Theoretical model for the Frank elastic moduli in the intercalated SmA_b phase of bent-shaped dimers

In our previous works we have shown that the elastic properties of the intercalated SmAb phase formed by bent-shaped dimers are governed by the nematic-like behaviour of the secondary director m that is associated with the projection of the molecular axes of the monomers on the plane of the smectic layer. From the experiment, the corresponding three Frank-like moduli and K-11(m) , K-22(m) , and K-33(m) related to the secondary director demonstrate the usual behaviour of the Frank moduli of the nematics formed by rod-like molecules: monotonously increase with decreasing temperature. This is contrary to the temperature dependence of the elastic moduli for the primary director of N and NTB phases formed by bent-shaped dimers (for which the bend elastic constant decreases with temperature to zero). However, the values of the Frank-like moduli for SmAb were found to be smaller than their nematic-phase equivalents, and demonstrate a strong and unusual anisotropy, with K-11(m) : K-22(m) : K-33(m) ratio being approximately 30 : 1 : 10. Here we present a theoretical model based on the assumption of the nematic-like order within the smectic layers that provides a qualitative explanation of the experimental results. [GRAPHICS] .