Slow dynamics of supercooled colloidal fluids: spatial heterogeneities and nonequilibrium density fluctuations
The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient D S ( Φ) becomes zero at the glass...
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Published in | Physica A Vol. 270; no. 3; pp. 380 - 402 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
15.08.1999
|
Subjects | |
Online Access | Get full text |
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Summary: | The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient
D
S
(
Φ) becomes zero at the glass transition volume fraction
φ
g
as
D
S
(
Φ)∼
D
0|1−
Φ(
x
,
t)/
φ
g
|
γ
with
γ=2 where
Φ(
x
,
t) is the local volume fraction of colloids,
D
0 the single-particle diffusion constant, and
φ
g=(
4
3
)
3/(7
ln
3−8
ln
2+2)
. This dynamic anomaly results from the many-body correlations due to the long-range hydrodynamic interactions. Then, it is shown how small initial disturbances can be enhanced by this anomaly near
φ
g
, leading to long-lived, spatial heterogeneities. Those heterogeneities are responsible for the slow relaxation of nonequilibrium density fluctuations. In fact, the self-intermediate scattering function is shown to obey a two-step relaxation around the
β-relaxation time
t
β
∼|1−
φ/
φ
g
|
−1, and also to be well approximated by the Kohlrausch–Williams–Watts function with an exponent
β around the
α-relaxation time
t
α
∼|1−
φ/
φ
g
|
−
η
, where
η=
γ/
β, and
φ is the particle volume fraction. Thus, the nonexponential
α relaxation is shown to be explained by the existence of long-lived, spatial heterogeneities. |
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ISSN: | 0378-4371 1873-2119 |
DOI: | 10.1016/S0378-4371(99)00172-7 |