Structural correlations in smectic-Fand smectic-Iphases

The x-ray diffraction pattern from aligned samples of the smectic-$I$ ($\mathrm{Sm}I$) phases of a number of compounds has been considered, with particular emphasis on TBDA (${\mathrm{C}}_{10}$ ${\mathrm{H}}_{21}$ PhNCHPhCHNPh${\mathrm{C}}_{10}$ ${\mathrm{H}}_{21}$, where Ph stands for the phenyl group) which exhibits both $\mathrm{Sm}I$ and smectic-$F$ ($\mathrm{Sm}F$) phases. It is established that both $\mathrm{Sm}I$ and $\mathrm{Sm}F$ phases are quasi-two-dimensional structures, with essentially no correlation of molecular positions between layers. They each have C-centered monoclinic lattices with long-range three-dimensional order of the lattice directions (bond orientational order) but do not have long-range positional order. The $\mathrm{Sm}F$ and $\mathrm{Sm}I$ phases differ in the direction of molecular tilt relative to the hexagonal packing of the molecular long axes: In terms of the unit cell axes, with $b$ the unique axis, $a>b$ for $\mathrm{Sm}F$ and $b>a$ for $\mathrm{Sm}I$. Analysis of intensity profiles from high-resolution powder measurements has led to a quantitative description of the correlation function for the molecular positions in the smectic layers. The $\mathrm{Sm}F$ phase has exponential decay of correlation with correlation lengths of order 100 Å, while the (higher temperature) $\mathrm{Sm}I$ phases show algebraic decay as expected for a truly two-dimensional crystal. Current theories do not account for this result.