Rubber elasticity is the ability of solid rubber to be stretched up to a factor of 10 from its original length, and return to close to its original length upon release. This process can be repeated many times with no apparent degradation to the rubber.
Rubber, like all materials, consists of molecules. Rubber's elasticity is produced by molecular processes that occur due to its molecular structure. Rubber's molecules are polymers, or large, chain-like molecules. Polymers are produced by a process called polymerization. This process builds polymers up by sequentially adding short molecular backbone units to the chain through chemical reactions. A rubber polymer follows a random winding path in three dimensions, intermingling with many other rubber polymers.
Polyisoprene from natural rubber, is extracted from plants as a fluid colloid and then solidified in a process called Vulcanization. During the process, a small amount of a cross-linking molecule, usually sulfur, is added. When heat is applied, sections of rubber's polymer chains chemically bond to the cross-linking molecule. These bonds cause rubber polymers to become cross-linked, or joined to each other by the bonds made with the cross-linking molecules. Because each rubber polymer is very long, each one participates in many crosslinks with many other rubber molecules, forming a continuous network. The resulting molecular structure demonstrates elasticity, making rubber a member of the class of elastic polymers called elastomers.
History Following its introduction to Europe from America in the late 15th century, natural rubber (polyisoprene) was regarded mostly as a 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.
By the mid-nineteenth century, the theory of thermodynamics was being developed and within this framework, the English mathematician and physicist Lord KelvinLord Kelvin, Quarterly J. Math., 1, 57 (1857) showed that the change in mechanical energy required to stretch a rubber sample should be proportional to the increase in temperature. This would later 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.
In 1838 the American inventor Charles Goodyear found that natural rubber's elastic properties could be immensely improved by adding a small amount of sulfur to produce 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 150 °C, 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 these 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 is observed when a rubber sample is deformed (e.g. subjected to tensile strain).
Molecular-level models There are actually several physical mechanisms that produce the elastic forces within the network chains as a rubber sample is stretched. Two of these arise from entropy changes and one is associated with the distortion of the molecular bond angles along the chain backbone. These three mechanisms are immediately apparent when a moderately thick rubber sample is stretched manually.
Initially, the rubber feels quite stiff (i.e. the force must be increased at a high rate with respect to the strain). At intermediate strains, the required increase in force is much lower to cause the same amount of stretch. Finally, as the sample approaches the breaking point, its stiffness increases markedly. What the observer is noticing are the changes in the modulus of elasticity that are due to the different molecular mechanisms. These regions can be seen in Fig. 1, a typical stress vs. strain measurement for natural rubber. The three mechanisms (labelled Ia, Ib, and II) predominantly correspond to the regions shown on the plot.
The concept of entropy comes to us from the area of mathematical physics called statistical mechanics which is concerned with the study of large thermal systems, e.g. rubber networks at room temperature. Although the detailed behavior of the constituent chains are random and far too complex to study individually, we can obtain very useful information about their "average" behavior from a statistical mechanics analysis of a large sample. There are no other examples of how entropy changes can produce a force in our everyday experience. One may regard the entropic forces in polymer chains as arising from the thermal collisions that their constituent atoms experience with the surrounding material. It is this constant jostling that produces a resisting (elastic) force in the chains as they are forced to become straight.
While stretching a rubber sample is the most common example of elasticity, it also occurs when rubber is compressed. Compression may be thought of as a two dimensional expansion as when a balloon is inflated. The molecular mechanisms that produce the elastic force are the same for all types of strain.
When these elastic force models are combined with the complex morphology of the network, it is not possible to obtain simple analytic formulae to predict the macroscopic stress. It is only via numerical simulations on computers that it is possible to capture the complex interaction between the molecular forces and the network morphology to predict the stress and ultimate failure of a rubber sample as it is strained.
The Molecular Kink Paradigm for rubber elasticity
Source:
The Molecular Kink Paradigm proceeds from the intuitive notion that molecular chains that make up a natural rubber (polyisoprene) network are constrained by surrounding chains to remain within a "tube." Elastic forces produced in a chain, as a result of some applied strain, are propagated along the chain contour within this tube. Fig. 2 shows a representation of a four-carbon isoprene backbone unit with an extra carbon atom at each end to indicate its connections to adjacent units on a chain. It has three single C-C bonds and one double bond. It is principally by rotating about the C-C single bonds that a polyisoprene chain randomly explores its possible conformations.
Sections of chain containing between two and three isoprene units have sufficient flexibility that they may be considered statistically de-correlated from one another. That is, there is no directional correlation along the chain for distances greater than this distance, referred to as a Kuhn length. These non-straight regions evoke the concept of "kinks" and are in fact a manifestation of the random-walk nature of the chain.
Since a kink is composed of several isoprene units, each having three carbon-carbon single bonds, there are many possible conformations available to a kink, each with a distinct energy and end-to-end distance. Over time scales of seconds to minutes, only these relatively short sections of the chain (i.e. kinks) have sufficient volume to move freely amongst their possible rotational conformations. The thermal interactions tend to keep the kinks in a state of constant flux, as they make transitions between all of their possible rotational conformations. Because the kinks are in thermal equilibrium, the probability that a kink resides in any rotational conformation is given by a Boltzmann distribution and we may associate an entropy with its end-to-end distance. The probability distribution for the end-to-end distance of a Kuhn length is approximately Gaussian and is determined by the Boltzmann probability factors for each state (rotational conformation). As a rubber network is stretched, some kinks are forced into a restricted number of more extended conformations having a greater end-to-end distance and it is the resulting decrease in entropy that produces an elastic force along the chain.
There are three distinct molecular mechanisms that produce these forces, two of which arise from changes in entropy that is referred to as the low chain extension regime, Ia and the moderate chain extension regime, Ib. The third mechanism occurs at high chain extension, as it is extended beyond its initial equilibrium contour length by the distortion of the chemical bonds along its backbone. In this case, the restoring force is spring-like and is referred to as regime II. The three force mechanisms are found to roughly correspond to the three regions observed in tensile stress vs. strain experiments, shown in Fig. 1.
The initial morphology of the network, immediately after chemical cross-linking, is governed by two random processes: (1) The probability for a cross-link to occur at any isoprene unit and, (2) the random walk nature of the chain conformation. The end-to-end distance probability distribution for a fixed chain length (i.e. fixed number of isoprene units) is described by a random walk. It is the joint probability distribution of the network chain lengths and the end-to-end distances between their cross-link nodes that characterizes the network morphology. Because both the molecular physics mechanisms that produce the elastic forces and the complex morphology of the network must be treated simultaneously, simple analytic elasticity models are not possible; an explicit 3-dimensional numerical model is required to simulate the effects of strain on a representative volume element of a network.
Low chain extension regime, Ia