X-ray Characterization of Free-Standing Smectic Films

Free-standing liquid crystal films are unique model systems because they combine the properties of controlled size and a high uniformity in the SmA ordering [14]. In practice, utilizing appropriate liquid crystal materials, uniform films of two to a few thousand molecular layers in thickness can be easily prepared [3]. Since these films are substrate-free and stable down to only two layers in thickness, they provide an important and unique physical system to investigate the evolution from three dimensional (thick films) to two dimensional (two-layer films) behavior, the nature of two dimensional phenomena and the effect of free surfaces as well as reduced dimensionality. 

Theoretical models of free-standing smectic films have been recently developed [15] that extend the smectic bulk free energy to include the effect of the surface tension y at the free surfaces. For an (N+ l)-layer freestanding film, the free energy can be written as 

The second integral describes the additional energy associated with the increase in surface area of the two outermost surfaces at z=0 and z=Nd. Both finite size and the surface tension will suppress the bulk smec- 

Shalaginov and Romanov [18] have recently developed a continuum model and obtained an explicit formula for the displacement-displacement correlation function. Furthermore, both the uniaxial properties of the SmA phase and multiple reflection from the interfaces have been included in this theoretical model. It offers excellent agreement with the X-ray scattering data [9] acquired at a temperature well into the SmA phase of FPP (or H7F6EPP) [5-n-heptyl-2-(4-/i-perfluorohexylethanophenyl)pyrimi-dine]. Both the specular reflectivity and off-specular diffuse diffraction from 4-, 20-, and 

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