Orientationally Glassy Crystals of Janus Spheres

Shan Jiang, Jing Yan, Jonathan K. Whitmer, Stephen M. Anthony, Erik Luijten, and Steve Granick

Phys. Rev. Lett. 112, 218301 – Published 27 May 2014

Abstract

Colloidal Janus spheres in water (one hemisphere attractive and the other repulsive) assemble into two-dimensional hexagonal crystals with orientational order controlled by anisotropic interactions. We exploit the decoupled translational and rotational order to quantify the orientational dynamics. Via imaging experiments and Monte Carlo simulations we demonstrate that the correlations in the orientation of individual Janus spheres exhibit glasslike dynamics that can be controlled via the ionic strength. Thus, these colloidal building blocks provide a particularly suitable model glass system for elucidating nontrivial dynamics arising from directional interactions, not captured by the consideration of just translational order.

Received 28 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.218301

Authors & Affiliations

Shan Jiang¹, Jing Yan¹, Jonathan K. Whitmer^1,2,4, Stephen M. Anthony³, Erik Luijten^4,5,*, and Steve Granick^1,2,3,†

¹Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
²Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
³Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
⁴Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
⁵Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA

^*Corresponding author. luijten@northwestern.edu
^†Corresponding author. sgranick@illinois.edu

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Vol. 112, Iss. 21 — 30 May 2014

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Images

Figure 1
(a) Schematic representation of the experiment. Particles sediment onto a slightly tilted ( $\sim 1 °$ ) sample cell such that multilayers form at the lower end and a dilute phase at the other end, with an extended region of close-packed monolayer in between. (b) Schematic representation of how the interactions between these Janus particles depend on their mutual orientation. (c) Representative optical image of a Janus monolayer at 2 mM NaCl. Black regions are hydrophobic hemispheres on silica, white regions are bare silica. Scale bar: $4 μ m$ . Inset: Fourier transform of the optical image. The sixfold symmetry between the two concentric rings reflects hexagonal positional order. (d) Schematic representation of the emergence of ordered structures as the particles maximize hydrophobic contacts.
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Figure 2
Static correlations. (a) Static angular correlation $G (r) = ⟨ \hat{n} (0) \cdot \hat{n} (r) ⟩$ in the presence of 2 mM NaCl; the intensity scale, denoted in shades of gray, is shown on the right. Inset shows the definition of $\hat{n}$ . (b) Radially averaged correlation $G (r)$ plotted as a function of distance at different salt concentrations (from bottom to top: 1.00, 1.25, 1.50, 1.75, and 2.00 mM NaCl). Inset: correlation length $ξ$ extracted from the positive peaks of $G (r)$ , plotted as a function of salt concentration in units of mM. Length scales are normalized by the lattice constant $a$ at each salt concentration.
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Figure 3
Local dynamics. (a) Single-particle angular autocorrelation function $C (t)$ and mean square angular displacement (MSAD) versus time in experimental samples at 2 mM NaCl. Units are degrees for angle and seconds for time. Overlaid on $C (t)$ is a stretched exponential fit with $\exp (- {(t / τ)}^{β})$ . (b) Relaxation time $τ$ and stretching parameter $β$ as a function of salt concentration. (c) MSAD versus time from simulations at various $d / λ$ (from bottom to top: 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 3.5), in which $d$ is the surface-to-surface separation and $λ$ the range of the hydrophobic interaction. Time is in units of Monte Carlo sweeps and angles are measured in degrees. Solid line segments in panels (a) and (b) indicate a slope of 1. (d) $τ$ and $β$ determined from simulation as a function of ${(λ / d)}^{2}$ .
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Figure 4
Orientation dynamics in various microenvironments. The experimental correlation function $C (t)$ is plotted for (a) 1.50 mM NaCl and (b) 2.00 mM NaCl for different local environments (characterized by the number of attractive contacts) shown schematically on the right. The magenta curve represents the ensemble-averaged dynamics. The percentages indicate the relative occurrence of the different microenvironments.
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Figure 5
Hierarchical dynamics. (a) Representative angular trajectories of three neighboring particles, showing their dynamic correlation during large angular jumps. The angle refers to the orientation of the director of the particle (pointing from the silica side to the coated side) with respect to the reference axis (horizontal black arrow). At the time indicated by the dashed vertical line, the center (black) particle switches partners and afterwards points its hydrophobic side towards the blue particle instead of the red one. (b) Excess joint probability distribution $P (Δ θ_{1}, Δ θ_{2}, Δ t) - P (Δ θ_{1}, Δ t) P (Δ θ_{2}, Δ t)$ for neighboring particles at $Δ t = 1 \min$ at $2 mM$ NaCl. Positive values along the $x = - y$ axis indicate the anticorrelated motion of neighboring particles. The bin size is 10 deg in each direction. (c) Excess joint probability distribution in simulation with $d / λ = 1$ at $Δ t = 10 000$ Monte Carlo sweeps. The bin size is 6 deg in each direction. (d) Example of interchain dynamics. Two parallel chains (first panel, $t = 0 s$ ) transition to a $Z$ -shaped chain flanked by two short chains (center panel, $t = 7 s$ ), which then breaks into an $L$ -shaped chain and a short chain near the top (right panel, $t = 98 s$ ). Scale bar: $2 μ m$ .
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