X-ray and dielectric measurements of the smectic- A -hexatic- B transitionin bulk and confined geometries.

We report x-ray and dielectric measurements on a liquid crystal exhibiting a smectic- A -hexatic- B (Sm- A -Hex- B ) transition in bulk and confined geometries. The confined geometry experiments have been performed by filling the compound, n -butyl 4(') - n -hexyloxybiphenyl-4-carboxylate, into Anopore membranes with 20 nm pore size. The surprising result seen in the x-ray studies on both the bulk and the Anopore samples is the presence of unusually strong second harmonic reflection arising from the smectic layers in both the Sm- A and Hex- B phases. In fact, the third harmonic reflection is also observed in the entire temperature range of the Hex- B phase and close to the transition in the Sm- A phase of the bulk sample, with the ratio of I(2qo) / I(qo), and I(3qo) / I(qo) being approximately 1/40 and 1/470, respectively (here I(qo), I(2qo), and I(3qo) correspond to the peak intensities of the first, second, and third harmonic reflections). These features point to the fact that the layering is much better defined in this system, unlike the usual description of pure sinusoidal mass density wave with a typical value of 10(-4) for I(2qo) / I(qo). Another notable feature observed is that whereas the extent of positional correlations of the molecules within the smectic layer, is comparable in the Sm- A phase of the bulk and Anopore samples, the correlations are reduced in the Hex- B phase. In the bulk as well as the Anopore case, the critical behavior of the positional correlations is found to be well described by a power-law expression with the exponent alpha being slightly larger for the Anopore sample. It is also seen that the weak first order nature of the transition seen in the bulk, gets weakened further, perhaps becoming second order. Despite such significant differences between the bulk and Anopore samples, the dynamics associated with the director fluctuations is only slightly influenced by confinement.