text: Following its introduction to Europe from the New World in the late 15th century, natural rubber (polyisoprene) was regarded mostly as a fascinating curiosity. Its most useful application was its ability to erase pencil marks on paper by rubbing, hence its name. One of its most peculiar properties is a slight (but detectable) increase in temperature that occurs when a sample of rubber is stretched. If it is allowed to quickly retract, an equal amount of cooling is observed. This phenomenon caught the attention of the English physicist John Gough. In 1805 he published some qualitative observations on this characteristic as well as how the required stretching force increased with temperature.<br>
  By the mid nineteenth century, the theory of thermodynamics was being developed and within this framework, the English mathematician and physicist Lord Kelvin showed that the change in mechanical energy required to stretch a rubber sample should be proportional to the increase in temperature. Later, this would be associated with a change in entropy. The connection to thermodynamics was firmly established in 1859 when the English physicist James Joule published the first careful measurements of the temperature increase that occurred as a rubber sample was stretched. This work confirmed the theoretical predictions of Lord Kelvin.<br>
  In 1838 the American inventor Charles Goodyear found that natural rubbers elastic properties could be immensely improved by adding a few percent sulphur. The short sulfur chains produced chemical cross-links between adjacent polyisoprene molecules. Before it is cross-linked, the liquid natural rubber consists of very long polymer molecules, containing thousands of isoprene backbone units, connected head-to-tail (commonly referred to as chains). Every chain follows a random, three dimensional path through the polymer liquid and is in contact with thousands of other nearby chains. When heated to about 150C, reactive cross-linker molecules, such as sulfur or dicumyl peroxide, can decompose and the subsequent chemical reactions produce a chemical bond between adjacent chains.  A crosslink can be visualized as the letter X' but with some of its arms pointing out of the plane. The result is a three dimensional molecular network. All of the polyisoprene molecules are connected together at multiple points by these chemical bonds (network nodes) resulting in a single giant molecule and all information about the original long polymers is lost. A rubber band is a single molecule, as is a latex glove! The sections of polyisoprene between two adjacent cross-links are called network chains and can contain up to several hundred isoprene units. In natural rubber, each cross-link produces a network node with four chains emanating from it. It is the network that gives rise to the elastic properties.
  Because of the enormous economic and technological importance of rubber, predicting how a molecular network responds to mechanical strains has been of enduring interest to scientists and engineers. To understand the elastic properties of rubber, theoretically, it is necessary to know both the physical mechanisms that occur at the molecular level and how the random-walk nature of the polymer chain defines the network. The physical mechanisms that occur within short sections of the polymer chains produce the elastic forces and the network morphology determines how these forces combine to produce the macroscopic stress that we observe when a rubber sample is deformed, e.g. subjected to tensile strain.