DOI: 10.1021/cg901279t
Nucleation and Polymorphism of Calcium Carbonate by a Vapor Diffusion Sitting Drop Crystallization Technique
2010, Vol. 10 963–969
Jaime G omez-Morales,* Angeles Hern andez-Hern andez, Gen Sazaki,§ and Juan Manuel Garcı´ a-Ruiz Laboratorio de Estudios Cristalogr aficos, IACT (CSIC-UGR) Ed. Inst. L opez Neyra. Avda. Conocimiento s/n. P.T. Ciencias de la Salud, 18100 Armilla, Granada, Spain. §Present address: The Institute of Low Temperature Science, Hokkaido University, N19-W8, Kita-ku, Sapporo 060-0819, Japan.
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Received October 14, 2009; Revised Manuscript Received December 2, 2009
ABSTRACT: The nucleation and polymorphism of calcium carbonate have been studied using a microdevice named the crystallization mushroom. This setup allows carrying out precipitation experiments reproducibly by the vapor diffusion sitting drop technique. Within the range of concentrations investigated (from 10 to 500 mmol/L CaCl2 and from 1 to 25 mmol/L NH4HCO3), the dominant polymorph to appear first in the drops was calcite, or mixtures of calcite and vaterite followed by aragonite. Additionally, amorphous calcium carbonate (ACC) was not observed. The order of appearance of the polymorphs in the droplets is explained by intrinsic features of the crystallization mushroom, that is, the slow increase in the ionic activity product caused by slow diffusion of NH3 and CO2 gases, which favors the least soluble phase calcite to crystallize before other more soluble polymorphs. The appearance of calcite as the first nucleating dominant polymorph in the drops allowed us to calculate its surface free energy from induction time measurements assuming the mononuclear nucleation model. The experimentally calculated result of 35 mJ/m2 is lower than the value predicted for homogeneous nucleation. The cause is the existence of heterogeneous nucleation taking place at the air-solution and solution-support interfaces.
1. Introduction The precipitation of calcium carbonate (CaCO3) plays an important role in a number of fields, such as geology,1 environmental sciences,2 and biomineralization,3,4 in addition to a broad number of applications in industry, where it is used, with a controlled polymorphism, morphology, and crystal size distribution, as a filler or pigment in rubber, paper, plastics, paints, food, etc.5,6 Moreover, CaCO3 provides a polymorphic model system to study nucleation and growth of minerals in classical7 and nonclassical crystallization.8 Hence, the precipitation processes of CaCO3 have been so far investigated by various methods, in various size scales. In the field of biomimetic mineralization of CaCO3, most studies employ a vapor diffusion technique based on the decomposition of (NH4)2CO3 or NH4HCO3 into CO2 and NH3 gases, which in turn are used as reagents to precipitate CaCO3 in flasks containing solutions of Ca ions.9 The whole reaction is carried out in normal laboratory desiccators which are used as isolated environmental chambers. This method has shown some disadvantages such as low reproducibility of the precipitation process, difficulty of monitoring, dependency of the precipitation process upon the volumes of the solution and of the desiccator,10 and a relatively high consumption of “tailored additives”. To overcome these disadvantages, our laboratory has developed a device called the “crystallization mushroom”,11,12 by which precipitation is carried out by slow vapor diffusion using the sitting drop method. The crystallization mushroom is a multidrop set up that enables us (i) to crystallize several samples in the volume range of microliters under different
conditions in the same run, (ii) to perform the precipitation with high reproducibility, (iii) to monitor the experiment in situ using an ion-selective electrode or a pH-electrode, and (iv) to observe the evolution of precipitates in situ using any type of optical microscopy and video recording. This micromethod has been successfully employed to study the effect of a number of macromolecules on the precipitation of CaCO3: lysozyme,11 carbonic anhidrase,13 ribonuclease-A,14 mioglobin,14 R-lactalbumin,14 eggshell matrix proteins fractions,15 hen uterine fluids proteins,16 chitosan,17 and many others. This study aims to clarify the intrinsic features in vapordiffusion crystallization of CaCO3 in absence of additives, using a crystallization mushroom. In particular, we have focused our study on the following aspects: (i) the relationship between the rate of increase of the ionic activity product, and also, of the supersaturation reached in droplets, with the type of dominant polymorph of CaCO3 first observed, (ii) the efficiency of the technique for quantitative studies on nucleation kinetics of this first observed CaCO3 polymorph by applying the classical theory, and (iii) comparison with results obtained in batch and microbatch precipitation of CaCO3. 2. Experimental Section
*To whom correspondence should be addressed. E-mail:
[email protected]; tel.: þ34 958 181643; fax: þ34 958 181632.
2.1. Apparatus. All precipitation experiments of CaCO3 were carried out by vapor diffusion using a crystallization mushroom (Triana Sc. & Tech, S.L.). The set up of the experiment is shown in Figure 1. A crystallization mushroom is composed of two cylindrical glass chambers and a glass cover. The upper and lower chambers are connected to each other through a hole 6 mm diameter to allow vapor diffusion. In this mushroom, nine polystyrene microbridges (a small plastic block with a shallow well to facilitate sitting drop crystallization) are placed concentrically every 36 inside the upper chamber. Each microbridge holds 40 μL of a CaCl2 solution. The NH4HCO3 solution is placed in the lower chamber.
r 2009 American Chemical Society
Published on Web 12/17/2009
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Figure 1. Set up of a “crystallization mushroom” used for the precipitation of CaCO3 by vapor diffusion using the sitting drop method. To monitor the chemistry of the precipitation process we used a pH electrode (Titan model, Sentron) placed on a hole situated on a side wall of the upper chamber. This electrode allows us to measure the pH in a 40 μL drop. The glass cover and the upper chamber are sealed with silicon grease. 2.2. CaCO3 Precipitation by CO2 and NH3 Diffusion. Experiments were carried out at 20 ( 2 C, by varying the concentrations of both CaCl2 and NH4HCO3 solutions from 10 to 500 mmol/L and from 1 to 25 mmol/L, respectively. Stock solutions were prepared under N2 atmosphere using analytical grade reagents from Sigma and deionized water (Elix 3, Millipore). Once the crystallizer was closed and sealed, the underlying NH4HCO3 solution released NH3 and CO2 gases into the free space of the crystallizer (0.158 L). Both the NH3 and CO2 gases redissolved into the droplets of CaCl2 solutions, increasing their pH and forming neutral and charged aqueous species, such as H2CO3*(aq), HCO3- and CO32-, CaCO30, CaHCO3þ, Ca(NH3)22þ, Ca(NH3)2þ, CaClþ, CaOHþ, Ca2þ, Cl-, Hþ,OH-, NH3(aq), and NH4þ. The experiments were finished after reaching the equilibrium conditions (i.e., the recorded pH reached a plateau and the number of crystals and polymorph composition, as visualized by optical microscopy, remained unaltered). 2.3. Monitoring of the Precipitation Process and Characterization of the Crystals Obtained. Each of the precipitation processes were observed in situ using an optical microscope (Leica MZ12 or Olympus SZH10) connected to a digital camera (Olympus, C3040ZOOM), or to a video camera (Sony, High Resolution MTV-3). Observations were carried out at every 15 or 60 min intervals. The time interval was adjusted according to the induction time for nucleation at each experimental condition. From these observations, the morphology and total number Ntotal of crystals appearing in each drop and induction time ti, at which onset of precipitation was first confirmed, were determined in situ. At the end of the experiments, the mushroom was opened and the precipitates were recovered from the microbridges, rinsed twice with deionized water, and dried at room temperature. The pH of the mother liquor was decreased to 7.0 to prevent further precipitation of carbonate, and residual Ca concentration was measured by atomic absorption spectrophotometry (AAS, Perkin-Elmer 510 model). The crystals obtained were observed by field emission scanning electron microscopy (FESEM, Gemini-1530). Polymorph of crystals with a rhombohedral habit was determined by X-ray diffraction (XRD, Siemens D5000 Kristalloflex diffractometer). Polymorph of crystals with a rounded shape (a relatively low fraction) was determined by both X-ray diffraction (XRD) in a grazing incidence mode (1, 24 h) and Fourier transform infrared spectroscopy (FT-IR, Nicolet 510). Finally, the rest of the crystals (a very small fraction) with a sheaf of wheat morphology was dispersed in KBr, and polymorph was determined by FT-IR. 2.4. Calculation of Supersaturation. Supersaturation β expressed as the ratio of ionic activity product (IAP) to solubility product Ksp was calculated by speciation software Visual MINTEQ18 using the following equations: β ¼ IAP=Ksp ð1Þ IAP ¼ aðCa2þ ÞaðCO3 2 - Þ
ð2Þ
Ksp ¼ aðCa2þ Þeq 3 aðCO3 2 - Þeq
ð3Þ
Here, a(Ca ) and a(CO32-) show activities of these ions, and a(Ca2þ)eq and a(CO32-) eq for activities at equilibrium. This software 2þ
uses as inputs the temperature, the initial CaCl2 concentration, the initial pH, the partial pressures of NH3 and CO2 (pNH3, pCO2), and either the Debye-H€ uckel or Davies equations to determine the activity coefficients, depending on the ionic strength I (I < 0.1 M or I < 0.5 M, respectively). As outputs, this software provides the activities of the aqueous species Ca2þ, Ca(NH3)22þ, Ca(NH3)2þ, CaClþ, CaCO30, CaHCO3þ, CaOHþ, Cl-, Hþ,OH-, CO32-, HCO3-, H2CO3*(aq), NH3(aq), and NH4þ, as well as the values of β with respect to polymorphs calcite, aragonite, and vaterite. The calculations of partial pressures pCO2 and pNH3, generated by gases released from the NH4HCO3 solution to the free-space of the crystallization mushroom according to eqs 4-7, were performed by software PHREEQC Interactive 2.8.19 þ NH4ðaqÞ þ OH - T NH3ðaqÞ þ H2 O
ð4Þ
NH3ðaqÞ T NH3ðgÞ
ð5Þ
þ Hþ T CO2ðaqÞ þ H2 O HCO3ðaqÞ
ð6Þ
CO2ðaqÞ T CO2ðgÞ
ð7Þ
Therefore, the values of β estimated with this procedure are the nominal supersaturations that could be reached in a droplet by completely disregarding the precipitation. During the course of most of the experiments, the droplets evolved from undersaturated to supersaturated, with precipitation starting once the system exceeded a certain critical supersaturation value.
3. Results and Discussion 3.1. Monitoring of the Precipitation and Determination of Induction Times. Once the mushroom was closed, the pH started to increase as a consequence of the diffusion and dissolution of NH3. As examples, Figure 2, panels a and b show, respectively, the time evolution of pH in experiments with CaCl2 concentrations of 10 mM and 200 mM under various NH4HCO3 concentrations (2.5-25 mM). As shown in Figure 2a, the rate of increase in pH strongly depends on the concentration of NH4HCO3 contained in the reservoir. In the case of 2.5 mM NH4HCO3, the increase in pH was slow enough that the solution remained undersaturated throughout the run and no crystal was obtained. However, when the concentration of NH4HCO3 was doubled to 5 mM NH4HCO3, the pH increased up to a plateau of 7.4, and three crystals were obtained (Table 1). Further increase in the concentration of NH4HCO3 to 15 and 25 mM resulted in a rapid rise in pH and formation of 70 and 80 crystals, respectively. Figure 2b demonstrates that the increase in the concentration of CaCl2 also quickens the precipitation process significantly. We also monitored the precipitation process of CaCO3 by optical microscopy. Figure 3 shows a typical time course of the in situ observation of a sitting drop. In this experiment, we recorded a frame every 5 min. In the early stage of the precipitation, the drop was clear (a). With increasing time, precipitates appeared and their size became larger. As indicated by a white circle in Figure 3b, we succeeded in identifying the precipitate to appear first in the drop. The earliest time at which the first precipitate could be visualized was defined as the induction time ti of nucleation. As shown in Figure 3e, after the precipitates were grown to certain sizes, we could differentiate the morphologies of the precipitates. We could also count the total number Ntotal of crystals, after the precipitation process had finished (Figure 3f). To make the movie sufficiently clear for the demonstration in this paper (Figure 3), we specially illuminated this drop continuously with a halogen lamp throughout the
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Figure 2. Evolution of the pH in the droplets containing 10 mM CaCl2 (a) and 200 mM CaCl2 (b), under various concentrations of NH4HCO3. Table 1. Summary of Crystallization Conditions, Supersaturation (β), Induction Time (ti) Number, and Percentage (%) of CaCO3 Crystals in Three Polymorphs: Calcite (C), Vaterite (V), and Aragonite (A) β CaCl2 (mM)
NH4HCO3 (mM)
pH0 (CaCl2)
500 10 20 50 100 200 10 20 50 200 10 20 50 200 10 20 50 100 200 10 20 50 100 200
1 2.5 2.5 2.5 2.5 2.5 5.0 5.0 5.0 5.0 10 10 10 10 15 15 15 15 15 25 25 25 25 25
5.1 5.9 5.8 5.7 5.2 5.1 5.5 5.3 5.2 4.4 5.4 5.3 5.2 3.8 5.9 5.8 5.7 5.8 5.5 5.9 5.8 5.7 5.8 5.9
a
C 10 16 26 38 55 18 28 47 98a 29 45 76 163a 36 58 99 144 212 47 77 134 198 292a
V 3 4 7 10 15a 5 7 13 26a 8 12 20 44a 10 15 26 39 57a 13 21 36 53 78a
no. (% polymorphs) A
ti (min)
7 11 19 27 39a 13 20 34 71a 21 33 55 118a 26 42 71 105 154a 34 55 97 143 211a
¥ ¥ ¥ 2100 1400 190 2500 1200 650 520 500 400 300 240 270 230 160 130 80 260 200 135 110 90
total
N
0 0 0 1 10 20 3 9 37 92 17 40 46 144 70 100 135 225 300 80 160 166 340 440
C
V
A
0 0 0 1(100) 10(100) 20(100) 2(66) 6(67) 21(56) 85(92) 7(41) 22(56) 30(65) 110(76) 49(70) 68(68) 115(85) 162(72) 246(82) 55(69) 141(88) 130(79) 204(60) 396(90)
0 0 0 0 0 0 1(33) 2(22) 12(34) 5(6) 4(24) 9(22) 7(15) 30(21) 8(11) 15(15) 8(6) 52(23) 36(12) 15(19) 11(7) 34(20) 92(27) 22(5)
0 0 0 0 0 0 0 1(11) 4(10) 2(2) 6(35) 9(22) 9(20) 4(3) 13(19) 17(17) 12(9) 11(15) 18(6) 10(12) 8(5) 2(1) 44(13) 22(5)
Values using activity coefficients at the limit of Davies equation; the ionic strength was I ≈ 0.5-0.52 M.
precipitation. Hence the temperature of the drop (23 C) became higher than the other at the room temperature of 20 C (observed by discontinuous illumination), resulting in a shorter induction time (225 min) than that listed in Table 1 (400 min) under the same conditions. The discontinuous lighting gave pictures of worse quality, but did not give any difficulty in identifying the induction time and the phases of the precipitates. Therefore, the data summarized in Table 1 does not reflect any effect of the rise of temperature shown in Figure 3. In previous studies in batch experiments,20,21 changes in pH or conductivity of the supersaturated solutions were mainly used to determine the induction times ti in experiments initiated by rapid mixing of Ca2þ and CO32-/HCO3solutions in larger volumes. As summarized in Table 1, ti determined in this study by visual examination roughly corresponds to the shoulder of the pH evolution curve. 3.2. Growth Morphology and Polymorph. We basically observed three types of morphologies: precipitates with rhombohedral, sheaf of wheat, and rounded shapes. We characterized these precipitates using either powder XRD or FTIR. The XRD diffractogram of the rhombohedral
crystals clearly exhibited diffraction peaks belonging to calcite (JCPDS 5-586): the reflections at 2θ = 29.45 (d = 3.035 A˚), 39.45 (d = 2.285 A˚), 36.00 (2.495 A˚), and 39.45 (d = 2.285 A˚). The XRD patterns of rounded precipitates were more noisy than calcite because of smaller amounts of precipitates available; however, the diffraction peaks at 2θ = 20.85 (d = 4.26 A˚), 2θ =24.85 (d = 3.58 A˚), 2θ =27.00 (d = 3.30 A˚), and 2θ =32.80 (d = 2.73 A˚) coincided with those of vaterite (JCPDS 13-192). Finally, precipitates with a sheaf of wheat morphology presented adsorption bands at 1470 cm-1, 1087 cm-1, 856 cm-1, and 712 cm-1 in the FTIR spectrum. These bands likely corresponded to vibrational modes of the aragonite mineral,10,22 that is,_ 1466 cm-1 (υ3), 1087 cm-1 (υ1), 866 cm-1 (υ2), and 712 cm 1 (υ4). As shown in Figure 4, the FESEM micrographs show that calcite crystals appear as rhombohedra bounded by the {104} faces, whereas vaterite is formed as agglomerates of tiny crystals displaying a hexagonal (hexalobulated) rosetteshape morphology. Such agglomerates of vaterite were probably formed by the aggregation of nanocrystals via an oriented attachment mechanism.10 Aragonite exhibits mainly a sheaflike morphology. The formation mechanism
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of this type of morphology in CaCO3 and in other systems such as Bi2S3 and β-FeO(OH) has been explained by a crystal splitting growth mechanism.23-25 3.3. Number of Crystals and Polymorph Distribution As a Function of Supersaturation. In this work, by selecting an appropriate range of crystallization conditions, we obtained relatively low numbers of crystals with well-defined morphologies in a very reproducible way, either among the different drops in the same mushroom or among duplicated runs of the same conditions (two duplicated runs were performed in some cases). The total number Ntotal of crystals
Figure 3. A sequence of photomicrographs of the time course of precipitation: (a) 70 min, (b) 225 min, (c) 500 min, (d) 1000 min, (e) 2000 min, and (f) 2990 min. A white circle in (b) shows the position where a first appeared precipitate could be observed with a very faint contrast level. A dotted square in (f ) corresponds to the area shown in (a-e). Scale bars in (a-e) and (f ) show 0.5 and 1 mm, respectively. Initial concentrations of CaCl2 and NH4HCO3 are 20 and 10 mM, respectively.
G omez-Morales et al.
obtained under the same conditions exhibited a maximum deviation of ( 5%. The results of the experiments performed under a range of CaCl2 and NH4HCO3 concentrations are summarized in Table. 1. As shown in this table, as the nominal supersaturation βcalcite increases from 10 to 292, so does the Ntotal from 0 to 440 (0-11 crystals/μL). Under the conditions used in Table 1, calcite was the most abundant polymorph. Vaterite and aragonite were obtained in smaller numbers. The number of calcite crystals obtained followed a tendency similar to Ntotal. It varied from 0 to 396 with increasing CaCl2 and NH4HCO3 concentrations. However, its percentage became smaller under the middle concentration range of NH4HCO3 (5-15 mM). The number and percentage of both aragonite and vaterite crystals did not show any tendency. An interesting feature found in the series of experiments was the “first nucleating polymorph”, which was determined by in situ optical observation during the experiments, as demonstrated in Figure 3. In the experiments at 2.5 mM NH4HCO3, calcite was the first and only precipitated polymorph. In the experiments at 10 mM NH4HCO3 and 20 mM CaCl2 as well as at 25 mM NH4HCO3 and 10 mM CaCl2 and at 25 mM NH4HCO3 and 200 mM CaCl2, the precipitation of calcite was followed by vaterite and aragonite. In the rest of the experiments we could not determine the first nucleating phase with enough accuracy, either because calcite and vaterite appeared almost simultaneously, or because the number of crystals that appeared in the drops was too large to identify individual phases by optical microscopy. In these experiments, there was no evidence of the appearance of amorphous calcium carbonate (ACC). Furthermore, in order to study the evolution of the polymorph composition with time, we monitored an experiment (20 mM CaCl2, 10 mM NH4HCO3) for 5 days by optical microscopy. The observations showed that after precipitation, the polymorph composition remained constant. However, after 4 days we observed the dissolution of vaterite crystals, which was followed by the dissolution of aragonite and simultaneous growth of existing calcite crystals. For the findings of this work, a reasonable thermodynamic explanation can be given considering the intrinsic features of this vapor diffusion method. In experiments with a low NH4HCO3 concentration (2.5 and 5 mM), the partial pressures of released gases NH3 (pNH3) and CO2 ( pCO2) were different but very low, and the diffusion rates of these gases into the aqueous droplets were slow, particularly that of NH3, which is reflected by the smooth increase in pH (Figure 2). Because of the slow increase of pH, and thus, of the ionic activity product of the solution, the droplets first reached the critical supersaturation of the least soluble
Figure 4. Field emission scanning electron (FESEM) micrographs of precipitates obtained by the sitting drop method using crystallization mushroom: (a) calcite, (b) aragonite, (c) vaterite.
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Figure 5. Optical microscopy pictures of a droplet containing (a) ACC, and (b) ACC transforming in vaterite and calcite crystals. The experiment was carried out by vapor diffusion using a closed rectangular quartz cell with two drops containing 1 mol/L CaCl2 and 1 mol/L NH4HCO3.
polymorph calcite (log Kspcalcite = -8.453),26 and then calcite had enough time to nucleate and grow before nucleation and growth of vaterite and aragonite took place. As the NH3 and CO2 gases further diffused into the drops continuously, the ionic activity product increased and surpassed the solubility products of aragonite and vaterite (log Ksparagonite = -8.306, log Kspvaterite = -7.873),26 which resulted in the nucleation and growth of these polymorphs. At higher NH4HCO3 concentrations, the diffusions of CO2 and NH3 gases in the drops were faster, the rates of development of the ionic activity product were higher and the supersaturation within the drops increased. In these conditions, calcite and vaterite appeared sequentially or simultaneously. Therefore, the crystallization mushroom works from lower to progressively higher supersaturations (bottom up approach). Nevertheless, the critical supersaturation for the nucleation of ACC was never reached in the series of experiments. Kawano et al.27 used a microbatch method by rapid mixing of CaCl2 and Na2CO3 solutions and monitored the precipitation by optical microscopy The concentration of the mixed solutions was adjusted to be higher than the solubility of the ACC phase (20 mM/L). They showed that ACC appeared first, and then vaterite and calcite nucleated and grew by consuming the amorphous phase precipitated previously and creating around the crystals a precipitation free zone. They also reported that in some cases calcite appeared before vaterite. In order to observe the precipitation of ACC particles as the primary precipitated phase by a vapor diffusion technique, it has been necessary to use a rectangular quartz cell in which we have placed two drops containing the reagents, and to increase largely the concentrations to 1 M CaCl2 and 1 M NH4HCO3. This experiment behaved like the microbatch experiment of Kawano et al.27 Figure 5 shows pictures of ACC particles obtained by optical microscopy, as well as vaterite and calcite crystals creating a dissolution zone around them. It is unclear whether calcite nuclei are heterogeneous nuclei forming on existing ACC particles or form spontaneously, but what is clearly shown is that growth of calcite or vaterite takes place at the expense of ACC dissolution. Another very interesting result is the appearance of aragonite (a high temperature polymorph) at 20 C, in the absence of any additive such as Mg2þ, SO42-, or any external factor such as a magnetic field. This would require a further study in itself. In fact, to the best of our knowledge, the presence of aragonite has not been reported in pure CaCO3 systems where the supersaturation is obtained by direct mixing of calcium and carbonate/bicarbonate solutions at 20 C. The minimum reported temperature for aragonite
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formation was 24 C (pH > 9)28 or 26 C,29 with optimal temperature for maximum relative abundance above 60 C. The authors suspect that very small fractions of aragonite crystals in mixtures of CaCO3 polymorphs obtained in large solution volumes could not be identified because of the detection limit of powder XRD. Therefore, in these cases the use of a micromethod can help us to better define the precipitation range of a polymorph when studying the effects of certain operating variables. 3.4. Nucleation Kinetics. We have succeeded in observing the nucleation of calcite as the first nucleating phase by optical microscopy. Hence we analyzed the induction time ti as a function of supersaturation β of calcite, and attempted to evaluate surface free energy of calcite. The induction time ti includes three time periods: relaxation, nucleation, and growth time. The relaxation time is the time the cluster distribution needs to respond to the imposed supersaturation, whereas the nucleation and growth times are the time needed to the formation of stable nuclei and the time for their subsequent growth to observable size, respectively. Kashchiev et al. reported a general equation for the calculation of the induction time that takes into account both the mononuclear (MN) and polynuclear (PN) mechanisms.30 When nucleation is dominated by the MN or PN mechanism, the relationship between ti and β can be respectively expressed as follows: ð8Þ
ln ti B=ln2 β ðthe case of MNÞ lnðti β1=8 ðβ1=2 -1Þ6=4 ÞB=ð4 3 ln2 βÞ ðthe case of PN : spiral growth is assumedÞ with B ¼
16πσ3 Ω2 ðkTÞ3
ð9Þ ð10Þ
Here, σ is the surface free energy of the nuclei, Ω is the molecular volume (6.13 10-29 m3 for calcite,31 k is the Boltzmann constant, and T is the absolute temperature. Figure 6a shows the plot of ti vs β obtained experimentally in this study. To evaluate the MN and PN mechanisms, the data were replotted according to eqs 8 and 9, as shown in Figure 6, panels b and c, respectively. In the case of the PN mechanism, we assumed the parabolic rate law of calcite crystals according to several previous reports.32-35 The experiments carried out showed that calcite was the first polymorph to appear except in the experiments where calcite and vaterite appeared at the same time, or its determination was ambiguous. Taking these results into account, to obtain these plots we have employed the supersaturation β expressed with respect to the polymorph calcite. The correlation coefficients corresponding to Figure 6, panels b and c are 0.92 and 0.47, respectively. The better fit of Figure 6b indicates that in our nucleation experiments using the micromethod (drops of 40 μL) the MN mechanism prevail, although the correlation coefficient obtained (0.92) was not very good. This result roughly agrees with the hypothesis of Verdoes et al.,36 who assumed that the MN mechanism operates only when volume of a solution phase is smaller than 10 μL. This is the first experimental evidence that confirm this hypothesis. In the MN mechanism, the time of nucleation dominates ti, and thus, the use of eq 8 is legitimate. From the slope of the straight line of Figure 6b, we obtained the surface free energy of calcite σ = 35 mJ/m2.
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Figure 6. (a) Plot ti vs β, (b) test of the MN mechanism according to eq 8, (c) test of the PN mechanism according to eq 9.
The induction time determined in this study is longer than the time of nucleation, because of the importance that the relaxation time have, in particular under low supersaturation. Therefore, the value of σ = 35 mJ/m2 shows the largest limit of the surface free energy of calcite; that is, real value would be smaller than this value. Concerning the surface free energy of calcite, S€ ohnel and Mullin reported σ = 83 and 98 mJ/m2 using batch reactors,37 although these values were considered intermediate between those of calcite and vaterite. They also reported a theoretical value of 120 mJ/m2.38 Other reported values using different experimental conditions in batch reactors show a big scatter (7,39 19.5,40 205,41 28042 mJ/m2). The value of σ obtained in this study is comparable to that of Westin and Rasmuson43 (37.8 mJ/m2), which is lower than that predicted for homogeneous nucleation37 and indicates that some degree of heterogeneous nucleation occurred in the drops considering that the use of eq 8 is legitimate. After analyzing the movie of Figure 3, we have observed the first precipitated crystals at the outer surface or border of the drops, followed by crystals in the center, indicating a supersaturation gradient. After careful analysis, we have identified the air-solution interface of the drops and the surface of the microbridges as the source of heterogeneous nucleation. Only the use of levitated droplets44 would permit a contact free crystallization. However, even using levitated droplets the solution/air interface would continue to be a source of heterogeneous nucleation. At present, accurate evaluation of the surface free energy of calcite from induction time measurements remains a difficult subject. Potential sources of errors in the calculation of σ include those associated to the specific technique employed to measure the induction times, the impossibility to eliminate completely the heterogeneous nucleation, and perhaps the most important, in batch and microbatch precipitation of CaCO3 the nucleation of ACC and/or vaterite normally precedes the nucleation of calcite.
Thus, we can highlight that the crystallization mushroom offer several advantages to carry out kinetic studies of calcite: (i) it favors the nucleation of calcite as the primary phase, (ii) it requires very small volumes thereby ensuring a mononuclear mechanism, (iii) it allows easy in situ observation and identification of the first nucleating phase, and (iv) it affords high reproducibility of the precipitation processes. Therefore, we believe that this micromethod should become a useful tool for the study of the crystallization of a wide variety of minerals in the near future. 4. Conclusions The precipitation of CaCO3 by the vapor diffusion sitting drop technique has been studied at 20 ( 2 C using the crystallization mushroom. The process has been monitored by optical microscopy, video microscopy, and by recording the pH versus time. Within the range of concentrations investigated (from 10 to 500 mmol/L CaCl2 and from 1 to 25 mmol/L NH4HCO3), the dominant polymorph to appear first in the drops was calcite, or mixtures of calcite and vaterite followed by aragonite. ACC was not observed. These findings are explained by the slow diffusion of NH3 and CO2 gases from the chamber containing NH4HCO3 to the chamber containing droplets of CaCl2 solution. The gas diffusion within the crystallization mushroom cell produces an increase in the ionic activity product that is slow enough to allow the nucleation of the least soluble polymorph calcite, as the first nucleating polymorph. It was necessary to use another set up, a closed rectangular quartz cell composed of only one chamber, and to largely increase the concentrations of both reagents to 1 mol/L in the droplets to observe the appearance of ACC. The appearance of calcite as the first nucleating dominant polymorph in the drops allowed us to calculate the surface free energy of calcite from induction time measurements assuming the mononuclear model. The calculated value
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Crystal Growth & Design, Vol. 10, No. 2, 2010
of the surface free energy of calcite (35 mJ/m2) is lower than that predicted for homogeneous nucleation due to the existence of heterogeneous nucleation taking place at the airsolution and solution-support interfaces. Acknowledgment. This work has been supported by MAT2006/11701 of the Spanish Ministry of Science and Innovation, by PIE200630l133 of the Spanish CSIC and by the Excellence Project RNM5384 of the Junta de Andalucia. A.H.H., J.G.M., and J.M.G.R. belong to the research team “Factorı´ a de Cristalizaci on” (Consolider Ingenio 2010). We also thank Angel Justo for FTIR and XRD analysis, Dr. Luis David Pati~ no Lopez for image treatment, and Dr. Alfonso Garcı´ a Caballero for English revision.
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