The aggregate model for chain-extended polyethylene and liquid crystalline polymers

6 The aggregate model for chain-extended polyethylene and liquid crystalline polymers 

On the compliance averaging scheme, the tensile modulus of the oriented polymer is given by 

As before, 6 represents the angle between the unit of the aggregate and the axis representing total alignment, and sin 0, etc. represent average values. 

For the very high degree of molecular orientation found in these polymers sin 6 -C 1 and cos 6 = cos 0=1. We can then rewrite Equation (7.8) as 

The aggregate model also has been used with success to describe the mechanical anisoti opy of several liquid crystalline polymers. Ward and co-workers [56] examined the dynamic mechanical behaviour of several thermotropic polyesters in tension and shear over a wide temperature range, and used the single-phase aggregate model to relate quantitatively the fall in tensile modulus with temperature to the corresponding fall in shear modulus. 

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The Aggregate Model for Chain-Extended Polyethylene and Liquid Crystalline Polymers... 

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