Smectic layer compression constant

The addition of a layer compression energy Wcomp such as those of the forms introduced at equations (6.147) and (6.148), can also be added to w. Some preliminary theoretical results involving the onset of layer undulations in a Helfrich-Hurault transition in SmC using such an energy obtained, for example, via (6.147), (6.299), (6.301) and (6.302), has been reported by Stewart [263]. Also, the smectic layer compression constant B has been measured for various materials that exhibit SmA and SmC phases see the comments and references on page 284. 

Similarly, the layer compressibility constant, B, exhibits a critical variation in the vicinity of the transition. This pretransitional behavior above AN has been recognized by de Vries [32], who, by X-ray diffraction experiments, has shown the existence of small domains with a smectic... 

For small-molecule thermotropic smectic-A phases, typical values of two elastic constants are K 10 dyn and B 10 dyn/cm (Ostwald and Allain 1985). For lyotropic smectics, such as those made from surfactants in oil or water solvents, the layer compression modulus B can be much lower (see Chapter 12). From B and K, a length scale A. = ( 1 /B) 1 nm is defined it is called the permeation depth and its magnitude... 

A more complete description of smectic A needs to take into account the compressibility of the layers, though, of course, the elastic constant for compression may be expected to be quite large. The basic ideas of this model were put forward by de Gennes. > We consider an idealized structure which has negligible positional correlation within each smectic layer and which is optically uniaxial and non-ferroelectric. For small displacements u of the layers normal to their planes, the free energy density in the presence of a magnetic field along z, the layer normal, takes the form... 

If the amplitude of the complex order parameter ij/ is constant, (10.8) describes changes of the free energy which are due to compression or dilation of the layers (i.e., deviations of Q from Qo ) or due to phase shifts of ij/, i.e., displacements of the smectic layers. In contrast to the gradient term appearing in the Ginzburg-Landau ansatz [44], two coefficients, C and C , appear because of the anisotropy of the liquid crystal. In a one-constant approximation, C = C = C, (10.8) is reduced to... 

Here Fq is tire free energy of the isotropic phase. As usual, tire z direction is nonnal to tire layers. Thus, two elastic constants, B (compression) and (splay), are necessary to describe tire elasticity of a smectic phase [20,19, 86]. 

Here the A terms describe curvature distortions of the smectic planes, the B terms the distortions of the director when the smectic planes are unperturbed, and the C terms the coupling between these two types of distortions. All the coefficients are approximately of the same order of magnitude as the nematic elastic constants. A term of the type B(du/dzY may also be included to allow for the compression of the layers, but we shall neglect it in the present discussion. 

Ribotta and co-workers were the first to observe that a uniaxial pressure applied normal to the smectic A layers induces a transition to the smectic C phase when the stress exceeds a threshold value [130]. The behavior is much more pronounced when the stress is applied at a temperature close the SmA-SmB transition. The finite tilt angle induced can be directly related to B, the elastic constant of compression. Further studies have shown that the temperature dependence of the critical stress and strain re-... 

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