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A letter to the editor, published in the Journal of Chemical Education in February 2003, vol. 80, no. 2, p. 145.

"Disorder" in Unstretched Rubber Bands?

In the February 2002 Journal Warren Hirsch  described the classic rubber band experiment and its oft-used thermodynamic implications (Activity #42 edited by Nancy Gettys and Erica Jacobsen) (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. actually represents a liquid polymer due to 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 ΔA = ΔU - TΔS of Helmholtz is proper because the volume is essentially constant) (4 ).

Literature Cited

  1. Hirsch, W. J. Chem. Educ. 2002, 79, 200A-200B.
  2. Lambert, F. L. J. Chem. Educ. 2002, 79, 187-192.
  3. Lambert, F. L. J. Chem. Educ. 2002, 79, 1241-1246.
  4. Byrne, J. P. J. Chem. Educ. 1994, 71, 531-533.
  5. Nash, L. K. J. Chem. Educ. 1979, 56, 363-368.

 

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Copyright © 2003. The Division of Chemical Education, Inc.,
of The American Chemical Society.

 

 

entropy.lambert@gmail.com
Originally published: J. Chem. Educ. 2003 80 145.
Last revised and updated: July 2003

 

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