The macromolecular basis of rubber elasticity

The existence of the rubbery state of polymers was introduced in Chapter 1. The present chapter provides a more formal development of the properties of rubber and explains the observed phenomena in terms of the structural properties of macromolecules developed in Chapter 2. A thorough understanding of the behavior of rubber is essential to explain the properties of macromolecules in dilute solution, which is the subject of Chapter 5. 

The development of the physical chemistry of rubber was greatly aided by the clear definition of an ideal state for this material. An ideal rubber is an amorphous, isotropic solid. The liquidlike structure of rubber was discovered very soon after the technique of X-ray scattering was developed. An isotropic material is characterized by physical properties that do not depend on the orientation of the sample. The deformation of an isotropic solid can be characterized by only two unique moduli the modulus of compression, K, and the shear modulus, G. A solid is characterized by equilibrium dimensions that are functions of temperature, pressure, and the externally imposed constraints. It is convenient to define a shape vector, L, whose components are the length, width, and height of a rectangular parallelepiped. For a system with no external constraints, the shape vector can be expressed as  

The volume of the sample is simply V pression for a sample of rubber is comparable to that for a liquid. The equilibrium shear modulus for a liquid is G = 0. For a rubbery solid, the 

To simplify the discussion of rubber elasticity, only uniaxial deformation will be considered in this chapter. More complicated strain functions will be considered in the chapter on gels. Consider a uniaxial deformation in the x-direction. It is convenient to define a deformation ratio  

It is then convenient to define a unique deformation variable called the elongation a = L /L o- The thermodynamics of ideal rubber can then be developed as a function of T, a, and the mass of the system, m. 

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Chapter four The macromolecular basis of rubber elasticity... 

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