^{1}, Zhao-Yan Sun

^{1,a)}and Li-Jia An

^{1}

### Abstract

By using event-driven molecular dynamics simulation, we investigate effects of varying the area fraction of the smaller component on structure, compressibility factor, and dynamics of the highly size-asymmetric binary hard-disk liquids. We find that the static pair correlations of the large disks are only weakly perturbed by adding small disks. The higher-order static correlations of the large disks, by contrast, can be strongly affected. Accordingly, the static correlation length deduced from the bond-orientation correlation functions first decreases significantly and then tends to reach a plateau as the area fraction of the small disks increases. The compressibility factor of the system first decreases and then increases upon increasing the area fraction of the small disks and separating different contributions to it allows to rationalize this non-monotonic phenomenon. Furthermore, adding small disks can influence dynamics of the system in quantitative and qualitative ways. For the large disks, the structural relaxation time increases monotonically with increasing the area fraction of the small disks at low and moderate area fractions of the large disks. In particular, “reentrant” behavior appears at sufficiently high area fractions of the large disks, strongly resembling the reentrant glass transition in short-ranged attractive colloids and the inverted glass transition in binary hard spheres with large size disparity. By tuning the area fraction of the small disks, relaxation process for the small disks shows concave-to-convex crossover and logarithmic decay behavior, as found in other binary mixtures with large size disparity. Moreover, diffusion of both species is suppressed by adding small disks. Long-time diffusion for the small disks shows power-law-like behavior at sufficiently high area fractions of the small disks, which implies precursors of a glass transition for the large disks and a localization transition for the small disks. Therefore, our results demonstrate the generic dynamic features in highly size-asymmetric binary mixtures.

We appreciate the fruitful discussions with Professor D. Frenkel, Professor Z.-G. Wang, Professor M. Miller, Professor M. Dijkstra, and Dr. Th. Voigtmann. W.S.X. would like to show special thanks to Professor Z.-G. Wang, Professor D. Frenkel, and Professor M. Miller for their face-to-face discussions when they were in a KITPC conference on complex fluids, held in July of 2011 in Beijing. This work is subsidized by the National Basic Research Program of China (973 Program, 2012CB821500), and supported by the National Natural Science Foundation of China (NNSFC) (21074137, 21222407, and 50930001) programs and the fund for Creative Research Groups (50921062).

I. INTRODUCTION

II. MODEL AND METHODS

III. RESULTS AND DISCUSSION

A. Glass transition in the absence of small disks

B. Influence of small disks on the structure of the large disks

C. Compressibility factor of highly asymmetric binary hard disks

D. Dynamics of highly asymmetric binary hard disks

IV. CONCLUSIONS

### Key Topics

- Glass transitions
- 37.0
- Diffusion
- 14.0
- Molecular dynamics
- 6.0
- Correlation functions
- 5.0
- Crystallization
- 5.0

##### B01J13/00

## Figures

(a) The pair correlation function *g* _{ l }(*r*) and (b) the static structure factor *S* _{ l }(*q*) at low-*q* region at varying ϕ_{ l } for ϕ_{ s } = 0.

(a) The pair correlation function *g* _{ l }(*r*) and (b) the static structure factor *S* _{ l }(*q*) at low-*q* region at varying ϕ_{ l } for ϕ_{ s } = 0.

(a) The self-intermediate scattering function at varying ϕ_{ l } for ϕ_{ s } = 0. (b) ϕ_{ l } dependence of α-relaxation time τ_{α} at ϕ_{ s } = 0. The red solid line is the result of the MCT power-law fitting τ_{α} ∼ (ϕ_{ c } − ϕ_{ l })^{−γ} with γ = 3.8 and ϕ_{ c } = 0.791. The green dashed line is the result of the Vogel-Fulcher-Tamman fitting with *D* = 0.28 and ϕ_{ c } = 0.805.

(a) The self-intermediate scattering function at varying ϕ_{ l } for ϕ_{ s } = 0. (b) ϕ_{ l } dependence of α-relaxation time τ_{α} at ϕ_{ s } = 0. The red solid line is the result of the MCT power-law fitting τ_{α} ∼ (ϕ_{ c } − ϕ_{ l })^{−γ} with γ = 3.8 and ϕ_{ c } = 0.791. The green dashed line is the result of the Vogel-Fulcher-Tamman fitting with *D* = 0.28 and ϕ_{ c } = 0.805.

(a) The pair correlation function *g* _{ l }(*r*) and (b) the bond-orientation correlation function *g* _{6}(*r*) at varying ϕ_{ s } for δ = 0.2 and ϕ_{ l } = 0.784.

(a) The pair correlation function *g* _{ l }(*r*) and (b) the bond-orientation correlation function *g* _{6}(*r*) at varying ϕ_{ s } for δ = 0.2 and ϕ_{ l } = 0.784.

ϕ_{ s } dependence of static correlation length ξ_{6} at δ = 0.2 and ϕ_{ l } = 0.784. ξ_{6} is obtained by fitting *g* _{6}(*r*)/*g*(*r*) with the OZ function (see text). The solid line is a guide for the eyes.

ϕ_{ s } dependence of static correlation length ξ_{6} at δ = 0.2 and ϕ_{ l } = 0.784. ξ_{6} is obtained by fitting *g* _{6}(*r*)/*g*(*r*) with the OZ function (see text). The solid line is a guide for the eyes.

Main: ϕ_{ s } dependence of the compressibility factor *Z* at varying ϕ_{ l } for δ = 0.2. Inset: effect of δ on *Z* at ϕ_{ l } = 0.784.

Main: ϕ_{ s } dependence of the compressibility factor *Z* at varying ϕ_{ l } for δ = 0.2. Inset: effect of δ on *Z* at ϕ_{ l } = 0.784.

Different contributions to the total *Z* for δ = 0.2 at several ϕ_{ l } values. s-s, s-l, and l-l indicate contributions from small-small, small-large, and large-large particle collisions, respectively. The zoom in the inset highlights the contribution from the small-small particle collision. The results are similar for δ = 0.15.

Different contributions to the total *Z* for δ = 0.2 at several ϕ_{ l } values. s-s, s-l, and l-l indicate contributions from small-small, small-large, and large-large particle collisions, respectively. The zoom in the inset highlights the contribution from the small-small particle collision. The results are similar for δ = 0.15.

Particle trajectories during a time interval of τ_{ l } at δ = 0.2 and ϕ_{ l } = 0.784 for ϕ_{ s } = 0.01 ((a), (d)), ϕ_{ s } = 0.03 ((b), (e)) and ϕ_{ s } = 0.05 ((c), (f)). (a), (b), (c) are for large disks and (d), (e), (f)) for small disks, respectively.

Particle trajectories during a time interval of τ_{ l } at δ = 0.2 and ϕ_{ l } = 0.784 for ϕ_{ s } = 0.01 ((a), (d)), ϕ_{ s } = 0.03 ((b), (e)) and ϕ_{ s } = 0.05 ((c), (f)). (a), (b), (c) are for large disks and (d), (e), (f)) for small disks, respectively.

ϕ_{ s } evolution of the self-intermediate scattering functions of the large disks at δ = 0.2 for (a) ϕ_{ l } = 0.77 and (b) ϕ_{ l } = 0.784. Here, *q* _{ p } corresponds to the first peak of *S* _{ l }(*q*) for ϕ_{ s } = 0. The results are similar for δ = 0.15.

ϕ_{ s } evolution of the self-intermediate scattering functions of the large disks at δ = 0.2 for (a) ϕ_{ l } = 0.77 and (b) ϕ_{ l } = 0.784. Here, *q* _{ p } corresponds to the first peak of *S* _{ l }(*q*) for ϕ_{ s } = 0. The results are similar for δ = 0.15.

ϕ_{ s } evolution of the self-intermediate scattering functions of the small diks at δ = 0.2 for (a) ϕ_{ l } = 0.77 and (b) ϕ_{ l } = 0.784. Here, *q* _{ p } corresponds to the first peak of *S* _{ l }(*q*) for ϕ_{ s } = 0. The green dashed lines highlight the logarithmic decay of . The results are similar for δ = 0.15.

ϕ_{ s } evolution of the self-intermediate scattering functions of the small diks at δ = 0.2 for (a) ϕ_{ l } = 0.77 and (b) ϕ_{ l } = 0.784. Here, *q* _{ p } corresponds to the first peak of *S* _{ l }(*q*) for ϕ_{ s } = 0. The green dashed lines highlight the logarithmic decay of . The results are similar for δ = 0.15.

Main: ϕ_{ s } evolution of relaxation times at δ = 0.2 for (a) large and (b) small disks. Inset: effect of δ on relaxation times.

Main: ϕ_{ s } evolution of relaxation times at δ = 0.2 for (a) large and (b) small disks. Inset: effect of δ on relaxation times.

ϕ_{ s } evolution of the mean squared displacements at ϕ_{ l } = 0.784 and δ = 0.2 for (a) large and (b) small disks.

ϕ_{ s } evolution of the mean squared displacements at ϕ_{ l } = 0.784 and δ = 0.2 for (a) large and (b) small disks.

The mean squared displacements of large (dotted lines) and small (solid lines) disks at varying ϕ_{ l } and ϕ_{ s } = 0.06 for (a) δ = 0.2 and (b) δ = 0.15.

The mean squared displacements of large (dotted lines) and small (solid lines) disks at varying ϕ_{ l } and ϕ_{ s } = 0.06 for (a) δ = 0.2 and (b) δ = 0.15.

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