pH-Resolved Surface Model Database

• pH-resolved surface model databases are structured compilations that quantify how surface chemistry, protonation, and charge vary with environmental pH for materials such as oxides, minerals, and biomolecules.
• They integrate titration, spectroscopic, and ab initio data to parameterize surface charge densities and protonation states using validated equations like the Henderson-Hasselbalch relation.
• These databases enable direct incorporation into simulation engines to predict interfacial phenomena including ion adsorption, catalytic behavior, and charge regulation under realistic conditions.

A pH-resolved surface model database is a structured compilation of quantitative models, atomistic surface structures, and associated parameters that encode how surface chemistry, speciation, and charge vary as a function of environmental pH. It operationalizes acid–base equilibria, protonation states, and interfacial partitioning for a diverse range of materials—oxides, minerals, biomolecules, nanocarbons, colloids, and composite interfaces—under experimentally relevant solution conditions. These models are central for predictive atomistic simulation, continuum electrostatics, and the interpretation of interfacial spectroscopies, providing per-pH assignments of surface site types, charge densities, hydration states, and associated force field or dielectric parameters. Rigorous integration of titration, spectroscopic, and ab initio data ensures transferability into simulation engines and enables direct benchmarking against experiment.

1. Core Physical Principles and Mathematical Formulations

The underlying principle of pH-resolved surface modelling is that the distribution of surface species—protonated, deprotonated, zwitterionic—is governed by site-specific acid–base equilibria. The canonical mass action relation is expressed as

$$\mathrm{p}K_{a} = -\log_{10}K_{a}, \qquad K_{a} = \frac{[\mathrm{A}^{-}][\mathrm{H}^{+}]}{[\mathrm{HA}]}$$

which, for surface-immobilized groups, determines the fraction of a given site in each state via the Henderson-Hasselbalch equation: $\alpha(pH) = \frac{1}{1 + 10^{(\mathrm{p}K_a-pH)}}$ For multi-site surfaces (as in silicas or aluminas), this is generalized to a vector of site populations, often including multiple pKₐ's corresponding to distinct local environments or motifs (e.g., defect vs. continuum sites) (Leung et al., 2010, Zhu et al., 18 Jan 2026).

The total surface charge density at a given pH becomes a population-weighted sum,

$\sigma(pH) = -e \sum_{i} N_i \alpha_i(pH) q_i,$

where $N_i$ is the surface density (sites per nm²), $\alpha_i$ is the fractional deprotonation, and $q_i$ is the net charge contributed by the $i$th site type.

For core-shell biological assemblies and nanoparticles, empirical or sigmoid fits to PDB-resolved structural/charge data as a function of pH provide a basis for surface charge assignment (Phan et al., 2019).

2. Methodological Framework: Database Construction and Parameterization

pH-resolved databases are built from a workflow integrating (a) atomic-scale structural models (PDB/GRO/JSON formats); (b) systematically adjusted surface stoichiometries and atomic charges to represent different pH-driven protonation states; (c) validated thermodynamic and kinetic parameters; (d) compatibility with major simulation force fields.

For mineral systems (e.g., hydroxyapatite, alumina), the methodology involves facet-specific slab construction, protonation/deprotonation reactions, and charge assignments, with each surface model entry recording the facet indices, applied pH, stoichiometric changes (ΔOH, ΔCa, ΔPO₄), new atomic charges, computed energetics (cleavage, immersion), and reference citations (Tzu-Jen et al., 2015, Zhu et al., 18 Jan 2026). For molecular systems, explicit chemical equilibrium reactions at the surface are implemented via reactive Monte Carlo or parameterized molecular dynamics with acid–base moves (Bakhshandeh et al., 2021, Fertig et al., 2018).

A typical JSON database entry will encode:

• Surface facet/orientation
• pH value
• Protonation state(s)
• Stoichiometry changes (removed/added ions per unit cell)
• Atomic charges for each species
• Files: coordinates (.pdb); force field parameters; metadata
• Surface and immersion energetics (mJ/m²)
• References

Nanopore and virus models utilize analytical or empirically-fitted expressions for pH-dependent surface charge, parameterized by functional group densities and pKₐ values, as in the sigmoid fits for the MS2 viral capsid (Phan et al., 2019) and the surface isotherms for functionalized nanopores (Fertig et al., 2018).

3. Representative Systems and Validated Ranges

Metal Oxides: Alumina, Silica

For alumina (α, γ, oxyhydroxides), protonation/deprotonation of surface ≡Al–OH groups is characterized by two intrinsic pKₐ's (e.g., pKₐ₁ ≃ 4.5, pKₐ₂ ≃ 9.4 on α-Al₂O₃(0001)), and per-facet site densities are derived from DFT and titration data. The database entries include explicit distributions of ≡Al–OH₂⁺, ≡Al–OH, and ≡Al–O⁻ species at each pH, with finely resolved pH grid points spanning pH 2–12 (Zhu et al., 18 Jan 2026).

On silica, a bimodal acidity distribution is established:

• Strained defect Q³ sites (∼20 %): pKₐ ≈ 4.5
• Canonical SiOH populations (∼80 %): pKₐ ≈ 8.0–8.5 Surface charge/pH relationships are generated by summing over these populations, with site densities calculated from atomistic surface topology (Leung et al., 2010).

Minerals: Hydroxyapatite (HAP)

Each low-index facet of HAP (001, 010, 020, 101) is represented at standard pH states (pH > 14, pH ≈ 10, pH ≈ 5), with explicit stoichiometric modifications and atomic charges reflecting protonation of PO₄³⁻ to HPO₄²⁻ and H₂PO₄⁻. Energetics are validated against experiment (<5% for immersion energy, <10% for elastic moduli), and the database is organized for seamless integration with major force fields (Tzu-Jen et al., 2015).

Interfaces: Water–Vapor, Viral Capsids, Carbon Nanodots

For the water/vapor interface, sum-frequency vibrational spectroscopy quantifies the hydronium adsorption free energy (ΔG_ads = –3.74 ± 0.56 kJ mol^–1), a partition coefficient (K_s = 11.2 ± 1.0 Å), and anion-independence up to 0.3 M; these metrics are directly translated into computational boundary conditions: fixed surface pH shift, fixed charge, or potential well depth for atomistic simulation (Chiang et al., 2019).

The MS2 capsid model uses a double-sigmoid parameterization for inner and outer surface charge densities as a function of pH, with a critical pH for charge inversion at pH ≈ 4.0 (Phan et al., 2019).

For functionalized carbon nanodots, the pH-dependence of the fluorescence lifetime is modeled via protonation-state–dependent transition rates, governed by the equilibrium fractions (via pKₐ) and the intrinsic radiative decay rates for each state. Multistate generalizations and environmental dependence are included via a full quantum dissipative formulation (Dilshener et al., 2024).

4. Practical Implementation in Simulations and Modeling

pH-resolved surface models are integrated into atomistic simulation engines (GROMACS, CHARMM, AMBER, PCFF, etc.) by direct import of coordinate/topology/parameter files and per-pH metadata. They provide all structural and electrostatic information needed for explicit interface–solvent–electrolyte simulations, charge regulation, and surface reactivity. Analytical pH–charge assignment formulas (Henderson-Hasselbalch, empirical sigmoid fits) are used for systems where dynamic adjustment of surface charge is needed, or for continuum models such as Poisson–Boltzmann and Poisson–Nernst–Planck schemes.

For nanopore transport, the surface charge pattern is discretized by grid tessellation and implemented as point charges in the local equilibrium Monte Carlo scheme, with pH-dependent input via the prescribed analytical relationships (Fertig et al., 2018). For reactive and constant-pH MD or MC schemes, protonation/deprotonation events are directly sampled with acceptance weights derived from mapped Kₐ values and corresponding changes in system free energy (Bakhshandeh et al., 2021).

5. Data Structure, File Formats, and Extensibility

Database organization follows a hierarchical tree, segregated by material, phase, and surface index. Each pH node contains:

• Coordinates: atomistic structure (PDB, GRO)
• Force field: parameter/topology files for multiple simulation packages
• Metadata: JSON entry with facet, pH, precise stoichiometry/charge, energetics, references
• Readme: details on protonation state, counter-ion placement, validation metrics

A representative JSON entry for HAP (001) at pH ≈ 10 encodes facet indices, surface area, fractional stoichiometric alteration, partial surface group composition, atomic charges, energy metrics, file paths, and reference list (Tzu-Jen et al., 2015). The database format is extensible to substituted/defective surfaces by appropriate stoichiometric and charge adjustments, and validated against experimental physical property benchmarks.

For virus and nanodot models, the database consists of parameter lists and functions (fit parameters for surface charge/lifetime vs. pH), with key variables tabulated for direct use in simulation or data analysis pipelines (Phan et al., 2019, Dilshener et al., 2024).

6. Validity Ranges, Limitations, and Application Domains

Database entries are strictly constrained to experimentally or computationally validated ranges. For instance:

• Water–vapor interface models are valid for [H^+] = 10^–3 M – 0.3 M, with halide counterions; Gouy–Chapman approximation applies for I ≤ 0.3 M (Chiang et al., 2019).
• Alumina pH-resolved models cover pH 2–12, each built for specific facets, with site densities and pKₐ's empirically and computationally benchmarked (Zhu et al., 18 Jan 2026).
• Silica and HAP models are annotated by site density, motif type, and decomposition of pKₐ distribution, with quantifiable uncertainty budgets from ab initio free energy calculations (Leung et al., 2010, Tzu-Jen et al., 2015).
• Nanopore, colloid, and viral particle models enumerate all fitting parameters and tabulated surface charge/pH points; empirical fits are only applied within the data-supported pH ranges (Phan et al., 2019, Bakhshandeh et al., 2021, Fertig et al., 2018).

These resources enable simulations and theoretical predictions for a spectrum of interfacial phenomena: ion-specific adsorption, electrolyte transport in nanoconfinement, biomolecular binding at charged surfaces, surface-driven catalysis, nanomaterial photophysics, and charge-dependent corrosion or passivation of functional materials.

7. Impact and Integration into Research Practice

The pH-resolved surface model database paradigm bridges atomic, mesoscale, and continuum approaches by providing rigorous, transferable, and systematically validated input for multi-physics simulation workflows. It supports quantitative prediction of zeta potentials, adsorption isotherms, titration curves, interfacial capacitance, and dependence of spectroscopic observables on pH and environmental variables. By encoding the relevant thermodynamic, structural, and force-field parameters in standardized, simulation-ready formats, researchers can accelerate the iterative cycle between experiment and atomistic theory, benchmark hypotheses against multiple physical observables, and extend the database to new materials systems or emerging experimental data sets (Tzu-Jen et al., 2015, Zhu et al., 18 Jan 2026, Chiang et al., 2019, Leung et al., 2010, Bakhshandeh et al., 2021, Dilshener et al., 2024).