Cooling the two-dimensional short spherocylinder liquid to the tetratic phase: Heterogeneous dynamics with one-way coupling between rotational and translational hopping

We numerically demonstrate the transition from the isotropic liquid to the tetratic phase with quasilong-range tetratic alignment order (i.e., with nearly parallel or perpendicular aligned rods), for the cold two-dimensional (2D) short spherocylinder system before crystallization and investigate the thermal assisted heterogeneous rotational and translational micromotions. Comparing with the 2D liquid of isotropic particles, spherocylinders introduce extra rotational degrees of freedom and destroy packing isotropy and the equivalence between rotational and translational motions. It is found that cooling leads to the stronger dynamical heterogeneity with more cooperative hopping and the stronger retardations of rotational hopping than translational hopping. Under topological constraints from nearly parallel and perpendicular rods of the tetratic phase, longitudinal and transverse translational hopping can occur without rotational hopping, but not the reverse. The empty space trailing a neighboring translational hopping patch is needed for triggering the patch rotational hopping with its translational motion into the empty space. It is the origin for the observed increasing separation of hopping time scales and the one-way coupling between rotational and translational hopping. Strips of longitudinally or transversely aligned rods can be ruptured and reconnected with neighboring strips through buckling, kink formation, and patch rotation, under the unbalanced torques or forces from their neighboring rods and thermal kicks.

Figure 1

(a) Typical rod packing configuration, color coded by $|S_4|$. (b) Color coded rod angle variation $\mathrm{\Delta }\theta$ over time interval $\tau$ = ${\tau }_{t,I}$ = 65 000 on the starting rod configuration. (c, d) Sequential snap shots of rod center trajectories over time interval ${\tau }_{t,I}$ on each starting rod configuration, showing the stick-slip cage rattling and avalanche cooperative TH. Panels (a) to (d) are from the TP run I at $T$ = 1.7. RH usually occurs within the region of TH. (e) to (h) Plots for the ILP of run II with poor alignment ordering and less cooperative hopping at $T$ = 10 and over time interval $\tau$ = ${\tau }_{t,II}$ = 300, with the same plotting methods and color codes as panels (a) to (d), respectively. Regions A to C in panels (a) to (d) are the typical regions in which particles exhibit translational TH, longitudinal TH, and TH with RH, respectively. The plotted rod width and length are 30% and 10% smaller than the actual scales for better viewing.

Figure 2

(a) Radial correlation functions $g_{4,r}$ of local tetratic order $S_4$, versus radial distance $r$, showing the transition to the tetratic phase with quasilong-range order following power law decay with decreasing $T$. (b, c) MSD = $\langle \mathrm{\Delta }{r}^2\rangle$, and $\mathrm{MSOV}=\langle \mathrm{\Delta }{\theta }^2\rangle$ vs $\tau$, respectively, at different $T$. The numbers by the gray straight lines are the scaling exponent $\alpha$. (d, e) Self-intermediate scattering function, $F(q,\tau )$, and the second order orientation temporal correlation function, $L_2\left(\tau \right)$, for characterizing rod translational and rotational motions, respectively, at different $T$.

Figure 3

(a) ${\tau }_t, {\tau }_r$ and $|\langle S_4\rangle |$ versus $1/T$. (b) Diffusivities $D_t$ and $D_r$ vs ${\tau }_t$. The numbers by the gray lines are the corresponding scaling exponents. (c) Temporal evolutions of the center radial position $\left|r\right(t)-r(0\left)\right|$ and orientation $\theta \left(t\right)-\theta \left(0\right)$ of typical rods from runs I and II, respectively.

Figure 4

Sequential plots with vector length corresponding to $\delta r$ over ${\tau }_{t,I}$/2, on top of each starting rod configuration for the tetratic phase run I at $T$ = 1.7. Rods can exhibit TH without rotation. Rod rotation can be achieved by the rotation of a small patch with 2 to 4 aligned rods, associated with the translational motion into the empty space left by the neighboring patch with TH.

Figure 5

(a,b) Joint probability distributions $P(\mathrm{\Delta }r,\mathrm{\Delta }\theta )$ over interval ${\tau }_{t,I}$ and ${\tau }_{t,II}$ for runs I and II, respectively. Unlike the isotropic distribution at high $T$ showing the weak correlation between TH and RH, the band like structure at $T$ = 1.7 indicates that TH can be excited without RH, but not the reverse. It leads to the higher TH rate than the RH rate.