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3D Design of self-assembled nanoporous colloids
I. Sokolova,b,c and Y. Kievskya
a
Department of Physics, Clarkson University, Potsdam, NY, 13699-5820, USA
b
Department of Chemistry, Clarkson University, Potsdam, NY, 13699-5810, USA
c
Center for Advanced Material Processing (CAMP), Clarkson University, Potsdam, NY, 136995665, USA
Recently discovered synthesis of unusual curved nanoporous silica shapes, such as rods,
discoids, spheres, tubes, and hollow helicoids, have brought forth the problem of understanding
the formation mechanism. Knowledge of such mechanism may lead to the ability to control the
nanoporous shapes. This is important in a variety of applications and new technologies where
nanostructure and geometry determine function.
In this work the problem of morphogenesis of nanoporous silica shapes is analyzed. A
theoretical basis is outlined to describe the variety of forms and surface designs that result from
the liquid crystal stage, silicification and rigidification of shapes. Further experimental evidence
in favor of the suggested mechanisms is presented.
1. INTRODUCTION
With the discovery of the liquid crystal templating (see, e.g., [1, 2], a review [3] and other
references cited there) of hexagonal, cubic and lamellar nano(meso)structured silica, materials
science has moved into the area of design and synthesis of inorganics with complex form. It is
possible to synthesize inorganics with structural features of a few nanometers and architectures
over rather large length scales, up to hundreds of microns. This nanochemistry is inspiring
research in materials science, solid state chemistry, semiconductor physics, biomimetics, and
biomaterials [3–26]. Various amphiphiles can be organized into supramolecular assemblies and
together with a range of inorganic precursors create a large number of composite
mesostructures. Manipulation of surfactant packing parameter, headgroup charge, cosurfactants, solvents, co-solvents, and organic additives have been used to template particular
mesostructures. Dimension of the pores can be tuned with angstrom precision over the size
range of 20-100 Å (see, e.g., [8]).
Distinct templating mechanisms of inorganic mesostructures based upon cationic, anionic
and neutral surfactant assemblies have also been studied, see, e.g., [5, 27, 28]. Nanoscale
synthesis using surfactant templates is founded upon the idea of complementarity of charge,
geometry and stereochemistry in an organic-inorganic co-assembly, where the inorganic portion
mineralizes to yield the rigidified mesophase.
It has been found that the cationic surfactants form and mineralize to a well-ordered
nanostructure that can extend up to a few hundred microns [4–26]. This is the reason why the
study of this process attracts great attention. A non-ionic surfactant can also participate in a
neutral templating pathway to form inorganic nanostructures through a hydrogen-bonded
surfactant-silicate co-assembly. The weaker interactions for such a neutral co-assembly
produces less well-ordered nanoporous silica materials, although the pore size distribution is
often just as narrow as that obtained through cationic surfactant templating.
In this work we will discuss shaping mechanism (morphogenesis) of the cationic
surfactant acidic self-assembly templating in the presence of a silica precursor. A cationic
assembly can exchange its counteranion, for example, chloride, with a mineralizable inorganic
anion, protonated silicate. Synthesis of mesoporous thin films [7, 14, 18, 21–23, 29], spheres
[17, 30, 31], curved shaped solids [16, 18], tubes [24, 32], rods and fibers [18, 33], membranes
[34], and monoliths [35] has been reported recently. While chemistry of this process is rather
well understood, the mechanism of formation of nanoporous silica shapes is not well
elaborated. Vast variety of shapes makes it hard to develop the mechanism of formation of
mesoporous silica.
In the series of works [21, 24, 25], we have been developing theory of the mechanism
responsible for the shaping of the nanoporous silicas. The main hypothesis is that the complex
morphology of the shapes is a result of both development of defects in the original liquid crystal
templates and relaxation of mechanical stresses which appeared due to different degree of
polymerization of silica precursor. In the present work, we discuss a unified view on the
shaping mechanism, and provide new evidence in favor of the suggested mechanisms.
2. EXPERIMENTAL
Analyzing the published data [7, 14, 16–18, 21–25, 29–34] is somewhat difficult because many
parameters were changed from one synthesis to another. Moreover, the published results
typically do not have enough information about the shape geometry. In particular, since those
works were focused mainly on the synthesis, the shapes of assembled particles were usually
mentioned without referring to all existing variety of shapes. That is why we sometime repeated
already reported synthesis.
To study the first mechanism, silicification of liquid crystals, we studied the acidic
synthesis described in below by changing only one parameter, the acidity. Silica precursor was
tetraethylorthosilicate (TEOS, 99.999%, Aldrich). We used cetyltrimethylammonium chloride
(CTACl, 25 wt. % aqueous solution, Aldrich) as a surfactant template. The required acidity was
created by means of hydrochloric acid (HCl 37.6 wt. % aqueous solution, SafeCote). All
chemicals were used as received. The surfactant, acid, and distilled (Corning, AG-1b, 1MΩ-cm)
water were mixed in a plastic bottle (HDPE), stirred first at room temperature (25°C) for 15
minutes, and then TEOS was added to the acidic solution of surfactant, stirred for 5 minutes.
The final molar composition of the reactants was 100 H2O : X HCl : 0.11 CTACl : 0.13 TEOS.
The value of part X was in the range of 3 – 18. The resulting solution was kept under quiescent
conditions for 3 hours at room temperature. Both low (4°C) and high (80°C) temperature were
used with the same components, but the TEOS and acidic surfactant bath were either cooled or
heated to the needed temperature before their mixing.
The material was collected by centrifugation (IEC Clinical Centrifuge, 5 minutes, 6000
rpm), then resuspended in distillated water, and centrifuge again. The resuspension procedure
was repeated three times.
To study the Origami mechanism, we used the synthesis reported in [24]. Several
modifications were as follows. First, to study the role of the air-water interfacial film, we gently
removed the film after 9 hours of synthesis. After another 9 hours, the assembled shapes were
collected. The second modification was done on the stage of the shape collection. Because
some interesting Origami shapes, e.g., the hollow helices [24], have thinner walls than other
typical Origami shapes (like cones, hollow tubes, long large fibers), they can be easily
discarded by using the standard collecting procedure described above. Therefore, the
centrifugation time was increased up to one hour.
A scanning electron microscope (SEM, JEOL JSM-6300) was used to characterize
morphology of the synthesized particles. A thin layer of gold was spattered on the particle
surface to improve the SEM contrast.
The pore periodicity was found by using low-angle powder X-ray diffraction (XRD)
technique (Ordela 1050X). Olympus BHM2 equipped with brightfield and Nomarski
differential imaging mode was used in the optical microscopy study.
3. EXPERIMENTAL RESULTS
3.1. Dependence on acidity and temperature
High acidity synthesis typically leads to a highly ordered fiber-type of shapes with a
relatively low content of discoidal shapes, Fig.1a. Decrease of acidity leads to the increase of
bending the fibers and increase of gyroids/discoid types of shapes, Fig.1b. Near zero pH (X=5),
the fibers almost disappear, and the yield consists almost completely of gyroids/discoids. For
lower acidity (X=3), the morphology of shapes remains about the same, they are mostly
discoids/gyroids. However, the amount of "shapeless" yield, junk increases. Variability of
different shapes and sizes also increases, Fig.1c.
To study dependence on temperature, we synthesized fibers (X=9) at 4oC. This resulted in
a very high yield of straight fibers, Fig.2. The same synthesis but at room temperature brought
more bent fibers. For acidity at pH1.0, the increase of temperature to 80oC resulted in formation
of spheres [17], whereas gyroids and discoids were formed at room temperatures.
It is interesting to note that the time of synthesis increases with the decrease of acidity.
When assembling fibers (high acidity), the first shapes appear within minutes. When
assembling discoids and gyroids (lower acidity), they appear only in a few hours.
a)
b)
c)
Fig.1. Typical shapes synthesized with different acidity: a) hexagonal fibers assembled with the amount
of HCl X=9 (the bar size is 5µm); b) mostly discoids with X=5 (the bar size is 5µm); c) a mix of “junky”
shapes (the bar size is 11µm), discoids and gyroids (not shown), X=3.
3.2. Origami shapes
The Origami shapes, Fig.3 were synthesized in the acidic bath with pH1.5–2. As was
noted above, the synthesis under such condition should take considerable time. Indeed, the first
Fig.2. Low temperature (4oC)
synthesis of fibers with the
amount of HCl X=9. The fibers
are not bent as in the case of
room temperature synthesis
(25oC), Fig.1a. (The bar size is
22µm).
Fig.3. Examples of the Origami shapes, a cone and hollow tube.
(The bar size is 5µm).
Origami shapes appear in about 9 hours. To prevent drifting of pH during such a long synthesis,
a pH stabilizer, formamide was added to the synthesizing bath. Without such a stabilizer, no
Origami shapes were found. It is interesting to note that without formamide the nanoporous
shapes grow much faster (3–4 hours). However, most of it is shapeless "junk". At the same
time, we do not observe such a junk during the Origami synthesis. This implies that formamide
inhibits the condensation of silica in the synthesizing bath.
To study the influence of the air-water interface nanoporous films on the Origami
synthesis, we repeated the regular Origami synthesis, but removed the film after nine hours of
synthesis. The result shows a considerable decrease of percentage of the Origami shapes.
Difference in morphology and quantity of the shapes (analyzed with optical microscopy)
showed that the portion of Origami particles decreased almost 3 times.
Nanoporosity of the synthesized shapes was confirmed with the low angle X-ray
diffraction technique (not shown).
4. DISCUSSION: SUGGESTED MECHANISMS OF MORPHOGENESIS
We organized the zoo of shapes described in the previous Section in a scheme presented in
Fig.4, which shows morphologies of shapes assembled experimentally under different
conditions. We hypothesize that there are at least two different mechanisms of morphogenesis
of silica shapes in the acidic cationic templating, a fiber-discoid (takes place inside the
medium) and an Origami–type of mechanism of folding and bending thin stripes of nanoporous
film grown on the air-water interface.
The first mechanism of the shaping is based on the assumption that the assembled
mesoshapes are the silicified replicas of the surfactant liquid crystals. Consequently, the
observed topological features of such shapes mimic those of the liquid crystals.
Fig.4. Morphology of self-assembled shapes and the major mechanism responsible for the
morphogenesis.
Alkoxysilanes, the silica precursors, play a role of glue for binding the liquid crystal
nano-rods into large shapes [13, 25]. The second mechanism we assign to the other class of
shapes, the hollow tubes, cones, helices. This hypothesis describes this process as a
supramolecular Origami and was presented in [24]. In contrast to the previous mechanism,
which presumably takes place in the bulk of the solution, the Origami process is applied to the
nanoporous film formed at the air-water interface.
There were some data analyzed in the cited works in support of the suggested models.
Let us show how the data obtained in this work can further support the described mechanisms.
4.1. Silicification of liquid crystal template
Let us demonstrate that the observed dependences of the morphogenesis on acidity and
temperature of the synthesis can be explained in the suggested mechanism of silicification of
liquid crystal templates. The main point of this mechanism is the minimization of free energy
of the liquid crystal template. Following [25], such energy is given by
r
r 2 K2 r
r 2 K3 r
r 2
| ∇n |2
 K1
Fd = ∫  ( div n ) +
( n rot n ) +
[n rot n ]  dV + σ ∫
dS ,
2
2
2
2

Volume 
Surface
(1)
r
where σ is the surface tension constant, n is a unit vector of the director-field of the nematic
crystal, and K1,2,3 are the elastic modulae, that denote splay, twist, and bend deformations,
respectively.
n
r
ψ
ϕ
O
r
Fig.5. Polar coordinate notation for a fiber-like liquid crystal, where n is the vector of the director-field.
Vertical z axis is perpendicular to the page.
Let us consider a fiber-type shape. Hereafter, as in [25] we assume that K2 = 0 (no
observed bending/twisting inside the shapes in z direction). Using cylindrical coordinate
system, Fig.5, and assuming that the shapes do not change in vertical direction (it can be called
as “rectangular fiber” approximation), one can rewrite Eq. (1) as follows:
Fd = C H ( K1 + K 3 )  ∫ dϕ (1 − α cos 2ψ ) (1 + ψ ′2 ) + ∆ ∫ dϕ | ∇ϕ r |2  ,
 ϕ 0

ϕ0
ϕ1
ϕ1
(2)
where ϕ0 (ϕ1) is the polar angle corresponding to the beginning (end) of the fiber, C is a
numerical constant, H is the z-dimension of the fiber. Also,
α=
K 3 − K1
,
K 3 + K1
ψ′=
∂ψ
,
∂ϕ
| ∇ϕ r |=
1 ∂R
,
R ∂ϕ
,
2
R
∆ =σ
K 3 + K1 ln R / Rin
(3)
where R (Rin ) is the external (internal) radius of the fiber.
The synthesizing shapes should be described by minimum of energy (2), or more
precisely, by the integrals of motion of Eq. (2). Similar to [25], it can be shown that solutions of
the integral of motion equation will have buckling type of defects (described by the Frank index
of disclination). Despite some occasional observation of such buckles, we will focus on nobuckle solution. As one can see from the experimental images, the fibers have about the same
radius of curvature and the diameter (like cylinders just bent). Therefore, we can put ψ = π/2
for all points in the fiber, as well as ∂R / ∂ϕ = 0 . This will eliminate the effect of surface
tension, and reduce Eq. (2) to
Fd = 2C HK 3 (ϕ1 − ϕ 0) = 2C HK 3
L
,
R
where L is the length of the fiber, R its radius of curvature.
(4)
This is an easy equation to analyze. Let us first consider the effect of temperature on the
curvature radius. In equilibrium, free energy (4) should be proportional to the thermal energy
(skipping the introduction of entropy for mesoscopic size shapes), i.e., temperature T.
Therefore, the curvature radius R~1/T. This is exactly what was observed, decrease of
temperature resulted in synthesis of straight fibers.
Let us analyze the next situation when we keep the temperature the same, but change the
pH. Because the liquid crystal templating is based on complimentarily of charges, each channel
in nematic liquid crystal is covered by protonated silicate, which is polymerizing to silica.
Isoelectric point of silica is close to pH2.5. The stronger acidity, the more charges on silica.
Hence, the bend deformation modulus should increase (it is harder to bend a charged rod). This,
according to eq.(4), should result in the increase of the curvature radius, R, to keep the free
energy constant. It is what observed and presented in the scheme of Fig.4. With the decrease of
acidity and approaching pH2.5, relatively straight fibers become more and more bent, and
finally self-closed into discoids/gyroids. Higher energy can relax in the Frank disclination
defects as was described in [24].
4.2. Origami
Our finding of the decrease of percentage of Origami shapes by a factor of three, which
happened after removal the air-water interfacial film, suggests direct evidence that the Origami
shapes form from that film. The shaping mechanism is considered to be a sort of Origami
folding of the nanoporous film. The reason for the folding is the following. The film is not
created instantly, but grows from a first monolayer. New layers of micellar rods grown on the
film are younger, and consequently, underwent less contraction due to the polymerization of
silicate to silica. To compensate the increase of internal stress, relatively weakly interacting
micellar rods are bent in the way shown in Fig.6. Because the contraction can be in longitudinal
(along the rod) and radial (across the rod) directions, there are two perpendicular directions of
bending as shown in Fig.7. Taking into account both such contractions, and consequently
bending in two perpendicular directions, it can be shown [24] that the resulting shape will be a
hollow tube with the mesoporous channels (micellar rods) running along a helix on the surface
of the tube, Fig.7. Assembly of helixes can be explained in a similar manner. If we assume that
the original mesoporous flat film was growing not only in thickness, but also in size along the
air-water interface, then we can describe the bending of the film similar to the previous case.
a)
b)
Fig.6. Bending of micellar rods due to the silica polymerization: a) due to longitudinal contraction, b)
due to contraction in radial direction, across the micellar rods.
Fig.7. Bending of mesoporous film in two perpendicular directions. Resulting shape is either a hollow
tube with the mesoporous channels (micellar rods) running along a helix on the surface of the tube or a
hollow helicoid. Angle α as shown is the helix angle.
a)
b)
Fig.8. a) Theoretical 3D simulation of a helix, b) experimentally found similar helix.
Fig.9. A rare event of helices in the process of formation.
Helices are the most interesting example of the Origami zoo. The suggested theoretical
model is very restrictive in prediction of the geometrical parameters of the helices. Therefore it
is rather interesting to compare it with the theoretical predictions. For example, we found that
the angle α, see Fig.7, for fully formed helices lies in a rather narrow range: α=61±2o, which is
in good agreement with the theoretical estimations [24]. Moreover, 3D simulations based on the
suggested model show a nice visual resemblance of the observed shapes. Fig.8a shows a result
of 3D simulation of a helix that should be synthesized according to the theory. Experimentally
found similar shape is presented in Fig.8b.
Finally, Fig.9 presents a couple of rather rare optical images of helices in the process of
formation, which is quite straight evidence in favor of the suggested model.
5. CONCLUSIONS
We analyzed a model that could explain 3D morphology of self-assembled nanoporous silica
shapes. We hypothesized that there were at least two distinctive mechanisms of morphogenesis
of silica shapes in the acidic cationic templating, a fiber-discoid (takes place inside the medium)
and an origami-type mechanism of folding and bending thin stripes of nanoporous film grown
on the air-water interface. The analysis of dependence of the shape morphology on the
synthesis conditions, such as temperature and acidity, shows a good agreement with the model
predictions (the first mechanism). Analysis of the second mechanism of synthesis shows that
the Origami shapes are indeed assembled from the film on air-water interface. Further analysis
of its geometry demonstrates a good agreement with the theoretical predictions. Finally, we
present a rare event, images of helices in the process of formation, which is quite straight
evidence in favor of the suggested model.
It should be noted that the present paper is not a final proof of the proposed model. More
quantitative analysis will be presented in our future works.
ACKNOWLEDGEMENTS
Fruitful discussions with Prof. G. A. Ozin and financial support from NYSTAR are
acknowledged by I.S.
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