Plastic Crystal-to-Crystal Transition of Janus Particles under Shear

Colloidal Janus spheres in the bulk typically spontaneously assemble into plastic crystalline phases, while particle orientations exhibit glasslike dynamics without long-range order. Through Brownian dynamics simulations, we demonstrate that shear can trigger a phase transition from an isotropic crystal with orientational disorder to an orientationally ordered crystal with lamellae along the shear direction. This nonequilibrium transition is accompanied with the orientational ordering following a nucleation and growth mechanism. By performing a phenomenological extension of free energy analysis, we reveal that the nucleation originates from the orientation fluctuations induced by shear. The growth of the orientationally crystalline cluster is examined to be disklike, captured by developing a lattice model with memoryless state functions. These findings bring new insights into the mechanisms for the ordering transition of anisotropic particles at nonequilibrium states.

Figure 1

(a) Schematic diagrams of the Janus-particle model (top) and the angular dependence $w(\theta )$ (bottom). (b) Representative snapshot of the initial state. (c) The snapshot of the shear-induced orientational crystal. (d) Radial distribution function for particle locations in (c). (e)–(f) Probability distributions of $U_z$ for phases in (b) and (c), respectively.

Figure 2

(a) Time evolutions of $⟨P_2⟩$ for systems with various $\alpha$ at $\dot{\gamma }=0.2{\tau }^{-1}$. (b) Representative local structures of systems under shear where $\alpha =65°$ (top), 105° (middle), and 150° (bottom), respectively. (c)–(e) Time dependences of $U_z$ for a single particle with $\alpha =105°$ under shear, where $\dot{\gamma }=0$ (c), $0.2{\tau }^{-1}$ (d), and $0.6{\tau }^{-1}$ (e), respectively. (f) Left: heatmap of $⟨P_2⟩$ on the $\dot{\gamma }-\alpha$ space. Right: the plot of $Q$ vs $\dot{\gamma }$.

Figure 3

(a) $f$ for both plastic and crystalline phases when $\epsilon =7k_{B}T$. The double sided arrow denotes the definition of $\mathrm{\Delta }{f}^{eq}$. (b) Phase diagram on the $\epsilon -\alpha$ space. (c) Heatmap of $N_c$ on the $\dot{\gamma }-\alpha$ space predicted by Eq. (4). The blue and red dashed lines are the contour lines for $N_c=8$ and 11, respectively. The blue crosses in (b) and (c) represent the systems where $⟨P_2⟩>0.5$. (d) The shear-rate dependence of $\zeta$ for $\alpha =105°$, 110°, and 115° respectively. The solid lines are theoretical predictions obtained by Eq. (5).

Figure 4

(a) Representative snapshots of the system with $\alpha =105°$ and $\dot{\gamma }=0.2{\tau }^{-1}$ at $t=10\tau$ (${\mathrm{a}}_1$), $200\tau$ (${\mathrm{a}}_2$), $400\tau$ (${\mathrm{a}}_3$), and $600\tau$ (${\mathrm{a}}_4$) respectively. (b) Schematic diagram of calculating the heatmap of $\widehat{\rho }$ on the $xz$ plane. (c) The heatmaps of $\widehat{\rho }$ in simulations. (d) The heatmaps of $\widehat{\rho }$ reproduced by the lattice model. Times of snapshots in (c) and (d) are the same with those in (a). (e) Time dependences of $\widehat{N}$ for $p=0.006$ and 0.010 (lattice model). The confidence intervals of $\widehat{N}$ in simulations for $\dot{\gamma }=0.10$ and $0.20{\tau }^{-1}$ ($\alpha =105°$) are also given. (f) The plot of $p$ vs $\dot{\gamma }$ when $\alpha =105°$.