Development of a ReaxFF reactive force field for NaSiOx/water systems and its application to sodium and proton self-diffusion

Evidence and attribution¶

Authority of statements

Prose summarizes the J. Phys. Chem. C article identified by doi. Glass composition and QM functional choices are in the Methods/SI.

Summary¶

A Na/Si/O/H ReaxFF parametrization is developed for sodium silicate–water interfaces, trained on quantum-mechanical data for crystalline NaSiO\(_x\) equations of state, Na\(^+\) migration barriers in silicate structures, hydroxylated silica interacting with Na\(^+\)–water environments, and [NaOH·\(H_2O\)_n] cluster dissociation energies. After optimization, the authors validate crystal and glass structures, Na\(^+\) and proton transport in amorphous matrices, and NaOH dissociation in bulk water, then relate the results to glass dissolution scenarios (interdiffusion, subsurface transport to interfacial vacancies, leaching). Nuclear waste glass leaching and geochemical weathering both require reactive models that allow Si–O–Na network hydrolysis while capturing mobile Na\(^+\) and H\(_3\)O\(^+\) transport (introduction themes).

Methods¶

Force-field training (ReaxFF, Na–Si–O–H)¶

The work extends the ReaxFF bond-order framework to Na/Si/O/H for sodium silicate–water chemistry. Parent models build on prior Si/O/H and glass–water ReaxFF lines cited in the article. QM reference data come from DFT calculations used to fit equations of state of NaSiO\(_x\) crystals, Na\(^+\) migration barriers in silicate hosts, hydroxylated silica interacting with Na\(^+\)–water clusters, and [NaOH·(H\(_2\)O)\(_n\)] dissociation energies (\(n=1\)–\(6\)) as summarized in the abstract. Optimization refits bonded, vdW, and Coulomb/QEq-related terms until those training targets are matched; full functional/basis/k-mesh tables are in Methods and Supporting Information on the version-of-record PDF.

MD application — glass preparation, ion transport, and aqueous NaOH¶

Engine / code. Reactive molecular dynamics with ReaxFF is implemented in LAMMPS using a velocity-Verlet integrator at \(\Delta t = 0.25\ \mathrm{fs}\). Berendsen thermostats (100 fs damping) are used for NVT segments, while NPT segments employ a Berendsen barostat (5 ps damping) as summarized in the computational overview.

System size and composition. Na\(_2\)Si\(_2\)O\(_5\) benchmarks use a \(1\times2\times2\) supercell (144 atoms). Na\(^+\)/H\(^+\) interdiffusion starts from the same amorphous framework with three Na\(^+\) ions replaced by protons. NaOH(aq) kinetics use 10 NaOH plus 782 H\(_2\)O in a (28.86\ \text{Å})^3 cubic cell (§2.4.3).

Boundaries / periodicity. Three-dimensional periodic boundary conditions apply to all bulk crystal, glass, and electrolyte cells in §2.4.

Ensemble. NPT appears for 1 K crystal relaxation, melt–quench with 0 GPa internal pressure, and 300 K density stabilization of glasses; NVT follows for additional 300 K relaxation. Na\(^+\) self-diffusion uses 200 ps NPT equilibration per temperature, then 100 ps NVE production. Na\(^+\)/H\(^+\) interdiffusion uses NVT at 800 K followed by 100 ps sampling. NaOH dissociation uses NVT at 300 K for 100 ps.

Timestep. 0.25 fs for the protocols quoted above.

Duration / stages. Glass construction: melt at 4000 K (NVT), cool at 10 K/ps under 0 GPa NPT to 300 K, then 0.5 ns NPT until density plateaus, plus 0.5 ns NVT at 300 K (§2.4.1). Na\(^+\) diffusion: 200 ps NPT equilibration then 100 ps NVE trajectories across 300–900 K (§2.4.2). Interdiffusion: NVT equilibration at 800 K, then 100 ps production (§2.4.2). NaOH(aq): 100 ps NVT at 300 K with bond-order 0.3 species analyses every 50 MD steps (§2.4.3).

Thermostat / barostat. Berendsen thermostat (100 fs damping) for NVT; Berendsen barostat (5 ps damping) whenever NPT is active.

Temperature. Glass workflow spans 1 K, 4000 K, and 300 K; Na\(^+\) diffusivity sweeps 300–900 K; interdiffusion at 800 K; NaOH benchmark at 300 K.

Pressure. NPT segments target 0 GPa hydrostatic conditions for melt–quench and density equilibration; NVE production fixes volume after NPT preconditioning.

Electric field. N/A — no applied electric field.

Replica / enhanced sampling. N/A — direct MD without metadynamics, umbrella sampling, or bond boost.

Findings¶

Outcomes and mechanisms¶

After optimization, ReaxFF reproduces QM equations of state for the NaSiO\(_x\) crystals examined and ranks Na\(^+\) vacancy migration pathways with the same low-energy ordering as DFT (Fig. 2). Melt–quenched Na\(_2\)Si\(_2\)O\(_5\) glasses remain stable under the subsequent NPT/NVT protocol, enabling Na\(^+\) self-diffusivity extraction across 300–900 K and Na\(^+\)/H\(^+\) interdiffusion studies in proton-substituted glasses. NaOH dissociation in bulk water proceeds on the 100 ps NVT window analyzed with a 0.3 bond-order criterion. Together, these validations motivate dissolution narratives involving Na\(^+\)–proton interdiffusion, subsurface Na\(^+\) transport toward interfacial vacancies, and post-leach ion–water chemistry.

Comparisons¶

Crystal/glass structural metrics and barrier trends are compared to DFT training data; broader leaching implications are discussed relative to experimental silicate–water literature cited in the introduction.

Sensitivity and design levers¶

Quench rate (10 K/ps), temperature (300–900 K diffusion sweep, 800 K interdiffusion), and stoichiometry of the Na\(^+\)/H\(^+\) substitution control the observed transport and speciation kinetics.

Limitations and outlook (as authored)¶

Nanosecond sampling and bulk benchmark cells bound direct extrapolation to field leaching times; the discussion highlights future interface-explicit models.

Corpus honesty¶

Numerical protocol details above are summarized from papers/Hahn_NaSiOx_JPCC_2018_online.pdf §2.4; cite the SI parameter file for authoritative ReaxFF coefficients.

Limitations¶

Glass structure realism depends on melt–quench protocol and composition; transport coefficients should be spot-checked against independent QM or experiment when extrapolating to long leach times.

Relevance to group¶

Sandia + Penn State collaboration with van Duin on geochemical glass dissolution and reactive MD at silicate–water interfaces.

Proof duplicate: 20180000-0002-1722-5631-x-development-reaxff.

Citations and evidence anchors¶

DOI: 10.1021/acs.jpcc.8b05852.