzmann identified the number of complexions, P, with the entropy through the relation S = k log P in which k represents Boltzmann’s universal constant: an entropy increase expresses growing molecular disorder, as indicated by the increasing number of complexions” (3). As far as disorder not being a viable model for rubber, the expression for the entropy of a rubber polymer chain may be obtained by means of the random coil model, which is
JChemEd.chem.wisc.edu • Vol. 80 No. 2 February 2003 • Journal of Chemical Education
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Chemical Education Today
Letters clearly related to the degree of disorder of the chain (4). Furthermore, as Nash says, “partial straightening of chain segments is an ordering process reflected in an entropy decrease” (5). Lambert has not included this point when citing the same reference. I do agree that energy is more “spread out” in relaxed than in stretched rubber chains; however, this leads to an increase in the molecular disorder in the relaxed state. The Gibbs free energy, ∆G, was selected in the rubber band activity (6) in lieu of the Helmholtz free energy, ∆A, since general chemistry texts do not ordinarily mention the latter. It was noted that the assumption of constant pressure was an approximation. I agree that using ∆A is more rigorous. However, even in applying the Helmholtz equation, the assumption of constant volume is not necessarily true, especially if one notes that rubber bands contract laterally when stretched (4). Regardless of which form of free energy is used, it is clear from the activity that the temperature in the T∆S term is not perfectly constant so that this term is also approximate. Nevertheless, in my view, making these approximations does not invalidate the conclusions the student obtains from performing the activity.
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Literature Cited 1. Lambert, F. L. J. Chem. Educ. 2002, 79, 187–192. 2. Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics, Vol. 1; Addison-Wesley: California Institute of Technology, 1977; pp 46-5–46-7. 3. Prigogine, I. From Being to Becoming-Time and Complexity in the Physical Sciences; W. H. Freeman: San Francisco, 1980; pp 9–11. 4. Atkins, P. W. Physical Chemistry, 3rd ed.; W. H. Freeman: New York, 1985; pp 625, 635–636. 5. Nash, L. K. J. Chem. Educ. 1979, 56, 363–368. 6. Hirsch, W. J. Chem. Educ. 2002, 79, 200A–200B.
Warren Hirsch Department of Chemistry Brooklyn College of CUNY Brooklyn, NY 11210-2889
[email protected] Journal of Chemical Education • Vol. 80 No. 2 February 2003 • JChemEd.chem.wisc.edu
