Soft materials are simply made of matter that is considered ‘soft’ at room temperature. In these materials, the application of weak forces will cause the molecules to move significant distances. Therefore, these materials are easily deformed.
Some examples of soft materials are polymers (such as nylon and rubber), liquid crystals (found in computer and TV screens) and biological materials, such as the elastin contained within tendons and ligaments.
Theory of Elasticity
There are two mechanisms of elasticity that solids exhibit. Most crystalline solids display energy elasticity where the equilibrium structure is determined by the minimum-energy configuration of the components. When a strain is applied the elements are displaced from their equilibrium positions, storing energy that is then able to return the system to its original state.
Rubbers and other amorphous polymers have entropy-elasticity. Entropy is a measure of the amount of disorder within a system. In a relaxed state, polymer chains are disordered and have high entropy. When strain is applied the polymer chains become aligned and the degrees of freedom are lowered, thus reducing the entropy and increasing its order. The restoring force for contraction now arises from the thermodynamic requirement for entropy to increase.
The Second Law of Thermodynamics states: “In a system, a process that occurs will tend to increase the total entropy of the universe.” So in any system experiencing any processes, for example mechanical or chemical, the overall entropy of the system cannot decrease. It can only increase. For an ideal chain of molecules, increasing the entropy means reducing the distance between free ends. Consequently, a force that will tend to collapse the chain is exerted.
Young's Modulus
To understand how stretchable a material is the proportionality between stress and strain for that material must be considered. The proportionality of stress and strain (under certain circumstances and valid for only a certain range) is called Hooke’s law.
When forces of equal magnitude are applied to both ends of an object, so that the object itself can’t move, we say that the object is in tension. When the object is under tension, an elongation Δl occurs. The tensile strain of the object is equal to the fractional change in length as the forces are applied. For a sufficiently small tensile stress, stress and strain are proportional and the corresponding elastic modulus is called Young’s modulus, Y. The higher the Young’s modulus of a material, the stiffer it is. This is one of the most important properties in engineering design.
Rubber-like elasticity can be studied using statistical mechanics. Microscopic Gaussian models are available which are based on a few common ideas and lead to similar results.
The Rubber Band Example
When a strain is applied to a rubber band the atoms are displaced from their equilibrium positions and gain potential energy. Once the extension is stopped, the energy that was stored is then used to bring the atoms and the system back to their original state. This is energy-elasticity.
Since the change in potential energy of the system is the work done moving the system between two states, all of the energy created through extension of the rubber band should be used when bringing it back to its equilibrium. However, this is not normally the case.
Plotting a stress-strain curve for extension and contraction of a rubber band creates a hysteresis curve – a loop created between extension and contraction curves which represent the energy that was dissipated at heat during the stretching of the band. This energy loss occurs because the rubber band does not obey Hooke’s law perfectly. It results in a lag between application of the force and removal of the force (i.e. more force required to stretch the band than to ‘un-stretch’ it).
If the rubber band were to have its temperature raised and then be subjected to the same extension force, entropy-elasticity can be observed. When stretched, the entropy of the elastic band has been lowered as the polymer chains have been made to align and become more ordered.
Due to the Second Law of Thermodynamics, the entropy of the rubber band system can only increase. For an ideal chain of molecules, increasing the entropy means reducing the distance between free ends. Consequently, as the temperature of the band is raised, giving the molecules of the rubber more energy to move around, the entropy is increased and a force that tends to collapse the chain is exerted.
Comparison with Biological Polymers
If the properties of a rubber sample are compared with those of an elastin sample from animal tissue, links between synthetic and biological materials can be made.
Elastin has a lower Young’s modulus than rubber. This means that for low strain elastin is more stretchable. Elastin in biological tissues is actually wrapped in collagen fibres, a much stiffer material in comparison to pure elastin. This will show in the hysteresis curve. An elastin sample cannot be stretched to the same proportion as rubber. This is due to the collagen fibres becoming tight, thus making the force needed to stretch the elastin tissue increase dramatically for less strain.
This must be an intentional design – tissue fibres are needed to stretch a little to provide animals and humans with movement and withstand small forces. However, if large forces were to be applied it could lead to destructive results.
Compared to a rubber sample, elastin experiences a small hysteresis and so loses less energy when being stretched and contracted. This suggests that a maximum working efficiency has been reached within animal and human bodies, allowing as little energy as possible to be wasted when providing motion.
Elastin shows the same entropy-elasticity property as rubber. A practical application of this is its necessity in conducting physical activities or sports. Elastin is found in muscles. It warms up through gentle movements which lead to improved extensibility and the recovery of more energy.
Future Applications
Due to the property similarities of rubber-like materials and biological polymers, there is reason to suggest that replacements for body tissues could be engineered from synthetic material. Suitable surrogates for natural fibres have not yet been fully developed but with further research, the possibilities for aiding joint and muscular problems within humans may be tackled.
Sources
- Young and Freedman, University Physics, 12th edition, 2008, 11.4, 364.
- Thermodynamics of Rubber Elasticity, J. Pellicer, J. A. Manzanares, J. Zuniga, and P. Utrillas, University of Valencia, Journal of Chemical Education, 2001.
- "Elastic Properties of Soft Materials" (sm01) experiment manuscript, Exeter University e-learning resources for physics, Newton.Ex.Ac.uk.
- Prof. C. Peter Winlove.
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