What is the equation that describes the relationship between Gibbs elasticity and elastic modulus in polymers?
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. T. Nguyen. (2009) .Fundamental Surfactant Properties of Foamersfor Increasing Gas Production. Petroleum Science and Technology, 27:733–745, 2009.
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The relationship between Gibbs elasticity (also known as the Gibbs energy elasticity) and the elastic modulus in materials is described by the following equation:
E= ρ² / β x ∂ ² G / ∂ ρ²
Where:
- E is the elastic modulus (Young's modulus) of the material.
- ρis the strain (deformation) of the material.
- β is the volume strain, which is the change in volume divided by the initial volume.
- G is the Gibbs free energy of the material.
This equation relates the elastic modulus of a material to its Gibbs elasticity, which is a measure of the change in Gibbs free energy with respect to strain. The equation essentially quantifies how the free energy of a material changes as it is subjected to deformation or strain.
It's important to note that this equation is derived based on certain assumptions and approximations, and its applicability might vary depending on the specific properties of the material and the nature of the deformation. In some cases, different forms of this equation or other constitutive equations might be used to model the relationship between mechanical properties and thermodynamic quantities.
Amirreza Malekzadeh Dirin & Alan Parker
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