Spherulitic Growth of Calcium Carbonate - ACS Publications

DOI: 10.1021/cg901460g

Spherulitic Growth of Calcium Carbonate

2010, Vol. 10 2934–2947

Ralf Beck* and Jens-Petter Andreassen Department of Chemical Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Crystal Growth & Design 2010.10:2934-2947. Downloaded from pubs.acs.org by DURHAM UNIV on 01/02/19. For personal use only.

Received November 23, 2009; Revised Manuscript Received May 10, 2010

ABSTRACT: The onset of crystal nucleation was studied for seeded semibatch experiments in aqueous solutions in which either the feed rate, the seed size, or seed amount was varied. The results of these experiments show that the nucleation behavior of polycrystalline vaterite features striking similarities with monocrystalline particles in general. Investigations of the nucleation rate of vaterite during spontaneous precipitation experiments have revealed that it would take orders of magnitude higher supersaturation values to obtain the particle numbers required for a proposed nanoaggregation process. The subunit “size” of polycrystalline vaterite is markedly different from particle to particle in seeded semibatch experiments in which nucleation occurred. Differences in the subunit “size” of particles formed under the same process conditions can hardly be explained by aggregation of precursor particles, as nanoaggregation would lead to a uniform distribution of nanoparticles among all particles. Crystal growth, on the other hand, can explain this phenomenon as it may depend on the underlying crystal surface and on the spherulite size. This points at spherulitic growth as the underlying particle enlargement mechanism. The same could be shown for spherulites of calcite for which the particle growth mechanism has been found to be dependent on the crystal surface structure. The current study suggests furthermore the performance of further studies concerning other substances forming polycrystalline particles to establish the correct particle enlargement mechanism. Introduction Polycrystalline particles seem not to be restricted with respect to their chemical nature but can be found for a large variety of chemical compounds and are thus far more common than usually believed. In inorganic systems, they are found in carbonate minerals such as calcium carbonate1-4 and strontium carbonate,5 oxides such as iron(III) oxide6,7 and tin dioxide,8 hydroxides such as for example in azurite,6 sulfates such as gypsum9 and barium sulfate,10,11 sulfides such as cadmium sulfide,12,13 fluorides such as barium fluoride,14 nitrates such as silver nitrate and barium nitrate,9 phosphates such as calcium phosphate,15 apatites such as fluoroapatite,16,17 and oxalates such as copper oxalate.18 Also chemical elements have been shown to form polycrystalline material. Carbon, for example, is such an element that forms polycrystals both in diamond19 and graphite. In addition, metals such as palladium, copper, nickel, and even gold20 and silver21,22 can evolve to form polycrystalline particles. Bisault and Ryschenkow23 arrive at the conclusion that also liquid selenium exhibits polycrystalline features. Besides inorganic substances that include metallurgical alloys,24 organic substances can also be formed as polycrystals. Among the organic substances that show polycrystalline features, amino acids such as L-glutamic acid,25,26 proteins,27,28 benzenes,9 and polymers29,30 are widespread. The list of chemical compounds giving rise to polycrystalline solids could easily be extended. In nature, polycrystalline solids are known to exist throughout our world and even on other planets.29 They were for example found in volcanic rocks31,32 and glasses,5 mineral aggregates,24 and human kidney tissue and human urine.15 Often, polycrystalline materials are the basis for everyday materials such as airplane wings and plastic grocery bags.24 Also explosives such as NTO33 have been shown to have a polycrystalline pattern. *To whom correspondence should be addressed. E-mail: RalfB@chemeng. ntnu.no (R.B); Email: [email protected] (J.P.A.). pubs.acs.org/crystal

Published on Web 05/19/2010

The concept of nanoaggregation in order to explain polycrystalline solids is well established in the literature dealing with precipitation of sparingly soluble salts from solution. Egon Matijevic has published numerous papers in the field. Privman,20 a co-worker of Matijevic, states that nuclei which form in supersaturated solutions grow first to primary particles of nanometer size which then in turn aggregate to larger secondary particles. In their model, primary particles only aggregate with secondary particles which as a consequence increase in size. Along the same lines, Dirksen and Ring34 state that crystal enlargement occurs analogous to diffusion-controlled growth, with growth units of 0.01-0.1 μm instead of ions and molecules. On the basis of their “controlled double-jet precipitation experiments” St avek et al.35 argue that primary particles continuously disappear from the investigated system either by Ostwald ripening or aggregation to increase the size of stable particles. Oca~ na et al.36 summarize that aggregation can occur either undirectional or directional. In their view, undirectional aggregation results in spherical particles, whereas ellipsoids, platelets, and other shapes are a consequence of directional aggregation. According to Xu et al.37 crystallization can be divided into classical and nonclassical. In classical crystallization, ions and molecules are the primary building units for the crystal growth of single crystals (a in Figure 1). However, in nonclassical crystallization particles in the nanometer range are considered to be the primary units in the construction of larger crystals. The aggregation of nanosized primary particles is reported to occur via “self-assembly” and oriented attachment of primary units38 in the same crystallographic orientation to give “iso-oriented” superstructures (b in Figure 1). The second pathway (c in Figure 1) involving nanocrystals is analogous to the first pathway with the difference from the latter that polymers or other additives are involved in the “mesoscale assembly” process as surface-active compounds.39 These “mesocrystals” might finally fuse to single crystals. Finally, also polycrystals can be the consequence of the “self-assembly” of r 2010 American Chemical Society

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Figure 1. Nanoaggregation mechanism according to C€ olfen and Antonietti,46 and Kulak et al.40 Printed with permission from John Wiley & Sons, Ltd (Copyright 2008).

nanosized building blocks, either with or without the presence of additives.40 Also the crystal structure of polycrystals might be restructured in such a way that the crystallographic orientation of the particle is equal in all directions. Judat and Kind10 give barium sulfate as an example for a system undergoing nanoaggregation. They attribute the monocrystalline structure in the end of the crystallization process to recrystallization within the core of the crystal. As an example for an organic polycrystalline material suggested to form according to an aggregation based mechanism, the work of Wohlrab et al.26 may be mentioned. The work group crystallized D,L-glutamic acid, L-lysine, and L-histidine by introduction of the antisolvent ethanol to aqueous amino acid solutions. They report the formation of liquid precursors if the initial solution contains a polymer which is oppositely charged to the amino acid. The research group observed that these precursor phases transform within several days to give rise to porous superstructures with 10-100 μm size if the initial amino acid concentration is high enough. They state that platelet-like crystals of nanometer size come together and align radially to form spherical particles. However, polycrystalline particles might also be the result of complex growth processes such as spherulitic growth, where each nucleated crystal results in a polycrystalline particle. Spherulitic crystal growth has traditionally been reported for systems of inorganic salts in gels,41 polymeric blends of large molecules, and in cooling of high temperature melts. High viscosity or presence of impurities is often regarded as an essential prerequisite for this growth phenomenon.29,42,43 Originally, the terms spherulitic and spherulite were used for spherical particles with polycrystalline patterns, but today they are used in a broader sense for polycrystalline solids with different shapes. Gr an asy et al.24 claim that spherulitic particles form by growth front nucleation (GFN) when new crystal grains nucleate at the surface with a different lattice orientation than the parent crystal, by a randomized orientation which accounts for the isotropy of spherulitic growth at large length scales and long times. Three different mechanisms can give rise to polycrystalline growth. The growth can be a result of dynamic heterogeneities when the reorientation of molecules is slow compared to the propagation of the growing surface. It can also be caused by the action of foreign particles or other static heterogeneities like phase separation in the system. Spherulites have been observed in pure systems at lower viscosity for which a mechanism of

Figure 2. (a) Category 1 spherulite arising from a central precursor via multidirectional growth; (b) category 2 spherulite forming from a precursor where edges fan out giving rise to intermediate “dumbbell-like” shapes which might ultimately lead to a spherical shape leaving two eyes (uncrystallized holes) in the core of the particle.24 Reprinted figure with permission from ref 24. Copyright 2005 by the Amercian Physical Society.

“noncrystallographic branching” is suggested by Gr an asy as a third alternative. The evolution of spherulitic particles can take place in two different ways as shown in Figure 2. Category 1 (Figure 2a) particles are comprised of a radiating array of crystalline subunits like fibers that arise from a common precursor, whereas category 2 spherulites (Figure 1b) grow from a precursor via low-angle branching starting first on the edges. Intermediate dumbbell-like (or sheaf-of-wheat) like shapes lead to nearly spherical crystals which can exhibit two “eyes” on the sides of the nucleation site.6 Andreassen et al.44 varied the initial supersaturation, temperature, and solvent composition to demonstrate that spherulitic growth of calcium carbonate (vaterite) occurs both by central multidirectional growth (in water) and by unidirectional growth followed by low angle branching (in 90 wt % ethylene glycol). The progression of noncrystallographic branching could be monitored as a function of time at intermediate initial supersaturation values, supplying direct visual evidence for spherulitic growth in this system. A reduction in the initial supersaturation resulted in insufficient branching and therefore dumbbell-shaped particles, whereas increased levels of supersaturation rapidly produced fully grown spherulites. Busch et al.16 use fluorapatite as a model compound for apatites which play an important role in the structure of human teeth45 and show that the morphogenesis of fluorapatite crystals in gelatin occurs in a similar way than for category two spherulites. In their study, elongated hexagonal, prismatic precursors evolve to dumbbell-shaped crystals which then develop to full spheres. However, the formation of fluorapatite crystals was suggested to

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Figure 3. Monocrystalline needle gives rise to a spherulite by introduction of foreign particles (middle) or by reducing the orientational mobility (right): phase field model by Gr an asy et al.24 Reprinted with permission from ref 24. Copyright 2005 by the Amercian Physical Society.

Figure 4. Phase field modeling24 according to the “noncrystallographic branching mechanism” shows transition from monocrystalline growth to spherulitic growth by increasing the supersaturation. Reprinted with permission from ref 24. Copyright 2005 by the Amercian Physical Society.

conform to a nanoaggregation type of mechanism.46,47 Carr and Subramanian48 show how 3PbO 3 2SiO2 can be grown from the melt by evolving from a sheaf-of-wheat-like shape to a spherical particle according to a spherulitic growth mechanism. Granasy’s work24 based on phase field modeling shows that monocrystalline particles no longer form when foreign particles are introduced or the orientational mobility is low (Figure 3). Instead, polycrystalline particles are then obtained which grow according to a spherulitic growth mechanism. The importance of the supersaturation as for the crystal morphology becomes also evident from the work of Gr an asy (Figure 4). While monocrystals are formed at low levels of supersaturation, noncrystallographic branching occurs more frequently at higher supersaturation as a consequence of a rise in growth front nucleation. At high supersaturation, the branching frequency is so high that the uncrystallized eyes cannot be observed anymore. Magill29 reports a similar transformation from monocrystalline to spherulitic structures in cooling crystallization experiments with 1,3-bis(1-naphtyl)-5-(2-napthyl)benzene (TNB, Figure 5) from the melt. Monocrystals were observed at small undercoolings, whereas higher undercoolings produced spherulites. Since the temperature in this case also is the parameter that controls the supersaturation level, it is not possible to extract the separate effects of supersaturation and temperature on the observed transition in morphology. Measurements of the accompanying growth rate showed that the spherulites form with higher growth rates than the monocrystals. In his book Crystals: Growth, Morphology, and Perfection, Sunagawa19 shows how the crystal morphology changes from monocrystalline to a hopper type of morphology, then to dendritic and finally to spherulitic when the driving force (supersaturation) is increased (Figure 6). Lately, Andreassen1,44 has demonstrated evidence that calcium carbonate grows according to a spherulitic growth mechanism in aqueous solutions. Kim33 gives the explosive NTO as a further example of a compound undergoing spherulitic growth in aqueous solutions. Formation of the explosive from water and NMP as cosolvent gave spherulites of several hundred micrometers. The particle morphologies ranged from perfect and smooth spheres to more open structures with a rougher surface.

Figure 5. From the work of Magill,29 it can be seen that the occurrence of polycrystalline material depends on the crystal growth rate (G). Reprinted from Magill et al.49 with permission from the American Institute of Physics (Copyright 1967).

Figure 6. Sunagawa shows in his book Crystals: Growth, Morpholgy and Perfection19 how monocrystalline and polycrystalline growth depend on the driving force for crystallization. Reprinted with permission from Cambridge University Press (Copyright 2005).

This type of particle growth has also been discussed in a paper by Heijna et al.27 which was given the name “Spherulitic growth of Hen Egg-White Lysozyme Crystals”. Spherulites in protein crystallography are “considered the result of a failed crystallization experiment”, and thus their formation has sparked an interest in this area in order to prevent their occurrence. The appearance of polycrystalline particles is usually explained by two coexisting theories in the literature, nanoaggregation and spherulitic growth. The two enlargement processes are influenced very differently by the parameters in the crystallization process. Crystal growth is mainly affected by the supersaturation and the temperature and may depend on the surface structure of the growing seed crystals. Besides depending on the

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growth rate, the aggregation rate is also affected by the number and size of the particles in the system, the stirring rate, and the strength of the crystalline bridge connecting the particles.50 If homogeneous nucleation is occurring, the newly formed crystals are not dependent on the seed crystals. As they are influenced in very different ways by the industrial processing environment, the discrimination between crystal growth and aggregation is of crucial importance for the control of particle morphology and size. This work is part of an industrially sponsored project. Polycrystalline particles with a roughly spherical shape were identified in the industrial production of a secondary aromatic amine derivative, where filtrations problems are considered to be the major bottleneck. The striking similarity to polycrystalline particles L-glutamic acid motivated a comparative study of both these organic substances with respect to crystallization from aqueous solutions51 and their filtration behavior.52 In order to fulfill this task in a broader context a third, inorganic substance had to be selected which could be precipitated as polycrystalline spheres. Calcium carbonate was chosen as an inorganic counterpart because of its importance in the oil and gas industry where both precipitation phenomena and solid-liquid separation are crucial for efficient solid liquid separation. The importance of calcium carbonate furthermore resides in its wide occurrence, in nature, as an important industrial product and problematic scaling mineral. In this article, the nucleation and growth behavior of calcium carbonate are investigated in the light of established nucleation and growth theories in order to point out spherulitic growth as the correct underlying crystal enlargement mechanism. In addition, to give further evidence for spherulitic growth the crystal surface structure has been investigated thoroughly and experiments with mixed shapes have been performed. Experimental Work Vaterite. The crystallization experiments yielding vaterite particles were performed at 30 °C in a stirred (three bladed propeller, 2000 rpm) lab-scale glass reactor. Unseeded batch (see Figure 7) and seeded semibatch precipitation experiments (see Figure 8) were carried out in aqueous solutions where crystallization of the model compounds was induced by reaction of solution constituents. The supersaturation ratio, S, defined by eq 1 was calculated for vaterite according to eq 2 for the unseeded (u) batch-experiments since the nucleation and growth of vaterite particles involved the initial formation of amorphous calcium carbonate53 in these experiments. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aCa2þ aCO3 2 S ¼ ð1Þ Ksp

Svaterite, u

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ksp, amorph ¼ Ksp, vaterite

ð2Þ

In eq 1 aCa2þ is the activity of calcium ions, aCO32- is the activity of carbonate ions, and Ksp is the solubility product, and in eq 2 Ksp, amorph and Ksp, vaterite are the solubility products of the amorphous form, and vaterite. The Ksp value of the amorphous compound was calculated as an average value from the data obtained from the work of Clarkson et al.54 and Brecevic and Nielsen.53 The solubility product of vaterite was computed from the data given in the publication of Plummer and Busenberg.55 For the seeded semibatch experiments, the initial supersaturation, S0, was calculated from the growth rate relationship of second order (eq 3)50,56 assuming the absence of crystal nucleation and aggregation. G ¼ kg ðS - 1Þ2

ð3Þ

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Figure 7. Batch crystallizer used for the precipitation experiments of calcium carbonate. The growth rate constant, kg, was computed to 0.56 nm/s at 30 °C based on the growth rate constants reported by Andreassen and Hounslow at T1 = 25 °C and T2 = 40 °C,50 the universal gas constant, R, and eq 4 expressing the activation energy Ea (integrated form of equation shown in ref 57). kg, 2 RT1 T2 ln Ea ¼ ð4Þ T2 - T1 kg, 1 The initial growth rate, G0, was calculated by the initial change in the particle radius with time: Δr ð5Þ G ¼ Δt The sphere radius, r, was computed based on the total particle volume, Vs, and the total number of particles, N, with help of the Coulter Counter Multisizer III (Beckman Coulter): rffiffiffiffiffiffiffiffiffiffi 3 3Vs r ¼ ð6Þ 4πN Prior to the Coulter Counter Multisizer measurements, 1-3 mL of the particle suspension was diluted with 200 mL of saturated aqueous solution (with respect to vaterite) containing 0.15 M NaNO3. In this work, saturated solution with respect to vaterite was prepared by first adding vaterite crystals to the solution in excess to solubility, then stirring the suspension for 1 h and finally filtering the suspension with the help of a filter medium with an average pore size of 0.22 μm. Onset of Nucleation. The onset of crystal nucleation was studied for seeded semibatch experiments (see Figure 8) in aqueous solutions in which either the feed rate (procedure 1), the seed size (procedure 2), or seed amount (procedure 3) was varied. Spherical seed crystals (7-8 μm) of vaterite were produced at 30 °C in batch experiments (Figure 7) by adding an aqueous solution of K2CO3 (0.2 M, 1 L; Sigma-Aldrich, g99%) instantaneously to a stirred (2000 rpm) solution of 0.2 M (1 L) Ca(CH3COO)2 3 H2O (Sigma-Aldrich, g99), to give a resulting concentration of 0.1 M CaCO3 (2 L). The crystallization

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Figure 8. Experimental setup for seeded semibatch precipitation experiments of calcium carbonate. time was 15 min, after which the seed crystals were separated from the mother liquor, washed with ethanol, and dried (100 °C). Influence of Feed Rate. The influence of the feed rate on the onset of crystal nucleation was studied by choosing the addition rate of Ca2þ either to be 0.75 mol/h or 102.9 mol/h (method 1). In these semibatch experiments 33 wt% (with respect to the expected final solid mass) seed crystals, equaling a mass of 10 g were first suspended in Na2CO3 (0.2 mol; Fluka, g99%) solution saturated with respect to vaterite. Then, saturated CaCl2 3 2H2O solution (0.2 mol; Fluka, g99%) was either added slowly to the reactor by a peristaltic pump (Figure 8) or manually in the experiment performed at higher feed rate ( fr = 102.9 mol/h). In these semibatch experiments, the stirring speed was set to 2000 rpm to suppress aggregation, the crystallization temperature was 30 °C. The crystallization process was finished directly after the calcium ions containing solution was added (0.75 mol/h) or 15 min after the completed addition (102.9 mol/h), respectively. Influence of Seed Size. The influence of seed crystal size on the onset of nucleation was investigated in stepwise crystallization experiments carried out at 30 °C and 2000 rpm. After drying of the seed crystals with a size of 7-8 μm, the resulting crystals were used as seed crystals in stepwise crystallization to enlarge the crystal size of the vaterite spherulites (procedure 2). A percentage of 33 wt% (with respect to the expected final solid mass) seed crystals equaling a mass of 10 g was used in each of the experiments. Influence of Seed Amount. Another strategy for size increase was applied by decreasing the amount of seed crystals (7-8 μm) below 33 wt% down to 1 wt% in a one-step procedure (procedure 3). The pumping rate was set to 0.75 mol/h in these experiments. Measurement of the Particle Size Distributions and Crystal Processing. The Coulter Counter Multisizer III (Beckman Coulter) was used to determine the particle size distribution. Prior to the measurements 1-3 mL of the particle suspension was added to 200 mL of saturated aqueous solution.

After each of the above-mentioned crystallization experiments, the crystal suspension was filtered, then washed with ethanol, and dried at 100 °C. Scanning electron microscopy (Zeiss Ultra 55 Limited Edition) and X-ray powder diffraction (Siemens, D-5005 X-ray) were used to investigate the morphology and polymorphism of the dry crystals. The approximate polymorphic abundance of the calcite polymorph was estimated from XRD diagrams by comparing the peak height of the pronounced calcite peak at a 2Θ value of 29.5 to the corresponding peak height of a pure calcite sample. The experimentally determined XRD diagrams of vaterite, aragonite, and calcite are shown in Figure 9. Nucleation Rate Investigations. In order to evaluate whether the observed vaterite crystals are formed by a nanoaggregation mechanism or by spherulitic growth, nucleation rates, J, were calculated according to classical nucleation theory (eq 7). J ¼ A exp

- 16πγ3 ξ2 3k3 T 3 ðνln SÞ2

ð7Þ

where A is the preexponential factor, k is the Boltzmann constant, ξ is the molecular volume, and ν is the number of moles of ions in one mole of electrolyte. For nonelectrolytes ν is 1. The preexponential factor A was calculated from eqs 7 and 8 based on kinetic data for calcium carbonate given in the work of S€ ohnel and Mullin58 assuming the time which elapses until the nuclei have grown to a detectable size to be small compared to the actual nucleation time. N J ¼ ð8Þ tind where N is the number of nucleated crystals and tind is the induction time. According to Roelands et al.,59 Sch€ oll et al.,60 and others the preexponential factor A is dependent on the supersaturation ratio S. The value for A increases with increasing S, and the supersaturation

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Figure 9. Experimentally determined XRD diagrams of the three anhydrous polymorphs of calcium carbonate, calcite, aragonite, and vaterite. ratio S and the nucleation rate J are interconnected in such a way that J increases with increasing S (eq 7). Therefore, in the current work the nucleation rate, J, was calculated for a high supersaturation ratio of S = 52 (from S€ ohnel and Mullin58) to yield maximal values for the nucleation rate. S€ ohnel and Mullin58 measured the number of particles nucleated within an induction time of tind = 3.8 10-3 s to be N = 3.2 1014 m-3 at S = 52 and T = 25 °C. Values for both the surface tension (γ = 85.0 mJ m-2) and the molecular volume ξ vaterite = VM,vaterite/Na (VM,vaterite = 18.47 cm3 mol-1) were also extracted from this work. The nucleation rate, J, was computed at a temperature of 30 °C (eq 7) for S = 7.1 in spontaneous batch-crystallization experiments, and S = 3 and S = 1.4 for seeded semibatch experiments. For the calculations, it was assumed that the particles form with a constant nucleation rate during the experiment time t. Andreassen1 and Brecevic et al.61 have earlier shown that vaterite is comprised of subunits which are about 10-35 nm in “size”. In order to account for the largest volume that could theoretically be taken by hypothetical nanoparticles, it was assumed that each nucleated particles exhibits a “size” of D = 35 nm. The size of one of those theoretical nanoparticles was calculated by Vp = π/6D3. The theoretical volume of the hypothetical nanoparticles, Vs, was computed according to Vs = JtVp. The total volume Vtot, occupied by the crystals, was determined assuming primary particles packing with a porosity of ε = 0.77762 and eq 9. Vtot - Vs ε ¼ ð9Þ Vtot The total volume was thus obtained by Vtot = Vs/(1 - ε). Calcite. To investigate the effect of the original particle morphology on the growth behavior of calcite, both plate-like particles and spherulites of calcite were used as seed crystals (ratio 46:54 wt% plates/spherulits to account for equal area per unit mass) in a semibatch experiment. Spherulites of calcite were obtained by adding 0.2 M Na2CO3 instantaneously to 0.2 M of CaCl2 3 2H2O at a temperature of 5 °C and a stirring speed of 300 rpm. The crystallization time was 22 h to ensure complete transformation from vaterite to calcite. The novel calcite plates were produced batch-wise (see Figure 7) by adding instantaneously a 0.2 L solution of 0.2 mol of CaCl2 containing 1.2 mol of LiCl (Sigma-Aldrich, g99) to a 1.8 L aqueous solution of 0.2 mol of Li2CO3 (Merck, g99). The crystallization was performed at 45 °C at 2000 rpm for 64 h, due to slower transformation of the initially precipitated vaterite polymorph. Both spherulites and plate-like calcite were filtered, washed with ethanol, and dried (100 °C) before used as seed material. The seed crystals (33 w-% with respect to the expected final solid mass) were suspended in Na2CO3 (0.2 mol; Fluka, g99%) solution saturated with respect to calcite. In this work, saturated solution with respect to calcite was prepared by first adding calcite crystals to the solution in excess to solubility, then stirring the suspension for 1 h and finally filtering the suspension with the help of a filter medium with an average pore size of 0.22 μm. Then, saturated CaCl2 3 2H2O solution (0.2 mol; Fluka, g99%) was added to the reactor by a peristaltic pump (Figure 8) at a feed rate of fr = 0.75 mol/h. In this experiment the stirring speed was set to 2000 rpm and the temperature was 30 °C. The crystallization process was finished directly after the calcium ions containing solution was added.

Figure 10. Vaterite seed particles 16 min after nucleation of the amorphous compound (exp. CaCO3 1). The vaterite crystals have nucleated and grown at a supersaturation ratio of Svaterite,u = 7.1 at 30 °C and a stirring speed of 2000 rpm. The magnification is 1600 in (a) and 6400 in (b). Thereafter, the crystal suspension was filtered, washed with ethanol, and dried at 100 °C. Scanning electron microscopy (Zeiss Ultra 55 Limited Edition) and X-ray powder diffraction (Siemens, D-5005 X-ray) were used to investigate the morphology and polymorphism of the dry crystals.

Results and Discussion Vaterite. Seed crystals (7-8 μm) were obtained from the batch experiment exp. CaCO3 1 (see Figure 10) and further parallel experiments were performed at the same crystallization conditions. The polymorphic composition was found to be approximately g89% vaterite (e11% calcite) in all of the runs which were carried out. For crystals produced at Svaterite,u=7.1, the theoretical nucleation rate was determined in order to shed light on the underlying enlargement mechanism. Furthermore, the onset of nucleation in seeded experiments was investigated by three different procedures. In all experiments smaller amounts of calcite (e5%) were detected along with the vaterite polymorph. Onset of Nucleation. The onset of crystal nucleation was studied based on dependence of the feed rate (procedure 1), the seed size (procedure 2), or the seed amount (procedure 3).

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Figure 11. Particle size distributions obtained from Coulter Counter Multisizer measurements of vaterite grown in seeded semibatch experiments at low (exp. CaCO3 2) and high (exp. CaCO3 3) feed rate, fr, of Ca2þ to a saturated solution containing CO32- ions and seed crystals. The seed and product crystals of exp. CaCO3 2 are shown in the upper part and the seed and product crystals of exp. CaCO3 3 in the lower part of the figure. Table 1. Experimental Conditions and Results for exp. CaCO3 1CaCO3 3a

experiment

polymorph

initial supersaturation ratio S0 [--]

CaCO3 1 CaCO3 2 CaCO3 3

mainly vaterite mainly vaterite mainly vaterite

7.1 3 >3

seed amount [wt-%]

feed rate fr [mol/h]

none 33 33

NAb 0.75 102.9

a Particles resulting from the batch experiment CaCO3 1 (and parallel experiments) were used as seed crystals for the semi-batch experiments CaCO3 2 and CaCO3 3. The temperature was 30 °C and the stirring speed was 2000 rpm in all of the experiments shown in this table. b N/A, Not Applicable.

Influence of Feed Rate (Procedure 1). In experiments in which the seed crystal size (7-8 μm) and amount (10 g, 33 wt%) were kept constant, the level of the feed rate was found to effect the resulting particle size and particle size distributions. This is shown in Figure 11 which presents the particle size distribution of crystals grown at a feed rate of 0.75 mol/h (exp. CaCO3 2) and a feed rate of 102.9 mol/h (exp. CaCO3 3). The experimental conditions are summarized in Table 1. From the bimodal size distribution of particles produced in exp. CaCO3 3, it can be concluded that the number of freshly nucleated vaterite crystals is significant in this experiment. The onset of nucleation throughout the crystallization process in exp. CaCO3 3 is verified by comparing Figures 12 and 13 and can be explained by the higher feed rate. The initial supersaturation ratio has been calculated to S0 = 3 in exp. CaCO3 2 (see Table 1). Because of the onset of nucleation in exp. CaCO3 3, the initial supersaturation ratio could not be determined by the same approach as used for experiment exp. CaCO3 2. Yet the initial supersaturation ratio is proposed to be higher in exp. CaCO3 2 as a direct consequence of the increased feed rate. Thus, for exp. CaCO3 3: S0 > 3. The results of these experiments show that nucleation and subsequent growth of new polycrystalline vaterite particles occurs at a higher supersaturation level (Figure 13). This finding is in accordance with the nucleation and growth behavior of monocrystalline particles for which nucleation is reported to occur at a higher supersaturation.57 The observed new polycrystalline particles (Figure 13) however would not be possible according to the model of Privman et al.20 which assumes that

Figure 12. Vaterite crystals grown from seed crystals (33 wt%) at 30 °C at 2000 rpm at an addition rate of 0.75 mol/h Ca2þ to a saturated solution containing CO32- ions and seed crystals (exp. CaCO3 2). The initial supersaturation ratio was found to be S0 = 3. The magnification is 400 in (a) and 1600 in (b).

primary nanoparticles aggregate only with secondary (larger) particles. The striking similarity in the nucleation and growth behavior of monocrystalline and polycrystalline particles thus points to spherulitic growth as the underlying particle enlargement mechanism. Influence of Seed Size (Procedure 2). Also the influence of the seed size on the nucleation behavior of vaterite was investigated. In the first stage of stepwise performed crystallization experiments, particles similar to those displayed in Figure 10 could be crystallized applying the same operational conditions. Particle size distributions of crystals formed in the third crystallization step in exp. CaCO3 5 (the second step exp. CaCO3 4 is not shown here) illustrate the absence of nucleation in this stage (Figure 14). Crystals obtained from exp. CaCO3 5 are depicted in Figure 15. Only when the particle size of the seed crystals was increased in the next step crystal nucleation started to appear. This becomes evident from Figures 14 and 16 which show a number of smaller-sized particles that appeared in exp. CaCO3 6. As the seed crystal size was further increased, the level of nucleation increased simultaneously. This is shown by the large width of the particle size distribution in Figure 14 and by the high amount of small particles in exp. CaCO3 9 (exp. CaCO3 7 and CaCO3 8 are not shown here) which have

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Figure 14. Particle size distributions obtained from Coulter Counter Multisizer measurements of vaterite grown in stepwise crystallization in seeded semibatch experiments with 33 wt % (10 g) seed crystals. The results of the 3rd and 4th step are shown in the upper part and the 7th step is shown in the lower part of the figure.

Figure 13. Vaterite crystals grown from seed crystals (33 wt %) at 30 °C at 2000 rpm at an addition rate of 102.9 mol/h Ca2þ to a saturated solution containing CO32- ions and seed crystals (exp. CaCO3 3). The initial supersaturation ratio was found to be in the range of S0 > 3. The magnification is 400 in (a) and 1600 in (b).

formed by nucleation (Figure 17). The larger vaterite crystals depicted in the same figure have grown from the initially added crystal seeds. The results show that the nucleation tendency is higher in experiments in which larger seed particles were used. Higher nucleation rates at larger seed sizes can be accounted for by the crystal surface area per unit mass being lower for larger particles. Besides primary nucleation, secondary nucleation might also play a role in the stepwise performed experiments, although the mechanism of secondary nucleation is normally negligible for sparingly soluble substances.63 However, the catalyzing effect of parent crystals on crystal nucleation increases with increasing crystal size.64 This could lead to secondary nucleation in the stepwise performed experiments as a result of the larger observed crystal sizes as compared to the other performed experiments. Generally speaking, the onset of nucleation at large seed crystal sizes in the stepwise performed experiments is analogous to the behavior of their monocrystalline counterparts and thus supports spherulitic growth as an enlargement mechanism for the investigated vaterite particles. Influence of Seed Amount (Procedure 3). The seed amount was found to have an effect on the nucleation behavior of vaterite. The experimental conditions are summarized in Table 2.

Figure 15. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.2 mol/h Ca2þ from seed crystals (33 wt %) in the third crystallization step (exp. CaCO3 5). The magnification is 400 in (a) and 1600 in (b).

Decreasing the amount of the seed crystals (7-8 μm) from 33 wt% (Figure 12) to 9 wt % involved only a small increase in the amount of newborn crystals (Figure 18).

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Figure 16. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.2 mol/h Ca2þ from seed crystals (33 wt %) shown in Figure 15 in the fourth crystallization step (exp. CaCO3 6). The magnification is 400 in (a) and 1600 in (b).

Figure 17. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.1 mol/h Ca2þ from seed crystals (33 wt % in the seventh crystallization step (exp. CaCO3 9). The magnification is 400 in (a) and 1600 in (b).

Experiment exp. CaCO3 10 performed with 15 wt % seed crystals yielded only a negligible amount of freshly nucleated crystals which is shown in Figure 19. Therefore, the initial supersaturation ratio could be calculated to S0 = 4 (see Table 2) in exp. CaCO3 10 according to the method presented in Experimental Work. On decreasing the seed amount from 15 wt % to 9 wt % the number of nucleated crystals increased (see Figures 18 and 20) slightly. Thus, the assumption of the absence of nucleation in exp. CaCO3 11 is not completely fulfilled which leads to a slight underestimation of the calculated initial supersaturation of S0 = 4.6. Yet this consideration allows for ascribing the larger amount of nucleated crystals in exp. CaCO3 11 (as compared to exp. CaCO3 10) to the smaller amount of seed crystals and the higher initial supersaturation ratio in this experiment. Only at a seed amount of 1 wt % the magnitude of nucleation is significant which becomes evident when observing Figures 21 and 22. XRD analysis showed that the nucleating polymorph was not vaterite, as could be expected from the other experiments performed experiments, but calcite which constituted approximately 30% of the identified polymorphic forms (70% vaterite). Because of the high nucleation rate during exp. CaCO3 12 and the concomitant growth of both calcite and vaterite, it was impossible in this case to calculate the supersaturation ratio according to the described approach (Experimental Work). Yet

Table 2. Experimental Conditions and Results of the Semi-Batch Experiments CaCO3 2 and CaCO3 10-CaCO3 12a experiment

polymorph

initial supersaturation ratio S0 [--]

seed amount [wt %]

CaCO3 2 CaCO3 10 CaCO3 11 CaCO3 12

mainly vaterite mainly vaterite mainly vaterite ∼70% vaterite

3 4 g4.6 >4.6

33 15 9 1

a Particles resulting from the batch-experiment CaCO3 1 (and parallel experiments) were used as seed crystals. The temperature was 30 °C, the feed rate fr was 0.75 mol/h, and the stirring speed was 2000 rpm in all of the experiments shown in this table.

it is assumed that the initial supersaturation ratio is higher than in exp. CaCO3 10 and exp. CaCO3 11 as a consequence of the lower seed amount used in exp. CaCO3 12. These results show that nucleation occurs in case the feed rate is high, when the seed crystal size is large, and in experiments with a low amount of seed crystals. This behavior of the polycrystalline vaterite crystals is analogous to nucleation and growth phenomena observed for monocrystalline particles of other substances and thus suggests that vaterite particles are not the consequence of the simultaneous aggregation of millions of nanosized particles but the result of crystal growth of a spherulitic type.

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Figure 18. Particle size distributions obtained from Coulter Counter Multisizer measurements of vaterite grown in seeded semibatch experiments at an addition rate of 0.75 mol/h Ca2þ with a seed amount of 15 wt % (exp. CaCO3 10) and 9 wt % (exp. CaCO3 11). The seed and product crystals of exp. CaCO3 10 are shown in the upper part and the seed and product crystals of exp. CaCO3 11 in the lower part of the figure.

Figure 20. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.75 mol/h Ca2þ from seed crystals with an amount of 9 wt % (exp. CaCO3 11). The supersaturation ratio was found to be S0 g 4.6. The magnification is 400 in (a) and 1600 in (b).

Figure 19. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.75 mol/h Ca2þ from seed crystals with an amount of 15 wt % (exp. CaCO3 10). The supersaturation ratio was determined to S0 = 4. The magnification is 400 in (a) and 1600 in (b).

Nucleation Rate Investigations. Nucleation rates were calculated according to classical nucleation theory in order to evaluate whether polycrystalline vaterite crystals form by

a nanoaggregation mechanism or by spherulitic growth. On the basis of the nucleation rates calculated from classical nucleation theory and the assumption of 35 nm sized precursor particles, the fictive nanoaggregation mechanism cannot account for the observed volume of vaterite crystals. This becomes evident from Table 3 which shows that only 0.34% of the measured vaterite particle volume (Coulter Counter Multisizer) can be explained by the aggregation mechanism when crystals form spontaneously at a constant supersaturation ratio of S = 7.1 at 30 °C (exp. CaCO3 1). In semibatch experiments performed at even lower supersaturation ratios of S = 3 (exp. CaCO3 2) and S = 1.4 (exp. CaCO3 12), the particle volume accounted for by nanoaggregation becomes even more marginal which favors a spherulitic growth mechanism as being responsible for the particle enlargement. This finding is supported by Andreassen1 who states that a relative supersaturation ratio of σ = S - 1 = 5 is too low to obtain the particle numbers required for a possible nanoaggregation process. In precipitation experiments of vaterite at 25 °C, Andreassen measured the final particle number by means of the Coulter Counter Multisizer to be 0.155 1013 m-3 - 4.37 1013 m-3. He refers to Walton65 when stating that the final numbers of vaterite spherulites are typical for a heterogeneous nucleation processes. He concludes that it would take orders of magnitude higher supersaturation values to obtain the particle

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Figure 21. Vaterite and calcite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.75 mol/h Ca2þ from seed crystals (1 wt %) (exp. CaCO3 12). The magnification is 400 in (a) and 1600 in (b).

Figure 22. Particle size distributions obtained from Coulter Counter Multisizer measurements of vaterite grown in semibatch experiments at an addition rate of 0.75 mol/h Ca2þ from seed crystals with an amount of 1 wt % (exp. CaCO3 12).

numbers required for a proposed nanoaggregation process. In the present work, the final particle number of exp. CaCO31 was measured to be 1.85 1013 m-3 ( 5.8 1012 m-3 which agrees well with Andreassen’s results. This supports the suggestion that nucleation, when occurring,

Beck and Andreassen

follows a primary heterogeneous mechanism in the performed experiments of this study. However, in the stepwise performed experiments, secondary nucleation may also play a role due to larger crystal sizes in these experiments. The nanoaggregation mechanism is furthermore disproved by the fact that the resulting vaterite spherulites are accounted for by ionic growth relationships. The crystal growth rate of vaterite has been found by several scientists (for example, Andreassen and Hounslow50 and Kralj et al.56) to obey a second-order rate law. Surface Structure Investigations. To reveal the particle enlargement mechanism also the surface structure of vaterite particles from various experiments was investigated. In Figure 23 vaterite crystals from exp. CaCO3 9 are shown at a magnification of 2400. The following figure which is a close-up of the area highlighted by the white circle in Figure 23 illustrates the surface area of different vaterite crystals. Figure 24 indicates a subunit “size” which is markedly different for the depicted crystals. Also in several other crystallization experiments a variation in the particle’s subunit “size” was observed. Differences in the subunit “size” of particles formed under the same process conditions can hardly be explained by aggregation of precursor particles according to Figure 1, as nanoaggregation would lead to a uniform distribution of nanoparticles among all particles. Crystal growth, on the other hand, can explain this phenomenon as growth may depend on the underlying crystal surface and on the spherulite size. Calcite. In exp. CaCO3 13 plate-like and spherulitic seed crystals were used in order to investigate the effect of the original particle morphology on the growth behavior of calcite. The morphologies of the seed crystals are illustrated in Figure 25. The outcome of this crystallization experiment is shown in Figure 26. It can clearly be seen that the morphologies of the resulting crystals are not alike. This is regarded as a consequence of the plate-like and spherulitic seed crystals and sheds light on the enlargement mechanism. In the hypothetical case of an aggregation based particle enlargement in exp. CaCO3 13, the result would have been different: all particles would be spherulitic and the morphology would not depend on the underlying crystal surface structure. But exactly this is shown by Figure 26: seed crystals maintain their spherulitic features and plate-like crystals remain monocrystalline. This justifies that the calcite crystals shown in Figure 26 have formed by spherulitic growth and highlights the fact that the underlying crystal surface structure plays an important role. Spherulitic Growth of Other Substances. Polycrystalline calcium carbonate has been shown to grow from solution by spherulitic growth which is in contrast to the opinion of many authors such as C€ olfen and Antonietti,66 Dupont 67 et al., and Schlomach et al.68 who claim that polycrystalline calcium carbonate forms by aggregation of primary nanoparticles. What about other substances that are reported in the literature to form polycrystalline particles according to a nanoaggregation process? Are they really a result of “selfassembly” of millions of precursor particles? Let us for instance consider polycrystalline particles of the inorganic fluorapatite which were crystallized in gelatin.16 Because of the high viscosity of gelatin it seems unlikely that the required amount of nanoparticles can be produced for

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Table 3. Theoretical Nucleation Rate, J, and Estimated Particle Volume (Vtot) of Polycrystalline Vaterite Particles Hypothetically Forming by Primary Nucleation of Nanosize Particles (35 nm) and Subsequent Aggregation

experiment

supersaturation ratio S [---]

nucleation rate J [m-3 s-1]

time t available for nucleation [min]

number N of crystals per m3 nucleated within t [m-3]

volume Vtot occupied by the nucl. crystalsa per m3 [m3 m-3]

Vtot as compared to the observed volume [%]

CaCO3 1 CaCO3 2 CaCO3 12

7.1 3 1.4

1.4 1014 1.0 106 1.4 10-9

15 16 440

1.3 1017 9.0 108 1.3 10-6

1.3 10-5 9.7 10-14 3.7 10-127

3.4 10-1 1.7 10-9 6.6 10-123

Vtot - volume occupied by the crystals based on the theoretical nucleation rate at 30 °C and assuming the nucleated crystals exhibiting spherical size with a diameter of 35 nm and packing with a porosity of ε = 0.777. a

Figure 23. Vaterite crystals grown at 30 °C at 2000 rpm at an addition rate of 0.1 mol/h Ca2þ from seed crystals (33 wt %) in the seventh crystallization step (exp. CaCO3 9).

Figure 24. Close-up of vaterite particles from the area highlighted by the white circle in Figure 23.

a possible aggregation process in this system, and if this would be possible the low translational mobility of nanocrystals in gelatin would make encounters a very rare event. From the work of Busch et al., it may be concluded that the crystals evolve like that shown in Figure 2 according to a spherulitic mechanism characteristic of type 2 spherulites. This kind of particle evolution has recently also been reported for polycrystalline vaterite44 spherulites and for polycrystalline particles of L-glutamic acid51 indicating that also L-glutamic acid forms according to a spherulitic growth mechanism. This is however contrary to the opinion of other authors such as Wohlrab et al.26 who state that D,L-glutamic acid is the result of “selfassembly” of nanosized building blocks. Many studies

Figure 25. Calcite crystals used as seed crystals in exp. CaCO3 13 in a ratio of platelike (a) and spherulitic (b) particles of 46:54 wt % to account for equal surface area per unit mass of both morphologies.

dealing with polycrystalline particles of other systems report a nanoaggregation-based mechanism for the particle evolution. The conclusions are however often only based on the observed particle morphology as investigated by SEM and TEM, and diffraction line broadening combined with the concept that polycrystalline particles can only be formed as a result of an aggregation processes. However, these studies do not deliver evidence for the existence of the relevant number of nanosized particles required in an aggregation process to build up larger sized polycrystalline particles. On the other hand, spherulitic growth has neither been proven yet for many of these systems. Further studies should therefore be performed for each system yielding polycrystalline particles to identify the correct particle formation mechanism.

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Figure 26. Calcite crystals with different morphologies resulting from exp. CaCO3 13.

Summary and Conclusions The onset of crystal nucleation was studied for seeded semibatch experiments in aqueous solutions in which either the feed rate, the seed size, or seed amount was varied. The results of these experiments show that the nucleation behavior of polycrystalline vaterite features striking similarities with monocrystalline particles in general. Investigations of the nucleation rate of vaterite during spontaneous precipitation experiments have revealed that it would take orders of magnitude higher supersaturation values to obtain the particle numbers required for a proposed nanoaggregation process. The subunit “size” of polycrystalline vaterite is markedly different from particle to particle in seeded semibatch experiments with occurring nucleation. Differences in the subunit “size” of particles formed under the same process conditions can hardly be explained by aggregation of precursor particles, as nanoaggregation would lead to a uniform distribution of nanoparticles among all particles. Crystal growth, on the other hand, can explain this phenomenon as it may depend on the underlying crystal surface and on the spherulite size. This points at spherulitic growth as the underlying particle enlargement mechanism for the formation of vaterite particles. The same could be shown for spherulites of calcite for which the particle growth mechanism has been found to be dependent on the crystal surface structure. The conclusion of nanoaggregation for other inorganic and organic substances is often based on “evidence” from SEM, TEM, and diffraction line broadening combined with the concept that polycrystalline particles can only be formed as a result of aggregation processes. However, the studies do not give evidence for the existence of the relevant number of nanosized particles required in an aggregation process to build up larger sized polycrystalline particles. Further studies should therefore be performed for these systems to identify if either spherulitic growth or nanoaggregation is the underlying particle formation mechanism. Acknowledgment. The authors thank the Norwegian Research Council, GE Healthcare, StatoilHydro, Dyno Nobel, Norcem and Hydro Aluminium for their financial support.

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