The Effect of Crystal Seeds on Calcium Carbonate Ion Pair Formation in Aqueous Solution: A ReaxFF Molecular Dynamics Study

Abstract

The effect of crystal seeds on calcium carbonate (CaCO₃) cluster formation in aqueous solution is of interest in the fields of geochemistry, inorganic chemistry, atmospheric science, biomedicine, biomineralization, and tissue engineering. Due to an instantaneous and microscopic process, it is still experimentally challenging to directly capture the CaCO₃ pre-nucleation. This study employed reactive force field (ReaxFF) molecular dynamics simulations to explore the variation among CaCO₃ ion pairs in an aqueous solution with or without crystal seeds. The results show that the addition of crystal seeds can improve CaCO₃ ion pair formation. We found that the surface of the calcite phase, compared with the metastable vaterite phase, prefers to attach the ion pairs from solution via proton transfer. This work sheds light on the effect of different crystal seeds on CaCO₃ ion pair formation as a precursor of pre-nucleation clusters.

1. Introduction

As an insoluble mineral, calcium carbonate (CaCO₃) is commonly found in nature and the household [1,2,3]. Crustaceans and marine organisms are mainly comprised of CaCO₃ [4,5,6]. Moreover, CaCO₃ is the most common fouling substance forming on the surface of the heat exchanger and transfer in engineering [7,8]. Thus, the precipitation/crystallization of CaCO₃ has significant implications for optimizing the functionality of tissue biomineralization and economic outcomes.

The nucleation of CaCO₃ has been investigated extensively to understand calcium carbonate crystal formation. In theory, the classical nucleation theory (CNT) [9] was proposed to illustrate CaCO₃ nucleation in aqueous solutions [10]. A single-step activated process in CNT conflicts with the pre-nucleation process in the nucleation of calcium carbonate [11]. The dynamical nucleation theory (DNT) combined with the liquid drop model [12,13] was later developed to predict the CaCO₃ nucleation rate [14]. Nonclassical pathways for CaCO₃ nucleation refer to the pre-nucleation cluster (PNC) aggregation and the transformation of amorphous calcium carbonate (ACC), usually operating under a wide array of biologically and environmentally relevant conditions [15,16]. Various ions, polymers, functional groups, etc., were used to control the nucleation and growth of calcium carbonate crystals [17,18,19,20]. Although CaCO₃ with various desired microstructures and polymorphs can be obtained, many aspects of the CaCO₃ nucleation and crystallization phenomenon remain unclear [21].

In order to understand the mechanism of CaCO₃ precipitation from solution, various investigations were performed for the pre-nucleation stage of CaCO₃ from a modeling perspective. The monomer structure of CaCO₃ hydrate (five water molecules and monodentate coordination mode) was obtained by using Car–Parrinello molecular dynamics (CPMD) simulations [22,23]. The role of the known hydrated CaCO₃ polymorphs in forming pre-nucleation clusters in both aqueous and CO₂-rich environments was investigated by ab-initio molecular dynamics (AIMD) simulations [24]. Classical molecular dynamics (MD) simulations able to generate nanoseconds to microseconds of simulation of large systems have been extensively used to study calcium carbonate precipitation from solution. In addition, the structure, dynamics, and energetics of hydrated CaCO₃ clusters have been analyzed using MD simulations [25,26]. However, the ion pairing and multiple ion binding in calcium carbonate solution are difficult to capture by MD simulations with an empirical force field. Proton transfer is a very important process of CaCO₃ precipitation/crystallization. Reactive force fields (ReaxFF) combined with Van der Waals, electrostatic interactions, and covalent terms can address reactivity within the system and are attractive for use in the investigation of CaCO₃ nucleation and growth [27].

In this study, ReaxFF MD simulations were employed to study the pre-nucleation of CaCO₃ in an aqueous solution. Different anhydrous crystalline polymorphs of CaCO₃ were chosen as the template for ion pair formation. The coordination, hydration structure, calcium ions mobility, and concentration distribution are analyzed to reveal the formation and evolution of the CaCO₃ ion pair. This work provides evidence of the formation of the CaCO₃ ion pair induced by the existence of CaCO₃ polymorphs.

2. Simulation Models and Methods

2.1. Models

There are three polymorphs (Figures S1 and S2) (see supplementary materials) of crystalline CaCO₃: calcite [28], aragonite [29], and vaterite [30]. The metastable vaterite, in particular, has multiple structures [30]. In this study, three relatively stable vaterite structures (vaterite_p3221, vaterite_c2, and centered_vaterite_c1_1) were chosen as the calcium carbonate seeds (Figure S2). The surface models of all CaCO₃ polymorphs were built based on the law of the lowest surface energy and the close-packed plane (Figure 1). It is worth noting that calcium-terminated surfaces for calcite and aragonite were observed owing to their thermodynamically stable forms, while the structures of the most unstable polymorph, vaterite, showed unsaturated oxygen atoms on their surfaces.

Supersaturation denotes the solution state above the threshold concentration for crystallizing. Supersaturated solution models were built to study the formation of the pre-nucleation CaCO₃ cluster in the aqueous solution. High supersaturations (0.5, 1, 2, and 4 mol/L CaCO₃ concentration) were chosen in the current calculation owing to the calcium carbonate growth time scales accessible to molecular dynamic simulation. Previously, experimental results have shown that amorphous calcium carbonate forms exceptionally rapidly with increasing calcium carbonate concentrations [31]. Typically, high supersaturations of CaCO₃ have been used for the MD simulation of calcium carbonate growth [26,27]. In our study, the initial homogeneous solution systems were created at a very low density by Packmol software [32]. The solution systems were then minimized and deformed to match the desired density (1 g/cm³) and shape of the CaCO₃ surfaces, as shown in Figure 1. The computational model consisted of two phases: the CaCO₃ crystals as seeds and the CaCO₃ solution for growth (Figure 2).

2.2. Methods

Molecular dynamics (MD) simulations were performed using LAMMPS software [33,34]. ReaxFF was employed to simulate the formation of CaCO₃ clusters involving the variation of chemical bonds. Aiming at metal carbonates, Duin et al. [27] developed ReaxFF parameters to study their chemical dynamics in aqueous solutions. In this study, we performed a series of canonical ensemble (NVT) ReaxFF MD simulations for CaCO₃ cluster formation on the surface of different crystal seeds. The simulated system was equilibrated for 1 ns using a time step of 0.25 fs at a temperature of 360 K (Nosé-Hoover thermostat) [35,36]. According to experimental results [21], vaterite and calcite are generally formed at ambient temperature, while aragonite becomes the main phase above 348 K. A further temperature increase, 360 K or more instead of ambient temperature, can result in less time for cluster formation in MD simulations [25,26]. After the thermal equilibration step, the production step with 5 ns NVT run was performed for the structure and dynamic analysis.

3. Results and Discussion

Figure 3 and Figure S3a–d show the radial distribution functions (RDFs) for Ca-Ca, Ca-O (in HCO₃⁻), Ca-O_water (in H₂O), and Ca-O_solid (in crystalline CaCO3), respectively. The RDFs were generated by averaging the results of the last 2 ns MD simulations in the production stage. Here, the semi-equilibrium structures were presented by RDFs instead of transient structures. Comparing the RDFs of crystalline CaCO₃ polymorphs (Figure S4) with the CaCO₃ in solution reveals that calcium carbonate in solution has the characteristic of short-range order and long-range disorder as an amorphous structure (Figure 3). We then calculated RDFs for different CaCO₃ concentrations (Figure S5). The 2 mol/L concentration, which is the lower-limit concentration for showing relatively obvious RDF characteristics, was chosen in the current study. Since the first peak of RDFs is the strongest one, it can be concluded that small CaCO₃ clusters were formed in both homogeneous and heterogeneous systems in this study. The presence of obvious peaks of Ca-Ca RDFs in homogeneous solution at 3.65, 4.95, and 6.85 Å was compared with the two peaks at ~4.0 and ~6.0 Å from the results generated by semi-empirical force field MD simulations [26]. The position of the first Ca-O RDF peak is located at 2.55 Å (Figure 3b) and is slightly larger than the experimental value (2.41 Å) for stabilized amorphous calcium carbonate [37]. For other Ca-O pairs, their first RDF peaks are found at 2.55 Å (Ca-O_water) and 2.65 Å (Ca-O_solid). Considering a higher temperature (360 K) than the experimental condition (ambient temperature), a slight expansion of Ca-O pairs is reasonable.

The intensity of the first peak of Ca-O and C-O in a homogeneous solution is relatively small, indicating a weak tendency for the combination of Ca²⁺ and CO₃²⁻ (Figure 3a,b and Figure S6). On the contrary, crystal seeds can strengthen the formation of CaCO₃ in solution (stronger peaks in Figure 3). In particular, both the vaterite_c2 and vaterite_p3221 phases show a positive effect in the formation of neutral ion pairs (relatively strong intensity of all peaks in Figure 3b and Figure S5).

A similar increasing trend can be found in the RDFs of the Ca-O_water pair for hydration number (Figure 3c). Reported results showed that the Ca and O_water bonding weakens when the Ca-O (HCO₃⁻) RDF peaks are strong [26]. Our study demonstrates that the existence of vaterite_c2 and vaterite_p3221 phases is beneficial for combining calcium and oxygen in solution (Figure 3c,d).

The slopes of the mean square displacement (Figure 4 and Figure S7) are the tracer diffusion coefficients, denoting the mobility of calcium ions in different systems. The effect of different concentrations of CaCO₃ on its diffusion has been illustrated in Figure S7. The results showed that a higher density of CaCO₃ (4 mol/L) could result in largely weakened diffusion. Therefore, 2 mol/L concentration was chosen for further analysis. Moreover, adding vaterire_c1_1, calcite, or vaterite_p3221 phase could enhance the diffusion of calcium ions (Figure 4), whereas the aragonite and vaterite_c2 phases barely influenced the diffusion of calcium ions. The low mobility of calcium ions in the solution–vaterire_c2 system can be attributed to more binding pairs based on the previous RDF analysis (Figure 3).

The effect of crystal seeds on calcium carbonate ion pair formation in the aqueous solution was further verified by the concentration profiles of water and calcium carbonate along the direction normal to the solution–solid interface (Figure 5). The solution phase is equally packed along the left and right surface of crystal seeds, generating two interface areas via solution–solid surface atomic interaction. In addition, a zone can be identified within the interface where both the solution and solid atoms overlap. This overlap zone exhibits monotonical decay of the solution density to zero upon approaching the solid surface. The highest concentration of the three types of atoms (Ca, C, and O) that constitute CaCO₃ can be found in the solution–calcite interface zone (Figure 5a). The concentration of CaCO₃ is high in the solution area when vaterite is used as crystal seeds (Figure 4b). This trend is consistent with the RDFs results shown in Figure 3.

Furthermore, a high concentration of water in the solution–solid interface zone can be observed (top in Figure 5), especially in the solution–calcite system. The water layer at the interface is reported to hinder calcium ions from moving toward the surface of the solid phase [25]. However, in this study, a large amount of CaCO₃ can be observed inside the water layer at the interface (Figure 5a).

In order to understand the coexistence of a large number of water and CaCO₃ molecules, the atomic structures at the solution–solid interface were analyzed and delineated in Figure 6. As shown in Figure 6, water molecules from the solution prefer to bond with the terminated calcium atoms regardless of the type of CaCO₃ polymorphs. In the case of calcite, all terminal calcium atoms with a surface density of 0.05 Å⁻² are completely saturated by water molecules. The surface density of the top calcium atoms for vaterite (~0.03 Å⁻²) is smaller than that for the calcite phase. Therefore, noticeable water layers can be observed at the solution–calcite interface (Figure 5).

Once calcium ions approach the surface of calcite crystal, the adsorbed water molecules release one proton and become electron negative, attracting the positive Ca²⁺ (Figure 6a). More water molecules then surround the Ca²⁺ to form its first hydration sphere. This hydration sphere around Ca²⁺, instead of CO₃^2-, has also been reported by other researchers [25,38]. Further growth repeats the process of water dissociation and bonding to new Ca²⁺.

The connection between the ion pairs and vaterite surface can be attributed to hydrogen bonding among water molecules (Figure 6b). The indirect connection resulted in ion pairs being mainly observed in solution and not on the surface of the vaterite crystal.

4. Conclusions

In this study, the effect of calcium carbonate polymorphs on calcium carbonate ion pair formation in an aqueous solution was investigated by employing ReaxFF molecular dynamic simulations. The results demonstrated that adding crystal seeds, especially vaterite_c2, can improve the combination of calcium carbonate ion pairs. The mobility of Ca²⁺ in solution can be attributed to the bonding number and the local concentration. A high concentration of water and CaCO₃ coexisted at the solution–calcite interface. Atomic structure analysis indicated that the terminal Ca atoms on the crystal surface can be saturated by water molecules from the solution. Moreover, the formation of the hydration sphere of Ca²⁺ was initially preferred in solution. Later, the CO₃^2- ions bond to Ca²⁺ by substituting the water in the hydration sphere. The surface water molecules on the calcite crystal release one proton to bond with the hydration sphere of Ca²⁺. The surface of the metastable vaterite_c2 phase was also found to be connected to the hydration sphere of Ca²⁺ in solution by hydrogen bonding among water molecules. Thus, the formation of the calcium carbonate ion pair depends on crystal seeds.