Thermal and mechanical behavior of rubber systems
The study of the physical behavior of rubbery materials is motivated by the desire to use these materials in a variety of environments, different mechanical conditions, and at different temperatures. For this to be possible, accurate testing conditions and modeling schemes need to be devised. These tests can be difficult to perform and existing mathematical models often neglect several basic physical requirements. One model is the statistical thermodynamic approach for calculating the thermoelastic behavior of an ideal rubber network, which assumes affine deformation of crosslinked junctions and no internal energy change with isothermal deformation. Yet, when the same relations have been manipulated according to the laws of thermodynamics, an internal energy contribution is revealed. This result is an artifact of improperly referencing strain measures and elasticity coefficients with regard to temperature. When a proper strain reference state is selected, thermoelastic stress-strain-temperature relations result that are totally entropic yet reduce to the usual isothermal conditions. This work proposes a phenomenological model that accurately models existing thermoelastic data. Experimental methods to determine the entropic and energetic contributions to rubber elasticity usually focus on the force-temperature behavior of a uniaxial sample held at constant length. Ideally, these thermoelastic measurements would be made at constant volume. Measurements are made at constant pressure and require complex corrections. It is demonstrated that two dimensionally constrained membrane samples can overcome these difficulties. By using time-average vibrational holographic interferometry, the two principal stresses of a membrane in anisotropic biaxial extension can be directly determined as a function of temperature. This two dimensionally constrained stress-temperature response greatly simplifies the resulting mathematical relations and yields no difference between constant pressure and constant volume manipulations of the data for several forms of the strain-energy function. This technique also eliminates problems inherent to the usual approaches to equilibrium thermoelastic measurements. Chemical stress relaxation of rubbers is another problem that is poorly addressed. Experiments to measure this phenomenon are conducted by measuring the force of a uniaxially constrained sample is monitored as a function of time. Holographic interferometry is an advantageous method for measuring this type of problem.