Confinement Induced Plastic Crystal-to-Crystal Transitions in Rodlike Particles with Long-Ranged Repulsion

Colloidal particles in geometrical confinement display a complex variety of packing structures different from their three-dimensional (3D) bulk counterpart. Here, we confined charged rodlike colloids with long-ranged repulsions to a thin wedge-shaped cell and show, by quantitative 3D confocal microscopy, that not only their positional but also their orientational order depends sensitively upon the slit width. Synchronized with transitions in lattice symmetry and number of layers confinement induces plastic crystal-to-crystal transitions. A model analysis suggests that this complex sequence of more or less rotationally ordered states originates from the subtle competition between the electrostatic repulsion of a rod with the wall and with its neighbors.

Figure 1

Crystalline structures formed by charged rods in confinement. Slit widths are (a) $8.84\mu \mathrm{m}$, (b) $14.89\mu \mathrm{m}$, (c) $15.13\mu \mathrm{m}$, (d) $16.91\mu \mathrm{m}$, (e) $17.68\mu \mathrm{m}$, (f) $24.04\mu \mathrm{m}$, (g) $24.44\mu \mathrm{m}$, (h) $26.99\mu \mathrm{m}$, and (i) $30.56\mu \mathrm{m}$. Insets show the lattice parameters. The 3-digit symbols characterizing each structure consist of the number of layers, lattice symmetry, and an index number. The uncertainty in angle measurement is estimated to be $\pm 1°$. The scale bar applies to Figs (a)–(i).

Figure 2

Transitions in crystal lattice versus slit width $d$. (a) Crystal layer positions relative to the walls and 2D bond orientational order parameters ${\psi }_4$ and ${\psi }_6$. (b) 2D Pair correlation functions $g(r)$ in the bilayer region. △, ⋄, and □ denote layers with hexagonal, rhombic, and square symmetry, respectively.

Figure 3

Orientational probability density functions (PDFs) and correlation functions. (a),(b) The distribution of the $z$ component of rods’ orientations $u_z$ in the monolayer (a) and bilayer (b) region. $S$ is the corresponding value of the orientational order parameter. Insets show trajectories that the orientation vector of a single rod traces out on the unit sphere. (c) Spatial orientational correlation function [$g_2(r)$, black, left axis] and positional pair correlation function [$g(r)$, brown, right axis] of rods for sample $1△1$. (d) Time-dependent orientational autocorrelation functions $C_2(t)$ of rods in the monolayer region. Bars indicate the statistical standard error. Symbols △, ⋄, and □ denote layers with hexagonal, rhombic, and square symmetry, respectively.

Figure 4

Average potential energy $U_s$ of a rod in a one-layer hexagonal lattice confined to a slit as a function of slit width $d$. (a) Comparison of $U_s$ between rods with different orientational distributions as measured on the systems indicated. (b)–(d) Close-ups of regions 1 (b), 2 (c), and 3 (d).