Continuum Description of the SmC Phase

The director deformations described by that do not lead to layer compressions, in the continuum range where the wavelengths A of the deformation are much larger than the molecular dimensions (A 10 nm) can be induced by stress K 27t/pf 10T N/m. This is usually smaller than of the layer compression modulus B l(f N/m , For this reason, deformations that do not lead to layer compression (such as splay in SmA) are usually called soft deformations, whereas those that require layer compression (such as bend and twist in SmA) are the so-called hard deformations. In SmC there will be six soft and three hard deformations, so it is basically impossible to take into account all elastic terms while keeping the transparent physics. (In the chiral smectic C materials, additional three terms are needed, as shown by de Gennes. ) Fortunately, however, the larger number of soft deformations enable for the material to avoid the hard deformations, which makes it possible to understand most of the elastic effects, even in SmC materials. 

In the following, we will mainly concentrate on the soft deformations, assuming undistorted layers, and only outline the hard deformations. 

Local structure of smectic C liquid crystals, k is the local smectic layer normal, c is the c-director, k is the layer normal, it is the director, and 0 is the tilt angle. 

To express director splay, twist and bend with the new variables is a simple formality. Accordingly  

In the case of incompressible and imdistorted layers V = 0 and V x fc = 0. With these, furthermore, utilizing that c and k are perpendicular unit vectors (for example, cxVxcf = kVx cf), in the soft deformation limit we get that  

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