Bilayers in nanoparticle-doped polar mesogens

Structures of the mesophases of five members of the 4-$n$-alkyl-4′-cyanobiphenyl homologous series (4-$n$-butyl-4′-cyanobiphenyl to 4-$n$-octyl-4′-cyanobiphenyl) doped with milled BaTiO${}_3$ nanoparticles were investigated by x-ray scattering. Clear solutions of each of the 4-$n$-alkyl-4′-cyanobiphenyls were first prepared in $n$-heptane and then doped with an $n$-heptane/nanoparticle dispersion, which led to gelation. The nanogels were found to be one-dimensional, multilayered, smectic nanostructures in each case. Surprisingly, a characteristic layer spacing of 4.5 nm was observed in all five homologues. Synchrotron x-ray scattering study of the multilayer structures of doped 4-$n$-pentyl-4′-cyanobiphenyl and 4-$n$-octyl-4′-cyanobiphenyl revealed nine orders of the primary Bragg reflection which were used to calculate the electron density profiles of the multilayers by Fourier analysis. The multilayers were found to consist of molecular bilayers wherein the mesogens were arranged in a head-to-head assembly of the polar head groups. The alkyl tails of the mesogenic molecules were freely movable and the tail-to-tail assembly was stabilized by heptane. The dissolved nanoparticles clearly induced a new self-assembled nanostructure in which the rigid aromatic part, and not the overall length, of the molecules defined the layer spacing.

Figure 1

The final weight of doped LC, for both 5CB (open symbols) and 8CB (filled symbols), is shown against the initial quantity of nanoparticles. Centrifugation of nanoparticle/$n$-heptane/LC gels and subsequent evaporation of $n$-heptane yielded (sedimented) doped LC (upside-down triangles) and a recovery of neat LC (triangles).

Figure 2

Scattering profiles of gel samples of 4CB, 5CB, 6CB, and 7CB LCs. The inset shows the central region of the 2D scattering pattern in the 7CB-gel sample. The scattering pattern of 7CB is oriented: An intensity vs azimuthal angle scan is shown to quantify the orientation of the scattering pattern. The dashed secant is a guide to the eye and indicates the orientation of the scattering pattern; the orientation of the molecular long axis is perpendicular to it.

Figure 3

Central regions of the two-dimensional diffraction patterns of (a) doped 5CB at 30 °C, (b) doped 5CB at 50 °C, (c) doped 8CB at 30 °C, and (d) doped 8CB at 50 °C. Dashed lines, drawn as a guide to the eye, indicate the orientation of the diffraction patterns and are perpendicular to the preferred orientation of the molecular long axis. The white arrows indicate the position of the Sm$A_d$ peak seen at 30 °C in (c) but absent at 50 °C in (d).

Figure 4

Azimuthal angle χ scans of the first-order diffraction rings at different temperatures in doped 5CB (black dashed lines) and doped 8CB (solid black lines). Additionally, the χ scan (solid gray line) of the Sm$A_d$ peak observed for doped 8CB at 30 °C is shown.

Figure 5

Intensity vs scattering vector plots for doped 5CB (black line) almost overlap with that of the doped 8CB (gray line) at 30 °C. Nine orders of the primary diffraction peak corresponding to 4.65 nm are indicated by numbers 1 to 9. The scattering arising from transverse short-range correlations among LC molecules is indicated by the horizontal double arrow. The composite peak corresponding to the (1 1 0) and (1 0 1) reflections of BaTiO${}_3$ nanoparticles is indicated by the arrow. The inset shows x-ray scattering in the small-angle region on a magnified scale.

Figure 6

Schematic scattering intensities of nine multiples of the $d$ ≈ 4.65 nm Bragg peak observed in doped 5CB and doped 8CB (black lines) and the residual LC (gray lines) present in doped 5CB (neat nematic phase) and doped 8CB (neat Sm$A_d$ phase) at 30 °C.

Figure 7

Model of 5CB and characteristic length scales of the cyanobiphenyl group and the 4′-benzylic methylene group of the alkyl chain.

Figure 8

Molecular model of 5CB and 8CB superimposed on plots of the relative electron density vs layer spacing. Only one-half of the symmetric bilayer is shown.

Figure 9

Plot of the relative electron density in the direction perpendicular to the smectic layers. Since the relative electron density distribution corresponds to the average distribution in the coherent scattering volume, more than two molecules have to be considered to describe the molecular arrangement in smectic layers. Molecular models of eight 5CB molecules and two $n$-heptane molecules are schematically shown to illustrate molecular arrangement in the smectic bilayer.

Figure 10

Two-dimensional schematic of the structure inside a small volume of a nanoparticle-doped sample. Three polar nanoparticles (gradient filled) and five nonpolar nanoparticles (uniformly filled) are shown. A surface layer of 4-$n$-alkyl-4′-cyanobiphenyl molecules is grafted to the surface of the inorganic nanoparticles. The black lines indicate the interfaces of the soft bilayers that form multishells.