Whether they are holding your newspaper together, being shot at you by a friend, or just cluttering your junk drawer, elastic bands are all around us. However, this seemingly mundane material has some amazing, and even surprising, properties which can be understood by considering the thermodynamics at play.
Elastic bands are elastomers and, like other rubbers, are made of long polymer chains (Ali, Hosseini and Sahari, 2010). Rubbers are made through the process of vulcanization, during which the rubber molecules are joined together via sulphur crosslinks, as seen in Figure 1 (Coran, 2002). Prior to vulcanization, the molecules themselves actually form a liquid, and historically rubber was made from natural latex obtained from certain trees, much like sap is extracted for the making of maple syrup (Hills, 1971). The sulphur crosslinks result in the rubber becoming insoluble, no longer able to flow as a liquid, and the degree to which the rubber is vulcanized determines the final stiffness of the material (Coran, 2002).
Elastomers have unique properties including being able to return to their original shape after exposure to very large strains (Ali, Hosseini and Sahari, 2010). This specific property displays the complicated behaviour of rubbers and for this reason the linear elastic theory, used to model most solid objects, is not adequate when modeling elastic bands. Another fascinating property of elastomers is that they contract when heated, unlike most materials which expand. This is referred to as the Gough-Joule effect (Roundy and Rogers, 2013). Like nearly every other phenomenon in the universe, these seemingly counter-intuitive observations can be explained by thermodynamics, and more specifically by considering the various energies of the system. The definition of Gibb’s free energy is:
where, G is the Gibb’s free energy, H is the enthalpy, T is the temperature, and S is the entropy, for a given system. Let’s consider the enthalpic and entropic contributions to the overall free energy when an elastic band, like that in Figure 2, is stretched. The spontaneous state is the non-stretched shape, telling us that change in free energy is positive. Determining the change in enthalpy can be done by stretching the elastic while holding it against your lips, which is one of the most temperature sensitive places on the body. You will notice that the stretched band feels hot and when the band is relaxed it cools down. This means that stretching the band is an exothermic change, and thus change in enthalpy is negative. Referring back to the equation for Gibb’s free energy, it follows that change in entropy must be negative. This implies that stretching adds order to the band, which is energetically unfavourable. As the temperature increases, the entropy plays a larger role in determining G and it can be seen that at higher temperatures the relaxed state becomes even more favourable.
Elastic bands are an excellent example of the ways basic thermodynamics can be used to explain some of the seemingly mysterious physical properties of materials we encounter every day. Whether we are studying elastic bands, chemical reactions, or the formation of a star, a fundamental understanding of thermodynamics can help us examine, explain, and explore the universe.
Works Cited:
Ali, A., Hosseini, M. and Sahari, B.B., 2010. A review and comparison on some rubber elasticity models. Journal of Scientific & Industrial Research, 69(2), pp.495–500.
Alliance Rubber Company, 2013. Home use. [online] Available at: <http://www.rubberband.com/easyblog/categories/listings/home-use.html> [Accessed 20 Sep. 2013].
Coran, A.Y., 2002. Chemistry of the vulcanization and protection of elastomers: A review of the achievements. Journal of Applied Polymer Science, 87(1), pp.24 – 30.
Hills, D., 1971. Heat Transfer and Vulcanisation of Rubber. Christchruch, NZ: Elsevier.
Roundy, D. and Rogers, M., 2013. Exploring the thermodynamics of a rubber band. American Journal of Physics, 81(1), p.20.