Optimization and Application of ReaxFF for the Aqueous Carbonation of Calcium Silicates in Steel Slag

Abstract

The existing ReaxFF for the C/H/O/Ca/Si system exhibits poor compatibility with aqueous multiphase reactions. In this work, the aqueous carbonation of dicalcium silicate (C₂S) derived from steel slag was selected as the research system, and parameter optimization and validation of the reactive force field were performed. Density functional theory with the GGA-PBE functional was adopted to conduct structural relaxation and potential energy surface scanning for C₂S polymorphs, carbonate species, and reaction intermediates, and a comprehensive structure-energy training data set was established. Subsequently, ReaxFF parameters were trained using the ParAMS module, and molecular dynamics simulations of aqueous C₂S carbonation were implemented via the LAMMPS code. The results show that the equation-of-state curves (volume-energy, bond length-energy, etc.) of the optimized C/H/O/Ca/Si force field agree well with the DFT reference data, which effectively addresses the difficulty in characterizing multiphase interfacial reactions involving water molecules. This optimized force field was applied to 10 ns MD simulations for the aqueous carbonation of β-C₂S and γ-C₂S. The simulations successfully reproduced the efficient adsorption and accumulation of CO₂ and H₂O on the C₂S surface, while maintaining favorable computational efficiency with conventional computing resources. The force field parameters obtained in this study provide a robust computational tool for further elucidating the microscopic mechanism of aqueous carbon sequestration by calcium silicates.

1. Introduction

Guided by the dual-carbon strategy, the collaborative resource utilization of industrial solid wastes and CO₂ serves as a vital approach for carbon emission reduction and ecological restoration. Steel slag is a high-yield typical calcium silicate solid waste, and its principal active constituent, dicalcium silicate (Ca₂SiO₄, C₂S), can realize carbon sequestration and high-value application in building materials via aqueous carbonation. Compared with dry carbonation processes, aqueous systems have evolved into a mainstream research hotspot for carbon sequestration using steel slag because of mild reaction conditions and superior carbon fixation efficiency. Numerous experimental investigations of the aqueous carbonation of steel slag have been conducted worldwide. Researchers commonly adopt macroscopic characterization methods including XRD, FTIR, SEM, and thermogravimetric analysis to quantify the influences of process parameters on carbonation efficiency, product morphology, and mechanical properties of materials through orthogonal tests, whereby macroscopic reaction phenomena can be directly characterized. Nevertheless, the experimental methods have inherent drawbacks. These techniques fail to capture atomic-scale dynamic microscopic behaviors, such as Ca²⁺ leaching, interfacial adsorption of water molecules, transient evolution of reaction intermediates, and depolymerization and reconstruction of silicate networks. The intrinsic differences in carbonation activity between the two C₂S polymorphs in aqueous environments cannot be clarified; only superficial laws can be summarized, while the full reaction pathway and kinetic regulation mechanism of multiphase carbonation cannot be uncovered on the atomic scale. Against this backdrop, reactive force field molecular dynamics (ReaxFF MD), which is capable of real-time simulation of chemical bond cleavage and formation, acts as a critical tool to break through existing research bottlenecks. It is urgent to adopt this technique to interpret the microscopic mechanism of aqueous C₂S carbonation at the atomic scale and fill the gaps in the fundamental theoretical system of steel slag carbonation.

MD simulations, especially ReaxFF-based MD approaches, provide powerful microscopic research tools for analyzing complex multiphase chemical reactions and dynamically tracking the cleavage and formation of chemical bonds. With this simulation method, researchers can overcome the observational limitations of macroscopic experiments and dynamically resolve mineral interfacial adsorption, ionic migration and diffusion, and the evolution of reaction intermediates in real time at the atomic scale, offering theoretical support for revealing the intrinsic carbonation mechanism of silicate minerals. In recent years, certain progress has been achieved in the development of ReaxFF parameters for silicate systems, laying a foundation for mechanistic investigations of dry carbonation. Our research group previously developed parameters for the C/H/O/Ca/Si system and performed systematic simulations on the direct dry carbonation reaction between C₂S and CO₂, clarifying how temperature, pressure, and crystal polymorph structure regulate interfacial reaction activity and ionic diffusion kinetics. Nevertheless, obvious deficiencies remain in available studies and parameter development targeting aqueous carbonation systems with broader prospects for industrial application. Wang et al. adopted the C/H/O/Ca/Al/Si parameter set to conduct ReaxFF MD simulations on γ-C₂S carbonation in aqueous environments with an extremely short simulation duration of only 1 ns. Within aqueous reaction systems containing coexisting solid–liquid–gas phases, water molecules do not merely act as an inert solvent but directly participate in intricate microscopic behaviors including water dissociation, ionic migration and diffusion in liquid phases, and competitive adsorption onto surface active sites. Existing ReaxFF parameters optimized for dry carbonation systems exhibit poor compatibility under high water content conditions. These parameters fail to accurately characterize the synergistic coupling effect between the prehydration process of C₂S and subsequent carbonation reactions and cannot fully reproduce the whole microscopic reaction mechanism of carbon sequestration by C₂S under aqueous conditions. Accordingly, there is an urgent need to optimize parameters specifically for the aqueous carbonation system of steel slag and adopt reactive MD simulations to deeply decipher the microscopic interaction mechanism of aqueous C₂S carbonation at the atomic scale. Apart from generating atomistic trajectories via parameter-driven computation, the optimized ReaxFF potential provides a powerful analytical tool for untangling highly coupled multivariable solid–liquid–gas interfacial processes. It enables us to disentangle intertwined reaction variables and gain mechanistic insights that cannot be fully acquired through experimental characterization alone.

Most current studies on calcium-based carbonation directly employ the well-established C/H/O/Ca series ReaxFF for high-temperature dry simulations of anhydrous CaO. These parameters are merely verified via crystal volume-energy curves and are poorly adapted to aqueous multiphase interfaces and hydrated intermediates. Ca/C/H/O-ReaxFF originally developed for coal pyrolysis is applicable only to high-temperature dry environments. It fails to depict interfacial interactions in aqueous multiphase systems; besides, its parameters are calibrated merely using discrete density functional theory (DFT) configurations, leading to incomplete coverage of potential energy surfaces. ReaxFF parametrization generally relies on fitting against DFT training data sets. The original ReaxFF underestimates long-range van der Waals interactions. Although ReaxFF-lg can correct dispersion terms, a dedicated ReaxFF for the carbonation of cementitious C₂S is still unavailable, and the generic ettringite ReaxFF cannot match the interfacial reactions during carbonation. In this work, a multidimensional DFT training data set was constructed for the aqueous carbonation system of C₂S, and water-associated interfacial parameters were finely calibrated. Joint verification using the equation-of-state data of volume, bond lengths, and bond angles was performed to accurately characterize three-phase interfacial reactions involving water. Compared to the original ReaxFF, the optimized version exhibits remarkably improved compatibility and prediction accuracy.

For this purpose, this work targets the aqueous carbonation system of C₂S and carries out targeted parameter optimization and reliability verification for the C/H/O/Ca/Si ReaxFF. First, high-precision quantum chemical calculations based on DFT were implemented to establish a comprehensive structure-energy training data set covering two typical polymorphs (β-C₂S and γ-C₂S), carbonate products, and critical intermediates generated during hydration and carbonation reactions. Iterative training of ReaxFF parameters was subsequently performed, with an emphasis on improving the description accuracy of water molecular behaviors at multiphase interfaces. Finally, the optimized ReaxFF was adopted in MD simulations of aqueous multiphase systems containing β-C₂S and γ-C₂S mineral phases to verify its practicability.

This study intends to provide a dependable computational tool for deeply revealing the microscopic mechanism of aqueous carbon sequestration in calcium silicates, clarifying the inherent law governing the coupled hydration–carbonation reactions of active components in steel slag and offering theoretical support for the iterative upgrading of steel slag carbon-sequestration technologies. Beyond its role as a computational tool, the optimized ReaxFF parametrization developed here also resonates with a broader methodological perspective in which structured computational frameworks function as interpretive engines rather than passive parameter calculators. Such frameworks have been characterized in transdisciplinary work as epistemic operators that coordinate heterogeneous variables and render emergent system behaviors legible. , The force field optimization reported in this study is not only a numerical fit to DFT reference data but also an interpretive instrument through which the coupled chemical–diffusional–structural dynamics of aqueous carbonation become computationally tractable and mechanistically interpretable.

2. Structural Relaxation

The construction of training data sets serves as the core prerequisite for ReaxFF parameter training and directly determines the prediction accuracy of system energy and structural properties obtained from the optimized ReaxFF. Geometric relaxation and electronic property calculations of molecules were conducted via the VASP code to acquire stable initial configurations. The calculated species consisted of core components and vital reaction intermediates, namely, two typical polymorphs of C₂S (β-C₂S and γ-C₂S) in steel slag, together with carbonate phases such as aragonite and calcite as well as other intermediates generated during aqueous carbonation. During the calculation procedure, full structural relaxation was first performed on the atomic coordinates and cell parameters of each system. The atomic positions and lattice constants were adjusted iteratively with the crystal symmetry constrained until the system energy reached the minimum convergence value and the atomic force was lower than 0.03 eV/Å.

As displayed in Figure a, β-C₂S belongs to the monoclinic crystal system with the space group (S.G.) P2₁/c. Its lattice parameters are α = γ = 90°, β = 131.0242°, a = 6.25130 Å, b = 7.09130 Å, and c = 10.84060 Å. As presented in Figure b, γ-C₂S corresponds to the orthorhombic crystal system with S.G. = Pnma. The corresponding lattice parameters are α = β = γ = 90°, a = 11.34380 Å, b = 6.80930 Å, and c = 5.12390 Å.

1.

Crystal models of β-C₂S (a) and γ-C₂S (b).

Given the high efficiency and accuracy of VASP with the plane-wave basis set for the geometric relaxation of periodic solid structures, this work first adopted this program to obtain ground-state configurations. When establishing the structure-energy training data set, the calculation was switched to the BAND module embedded in the AMS code within the framework of DFT. This switching strategy guaranteed seamless compatibility between the output data formats and the subsequent ParAMS parameter-training module; meanwhile, the Slater-type orbital (STO) basis set possesses distinctive superiority in describing inhomogeneous electronic systems and localized bond cleavage behaviors.

The GGA-PBE functional was adopted for theoretical calculations to perform potential energy surface scanning (PES Scan) on the optimized stable initial configurations. The scanning targets mainly involved the unit cell volume, bond lengths of critical chemical bonds, including Ca–O, Si–O, C–O, and H–O, and key bond angles such as C–O–Ca and Ca–O–Si. Energy values corresponding to various structural parameters were collected to establish a training data set with complete structure-energy correlations. This training data set fully contains the intrinsic structural information and reaction intermediate configurations of the C/H/O/Ca/Si system. It supplies accurate and comprehensive data support for subsequent ReaxFF parameter training and enables the optimized ReaxFF to precisely characterize microstructural evolution and energy variation during aqueous carbonation.

3. ReaxFF Parameter Optimization

3.1. Optimization Scheme

The C/H/O/Ca/Si parameters developed by Wang et al. have been successfully adopted in MD simulations of dry carbonation for β- and γ-C₂S via ReaxFF, which verifies the feasibility of ReaxFF in research on the carbonation of calcium silicates and lays a foundation for follow-up investigations. Nevertheless, the development and validation of the above parameters only focus on carbonation reactions under dry conditions. For aqueous carbonation systems, the reaction environment evolves from solid–gas two-phase systems to solid–liquid–gas three phase systems. The introduction of water greatly complicates the overall reaction process, including water dissociation, ionic migration and diffusion in the liquid phase, and competitive adsorption between water molecules and surface active sites on calcium silicate.

The existing C/H/O/Ca/Si ReaxFF suffers from insufficient accuracy and limited applicability when characterizing multiphase coupling mechanisms. Accordingly, on the basis of published research outcomes, this work further optimizes the parameters of the C/H/O/Ca/Si ReaxFF in response to the complex characteristics of aqueous carbonation systems. With priority given to critical solid–liquid interfacial interactions in aqueous environments, nonbonded interaction parameters (van der Waals and Coulombic parameters between water molecules and calcium silicate surfaces) were recalibrated. Meanwhile, bond and angle parameters related to proton transfer and chemical bond reconstruction were refined, including Ca–O­(water/hydroxyl), H–O­(water), and bond order parameters for carbonate formation. These revisions aim to improve the capability of the ReaxFF to depict interfacial reactions and ionic migration behaviors in water-containing environments, delivering a more accurate simulation tool for illuminating the microscopic carbonation mechanism of steel slag mineral phases in aqueous media.

ReaxFF training was accomplished via the ParAMS module integrated in the AMS code. The predownloaded initial C/H/O/Ca/Si parameters and the DFT-derived training data set were imported for subsequent ReaxFF training. To guarantee the stability and convergence of parameter optimization, the training hyperparameters were configured as follows: max loss function calls = 1000, initial standard deviation σ₀ = 0.05, Popsize = 8, output interval = 600 s. Convergence of molecular structures was adopted as the criterion for successful training, and a new force field file in .ff format matching aqueous multiphase reaction systems was exported eventually. Figure displays the flowchart of the whole ReaxFF optimization workflow.

2.

Workflow of the ReaxFF optimization process.

3.2. Reliability Verification

The training data set contains structural data of two C₂S polymorphs, carbonates, and reaction intermediates. The equation-of-state curves corresponding to these crystal structures, including volume-energy, bond length-energy, and bond angle-energy curves, were taken as reference benchmarks. Parameter calibration of ReaxFF was realized through iterative optimization to guarantee the accuracy of ReaxFF in calculating energies under various structural configurations. Figure compares the DFT-calculated values and the predicted data obtained from ReaxFF for various crystal structures. ,−

3.

Volume–energy curves of aragonite (a) and calcite (b), bond angle–energy curves of β-C₂S (Ca–O–Si) (c) and γ-C₂S (Ca–O–Ca) (d), and bond length–energy curves of Ca­(OH)₂ (H–O) (e) and SiO₂ (Si–O) (f).

According to the fitting results, ReaxFF can effectively distinguish various oxide configurations and its energy curves are in satisfactory agreement with DFT data. This demonstrates that the optimized ReaxFF possesses high reliability and prediction accuracy when characterizing the structure-energy correlations of the C/H/O/Ca/Si system.

4. Molecular Dynamics Simulation

4.1. Model Construction

To further verify the feasibility and reliability of the optimized ReaxFF in practical multiphase reaction systems, molecular dynamics simulations of aqueous carbonation for β-C₂S and γ-C₂S were implemented using the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) code. − The construction of the simulation systems is displayed in Figure . Nanosized clusters of β-C₂S and γ-C₂S were adopted as solid-phase models with a fixed cluster radius of 18 Å, containing 276 β-C₂S molecules and 246 γ-C₂S molecules, respectively, to adequately characterize active reaction sites on mineral surfaces. A gas–liquid two-phase environment consisting of 300 CO₂ molecules and 300 H₂O molecules was established surrounding the clusters to reproduce the actual reaction conditions of aqueous carbonation. The canonical NVT ensemble was applied throughout the simulation, where the system temperature was maintained constantly at 298 K (room temperature). The time step was defined as 0.5 fs with a total simulation duration of 10 ns for sufficient system evolution. This setup mainly aimed to capture multiphase interfacial adsorption and molecular activation behaviors at the initial reaction stage. −

4.

Schematic diagram of model construction.

Figure compares the molecular configurations of β-C₂S and γ-C₂S before and after aqueous carbonation reactions. To distinguish oxygen atoms from different sources, oxygen atoms inside C₂S are denoted as Os, oxygen atoms from CO₂ are marked as Og, and oxygen atoms originating from H₂O are defined as Ow. The simulation results reveal that CO₂ and H₂O molecules are efficiently adsorbed and accumulated on the C₂S surface. Water dissociation at the interface and the formation tendency of carbonate/bicarbonate precursors can be clearly observed, which verifies the capability of the optimized ReaxFF to characterize chemisorption at multiphase interfaces and early-stage reaction processes. In addition, the total wall-clock time for the two simulation systems under conventional computing resources was 86 h 50 min 5 s and 132 h 27 min 43 s, respectively, reflecting favorable computational efficiency. It is demonstrated that the optimized ReaxFF can support large-scale and long-time molecular dynamics simulations while maintaining simulation precision, laying a solid foundation for further systematic investigations on the aqueous carbonation mechanism of C₂S under various working conditions including different temperatures and pressures.

5.

Molecular reaction models of β-C₂S (a) and γ-C₂S (b) at 0 ns, 0.1 ns, 1 ns, and 10 ns.

4.2. Results and Discussion

4.2.1. Evolution Law of CO₂ Consumption

Material distribution and bonding information on the reaction system at each time step can be acquired from LAMMPS calculations. The formation of carbonates as well as silicon- and calcium-containing oxygenated hydrated intermediates demonstrates that hydration and carbonation reactions have occurred on mineral phases. The dynamic consumption amount of CO₂ over simulation time can be quantified according to species distribution data, which directly reflects the carbon sequestration kinetic characteristics during the carbonation of β-C₂S and γ-C₂S. , Figure presents the variation curves of CO₂ consumption quantity versus simulation time ranging from 0 to 10 ns for the two polymorphs of dicalcium silicate.

6.

CO₂ consumption of β-C₂S and γ-C₂S during a 10 ns reaction.

Within the whole simulation period, CO₂ consumption of both reaction systems follows a two-stage evolutionary trend: rapid consumption in the early stage, followed by a slow growth rate that gradually plateaus toward saturation.

The period of 0–1 ns corresponds to the rapid carbonation stage. Continuous dissociation of the mineral lattice releases Ca²⁺, and abundant CO₂ coordinates with free calcium ions and lattice oxygen, leading to an approximately linear, sharp rise in CO₂ consumption. , Meanwhile, dissolved CO₂ reacts with OH^– dissociated from water molecules to continuously generate carbon-containing intermediates such as HCO₃ ^–, jointly realizing the carbon sequestration process.

The reaction proceeds at a moderate rate during 1–3 ns with an obvious reduction in reaction velocity. In the middle and later reaction stages of 3–10 ns, the concentration of active free Ca²⁺ available for coordination reactions in the system decreases continuously. The carbon sequestration reaction gradually approaches the thermodynamic equilibrium state, so the increment of CO₂ consumption drops drastically and finally levels off into a stable plateau. This transition from early-stage chaotic interfacial reactions toward a later thermodynamic plateau is analogous to the systemic structural saturation phenomenon, in which diverse local structural perturbations gradually converge into a recurrent stable equilibrium state. In the vocabulary of interpretive frameworks, this two-stage profile may also be understood as a transition between distinct regimes of structural saturation, a concept that has been explored in the context of cross-domain interpretive work. Even though minor local structural fluctuations persist within the mineral-water interface, the overall carbonation system no longer drives net macroscopic CO₂ uptake, marking the arrival of this saturated thermodynamic regime.

During the fast reaction stage, the CO₂ consumption of the γ-C₂S system is higher than that of β-C₂S in the time intervals of 0–0.085 ns and 0.71–4 ns. As the reaction proceeds continuously, the two consumption curves gradually converge. At the termination of the 10 ns simulation, the total carbon sequestration capacities of the two polymorph systems are roughly equivalent. The above results indicate that γ-C₂S exhibits superior kinetic activity for carbonation in the early reaction stage, whereas the two phases possess similar theoretical total carbon sequestration potentials in the final state.

Bonding information extracted from the bonds.reaxff file was processed to calculate the quantity of Ca-coordinated carbonates frame by frame. Specifically, a carbon atom is categorized as Ca-associated carbonate C if the C atom forms C–O bonds with no less than three oxygen atoms, and at least one of these bonded oxygen atoms is simultaneously coordinated with calcium. Eq is defined as the effective carbonation rate, and the temporal evolution of the carbonation rate for the two systems is illustrated in Figure .

$$\mathrm{Calculated\; Effective\; Carbonation\; Rate}=\frac{\mathit{N}(\mathit{Ca\_}\mathit{Associated\; Carbonate\; C})}{N(\mathrm{Initial}{\mathit{CO}}_2=300)}$$ 1

7.

Carbonate rate of β-C₂S and γ-C₂S during a 10 ns reaction.

At 298 K, the carbonation ratios of both β-C₂S and γ-C₂S show kinetic characteristics of rapid initial growth followed by a slowly rising plateau region. This tendency indicates that the formation of carbonate species at the early simulation stage is mainly driven by C–O bond generation and Ca–O coordination. The declined growth rate in the later stage reveals the gradual consumption of reactive Ca-related oxygen sites, and further carbonation of the system relies on local structural rearrangement.

Quantitatively, the period of 0–0.1 ns corresponds to the induction initiation stage. Carbonate generation is triggered simultaneously for both polymorphs, while γ-C₂S exhibits an instantaneously higher carbonate formation rate than β-C₂S. The fast bonding stage ranges from 0.1 to 1.22 ns, during which β-C₂S maintains a higher cumulative amount of produced carbonates. A large fraction of consumed CO₂ in this interval is converted into coordinated carbonate products. From 1.22 to 3.09 ns, the carbon sequestration ratio of γ-C₂S surpasses that of β-C₂S, which is consistent with the previously observed faster CO₂ consumption rate of the γ-C₂S system. In the middle and late reaction period (after 3 ns), the carbonate formation rate of β-C₂S overtakes γ-C₂S and retains a slight gap until the end of the simulation.

This phenomenon reveals that γ-C₂S rapidly consumes CO₂ and accomplishes effective carbon sequestration at an early stage owing to its superior interfacial reaction activity. By contrast, part of the CO₂ consumed by β-C₂S in the initial stage is merely adsorbed physically without forming coordination bonds. As the simulation proceeds, free CO₂ adsorbed on the β-C₂S surface gradually binds with dissolved calcium ions to generate carbonate species, realizing effective carbon sequestration in a delayed manner. Consequently, β-C₂S presents a higher carbon sequestration rate than γ-C₂S in the later reaction stage with a persistent marginal difference until the end of the simulation.

In terms of kinetic behaviors, γ-C₂S shows a faster CO₂ capture response and higher instantaneous effective carbon sequestration efficiency than β-C₂S at the initial carbonation stage, possessing stronger short-term carbonation activity. In view of the final carbon sequestration performance, β-C₂S displays a delayed conversion effect for carbon immobilization. Relying on the secondary bonding reaction of slowly adsorbed CO₂ molecules, β-C₂S eventually achieves a higher steady-state proportion of carbonate products.

The two polymorphs of dicalcium silicate apply to carbon sequestration scenarios with different reaction durations: γ-C₂S is more suitable for systems requiring rapid short-term carbon fixation, while β-C₂S delivers superior permanent carbon sequestration performance in long-term reaction systems. The evolutionary trends of the CO₂ consumption curve and carbonate formation rate curve are mutually corroborated, revealing the distinct microscopic kinetic pathways of “reactant consumption-product formation” during the aqueous carbonation of β-C₂S and γ-C₂S.

4.2.2. Analysis of Diffusion Behavior via Mean Square Displacement

Mean square displacement (MSD) is a key parameter used to quantify the magnitude of molecular migration and diffusion motion within the reaction system. , The evolutionary characteristics of MSD can be utilized to elucidate the coupled hydration–carbonation reaction mechanism on the basis of molecular diffusion kinetics. The MSD variations for various components are displayed in Figures –.

8.

MSD of CO₂ in β-C₂S and γ-C₂S reaction systems.

10.

MSD of β-C₂S and γ-C₂S in the reaction systems.

The MSD curves of CO₂ are displayed in Figure . The MSD values of CO₂ in both systems increase monotonically with simulation time and present a linearly increasing trend accompanied by periodic fluctuations, demonstrating that CO₂ molecules maintain persistent thermal diffusion motion throughout the simulation process. The MSD values of CO₂ in the γ-C₂S system are consistently higher than those in the β-C₂S system over the whole simulation period, and the numerical gap between the two curves gradually widens as the simulation proceeds. A higher MSD value corresponds to a larger diffusion coefficient, which verifies that free CO₂ molecules possess superior diffusion and transport efficiency in the γ-C₂S system. Accordingly, CO₂ molecules can migrate more rapidly toward active sites on the solid surface of C₂S to participate in carbonation reactions. Combined with the above results of CO₂ consumption and effective carbonation ratio, the γ polymorph achieves faster CO₂ capture and carbonate formation in the early reaction stage owing to its enhanced supply capacity via CO₂ diffusion. Although partial CO₂ molecules are immobilized through coordination bonding at the phase interface and the concentration of free CO₂ declines slightly, the overall diffusion behavior of CO₂ in the γ-C₂S system is still markedly superior to that in the β-C₂S system.

As the reaction medium for aqueous carbonation, water molecules perform multiple functions: dissociating to release H⁺ and hydroxyl groups, participating in interfacial hydration, and transporting reactants. Different from the monotonically rising tendency of CO₂ MSD curves, the MSD curves of water molecules (Figure ) rise first and then fluctuate continuously. In the initial reaction stage of 0–3 ns, the MSD values of water molecules in both systems rise rapidly and synchronously. Water molecules continuously infiltrate and adsorb onto the mineral surface with a gradually expanded free motion range. After 3 ns, the MSD stops growing persistently and fluctuates violently around a constant value.

9.

MSD of H₂O in β-C₂S and γ-C₂S reaction systems.

Throughout the whole simulation period, the overall MSD magnitude and fluctuation peak value of water molecules in the β-C₂S system are remarkably higher than those in the γ-C₂S system. This phenomenon indicates that free water molecules possess stronger spatial migration and diffusion activity within the β-C₂S reaction environment. In contrast, abundant water molecules in the γ-C₂S system are immobilized on the mineral surface or embedded in hydrated product structures via coordination adsorption and dissociative bonding, which greatly restricts their free diffusion capacity. Highly active water molecules adsorb and permeate toward the solid mineral interface to drive the hydration of dicalcium silicate and react with CO₂ to produce HCO₃ ^–. The higher diffusion capacity of water molecules facilitates the sustainable progress of carbonation reactions.

The MSD curves of β-C₂S and γ-C₂S (Figure ) both exhibit periodic oscillation characteristics, which originate from the thermal vibration effect of the silicate crystal framework. The overall MSD values of framework atoms in solid C₂S are far lower than those of CO₂ and H₂O molecules. This manifests that the integral structure of the solid lattice maintains stability without large-scale atomic migration. The fluctuations in MSD merely stem from lattice vibration as well as local atomic displacement induced by hydration dissociation and structural relaxation of surface atoms.

In the initial reaction stage, the MSD of γ-C₂S rises at a higher rate with larger values, demonstrating that the lattice of the γ polymorph is prone to lattice distortion and possesses a higher activation degree of surface atoms. Its inferior lattice stability accelerates hydration dissociation and the release of Ca²⁺ ions. In comparison, the β-C₂S lattice features a denser and more stable structure accompanied by smaller vibrational displacements of atoms. As the reaction proceeds, the MSD of β-C₂S shows periodic, intense spike fluctuations, while the MSD of γ-C₂S fluctuates slightly within a relatively stable range. This reveals that lattice destruction and ion leaching of β-C₂S proceed in an intermittent and delayed manner, which is consistent with the previously observed simulation law that its effective carbonation ratio surpasses that of γ-C₂S in the later stage. By contrast, the surface lattice activation and Ca²⁺ release of γ-C₂S proceed continuously and steadily, matching its kinetic feature of rapid carbon sequestration in the early reaction period.

4.2.3. Radial Distribution Function Analysis on Coordination and Bond Evolution

To qualitatively uncover the bonding evolution rules of β-C₂S and γ-C₂S in the aqueous carbonation system at the atomic scale, the Radial Distribution Function (RDF) is calculated using trajectory data collected before and after the reaction. The variations in coordination characteristics of three critical atomic pairs, including Ca–O, C–O, and H–O, are systematically analyzed, and the discrepancies in bond formation and bond cleavage between the two polymorphs during the coupled carbonation process are compared.

As illustrated in Figure , sharp characteristic coordination peaks for Ca-Os, C-Og, and H-Ow emerge in the β-C₂S system at the initial reaction state, which correspond to the intrinsic coordination structures of the original crystal framework, free CO₂, and bulk water molecules, respectively. After the 10 ns reaction simulation, the peak intensity of lattice Ca–Os decreases slightly, demonstrating the fracture of the silicate framework and the leaching of Ca²⁺ ions. Meanwhile, the peak heights of Ca-Og and Ca-Ow increase remarkably, verifying that the dissolved Ca²⁺ ions construct new coordination configurations with CO₂ and H₂O. The main peak of gaseous C-Og declines drastically, accompanied by peak position shifting, and the generation of new C-Os and C-Ow peaks, which evidence the conversion of CO₂ molecules into carbonate species. The H-Ow peak becomes broadened with an obvious reduction in peak intensity, whereas the peaks of H-Os and H-Og are strengthened. This phenomenon indicates the synchronous occurrence of water dissociation, proton transfer, and the formation of silanol groups.

11.

RDF of Ca-Og (a), Ca-Os (b), Ca-Ow (c), C-Og (d), C-Os (e), C-Ow (f), H-Og (g), H-Os (h), and H-Ow (i) in β-C₂S reaction system.

The overall evolutionary trends of RDF curves for γ-C₂S (Figure ) are analogous to those of β-C₂S, while the differences in coordination intensity can reflect the discrepancy in chemical activity between the two polymorphs. After the reaction, the lattice Ca-Os bonds of both phases are weakened, and the coordination peaks of Ca-Og and Ca-Ow rise synchronously. The peaks of the γ-C₂S system are sharper with slightly higher intensities, suggesting more sufficient Ca²⁺ leaching and carbonate coordination reactions in this system. The C-Os peak intensity of γ-C₂S is marginally higher, meaning more CO₂ molecules bind with lattice oxygen atoms. In terms of water molecule dissociation and silanol group formation, the characteristic peaks of H-Os and H-Og for γ-C₂S are slightly stronger than those for β-C₂S, and no order-of-magnitude difference is observed between the two systems. From a methodological standpoint, the divergent kinetic pathways observed for β-C₂S and γ-C₂S can be read as a form of epistemic nonconvergence accompanied by adaptive reprogramming of reaction coordinates.

12.

RDF of Ca-Og (a), Ca-Os (b), Ca-Ow (c), C-Og (d), C-Os (e), C-Ow (f), H-Og (g), H-Os (h), and H-Ow (i) in the γ-C₂S reaction system.

The three sets of experimental results, including CO₂ consumption amount and system carbon sequestration ratio, MSD diffusion kinetics, and RDF microscopic coordination, construct a multiscale corroboration relationship covering the macroscopic, molecular, and atomic scales. The crystal framework of γ-C₂S presents weak structural constraints and susceptible lattice dissociation, accompanied by faster diffusion and transport of CO₂ as well as stronger interfacial adsorption of water molecules. At the atomic scale, γ-C₂S achieves more sufficient Ca²⁺ leaching and coordinated conversion of CO₂, thereby possessing superior kinetic activity for carbon sequestration in the early reaction stage. Benefiting from its compact lattice structure, β-C₂S exhibits mild molecular diffusion and delayed lattice reaction. It ultimately acquires a higher steady-state carbon sequestration capacity via continuous bonding and immobilization reactions in the later reaction period. The high consistency among multidimensional data sets clarifies the distinct microscopic action mechanisms governing the aqueous carbonation processes of the two polymorphs of dicalcium silicate.

5. Conclusions

• 1.The training data set constructed via DFT calculations with the GGA-PBE functional can fully characterize the structural and energetic properties of the C/H/O/Ca/Si system, laying an accurate data foundation for the optimization of the ReaxFF.
• 2.The optimized ReaxFF greatly improved its compatibility with aqueous multiphase systems. The predicted structural and energetic properties showed excellent consistency with the DFT reference data. This force field supports stable long-time scale reaction simulations accompanied by greatly improved computational efficiency, which overcomes the limitations existing in the original force field.
• 3.Molecular dynamics simulation results reveal that the CO₂ consumption and effective carbon sequestration ratio in both β-C₂S and γ-C₂S systems rise rapidly at first and then gradually reach an equilibrium state. γ-C₂S possesses a higher lattice activation degree and superior CO₂ diffusion capacity. Combined with a stronger restraint effect on interfacial water molecules, this polymorph exhibits faster carbonation reaction and carbon sequestration rates in the early reaction stage. Benefiting from its compact and stable crystal structure, β-C₂S enables stronger free migration of water molecules and shows a delayed characteristic during carbon immobilization. Accordingly, a higher steady-state carbon sequestration efficiency can be achieved in the later stage of the reaction.
• 4.Lattice bond cleavage, small-molecule activation, and new bond formation take place in both β-C₂S and γ-C₂S systems. The extents of ionic coordination, water dissociation, and silanol formation in γ-C₂S are slightly greater than those in β-C₂S. The mutually consistent multiscale simulation results clarify the microscopic mechanism responsible for the reactivity difference between the two polymorphs and offer theoretical support for research on aqueous carbon sequestration technology based on steel slag-derived dicalcium silicate.

The authors declare no competing financial interest.