Algebraic dependence of the structure factor and possible anharmonicity in a high-resolution x-ray study of a side-group polymeric liquid crystal

We report on a high-resolution x-ray study of the smectic-A phase near the nematic–smectic-A transition of a side-group polymeric liquid crystal, polyacrylate. Except at the very near vicinity of the phase transition, the first- and the second-harmonic x-ray structure factors were found to be consistent with the harmonic theory of de Gennes and Caille. However, very close to the phase transition, the attempts to fit the two harmonics completely failed. We believe that this is evidence for the importance of anharmonic corrections near the phase transition. The fits to the experimental data yield the compressibility constant B and the splay elastic constant ${\mathit{K}}_{\mathit{s}}$. We found that B can be described by a power law B∼${\mathit{t}}^{\mathrm{\phi }}$, where t=(${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$,${\mathit{T}}_{\mathit{c}}$ being the phase-transition temperature. φ was found to be 0.82±0.08, in good agreement with theoretical predictions using exponents from the literature, but in disagreement with previous experimental results on monomeric liquid crystals. The splay elastic constant ${\mathit{K}}_{\mathit{s}}$ has roughly the same magnitude as in monomeric liquid crystals but tends to decrease by approximately 50% upon approaching the transition from below. This temperature dependence is further evidence for the importance of anharmonicity in the system.