Landau-de Gennes Description of Nematic Elastomers

De Gennes [81, 82] first suggested that remarkable effects, such as mechanical critical points, shifts in the phase transition temperature, jumps in the stress-strain relation, and a spontaneous shape change, would take place in nematic elastomers. His proposal was based on symmetry arguments independent of any microscopic consideration. 

According to this model, the free energy expansion, in the case of uniaxial nematic order and incompressible strain of the sam- 

IV Behavior and Properties of Side Group Thermotropic Liquid Crystal Polymers 

Without mechanical stress (a=0), spontaneous deformation must occur in the nematic phase because of the linear coupling between S and e. Minimizing F with respect to e gives the equilibrium value of = USIE. Inserting this value and the form for Fq, the above equation takes the follow- 

With an applied stress, an additional deformation arises and the minimum condition yields the strain e = a+US) E. Neglecting terms in the shift in F away from Fq becomes 

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