Nonlocal elasticity theory of polymeric liquid crystals

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Abstract
We construct a nonlocal theory of elasticity for a nematic polymer composed of rigid or semiflexible molecules. We then introduce a mean-field theory for the calculation of wave-vector-dependent elastic moduli. Because the length of the molecules can be comparable to observable elastic distortions, the wave-vector dependence of the Frank moduli, i.e., their nonlocality, can be quite important. For rodlike molecules we obtain analytic results valid for arbitrary wave vector and strong nematic ordering. For flexible chains we are unable to obtain analytic results for the nonlocal elastic constants except in the limit of chains whose lengths are short compared to their global persistence length. However, our formalism is readily amenable to numerical techniques which should allow future consideration of the interplay of nonlocality and flexibility.