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A Molecular Dynamics Study of the Early Stages of Calcium Carbonate Growth Gareth A. Tribello,*,† Fabien Bruneval,‡ CheeChin Liew,§ and Michele Parrinello† Computational Science, Department of Chemistry and Applied Biosciences, ETHZ Zurich USI-Campus, Via Giuseppe Buffi 13 C-6900 Lugano, Switzerland, CEA, DEN, SerVice de Recherches de Me´tallurgie Physique, F-91191 Gif-sur-YVette, France, and Polymer Research, BASF SE, D-67056 Ludwigshafen, Germany ReceiVed: March 23, 2009; ReVised Manuscript ReceiVed: June 4, 2009

The precipitation of calcium carbonate in water has been examined using a combination of molecular dynamics and umbrella sampling. During 20 ns molecular dynamics trajectories at elevated calcium carbonate concentrations, amorphous particles are observed to form and appear to be composed of misaligned domains of vaterite and aragonite. The addition of further calcium ions to these clusters is found to be energetically favorable and virtually barrierless. By contrast, there is a large barrier to the addition of calcium to small calcite crystals. Thus, even though calcite nanocrystals are stable in solution, at high supersaturations, particles of amorphous material form because this material grows much faster than ordered calcite nanocrystals. 1. Introduction The precipitation/crystallization of calcium carbonate plays an important role in nature and in the household. In nature, calcium carbonate is one of the most prevalent biominerals and forms the shells and crusts of a wide variety of undersea animals.1 These animals have a remarkable ability to control the structure and morphology of calcium carbonate crystals and thus are able to optimize their shell’s functionality.2,3 Humans also have some ability to control the nucleation of calcium carbonate, by the addition of additives to precipitation mixtures,4-6 but for the most part find the formation of calcium carbonate and other scales in kettles, heating devices, washing machines and on fabrics after washing a menace.7 In contrast with many other crystals, the rate of formation of calcium carbonate in solution is fast and increases with temperature,8 which implies the solubility decreases with increasing temperature. Despite these observations, textbooks usually describe calcium carbonate formation using ideas from classical nucleation theory.9 In this theory, one assumes that there is an activation barrier to formation of an initial crystalline nucleus which once formed grows by step-by-step addition of further atoms or molecules. However, in calcium carbonate solutions, it would appear that something far more complicated is occurring as newer experimental papers and reviews have begun to testify.1,8,10 Ogino et al.11 have shown that, in highly supersaturated calcium carbonate solutions, particles of amorphous calcium carbonate precipitate rapidly. These particles are initially amorphous but convert to a mixture of all three dehydrated phases on the order of a few minutes before being converted eventually to crystalline calcite. Subsequent investigations have shown the particles which are formed first are strongly hydrated.12,13 The formation of these amorphous nanospheres has been explained using a liquid-liquid (spinodal) phase separation mechanism14 and an alternative suggestion,15 based on classical nucleation theory. This second explanation assumes the amorphous particles have a lower surface energy, and hence * Corresponding author. Phone: +41 58666 4808. E-mail: gareth.tribello@ phys.chem.ethz.ch. † ETHZ Zurich USI-Campus. ‡ CEA, DEN. § BASF SE.

lower nucleation barrier, than calcite nanoparticles and is supported by computer simulations, which show that very small calcite clusters (∼1.6 nm) spontaneously amorphize in gas and in solution (albeit less so than in gas).16 Recently, investigations using cryo-TEM, SEM, and in situ WAXS8,17 have examined the growth of calcium carbonate in highly supersaturated solutions. Again, an initial amorphous, hydrated precursor phase is observed, which quickly converts to a mixture of both calcite and vaterite particles. These experiments suggest that initially amorphous nanoparticles form which subsequently agglomerate to form vaterite spheres. These spheres are then slowly converted to calcite, crystals of which are seen to grow in the immediate vicinity of the spheres. Calcium carbonate has a very low solubility, and as such, the majority of experiments are performed at high supersaturations. Those experiments that probe the low and high solubility nucleation paths show that the growth mechanism depends on the concentration of calcium carbonate.18 The behavior described in the previous paragraph happens at high supersaturations, while at low supersaturations calcite crystals are observed very early in the reaction mixture. Recent experimental work19,20 supports the view that the nucleation pathway depends on the calcium carbonate supersaturation. It shows that small clusters of calcium carbonate play a role in the prenucleation of calcite and that even in undersaturated solutions small, stable clusters of calcium carbonate are observed. Furthermore, the strength of binding to these clusters and hence their structure is dependent on the pH, which, because of the equilibrium between carbonate and bicarbonate, greatly affects the concentration of carbonate ions. The study of calcium carbonate precipitation from solution by computer simulation is hampered because simulations of large numbers of atoms over long time scales are required. However, extensive simulations of the calcium and carbonate ions in water have been carried out21,22 as well as simulations of the calcite-water interface.16,23-25 Furthermore, a simulation starting from small nanoparticles (∼1.6 nm) of amorphous calcium carbonate in water has shown that these nanoparticles agglomerate to form larger amorphous particles.26 Finally, a recent paper used metadynamics to explore the conformational space available to an amorphous calcium carbonate nanoparticle containing 75 calcium carbonate units.27

10.1021/jp902606x CCC: $40.75  2009 American Chemical Society Published on Web 08/03/2009

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Figure 1. Cluster sizes that are present in the solution as a function of simulation time for simulations at 300 and 365 K.

Recently, we have developed a new calcium carbonate potential21 by combining established literature potentials for water,28 calcium carbonate,29 and the interaction between the two.30 We have also examined the hydration properties of calcium and carbonate ions and shown that there is no activation barrier to the binding of the two ions in water. In this paper, we extend this work to examine the aggregation of amorphous calcium carbonate (ACC) in solution from its constituent ions. Our attention is confined to strongly basic environments (pH > 10) where the equilibrium between bicarbonate (pKa 10.5) and carbonate is pushed toward carbonate, as it is in these conditions that calcium carbonate growth is most rapid. The paper is organized as follows. In section 2, we detail the computational methods employed in the study. In section 3, we study the growth of ACC from solution. Section 4 is devoted to the analysis of the ACC particles we obtained. Finally, in section 5, we provide a discussion and conclusion. 2. Methods The simulations presented in what follows use a combination of molecular dynamics and umbrella sampling, which have been performed using a modified version of dl_poly_2.16.31 A time step of 1 fs and the velocity Verlet algorithm is used throughout, while the equations of motion of the rigid water molecules are solved using the NOSQUISH algorithm of Miller et al.32 Equilibrations are performed in the NPT ensemble using the Berendsen thermostat (τ ) 0.5 ps) and barostat (τ ) 2.0 ps) to control temperature and pressure, respectively. During production runs, temperature is controlled using the global stochastic thermostat of Bussi et al.33 (τ ) 0.5 ps) and the volume is kept constant. In all umbrella sampling calculations, dynamics were run for 0.5 ns and free energy profiles were reconstructed using the weighted histogram method (WHAM) as implemented in ref 34. In those calculations that used distances as collective coordinates, force constants of 46.12 kcal mol-1 Å-1 were used on each umbrella and umbrellas were placed at 0.3 Å intervals between 2.3 and 6.5 Å. The potentials employed include the polarizability of the carbonate ions and water molecules through a shell model. Elsewhere,21 the expediency and efficiency of different approaches to solving the equations of motion of the shell degrees of freedom has been examined. It is found that the most efficient route is to treat the dynamics adiabatically in the same spirit as Car-Parrinello MD.35 Accordingly, in this work, the shells are assigned a small mass (0.3 au) and their positions and velocities are obtained by integrating their equations of motions. Finally,

a simple 0 K thermostat with a 0.5 ps relaxation time damps the shell velocities and ensures that the shells do not “heat up” because of heat flux between the shells and cores. 3. Growth of ACC from Solution One can observe the formation of amorphous calcium carbonate from a solution of calcium and carbonate ions on the short time scales assessable in atomistic MD simulations provided that the initial concentration of the solution is sufficiently large. In the sections that follow, the results of such unbiassed MD runs are discussed and evidence is gathered which demonstrates that growth of ACC is barrierless. In contrast, it is shown that there are large free-energetic barriers to the addition of ions to small calcite crystals which would be expected to slow calcite growth. Throughout what follows, the bicarbonate ion is neglected as calcium carbonate grows most rapidly in basic conditions in which the carbonate ion is the dominant species. Furthermore, recent experimental work19 shows that calcium carbonate prenucleation clusters do not contain bicarbonate and that this ion acts only as a reservoir for the carbonate ions which grow into the amorphous or crystalline solid. 3.1. ACC Growth. Given that, at high supersaturations, experiments8,17 show that amorphous calcium carbonate forms exceptionally rapidly, it seems reasonable to expect that, for relatively high calcium carbonate concentrations, calcium carbonate growth will be seen on time scales accessible to molecular dynamics. With this in mind, two long simulations of 64 CaCO3 units in a box of 6400 water molecules (a concentration of 0.53 mol dm-3 and a saturation index of 6.6) were carried out at 300 K (20 ns simulation) and 365 K (5 ns simulation).36 As expected, small amorphous calcium carbonate clusters began to grow rapidly. Figure 1 shows the cluster sizes present as a function of the simulation time.37 It is clear from these figures that initially longrange Coulomb interactions between the oppositely charged ions drive the formation of solid calcium carbonate. Hence, single ions disappear very quickly (in less than 0.5 ns) and also charged clusters (those with odd numbers of ions) are rarely observed. Similar behavior has been observed in experiments,19 which show that the clusters formed are overall charge neutral and contain equal numbers of calcium and carbonate ions. The strongly attractive, electrostatic forces disappear once all the charged clusters have aggregated and are replaced by rapidly decaying dipole-dipole interactions. These interactions are further weakened by the large amounts of screening attributable to water’s high dielectric constant. Hence, further

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growth of calcium carbonate clusters is largely diffusion-driven as the small clusters, formed during the earlier stage, merge to form progressively larger and larger clusters, as can be seen in Figure 1 and as has been observed in ref 26 for systems at higher concentrations. Figure 1 also shows that the rate of growth is strongly dependent on the temperature further suggesting strengthening the assertion that the agglomeration is diffusion controlled. Finally, whereas initially the growth of the particles is rapid, subsequent growth is slower. This is because the number of clusters in solution decreases, which results in a decrease in the collision frequency, and because the larger clusters, which form later, have lower diffusivities. 3.2. Calcium Carbonate Oligomerization. Recent work22,38 has shown that, although the pairing of a calcium ion with a bicarbonate ion in solution is thermodynamically favorable, the subsequent addition of a further calcium, bicarbonate, or calcium bicarbonate unit to that first calcium-bicarbonate pair is endergonic. This observation helps explain why surface seawater is generally supersaturated with CaCO3.39 In prior work,21 it has been shown that calcium binds strongly to carbonate in solution and that there is no barrier to association of these two ions. To examine whether or not “oligomerization” of calcium carbonate is thermodynamically favorable, three further umbrella sampling calculations were carried out to examine the addition of a second calcium, a second carbonate, and a second calcium carbonate unit to a preformed calcium carbonate unit. In these simulations, the minimum distances, defined as the shortest distance between the calcium ions/carbon atoms of the first and second cluster, were employed as collective coordinates. This distance alone is a suitable collective coordinate in these calculations because, as shown in the Supporting Information, the carbonate rotation is fast and barrierless. Each of these calculations was done at 300 K, in a box of 264 water molecules that was first equilibrated for 0.5 ns. The distance between the calcium and the carbon of the carbonate in the original complex was monitored throughout and was found to oscillate around the mean calcium-carbonate distance for an isolated cluster (∼3.0 Å). To understand the addition of a second calcium carbonate, the system was first equilibrated while holding the minimum distance between the two calcium carbonate units fixed. A second equilibration was then carried out to pull the two units to the required distance before the statistics for umbrella sampling were accumulated. During this second equilibration, an upper harmonic wall was placed at 4 Å on each of the calcium carbonate distances to ensure the clusters remained intact. The results for these umbrella sampling calculations on the very early stages of growth of calcium carbonate are provided in Figure 2. Figure 2 shows clearly that formation of calcium carbonate complexes, which consist of more than a single calcium combined with a single carbonate, is exergonic. This is in direct contrast to the situation for bicarbonate. Furthermore, the barrier to addition of further ions to a carbonate pair is at most ∼1.4kBT. This, if it holds true for larger clusters (which is demonstrated for amorphous clusters up to 64 units in the following two sections), means that growth of calcium carbonate is, for the most part, diffusion limited. Figure 2 also shows that the addition of carbonate ions is more favorable than the addition of calcium ions, which, in turn, is more favorable than the addition of calcium. Figure 2 also shows the binding of calcium to carbonate is strongly exothermic because both ions are highly charged and so will bind together very tightly. By contrast, calcium-carbonate clusters have no charge and so binding between two of them will be

Tribello et al. considerably weaker as is seen in Figure 2. Finally, prior calculations21 have shown that carbonate ions have some hydrophobic regions around them and that the residence times of water molecules in the first hydration sphere of calcium are longer than the residence times in the first hydration sphere of carbonate. These observations suggest that the binding of calcium to calcium-carbonate will be weaker than the binding of carbonate to calcium-carbonate because an unbound calcium ion in solution is more stable than an unbound carbonate in agreement with Figure 2. A final point of interest from Figure 2 is the shelf in the free energy that occurs for distances between 3 and 3.5 Å, which becomes more pronounced in the profiles for Ca2 + + CaCO3 and CaCO3 + CaCO3. For the case of a single calcium and carbonate, this shelf is a consequence of the alternative, weaker, mode of calcium binding in which, instead of binding in between two carbonate oxygen atoms, it binds linearly to one oxygen. This binding mode is examined, along with the virtually barrierless interconversion between the two binding modes, in more detail in the Supporting Information. The same alternate binding mode also gives rise to the shelf in the profile for the addition of Ca2 + to CaCO3. However, it is now more pronounced because there is a larger distance, and hence lower electrostatic repulsion, between the two calcium ions in this geometry. By contrast, for the addition of CaCO3 to CaCO3, the reason for the more pronounced shelf in the free energy profile is that there are two ways the CaCO3 can bind together (see Figure 2). In the first, the minimum distance between the two clusters is shorter and both calcium ions sit between the two carbonates. In the second, only one calcium sits between the two clusters, while the other sits on the “outside” of the complex. 3.3. Addition to the Calcite (101j4) Surface. The most stable surface of calcite is the (101j4), as it has the lowest surface energy when hydrated and also when nonhydrated.30 Simulations24 show that the diffusivities of the water molecules in the vicinity of this surface are greatly reduced as a consequence of the formation of an ordered adlayer of water above the surface. This ordering of water molecules causes sharp oscillations in the electrostatic potential. This, in turn, introduces a barrier (∼4.5 kcal mol-1) to the adsorption of positively charged calcium ions because, on their way to the surface, they must pass through a layer which contains an excess of positively charged hydrogen atoms. We have shown previously21 that events which perturb the distribution of the six molecules in the first hydration sphere of calcium are relatively rare. It is therefore necessary to elucidate whether the destruction of this hydration sphere which accompanies the adsorption of a calcium on a surface is a rare event on the simulation time scale because, if it is rare, this may have an effect on the adsorption pathway. To investigate this, a slab of 240 CaCO3 units was used and one further CaCO3 unit was placed in a solution with 600 water molecules next to this slab. An umbrella sampling calculation with two collective coordinates (the distance between the extra calcium and the carbon atom of one of the carbonate ions on the surface and the coordination number of the excess calcium) was then carried out using umbrellas placed at 0.25 intervals in the coordination number variable and in 0.3 Å intervals in the distance variable. Force constants of 69.18 kcal mol-1 coord-1 and 46.12 kcal mol-1 Å-1 were used on the coordination number and distance, respectively. Figure 3 shows the 300 K free energy surface that results from this calculation. A barrier to calcium addition of ∼5.1 kcal mol-1 is observed in agreement with the results of

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Figure 4. Free energy profiles for adsorption of a calcium onto an infinite, periodic calcite (101j4) surface as a function of distance from the surface. The solid line is obtained from the surface shown in Figure 3 by integrating out the coordination number collective variable. The dashed line is from an umbrella sampling calculation in which only the distance was used as a collective coordinate.

Figure 2. Free energy profiles for addition reactions between calcium carbonate species in water calculated using umbrella sampling. Figure 5. Free energy profiles for addition of a calcium ion to the edge (dashed line) and the face (solid line) of a 125 ion calcite nanocrystal. The distance collective coordinate used here is the distance between the calcium in solution and the nearest carbon to the site at which it is absorbing.

Figure 3. Free energy surface for adsorption of a calcium onto an infinite, periodic calcite (101j4) surface as calculated using umbrella sampling in the space of Ca-surface distance and coordination number of the extra calcium. Each isoline represents a 0.59 kcal/mol increment in the free energy, which corresponds to 1 kBT.

Kerisit and Parker.24 Furthermore, as Figure 4 shows, examining addition with the single distance collective coordinate is reasonable, as when the coordination number collective coordinate is integrated out the free energy profile looks very similar to that obtained from a 1D umbrella sampling calculation.

3.4. Addition to Rhombohedral Calcite Crystals. To examine the growth of calcite from solution in a more realistic manner, the growth of small clusters of calcite in water was investigated. It is straightforward to create calcite nanocrystals of any size because the most stable morphology of a calcite crystal is rhombohedral, with the lowest energy, (101j4) surface exposed on all its faces.30 Elsewhere,16,26 it has been shown that very small clusters (∼1.6 nm) of calcite are stable in water but unstable in a vacuum. Repeating similar calculations, we find that the smallest clusters (13 Ca + 14 CO3) are unstable in water (the structure fluctuates a great deal during a 5 ns simulation and is clearly not crystalline). However, larger clusters (63 Ca + 62 CO3) are more stable and remain in a highly ordered crystalline arrangement for the duration of a 5 ns simulation at 300 K. The addition of calcium ions to a 125 ion calcite nanocrystal (in a box with 800 water molecules at 300 K) was examined using umbrella sampling. This particular cluster size was employed because it contains a similar number of ions to the largest amorphous cluster that formed spontaneously during the unbiassed molecular dynamics simulations which, in the next

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Figure 6. (left) The structure of the amorphous cluster grown from simulations with the addition sites considered in the umbrella sampling calculations highlighted. (right) Free energy profiles obtained from umbrella sampling for the addition of calcium ions to the various sites of an amorphous cluster. The large spheres in the left panel show the positions of the various addition sites (their color corresponds to those of the profiles in the right panel).

section, we employ in similar umbrella sampling calculations on the growth of amorphous clusters. Addition to two different sites (the center of one of the faces and one of the edges) on the surface of the cluster was examined. The results are shown in Figure 5. In these calculations, the distance between the calcium ion in solution and the carbon of one of the carbonate ions on the surface of the cluster was used as a collective coordinate. The use of a single collective coordinate is justified because, as shown in the previous section, the solvation degrees of freedom are fast variables. The first thing to note from Figure 5 is that the barrier to adsorption on the center of a face is almost identical to the barrier to adsorption on the infinite periodic (101j4) surface. Thus, even a surface this small causes an ordering of the water molecules above it and, since the water molecules are tightly bound to the cluster surface and ordered, there is a large barrier to calcium addition for the same reasons there is a barrier for addition to the flat surface.24 In contrast to the surface, adsorption at the edge of the nanocrystal comes with a much lower barrier (2.6 kcal mol-1 as opposed to 4.7 kcal mol-1). Spagnoli et al.25 have examined the distribution of water molecules above stepped (101j4) surfaces and have shown that the presence of the step drastically affects the distribution of water molecules around it. Hence, because the ordering of the water molecules is weaker close to the edges of the clusters, the barrier to addition of calcium is smaller partly because it is less costly to displace a water molecule and partly because the layer containing the excess of positively charged hydrogen atoms is expected to be less well developed. 3.5. Addition to ACC Nanoparticles. In the long simulations, it was observed that, as in experiments,8 amorphous calcium carbonate clusters form rapidly from solution. Although not observed in our simulations, the presence of both ACC and calcite crystals in experimental samples8 suggests that there must be a competition between the growth of ACC and the growth of calcite. Quantitative study, though, of the growth of ACC clusters is difficult because all the adsorption sites on an ACC cluster are different. However, here, a practical approach to screen through the most “nonequivalent” sites is devised. To investigate the free energetics for addition of calcium to amorphous calcium carbonate, the amorphous cluster, grown during the 365 K simulation, was employed. Addition sites were selected on the basis of an initial examination of the binding to the cluster in the gas phase. In this examination, a coarse grid of possible addition sites was created by using the positions of the oxygen atoms of the water molecules that lay within 3.5 Å

of the cluster in solution. Calcium ions were then placed, in turn, on each point in this grid and their position was relaxed to the nearest local minima (during this relaxation, the atomic cores in the cluster were held rigid but the shells were allowed to move). Those calcium ions that bound to the surface were found to have binding energies between -15.42 and -76.12 eV. Six points that uniformly covered this range of energies were selected for the umbrella sampling, as shown in Figure 6. For the umbrella sampling itself, the minimum distance between the calcium ion and the atoms in the binding site was used as a collective coordinate. Calcium and carbon atoms were said to be in the binding site if they were within 4 Å of the site at which the calcium adsorbed during the minimization of the cluster in vacuum. Furthermore, the minimum distance between the rest of the ions in the cluster was monitored throughout the simulations to ensure that calcium ions did not bind to alternative sites on the cluster and then diffuse across the surface to the desired adsorption site. Umbrellas were placed at 0.3 Å intervals between 2.3 and 6.5 Å and, with the exception of those at 2.3 and 2.6 Å, were given force constants of 46.12 kcal mol-1 Å-1 (those at 2.3 and 2.6 had a force constant of 92.24 kcal mol-1 Å-1).40 The results of the umbrella sampling calculations are shown in Figure 6. Figure 6 shows that, unlike the addition to calcite, there is virtually no barrier to the addition of calcium to an amorphous cluster. Furthermore, addition of calcium to the cluster is associated with a large drop in the free energy, which is itself strongly dependent on the geometry of the particular site of addition. Interestingly it seems that relaxation effects are important, as the magnitude of this drop is not correlated with the binding energy to the gas phase cluster (green, -15.42 eV; blue, -27.56 eV; purple, -39.70 eV; red, -51.84 eV; black, -64.59 eV; yellow, -76.12 eV). Examining the left panel of Figure 6 one sees that the lowest free energy gains are from calcium ions which sit on the surface of the amorphous cluster. Unsurprisingly, those calcium ions that can enter the cluster and hence be better surrounded by carbonate ions gain far more free energy on binding. To conclude, this section on the growth of calcium carbonate in solution has shown that ACC growth is barrierless and thus limited only by diffusion. In the above sections, this statement was inferred from the simulations of small oligomers, strengthened by the observations made during unbiassed MD simulations and then confirmed using umbrella sampling to examine the addition of calcium to larger clusters. In direct contrast, there is a considerable barrier to the addition of calcium ions to calcite

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Figure 7. Snapshots 0.58 ns apart from the 365 K trajectory which show how water (in yellow) can become kinetically trapped in the growing amorphous calcium carbonate clusters.

particles. This barrier is due to water molecules that form an ordered, thin film which wraps around the cluster. 4. Characterization of Grown ACC 4.1. Does ACC Contain Water? Experiments1,41 on synthesized, stabilized amorphous calcium carbonate phases have shown that the amorphous materials formed contain water, which seems at odds with the known amphiphilicity of the carbonate ions.21 Furthermore, this situation disagrees with the thermodynamics; in the preceding section, it was shown that the bonding between calcium and carbonate, even in the amorphous state, is always greater than 5 kcal mol-1, which is considerably stronger than any bond between water and ACC. Hence, inclusion of water inside ACC is energetically costly and thus this experimental observation is somewhat of an enigma. Examination of our 20 ns trajectories provides an explanation of how this water can come to be incorporated into the amorphous clusters. Figure 7 shows two snapshots from the 365 K trajectory taken 0.58 ns apart. In these snapshots, two ACC clusters agglomerate and trap a water molecule between them as they coalesce. This trapping occurs because of the long residence times (∼100 ps21) of water molecules in the first hydration sphere of calcium carbonate and the short times in which calcium carbonate clusters coalesce. These factors combine to make it difficult for all of the water molecules to escape from the region between colliding clusters prior to their coalescence. As a result, the clusters coalesce around water molecules, effectively trapping them in the inorganic matrix. Furthermore, because the dynamics inside the ACC cluster are extremely slow, the water molecule trapped in the cluster is not released during the remainder of the 20 ns simulation. In fact, even at temperatures high enough to anneal the structure

J. Phys. Chem. B, Vol. 113, No. 34, 2009 11685 of the cluster, this failure to release trapped water molecules on the nanosecond time scale is still observed. Similar water trapping events were observed in the 300 K trajectory and also, and with a greater frequency, in simulations performed at higher concentrations. Hence, water molecules become trapped in the growing amorphous materials for kinetic reasons and not because hydrated ACC is thermodynamically stable. It would thus be expected that at the lower supersaturations investigated in experiments these water trapping events would be more rare which is in line with more recent experimental observations that calcite prenucleation clusters are relatively anhydrous.17,19,20 4.2. Local Order in ACC. Experimentally, it is very difficult to characterize the transient ACC that is the precursor to calcite because it exists for only a short time before conversion and because it is amorphous. As such, experimental efforts have focused on examining stabilized amorphous calcium carbonate phases.1,41 These structures contain a large fraction of water, which is believed to help stabilize them (transient amorphous structures are almost anhydrous1,42), and also have a structure that is not closely related to any of the known hydrated or dehydrated phases.41 In regard to the true transient phase, TEM studies have shown that the amorphous precursor converts to vaterite and then on to calcite.8 However, in microcalorimetry experiments,43 only two exothermic features are observed. The first of which is believed to correspond to the initial aggregation of ACC and the second is due to the subsequent conversion to calcite. If the transient amorphous phase were similar to vaterite, this would explain why no thermodynamic feature for conversion from amorphous calcite to vaterite is observed. Crystalline vaterite is often found to contain multiple stacking faults44,45 and crystalline defects. Numerous attempts to determine the structure of vaterite using X-ray scattering have been made,46-50 and three different structures have been proposed. Recent Raman spectroscopy experiments51 are most consistent with Meyer’s 1969 structure49 which has a unit cell containing 12 calcium carbonate units. A characterization of the amorphous cluster grown during the 365 K trajectory is shown in Figure 8.52 Shown are the radial distribution functions of those calcium ions in the bulk of the amorphous cluster (25% of the calcium ions in the cluster). The position of first peak of the Ca-O radial distribution function at 2.42 Å matches closely the experimental determinations for stabilized amorphous calcium carbonate from EXAFS41 (2.41 Å). The match in the coordination number is less good, being 8 here and 6.1-6.742,53 in the experiments. However, we note

Figure 8. Ca-O (blue), Ca-C (red), and Ca-Ca (black) radial distribution functions, g(r), for vaterite and for the amorphous cluster grown during the simulations performed in this work. Dashed lines show running integration numbers, n(r).

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Figure 9. Figures showing how the amorphous cluster grown in this work contains short-range features like those found in aragonite and in vaterite. The insets show the features from the crystals, while the larger figures show the positions of the calcium ions in the amorphous cluster and highlight the presence of these structural features.

that the transient amorphous precursor examined here and the stabilized phase examined in experiments may or may not be the same. Figure 8 also shows the radial distribution functions, obtained from a molecular dynamics simulation at 300 K, of Meyer’s 1969 vaterite structure which has 12 formula units in the smallest repeat unit.49 It is clear from this figure that, although the longer range features of the vaterite radial distribution functions are not reproduced, many of the shorter range features are closely reproduced. This suggests that the amorphous cluster may be formed of small, misaligned domains of vaterite and indeed, as shown in Figure 9, structural features similar to those seen in vaterite are observed in the cluster. However, Figure 9 also shows that structural features corresponding to those seen in aragonite crystals are present in the amorphous cluster. Hence, it is too simplistic to assume that the amorphous precursor closely resembles vaterite. It seems instead that the amorphous precursor phase is ordered on very short ranges with patterns from both vaterite and aragonite. Nonetheless, because at longer ranges these crystalline domains are misaligned, the structure is truly amorphous. Zhang and Liu54 have shown that, in a 2D colloidal suspension, ordered crystalline structures form from an amorphous precursor through the formation and subsequent coalescence of smaller subcrystalline nuclei. Pouget et al.20 believe that a similar process drives the formation of crystals from amorphous calcium carbonate precursors. This suggestion is strengthened by the observation of small crystalline features in the amorphous structures grown during our simulations. 5. Conclusions The growth of calcium carbonate in water has been examined using molecular simulation. It would seem that the binding of calcium to carbonate in solution is strongly exergonic, as is the subsequent growth of amorphous calcium carbonate. What is more, there is virtually no free-energetic barrier to these processes and so the growth of amorphous calcium carbonate can be observed on time scales accessible to molecular dynamics if one uses a concentrated solution. The radial distribution functions of the amorphous clusters grown in this way show some structural similarity to vaterite but actually appear to be composed of misaligned domains of aragonite and vaterite. In contrast to amorphous calcium carbonate, there is a large free energetic barrier to the addition of calcium to calcite nanocrystals. Elsewhere,25 it has been shown that this barrier is a consequence of the formation of an ordered layer of water molecules above the (101j4) surface. Where this layer is disturbed, by, for example, the edge of the cluster, it seems that the barrier is reduced. This may go some way to explain

Tribello et al. why the amorphous clusters form so much more readily than the crystal; the amorphous material enforces much less ordering in the surrounding water, and consequentially, the barrier to addition of calcium to the amorphous cluster is negligible. This difference in the barriers for addition to calcite and amorphous material mean that calcite growth is slow, while amorphous growth is fast. Hence, at high supersaturations, amorphous calcium carbonate forms because its growth is essentially diffusion controlled. By contrast, at lower supersaturations, the diffusion controlled growth of amorphous particles is slowed and there is perhaps time for the small clusters to rearrange to a structure that more resembles calcite. Acknowledgment. The authors would like to acknowledge CSCS who provided much of the computer time utilized during the course of this project. Supporting Information Available: Description and figures showing the effect of carbonate rotation on the free energy profiles for calcium addition to carbonate. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Addadi, L.; Raz, S.; Weiner, S. AdV. Mater. 2003, 15, 959. (2) Meldrum, F. C. Int. Mater. ReV. 2003, 48, 187. (3) Hasse, B.; Ehrenberg, H.; Marxen, J. C.; Becker, W.; Epple, M. Chem.sEur. J. 2000, 6, 3679. (4) Suzuki, M.; Nagasawa, N.; Kogure, T. Cryst. Growth Des. 2006, 6, 2004. (5) Mukkamala, S. B.; Anson, C. E.; Powell, A. K. J. Inorg. Biochem. 2006, 100, 1128. (6) Kulak, A. N.; Iddon, P.; Armes, S. P.; Co¨lfen, H.; Paris, O.; Wilson, R. M.; Meldrum, F. C. J. Am. Chem. Soc. 2007, 129, 3729. (7) Schlomach, J.; Quarch, K.; Kind, M. Chem. Eng. Technol. 2006, 29, 215. (8) Rieger, J.; Frechen, T.; Cox, G.; Heckmann, W.; Schmidt, C.; Theime, J. Faraday Discuss. 2007, 136, 265. (9) Mullin, J. W. Crystallization; Butterworth-Heinmann: Oxford, U.K., 1992. (10) Co¨lfen, H.; Mann, S. Angew. Chem., Int. Ed. 2003, 42, 2350. (11) Ogino, T.; Suzuki, T.; Sawada, K. Geochim. Cosmochim. Acta 1987, 51, 2757. (12) Rieger, J.; Ha¨dicke, E.; Rau, I. U.; Boeckh, D. Tenside, Surfactants, Deterg. 1997, 34, 430. (13) Bolze, J.; Peng, B.; Dingenouts, N.; Panine, P.; Narayanan, T.; Ballauf, M. Langmuir 2002, 18, 56. (14) Faatz, M.; Gro¨hn, F.; Wegner, G. AdV. Mater. 2004, 16, 996. (15) Navrotzky, A. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 12096. (16) Kerisit, S.; Cooke, D. J.; Spagnoli, D.; Parker, C. J. Mater. Chem. 2005, 15, 1454. (17) Wolf, S. E.; Leiterer, J.; Kappl, M.; Emmerling, F.; Tremel, W. J. Am. Chem. Soc. 2008, 130, 12342. (18) Clarkson, J. R.; Price, T. J.; Adams, C. J. J. Chem. Soc., Faraday Trans. 1992, 88, 243. (19) Gebauer, D.; Vo¨lkel, A.; Co¨lfen, H. Science 2008, 322, 1819. (20) Pouget, E. M.; Bomans, P. H. H.; Goos, J. A. C. M.; Frederik, P. M.; de Width, G.; Sommerijk, N. A. J. M. Science 2009, 323, 1455. (21) Brunenal, F.; Donadio, D.; Parrinello, M. J. Phys. Chem. B 2007, 111, 12219. (22) Di Tommaso, D.; de Leeuw, N. H. J. Phys. Chem. B 2008, 112, 6965. (23) de Leeuw, N. H.; Parker, S. C. J. Chem. Soc., Faraday Trans. 1997, 93, 467. (24) Kerisit, S.; Parker, S. C. J. Am. Chem. Soc. 2004, 126, 10152. (25) Spagnoli, D.; Kerisit, S.; Parker, S. C. J. Cryst. Growth 2006, 294, 103. (26) Martin, P.; Spagnoli, D.; Marmier, A.; Parker, S. C.; Sayle, D. C.; Watson, G. Mol. Simul. 2006, 32, 1079. (27) Quigley, D.; Rodger, P. M. J. Chem. Phys. 2008, 128, 221101. (28) Lamoureux, G.; Harder, E.; Vorohyov, I. V.; Roux, B.; Jr, A. D. M. Chem. Phys. Lett. 2006, 418, 245. (29) Archer, T. D.; Birse, S. E. A.; Doye, M. T.; Redfern, S. A. T.; Gale, J. D.; Cygan, R. T. Phys. Chem. Miner. 2003, 30, 416. (30) de Leeuw, N. H.; Parker, S. C. Phys. Chem. Chem. Phys. 2001, 3, 3217.

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