Understanding the Kinetics of Barium Sulfate Precipitation from

Crystallization experiments were performed in 20 mL glass vials. ... Small drops of water/methanol solutions of volume ranging between 0.1 and 3.5 µL...
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Understanding the Kinetics of Barium Sulfate Precipitation from Water and Water–Methanol Solutions F. Jones,* S. Piana, and J. D. Gale Nanochemistry Research Institute, Curtin UniVersity of Technology, GPO Box U1987, Perth 6845, Western Australia

CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 3 817–822

ReceiVed January 30, 2007; ReVised Manuscript ReceiVed NoVember 2, 2007

ABSTRACT: It is well understood that the solvent can affect precipitation kinetics, and all chemists are very familiar with the notion that adding an organic solvent to an aqueous solution induces the rapid precipitation of dissolved inorganic salts. The general explanation for this observation is that the solubility of the salt in the organic/water mixture is lower than in pure water and therefore precipitation occurs. Here we study the kinetics and thermodynamics of precipitation of barium sulfate from water/methanol mixtures. It is shown that addition of an organic solvent to a water solution affects not only the thermodynamics but also the kinetics of the precipitation. The kinetics of precipitation in water/methanol mixtures is faster than in pure water. This is the opposite of what would be expected from classical nucleation theory. Molecular dynamics simulations show that nucleation proceeds through the formation of amorphous aggregates that are thermodynamically more stable than the crystalline phase. The formation of a crystalline nucleus involves the restructuring of the amorphous aggregates to form ordered particles. We suggest that this step can be ratelimiting for nucleation. The kinetics of crystallization for divalent salts in general are usually very similar; therefore, this result may be also valid for other salts of industrial or biological relevance. Introduction The process of crystallization is one of the fundamental processes in chemistry, often used in the separation of products from their waste. Extensive studies have focused on barium sulfate crystallization, and, in particular, atomic force microscopy (AFM) has been used to obtain some important fundamental information on the crystal growth mechanisms.1–4 All of these studies involve the process of crystallization from aqueous solutions. While it is known that the solvent can influence the energetics and kinetics of crystallization,5–7 the systematic study of solvent effects on the crystallization of inorganic solids has, surprisingly, received little experimental attention. Amsler8 published studies on potassium chloride precipitation in water and water/ethanol mixtures in 1942, and Seo et al.9 have investigated the precipitation of calcium carbonate from ethanol mixtures. However, this later work is actually an investigation of the influence of supersaturation on the precipitation of different polymorphs. Kan et al.10 have looked at Barite in methanol but at much higher ionic strengths not directly comparable to the work that will be discussed in this paper. Nielsen11,12 introduced the idea that ion desolvation may be an important kinetic step in the crystal growth of polyelectrolytes about 20 years ago. However, although the theoretical notion of solvents influencing crystallization kinetics is widely accepted, experimental results supporting this concept are almost exclusively found for the crystallization of organic crystals. In the present work the influence of the solution composition on the thermodynamics and kinetics of crystallization of a divalent ionic salt is investigated with the aim of obtaining insight into the mechanism of nucleation. Barium sulfate is especially suited to this study since its precipitation leads to only one polymorph over a large temperature and pressure range unlike the work of Seo et al.9 where, as supersaturation increased * Corresponding author: Parker CRC for Integrated Hydrometallurgy Solutions, Nanochemistry Research Institute, Curtin University of Technology, GPO Box U1987, Perth 6845, Western Australia. Phone: +618 9266 7677. Fax: +618 9266 4699. E-mail: [email protected].

in ethanol, different polymorphs of calcium carbonate were favored. As a first step, the solubility of barium sulfate in water/ methanol mixtures has been determined. Crystallization experiments were then carried out at fixed supersaturations in various water/methanol concentrations to determine the effect of solvent on morphology and desupersaturation kinetics. Anticipating our results, it is observed that the rate of desupersaturation is not consistent with classical nucleation theory, and molecular dynamics simulations were performed to investigate the atomistic detail of the nucleation process. Experimental Procedures Materials. Analytical reagent grade Na2SO4 and BaCl2 were both obtained from BDH. The methanol (MeOH) was anhydrous (minimum 99.8%, from Univar) and used as received. Solubility of Barium Sulfate in Methanol/Water Mixtures. The solubility of barium sulfate in water/methanol mixtures were determined by preparing freshly precipitated barium sulfate. This was formed by mixing Na2SO4 and BaCl2 in milliQ water, filtering (0.2 µm membrane), and thoroughly washing to remove traces of residual salt. The solids were then dried in a desiccator for ∼1 week after which the barium sulfate solids were added to 500 mL of solvent (100% H2O, 75% H2O, 40% H2O, and 0% H2O), in excess, and kept at constant temperature (25 ( 0.1 °C). After more than a week of equilibration an aliquot was filtered through a 0.2 µm filter membrane, and 10 mL of this filtrate was evaporated to dryness (to avoid methanol contamination in the ICP instrument). The sample was placed in an oven at 50 °C to completely remove all traces of methanol and then reconstituted in 10 mL of 5% HNO3. The Ba and S content was measured using ICP. The Ba and S values were used to calculate the Ksp (the solubility product) for each of the solutions. Four replicates for each of the four solutions were obtained. Crystallization of Barite from Water and Methanol/Water Mixtures. Crystallization experiments were performed in 20 mL glass vials. In each of four vials, a cleaned glass coverslip was placed, and 10 mL solution (either 100% H2O, 75% H2O) was added to each. Barium chloride solution (0.01 or 0.1 M) was added so that the final S* value (after addition of sulfate solution) in each vial was one of the following: 5, 25, 50, or 100. The four vials were then placed in a bath and allowed to equilibrate (∼1 h). Here the supersaturation ratio, S*, is defined as S* ) c/ceq, where c is the solution concentration and ceq is the equilibrium value of c since the ICP method measures total Ba

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818 Crystal Growth & Design, Vol. 8, No. 3, 2008 and S concentrations in solution and does not account for ion-pair formation. Subsequently, a stoichiometric quantity of Na2SO4 solution was added, the vial cap was replaced, and the vial was shaken gently by hand to commence precipitation. The vials were left in the bath for 24 h before removing the glass slide. The excess solution was removed (using a filter membrane), and the slide was subsequently prepared for scanning electron microscope (SEM) observation. SEM Procedure. The glass slide (or filter paper portion) obtained from the crystallization experiments was placed onto a carbon-coated SEM stub. Carbon paint was applied around the slide to ensure electrical contact. The samples were then dried in a desiccator and gold sputtered before viewing in a Philips XL30 SEM. Conductivity Procedure. The method adopted to measure conductivity for in situ monitoring of Barite precipitation has been discussed in detail elsewhere.13,14 Briefly, a known amount of barium chloride is equilibrated at a given temperature, and an equivalent amount of sodium sulfate is added to commence the precipitation reaction. The system is mixed with a glass stirrer, and the conductivity probe measures the loss of mobile ions during the reaction (which, in the case of barium sulfate, is due to the reaction of barium ions with sulfate ions to produce Barite). In 25% methanol, the mobility of ions is less due to the lower dielectric constant, but the rate of loss of mobile ions should be equivalent if the crystallization kinetics are the same at the same supersaturation ratio. Surface Tension Measurements. Surface tensions γSL were calculated from the equilibrium contact angle between drops of methanol/ water solution and the Barite [001] surface using the Young-Laplace equation γSL ) γSV - γLV cos θ where γSV is the surface tension of Barite in air, γLV is the surface tension of the water/methanol solution, and θ is the contact angle between the surface and a drop of solution. Values for γLV were taken from ref 15. γSV is difficult to measure, but this is less of an issue when only relative surface tensions are required. In this case, provided the contact angle measurements are made in a consistent manner, the relative changes in surface tension can be observed. Equilibrium contact angles, θ, were measured with a KSV CAM101 instrument. Small drops of water/methanol solutions of volume ranging between 0.1 and 3.5 µL were deposited on a flat [001] surface of Barite. Barite surfaces were freshly cleaved from a mineral sample and immediately used for the measurement. At least 10 measurements were performed for each solution on two different Barite samples. Molecular Dynamics Simulations. Molecular dynamics simulations of 0.05 M barium sulfate solutions were performed with the program GROMACS16 using the force field developed in a previous study.17 Starting structures were generated by placing 48 Ba and 48 SO4 ions in random positions in a 12 × 12 × 12 nm cubic cell. The empty space was filled with a total of 57 481 solvent molecules (either water or methanol). While this would appear to represent a very high supersaturation (S* ∼ 5000), lower concentrations would lead to the requirement of a prohibitively large number of water molecules, making the simulation unfeasible. All bond lengths were constrained to their equilibrium values with the LINCS algorithm.18 Nonbonded interactions were evaluated out to a cutoff of 1.0 nm, and the Particle Mesh Ewald method19 was used to treat the long-range electrostatic interactions. The time step for the simulations was 2 fs, and the nonbonded pair list was updated every five steps. Constant temperature simulations at 298.15 K were performed by coupling the system to a Nosé-Hoover thermostat20 with a relaxation time of 3.0 ps. Constant pressure was obtained by coupling to an anisotropic Berendsen barostat21 with relaxation time of 5.0 ps. The systems were equilibrated by performing 100 ps of NVT simulation at 298 K. Subsequently, 10 ns of NPT simulation at 298 K were performed. Calculations of cluster energies with implicit solvation were performed with the COSMO model22,23 as implemented in the GULP program.24 The radii of the ions used were 0.2074, 0.15, and 0.144 nm for Ba, S, and O, respectively, while the solvent radius and radius shift were both set to 0.13 nm. The solvent accessible surface was generated using a mesh of 110 points per sphere

Jones et al.

Figure 1. Ksp value versus methanol content of solvent. The parabolic and linear fits are defined such that x ) MeOH(%) and y ) Ksp. based on an octahedral symmetry with a smooth tapering over 0.05 nm for removal of points in overlapping regions.

Results and Discussion Barite Solubility in Water/Methanol Mixtures. Figure 1 shows that the solubility of Barite (barium sulfate) in methanol/ water mixtures decreases with increasing methanol content. This is not unexpected and is related to the decrease in the dielectric constant of the solvent. Both a linear and a parabolic relationship could describe the solubility product. However, the errors in the Ksp determination and the limited amount of data do not justify fitting to the higher polynomial. However, the solubility curve need not be linear, especially when it is considered that other physical constants (such as the surface tension) do not change linearly with methanol content. The difference between the two curves at 60% methanol (maximum difference) is 7.37 × 10-11 (linear case) versus 8.85 × 10-11 (parabolic case), which, if the midpoint is taken, reflects a 9% error. Figure 1 and the linear relationship between MeOH content and Ksp was subsequently used to determine the S* value for the crystallization experiments. Note, that this choice implies that the supersaturation in the crystallization experiments at 25 and 60% MeOH may be overestimated. Kinetics of Crystallization of Barium Sulfate from Water/Methanol Mixtures. The kinetics of crystallization was studied by monitoring the conductivity of the solution during the crystallization experiment. Results for a supersaturation of S* ) 25 in pure water and 25% MeOH are shown in Figure 2. At lower supersaturation, the conductivity of the solution was too low to obtain meaningful data. The precipitation of Barite crystals under these conditions is still a relatively slow process with an induction time of ∼200 s in aqueous solution (Figure 2, inset). In 25% MeOH, the induction time is 3–4 times smaller, and the precipitation reaction is essentially complete in ∼1500 s, as compared to >3000 s for the pure aqueous solution (Figure 2). As the induction period is expected to be dominated by the nucleation rate, these results suggest that both nucleation and growth are faster in methanol than in water. The Barite particles grown from 25% MeOH have a morphology that suggests a dendritic growth (Figure 3), typical of Barite particles grown from pure water at higher supersaturations.17 First, the particles are flatter than in pure water suggesting that the (hk0) faces become (100) faces. This is also observed when supersaturation is increased in pure water.25 Second, the (001) ends of the particles become rougher and appear to have several growth “arms” giving some indication of dendritic-like growth. This is again an indication that growth in methanol solutions is faster

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linearly dependent on the concentration of the solution; however, this is smaller in 25% MeOH than in pure water, which should also decrease the nucleation rate. The pre-exponential factor, VD, in eq 1 may also influence the rate of nucleation since VD is linearly proportional to the surface area of a critical nucleus and to the rate of diffusion of ions in solution. The conductivity measurements show that the mobility of ions in 25% MeOH is lower than in pure water, which should also decrease the nucleation rate. The surface area of a critical nucleus is expected to be larger in 25% MeOH than in water given that the critical radius rc is proportional to the surface tension: rc )

Figure 2. Conductivity versus time for pure water (black curve) and 25% MeOH (grey curve) barium sulfate precipitation runs. Data for 25% MeOH have been translated in the y direction in order to be easily compared to the control run. Inset: first 500 s showing the induction period.

than in pure water. The latter finding has been rationalized by a recent study where it is shown that desolvation of the surface and incoming ions is the rate-limiting step for crystal growth on the morphologically most important faces of Barite crystals.17 The conductivity data indicate that not only crystal growth, but also nucleation is faster in the water/methanol solutions. The presence of methanol is expected to affect the surface tension of Barite particles. According to classical nucleation theory,26 based on the Gibbs–Thomson equation, surface tension can influence the nucleation rate J according to J ) VDcN

(1)

where VD is the rate of impingement of ions on the nuclei and cN is the concentration of critical nuclei. If it is assumed that the nucleus has a spherical symmetry, the concentration of critical nuclei is given by25 ∆Gc

cN ) ce- kBT ∆Gc )

16πγ3V20 3k3BT3

ln(S*)

(2) 2

where c is the concentration of the solution, γ is the surface tension, V0 is the volume of a unit cell, and S*) c/ceq is the supersaturation. When comparing water and water/methanol experiments performed under the same conditions of temperature and supersaturation the only factor that can strongly influence the nucleation rate is the change in surface tension, γ, that appears as the third power in the exponential term. According to eq 2 positive changes in the surface tension should greatly decrease the nucleation rate. The sign of the surface tension change in water/methanol solution has been calculated by measuring the contact angle of droplets of solution deposited on a flat [001] Barite surface. Although it is not possible to calculate the absolute surface free energy, the data show that addition of methanol to the water solution increases the surface tension of Barite (Figure 4). A change of the same sign is expected also for the other faces, since all surfaces of Barite are highly hydrophilic. Equation 2 predicts that a positive change in surface tension should decrease the nucleation rate, which is the opposite of what is observed experimentally. The concentration of critical nuclei is also

2γV0 kBT ln(S*)

(3)

This may increase the nucleation rate, although the surface dependence is only quadratic with respect to variations in the surface tension and cannot compensate for the exponential dependence of the nucleation rate on the third power of the surface tension. It is concluded that, under these conditions, either the induction time is not dominated by nucleation or the rate of nucleation is not limited by the surface free energy of the critical nucleus and therefore cannot be described by classical nucleation theory. Molecular Dynamics Simulations of Nucleation. To rationalize this finding, a molecular dynamics simulation of a 0.05 M barium sulfate solution in water was carried out. Although this concentration is relatively high, simulating a lower concentration of ions would require a larger simulation cell and make the calculation prohibitively expensive. This concentration still falls within the range of concentrations explored experimentally25 and therefore the results obtained are expected to be meaningful. It is observed that, within a few nanoseconds of simulation, the ions aggregate to form several amorphous clusters such that the activity of the Ba2+ and SO42- ions drops to 0.01 M. The size of the clusters ranges from an ion pair up to 18 ions (Figure 5). Larger clusters are not observed, possibly because their formation is prevented by the limited number of ions present in the simulation (48 Ba2+ and 48 SO42-). During the MD simulation ion pairs are formed and disrupted while ions diffuse to and from the clusters. In the data analysis, the ions have been subdivided into isolated ions (ions not coordinated to any other ion), ions involved in an ion pair (ions coordinated to one other ion), and ions belonging to a cluster (ions coordinated to two or more other ions). The cutoff for the coordination distance was set to 0.48 nm, which corresponds to a minimum in the Ba-S radial distribution function. Relative populations of isolated ions, ion pairs, and ion clusters during the simulation were calculated within this approach (Figure 6). It turns out that the relative concentration of species undergoes some fluctuation, but overall does not change significantly on the time scale investigated here. On the other hand, in the first stages of the simulation, the clusters undergo a slow transition toward more and more compact structures, as indicated by the average coordination number calculated for the cluster atoms (Figure 7). The final cluster structures, although semiregular, are not crystalline and cannot grow into a macroscopic crystal. One of the most commonly occurring clusters in the simulation is (BaSO4)4 (Figure 8b). A dense cluster with the same stoichiometry can also be cleaved from the bulk structure of Barite, as shown in Figure 8a. However, it is interesting to note that the relative arrangement of the ions within these two clusters is quite distinct. The relative energy of this solution-phase cluster is compared to the crystal-like compact cluster structure by

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Figure 3. Barium sulfate particles obtained from S* ) 25 and (A) pure water and (B) 25% MeOH with stirring, with the inset showing a slightly higher magnification image of a single particle.

Figure 4. Relative surface tension of the Barite [001] surface plotted as a function of methanol concentration. The surface tension was calculated from contact angle measurements using the Young-Laplace equation.

performing energy minimization calculations on the configurations both in vacuo, and in the presence of an implicit solvent model. The energy of the solution-phase cluster relative to that cleaved from the crystal is reported in Figure 9 (the relative energy of this cluster in methanol is given so that the impact of the dielectric constant of the solvent can also be seen). Under the dielectric conditions appropriate to both aqueous and methanolic solution, the stability of the cluster observed during MD simulation is higher than that of the crystal-like structure; this is consistent with our failure to observe clusters during the dynamical simulation that resembled the expected crystal structure of Barite. For comparison, the average ondiagonal element of the static dielectric constant tensor for Barite within the present force field model is 3.1, which is considerably lower than the dielectric constants for methanol and water at 32.6 and 78.4, respectively. Hence, if the stability of the clusters within a simple dielectric model for the crystal were considered then the behavior would be closer to vacuum than solvation by methanol, thus favoring the higher density structure. While the full computation of free energy differences between different clusters is challenging and beyond the scope of the present study, investigation of the relative stability was under-

Figure 5. Snapshots taken after 10 ns of MD simulation in water. Only solvent molecules within 0.7 nm from a solute ion are shown. The colors of the Barite ions are green, yellow, and red for barium, sulfur, and oxygen, respectively. The water molecules are shown as small red spheres centered on oxygen, whereas hydrogen atoms are not shown for clarity.

taken via an analysis of the cluster dissociation constant (Kd, Figure 10) as defined by the following relationship: cluster(size n) T cluster(size n - 1) + ion (Ba2+ or SO24) (4) where Kd for this reaction is given by Kd ) [clustern-1][ion] ⁄ [clustern] While no overall trend was observed as a function of the number of ions within the cluster, a local pattern in the data was noted. It is observed that, for small sizes, the even numbered clusters have a lower Kd value and thus should be more stable thermodynamically. We believe this is because even numbered clusters are more likely to be charge neutral (have equal numbers of Ba2+ and SO42- ions) and that those clusters that are not undergo strong repulsive forces in such small clusters. As the cluster size increases, the odd numbered clusters become more stable than the even ones. This may be because, although the odd numbered clusters are more likely to be charged, the

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Figure 9. The relative energies of the clusters as calculated with a COSMO dielectric continuum model: red - cluster (Figure 8a) calculated in vacuo, blue - cluster (Figure 8b) found from the MD simulations calculated in water and methanol. Figure 6. Relative fraction of isolated ions (red), ion pairs (blue), and clusters (green) in the water simulation plotted as a function of time.

Figure 10. Dissociation constant Kd (as defined by eq 4) for clusters observed during the MD simulation in water versus cluster size (numbers of ions within the cluster).

Figure 7. Average coordination number of ions within clusters plotted as a function of time.

reorganization of the aggregates to form ordered crystalline nuclei once the critical size is reached. Unfortunately, the length and timescales required to study this transition directly are beyond current unbiased molecular dynamic simulations. The transformation step to a crystalline cluster requires a substantial reorganization of the cluster bulk and surface structure and may be faster in methanol-containing solutions since the stability of the clusters is slightly lower and the critical size may be reached earlier in these solutions. Furthermore, methanol coordination to the inorganic ions is weaker than for water, and therefore the activation free energy for the reorganization is expected to be lower. Summary

Figure 8. Structure (a) The compact (BaSO4)4 cluster structure cleaved from the bulk crystal; structure (b) (BaSO4)4 cluster that resulted after the MD simulation in water.

repulsive force is expected to be lower in larger clusters and may be stabilized by the cluster’s interaction with water. Further investigation of the trend for much larger clusters would be required to determine if there is an overall pattern for cluster stability. We conclude that small, noncrystalline clusters are stabilized by the interaction with the solvent. It is expected that when a critical size is reached, crystal-like particles will become more stable than the amorphous clusters. These results suggest that the rate-limiting step for nucleation may be related to the

In conclusion, the solubility of barium sulfate decreases with increasing MeOH content as expected. However, even when the crystallization of barium sulfate is performed at the same S* value, the morphology in pure water is different from that in water/MeOH mixtures. At low S* in particular, the morphology in 25% MeOH has a much less pronounced (001) face. At 25% MeOH concentrations we also observe increased nucleation. This goes against what would be expected if the nucleation rate is described by classical nucleation theory based on the Gibbs–Thomson equation. Molecular dynamics simulations suggest that the reason for the discrepancy can be ascribed to the mechanism of nucleation, which involves the initial formation of metastable amorphous aggregates that subsequently evolve into stable crystalline nuclei. The latter step involves a

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substantial ion desolvation and is expected to be faster in methanol containing solutions. The appearance of a metastable polymorph during nucleation is not a new concept,27 and it has been postulated that this may be a rather general rule (the Ostwald step rule). Here we propose that the interconversion of the amorphous clusters into crystalline material can be an important kinetic step for nucleation. These findings may be valid also for other salts of industrial and biological relevance since the kinetics of divalent salt precipitation for a range of materials is often remarkably similar. The molecular mechanisms of biomineralization are still poorly understood. The work of Gower,28–30 for instance, postulates the polymer induced liquid precursor (a hydrated liquid-like amorphous calcium carbonate) to be the initial phase for biomineralisation of calcium carbonate polymorphs. This raises the question of how living systems may control the process of interconversion of the amorphous aggregates into crystalline nuclei of the desired polymorph. In this respect, the results of the present study indicate that the dielectric environment can play a critical role in determining the relative stability of the amorphous and crystalline phases. Acknowledgment. We gratefully acknowledge the support of the Australian Government’s Cooperative Research Centre (CRC) Program, through the Parker CRC for Integrated Hydrometallurgy Solutions for support of F.J., the ARC for a Fellowship for S.P., the Government of Western Australia for a Premier’s Research Fellowship for J.D.G., and iVEC and APAC for the provision of computing resources. We would also like to thank Andrew Rohl for valuable discussions.

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