Mechanical instabilities of smectic-A liquid crystals under dilative or compressive stresses

Abstract

Using the mixed-type elasticity for smectics introduced by de Gennes a model is built to describe the behaviour of homeotropic smectic-A liquid crystals submitted to compressive or dilative forces normal to the layers. This model predicts respectively two types of mechanical instabilities : molecular tilt inside the layers, or undulation of the layers. The expressions for the thresholds of these instabilities and the amplitude of the deformations produced are given. Experimental results are presented which confirm these predictions and give measurements of the rigidity B〉 of the layers compared to the molecular tilt and of the penetration length λ of de Gennes. In addition the time dependence of the instabilities is observed and is explained in term of the relaxation of the applied stress due to the motion (climb) of edge-dislocations. The temperature dependence of the instability thresholds is measured in materials presenting quasi-second order transitions towards nematic or smectic-C phases. Close to a nematic phase the dilative instability threshold and thus λ diverge as expected, but with an apparent critical exponent (0.16), significatively smaller than the expected exponent v/2 (0.25 or 0.33 in a mean-field or in a non-classical model respectively). This discrepancy has not been explained yet. Close to a smectic-C phase the rigidity modulus B〉 vanishes with an apparent classical exponent γ ≃ 1.