Tensile modulus and stress relaxation

The two similar triangles in Fig. 8.13 can be used to relate the transverse amplitude hy and the longitudinal amplitude h - 

The longitudinal amplitude of each mode can then be written in terms of the mode wavelength and the Kuhn length  

The final relation made use of Eq. (8.105). The spring constant(units of force/length) arising from the mode with wavelength A can be estimated from the fact that the energy of each mode is of the order of kT. 

The tensile force f from the mode with wavelength A arising from application of a small stretch 5L is the product of the spring constant and the stretch  

The last relation introduces the extensional strain 5a = bLjX. 

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