Successive exponential and full aging regimes evidenced by tracer diffusion in a colloidal glass
S. Kaloun,
1,3
R. Skouri,
4
M. Skouri,
3
J. P. Munch,
1
and F. Schosseler
2,
*
1
I.P.C.M.S., UMR 7504, 23 rue du Loess, BP 43, 67034 Strasbourg Cedex, France
2
I.C.S., UPR 22, 6 rue Boussingault, 67083 Strasbourg Cedex, France
3
L.E.I., Faculté des Sciences Semlalia, Université Cadi ayyad, Marrakech, Morocco
4
Faculté des Sciences et Techniques, BP 509 Boutalamine, Errachidia, Morocco
Received 3 December 2004; revised manuscript received 4 February 2005; published 8 July 2005
We study the aging of a colloidal laponite glass by measuring the dynamic structure factor of dilute embed-
ded tracer particles on micrometric length scales. We show that an initial aging regime, where the decay time
grows exponentially with aging time t
w
, expt
w
, is followed by a full aging regime, t
w
v
with v 1. The
dynamics of the tracers is diffusive in the exponential regime and hyperdiffusive in the full aging regime, up
to micrometric length scales.
DOI: 10.1103/PhysRevE.72.011403 PACS numbers: 82.70.Dd, 64.70.Pf, 61.20.Lc, 83.85.Ei
I. INTRODUCTION
Glasses are out of equilibrium systems and their physical
properties never stop evolving after they have been quenched
out of equilibrium. This evolution is called physical aging
and is usually dependent on the whole history of the sample
and in particular on the aging time, i.e., the time elapsed
since the system has been quenched. This process has been
observed and studied for numerous examples, in particular in
colloidal suspensions 1–4.
Recent theories 5–8 and experiments 9 have focused
on isolating the universal, i.e., system and history indepen-
dent, features of physical aging. Physical aging can be stud-
ied through the measurement of macroscopic quantities re-
laxation time, viscosity, etc. as a function of the aging time
t
w
. A nonperturbative approach is possible by following the
evolution with aging time of the dynamic structure factor
f q , t , t
w
of the glassy system, defined as the normalized
spatial Fourier transform of the time dependent autocorrela-
tion function of concentration fluctuations. Here q is the
wave vector associated with the fluctuations of concentra-
tion.
Alternately, it is possible to follow the evolution of the
macroscopic viscosity by measuring the dynamic structure
factor of dilute tracer particles embedded in the aging matrix
since the relaxation time of the dynamic structure factor of
Brownian tracers is proportional to the viscosity they expe-
rience. Significant advances in this second approach have
been made possible by the elaboration of a rigorous link
between the characteristics of the motion of embedded tracer
particles and the viscoelastic properties of the surrounding
matrix 10, thus introducing the new microrheology tech-
nique. Moreover, the design of dynamic light scattering ex-
periments with multispeckle detection on CCD chips has al-
lowed the measurement of relaxation times on a time scale
with the same order of magnitude 11,12. This is a critical
improvement for systems that are evolving in time.
We study aqueous colloidal suspensions of laponite clay
by following the diffusion of Brownian tracer particles em-
bedded in the aging matrix. Laponite platelets are 1 nm thick
disks with a diameter about 30 nm and are negatively
charged at pH = 10. The phase diagram as a function of ionic
strength and volume fraction exhibits a nematic phase at high
concentration. At lower concentrations, corresponding
roughly to the close packing of the spherical volume ex-
cluded by the rotating disks, the system is amorphous. The
following interactions are at work in Laponite suspensions at
pH 10: hard core excluded volume, Coulombic repulsion be-
tween negatively charged surfaces of the disks, Coulombic
attraction between oppositely charged rims and surfaces of
the disks, attractive dispersive forces between parallel disks.
Depending on their balance, the amorphous system can be
trapped in the glassy state net repulsive forces or in the gel
state net attractive forces. Throughout this paper, we work
at low ionic strength and close to the overlap concentration
of the rotating disks. In these conditions, the orthogonal ori-
entation rim on surface that would minimize the energy of
an isolated pair of disks does not necessarily minimize the
interactions with the surrounding pairs: the equilibration of
the system implies a high level of cooperativity generating a
lot of frustrations that become increasingly difficult to relax
as the system evolves, and a glassy state is obtained. The
preparation of this glass is possible after a careful filtration of
the concentrated laponite suspension 1,3.
Our group has shown 3 that the physical aging of this
system proceeds then with the following characteristics: i
the scattering intensity remains independent of q; ii the
average level of total scattering intensity decreases; iii the
relaxation time increases linearly with the aging time. These
are the features expected in the full aging regime of a glassy
system. This would not be expected for a gelling system: in
particular attractive forces between platelets with diameter
circa 30 nm would result in an increase of the scattering
intensity in the investigated q range. Abou et al. 4 studied
the dynamics of laponite glasses at short aging times and
reported a different behavior, i.e., the relaxation time in-
creases exponentially with the aging time. They suggested
that the exponential aging at short t
w
could be followed by
the full-aging regime observed in 3 for larger t
w
.
Indeed experiments made in the absence of tracer par-
ticles and measuring the dynamics of the matrix gave some *Electronic address: schossel@cerbere.u-strasbg.fr
PHYSICAL REVIEW E 72, 011403 2005
1539-3755/2005/721/0114035/$23.00 ©2005 The American Physical Society 011403-1