From $n$-layer planar ordering to the monolayer homeotropic structure of confined hard rods: The effect of shape anisotropy and wall-to-wall separation

Using the Parsons-Lee theory, we examined the effect of shape anisotropy and the wall-to-wall separation (H) on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D ($L>D$) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range $2.5D\le H\le 10.0D$ for $H-D\le L<H$.

Figure 1

Schematic diagram of the phase transitions of the particles by increasing η for $H/D=4.5$ and $L/D=4.30$.

Figure 2

(a) The coexisting packing fractions versus $L/D$ for $H/D=4.5$, (b)–(e) the density profiles of the different phases versus z* for $L/D=4.10$ marked by different symbols in (a). These phases are (b) planar isotropic with three layers (3IL) at $\eta =0.300$, (c) biaxial planar nematic with three layers (3BPL) at $\eta =0.450$, (d) biaxial planar nematic with four layers (4BPL) at $\eta =0.550$, and (e) homeotropic (H) at $\eta =0.750$.

Figure 3

(a) The coexisting packing fractions versus $L/D$ for $H/D=6.0$, (b)–(e) the density profiles of different phases versus z* for $L/D=5.40$ marked by different symbols in (a). These phases are (b) planar isotropic with four layers (4IL) at $\eta =0.200$, (c) biaxial planar nematic with four layers (4BPL) at $\eta =0.400$, (d) biaxial planar nematic with five layers (5BPL) at $\eta =0.500,$ and (e) homeotropic (H) at $\eta =0.750$.

Figure 4

The phase structures of confined hard rods for $H/D=8.0$, (a) The coexisting packing fractions versus $L/D$, (b)–(e) the density profiles of different phases versus z* for $L/D=7.20$ marked by different symbols in (a). These phases are (b) planar isotropic with six layers (6IL) at $\eta =0.140$. The inset shows part of in-plane density profiles, and it depicts the number of planar layers clearly, (c) biaxial planar nematic with six layers (6BPL) at $\eta =0.550$, (d) biaxial planar nematic with seven layers (7BPL) at $\eta =0.600$, and (e) homeotropic (H) at $\eta =0.750$.

Figure 5

The phase structures of confined hard rods for $H/D=10.0$ (a) The coexisting packing fractions versus $L/D$, (b)–(f) the density profiles of different phases versus z* for $L/D=9.25$ marked by different symbols in (a). These phases are (b) planar isotropic with seven layers (7IL) at $\eta =0.090$. The inset shows part of in-plane density profiles, and it depicts the number of planar layers clearly, (c) biaxial planar nematic with seven layers (7BPL) at $\eta =0.300$, (d) biaxial planar nematic with eight layers (8BPL) at $\eta =0.470$, (e) biaxial planar nematic with nine layers (9BPL) at $\eta =0.670$, and (f) homeotropic (H) at $\eta =0.780$.

Figure 6

The phase structures of confined hard rods for (a) $H/D=3.3$, (b) $H/D=3.5$. (c)–(f) The density profiles of different phases of $H/D=3.3$ versus z* marked by different symbols in (a). These phases are (c) planar isotropic with two layers (2IL) at $\eta =0.400$ and $L/D=3.15$, (d) biaxial planar nematic with two layers (2BPL) at $\eta =0.440$ and $L/D=3.15$, (e) planar isotropic with three layers (3IL) at $\eta =0.500$ and $L/D=2.95$, and (f) biaxial planar nematic with three layers (3BPL) at $\eta =0.530$ and $L/D=2.95$.

Figure 7

The phase transitions of confined hard rods for (a) $H/D=2.7$ with the density profiles of the planar isotropic (in the inset) with two layers (2IL) at $\eta =0.600$ and $L/D=2.20$ and (b) $H/D=2.9$ with the density profiles of the planar isotropic (in the inset) with two layers (2IL) at $\eta =0.560$ and $L/D=2.30$.

Figure 8

(a) The critical packing fractions (b) the critical aspect ratios of the nBPL-H transitions and (c) the minimum coexisting packing fractions in nBPL-H transitions versus wall-to-wall separation. The hollow circles are related to Ref. [27] and other symbols are related to our calculations.