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3D design of self-assembled nanoporous colloids
Studies in Surface Science and Catalysis 156 M. Jaroniec and A. Sayari (Editors) 9 2005 ElsevierB.V. All rights reserved
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3D Design of self-assembled nanoporous colloids I. S o k o l o v a'b'c and Y. K i e v s k y a aDepartment of Physics, Clarkson University, Potsdam, NY, 13699-5820, USA bDepartment of Chemistry, Clarkson University, Potsdam, NY, 13699-5810, USA CCenter 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 A (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
434
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 (CTAC1, 25 wt. % aqueous solution, Aldrich) as a surfactant template. The required acidity was created by means of hydrochloric acid (HC1 37.6 wt. % aqueous solution, SafeCote). All chemicals were used as received. The surfactant, acid, and distilled (Coming, AG-lb, 1Mf~-cm) water were mixed in a plastic bottle (HDPE), stirred first at room temperature (25~ 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 H20 :X HCI : 0.11 CTACI : 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~ and high (80~ 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
435 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.la. 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 0(=9) at 4~ 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 pH 1.0, the increase of temperature to 80~ 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 HC1X=9 (the bar size is 5~tm); b) mostly discoids with X-5 (the bar size is 5p,m); c) a mix of"junky" shapes (the bar size is 1l~tm), discoids and gyroids (not shown), X=3.
436
3.2. Origami shapes The Origami shapes, Fig.3 were synthesized in the acidic bath with pill.5-2. As was noted above, the synthesis under such condition should take considerable time. Indeed, the first
Fig.2. Low temperature (4~ synthesis of fibers with the amount of HC1X=9. The fibers are not bent as in the case of room temperature synthesis (25~ Fig. la. (The bar size is 22~tm).
Fig.3. Examples of the Origami shapes, a cone and hollow tube. (The bar size is 5~tm).
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.
437
<
,Origami mechanism , 2.0
Silicification of liquid crystals -0.1 1.0 -0.6
I
'I
0 fibers
gyroid, discoid
pH
I ! I ! I I I I I I
sphere, discoid,
film
i
I
! !
cone
hollow tube etc.
helicoid
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
Fd =
~KJ(dive) 2 +--2-(n r~ Vo
e
+--2[ft rotn] 2 dV +or ~ IV~ J2 Surface 2
(1)
where ~ is the surface tension constant, ~ 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.
438
Fig.5. Polar coordinate notation for a fiber-like liquid crystal, where ~ 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 1(2 = 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: F a = C H ( K ~ + K3)
0 dip ( 1 - a c ~
(1 + g t ' 2 ) + 6
dip ] V ~ r 12
(2)
where q~0 (r 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, a=
K 3 - Kl
gt'
K, + x-------7' A=cr
2
oqgt
- aq,'
1 OR
L
R
I= ,
(3)
g 3 +K 1 lnR/R~. where R (Ri,) 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 N = W2 for all points in the fiber, as well as b R / b q ~ - 0 . This will eliminate the effect of surface tension, and reduce Eq. (2) to
F a - 2 C HK3 (r
- r
L ) - 2C HK 3 -R'
where L is the length of the fiber, R its radius of curvature.
(4)
439 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~I/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 fiat 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.
o a)
voOoOOOOU 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.
440
c__~
'
..... : ,.
~ , i i i l i,i ],]]~/~
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 ct 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.
441 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 t~, see Fig.7, for fully formed helices lies in a rather narrow range: t~=61+2 ~ 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. REFERENCES [ 1]' T. Yanagisawa, T. Shimizu, K. Kuroda, C. Kato, Bull. Chem. Soc. Jpn., 63 (1990) 988. [2] C.T. Kresge, M. Leonowicz, W. J. Roth, J. C. Vartuli, and J. C. Beck, Nature 359 (1992) 710. [3] U. Ciesla, F. Schiith, Microporous and Mesoporous Materials 27 (1999) 131. [4] S. Mann and G. A. Ozin, Nature 382 (1996) 313. [5] D.M. Antonelli and J. Y. Ying, Curr. Opin. Coll. Interf. Sci. 1 (1996) 523. [6] T. Jiang and G. A. Ozin, J. Mater. Chem. 8 (1998) 1099. [7] G. S. Attard, P. N. Bartlett, N. R. B. Coleman, J. M. Elliott, J. R. Owen., and J. H. Wang, Science 278 (1997) 838. [8] D.Y. Zhao, J.L. Feng, Q. S. Huo, N. Melosh, G. H. Fredrickson, B. F. Chmelka, and G. D. Stucky, Science 279 (1998) 548. [9] H. Yang, N. Coombs, and G. A. Ozin, Nature 386 (1997) 692. [ 10] C. du Fresne von Hohenesche, V. Stathopoulos, K. K. Unger, A. Lind, M. Linden, Stud. Surf. Sci. Catal., 144, F. Rodriguez-Reinoso, B. McEnaney, J. Rouquerol, K. K. Unger (eds.), Elsevier, Amsterdam, 2002, p. 339.
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3D Design of self-assembled nanoporous colloids I. S o k o l o v a'b'c and Y. K i e v s k y a aDepartment of Physics, Clarkson University, Potsdam, NY, 13699-5820, USA bDepartment of Chemistry, Clarkson University, Potsdam, NY, 13699-5810, USA CCenter 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 A (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
434
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 (CTAC1, 25 wt. % aqueous solution, Aldrich) as a surfactant template. The required acidity was created by means of hydrochloric acid (HC1 37.6 wt. % aqueous solution, SafeCote). All chemicals were used as received. The surfactant, acid, and distilled (Coming, AG-lb, 1Mf~-cm) water were mixed in a plastic bottle (HDPE), stirred first at room temperature (25~ 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 H20 :X HCI : 0.11 CTACI : 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~ and high (80~ 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
435 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.la. 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 0(=9) at 4~ 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 pH 1.0, the increase of temperature to 80~ 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 HC1X=9 (the bar size is 5~tm); b) mostly discoids with X-5 (the bar size is 5p,m); c) a mix of"junky" shapes (the bar size is 1l~tm), discoids and gyroids (not shown), X=3.
436
3.2. Origami shapes The Origami shapes, Fig.3 were synthesized in the acidic bath with pill.5-2. As was noted above, the synthesis under such condition should take considerable time. Indeed, the first
Fig.2. Low temperature (4~ synthesis of fibers with the amount of HC1X=9. The fibers are not bent as in the case of room temperature synthesis (25~ Fig. la. (The bar size is 22~tm).
Fig.3. Examples of the Origami shapes, a cone and hollow tube. (The bar size is 5~tm).
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.
437
<
,Origami mechanism , 2.0
Silicification of liquid crystals -0.1 1.0 -0.6
I
'I
0 fibers
gyroid, discoid
pH
I ! I ! I I I I I I
sphere, discoid,
film
i
I
! !
cone
hollow tube etc.
helicoid
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
Fd =
~KJ(dive) 2 +--2-(n r~ Vo
e
+--2[ft rotn] 2 dV +or ~ IV~ J2 Surface 2
(1)
where ~ is the surface tension constant, ~ 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.
438
Fig.5. Polar coordinate notation for a fiber-like liquid crystal, where ~ 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 1(2 = 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: F a = C H ( K ~ + K3)
0 dip ( 1 - a c ~
(1 + g t ' 2 ) + 6
dip ] V ~ r 12
(2)
where q~0 (r 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, a=
K 3 - Kl
gt'
K, + x-------7' A=cr
2
oqgt
- aq,'
1 OR
L
R
I= ,
(3)
g 3 +K 1 lnR/R~. where R (Ri,) 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 N = W2 for all points in the fiber, as well as b R / b q ~ - 0 . This will eliminate the effect of surface tension, and reduce Eq. (2) to
F a - 2 C HK3 (r
- r
L ) - 2C HK 3 -R'
where L is the length of the fiber, R its radius of curvature.
(4)
439 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~I/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 fiat 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.
o a)
voOoOOOOU 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.
440
c__~
'
..... : ,.
~ , i i i l i,i ],]]~/~
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 ct 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.
441 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 t~, see Fig.7, for fully formed helices lies in a rather narrow range: t~=61+2 ~ 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.
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