Mechanically induced Helfrich-Hurault effect in a confined lamellar system with finite surface anchoring

Soft lamellar phases confined between two parallel plates and subject to a dilatative strain can become unstable exhibiting periodic deformations patterns of the layers. By a variational energy approach, a critical threshold for the imposed finite strain is derived in the case of weak anchoring conditions. The potential, associated to the system, includes a two terms energy which accounts for the bending of the layers and the dilatation of the bulk as well as an anchoring potential. Classical results for strong anchoring at the walls are recovered. It is shown that weak anchoring conditions, can lead to a lower critical threshold of the field, similarly as it happens for the instability induced by a magnetic or an electric field normal to the layers. Nevertheless, in the limit of weak anchoring, the model reveals that this instability does not occur. Analytical formulas are provided which certainly encourage further experimental invetigations.