Enthalpic and Entropic Contributions to Rubber Elasticity Force-Temperature Relations

ENTHALPIC AND ENTROPIC CONTRIBUTIONS TO RUBBER ELASTICITY FORCE-TEMPERATURE RELATIONS 

Force-temperature 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 [5-7,31,38,39] 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 Eq. (59), an expression for the total tensile force/is needed. One may use the expression given by Eq. (28) for the phantom network model. Applying the right-hand side of Eq. (59) to Eq. (28) leads to 

Equation (60) is important because the right-hand side relates to a microscopic quantity, (r, and the left-hand side is the ratio of the energetic component of the force to the total force, both macroscopic quantities. It should be noted that Eq. (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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VII. Enthalpic and Entropic Contributions to Rubber Elasticity Force-Temperature Relations Vtn. Direct Determination of Molecular Dimensions IX. Single-Molecule Elasticity References... 

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