Electron density distribution of symmetric liquid crystal dimer linked by flexible alkyl chain*

The results of x-ray scattering study combined with electron density distribution of a symmetric liquid crystal dimer linked by flexible chains, specifically 1",7"-bis(4-cyanobiphenyl-4'-yl) heptane (CB7CB) provide compelling new insights into the molecular organization in the nematic (N) and twist-bend nematic (N$_{TB}$) phases. The electron density ($\rho$) of the liquid crystal molecule has customarily been assumed to be uniform rather than a function of distance, $\rho$(z) along the molecular axis. We introduce a functional model of the electron density using Gaussian distribution for different parts of the molecule. The observed diffraction peak at $d \sim$ 0.41$L$ ($L$, molecular length) expected to appear at $d \sim L$, is found to primarily arise from the form factor, F(q) = $| f(q) \rvert| ^2$ where $f(q)$ is the Fourier transform of $\rho$(z). Modeling the functional form of $\rho$(z) was verified in the N phase of different rod-like molecules, with and without intercalation. The results further suggest that there is no intercalation of the dimer molecules in the N and N$_{TB}$ phases.