Article pubs.acs.org/crystal
Dominant Role of Compromise between Diffusion and Reaction in the Formation of Snow-Shaped Vaterite Han Wang,†,‡ Yongsheng Han,*,† and Jinghai Li† †
EMMS Group, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ University of Chinese Academy of Sciences, Beijing 100490, China ABSTRACT: The diffusion and reaction are two general kinetic factors playing an important role in the structure development of materials. Upon diffusion limitation, a noncompact structure is easily formed, while a compact structure is usually formed in a reaction-limited condition. In this Article, we take the precipitation of calcium carbonate as an example to discover the roles of diffusion and reaction in shaping particles. By adjusting the diffusion and reaction in a threecell reactor, we synthesize snow-shaped particles, which are a new morphology of calcium carbonate. The microscopic characterization shows that the microparticle is composed of aggregates of nanoparticles. Computer simulation suggests that the snow-shaped particle is formed in a condition that the diffusion and reaction compete to regulate the structure of particles and their compromise leads to the formation of snow-shaped morphology, which is confirmed by later experiments. The following discussion concentrates on the compromise concept to disclose its essence and role in shaping particles, which brings us a new view on the physical mechanisms governing the diversity of materials structures.
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structure. The compromise is a new concept in the field of materials engineering,39 but its significance has been recognized in the field of chemical engineering for more than two decades.23−25 In this Article, we aim to discover the role of compromise between diffusion and reaction in shaping the structure of materials. We design a three-cell reactor to manipulate the chemical diffusion and reaction. We restrict our study to calcium carbonate precipitation, because this process is well studied. The diffusion is regulated by setting a concentration gradient among the cells, while the reaction rate is adjusted by temperature. By controlling diffusion and reaction kinetics, snow-shaped calcium carbonate particles are synthesized. To our knowledge, the snow shape is a new morphology for calcium carbonate. To disclose its formation mechanism, we conducted microscopic characterizations and computer simulations, respectively. The results suggest that snow-shaped particles are formed by an aggregation of nanoparticles. Further experiments confirm the aggregation mechanism and point out that the compromise between diffusion and reaction plays a dominant role in the formation of the snow-shaped particles.
INTRODUCTION The properties of particles are not only dependent on their size, but also on their shape.1,2 Therefore, shape control on particles is an important topic in the field of materials science.3−6 Various approaches have been developed to realize this control, such as template-directing methods,7,8 surfactant-stabilizing methods,9−12 and kinetic-driving methods.13−15 Because most specific shapes are formed at conditions far from thermodynamic equilibrium, the kinetic parameters play an important role in shaping particles.16 Among the kinetic factors, diffusion and reaction are two general important factors influencing the structure of materials.17,18 Here, the diffusion refers to a randomized move of solute toward to the surface of growing material, while the reaction refers to the solute sticking on the surface of a growing material followed by crystallization. These factors have been studied widely by the physics community but were much less investigated in material science. It was reported that diffusion and reaction play different roles in regulating the structure of materials. When the reaction is slowed, a reactioncontrolled condition is created, leading to the formation of more compact structures dominated by a reaction-limited aggregation (RLA) process,19,20 whereas open structures, such as dendritic ones, are formed in a diffusion-limited condition, via a diffusion-limited aggregation (DLA) process. 21,22 According to our recent understanding, when the diffusion and reaction are manipulated synchronously, their joint effect, a compromise between diffusion and reaction, becomes a key factor in shaping particles. In such a condition, the compromise in competition dominates the development of a material © 2013 American Chemical Society
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RESULTS AND DISCUSSION Figure 1 shows typical SEM images of snow-shaped particles, which are synthesized in a double-diffusion experiment in Received: August 27, 2012 Revised: March 9, 2013 Published: March 15, 2013 1820
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Figure 1. Scanning electron microscope images of snow-shaped calcium carbonate particles synthesized by a double-diffusion experiment. (a) Lowmagnification SEM image of products showing high yield of snow-shaped calcium carbonate particles. (b) High-magnification SEM image of the snow-shaped particle showing a 6-fold-symmetric structure.
which the separated reactive ions diffuse to the middle cell to induce a precipitation of calcium carbonate. The lowmagnification image in Figure 1a shows that the majority of products are snow-shaped particles, accompanied by a minor fraction of needle-like particles. The accompanying formation of needle-like particles is under study. Figure 1b shows a highmagnification SEM image of an individual snow-shaped particle, which shows that the particle consists of six main trunks and orderly distributed branches on both sides of the trunk. In the center of the snow-shaped particle, a spherical particle can be identified. Other particles connect with the center particle in six directions symmetrically, forming the main trunks with rough surface. Along a trunk, the branches grow parallel on each side, forming a dendritic pattern. Among the trunks, the branches are interconnected, having a clear boundary. Further characterization on the snow-shaped particles is carried out by high-resolution transmission electron microscopy (HRTEM). Figure 2a shows an overall 6-fold symmetric structure of the snow-shaped particle, which indicates that the snow-shaped particle results from aggregation of nanoparticles. The selected area electron diffraction pattern (Figure 2b) taken from Figure 2a indicates that the building block of the snowshaped particle is single-crystalline or exists of crystallites with uniform orientation. The diffraction spot can be perfectly indexed to a hexagonal vaterite crystalline structure (hexagonal space group P63/mmc), which indicates that the snow-shaped particle is vaterite. Figure 2c and d shows HRTEM images taken from the areas labeled in Figure 2a. Figure 2c shows the lattice structure of the particle located at the tip of the branch, while Figure 2d shows the lattice structure of the particle at the tip of the main trunk. Both images show a lattice spacing of 2.98 Å, which corresponds to the distance between two (200) crystal planes of vaterite. The microscopic information indicates that the trunk grows along [11̅ 0] direction and the snowshaped particle largely exposes the (001) faces. To discover the formation mechanism of snow-shaped vaterite, a Monte Carlo simulation has been carried out. The simulation is based on the model proposed by Vladishlav A.
Figure 2. TEM images of a snow-shaped calcium carbonate particle. (a) TEM image of a 6-fold-symmetric structure comprised of nanosized building blocks; (b) selected area electron diffraction pattern taken from a single building block in (a); and (c,d) highresolution TEM images for specific site labeled in (a).
Bogoyavlenskiy.26 According to the model, the growth unit diffuses and collides on the growing surface followed by a reaction. The collision frequency is determined by the diffusion rate of the unit. The reaction rate is determined by the thermodynamic condition, which is associated with the heat transfer rate in the aggregation. We define a new parameter η, which is the ratio of heat to mass transfer coefficient, corresponding to the ratio of reaction rate to diffusion rate. By adjusting the value of η, we can change the reaction and diffusion effect. It is found that at a low η condition, the reaction is the controlling step, in which particles undergo multiple collisions before getting attached (reaction limited aggregation, RLA), leading to a structure of compact aggregate as shown in Figure 3a. When η is greatly increased, diffusion becomes the controlling step, in which particles adhere once they encounter each other (diffusion-limited aggregation, DLA), leading to an open dendritic structure as shown in 1821
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formation of an ordered structure, such as the obtained snowshaped particles. Our following discussion will be concentrated on the formation mechanism of the snow-shaped structure, in which the compromise between diffusion and reaction will be emphasized. The formation mechanism of snow-shaped vaterite is proposed as shown in Figure 5. In the precipitation of calcium Figure 3. Morphology evolution of growing aggregate as a function of the parameter η, which is defined as the ratio of heat and mass transfer coefficient corresponding to the ratio of reaction rate and diffusion rate. The values of η are set as minimum (a), 1.2−2.5 (b), and maximum (c).
Figure 3c. When η is in the middle range, neither too high nor too low (we set η in the range of 1.2−2.5), we obtain hexagonal branched structure as shown in Figure 3b, which looks like a snowflake. The simulation results indicate that the snow-shaped structure is formed in a condition that the reaction and diffusion play a comparable role in the development of structure. To testify the simulation results, we have conducted two more precipitation experiments. In the first experiment, the chemicals are poured into a cylindrical beaker at room temperature under vigorous stirring to create a reaction-limited environment. The products prepared in this experiment are mainly spherical particles, as shown in Figure 4a, which corresponds to the RLA result (Figure 3a). The second experiment is conducted in the three-cell reactor. Yet the middle cell is occupied by agar gel instead of water. The diffusion of solutes in the gel is slowed, creating diffusionlimited condition. In such a condition, the precipitated products consist of a branch-like structure, as shown in Figure 4c, which agrees well with the result of DLA simulation. Both simulation and experimental results suggest that the sole role of RLA or DLA leads to the formation of normal structures without microscopic order. This is because the diffusion/reaction effect is magnified in a DLA/RLA condition. In such a condition, the assembly of building blocks is dominated by random collisions or a reaction. However, when the diffusion and reaction play a comparable role, neither of them dominates the development of structure. They have to compromise in the assembly of building blocks leading to the
Figure 5. Proposed formation mechanism of the snow-shaped vaterite. (a) The primary hexagonal vaterite building units. (b) The primary building units assembling along the six equivalent [11̅ 0] directions. (c) Growth on the junctions of the main trunks due to the roughness of these areas. (d) Continuous growth of particle via a fast growth of the six main trunks and a subsequent growth on the intersection area.
carbonate, vaterite is first nucleated.27,28 Some of the vaterite nuclei grow up forming stable vaterite particles, while others transform to calcite and aragonite. In this study, because the snow-shaped particles are vaterite, we take the original vaterite nucleus as building blocks. In accordance with a suggestion made in a previous study,29 we use a hexagonal plate to represent the vaterite building block. These hexagonal plates endow the building units with high shape anisotropy, which is characterized as six equivalent faces perpendicular to [1̅10] directions, and two c-planes perpendicular to [001] direction. Because the c-plane is terminated with either Ca2+ or CO32− and has a net ionic charge on the surface,29,30 the c-plane is sensitive to neutralization by adsorbing polar H2O molecules.
Figure 4. The morphology of calcium carbonate particles synthesized at different rates of diffusion and reaction. (a) Spherical vaterite produced in a reaction-limited experiment via directly mixing CaCl2 and NaCO3 solution under vigorous stirring. (b) Hexagonal particle synthesized in a reactiondiffusion compromise experiment. (c) Dendritic particles formed in a gel in the diffusion-limited experiment. 1822
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the formation of such symmetric structures. All of these factors compete and collaborate together, producing a compromise condition in which a novel ordered structure is formed. Therefore, the finding in this Article shows a new direction to disclose the formation mechanism of ordered structures, which probably leads to a deep understanding on the physical mechanism governing the formation of hierarchically shaped structures.
This is analogous to literature examples of vaterite (001) face stabilization by ammonia28 or lithium cations,31 and has been proven by Nora H. de Leeuw using an atomistic approach.32 As the {100} facets have a zero charge and are not stable in solution, thus the building blocks tend to aggregate by sharing the {100} facets, leading to the formation of 2D superstructures. The aggregation process is normally followed by a fusion process to produce a stable structure. With the aggregation of building blocks, the six main trunks are formed. The growth of the trunks produces a rough surface on their junction, which attracts the building blocks to attach there, leading to the formation of branches. Through a continuous collision and aggregation of the building blocks, both the trunks and the branches grow up, forming a snow-shaped structure. In the proposed model, we use two types of building blocks with different sizes to represent the nonuniformity of the nuclei in the real system. As discussed previously in this Article, the collision frequency is determined by the diffusion rate, while the aggregation rate is determined by the reaction rate. In a condition that diffusion and reaction play their roles on the aggregation, the assembly of building blocks is dominated by the compromise between diffusion and reaction. In such a condition, the assembly of building blocks follows a compromise role, resulting in the formation of novel orderly structures such as snow-shaped structure. It is worthy to discuss the reason the compromise of diffusion and reaction is achieved in the double-diffusion experiment. In our experiment, the chemical ions (Ca2+ and CO32−) diffuse from the side cell into the middle cell where precipitation occurs. The control on chemical diffusion creates a concentration gradient in the cells, which produce a continuous supersaturation in the middle cell. The continuous supersaturation not only stabilizes the vaterite nuclei but also leads to a frequent collision of the building blocks. On the other hand, the increased temperature of 70 °C greatly enhances the reaction rate, which speeds up the attachment and fusion of building blocks. In such a condition, the building blocks have relatively sufficient collision and reaction. The interaction among the building blocks starts to play a role, leading to the formation of orderly snow-shaped particles. The compromise concept discussed in this Article provides a new view in understanding the physical mechanisms governing the formation of snow crystals, which attracted considerable curiosity and scientific studies for centuries due to their beautiful patterns and diverse shapes. In the beginning of the 20th century, Nakaya found that the growth of snow crystals is dependent on the temperature and supersaturation.33 Later, it was found that the growth of snow crystal was typically dominated by the attachment kinetics via two transport effects: particle diffusion, which carries water molecules to the growing crystal, and heat diffusion, which removes latent heat generated by solidification.34,35 The particle diffusion is equal to the diffusion process discussed in this Article, while the heat diffusion is determined by a reaction rate. Therefore, the morphologies of snow crystal are also dominated by the diffusion and reaction processes. Their compromise leads to the diversity and complexity of snow morphologies. The snow-shaped structures, especially the dendritic patterns, have been synthesized in other materials systems.36−38 For the formation mechanism of snow-shaped structures, most studies suggest that the DLA plays important roles in their formation. However, only DLA cannot explain the symmetry of the ordered structure. Other factor(s) should also be involved in
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CONCLUSIONS A new morphology of snow-shaped calcium carbonate particles was synthesized in a double-diffusion experiment. The microscopic characterization indicated that the snow-shaped particle is composed of aggregates of small particles. By employing a suitable theoretical model capable of taking into account both diffusion and reaction, a Monte Carlo simulation was performed. The results suggest that the snow-shaped particles are formed in a condition that diffusion and reaction play a joint and comparable role. Further experiments confirm the simulation results and point out that the compromise between diffusion and reaction leads to the formation of snowshaped particles. This Article first shows the significance of compromise effect in shaping nanoparticles, pointing out a new way to control the shape of particles by regulating kinetic factors without using surfactants. Except for the results reported in this Article, the compromise concept has been proven in the synthesis of metallic particles, and a more in-depth study is on the way. Therefore, the compromise concept promises a universal and general protocol for the development of new structured materials.
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EXPERIMENTAL SECTION
Materials. CaCl2 (AR grade) and Na2CO3 (AR grade) were purchased from Sigma (Beijing, China) and used as received. Aqueous solutions of the reactants were made using Milli-Q high pure water with a resistivity higher than 18 mΩ. Agar gel (0.1 g/100 g of water) was used as gel media in the diffusion-limited experiment. Synthesis of Calcium Carbonate Precipitate. The doublediffusion experiment was conducted in a newly designed three-cell reactor, as depicted in Figure 6. The new reactor is comprised of three
Figure 6. An illustration of a double-diffusion experiment. cells, which are separated by movable baffles and micro membranes. 150 mL of calcium chloride and 150 mL of sodium carbonate (both were 0.1 mol/L) at 70 °C were poured into the side cells of the designed reactor, respectively. 150 mL of pure water at the same temperature was placed in the middle cell. Before the baffles were drawn out, there was no diffusion of solutes across the cells due to the blockage of the baffles. The reactor was placed into a water bath to keep 70 °C. When the temperature stabilized, the baffles were quickly drawn out and the diffusion started. After a short induction time, the solution in the middle cell became turbid, indicating the formation of calcium carbonate precipitates. One minute after the diffusion, the suspension in the middle cell was collected and filtered via a Whatman 40 filter paper. The solid obtained was dried at room temperature and prepared for characterization. To study the influence of diffusion and reaction on the polymorph of vaterite, two more experiments were carried out, reaction-limited 1823
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experiment and diffusion-limited experiment. In the reaction-limited experiment, solutions of 150 mL of CaCl2 and 150 mL of Na2CO3 (both are 0.1 mol/L) were poured into the beaker simultaneously under vigorous stirring by a Teflon-coated magnetic stirring bar to achieve a fast mass transport. The diffusion-limited experiment was similar to the double-diffusion experiment. The only difference was that the reaction media placed in the middle cell of the three-cell reactor was 0.1% (g/100 g of water) agar gel instead of pure water. In the preparation of the agar gel, 0.15 g of agar powder was dissolved in 150 mL of hot pure water by heating and constantly stirring. Once the agar powder was completely dissolved, the hot solution was poured into the middle cell. The agar solution was maintained at 25 °C for several days, during which gelation occurred. The resulting agar gel served as reaction medium to slow the diffusion rate of solute during the reaction. Simulation on the Formation of Snow-Shaped Particles. In the Monte Carlo simulation, we restrict our simulation on the aggregation process. We did not consider the nucleation and ripening processes. To simplify the simulation, we only simulate the growth of one aggregate, which is attached by the uniform building blocks coming from the solution. Hence, the simplified physical model in our simulation has the following features: (i) The simulated system consists of solution and building blocks, which disperse in the solution. In the center of the solution phase, we set a stationary cool site as the seeding site for the growth of vaterite. (ii) To reduce the simulation time, we set a circle enclosing the growing vaterite. We only track the building block entering into the circle. When the building block attaches on the growing vaterite, it becomes a part of the vaterite particle. Otherwise, it rebounds into the solution phase and continues a random movement. (iii) Whether the coming building units can attach onto the surface of growing vaterite is determined by the thermodynamic condition.
pgrowth = 1
if
Δμ < 0
(1)
pgrowth = 0
if
Δμ > 0
(2)
Figure 7. Schematic demonstration of the simulated aggregation process.
L (T − TA ) + Σ TA
L (3 − n)Tsurf TA
T (0, t ) = T0
(6)
T < TA + (n − 3)Tsurf
(7)
It becomes clear that only when the surface temperature (T) of the vacant position is below the equilibrium temperature Tequilibrium (Tequilibrium = TA + (n − 3)Tsurf) can reaction between the vaterite surface and the building blocks take place. That is to say, the reaction rate is dominated by the cooling process, which is determined by the thermal diffusivity D. To describe the diffusion, we assume that the moving step of the building blocks in a unit time is Nstep. We then can introduce a dimensionless parameter as
η=
D a Nstep 2
(8)
where a is the parameter of the hexagonal lattice. On the basis of the discussion above, it is clear that the parameter η represents the ratio of reaction and diffusion rate. Therefore, by adjusting the value of η in the simulation, we can easily create reaction-limited conditions (η = maximum), diffusion-limited conditions (η = minimum), and the compromise conditions (η is set a defined value). Characterization. The morphology of samples was taken on a JSM-6700F scanning electron microscope fitted with a field emission source at an accelerating voltage of 20 kV. Samples were spread on double-sided carbon wafer tapes and coated by gold prior to microscopy experiments. The products were further investigated by transmission electron microscopy (TEM) using a JEM-2100 (UHR) high-resolution transmission microscope at an accelerating voltage of 200 kV.
(3)
Here, T is the temperature of the vacant surface site of the solid phase. L is the latent heat that is released to the solid phase in the binding process. TA is the temperature of building units in the solution phase. Σ is the increment of surface chemical potential after the attachment. It can be calculated by eq 4.
Σ(n) =
(5)
Here, T0 is the original temperature of the cool seeding site described in (i), r(x,y) is the coordinate vector, T(r) is the temperature of the building unit at the occupied site r(x,y), D is the thermal diffusivity of the solid phase (we consider D = 0 in the solution phase), C is the specific heat, and NA(r,t) is the density of the aggregation units at site r(x,y) (it is 1 when it is occupied by the building units, while it is 0 when it is not occupied). Equations 3−6 describe the surface thermodynamics and the heat transfer. By combining eqs 1−4, we have the thermodynamic condition required for the coming building blocks attaching onto the vaterite surface.
where Δμ = Δμsolid + Δμsolution is the chemical potential increment of the system after the building unit attaches to the solid surface. From eqs 1 and 2, we can see that the building blocks can attach to the vaterite particle only when the attachment leads to the reduction of chemical potential. (iv) The aggregation of the building blocks takes place on a hexagonal 2D grid. In this hexagonal 2D grid, every building unit has 6 equivalent neighbor sites. In this way, the hexagonal 2D grid can approximately simulate the feature of the hexagonal shape of the building units. The chemical potential increment of the two phases is considered to be the following: (1) the solution chemical potential μsolution is constant and (2) the solid chemical potential is a function of temperature, as shown in eq 3.
Δμsolid (T , Σ) =
∂T (r ) L ∂NA(r , t ) = D∇2 T (r , t ) + ∂t C ∂t
(4)
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where n is the number of occupied nearest neighbors of the vacant surface position, and Tsurf is the configuration increment, which is relative with the surface energy. The overall picture of the simulated process is summarized in Figure 7. The surface aggregation releases the heat, which diffuses to the cool region. The heat transfer obeys the diffusion equation and appropriate boundary condition, as shown in eqs 5 and 6:
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 1824
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ACKNOWLEDGMENTS This study was supported by the Hundreds Talent Program from the Chinese Academy of Sciences and the project from the State Key Laboratory of Multiphase Complex Systems (MPCS-2011-C-01). Financing from the National Science and Technology Support Program (2012BAA03B03) and Development and Application of Isothermal Differential Microfluidized Bed Analyzer for Fluid−Solid Reaction was appreciated.
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NOTE ADDED AFTER ASAP PUBLICATION This paper was published to the Web on April 1, 2013, with an error to the Introduction. The corrected version was reposted on April 16, 2015.
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