Rubber and rubber balloons: paradigms of thermodynamics

Ingo Müller, Peter Strehlow (auth.), Ingo Müller, Peter Strehlow (eds.)3540202447, 9783540202448

Experiments with rubber balloons and rubber sheets have led to surprising observations, some of them hitherto unknown or not previously described in the literature. In balloons, these phenomena are due to the non-monotonic pressure-radius characteristic which makes balloons a subject of interest to physicists engaged in stability studies. Here is a situation in which symmetry breaking and hysteresis may be studied analytically, because the stress-stretch relations of rubber – and its non-convex free energy – can be determined explicitly from the kinetic theory of rubber and from non-linear elasticity.

Since rubber elasticity and the elasticity of gases are both entropy-induced, a rubber balloon represents a compromise between the entropic tendency of a gas to expand and the entropic tendency of rubber to contract.

Thus rubber and rubber balloons furnish instructive paradigms of thermodynamics. This monograph treats the subject at a level appropriate for post-graduate studies.

Table of contents :
1 Stability of Two Rubber Balloons….Pages 1-5
2 Kinetic Theory of Rubber….Pages 7-20
3 Non-linear Elasticity….Pages 21-34
4 Biaxial Stretching of a Rubber Membrane – A Paradigm of Stability, Symmetry-Breaking, and Hysteresis….Pages 35-50
5 Stability of a Single Balloon….Pages 51-61
6 Stepwise Inflation of a Balloon….Pages 63-68
7 Two Balloons – Revisited….Pages 69-77
8 Many Balloons – The Emergence of a Pseudoelastic Hysteresis….Pages 79-86
9 Stability of the Spherical Shape….Pages 87-96
10 Stress-Induced Crystallization of Rubber….Pages 97-104
11 History of Rubber and Its Use….Pages 105-110