Effects of Magnesium Ions and Water Molecules on the Structure of

Article pubs.acs.org/JPCB

Effects of Magnesium Ions and Water Molecules on the Structure of Amorphous Calcium Carbonate: A Molecular Dynamics Study Hidekazu Tomono,†,§ Hiroki Nada,*,† Fangjie Zhu,‡ Takeshi Sakamoto,‡ Tatsuya Nishimura,‡ and Takashi Kato‡ †

National Institute of Advanced Industrial Science and Technology (AIST), Onogawa 16-1, Tsukuba 305-8569, Japan Department of Chemistry and Biotechnology, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

‡

ABSTRACT: Molecular dynamics simulations were conducted to elucidate the effects of Mg2+ and H2O additives on the structure of amorphous calcium carbonate (ACC). New potential parameters for Mg2+ ions were developed. The distribution function of the angle formed by three nearest-neighbor atoms was introduced to analyze the short-range local structure of ACC. The simulation indicated that ACC had a weakly ordered local structure resembling the local structure of a CaCO3 crystal. The local structure of pure ACC resembled that of vaterite. The formation of the vaterite-like local structure was hindered by Mg2+ ions, whereas H2O molecules did not significantly influence the structure of ACC when the fraction of H2O molecules was low. However, when the fraction of H2O was high, the formation of a monohydrocalcite-like local structure was promoted. The effects of the additives on the structure of ACC were verified using the size of the additives and the interaction between the additives and CaCO3. The simulated structure of ACC was compared with the structure of CaCO3 crystals nucleated through the formation of ACC particles in real systems.

1. INTRODUCTION Calcium carbonate (CaCO3) is a common naturally occurring mineral and has been extensively studied in physics, chemistry, mineralogy, earth science, and engineering.1−10 In particular, CaCO3 polymorphism has attracted great interest. The most thermodynamically stable CaCO3 crystal at 1 atm is calcite. However, the nucleation of metastable vaterite or metastable aragonite occurs instead of calcite, depending on the temperature.11−16 Moreover, the nucleation of metastable aragonite or metastable hydrated CaCO3 crystals, monohydrocalcite and ikaite, also occurs in the presence of additives, such as acidic polymers,17 and Mg2+ ions.18−23 The CaCO3 polymorphism indicates that the nucleation of metastable CaCO3 crystals can be kinetically favored over the nucleation of calcite, depending on the temperature and the presence of additives. However, the cause of the polymorphism remained unclear for a long time, because it was difficult to observe the initial stage of nucleation at the atomic scale in solution. Recently, several experimental studies have reported nanoscale amorphous CaCO3 (ACC) particles, formed by the aggregation of ion clusters in solution, and the nucleation of CaCO3 crystals from the particles.17,24−35 Similarly, the nucleation of CaCO3 crystals from ACC has been observed during biomineralization.36−40 The nucleation of crystals from amorphous-like particles has also been reported for other species,41−45 and it has been proposed that the structure of © 2013 American Chemical Society

such particles determines which crystal structure is formed preferentially.43 Hence, the atomic-scale structure of ACC particles is particularly relevant to CaCO3 polymorphism.28 Although it is difficult to determine the atomic-scale structure of ACC experimentally, computer simulations, such as molecular dynamics (MD) simulations, can predict the structure in detail. Several simulations have been performed for ACC.46−48 Quigley and Rodger reported the appearance of a vaterite-like structure in an ACC particle.46 Tribello et al. reported that the ACC particle is composed of vaterite-like and aragonite-like regions.47 Raiteri and Gale reported that an ACC particle thermodynamically stably contains H2O molecules.48 These simulation studies focused on a thermodynamically stable ACC particle that is formed in pure solution. However, more extensive studies are required to elucidate the relationship between the ACC particles and CaCO3 polymorphism. For example, understanding the effect of Mg2+ ions on the structure of ACC particles is particularly important.18−23,49,50 The effect of H2O molecules on the structure of ACC particles should also be examined for a wide range of H2O concentrations, because the H2O concentration varies with time and particle size in ACC particles formed in solution.48 Very recently, an MD simulation was performed for Received: August 2, 2013 Revised: October 25, 2013 Published: November 4, 2013 14849

dx.doi.org/10.1021/jp407721x | J. Phys. Chem. B 2013, 117, 14849−14856

The Journal of Physical Chemistry B

Article

ACC in the presence of Mg2+ ions to support an experimental result that Mg2+ ions suppressed crystal nucleation from ACC.50 However, the relationship between the structure of ACC and that of the CaCO3 crystals in the presence of Mg2+ ions has not yet been investigated by an MD simulation. In this study, we investigated the effects of Mg2+ ions and H2O molecules on the structure of ACC over a wide range of concentrations with an MD simulation. We developed new potential parameters for Mg2+ ions. The distribution function of the angle formed by three nearest-neighbor atoms was introduced to analyze the short-range local structure of ACC. The structure of ACC obtained from the simulation was compared with that of the CaCO3 crystals nucleated through the formation of ACC particles in real systems.

Table 1. Parameter Values in the Buckingham Potential, UB(r) = A exp(−r/r0) − C/r6, and the Lennard-Jones Potential, ULJ(r) = 4ε{(σ/r)12 − (σ/r)6}a A (eV)

Buckingham Ca Ca Mg Mg O O O

O C O C O Ow Hw Lennard-Jones

Ca Mg Ow

2. SIMULATION METHOD 2.1. Potential Models. The CaCO3 potential model proposed by Raiteri et al. was used to estimate the CaCO3 interactions in ACC.51 In this model, the interaction between a pair of ions is represented as the sum of the Coulomb potentials plus the sum of the Buckingham potentials. The CO32− ion is treated as a rigid body with all four atoms of the CO32− ion lying on a single plane. The C−O length is fixed at the experimental value of 1.284 Å and ∠OCO is fixed at 120°. The charge on the Ca2+ ion is +2.0e, and the charges on C and O atoms of the CO32− ion are +1.123282e and −1.041094e, respectively. Although the CO32− ion in this model is a simplification of the actual CO32− ion, it adequately reproduces the relative thermodynamic stability between calcite and aragonite.51 In this study, we introduced a potential model of a Mg2+ ion. The interaction for the Mg2+ ions was represented as the sum of the Coulomb potential plus the sum of the Buckingham potential, similar to the interactions for the Ca2+ and CO32− ions in the Raiteri CaCO3 model. The charge on the Mg2+ ion was +2.0e. The Buckingham potential parameters for the Mg2+ ion were determined by referring to the parameter values for Ca2+ ions in the CaCO3 potential model proposed by Paverse et al.52 and those for Mg2+ ions in the potential model proposed by de Leeuw and Parker.53 In these models, the values of the constants, A and r0, in the Buckingham potential (=A exp(−r/ r0) − C/r6) are 30% and 6% smaller, respectively, for the Mg2+ ion than for the Ca2+ ion. Thus, in the present model the values of A and r0 for the Mg2+ ion were also smaller by 30% and 6%, respectively, than the values for the Ca2+ ion in the Raiteri CaCO3 model. The value of the constant, C, in the Buckingham potential for the Mg2+ ion was set to zero, as it was for the Ca2+ ion in the Raiteri CaCO3 model. The interaction for the H2O molecules was estimated using the TIP4P-Ew model.54 The H2O−CaCO3 interaction, which was represented as the sum of the Coulomb potential, the H2O−CO32− Buckingham potential, and the H2O−Ca 2+ Lennard-Jones (LJ) potential, was estimated using the set 2 parameter values proposed by Raiteri et al.51 The values of ε and σ for the H2O−Mg2+ LJ potential were also calculated to be 30% and 6% smaller than the values for H2O−Ca2+ LJ potential, respectively, using the same approach as for the Mg2+ ion Buckingham potential parameters. All the parameter values for the Buckingham potential and the LJ potential used in this study are listed in Table 1. The Raiteri CaCO3 model reproduces the lattice parameters of calcite, aragonite, and vaterite.51 The combination of the

r0 (Å)

3161.6335 120000000.0 2227.8297 84557419.35 63840.199 12534.45513 396.320957 ε (eV)

Ow Ow Ow

0.271511 0.120000 0.255294 0.112832 0.198913 0.215172 0.230006 σ(Å)

0.0010 0.0007042 0.0070576

C (eV/Å) 0.000000 0.000000 0.000000 0.000000 27.899008 12.090225 0.000000

3.25 3.06604 3.16435

a C and O represent the C and O atoms of the CO32− ion, respectively. Ow and Hw represent the O and H atoms of the H2O molecule, respectively.

Raiteri CaCO3 model and the TIP4P-Ew model reproduces the lattice parameters of monohydrocalcite and ikaite.51 We verified that the combination of the Raiteri CaCO3 model with our Mg2+ ion model reproduces the lattice constants of MgCO3 magnesite and CaMg(CO3)2 dolomite (Table 2). Moreover, we also confirmed that the enthalpy, ΔH, of the following reaction is also reproduced in the potential models (Table 2). Ca 2 +(g) + MgCO3(s) → Mg 2 +(g) + CaCO3(s)

(1)

Table 2. Lattice Constants of Magnesite and Dolomite, and the Enthalpy of Reaction, ΔH (Eq 1 in Text) in the Present Simulation Modelsa magnesite magnesite magnesite dolomite dolomite

a (Å) b (Å) c (Å) a (Å) c (Å) ΔH (kJ/mol)

present models

expt

4.593 ± 0.009 4.593 ± 0.008 15.082 ± 0.025 4.786 ± 0.007 15.946 ± 0.023 317.33 ± 0.012

4.633a 4.633a 15.0163 4.8112b 16.02b 311.5a

a

Reference 53. bDolomite (JPCDS No. 11-78). aThe experimental values of the lattice constants of dolomite were obtained from JPCDS No. 11-78.

We checked that the structure of ACC in the presence of Mg2+ ions, which was given by the combination of the Raiteri CaCO3 model and our Mg2+ ion model, was the same as that given by the combination of the CaCO3 potential model proposed by Paverse et al. and the Mg2+ ion model proposed by de Leeuw and Parker.50 Consequently, the combination of our Mg2+ ion model, the Raiteri CaCO3 model, and the TIP4P-Ew model was suitable for the qualitative elucidation of the structure of ACC in the presence of Mg2+ ions and H2O molecules. Notably, following to the present Raiteri CaCO3 model,51 Raiteri and Gale also proposed an improved CaCO3 potential model for the flexible CO32− ion.48 It would be better to use this improved model if the purpose of the simulation was the quantitative reproduction of the structure of ACC. However, the present Raiteri CaCO3 model was sufficient for this study aimed at the qualitative elucidation of the structure of ACC. 14850



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We also investigated the hydrated structure of Mg2+ ion at 300 K and 1 atm in our Mg2+ ion model with the TIP4P-Ew model by a MD simulation for the system consisting of a Mg2+ ion and 500 H2O molecules. The Mg2+−O pair distribution function indicated the first peak at 1.94 Å, which was slightly smaller than the experimental value of 2.00−2.15 Å.55 However, the number of H2O molecules in the first hydration shell around the Mg2+ ion was equal to the experimental value of 6.55 Thus, we confirmed that our Mg2+ model also roughly reproduces the hydrated structure of Mg2+ ion. It is expected that use of the Buckingham potential instead of the LJ potential for the short-range Mg2+−H2O interaction improves the quantitative reproduction of the hydrated structure. 2.2. Simulation Systems. We aimed to qualitatively elucidate the changes in the atomic-scale structure in ACC particles caused by adding Mg2+ ions and H2O molecules, but we did not attempt to quantitatively reproduce the experimentally observed ACC particles. Therefore, it was not necessary to simulate the formation of a realistic ACC particle from solution. In this study, we assumed that the structure of ACC particles can be approximated to the structure of bulk ACC. The simulation was performed for bulk ACC in which Mg2+ ions and H2O molecules were included. The system for ACC was a cubic consisting of 840 particles, which was the sum of the number of Ca2+ ions, Mg2+ ions, CO32− ions, and H2O molecules (NCa, NMg, NCO3, and NH2O, respectively). Three-dimensional periodic boundary conditions were imposed on the system. The fraction of the Mg2+ ions, f Mg = NMg/(NCa + NMg), was 0.0, 0.25, 0.5, 0.75, and 1.0. The fraction of H2O molecules, f H2O = NH2O/(NH2O + NMg + NCa), was also 0.0, 0.25, 0.5, 0.75, and 1.0 (pure water). For all simulations, NCO3 was equal to the sum of NCa + NMg. In addition to the simulation of ACC, we also performed an MD simulation for calcite, aragonite, vaterite, magnesite, monohydrocalcite, and ikaite. The system for calcite, aragonite, vaterite, and magnesite consisted of NCa (or NMg) = 432 and NCO3 = 432. The system for monohydrocalcite consisted of NCa = 288, NCO3 = 288, and NH2O = 288, and the system for ikaite consisted of NCa = 108, NCO3 = 108, and NH2O = 648. The precise structures of calcite, aragonite, monohydrocalcite, and ikaite are known.51,56,57 However, several different structures have been proposed for vaterite.58 We used the structure of vaterite predicted from the quantum chemical calculations reported by Wang et al.,59 because this structure is energetically more stable than other vaterite structures.51 2.3. MD Simulation. The computation was carried out by the Verlet leapfrog algorithm. 60 The temperature was controlled by the Nosé−Hoover thermostat with a relaxation time of 0.1 ps.61 The pressure was controlled by a barostat proposed by Melchionna et al. with a relaxation time of 2 ps.62 The Coulomb potential energy and force were calculated using the smooth particle mesh Ewald method.63 DL_POLY version 2.20 was used for the present MD simulation.64 The ACC structure was obtained using the following method. Initially, all the ions were randomly arranged in the system. An MD simulation of the NVT ensemble was carried out for the system at T = 10 000 K to accelerate the formation of an amorphous state for a period of 1 ns with a time step of 1 fs. During this NVT ensemble simulation, the volume, V, of the system was fixed so that the density, ρ, of the system was 30% lower than that of calcite at 300 K and 1 atm. The final structure obtained from this simulation was used as the initial structure for a subsequent MD simulation of the NPT ensemble

carried out at 300 K with a time step of 2 fs. The system without H2O molecules reached a stable state within 1 ns; therefore, the simulation data for the subsequent 1 ns period was used to analyze the structure of ACC. The system containing H2O molecules did not reach a stable state within 1 ns. In this study, the simulation for the system containing H2O molecules was carried out for a period of 10 ns. We checked that the structure of ACC did not change significantly after 6 ns. Therefore, the structure of ACC analyzed with the simulation data collected between 9 and 10 ns was used. Simulations with a much longer run than 10 ns were required to confirm that this structure corresponded to the thermodynamically stable structure of ACC containing H2O molecules.48,65 However, the purpose of this study was elucidating the structures that may appear in ACC particles, including transient structures. The structure of ACC obtained in this way was verified by comparing it with the structure obtained using another method. In the alternative method, before the beginning of the NPTensemble simulation at 300 K, an additional 1 ns NVTensemble simulation at T = 5000 K was carried out using the final structure of the NVT-ensemble simulation at 10 000 K as the initial structure. No significant difference was detected in the pair distribution function, g(r), of ACC between the two methods. We also checked that the g(r) of ACC obtained from the simulation agreed with that obtained from experimental Xray scattering data reported by Goodwin et al.66 and with that obtained from a MD simulation for an ACC particle reported by Tribello et al.47 Thus, the method for calculating the structure of ACC used in this study was suitable. Figure 1 shows g(r) of ACC obtained from the simulation for two different initial arrangements of ions in the system and that

Figure 1. g(r) of Ca2+−Ca2+ for pure ACC created by two simulations, each of which started from a different initial arrangement of ions (initial 1 and initial 2), and the g(r) created by a simulation using a larger system consisting of 1800 CaCO3 (light green). The g(r) obtained by Goodwin et al.66 (red) and that obtained by Tribello et al.47 (blue) are also shown for comparison.

from the simulation for a larger system consisting of 1800 CaCO3. Strictly speaking, g(r) of ACC were not perfectly the same for those simulations. However, the heights and positions of the first and second peaks appearing in g(r) were almost the same for the simulations. Consequently, we assumed that the ACC structure obtained in this study did not significantly depend on the initial arrangement of ions and on the system size. Examining many different initial arrangements of ions and many different system sizes is needed to confirm this 14851



Article (2) crystal for which r(1) max and rmax were closest to those values for (1) pure ACC was vaterite (rmax = 4.1 Å and r(2) max = 5.9 Å). Thus, the results for gcation(r) indicated that the long-range structure of pure ACC resembled that of vaterite, which is consistent with the simulation studies published by Quigley and Rodger46 and by Tribello et al.47 (2) However, the values of r(1) max and rmax for ACC gradually decreased as f Mg increased. This is because Mg2+ ions are smaller than Ca2+ ions, which meant that r between a pair of cations decreased as f Mg increased. Because of the shifts of r(1) max and r(2) max, gcation(r) of ACC deviated from that of vaterite. Figure 3 shows pcation(θ) for ACC at each f Mg and for the CaCO3 crystals. The dashed line shows p(θ) for the random

assumption. In addition, we also checked that g(r) for both anhydrous and hydrated ACC obtained in the present simulations are almost the same as those given in a paper of a simulation study of ACC particles using the improved CaCO3 potential model by Raiteri and Gale.48 We note that the bulk ACC sample generated with the present procedure could be different from a real sample where ACC grows from solution by subsequent addition of ion, ion-pairs or small clusters. 2.4. Analysis of the Structure of ACC. To analyze the structure of ACC in detail, we introduced the distribution function, p(θ), for the angle, θ, formed by the three nearestneighbor atoms, in addition to g(r). A selected pair of atoms was judged to be the nearest-neighbor pair if the distance, r, between the pair was less than r at which the first minimum appeared in the g(r) for ACC. In this study, we used p(θ) and g(r) for evaluating the local structure and the long-range structure of ACC, respectively. The p(θ) and g(r) for the ACC structure were compared with those of each CaCO3 crystal structure to assess the structural similarity. We constructed p(θ) for θ formed by all possible sets of the three atomic species. It proved that p(θ) for θ formed by three nearest-neighbor cations, pcation(θ), was suitable for judging which crystal structure the local ACC structure resembled. Because the CaCO3 crystals had different pcation(θ), it was simple to judge which crystal structure the local ACC structure resembled by comparing pcation(θ) for ACC with that for each CaCO3 crystal. Therefore, we mainly used gcation(r), which was g(r) as a function of r between a pair of cations, and pcation(θ) to discuss the structure of ACC. Each of g(r), p(θ), and the analytic values shown in the figures of this paper was obtained by analyzing data of two simulations, each of which started from different initial arrangements of ions.

Figure 3. pcation(θ) for ACC at each f Mg (upper panel) and for the CaCO3 crystals (lower panel). The dashed lines in the upper panel denote p (θ) for the random distribution, p(θ) = 1/2 sin θ. The definition of θ is given as an illustration in the lower panel. The green circles in the illustration show the cations.

3. RESULTS AND DISCUSSION 3.1. Effect of Mg2+ Ions on the Structure of ACC. Figure 2 shows gcation(r) for ACC at each f Mg. For comparison, gcation(r) for the CaCO3 crystals are also shown. Both a first peak and a broad second peak appeared in gcation(r) for ACC, indicating a weakly ordered long-range structure. For pure ACC (f Mg = 0.0), the r at which the first and second peaks of gcation(r) (2) appeared, r(1) max and rmax, were 3.9 and 6.1 Å, respectively. The

distribution, p(θ) = 1/2 sin θ. Two distinct peaks appeared around θ = 60° and 90° in pcation(θ) for ACC. For vaterite and aragonite, pcation(θ) also showed a distinct peak around θ = 90°. However, pcation(θ) for vaterite only shows a distinct peak around θ = 60°. Thus, pcation(θ) provided clear evidence that the local structure of ACC had vaterite-like characteristics. However, as f Mg increased, the height of the peak around θ = 60° decreased (arrow in the upper panel of Figure 3), indicating the disappearance of the vaterite-like local structure in ACC. As a result, pcation(θ) approached a random distribution. Furthermore, p(θ) for θ created by other atomic species also approached a random distribution as f Mg increased. As an example of it, p(θ) for θ formed by an O atom of the CO32− ion and the two nearest-neighbor cations, pcat‑o‑cat(θ), is shown in Figure 4. Thus, the results for p(θ) indicated that Mg2+ ions hinder the formation of crystal-like structures, particularly the vaterite-like structure of ACC. To confirm that the structure of pure ACC resembled that of vaterite rather than those of calcite and aragonite, we also examined the number of first-nearest-neighbor cations around a cation, ncation, which was estimated by integrating gcation(r) over the first peak. ncation for pure ACC was 9.2. ncation for calcite, aragonite, and vaterite were 6.0, 6.0, and 8.0, respectively. Thus, ncation for pure ACC was closer to that for vaterite than to those for calcite and aragonite. This result of ncation supports that the

Figure 2. gcation(r) for ACC at each f Mg (upper panel) and for the CaCO3 crystals (lower panel). 14852



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The Coulomb interaction between the nearest-neighbor cations was strongly repulsive. Therefore, the nearest-neighbor cations did not form a small θ, which is reflected in pcation(θ) = 0 for θ < 50° in Figure 4. The nearest-neighbor cations in ACC at f Mg = 0 could form a relatively small θ of 60°, similar to vaterite. However, because ρ increased as f Mg increased, r between the nearest-neighbor cations was reduced, and the repulsive Coulomb interaction between them was strengthened. Thus, forming an angle of θ = 60° with the nearest-neighbor cations became difficult as f Mg increased. This explains why the formation of a vaterite-like local structure in ACC was hindered by adding Mg2+ ions. 3.2. Effect of H2O Molecules on the Structure of ACC. Figure 6 shows gcation(r) for ACC at each value of f H2O without

Figure 4. p(θ) for θ created by an O atom of the CO32− ion and the two nearest-neighbor cations, pcat‑o‑cat(θ), for ACC at each f Mg (upper panel) and for the CaCO3 crystals (lower panel). The dashed lines in the upper panel denote p(θ) for the random distribution, p(θ) = 1/2 sin θ. The definition of θ is given as an illustration in the lower panel. The green, sky blue, and red circles show the cation, C, and O atoms of the CO32− ion, respectively.

structure of pure ACC resembled that of vaterite rather than those of calcite and aragonite. The structural similarity would also be confirmed even if another method to evaluate the ACC structure, for example, an order parameter,46 was used. Figure 5 shows ρ and the potential energy, U, for ACC as a function of f Mg. For pure ACC, ρ was close to that of vaterite. Figure 6. gcation(r) for ACC at each f H2O for both f Mg = 0.0 and 0.5 (upper panel) and for the CaCO3 crystals (lower panel).

and with Mg2+ ions (f Mg = 0.0 and 0.5, respectively). No significant difference in the gcation(r) between f H2O = 0.0 and 0.25 was observed for f Mg = 0.0 and 0.5. This is because the interaction between the cation and H2O molecules was much weaker than the interaction between the cation and the surrounding ions in ACC; therefore, the ion arrangement in ACC was not strongly influenced by the H2O molecules. However, for f H2O ≥ 0.5, the second peak of gcation(r) became distinct and a small peak appeared around 4.5 Å near the first peak for f Mg = 0.0 (outline arrow, Figure 6). For f Mg = 0.5, the first and second peaks of gcation(r) became distinct and an additional peak appeared around 4.9 Å at f H2O = 0.75 (solid arrow, Figure 6). These results suggest that, for both f Mg = 0.0 and 0.5, the long-range structure of ACC was enhanced at high f H2O values. Notably, gcation(r) for vaterite did not show any peaks around 4.9 Å. Thus, gcation(r) for f Mg = 0.5 implied that the long-range structure of ACC was different from that of vaterite and it became more similar to other crystal structures at f H2O = 0.75. Figure 7 shows pcation(θ) of ACC at each f H2O for f Mg = 0.0 and 0.5. The peak around θ = 96° increased with f H2O for both f Mg = 0.0 and 0.5. This peak corresponded to the large peak around θ = 98.5° in pcation(θ) for monohydrocalcite. This result suggests that the local structure of ACC became similar to that of monohydrocalcite as f H2O increased. In addition, the peak around θ = 60°, which was characteristic of the local structure of vaterite, decreased as f H2O increased for f Mg = 0.5. However,

Figure 5. ρ and U for ACC as functions of f Mg. ρ for calcite (blue), aragonite (red), and vaterite (dark green) are also shown. ρ was calculated from (NCa + NMg + NCO3)/V.

However, as f Mg increased, ρ shifted from that of vaterite to larger values, which was consistent with the Mg2+ ions hindering the formation of a vaterite-like structure. U decreased as f Mg increased. Because Mg2+ ions are smaller than Ca2+ ions, r between Mg2+ and the surrounding CO32− ions was smaller than for Ca2+ ions. Thus, as f Mg increased, the strength of the Coulomb attractive interaction between the cation and the surrounding CO32− ions and the density of the structure of ACC both increased. This explains why ρ increased and U decreased as f Mg increased. Notably, the result of the decrease in U with increasing f Mg was not sufficient to discuss whether the structure of ACC including Mg2+ ions was thermodynamically more stable than the structure of pure ACC. More detailed studies including free energy calculation are needed to discuss it. 14853



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= 40° decreased as f H2O increased, indicating that the vaterite structural characteristics disappeared from ACC as f H2O increased. Thus, we confirmed that the results for p(2) cation(θ) were consistent with those for pcation(θ). In summary, the results for gcation(r), pcation(θ), and p(2) cation(θ) show that, in the presence of Mg2+ ions, the structure of ACC approached that of monohydrocalcite as f H2O increased and became less like that of vaterite. In the absence of Mg2+ ions, the structure of ACC also approached that of monohydrocalcite as f H2O increased, whereas the vaterite-like structure remained. Figure 9 shows ρ for ACC as a function of f H2O. The number of the first-nearest-neighbor H2O molecules around a cation,

Figure 7. pcation(θ) for ACC at each f H2O for both f Mg = 0.0 and 0.5 (upper panel) and for the CaCO3 crystals (lower panel). The dashed lines in the upper panel denote p(θ) for the random distribution, p(θ) = 1/2 sin θ.

for f Mg = 0.0, the peak around θ = 60° did not decrease significantly even as f H2O increased to be 0.5. In Figure 6, gcation(r) implied that a high f H2O enhanced the long-range structure. Therefore, in order to investigate the effect of H2O molecules on the structure of ACC in more detail, we analyzed pcation(θ) for θ formed by three secondnearest-neighbor cations, p(2) cation(θ). A pair of cations was judged to be in the second-nearest-neighbor position of each if r for the cations satisfied 5.4 Å ≤ r ≤ 6.7 Å. Figure 8 shows p(2) cation(θ) of ACC and CaCO3 crystals at each f H2O for both f Mg = 0.0 and 0.5. The appearance of a peak

Figure 9. ρ and nH2O for ACC as functions of f H2O for both f Mg = 0.0 and 0.5. The dotted lines are intended as a visual guide. For comparison, ρ for calcite (blue), aragonite (red), vaterite (dark green), and monohydrocalcite (sky blue) are also shown. ρ was calculated from (NCa + NMg + NH2O + NCO3)/V. nH2O was calculated by integrating g(r) for r between the cation and the O atom of the H2O molecule from r = 0.0 to 3.0 Å.

nH2O, for ACC is also shown as a function of f H2O. For both f Mg = 0.0 and 0.5, ρ increased and approached that of monohydrocalcite as f H2O increased. nH2O also increased and approached that of monohydrocalcite as f H2O increased. The increase in ρ with f H2O occurred because H2O molecules are smaller than cation−CO32− ion pairs. The increase in nH2O with f H2O occurred because the cations in ACC were hydrated preferably, like Ca2+ ions in monohydrocalcite. Figure 10 shows ncation for ACC as a function of f H2O. ncation decreased as f H2O increased and approached that of monohydrocalcite at high f H2O, especially for f Mg = 0.5. These results of ρ, nH2O, and ncation might not be sufficient to verify the structural similarity between ACC and monohydrocalcite at high f H2O. However,

Figure 8. p(2) cation(θ), which is p(θ) as a function of θ formed by three second-nearest-neighbor cations, at each f H2O for both f Mg = 0.0 and 0.5 (upper panel) and for the CaCO3 crystals (lower panel). The dashed lines in the upper panel denote p(θ) for the random distribution, p(θ) = 1/2 sin θ.

around θ = 40°, 60°, and 90° confirmed the existence of a weakly ordered long-range structure in ACC. The size of the peak around θ = 60°, which was characteristic of the structure of monohydrocalcite, increased as f H2O increased for both f Mg = 0.0 and 0.5 (arrow, Figure 8). For f Mg = 0.5, the peak around θ

Figure 10. ncation for hydrated ACC as a function of f Mg. ncation for calcite (blue), aragonite (red), vaterite (dark green), and monohydrocalcite (sky blue) are also shown. 14854



Article

Present Address

these results are qualitatively consistent with the structure of ACC approaching that of monohydrocalcite as f H2O increased, especially for f Mg = 0.5, which gcation(r), pcation(θ), and p(2) cation(θ) suggested. More detailed analysis of the ACC structure will promote better understanding of the structural similarity. Notably, for f Mg = 0.5, nH2O around a Mg2+ ion were 0.61 and 1.47 for f H2O = 0.25 and 0.5, respectively. These values were larger than the values around a Ca2+ ion, 0.41 and 1.33, for f H2O = 0.25 and 0.5, respectively. These results for f H2O = 0.25 and 0.5 are consistent with the stronger hydration properties of the cation for Mg2+ ions than for Ca2+ ions. However, for f H2O = 0.75, nH2O around a Mg2+ ion was 2.7, which was smaller than that around a Ca2+ ion, 3.0. This result implies that the hydration structure of the cation in ACC for f H2O = 0.75 was different from those for f H2O = 0.25 and 0.5. More detailed studies are needed to elucidate it.

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(H.T.) Advanced Applied Science Department, Research Laboratory, IHI Corp., 1, Shin-Nakahara-Cho, Isogo-ku, Yokohama 235-8501, Japan.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aid for Scientific Research (no. 22107004) on Innovative Areas of “Fusion Materials” (Area no. 2206) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT). Some of the computations in this work were conducted using the facilities of the Super Computer Center, the Institute of Solid State Physics, The University of Tokyo.

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4. CONCLUSIONS The effects of adding Mg2+ ions and H2O molecules on the structure of ACC was investigated by means of MD simulation over a wide range of f Mg and f H2O values. New potential parameters for Mg2+ ions, which reproduce the structure of magnesite and its enthalpy of formation by using them with the Raiteri CaCO3 model,51 were introduced. The distribution function of the angle formed by three nearest-neighbor cations was used to analyze the local structure of ACC in detail, and the pair distribution function was used to analyze the long-range structure of ACC. The structure of pure ACC resembled that of vaterite rather than those of calcite and aragonite, as has been reported in earlier simulation studies.46,47 However, Mg2+ ions hindered the formation of a vaterite-like structure in ACC. The presence of H2O molecules did not significantly influence the structure of ACC when f H2O was low. When f H2O was high and Mg2+ ions were present, the formation of the monohydrocalcite-like structure was promoted, and the formation of vaterite-like structure was hindered. When f H2O was high and Mg2+ ions were absent, the formation of the monohydrocalcite-like structure was promoted, whereas the vaterite-like structure remained. We intend to conduct more extensive studies to elucidate the relationship between the structure of the ACC particles and the nucleation of CaCO3 crystals. For example, examining the structure of ACC with other additives, such as poly-Laspartate67 and poly(acrylic acid) ,17 would also be useful for explaining this relationship. The mechanism of nucleation, which includes dehydration processes, is an important future study. Recently, Demichelis et al. suggested that prenucleation clusters are made of an ionic polymer (dramatically ordered liquidlike oxyanion polymer, DOLLOP), and that ACC particles are formed by the aggregation of the clusters.33 The mechanism of the formation of ACC particles by the aggregation of the clusters and the effect of Mg2+ ions on the structure of DOLLOP are also important future studies.

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Effects of Magnesium Ions and Water Molecules on the Structure of

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