Rubber elasticity

The terms entropy elasticity or rubber elasticity are used to describe the property characteristic of polymers of returning to the entropically more favorable coiled state after a deformation based on the stretching of entire macromolecules or molecule segments. It is based on a reversible change in entropy in the macromolecules of the material matrix, which consist of long chains of the same building blocks:

• When the molecule is stretched by applying an external force, the bond angles of neighboring atoms along the main chain become frictionless, i.e. H. changed without expenditure of energy; at the same time the entropy is reduced (reduction of the disorder). However, this can also save energy.
• If the force leading to the stretching is removed, thermally induced intramolecular movements (so-called microbrown movements) cause the molecules to twist again; the entropy is increased and the molecule contracts.

Rubber elasticity occurs in all polymers in the temperature range above the glass transition temperature . In the case of semi-crystalline thermoplastics , the entropy-elastic state area is limited upwards by the crystallite melting area, in the case of elastomers (e.g. rubber , silicone rubber ) by the start of thermal decomposition processes . It also plays an important role in amorphous thermoplastics with a sufficiently high molar mass , but continues above the glass transition into the flow area. In the case of thermoplastics, van der Waals forces and entanglement of the polymer chains take on the role of temporary cross-linking points, in the case of elastomers, the covalent cross-links ensure mechanical stability during the deformation processes.

The stress that  occurs with a relative increase in length ε (i.e. restoring force per cross-sectional area) defines, as usual, a - comparatively small - modulus of elasticity E (or non-linear generalizations): ${\displaystyle \sigma }$ 

${\displaystyle E={\frac {\sigma }{\varepsilon }}}$

The affected material groups are characterized in the corresponding temperature range by a non-linear stress-strain characteristic , damping and deformation-historical effects as well as pronounced incompressibility .

A Greens material model should be used to describe these materials . In it, the stresses are calculated using the density of the deformation energy as a function of the strain. Well-known approaches for the energy density are the Mooney-Rivlin , Neo- Hookeschen, Yeoh or Ogden models. For rubber-elastic materials, this procedure was derived from the thermodynamics of entropy elasticity.

From a thermodynamic point of view, the rubber elasticity is essentially based on a decrease in entropy  S in the general formula for the change in free energy for a given elongation. In contrast, based elasticity of hard materials (eg. B. metals ) on the increase  of the internal energy U . ${\displaystyle F=U-T\cdot S}$ 

See also

• Cauchy elasticity
• Hyperelasticity

Individual evidence

1. ^ R. Johannknecht: The Physical Testing and Modeling of hyperelastic Materials for Finite Element Analysis. (= VDI progress reports, series 20. No. 302). VDI-Verlag, Düsseldorf 1999.
2. ↑ RW Ogden: Non-Linear Elastic Deformations . Dover Publications, Mineola, New York 1984.
3. ^ LRG Treloar: The physics of rubber elasticity . Clarendon Press, Oxford 1975.

literature

• T. Lüpke: Fundamentals of mechanical behavior . In: Wolfgang Grellmann, Sabine Seidler (Hrsg.): Kunststoffprüfung . 3. Edition. Carl Hanser Verlag, Munich 2015, ISBN 978-3-446-44350-1 , p. 86 .
• Manfred Dieter Lechner, Klaus Gehrke, Eckhard H. Nordmeier: Makromolekulare Chemie: A textbook for chemists, physicists, materials scientists and process engineers , 4th revised and expanded edition, Springer Verlag 2009, ISBN 978-3764388904 , p. 371f.