Thermoelasticity in Polymeric and Crystalline Solids from the Atomistic Viewpoint
On the macroscopic level, the difference in the thermoelastic behavior between crystalline solids and amorphous polymeric solids such as rubber is striking. While crystalline solids expand with increase in temperature, stretched rubber contracts upon heating. On the atomic level this difference may be traced to the greater degree of disorder in amorphous polymeric solids and consequently to the central role played by entropy in their mechanical behavior.
In this paper we present two simple linear chain atomistic models with prescribed nearest-neighbor interactions, one which represents, in highly idealized form, a crystalline solid and the second a long-chain molecule under tension. For these models, it is possible to calculate the thermoelastic relation by the application of the basic principles of classical equilibrium statistical mechanics. The model1 for the long-chain molecule is found to exhibit a transition in behavior, over a narrow range of temperature, from that expected for a harmonic crystal at low temperature levels, to that characteristic of a polymer at higher temperature levels.