Layer-by-layer crystallization and the role of fluctuations in free standing smectic films

Specular x-ray reflectivity has been used to study the changes in the thermal fluctuation behavior of eight layer freely suspended $N-(4-n-\mathrm{butoxybenzilidene})-4-n-\mathrm{octylaniline}$ $(4\mathrm{}\mathrm{O}.8)$ films during the process of successive layer-by-layer crystallizations. Each of these steps is preceded by the formation of an intermediate layer structure with in-plane hexatic ordering. We find an unusually large reduction of the fluctuations after the emergence of only the first hexatic toplayer. The fluctuation profiles over the film are in all cases quenched at the surfaces though less so after each crystallization step. This behavior supports theoretical arguments that hexatic order is reduced by out-of-plane smectic layer fluctuations.