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Dynamics of thermal vibrational motions and stringlike jump motions in three-dimensional glass-forming liquids
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10.1063/1.4770337
/content/aip/journal/jcp/138/12/10.1063/1.4770337
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4770337

Figures

Image of FIG. 1.
FIG. 1.

Fractions of the particles with n b bonds p 1(n b ) and p 2(n b ) for the species 1 and 2 at T = 0.24.

Image of FIG. 2.
FIG. 2.

Fractions of the B and BL particles, ϕ b (t) and , respectively, together with 1 − F b (t) and 1 − F s (t) on a double logarithmic scale for T = 0.24. Here, for t ≲ 103 and for t ≳ 103. From F b b ) = e −1 and F s α) = e −1, we have τ b = 2.7 × 105 and τα = 1.1 × 105.

Image of FIG. 3.
FIG. 3.

Typical time-smoothed vibration lengths S i (t) in Eq.(4.4) in time interval [t 0, t 0 + 500] for three non- B particles without bond breakage, where Δt = 40 (left) and 100 (right) for T = 0.24 (top) and T = 0.20 (bottom).

Image of FIG. 4.
FIG. 4.

(a) Particles with vibration length S i (t 0) in Eq. (4.4) exceeding 0.16 at a time t 0 for T = 0.24, where those with 0.16 < S i (t 0) < 0.25 have colors according to the color bar and those with S i (t 0) > 0.25 are written in red. Arrows represent the displacements of the BL particles. (b) BL particles in the same run, which are determined in one of ten time intervals [t k , t k + 1] with t k = t 0 + k × 103 (0 ⩽ k ⩽ 9) and . At jump time , they undergo large displacements (>0.8). Their colors represent according to the color bar. Arrows represents .

Image of FIG. 5.
FIG. 5.

Displacement vectors of the BL particles for T = 0.24. Data are the same as in Fig. 4 . Colors represent (red for ).

Image of FIG. 6.
FIG. 6.

Snapshots of S i (t) exceeding 0.16 at (a) t = t 0 + 104, (b) t = t 0 + 5 × 104, (c) t = t 0 + 105, and (d) t = t 0 + 2 × 105, where T = 0.24. Snapshot of S i (t 0) is given in Fig. 7(a) . Arrows are displacement vectors . These four snapshots are taken consecutively in the same run, indicating slow time-evolution of the mesoscopic vibrational heterogeneity.

Image of FIG. 7.
FIG. 7.

Structure factor S vi(q) for the vibration amplitude in Eq. (4.7) (left) and structure factor S b (q, t) for bond breakage in Eq.(4.8) with t = 104 and 2 × 104 (right) for T = 0.24. Solid curves represent the Ornstein-Zernike fitting.

Image of FIG. 8.
FIG. 8.

(a) Distributions P 1(S) and P 2(S) of the thermal vibration length S i (t) for the small and large particles in Eq. (4.9) on a semilogarithmic scale for T = 0.24. The small particles are more mobile than the larger ones. (b) Distribution P 1(S, n b ) in Eq. (4.11) for n b = 9, 10, 11, and 12 on a semilogarithmic scale for T = 0.24.

Image of FIG. 9.
FIG. 9.

Distribution P(S) = P 1(S) + P 2(S) for the thermal vibration length S i (t) (upper curve) and conditional probability distribution in Eq. (4.14) at t = 104 (lower curve) on a semi-logarithmic scale, where T = 0.24. Inset gives P(S) on a linear scale. Here, approaches P(S) for S ≳ 0.2, indicating close correlation between structure and slow dynamics.

Image of FIG. 10.
FIG. 10.

(a) Surviving fraction vs t for the particles with and S i (t 0) > λ in Eq. (4.17) for various λ at T = 0.24. Here, is the conditional probability of undergoing stringlike motions for particles with S i (t 0) > λ, so (see Fig. 2 ). (b) Surviving fraction of the particles with and in Eq. (4.18) as functions of t for T = 0.24.

Image of FIG. 11.
FIG. 11.

Fraction of the B L particles at time t 0 + t with initial S i (t 0) larger than λ. For λ = 0, it becomes the fraction of the total BL particles in Fig. 2 .

Tables

Generic image for table
Table I.

Numbers of particles with S i (t 0) > λ and S i (t 1) > λ with λ = 0.16 or 0.20 in the same run, where t 1t 0 = 102, 103, 104, 5 × 104, 105, and 2 × 105. The initial particle numbers with S i (t 0) > λ is 1207 for λ = 0.16 and 274 for λ = 0.20 in Fig. 4(a) . See Fig. 6 for the subsequent particle configurations at the later four times.

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/content/aip/journal/jcp/138/12/10.1063/1.4770337
2013-01-03
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamics of thermal vibrational motions and stringlike jump motions in three-dimensional glass-forming liquids
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4770337
10.1063/1.4770337
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