Enthalpic and Entropic Contributions to Rubber Elasticity The Force-Temperature Relations

ENTHALPIC AND ENTROPIC CONTRIBUTIONS TO RUBBER ELASTICITY THE FORCE-TEMPERATURE RELATIONS 

Force-temperature ( thermoelastic ) relations lead to a quantitative assessment of the relative amounts of entropic and energetic components of the elasticity of the network. 

In uniaxial deformation, the energetic contribution to the total elastic force [4,5,16,80-82] is given by the thermodynamically exact relation 

The subscripts L and V denote that differentiation is performed at constant length and volume. To carry out the differentiation indicated in Equation (59), an expression for the total tensile force / is needed. One may use the expression given by Equation (28) for the phantom network model. Applying the right-hand side of Equation (59) to Equation (28) leads to 

Equation (60) is important because the right-hand side relates to a microscopic quantity, r2) 0, and the left-hand side is the thermodynamic ratio of the energetic component of the force to the total force, both macroscopic quantities. It should be noted that Equation (60) is obtained by using a molecular model. Experimentally, the determination of the force at constant volume is not easy. For this reason, expressions for the force measured at constant length and pressure p or constant a and p are used. These expressions are 

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