Temperature-induced particle self-assembly

Article abstract of DOI:10.1016/j.jpcs.2009.09.011

Agglomeration of monodisperse thiol-stabilized gold particles with diameters of 6 nm, suspended in organic solvents, was induced by the cooling of the suspension. A sharp transition between the stable suspension and agglomeration resulted. The temperature of the transition depends on the concentration and the compatibility of the solvent. The morphology of the formed particle structures upon agglomeration implies that the used metal colloid can be described as a van der Waals-gas. The particles undergo phase transitions from a stable fluid phase to a metastable phase, in which nucleation and growth occur, or to an instable phase, in which spinodal decomposition occurs. The results will direct research on routes to nanostructured materials using nanoparticles as building blocks.

Full text of DOI:10.1016/j.jpcs.2009.09.011

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Journal of Physics and Chemistry of Solids 71 (2010) 95–99
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids
journal homepage: www.elsevier.com/locate/jpcs
Temperature-induced particle self-assembly
Ã
Philip Born, Eoin Murray, Tobias Kraus
INM – Leibniz Institute for New Materials, Campus D2 2, 66123 Saarb u¨ cken, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
Agglomeration of monodisperse thiol-stabilized gold particles with diameters of 6 nm, suspended in
organic solvents, was induced by the cooling of the suspension. A sharp transition between the stable
suspension and agglomeration resulted. The temperature of the transition depends on the concentra-
tion and the compatibility of the solvent. The morphology of the formed particle structures upon
agglomeration implies that the used metal colloid can be described as a van der Waals-gas. The particles
undergo phase transitions from a stable fluid phase to a metastable phase, in which nucleation and
growth occur, or to an instable phase, in which spinodal decomposition occurs. The results will direct
research on routes to nanostructured materials using nanoparticles as building blocks.
Received 2 June 2009
Accepted 18 September 2009
Keywords:
A. Nanostructures
C. Electron microscopy
D. Phase transitions
D. Superlattices
&
2009 Elsevier Ltd. All rights reserved.
1
. Introduction
purely an entropic effect and is dominant for particles with little
van der Waals interaction such as polymer or oxide particles in
water which can be treated as hard spheres. For metallic
nanoparticles, however, agglomeration and ordering is observed
at much lower volume fractions than required for a Kirkwood–
Alder transition. The agglomeration of the particles to densely
packed structures can be explained by the destabilization of the
particles by shielding of the electrostatic repulsion [14,15] or
adding incompatible solvents to suppress steric stabilization [1],
or effects inside drying thin films or droplets of suspensions
[16,17]. However, the process parameters which distinguish
between randomly and cubic close-packing have yet to be
elucidated.
Here we study the arrangement process of gold nanoparticles
which directly assemble into superstructures from the bulk
suspension. This experimental system excludes non-equilibrium
processes and instabilities such as convective flow and confine-
ment, effects that would complicate the description of the
processes and hinder the search for basic concepts of particle
arrangement. Varying the growth speed should clarify whether
order is always achieved in equilibrium or if kinetic effects
dominate, i.e. the particles get jammed under certain conditions
before reaching the ordered state.
Many technologies, including optoelectronics, thermoelectrics,
separation methods, functional coatings, and energetic materials,
could profit from the ability to control the structure of materials
on
a nanometer length scale. One approach to synthesize
nanostructured materials is to use suspended nanoparticles as
building blocks [1–11]. Energetic materials will benefit from the
higher reactivity due to the high surface-to-volume ratio and the
lower ignition temperatures caused by the lower melting point
[
12]. A way to further improve a nanostructured energetic
material is to control the arrangement of the particles in the
system. When replacing a randomly close-packed granulate by a
cubic close-packed system, the volume fraction occupied by
particles increases from a maximum of 64% in the random system
to 74% in the cubic system, thus increasing the stored chemical
energy per unit volume. Additionally, the number of next
neighbors for each particle doubles from 6 to 12 and the
interparticle space is uniform, ensuring homogeneous combus-
tion. Recent experiments have demonstrated that mixed nano-
particles can also form regular superstructures, in which the
stoichiometry of the formed assemblies and the chemical
environment of each individual particle are precisely controlled
[
8,9,11].
In many cases, the disorder–order transition for sub-micron
particle suspensions can be described as a Kirkwood–Alder
transition. When the particle volume fraction of the suspension
exceeds 50%, there is a transition to an ordered state, in which the
available volume per particle is maximized [13]. This transition is
2. Experimental
2.1. Nanoparticle synthesis
Low polydispersity is crucial to gain ordered close-packed
structures of particles [18]. A synthetic route adapted from Zheng
et al. [19] was used in this work. Gold nanoparticles were formed
by a one-pot reduction of a gold source by an amine–borane
Ã
Corresponding author.
E-mail address: tobias.kraus@inm-gmbh.de (T. Kraus).
0
022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2009.09.011

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P. Born et al. / Journal of Physics and Chemistry of Solids 71 (2010) 95–99
complex in the presence of an alkyl thiol. In a typical synthesis,
.31 g chlorotriphenylphosphine gold (AuPPh Cl, ABCR 98%) was
0
3
stirred in 50 ml benzene (Riedel-de-Hahn 499.5%) forming a
colorless solution. A mixture of 0.53 g tert-butylamineborane
(Fluka 97%) and 0.18 ml dodecanethiol (Fluka 498%) was added
to the AuPPh Cl solution and reacted at 55 1C for 2 h. Following
3
completion of the reduction reaction the deep red solution was
cooled to room temperature, precipitated by the addition of
ethanol and washed by centrifugation and subsequent resuspen-
sion in toluene. Finally, the particles were resuspended in
heptane.
2.2. Characterization techniques
Transmission electron microscopy (TEM) was performed using
a Philips CM 200 TEM operating at 200 keV with a point-to-point
resolution of 0.24 nm and a lattice resolution of 0.14 nm. For
selective-area small-angle electron diffraction (SASAED), the
camera length was set to 4.7 m. For particle characterization,
copper TEM grids with carbon coating were dipped into the
suspension and were dried in an oven at 105 1C. To determine the
mean size and size distribution of the gold cores of the particles,
several hundred particles were evaluated.
In order to characterize particle structures grown in suspen-
sion at certain temperatures drying at elevated temperatures
must be avoided. Therefore, TEM grids were dipped into the
suspension with the particle agglomerates and then immediately
into liquid nitrogen to vitrify them, and were finally freeze-dried
Fig. 1. Transmission electron micrograph of dodecanethiol-capped gold particles.
The scale bar corresponds to 10 nm.
Table 1
ꢀ
5
Overview over particle characterization results.
in a vacuum of 10
bar.
Dynamic light scattering (DLS) analysis was performed using a
Wyatt Technology DynaPro Titan operating at a wavelength of
ꢀ
1
capping ligand
r
C
(nm)
r
H
(nm)
l
CL (nm)
Conc. (parts per ml
)
8
31.2 nm to measure the hydrodynamic radius of the particles.
C10-thiol
2.9 (17%)
2.8 (10%)
2.1 (19%)
2.7 (18%)
4.2 (12%)
4.5 (10%)
5.0 (24%)
5.8 (9%)
1.3
1.7
2.9
3.1
1
5
The thickness of the capping layer was calculated by subtracting
the core radius measured with TEM from the hydrodynamic
radius. The temperature in the sample chamber was varied
between ꢀ8 and 60 1C with humidity control to avoid condensa-
tion of vapor.
C12-thiol
C16-thiol
C18-thiol
2.74 ꢁ 10
14
1.62 ꢁ 10
rC is the radius of the gold core measured with TEM, rH the hydrodynamic radius
measured with DLS, CL the thickness of the capping layer, and Conc. the
l
concentration measured with ICP-AES. Polydispersities are given in brackets.
The gold concentration was measured by inductively coupled
plasma atomic emission spectroscopy (ICP-AES) on a Horiba Jobin
Yvon Ultima 2 instrument. Results from diluted suspensions of the
gold colloid were compared to a standard gold salt solutions
concentration curve for quantitative analysis.
2.3. Growth experiments
The growth of particle assemblies in bulk liquids was
monitored in-situ by DLS. The sample temperature was decreased
in steps of 1 K and equilibrated for 1 min, followed by a DLS
measurement of 100 s. When the cumulant fit of the autocorrela-
tion function showed an increase in the mean particle diameter,
the sample was heated again above the threshold temperature to
disassemble the particle structures. By setting and maintaining a
temperature close to or far below the threshold temperature, the
agglomeration rate could be adjusted.
3
. Results
3
.1. Particle characterization
Fig. 2. Typical DLS measurement of a temperature-induced particle agglomera-
tion. Below 3 1C the particles agglomerate, above 3 1C the agglomerates
disassemble again.
In Fig. 1 a typical TEM image of the gold particles synthesized
with dodecanethiol as a stabilizer can be seen. The particles form
hexagonally close-packed layers; the particle distance is
determined by the minimum of the interparticle potential.
A good size and shape uniformity is visible. An overview of
particle characterization results is given in Table 1. Notable is
the minimum in polydispersity for the sample synthesized
with dodecanethiol, which was used for further experiments.

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n-Heptane was found to be the best solvent in terms of particle
3.2. Growth of particle superlattices
stability. In solvents with even only slightly higher polarity, such
as chloroform or toluene, DLS confirmed that small particle
agglomerates were always present at room temperature.
A dependence of the particle stability on temperature was
observed. Cooling the suspension eventually led to agglomeration
of the particles, indicated by an increase of the hydrodynamic
radius measured by DLS. A typical temperature-induced transition
between a stable gold colloid and particle agglomeration can
be seen in Fig. 2. When this sample is cooled below 3 1C,
agglomeration begins. The agglomeration ceases only when the
temperature is increased above the threshold. The agglomerates
disassemble and the hydrodynamic radius returns to the value
of free particles. Using known transition temperatures, variable
growth rate experiments can be performed and the influence of
the growth rate on the particle ordering can be observed. One
might assume that a fast growth would lead to a jamming of the
particles and prevent ordering.
By setting the temperature just below the transition threshold,
ꢀ
4
ꢀ1
slow growth (10 nm s at 2 1C) of the particle agglomerates
was observed (Fig. 3). By cooling further, a faster agglomeration
ꢀ
1
(
1 nm s
at ꢀ6 1C) was induced. The agglomerates grown at a
low growth rate had diameters of roughly 100 nm and showed no
order as shown in Fig. 4. The structures grown at the lower
temperature formed large percolating networks, again with no
ordering of particles.
To test the influence of the absolute temperature, the transition
temperature was altered. The transition temperature depends on
the concentration of the suspension. A test series of transition
measurements at different concentrations is given in Fig. 5.
Another way to increase the transition temperature is to add a
Fig. 3. Hydrodynamic radius as function of time measured with DLS at different
temperatures. Noteworthy is the high agglomeration rate at ꢀ6 1C.
Fig. 4. Particle agglomerates grown at (a) ꢀ6 1C, (b) 2 1C, and (c) 22 1C. The insets show SASAED patterns, proving the ordering of the agglomerates grown at 22 1C. Scale
bars correspond to (a) 1 m,( b) 50 nm, and (c) 0.1 m.
m
m

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slightly more polar solvent to the suspension. With 10% toluene in
the suspension, the transition temperature has shifted above
room temperature and allows an intermediate growth rate of
Dipping of the TEM grid creates a thin liquid film that may
have an influence on the particle agglomerates. To rule this effect
out, test tubes containing a TEM grid were filled with 100 mm of
ꢀ
2
ꢀ1
10
nm s
at 22 1C (Fig. 3). The agglomerates grown at this
gold suspension using pure heptane as solvent and were placed in
a small temperature-controlled and convection-free chamber to
allow solvent evaporation. Evaporation of the liquid in the small
chamber took approximately a day at room temperature and up to
several days at lower temperature. Thus the drying occurred
on time scales far removed from the particle time scales for
diffusion and relaxation. The results (Fig. 6) correlate well
with the structures grown earlier. At ꢀ20 1C, large percolating
agglomerates of unordered particles remain on the grid. At 5 1C,
ordered micrometer-sized agglomerates and unordered agglo-
merates with a diameter of several hundred nanometers are
formed. At 20 1C, well ordered agglomerates with diameters of
several hundred nanometers are deposited, which probably
formed in the later stages of the evaporation when the loss of
solvent had increased the concentration and transition tempe-
ratures near room temperature were attained.
temperature had excellent particle ordering (Fig. 4), although the
growth rate was much higher than for the structures grown at
2
1C. These results suggest that the absolute temperature, not the
growth rate, is responsible for the close-packing of the particles.
4. Discussion
We found that a suspension of sterically stabilized metallic
nanoparticles undergoes a transition from a stable dispersed state
to an unstable state when it is cooled. The temperature at which
the transition occurs depends on the concentration of the
suspension. The condensates formed in the unstable state can
be either small, almost spherical agglomerates, or (at lower
temperatures) large percolating networks resembling structures
Fig. 5. The transition temperature as function of the sample concentration, as
measured with DLS. The lines are guidelines for the eye.
Fig. 6. Particle structures grown at (a) 20 1C, (b) and (c) 5 1C, and (d) ꢀ20 1C. (b) and (c) show the coexistence of ordered and unordered agglomerates. The scale bars
correspond to (a) 0.2 m, (b) 0.2 m, (c) 50 nm, and (d) 0.5 m. Inset in (b) shows the SASASED pattern of the agglomerate.
m
m
m

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fluid–fluid transition disappear. Thus the shape of the particle
potential determines whether the phase separation leads to an
ordered solid phase or an unordered liquid phase of the particles.
Treating the suspension as
a van der Waals-gas quite
accurately accounts for the agglomeration behavior, but it does
not fully explain the temperature-dependence of the ordering. To
describe this behavior, it may be necessary to take into account
parameters such as particle kinetic energy or particle mobility.
Consequently it may be possible to assign regions in a phase
diagram, where particles form ordered structures and to make
predictions for other particle systems.
5. Conclusions
Agglomeration of gold nanoparticles has been studied as a
function of the temperature. Phase behavior similar to that
of a van der Waals-gas was observed, explaining the general
conditions which are necessary for the formation of ordered
particle superstructures. To obtain a well-aligned close-packed
mesoscopic material, the binodal decomposition line of the source
suspension must be determined. The temperature must then be
adjusted to start nucleation and growth but still keeps the
suspension from spinodal decomposition.
Fig. 7. Schematic phase diagram of
a hard sphere system interacting via a
Lennard–Jones potential (adapted from [21]).
formed by spinodal decomposition. Ordering only occurs for
particle assembly at high temperatures, despite of the slow
assembly process at low temperatures.
However, the process of structure formation is not yet fully
understood and can probably not be described by a temperature–
concentration phase diagram. Although quantative predictions of
the phase behavior for different systems cannot yet be made, the
qualitative result should be transferrable to similar colloids with
strong van der Waals interaction, e.g. metals such as aluminum or
iron and other materials with interesting energetic applications.
According to the model of Edwards and Dolan [20], the
interparticle potential of two sterically stabilized particles can
be described by the formula
1
6 r6
V ¼ ꢀ 9
NkbT
2
ꢀð3d =2lLÞ
A
Ham
þ
2e
;
d6
A
where r is the particle radius, d the surface separation of the
particles, AHam the Hamaker-coefficient, N the number of inter-
b
acting polymers, A the interacting surface, k T the thermal energy,
l the linker length, and L the length of the ligand.
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interpretation of our results. Fig. 7 shows a schematic phase
diagram for spheres interacting via a Lennard–Jones potential
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