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Journal of Non-Crystalline Solids 353 (2007) 3891–3905
www.elsevier.com/locate/jnoncrysol
Liquid, glass, gel: The phases of colloidal Laponite
Herman Z. Cummins
*
Department of Physics, The City College of CUNY, New York, NY 10031, United States
Available online 30 August 2007
Abstract
Laponite is a synthetic disc-shaped crystalline colloid that is widely used to modify rheological properties of liquids in applications
such as cosmetics, paints, and inks so that understanding its flow properties and aging behavior is of considerable practical as well as
fundamental importance. However, some recent studies of the liquid–glass and sol–gel transitions in aqueous Laponite suspensions have
produced results that do not fully agree with each other. Because Laponite is sensitive to sample preparation procedures, it is not
straightforward to compare results reported by different groups. We have begun a study of the dynamics of Laponite suspensions during
aging using photon correlation spectroscopy to explore the consequences of specific sample preparation procedures which may underlie
these differences, including: (1) filtration of the sample through filters with different pore sizes before beginning the experiments, (2)
adjusting and monitoring the pH of the solution, (3) varying the Laponite concentration, (4) carrying out the sample preparation in
either ambient air or dry nitrogen atmospheres, (5) baking the ‘dry’ powder to remove adsorbed water, and (6) modifying the ion concentration by the addition of salts. We will compare the effects of different methods of preparation on the intermediate scattering function
F(q, t) and its time evolution. In this report we will describe experiments that explore (1)–(3). The other three will be discussed in a future
publication.
Ó 2007 Elsevier B.V. All rights reserved.
PACS: 83.80.Hj; 78.35.+c; 67.40.Fd; 82.70.Gg
Keywords: Rayleigh scattering; Transport properties gel; Transport properties – Liquids; Colloids; Nano-clusters
1. Introduction
Most recent experimental studies of the liquid–glass
transition and comparisons of the results with various theories have concentrated on fragile molecular glass-forming
materials. However, several groups have explored the
liquid–glass transition in colloidal suspensions and found
that the data obtained are well suited to testing theories.
There are two particular advantages to these systems. First,
their relaxation dynamics occur on a considerably longer
time scale than for molecular liquids, and can be followed
completely with the single experimental light scattering
technique of photon correlation spectroscopy (PCS). Second, in carrying out comparisons with predictions of the
*
Tel.: +1 212 650 6921; fax: +1 212 650 6923.
E-mail address: Cummins@sci.ccny.cuny.edu
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnoncrysol.2007.02.066
mode coupling theory (MCT), the crossover with decreasing temperature from cage-effect dominated dynamics to
hopping dynamics exhibited by molecular glass-formers
does not occur, greatly simplifying the analysis. Also, the
phase diagrams of colloidal suspension often exhibit rich
structure since, if attractive interactions are present, new
phases may occur that are absent in molecular glassformers.
Colloidal particles in dilute suspensions initially undergo
independent diffusional dynamics. With increasing particle
concentration or with aging, particle interactions can lead
to more complex dynamical behavior and to transformations to various new phases including fractal or compact
clusters, cluster gels, repulsive or attractive glasses, and
liquid-crystal phases. The widespread use of colloidal suspensions and gels in foods, pharmaceuticals, cosmetics,
paints and inks, etc. gives these transformations practical
as well as fundamental interest and has led to an extensive
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literature of studies using various theoretical and experimental techniques (cf., [1–4]).
The simplest colloidal system, hard-spheres that interact
only at contact (HSS) suspended in a neutral solvent,
undergoes crystallization to a FCC close-packed structure
when the particle concentration (volume fraction /) reaches
0.50. However, if there is sufficient polydispersity, crystallization may be avoided and, at / 0.58, a liquid–glass
transition occurs as each colloidal particle becomes trapped
in the cage formed by its neighbors. This HSS liquid–glass
transition has been studied extensively by the groups of van
Megen and Pusey [5–11] and Bartsch [12] and has provided
critical tests of theories of the liquid–glass transition.
These studies showed that with increasing volume fraction / the relaxation dynamics slows dramatically, and
the quantitative structure of the intermediate scattering
function F(q, t) and its evolution with concentration, as
determined by dynamic light scattering (photon correlation
spectroscopy), are closely described by quantitative predictions of the mode-coupling theory (MCT) for the hardsphere system [13–15]. In the experiments, kinetic arrest
was found to occur at a volume fraction of / 0.58, somewhat higher than the MCT ideal glass transition prediction
/C = 0.516 for the hard-sphere system (HSS), although
recent extensions of MCT to include higher-order terms
reportedly lead to an increase in this MCT value [16].
If, in addition to the hard-sphere repulsive potential
there is a short-range attractive potential, an additional
soft-solid phase can occur. In 1999, Fabbian et al. carried
out MCT calculations for a system of colloidal spheres
characterized by a hard-sphere potential supplemented by
a short-range attractive square-well potential (‘sticky
hard-spheres’) [17–20]. They found that this system exhibits
two glass transitions; first, with increasing strength of
attraction, the volume fraction /C for the usual cage-effect
mediated glass transition increases (glass I). Second, within
the glass I phase, further increase of the attraction causes
pairs of particles to move together, opening holes in the
cages, and causing the glass to melt. Finally, as the attraction increases further, a second transition dominated by
attractive forces occurs (glass II). These predictions were
verified in experiments in which the attractive interaction
was produced by adding small polymers to the colloidal
suspension, which causes a short-range depletion attraction
[21–23].
Soft-solid phases of colloids held together by attractive
forces are usually considered as gels, but the distinction
between gels and attractive glasses is not clear. Analogies
between the two have been studied by several groups, e.g.
[24,25]. Segre et al. have shown that relaxation dynamics
near gelation and near the liquid–glass transition are
remarkably similar [26]. Bergenholtz and Fuchs [27–29]
examined the mode-coupling theory predictions for the
behavior of colloidal suspensions with attractive interactions at low volume fractions and concluded that the sol–
gel transition could also be described by MCT. They noted
that if the short-range attractive interaction is represented
by a Yukawa potential rather than the square-well potential considered previously, then the liquid–glass II transition line would extend to very low volume fractions,
suggesting that the sol–gel transition is a low-/ continuation of the glass II transition.
A modification of standard MCT was proposed by Kroy
et al. [30] in which two MCT ergodicity-breaking transitions
occur: a first short length-scale transition involving the
formation of clusters, and a second larger length-scale transition in which the clusters aggregate to form a gel (CMCT).
A related scenario was identified in simulation studies by
Sciortino et al. [31,32]. These analyses suggest that the same
mechanism underlying the liquid–glass transition also
underlies the sol–gel transition, so that the characteristic
dynamical signatures of the liquid–glass transition should
also appear at the sol–gel transition. The quantitative
aspects of these theoretical predictions largely remain to
be explored experimentally, especially those regarding their
dynamics.
If the colloidal particles are electrically charged, additional phases can occur. Kumar and Wu [33] reported
molecular dynamics simulations of colloids interacting
through a short-ranged van der Waals attraction and a
longer-ranged electrostatic repulsion. They observed a variety of ‘jammed states’ at volume fractions between / = 0.4
and / = 0.1, ranging from nearly uniform glass-like structures to network-like gel structures. The relation between
cluster formation and combined short-range attraction
and long-range repulsion has been studied by Sciortino
et al. [32]. Lu et al. have reported that suspensions of colloids with attractive interactions induced by polymers exhibit a stable phase of clusters even in the absence of longrange repulsion, and that clusters can percolate across the
sample to form a gel [34]. Also, if the colloidal particles
are electrically charged, a third glass phase can occur, stabilized by electrostatic repulsion. This phase is sometimes
called the ‘Wigner glass’.
In the colloidal systems described so far, the individual
particles are assumed to be spherical. In the case of asymmetric particles (e.g. round discs as in Laponite), there is
also the possibility of orientational order and liquid-crystal
phases. Also, asymmetry of the charge distribution can
produce dense soft-solid phases stabilized by electrostatic
interactions.
1.1. Laponite
Many recent studies of the liquid–glass and liquid–gel
transitions have employed the synthetic colloid Laponite
which has all the characteristics discussed so far: both
attractive and repulsive interactions, anisotropy and net
charge, as well as an anisotropic charge distribution. It
exhibits an array of different phases and behaviors and
has become a widely used model system for testing theories
of liquid–glass and liquid–gel transitions as well as various
aspects of aging phenomena. However, Laponite is not a
simple material to handle, since it is sensitive to the meth-
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H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
ods of sample preparation. Comparing the different
reported studies therefore requires evaluating the importance of the different methods of preparation employed
by different authors. There are potentially many different
Laponite phases possible, and a major challenge is to sort
out which of these phases are observed under particular
experimental conditions, and how they are influenced by
the sample preparation method followed.
Laponite (hydrous sodium lithium magnesium silicate)
is a synthetic crystalline layered silicate colloid with crystal
structure and composition closely resembling the natural
smectite clay hectorite. It is manufactured by Rockwood
Additives Ltd (formerly Laporte Ind. Ltd.), Cheshire
UK, and Southern Clay Products, Inc., Gonzales, Texas.
Chemical analysis of Laponite RD by Levitz et al. [35] gave
mean chemical composition: SiO2, 65.82%; MgO, 30.15%;
Na2O, 3.20%; LiO2, 0.83%. The melting point is 900 °C.
Extensive information on the structure and applications
of Laponite can be found on the manufacturer’s websites
http://www.laponite.com and http://www.scprod.com.
The density of Laponite is 2.53 g m/cm3. Single Laponite crystals are disc shaped and nearly uniform, typically
25 nm in diameter by 0.92 nm thick, much smaller than
natural clays. Within a single crystal, each sheet of octahedrally coordinated aluminum or magnesium oxide is sandwiched between two layers of tetrahedrally coordinated
silica.The crystal faces have negative charge; the edges have
small pH-dependent positive charge, typically 10% of the
negative charge. The overall net negative charge of a single
Laponite disc is approximately 700 electron charges. The
charge is balanced by interlayer cations which are predominantly Na+. In the dry powder, the Laponite crystals form
into stacks with the crystals sharing interlayer Na+ ions.
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When dispersed in water, Laponite hydrates and swells to
form a clear colloidal dispersion with the Na+ ions forming
double layers on the faces. The pH for a 2% Laponite suspension in pure water is 9.8.
At low ionic strength, electrostatic repulsion keeps the
particles apart. Laponite is decomposed by acids, leading
to an increase in ion concentration with time at low pH.
At concentrations of 2% or greater in water a gel will form
rapidly. However, gel formation has been observed at concentration well below 2% in several studies including the
present one.
Laponite gel is strongly thixotropic, i.e. its viscosity
decreases rapidly under shear. After the shear stress is
removed, the gel reforms; the rate of restructuring depends
on composition, electrolyte level, age of the dispersion, and
temperature. The addition of salts reduces the thickness of
the electrical double layer, promoting gel formation.
Laponite contains approximately 8 wt% water which is
chemically absorbed into the crystal structure and can only
be removed by baking at temperatures above 150 °C. In
addition, Laponite is hygroscopic and will adsorb additional water from the atmosphere, typically up to 15% at
50% relative humidity. The structure of individual Laponite particles and a schematic drawing of the proposed
‘house of cards’ soft-solid phase are illustrated in Fig. 1.
There are several different grades of Laponite available
for different commercial applications. Laponite RD, the
most frequently studied grade, is used in many household
and industrial products including cleansers, surface coatings, and ceramic glazes. Laponite XLG is a high-purity
grade of Laponite RD, processed to remove impurities
such as heavy metals e.g. lead and arsenic. This grade is
used in personal care and cosmetic products including
Fig. 1. Structure of individual Laponite particles and schematic house of cards structure of Laponite gel stabilized by electrostatic interaction between the
negatively charged faces and positively charged edges of the disc-shaped colloidal particles (from southern clay products product information website).
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shampoos and sunscreens. Laponite XLG was used in the
studies of Thompson and Butterworth [36] and in the work
discussed in this report.
1.2. Laponite phases discussed in the literature include the
following
1.2.1. Liquid with clusters
Some studies of Laponite suspensions at concentrations
of 0.9–5 wt% using angle resolved static light, neutron, and
X-ray scattering suggested that they contain clusters that
have fractal structure [37,38]. Bonn et al. [39] compared
light scattering from two samples prepared with 3.5 wt%
Laponite and found that the angle-dependent intensity
characteristic of fractal structures was present in the freshly
prepared solutions, but that filtration through a 0.8 lm
millipore filter resulted in the complete absence of the angle
dependence. Clusters should be more likely to form in suspensions having higher ionic concentration since at low ion
concentrations repulsive electrostatic interactions will keep
the particles apart.
1.2.2. Wigner glass
At low ionic strength, electrostatic repulsion keeps the
colloidal particles apart and can produce a transition to
an arrested state stabilized by long-range electrostatic
repulsion [40].
1.2.3. High-density gel
At higher ionic strength, as the screening length
decreases, the positive double layers at the edges of platelets can approach the negatively charged double layers on
the faces. The high-density gel state of Laponite, called
the ‘house of cards’ structure, occurs when the screening
length is sufficiently short so that this attractive interaction
dominates. This structure is readily observed if dry Laponite powder is mixed with tap water which typically has a
high ion concentration.
1.2.4. Low-density gel
Ruzicka et al. [41] studied Laponite suspensions with
concentrations between 0.3 and 3.1 wt%. They found that
even for the lowest concentrations a transition to an
arrested phase occurs after a sufficiently long time
(6 months for 0.3 wt%). They also found that the time
evolution of the dynamics differed for concentrations
above and below 0.17 wt% suggesting that there are
two different gel structures for this material. One possibility
is that the high-density gel is the ‘House of Cards’ structure
while the low-density gel consists of a network of chains as
one finds in polymer gels, which can form gels at very low
concentrations. Alternatively, the low-density gel may consist of a network of clusters as discussed by Lu et al. [34].
1.2.5. Nematic phases
Lemaire et al. [42] studied Laponite gels with SAXS and
found evidence of anisotropy in the scattering patterns,
indicative of nematic orientational order, for Laponite concentrations above 2 wt%. Gabriel et al. [43] observed suspensions of Laponite (Laponite B) between crossed
polarizers and found optical birefringence for concentrations above 2.4 wt%, again indicative of nematic order.
Agra et al. [44] have shown theoretically how a rich variety
of orientational ordered phases in colloidal crystals can be
understood.
Previous light scattering studies of Laponite have been
reported in numerous references including [37–41,45–57].
Sample preparation methods differ widely among the
published studies. Some of the specific aspects of the preparation procedures whose importance we are investigating,
are:
1. Sample filtration: What type and pore size filter was
used? Was there a delay between mixing and filtration?
2. Is the water pH adjusted before/after adding the Laponite? Is it monitored later?
3. What is the Laponite concentration?
4. Is the sample prepared under nitrogen or in a normal
ambient atmosphere?
5. Is the sample dried to remove moisture?
6. What is the ion concentration (possible modification by
addition of salt)?
In this report we will concentrate on points 1–3. The
others are currently under study and will be discussed in
a future publication.
2. Experimental
2.1. Sample preparation
The Laponite XLG used in the experiments described in
this report was lot 04-239, purchased from Southern Clay
Products in Feb 2005. The certificate of analysis indicates
6.8% moisture content, although this should be expected
to increase during handling and transfer to storage jars.
The moisture content was measured during preparation
of the samples with a Sartorius MA100C moisture analyzer
and was found to be 9.8%.
Samples for the PCS experiments were prepared with the
Laponite as provided without further drying. Samples were
loaded in screw-top cylindrical glass vials with outside
diameters of either 20 or 28 mm. Three different series of
Laponite samples were prepared. Each series included several stock solutions with different concentrations prepared
following the same procedure. From each stock solution,
three (or more) samples were prepared by extracting some
of the stock solution with a syringe and forcing it through
various Millipore millex sealed syringe filters with 33 mm
mixed cellulose ester membranes. For each such preparation, one sample was prepared without a filter. The samples
are listed in Table 1. Concentrations are given in weight
percent of Laponite, uncorrected for water content of the
powder. Using the Laponite density of 2.53 g m/cm3 and
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Table 1
Laponite samples and the results of PCS measurements as discussed in the text
Series
Sample
Filter
Loaded
Gelled
A (measure pH later)
AA (0.89%) Mix: 6/30/05
pH = 9.53
AA2
AA3
AA4
AA5
None
0.1
0.8
0.45
7/6/05
7/6/05
7/14/05
7/14/05
1/4/06
1/4/06
pH = 9.28
AB1
None
AB2
0.45
AB3
0.8
7/18/05
7/19/05
7/19/05
pH = 9.90
AC1
None
AC2
0.8
AC3
0.45
8/9/05
8/9/05
8/9/05
pH = 10.12
BA1
None
BA2
0.8
BA3
0.45
AB (0.06%) Mix: 7/18/05
AC (1.50%) Mix: 8/8/05
B (adjust pH after mixing if pH < 10.0)
BA (1.00%) Mix 1/2/06
BB (0.18%) Mix: 2/6/06
C (use water with pH = 10)
CA (0.98%) Mix: 1/3/06
CB (0.04%) Mix: 1/9/06
CC (0.18%) Mix 1/12/06
Bad KWW
Last PCS
7/18/06
since load (days)
9/14/05
9/14/05
7/10/06
9/10/05
GEL
GEL
liq(7/17)
GEL
(G)182
(G)182
368a
(G)60
2/16/06
2/9/06
1/5/06
9/22/05
2/9/06
9/14/05
liq(7/17)
liq(7/17)
liq(7/17)
3/2/06
9/15/05
3/6/06
3/2/06
GEL
GEL
GEL
1/2/06
1/2/06
1/2/06
7/10/06
7/10/06
7/10/06
liq(7/17)
liq(7/17)
liq(7/17)
196
196a
196
pH = 10.37
BB1
None
BB2
0.8
BB3
0.45
2/6/06
2/6/06
2/6/06
7/10/06
7/10/06
7/10/06
liq(7/17)
liq(7/17)
liq(7/17)
161
161
161
pH = 10.27
CA1
None
CA2
0.8
CA3
0.45
1/3/06
1/3/06
1/3/06
7/10/06
4/11/06
6/26/06
liq(7/17)
GEL
Soft GEL
pH = 10.29
CB1
None
CB2
0.8
CB3
0.45
1/10/06
1/10/06
1/10/06
7/10/06
7/10/06
7/10/06
liq(7/17)
liq(7/17)
liq(7/17)
188
188
188
pH = 10.42
CC1
None
CC2
0.8
CC3
0.45
1/13/06
1/13/06
1/13/06
7/10/06
7/10/06
7/10/06
liq(7/17)
liq(7/17)
liq(7/17)
185
185
185
9/12/05
9/15/05
6/13/06
6/13/06
5/3/06
7/10/06
4/11/06
6/5/06
364
363
363
(G)37
(G)308
(G)308
195
(G)123
(G)194
The final column shows the elapsed time (in days) before sample gelation (G) or, if gelation was not observed by 7/18/06, the elapsed time since it was
prepared.
a
Note: by 10/25/06 samples AA4 and BA2 had also gelled.
water content of 9.8%, the relation between volume fraction / and concentration C is / = 0.9C/(2.5 1.35C) (with
C = 0.01*C (wt%)). For the samples studied / ranges from
a maximum of 5.4E3 for the 1.5 wt% samples to 1.4E4
for the 0.04 wt% samples. The samples were all prepared
under normal ambient atmosphere. Preparation of samples
in a glove box under dry nitrogen atmosphere is currently
in progress and will be discussed in a future publication.
Three series of samples (A, B, C) were prepared, each
following a different pH adjustment protocol. The pH values measured after completion of the mixing procedures
are shown in the second column of Table 1.
A series Laponite powder was added slowly to distilled
or DIUF water while stirring. There was no measurement or control of pH during preparation. The pH of
each stock solution listed in the table was measured
later.
B series Laponite powder was added slowly while stirring; after mixing was complete the pH was adjusted
to pH > 10 by addition of 1% NaOH solution, if
required. Because the DIUF water pH is 4, some acid
dissociation of these B series samples may have occurred
before the pH was adjusted. Therefore, for the C series,
the water pH was adjusted before adding the Laponite.
C series Laponite powder was added slowly to DIUF
water with pH adjusted to >10 by addition of 1% NaOH
solution before mixing.
Periodically all samples were removed from the storage
rack and tilted slightly to see if gelation had occurred. This
tilting may have caused some slight mixing in those samples that had not gelled. In the right-hand column of Table
1 we show the elapsed time (in days) from preparation until
a gel was observed. For samples that had not gelled, we
give the elapsed time from sample preparation until the last
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observation of the liquid. Note that for samples with
C < 0.2 wt% no gelation was observed.
The elapsed time (in days) from sample preparation
until a gel was observed is shown for all samples by the
solid symbols in Fig. 2. For the samples where gelation
was not seen, the sample is represented by an open symbol.
We note that the filters were used as provided by the
manufacturer. Some surprising inconsistencies that we
observed, especially with the 0.8 lm filters, may be related
to residual traces of detergent or solvent in the filters. This
could be checked by rinsing the filters with pure water
before passing the Laponite solution through them, but
this has not yet been done.
2.2. PCS measurements
PCS measurements were carried out with a Brookhaven
Instruments BI-9000AT digital correlator. Excitation was
provided by a Coherent Innova I306C Argon laser operating in single-mode at 488 nm with typical output power of
150 mW. Power at the sample was approximately 50 mW.
All experiments were performed at a 90° scattering angle
with data collection time of 10 min.
For ergodic samples the normalized intensity correlation
function g2(t) = C(t)/B (where B is the background) is
related to the intermediate structure factor F(q, t) by
2
g2 ðtÞ ¼ 1 þ ajg1 ðtÞj ¼ 1 þ a½F ðq; tÞ=F ðq; 0Þ
2
ð1Þ
In the simplest case of uncorrelated spherical particles of
radius r undergoing independent translational diffusion,
g2 ðtÞ ¼ 1 þ a expð2t=sÞ ¼ 1 þ a expð2Dq2 tÞ
ð2Þ
where the translational diffusion constant D = kT/6pgr.
For a distribution of particle sizes, a simple generalization
(which we will use here) is to replace the exponential in Eq.
(2) with a KWW stretched exponential function and to use
a free baseline b 1:
h
i
b
g2 ðtÞ ¼ b þ a exp 2ðt=sÞ
ð3Þ
For 4880 Å light and 90° scattering, the mean hydrodynamic radius rh is approximately related to the measured
correlation time s by
rh ðnmÞ ¼ sðlsÞ=7:76
ð4Þ
We used Eqs. (3) and (4) to find approximate scatterer sizes
from the PCS data. For independent single Laponite particles we expect rh 13 nm. We emphasize that this fitting
procedure was a simple approximation used to provide a
rough estimate of the time evolution of cluster sizes and
polydispersity under different preparation procedures.
Since the experiments were performed at fixed q, the q2
dependence of Eq. (2) was not tested. Furthermore, the
cluster size was estimated from Eq. (4) using the value of
s from the fits to Eq. (3). The mean value of s would be increased for b < 1, reaching hsi = 2s for b = 0.5.
If the colloidal sample is a gel, then extracting dynamical
information from PCS data is much more difficult as discussed in detail by Pusey and van Megen in 1989 [58].
We will discuss the PCS data analysis problem for gels
briefly in Section 3.4 below.
If the correlation function of a monodisperse solution is
fit to Eq. (3), the KWW stretching coefficient should be
b = 1. If the sample is polydisperse then b < 1. To explore
the dependence of b on polydispersity, we constructed synthetic g2(t) data and performed KWW fits for theoretical
polydisperse solutions with radii ranging from 13 nm to a
maximum rmax between 13.1 nm and 300 nm, assuming
that the product of particle concentration and particle scattering strength was constant across the range of sizes
included. For a size distribution whose width is 0.4 times
the mean size, b is 0.99, still very close to 1. For the most
polydisperse C(t) considered, with width 1.8 times the
mean size, b decreased to 0.79. Also, for that fit, there is
a small systematic error as C(t) begins to decay from the
initial plateau; the error is very similar to fitting errors seen
in the PCS experiments as discussed below.
3. Results
Fig. 2. Elapsed time in days from sample preparation until first
observation of a gel (solid symbols) vs concentration in wt%. Open
symbols indicate samples that were still liquid at the latest observation.
Series A-circles, series B-Squares, series C-triangles. No filter: large
symbols; 0.8 lm filter: medium symbols; 0.45 lm filter: small symbols.
PCS experiments on the Laponite samples listed in
Table 1 were performed frequently, beginning soon after
each sample was prepared. The PCS data was analyzed
with the four-parameter KWW function (Eq. (3)) from
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which an estimate of the average size rh of the scatterers
was obtained with Eq. (4). The relaxation time s (and
estimated radius rh) increased with time for all samples
studied, although in some cases a small decrease was
observed during the first few days after sample preparation.
In Fig. 3 we show PCS data for samples CC1, CC2, and
CC3 (0.18 wt%), 6 days after preparation (squares) and 137
days after preparation (circles). The KWW fits are also
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included for the 137-day data. The relaxation slows with
increasing time for all three samples as expected due to
growth of clusters. From the KWW fits with Eq. (3), we
obtained average sizes rh at 6 days and 137 days for the
three samples: (CC1) 14.8 nm, 360.4 nm; (CC2) 14.6 nm,
154.0 nm; (CC3) 14.3 nm, 53.9 nm. At 6 days, all three
samples had correlation times of about 100 ls and corresponding estimated radii of rh 14 nm, indicating that
Fig. 3. PCS data for 0.18 wt% Laponite samples CC1, CC2, and CC3 six days (squares) and 137 days (circles) after preparation. The solid lines are KWW
fits used to extract estimates of the average radius of the scatterers as described in the text.
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the scatterers were individual Laponite particles or very
small clusters. (Rosta and von Gunten concluded that their
Laponite suspensions contained very small clusters of
between two and four platelets [57]). Note that at 6 days
rh does not depend on the filter used, but after 137 days
rh of the unfiltered sample has increased the most, while
the 0.45 lm filtered sample has increased the least. However, as we shall see, the correlation between filter pore size
and cluster size is not generally consistent.
The systematic departures from the KWW fit in Fig. 3
for sample CC1 closely resemble those seen in our fits to
synthetic data for the most polydisperse case, indicating the
presence of considerable polydispersity in this sample.
At longer times, the correlation functions of samples
that remain liquid often evolve into shapes with long tails,
signaling the existence of large slow-moving clusters with
large polydispersity and limiting the utility of KWW fits.
Fig. 4 shows PCS data for samples CC1, CC2, and CC3
Fig. 4. PCS data for 0.18 wt% Laponite samples CC1, CC2, and CC3 166 days after preparation showing the ‘tails’ on C(t) for CC1 and CC2, but not for
CC3. The insets for CC1 and CC3 show the counts accumulated during each second of the 10-min runs.
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H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
recorded 166 days after preparation. For CC1 and CC3 we
also include the count rate histories as insets which show
the number of photocounts collected each second during
the 10-min runs. Sample CC1 (unfiltered) has a prominent
PCS tail, and the count rate exhibits large fluctuations on a
time scale of 1 min, indicating (via Eq. (4)) the presence
of large clusters with rh 10 lm. Sample CC2 also has a
prominent tail, but CC3, which was passed through the
0.45 lm filter, has no tail and the count rate history shows
no slow fluctuations.
The evolution of rh and b obtained from the KWW fits
for all samples studied is shown in Figs. 5–7. From these figures, and from Fig. 2, some general observations can be
made. First, for the lowest concentration samples
(C < 0.2 wt%), no gelation was observed within the observation time of 1 year. Second, for the highest concentration samples AC, the unfiltered sample gelled first (37
days) while the two filtered samples did not gel until 308
days. But for the AA 0.89% samples, the unfiltered and
0.45 lm filtered samples gelled at 182 days and 60 days,
respectively, while the 0.8 lm filtered sample was still liquid
after a full year.
Third, for the samples that gelled, there was a rapid
increase in size and corresponding decrease in b, indicating
60
50
30
10July06
( 361 days)
AA4
AA2 gelled
after 14 Sept
KWW parameter β vs elapsed time - samp les AA, AB, AC ( 12 July 06)
0.89 wt%
AA3 gelled
after 14 Sept
40
A series: Of the samples with 0.89 wt% concentration, all
but one (AA4) had gelled within 75 days of preparation while the third sample (AA4) was still
liquid after 250 days. The 1.50 wt% AC samples
all gelled, with the unfiltered sample AC1 after
60 days and the other two after 340 days.
The AB 0.06 wt% samples showed constantly
increasing cluster sizes but did not gel within
one year.
B series: Samples BB1, BB2, and BB3 (0.18 wt%) PCS
data obtained for up to 154 days after preparation. Note that the unfiltered sample (BB1) and
the 0.45 lm filtered sample (BB3) have
rh 12.3 nm indicating that no significant aggregation has occurred while sample BB2, filtered
with a 0.8 lm filter, has rh 56 nm indicating
considerable aggregation.
C series: Aggregation of the C samples proceeded as least
as fast as the B samples. This indicates that there
is no advantage to adjusting the water pH before
addition of the Laponite.
A_ rh-v s-et .pxp
AA : 0.89 wt% - mixed inpure
DIUF water - no pH control
red AA2 (no filter)
green AA4 (0.8micron filter)
blue AA5 (0.45 micron filter)
black AA3 (0.1micron filter)
AA5 gelled
12 Sept
increasing polydispersity, that precedes gelation (see, e.g.,
BA2, BB2, and CA2).
20
10
1. 0
KWW stretching parameter β
radius (nm)= tau (microsec)/7.76
Hydrodynamic radius vs elapsed time - samples AA,AB,AC (12 JULY06)
70
3899
A_ bet a-v s-et .pxp
red: AA2 (no filter)
green: AA4 (0.8micron filter)
blue: AA5 (0.45 micron filter)
black: AA3 (0.1micron filter)
0. 9
0. 8
0. 7
0. 6
10July06
t=361 days
0. 5
0
50
100
150
200
250
elapsed time since loading (days)
300
350
50
100
150
200
250
300
350
elapsed time since sample loading (days)
AB: 0.06 wt% - mixed in DIUF
water (no pH adjustment)
4
0
0. 06 wt %
2
red: AB1 (no filter)
green: AB3 (0.8 micron filter)
blue: AB2 (0.45 micron filter)
0.8
5 Jan
1000
9 Feb
6
4
0.6
2
red AB1 (no filter)
green AB3 (0.8micron gilter)
blue AB2 (0.45 micron filter)
NOTE: Beyond ~ 60 days, PCS datanot
described by KWW - have big tails
BUT AB SAMPLES DONOT GEL
100
6
4
2
0.4
9 Feb06
0.2
0.0
50
100
150
200
20
40
60
80
100
120
0.7
1000
AC 1.50 wt % - mixed in oure DIUF water - no pH adjustment
red AC1 ( no filter)
green AC2 (0.8micron filter)
blue AC3 (0.45 micron filter)
8
6
4
1. 50 wt %
6 March
140
160
red: AC1 (no filter)
green: AC2 (0.8 micron filter)
blue: AC3 (0.45 micron filter)
0.6
0.5
2
100
gel ( 60 days)
0.4
8
6
4
AC2 & AC 3
Poor KWW
fi ts ; gelled after
~340 days
2
10
0.3
6 Marc h06
0.2
0
50
100
150
200
250
0
50
100
150
200
250
300
Fig. 5. Approximate hydrodynamics radius (left) and KWW stretching parameter b (right) vs elapsed time since sample preparation in days from KWW
fits for all samples in series A.
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Stretching coefficient beta vs elapsed time - samples BA, BB [10 July 06]
B_beta -v s-et .pxp
B_rh-v s-et .pxp
Hydrodynamic radius vs elapsed time - samples BA, BB (10July06)
0.8
8
7
6
5
BA:1.0 wt %
radius(nm) = tau(microsec)/7.76
4
3
BA: 1.0 wt% mixed in pure DIUF water
adjust pH = 10 afterwards
if needed with 1% NaOH
red: BA1 (no filter)
green: BA2 (0.8 micron filter)
blue: BA3 (0.45 micron filter)
0.7
BA: beta vs elapsed time
red: BA1 (1.0 wt%)
green: BA2
blue: BA3
2
10 July06
0.6
100
8
7
6
5
0.5
10 July 06
189 days
4
3
0.4
2
10
0.3
0
50
BB: 0. 18 wt %
100
9
8
100
elapsed time since loading (days)
150
200
0
50
0.90
BB:0.18 wt% mixed in pure DIUF water,
adjust pH = 10 afterwards if needed
red: BB1 (no filter)
green: BB2 (0.8 micron filter)
blue: BB3 (0.45 micron filter)
100
150
BB: beta vs elapsed time
red:
BB1 (0.18 wt%)
gr een: BB2
blue: BB3
0.88
7
0.86
6
10 July 06
5
0.84
4
0.82
3
0.80
2
10 July 06
154 days
0.78
0.76
10
0
20
40
60
80
100
120
140
160
0
20
40
60
80
100
120
140
160
Fig. 6. Approximate hydrodynamics radius (left) and KWW stretching parameter b (right) vs elapsed time since sample preparation in days from KWW
fits for all samples in series B.
3.1. Cluster formation vs gel formation
Most samples showed increasing s (and rh) and decreasing b with increasing time, in some cases following an initial short-time decrease in rh, demonstrating that both
mean cluster size and polydispersity generally increase as
aging proceeds. For some samples, the intercept/background ratio a/b suddenly decreased from 1 to 0.5 or less,
and tipping these samples then showed that a gel had
formed. The dates and corresponding elapsed times since
preparation when a gel was first observed for each sample
are also shown in Table 1. For other samples, especially
those prepared at low concentrations, s (and rh) continued
to increase while a/b remained at 1. For these samples,
the correlation function C(t) usually developed a long high
tail indicating that cluster size and polydispersity continue
to increase, but the samples remained liquid. Also, the
count rate record for these samples show very slow fluctuations, indicating the presence of very large clusters. These
two distinct patterns of time evolution of the PCS data are
illustrated in Fig. 8.
For polymer suspensions, as the particles aggregate, the
form of the aggregates (or clusters) can take on different
structures depending primarily on the coagulation rate.
When coagulation is rapid, the cluster structure is open
and can be characterized as a fractal structure with fractal
dimension D in the range 1.7 < D < 2.2. When coagulation
is slow, the aggregates tend to be much more dense [2]. This
distinction was discussed by Lin et al. [2] for colloid aggregation and may underlie the two routes to gelation
reported by Ruzicka et al. [41].
3.2. When does aging begin?
It has sometimes been asserted that when stock Laponite solutions are passed through a filter into a sample cell,
all clusters are broken up and the sample aging process
effectively starts over, so the aging time clock is reset to
zero. However, we observed three effects that appear to
contradict this claim:
(1) Stock solution AA was mixed on 6/30/05 with concentration C = 0.89 wt%. Samples AA2 through AA5
were loaded within the next two weeks. Another sample, AA6, was loaded 88 days after mixing. Samples
AA5 and AA6 were both prepared using 0.45 lm filters. The first PCS run for sample AA6, carried out
on the same day that the sample was prepared, gave
an initial s value of 1020 ls, 8 times larger than the
125 ls found for sample AA5. Presumably, some clus-
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H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
radius (nm) = tau (microns)/7.76
Hydr odynamic radius vs elapsed ti me - samp les CA, CB, CC (13July06)
6
CA : 0.89 wt% mixed in pH=10 DIUF water
(adjusted with 1% NaOH)
red: CA1 (no filter)
green: CA2 (0.8 micron filter)
(98days BIG TAIL - stop KWW)
blue: CA3 (0.45 micron filter)
4
2
C_rh-v s-et .pxp
CA3
Gel - 13July
174 days
CA2
Gel-3May
120 days)
CA: 0.89 wt%
C_beta -v s-et .pxp
CA: beta vs elapsed time
red - CA1 (0.89%)
green - CA2 (stop at 98)
blue - CA3
0.89 wt %
0.9
0.7
0.6
4
0.5
2
10July06
CA2
Gel-3May
(120 days)
0.4
0.3
10
0
50
100
elapsed time since loading (days)
0
150
1.0
CB: 0.04 wt% mixed in pH=10 DIUF water
red: CB1 (no filter)
green: CBA2 (0.8 micron filter)
blue: CB3 (0.45 micron filter)
2
1000
6
4
50
100
150
CA3
GEL-13July
(188 days)
0.04 wt %
0.9
10July06
0.8
CB: 0.04 wt%
2
0.7
0.6
100
6
4
CB : beta vs elapsed time
red - CB1 (0.04%)
green - CB2
blue - CB3
0.5
2
0.4
10July06
0.3
10
0
1000
Dependence of KWW beta on elapsed time - Series C (13July2006)
1.0
0.8
10July06
100
8
6
3901
50
100
150
200
0
1.0
CC: 0.18 wt% mixed in pH=10 DIUF water
red: CC1 (no filter)
green: CC2 (0.8 micron filter)
blue: CC3 (0.45 micron filter)
8
6
4
100
150
CC: beta vs elapsed time
red - CC1 (0. 18% )
gr een - CC2
blue - CC3
0. 18 wt %
0.9
0.8
CC: 0.18 wt%
2
50
0.7
100
8
6
10July06
13July06
0.6
4
0.5
2
0.4
10
0
50
100
150
0
50
100
150
Fig. 7. Approximate hydrodynamics radius (left) and KWW stretching parameter b (right) vs elapsed time since sample preparation in days from KWW
fits for all samples in series C.
ters that had formed in the AA stock solution during
the 88 days after it was mixed were not fully broken
up by filtration in the preparation of sample AA6.
(2) For many of the samples (e.g. BA) the value of s
decreased for several days after the sample was
loaded and then began to increase again (see
Fig. 6). This observation suggests that some small
aggregates present in the dry powder survive several
hours of mixing and filtration but do dissolve slowly
in the sample cells after several days.
(3) The records of radius vs elapsed time shown in Figs
5–7 allow a comparison of results for different filter
sizes. From the figures, there is no clear correlation
of radius with filter size. In fact, for some samples
prepared with no filter (e.g. CA1 and CB1) the mean
cluster size increases less with time than the samples
prepared with 0.45 or 0.8 lm filters. The origin of this
inconsistency is currently unknown.
increases (for PCS spectra of a standard 22 nm polystyrene
suspension, the same procedure gives excellent KWW fits).
To see if this effect is due to anisotropy or polydispersity,
we carried out several runs with polarization selection,
using samples contained in square optical cuvettes to avoid
polarization distortion. The experiments were performed
with the incident light polarized vertically, perpendicular
to the scattering plane (V) and the scattered light polarization was selected as either vertical (VV), horizontal (VH) or
all scattered light was collected (VT).
For a 1% Laponite dispersion (CA) the Laponite VT and
VV fits were nearly identical, giving rh = 12.6 and 12.7 nm,
respectively. The VH spectrum was very weak, with intensity
about 3% of the VV intensity. This indicates that the anisotropy of the Laponite particles is not a significant factor in the
PCS data, and that the typical departure from the KWW fit,
visible in the short-time behavior of the VT and VV spectra,
is due to polydispersity and not to anisotropy.
3.3. Anisotropy vs polydispersity
3.4. Gels
The fits of Laponite PCS data to Eq. (3) were primarily
used to estimate rh, but some of the fits were poor, especially in the region of the initial decay away from the plateau. Departures becomes more visible as the mean size
As the colloidal solution transforms from a sol to a gel
there are dramatic changes in the structure and dynamics
that continue to evolve as the sample ages. We intend to
explore this aspect of Laponite in detail. So far, however,
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Fig. 8. Correlation data with KWW fits for sample AA5 (top) and AB1 (bottom). AA5 was a gel by 62 days after preparation and shows a drop in its a/b
ratio. AB1 remained liquid, but developed a long tail indicating the presence of large clusters.
we have only carried out a preliminary study of one aspect
of the gel transition: how the PCS data are affected by the
onset of nonergodicity as described briefly below.
When a colloidal dispersion gels, the range of motion of
each particles becomes limited and the dynamics becomes
nonergodic. Time averages and ensemble averages are no
longer equivalent and Eq. (1) and (2) are then not valid. To
overcome the problem of nonergodicity, several methods
have been described. First, the sample can be slowly rotated
[23] or translated during the PCS measurement so that many
independent scattering volumes are sampled sequentially,
making the time-averaged PCS data effectively an ensemble
average. Second, scattered light can be collected simultaneously over a range of scattering vectors and the multispeckle correlation functions averaged over the different spots,
again resulting in an ensemble average [5,6,58–61].
In their 1989 paper, Pusey and van Megen [58] suggested
another way to overcome the nonergodicity problem by
looking for a place in the scattering volume where the static
component of the scattering is very weak. Fig. 9 shows PCS
spectra of Laponite sample AA5 (0.89 wt%). In the upper
panel, the sample is a liquid with a/b ratio 0.95, at times
of 0, 20, and 25 days after loading the sample. The initial
hydrodynamic radius is 15 nm, increasing to 70 nm by
25 days. By 62 days after loading, the sample has gelled
and the a/b ratio has dropped from 0.95 to 0.35. The
PCS spectra shown in the lower panel are all at 62 days
or later. The a/b ratio varies between a maximum of
0.8 to a minimum of 0.05, depending on location in
the sample. The higher a/b ratios corresponded to lower
average count rates. This extreme variation occurs because
the detected signal consists of a dynamical component
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H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
3903
Fig. 9. PCS data for sample AA5. Upper panel: C(t) and KWW fits after zero days (circles). 20 days (triangles), and 25 days (squares) when the sample is a
liquid. Lower panel: C(t) after 62 days the sample has gelled. Different data correspond to different heights in the cell and show the large variation in a/b
ratio caused by the random nature of the static scattering intensity.
superimposed on a static component which, if the particles
were immobile, would produce the familiar speckle pattern
characteristic of scattering from a system of random fixed
scatterers. As Pusey and van Megen noted, this random
spatial property of the static component is the reason
why the a/b ratio is so variable, and can be exploited by
moving the sample around until a value near zero is found
for the static component, resulting in an a/b ratio near to
1.0. As shown in Fig. 9, one spectrum has an a/b ratio of
0.8 and is therefore close to the case they described. Also,
it appears that the apparent decay time becomes longer as
the a/b ratio decreases, but we have not attempted to verify
this correlation quantitatively.
We also recorded PCS spectra of some gelled samples
while slowly translating the sample tube vertically. The
a/b ratio was then nearly 1.0 as expected if ergodicity is
restored, and C(t) exhibits a high plateau that decays at
long times. We also recorded count rate histories for these
spectra. For the stationary sample cases, the count rate is
largest for the small a/b ratio runs (large static intensity
causes a small a/b ratio) and is relatively constant. For
the translated samples, the count rate is very large and fluctuates wildly as the sample moves. The decay of C(t) at
times of 0.1 s observed for these translated samples is
due to the motion of the sample and does not relate to
the intrinsic dynamics of the colloidal particles.
4. Discussion
We have carried out PCS measurements on aqueous
solutions of Laponite XLG for three different preparation
methods, for a range of concentrations, and with different
filtration procedures. As in previous studies we found that
at concentrations below 1 wt% the aging process is very
slow and the PCS data are still evolving at times approaching one year. Samples prepared without pH control aggregated fastest in general, although one sample in this series
(AA4) had not gelled a full year after preparation. For
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H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
the samples prepared with pH control, there was little difference between those for which the pH was adjusted to a value
>10 after mixing was complete and those mixed with
water whose pH had already been adjusted to a value >10.
Comparing samples prepared without filtration, filtration with a 0.8 lm pore size filter or with a 0.45 lm filter
gave ambiguous results. In some cases the unfiltered sample gelled first, the 0.8 lm sample second, and the
0.45 lm sample last, with the rate of increase in cluster size
following the same sequence. But in some samples this
order was permuted or reversed. The filters were used as
obtained from the manufacturer (Millipore) and may contain small residues of detergent or solvent that influences
the cluster growth and gelation processes. In future experiments the effect of flushing the filters with pure water
before use will be explored as will the effects of preparing
samples under a dry nitrogen atmosphere.
5. Conclusions
We conclude that the aging behavior of Laponite suspensions is strongly affected by the sample preparation procedure, making it essentially impossible to compare the
results of experiments that follow different methods of
preparation. First, the speed with which Laponite particles
aggregate to form growing clusters is significantly higher
for samples with no pH adjustment than for those with
the pH >10. Second, filtration affects the rate of aggregation, but the relation between filter pore size and aggregation rate is not consistent. It is possible that residual
impurities in the filters used play a role, a possibility that
requires further study. Finally, in contrast to previous
claims, we conclude that filtration does not completely
break up the existing clusters and that aging that takes
place between mixing and filtration is not completely
reversed by filtration.
Acknowledgement
This research was supported by the NSF under Grant
No. DMR-0243471.
References
[1] W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions,
Cambridge University, Cambridge, 1991.
[2] R.J. Hunter, Introduction to Modern Colloid Science, Oxford
University, Oxford, 1993;
M.Y. Lin, H.M. Lindsay, D.A. Weitz, R.C. Ball, R. Klein, P.
Meakin, Phys. Rev. A 41 (1990) 2005.
[3] S.-H. Chen, F. Mallamace, F. Sciortino (Eds.)J. Phys. Condens. Mat.
16 (42) (2004).
[4] L. Cipelletti, L. Ramos, J. Phys. Condens. Mat. 17 (2005) R253.
[5] P.N. Pusey, W. van Megen, Phys. Rev. Lett. 59 (18) (1987) 2083.
[6] W. van Megen, P.N. Pusey, Phys. Rev. A 43 (10) (1991) 5249.
[7] W. van Megen, S.M. Underwood, P.N. Pusey, Phys. Rev. Lett. 67
(12) (1991) 1586.
[8] W. van Megen, S.W. Underwood, Phys. Rev. Lett. 70 (18) (1993)
2766.
[9] W. van Megen, S.M. Underwood, Phys. Rev. E 47 (1) (1993) 248.
[10] W. van Megen, S.M. Underwood, Phys. Rev. E 49 (5) (1994)
4206.
[11] W. van Megen, Transport Theor. Stat. Phys. 24 (6–8) (1995) 1017.
[12] E. Bartsch, M. Antonietti, W. Schup, H. Sillescu, J. Chem. Phys. 97
(6) (1992) 3950.
[13] W. Götze, in: J.-P. Hansen, D. Levesque, J. Zinn-Justin (Eds.),
Liquids, Freezing and the Glass Transition (Les Houches Summer
Schools of Theoretical Physics Session LI (1989)), North-Holland,
Amsterdam, 1991, p. 287.
[14] W. Götze, L. Sjögren, Rep. Prog. Phys. 55 (1992) 241.
[15] W. Götze, J. Phys.: Condens. Mat. 11 (1999) A1.
[16] J. Wu, J. Cao, Phys. Rev. Lett. 95 (2005) 78301.
[17] L. Fabbian, W. Götze, F. Sciortino, P. Tartaglia, F. Thiery, Phys.
Rev. E 59 (2) (1999) R1347.
[18] L. Fabbian, W. Götze, F. Sciortino, P. Tartaglia, F. Thiery, Phys.
Rev. E 60 (2) (1999) 2430.
[19] K. Dawson, G. Foffi, M. Fuchs, W. Götze, F. Sciortino, M. Sperl, P.
Tartaglia, T. Voigtmann, E. Zaccarelli, Phys. Rev. E 63 (2000) 11401.
[20] W. Götze, M. Sperl, J. Phys. Condens. Mat. 15 (2003) S869.
[21] T. Eckert, E. Bartsch, Phys. Rev. Lett. 89 (12) (2002) 125701.
[22] K.N. Pham, A.M. Puertas, J. Bergenholtz, S.U. Egelhaaf, A.
Moussaı̈d, P.N. Pusey, A.B. Schofield, M.E. Cates, M. Fuchs,
W.C.K. Poon, Science 296 (2002) 104.
[23] K.N. Pham, S.U. Egelhaf, P.N. Pusey, W.C.K. Poon, Phys. Rev. E 69
(2004) 11503.
[24] V. Trappe, P. Sandkühler, Curr. Opin. Colloid Interf. Sci. 8 (2004)
494.
[25] S. Mossa, F. Sciortino, P. Tartaglia, E. Zaccarelli, Langmuir 20
(2004) 10756.
[26] P.N. Segre, V. Prasad, A.B. Schofield, D.A. Weitz, Phys. Rev. Lett.
86 (2001) 6042.
[27] J. Bergenholtz, M. Fuchs, Phys. Rev. E 59 (5) (1999) 5706.
[28] J. Bergenholtz, M. Fuchs, J. Phys. Condens. Mat. 11 (1999) 10171.
[29] A.M. Puertas, M. Fuchs, M.E. Cates, Phys. Rev. Lett. 88 (9) (2002)
98301.
[30] K. Kroy, M.E. Cates, W.C.K. Poon, Phy. Rev. Lett. 92 (2004)
148302.
[31] F. Sciortino, S. Mossa, E. Zaccarelli, P. Tartaglia, arXiv:cond-mat
(0312161v1) (2003).
[32] F. Sciortino, S. Mossa, E. Zaccarelli, P. Tartaglia, Phys. Rev. Lett. 93
(5) (2004) 55701.
[33] A. Kumar, J. Wu, Colloid. Surface A 247 (2004) 145.
[34] P.J. Lu, J.C. Conrad, H.M. Wyss, A.B. Schofield, D.A. Weitz, Phys.
Rev. Lett. 96 (2006) 28306.
[35] P. Levitz, E. Lecolier, A. Mourchid, A. Delville, S. Lyonnard,
Europhys. Lett. 49 (5) (2000) 672.
[36] D.W. Thompson, J.T. Butterworth, J. Colloid Interf. Sci. 151 (1)
(1992) 236.
[37] F. Pignon, J.-M. Piau, A. Magnin, Phys. Rev. Lett. 76 (1996) 4857.
[38] F. Pignon, A. Magnin, J.-M. Piau, B. Cabane, P. Lindner, O. Diat,
Phys. Rev. E 56 (3) (1997) 3281.
[39] D. Bonn, H. Kellay, H. Tanaka, G. Wegdam, J. Meunier, Langmuir
15 (1999) 7534.
[40] D. Bonn, H. Tanaka, G. Wegdam, H. Kellay, J. Meunier, Europhys.
Lett. 45 (1) (1998) 52.
[41] B. Ruzicka, L. Zulian, G. Ruocco, Phys. Rev. Lett. 93 (2004) 258301.
[42] B.J. Lemaire, P. Panine, J.C.P. Gabriel, P. Davidson, Europhys. Lett.
59 (1) (2002) 55.
[43] J.-C.P. Gabriel, C. Sanchez, P. Davidson, J. Phys. Chem. 100 (1996)
11139.
[44] R. Agra, F. vanWijland, E. Trizac, Phys. Rev. Lett. 93 (1) (2004)
18304.
[45] B. Abou, D. Bonn, J. Meunier, Phys. Rev. E 64 (2001) 21510.
[46] R.G. Avery, J.D.F. Ramsay, J. Colloid Interf. Sci. 109 (1986) 448.
[47] M. Bellour, A. Knaebel, J.L. Harden, F. Lequeux, J.-P. Munch, Phys.
Rev. E 67 (2003) 31405.
[48] S. Bhatia, J. Barker, A. Mourchid, Langmuir 19 (2003) 532.
Author's personal copy
H.Z. Cummins / Journal of Non-Crystalline Solids 353 (2007) 3891–3905
[49] D. Bonn, S. Tanase, B. Abou, H. Tanaka, J. Meunier, Phys. Rev.
Lett. 89 (2002) 15701.
[50] R. DiLeonardo, F. Ianni, G. Ruocco, Phys. Rev. E 71 (2005) 11505.
[51] A. Knaebel, M. Bellour, J.P. Munch, V. Viasnoff, F. Lequeux, J.L.
Harden, Europhys. Lett. 52 (1) (2000) 73.
[52] M. Kroon, G.H. Wegdam, R. Sprik, Phys. Rev. E 54 (1996) 6541.
[53] M. Kroon, W.L. Vos, G.H. Wegdam, Phys. Rev. E 57 (2) (1998) 1962.
[54] T. Nicolai, S. Cocard, Langmuir 16 (2000) 8189.
[55]
[56]
[57]
[58]
[59]
[60]
3905
T. Nicolai, S. Cocard, Eur. Phys. J. E5 (2001) 221.
T. Nicolai, S. Cocard, J. Colloid Interf. Sci. 244 (2001) 51.
L. Rosta, H.R. vonGunten, J. Colloid Interf. Sci. 134 (2) (1990) 397.
P.N. Pusey, W. van Megen, Physica A 157 (1989) 705.
A.P.Y. Wong, P. Wiltzius, Rev. Sci. Instrum. 64 (1993) 2547.
S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, J. Chem.
Phys. 104 (1995) 1758.
[61] V. Viasnoff, F. Lequeux, Rev. Sci. Instrum. 73 (2002) 2336.