Fragile-Strong Fluid Crossover and Universal Relaxation Times in a Confined Hard-Disk Fluid

We show that a system of hard disks confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adam-Gibbs relation does not predict the relaxation behavior. We also show that a facilitated dynamics description of the system, where kinetically excited regions are identified with local packing arrangements of the disks, successfully describes the fragile-strong crossover.

Figure 1

Local packing arrangements that can be combined to give collectively jammed states. Dashed lines connect the centers of neighboring disks in contact, and the numbers identify different “bonds.” Bonds 1 and 3 are the locally most dense states. Bonds 2 and 4 represent the defect states.

Figure 2

$C_p/Nk$ for different values of $H_d$ as a function of (a) $(\varphi PV/NkT{)}^{-1}$ and (b) $\theta$.

Figure 3

(a) Equilibrium $S_c$, (b) $P_{\mathrm{IS}}$, and (c) $P_{\mathrm{vib}}$ as a function of $\varphi$ for different values of $H_d$.

Figure 4

Arrhenius plot for the relaxation times for $H=1.866$. The dashed and dashed-dotted lines represent fits to the data in the fragile region of the parabolic and VFT equations, respectively. The solid line is the Arrhenius fit to the strong fluid region. Inset: Adam-Gibbs plot for $\tau$.

Figure 5

Master curve for the $C_p$ maximum rescaling of the relaxation times and temperatures for the Arrhenius plot (a) and the facilitated dynamics model (b). The solid lines represent linear fits to the strong fluid region.