Biaxial layering transition of hard rodlike particles in narrow slitlike pores

The phase behavior of hard rectangular rods with edge lengths $L$, $D$, and $D$ is studied in a narrow slitlike pore using the Parsons-Lee density functional theory. Using the restricted orientation approximation, we find strong adsorption at the walls with planar ordering, second order uniaxial-biaxial ordering transitions, and first order layering transitions. The layering transition takes place between two fluids having $n$ and $n+1$ layers, where the layer spacing is on the order of $D$. In the case of weak shape anisotropy ($L/D=3$), the coexisting fluids can be either uniaxial or biaxial, while both phases are found to be biaxial for $L/D=6$ and $L/D=9$. Interestingly, even two or more layering transitions can be observed with increasing density at a given shape anisotropy and pore width.

Figure 1

Phase diagram and observed phases of confined hard parallelepipeds of square cross section with $L/D=3$. The coexisting packing fractions as a function of wall-to-wall distance (a) and the density profiles of different phases from (b) to (e) are shown. The observed phases are isotropic with planar adsorption at the walls ($I$), surface induced biaxial nematic ($\mathrm{B}N$), three-layer isotropic ($3\mathrm{L}I$), and three-layer biaxial nematic ($3\mathrm{LB}N$). The locations of the density profiles of (b–e) are marked by different symbols in the phase diagram. The dotted curve comes from the condition of ${\rho }_x\left(z=H/2\right)={\rho }_z\left(z=H/2\right)$. The biphasic region is shaded in green (patterned with vertical lines).

Figure 2

Phase diagram and observed phases of confined hard parallelepipeds of square cross section with $L/D=6$. The coexisting packing fractions as a function of wall-to-wall distance (a) and the density profiles of biaxial phases with four (b) and five layers (c) are shown. The observed phases are the isotropic with planar adsorption at the walls with four or five planar layers ($4\mathrm{L}I$ and $5\mathrm{L}I$) and surface induced biaxial nematic with four to six planar layers ($4\mathrm{LB}N$, $5\mathrm{LB}N$, and $6\mathrm{LB}N$). The locations of the density profiles of (b,c) are marked by different symbols in the phase diagram. The dotted curve comes from the condition of ${\rho }_x\left(z=H/2\right)={\rho }_x\left(z=H/2-\mathrm{\Delta }z\right)$. The biphasic regions are shaded with different colors and different patterns.

Figure 3

Phase diagram and observed phases of confined hard parallelepipeds of square cross section with $L/D=9$. The coexisting packing fractions as a function of wall-to-wall distance (a) and the density profiles of some phases (b,c) are shown. The observed phases are isotropic with planar adsorption at the walls with six or seven planar layers ($6\mathrm{L}I$ and $7\mathrm{L}I$) and surface induced biaxial nematic from six to nine planar layers ($6\mathrm{LB}N$, $7\mathrm{LB}N$, $8\mathrm{LB}N$, and $9\mathrm{LB}N$). The locations of the density profiles of (b,c) are marked by different symbols in the phase diagram. The dotted curve comes from the condition of ${\rho }_x\left(z=H/2\right)={\rho }_x\left(z=H/2-\mathrm{\Delta }z\right)$. The biphasic regions are shaded with different colors and also with different patterns.