Analysis of the Effects of Silica Surface Structure on the Local Diffusion and Hydrogen Bonding of Water via Molecular Dynamics

Abstract

Water near solid–liquid interfaces is well known to exhibit structural and dynamical properties distinct from those of the bulk, owing to strong interactions with the solid surface. While water dynamics near the interface have been quantified, a direct atomistic link between spatially heterogeneous surface–water hydrogen bonding and local diffusion remains elusive. Here, using classical molecular dynamics simulations of water confined by silica, we examine how surface topology and silanol distributions modulate the local structure and diffusion of water. To characterize the structure of water near the interface, water density profiles and spatial density maps were analyzed. The results show that multiple adsorbed water layers form on crystalline silica surfaces, whereas no clearly defined adsorbed water layers are observed on amorphous silica surfaces. The diffusion properties of water were evaluated by calculating the local self-diffusion coefficient in the direction parallel to the interface. The results indicate that the local self-diffusion coefficient decreases as the distance from the wall decreases. To further clarify the diffusion behavior of water near the interface, we introduced a spatially resolved local diffusivity (LD) metric. The LD analysis reveals a pronounced suppression of water mobility that strongly and negatively correlates with the local probability density of silanol–water hydrogen bonds (R ≈ −0.8 for the crystalline system and R ≈ −0.6 for the amorphous system).

Introduction

The structure and diffusion properties of water near solid–liquid interfaces have attracted considerable attention from both industrial and academic perspectives because of their relevance to semiconductor miniaturization, − drug delivery in biomedical applications, , energy transfer under increasing energy demands, − and the development of analytical techniques for liquids at interfaces. − Over the past several decades, numerous experimental and numerical studies have investigated the properties of liquids at solid–liquid interfaces. −

Experimentally, J. Hassan et al. investigated the diffusion coefficients of water in carbon nanotubes using two-dimensional D–T₂ nuclear magnetic resonance spectroscopy. They reported that the diffusion coefficient of a central water component in double-walled carbon nanotubes was approximately 8–9 times higher than that of bulk water. Y. Kazoe et al. developed nanofluidic devices to investigate the flow properties of liquids confined within nanochannels. Their results suggested the presence of three distinct phasesadsorption, proton transfer, and bulknear the interface as a result of wall–solvent interactions. In addition, they reported that the apparent viscosity of the solvent increases markedly in nanochannels with diameters below 100 nm, which they attributed to the dominance of the proton transfer phase in the confined space. These findings indicate that the behavior of water can change significantly in nanoscale spaces where interfacial effects dominate.

As a numerical approach for investigating solid–liquid interfaces, molecular dynamics (MD) simulations are widely used to study the structural and diffusion properties of liquids near interfaces. ,− The diffusion properties of water are typically quantified using the self-diffusion coefficient, which can be derived from two methods based on Einstein’s relation and the Green–Kubo formalism. However, these methods rely on averages over the entire system and therefore cannot accurately describe the local diffusion of water near interfaces characterized by strong spatial inhomogeneity and anisotropy.

To address this limitation, P. Liu et al. defined local rectangular regions subdivided along the direction normal to the interface and proposed a method for calculating local self-diffusion coefficients within each region by weighting the contribution of water molecules using their survival probability within the region. Y. Naruke et al. calculated local self-diffusion coefficients in the direction parallel to the interface for water and isopropyl alcohol (IPA) confined between α-quartz surfaces with different orientations. Their results showed that the local self-diffusion coefficient of water decreases near quartz surfaces and that this decrease becomes more pronounced when water molecules penetrate the silanol gaps, depending on the surface orientation. Furthermore, they demonstrated that IPA is more strongly affected by confinement than water, resulting in suppressed diffusivity over a wider region. Alex M. Schrader et al. quantitatively investigated the relationship between silanol group density on silica surfaces and the diffusivity of water near the interface using a combination of Overhauser dynamic nuclear polarization experiments and molecular dynamics simulations. Both experimental and computational results demonstrated that the diffusivity of water molecules near the interface decreases with increasing silanol group density.

To evaluate diffusion properties with higher spatial resolution, dynamical propensity (DP), which represents the spatial propensity for molecular motion, has been introduced. ,− M. Fitzner et al. examined the relationship between DP and ice nucleation in supercooled bulk water and found that ice nucleation tends to occur in regions where DP is locally reduced. These phenomena can be interpreted by considering that molecules with low DP are associated with dynamically constrained environments, where reduced molecular mobility facilitates the formation of the ordered structures required for nucleation. Thus, DP provides a direct link between molecular dynamics and structural evolution at the molecular scale. P. Gasparotto et al. introduced local diffusivity (LD), which does not normalize DP by the mean square displacement, thereby enabling comparisons between different systems. Their results showed that LD is relatively high at gas–liquid interfaces and lower in the bulk phase, suggesting enhanced molecular mobility at the interface. These phenomena have been attributed to faster hydrogen-bond dynamics compared to bulk water. Consequently, LD serves as an effective descriptor of spatial variations in molecular mobility. Masuda et al. applied LD to investigate the relationship between water mobility and ice nucleation in a solid–liquid system. They showed that ice nucleation can occur even near the interface in regions where molecular mobility is suppressed, particularly on smooth surfaces, suggesting that reduced local dynamics facilitate structural ordering.

Although DP and LD enable the investigation of spatial distributions of molecular motion with high spatial resolution, these quantities cannot be measured experimentally, unlike the self-diffusion coefficient. Recently, Watanabe et al. examined the relationship between the local self-diffusion coefficient and DP for argon particles near a platinum wall. They identified a linear correlation between these two indices and concluded that high-resolution evaluation of local diffusion properties can be achieved using DP as an alternative to the local self-diffusion coefficient. Since both LD and DP are derived from particle displacement distributions, ,− these findings further support the validity of LD as a physically meaningful indicator of microscopic mobility.

Many numerical studies of solid–liquid interfaces have employed crystalline silica surfaces because they are relatively straightforward to model. ,,− ,,,− In practical applications, such as semiconductor manufacturing processes, however, amorphous materials with varying surface roughness and chemical heterogeneity are more commonly used. Under these conditions, the hydrogen-bond network, adsorption structure, and diffusion properties of water can differ markedly from those on crystalline silica surfaces. As a result, it remains unclear to what extent insights obtained from crystalline surfaces can be applied to amorphous surfaces.

This limited applicability largely stems from the pronounced spatial heterogeneity of amorphous surfaces, for which averaged descriptors may obscure the local environments that govern water dynamics. While the relationship between quantities such as the local self-diffusion coefficient and silanol group density has been investigated, these quantities are typically evaluated as spatially averaged representative values. Consequently, establishing a direct, spatially resolved atomistic relationship between heterogeneous water–silanol hydrogen bonding and the local dynamics of water remains challenging.

Therefore, the aim of this study is to clarify how spatial heterogeneity in silica surface states governs the local hydrogen-bonding structure and diffusion dynamics of water near the interface, beyond what can be captured by spatially averaged descriptors. Using classical molecular dynamics simulations, we quantify the structural and diffusion properties of water near crystalline and amorphous silica walls. Silica surfaces with distinct atomic-scale structures are constructed, and the local self-diffusion coefficient and LD are evaluated within slabs defined along the surface-normal direction. By correlating diffusion metrics with spatial distributions of water density and water–silanol hydrogen bonding, we investigate the molecular origins of the reduced diffusion of water near silica walls with different surface states. The results of this study provide fundamental insights into water behavior near silica–water interfaces, particularly the effects of surface roughness and water penetration on spatial variations in molecular mobility. These findings offer theoretical guidance for tailoring surface structures to control interfacial transport and adsorption in nanofluidic devices and semiconductor wet processing.

Methods

In the present study, molecular dynamics (MD) simulations were performed to investigate the structural and diffusion properties of water in the vicinity of silica walls. All simulations were conducted using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).

Crystalline and amorphous silica were employed as wall materials to elucidate the effects of different silica surface states on the local structure and diffusion behavior of water. α-quartz (100), α-cristobalite (101), and β-cristobalite (111) were used as crystalline silica walls. α-quartz is the most stable crystalline form of silica and has been widely used in experimental and numerical studies. ,,− The α-quartz (100) surface is known to contain two types of silanol groups, Q² and Q³, depending on the cutting position. ,, In the present study, the more stable Q³ silanol configuration was adopted. Although α-cristobalite and β-cristobalite are metastable crystalline forms of silica, they have been used in previous numerical studies because their mass density and silanol density are similar to those of amorphous silica. ,,,

Amorphous silica is used less frequently in simulations than crystalline silica because of the difficulty associated with its modeling and evaluation. ,,, Nevertheless, amorphous silica is widely used in practical applications, including natural oxide films, insulating films, catalyst supports, and coating materials. In this study, three amorphous silica models with different surface roughness and silanol group densities (amorphous silica 1–3) were employed. The structures of the silica walls are shown in Figure S1a–f of the Supporting Information.

Amorphous silica was generated using the melt–quench–cleave method. , In this procedure, crystalline silica was first heated to 5000 K under NP _z T conditions to obtain a molten silica. Under these conditions, only the simulation cell length in the z direction was allowed to fluctuate to maintain a pressure of 1 atm, while the x and y dimensions were kept fixed. The molten silica was equilibrated for 0.8 ns in the NVT ensemble. The system was then cooled at a rate of 1 K/ps under NP _z T conditions to obtain amorphous silica. The mass density and radial distribution function (RDF) peak positions of the resulting amorphous silica structure agree well with the experimental values, , as summarized in Table S1 of the Supporting Information. After the melt-quench process, a vacuum layer was introduced to create free surfaces. For amorphous silica 1 and 2, the simulation cells were cleaved along a flat plane, whereas amorphous silica 3 was generated using the rough-surface cleaving method proposed by Wimalasiri et al. The atoms in the bottom region of the silica slab were fixed, and the silica atoms within 5 Å above the fixed region were maintained at 800 K using a Langevin thermostat with a damping coefficient of 50 fs. The fixed region and the temperature-controlled region are illustrated in Figure . The surface structure was relaxed for 0.8 ns. After relaxation, surface dangling bonds were terminated by attaching OH groups to undercoordinated Si atoms and H atoms to undercoordinated O atoms. The silanol densities and the root-mean-square (RMS) height (S _q) of all silica surfaces are summarized in Table .

1.

Calculation model: amorphous silica–water system. Brown, red, and white spheres represent silicon, oxygen, and hydrogen atoms, respectively.

1. Surface Roughness and Silanol Density of Silica Models.

System	S q nm	Silanol density nm–2
α-quartz (100)	0.36	7.12	7.54
α-cristobalite (101)	0.61	4.50	4.7
β-cristobalite (111)	0.51	4.36	4.35
Amorphous silica 1	1.24	4.75	4.6 ,
Amorphous silica 2	1.01	4.69
Amorphous silica 3	1.38	4.31

Figure shows the silica wall–water system used in the simulations. The dimensions of the simulation cells for the α-quartz–water, α-cristobalite–water, and β-cristobalite–water systems are 4.07 × 3.87 × 9.00, 4.11 × 4.33 × 9.00, and 4.12 × 4.46 × 9.00 nm³, respectively. For the amorphous silica–water systems, the lateral dimensions were fixed at 4.0 × 4.0 nm² for all models, while the cell length in the z direction was 9.0 nm for amorphous silica 1 and 2, and 10.0 nm for amorphous silica 3. The larger z dimension of amorphous silica 3 was required due to the increased surface roughness of the model. In all systems, the distance between the opposing silica walls was approximately 4 nm.

The Tersoff potential was used to model the silica walls because it is widely applied for amorphous silica and accounts for bond-order effects across a wide range of coordination environments. Water molecules were represented using the SPC/E model, a rigid three-site water model that offers relatively low computational cost while reproducing experimental self-diffusion coefficients with reasonable accuracy. The bond length and angles of water molecules were constrained using the SHAKE algorithm. Interactions between the silica walls and water molecules were described using the 12–6 Lennard–Jones (LJ) and Coulombic interactions, as expressed in eq :

$${\phi }_{ij}=\frac{1}{4\pi {\epsilon }_0}\frac{q_i{q}_j}{r_{ij}}+4\epsilon [{\left(\frac{\sigma }{r_{ij}}\right)}^{12}-{\left(\frac{\sigma }{r_{ij}}\right)}^6]$$ 1

where i and j denote particle indices, r _ij represents the distance between particles i and j, and ε ₀ is the vacuum permittivity. Parameters σ and ε were obtained using the Lorentz–Berthelot mixing rules. Atomic charges and LJ parameters for the silica wall atoms and silanol groups were taken from the density-derived electrostatic and chemical (DDEC) force field. , In that work, first-principles calculations were combined with the DDEC method to derive atomic charges that reproduce the electrostatic potential of silica surfaces. The LJ parameters for silica–water interactions were optimized so that interatomic distance distributions obtained with the SPC/E water model reproduce those predicted by first-principles calculations. The atomic parameters used in this study are summarized in Table S2 of the Supporting Information. Atoms labeled with subscripts b, s, and w correspond to silica bulk atoms, silanol group atoms, and water molecules, respectively. Selected sections of the LAMMPS input files used in this study are provided in the Supporting Information.

Periodic boundary conditions were imposed in the directions parallel to the interface (x and y directions), whereas a mirror boundary condition was applied in the direction normal to the interface (z direction). Because the outermost layer of the silica walls is fixed, particles cannot traverse the boundaries in the z direction. As a result, the particle dynamics are effectively non-periodic along the z direction.

The cutoff distances for both the LJ and Coulombic interactions were set to 1.2 nm. Long-range electrostatic interactions were calculated using the particle–particle particle–mesh (PPPM) method with a precision of 1 × 10^–6. To improve the convergence of electrostatic calculations in interfacial systems, the slab correction method proposed by Yeh and Berkowitz was applied. In LAMMPS, this is implemented via the slab option, in which the system is formally treated as periodic in the z direction for the purpose of long-range electrostatic calculations, with empty space introduced between periodic images and dipole inter-slab interactions removed. In the present system, the box length used for long-range electrostatic calculations was extended to three times its original value, thereby suppressing artificial slab–slab interactions.

The velocity Verlet algorithm was used for time integration with a time step of Δt = 0.5 fs. The outermost 5 Å of the silica walls were fixed, while the adjacent 5 Å layer above them was maintained at 298 K using the Langevin thermostat with a damping coefficient of 50 fs. The temperature of the water molecules was initially controlled at 298 K using a Nosé–Hoover thermostat. The simulation procedure was as follows. First, the wall and water systems were equilibrated independently at 298 K. The two systems were then combined, followed by a 2 ns relaxation run. After this equilibration, production data were collected over an additional 38 ns. During both the 2 ns relaxation run and the subsequent 38 ns simulation for data collection, temperature control was applied only to the Langevin-thermostat layer of the silica walls, while the temperature of the remaining wall atoms and water molecules was not controlled.

The diffusion properties of water near solid surfaces differ from those in the bulk and depend strongly on the distance from the wall. ,− ,− ,,, To quantitatively evaluate the diffusion behavior of water near the interface, the local self-diffusion coefficient was calculated following the method proposed in previous studies. In this approach, rectangular local regions (LRs) subdivided along the direction normal to the interface are defined (Figure ). The local self-diffusion coefficient parallel to the interface is then computed for each region by weighting the contribution of water molecules using their survival probability within each LR _k . The local self-diffusion coefficient parallel to the interface (x and y directions), D _k , for each region LR _k , is calculated using the following expressions:

$$D_k=\frac{1}{2}{\int }_0^{\infty }\frac{{⟨\mathit{v}}_i(t_0+t)·{\mathit{v}}_i(t_0)⟩}{P_k}dt$$ 2

$${⟨\mathit{v}}_i(t_0+t)·{\mathit{v}}_i(t_0)⟩=\frac{1}{N_k(t_0)}\sum _i{\mathit{v}}_i(t_0+t)·{\mathit{v}}_i(t_0)$$ 3

$$P_k(t)=\frac{N_k(t_0,t_0+t)}{N_k(t_0)}$$ 4

where v _i represents the velocity vector of oxygen atom i parallel to the interface within LR _k , and ⟨ ⟩ denotes the ensemble average. P _k (t) is the survival probability of an oxygen atom remaining within LR _k , defined as the fraction of the particles that remain continuously in the same region between the initial time t ₀ and t ₀ + t. Particles that leave the region and subsequently re-enter it are not counted as surviving particles. In this study, the velocity components (v _x and v _y ) of the oxygen atoms in water molecules were recorded every 5 fs. The velocity autocorrelation function (VACF) was calculated for each LR _k using time-origin averaging over 11,850 sampling points. The VACF was evaluated up to 15 ps, and the local self-diffusion coefficient was obtained by numerically integrating the VACF according to eq . D _k was determined as the average value of the cumulative integral between 10 and 15 ps. To ensure statistical reliability, five independent simulations with different initial atomic velocities were performed, and the final D _k for each LR _k was obtained by averaging the results from the five simulations. To assess the sensitivity of the calculated D _k to the Langevin damping coefficient and silica slab thickness, additional calculations were performed. As shown in Figures S2–S4 of the Supporting Information, the calculated D _k exhibits little sensitivity to the damping coefficients and slab thicknesses examined in this study.

Water molecules near silica walls experience different interactions depending on their spatial position because each silica surface has a distinct atomic structure. Consequently, the diffusion behavior may be spatially nonuniform. To further elucidate the relationship between atomic-scale phenomenasuch as hydrogen bondingand molecular mobility, it is desirable to evaluate dynamical properties with higher spatial resolution. However, within sufficiently small subregions, the conventional diffusion coefficient cannot be defined in a rigorous manner, because the particle motion does not reach the long-time diffusive regime and frequent transitions across region boundaries violate the assumptions underlying Fickian diffusion. For this reason, we introduce the LD ,,, as an alternative metric to characterize dynamical properties with higher spatial resolution. LD is defined as the particle displacement evaluated at the time at which dynamical heterogeneity is maximal. It quantifies the local mobility, i.e., how easily a particle can move within its local environment. Although LD does not represent diffusivity itself, it is correlated with the diffusion coefficient and thus serves as a useful proxy for spatial variations in molecular mobility at the atomic scale.

In previous studies, M. Fitzner, P. Gasparotto, and their coworkers obtained LD using iso-configurational analysis (ISOCA) to eliminate the influence of thermal fluctuations associated with the same initial particle configuration. , Because the present simulations are in a steady-state regime, statistically stable evaluations of molecular mobility can be obtained from sufficiently long-time averaging. Therefore, rather than employing the ISOCA approach, we adopt a modified definition of LD that reduces sensitivity to thermal fluctuations through time averaging. , The expression for the modified LD is given in eq :

$$L{D}_s={⟨\frac{1}{N_s(t)}\sum _{i,s}|{\mathit{r}}_{i,s}(t_0^{\prime }+t)-{\mathit{r}}_{i,s}(t)|⟩}_t$$ 5

where r _i,s (t) = (x _i (t), y _i (t)) is the two-dimensional in-plane position vector of particle i at time t within a small local region s, and t ₀′ is the time at which the heterogeneity in water molecular motion is maximized. In this study, a single value of t ₀′ = 0.95 ps, derived from SPC/E water bulk at 298 K, was consistently employed in the LD calculations for all systems to ensure comparability across different interfacial systems and local regions. ,,, Additional analyses using alternative t ₀′ values of 0.5 and 1.9 ps are provided in Figures S5–S12 of the Supporting Information. The brackets ⟨ ⟩ denote the ensemble average, and a total of 40,000 samples were used in the LD calculations. The small local region s was defined by further subdividing each LR (Figure ), which had already been partitioned along the z-direction for the calculation of the local self-diffusion coefficient, into 40 subregions in the x and y directions.

Results and Discussion

Water near solid–liquid interfaces is known to exhibit structural characteristics distinct from those of the bulk phase because of strong interactions with the solid surface. − ,− To investigate the influence of each silica wall on the structure of water, the mass densities of silica and water were calculated.

Figure shows the mass density and potential energy profiles of water and silica along the z-direction for the α-quartz–water, α-cristobalite–water, β-cristobalite–water, and three amorphous silica–water systems. The density peaks observed near the silica surfaces indicate the formation of adsorbed water layers. Differences in the density peaks near each silica wall suggest that the adsorption structure of water depends on the surface characteristics of the silica.

2.

Potential energy profiles and mass density profiles of water and silica walls. Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. The red and black dashed lines indicate the solid–liquid interface and the boundaries of the local regions (LRs), respectively.

In the α-quartz–water system, the highest density peak appears at z = 0.25 nm, followed by several smaller peaks, which is consistent with previous studies , reporting such layered interfacial structures. Similar adsorption-layer formation is also observed in the α-cristobalite–water and β-cristobalite–water systems. The mass density maps shown in Figure also confirm the presence of multiple adsorption layers near crystalline silica surfaces. In addition, in the vicinity of the α-cristobalite and β-cristobalite walls, the water density overlaps with the silica walls at approximately z = 0.05 nm. This overlap occurs because water molecules can more easily penetrate the gaps between silanol groups owing to the lower silanol density of α-cristobalite (4.50 nm^–2) and β-cristobalite (4.36 nm^–2) compared with that of α-quartz (7.12 nm^–2). In contrast, such penetration is not observed for α-quartz because of its higher silanol density. The overlap is larger in the β-cristobalite–water system than in the α-cristobalite–water system. This observation suggests that the penetrated water molecules are located closer to the silica wall in the β-cristobalite–water system and therefore interact more strongly with the surface.

3.

Mass density maps of water. Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. The red and black dashed lines indicate the solid–liquid interface and the boundaries of the local regions (LRs), respectively. The red dashed rectangles indicate regions with strong surface interactions, while the black dashed rectangles indicate regions with weak surface interactions.

In the amorphous silica–water systems, at most a single small density peak is observed near the wall, and in some cases, no distinct peak can be identified. This behavior arises because amorphous silica exhibits variations in surface height, as shown in Figure S13 of the Supporting Information, leading to spatial variations in water–surface interactions. As illustrated in Figure d, near the water density peak at z = 0.28 nm, both a high-density region (red dashed rectangle) and a nearly uniform-density region (black dashed rectangle) coexist. In the high-density region, water molecules are located near convex surface features, where strong interactions with the wall promote localized water adsorption. In contrast, in regions with nearly uniform density, the distance between water molecules and the concave surface regions is larger, resulting in weaker interactions and the absence of adsorption. In the water density profile along the z-direction, the density values represent averages over the corresponding x–y plane regions in the density maps. Consequently, the peak in the amorphous silica 1–water system appears smaller than those in the crystalline systems, consistent with previous studies. ,

As in the α-cristobalite and β-cristobalite systems, a region (z < 0.12 nm) exists in which silica and water coexist, indicating that water molecules penetrate the concave regions of the amorphous silica 1 surface. Furthermore, closer to the wall (z < 0 nm), trapped water molecules appear as discrete points in the density map (Figure d). A similar spatial distribution of water, including water penetration into concave surface regions and trapped water molecules near the wall, is observed in the other amorphous silica systems, as shown in Figure e and f, suggesting that the above interpretation is applicable across different amorphous silica models. Because the diffusion of these trapped water molecules is expected to be significantly reduced, the local regions used for diffusion analysis were defined to minimize their influence on the calculated diffusion properties.

For the crystalline silica–water systems, local regions were defined based on the positions of local minima in the water density profile in order to evaluate the self-diffusion coefficient for each adsorption layer. The solid–liquid interface, corresponding to the left boundary of LR₁, was defined as the center-of-mass position of the surface silanol groups. For the bulk region, local regions of constant width were employed. In the crystalline systems, the local minima in the water density profile correspond to local maxima in the potential energy profile of water. In the amorphous silica–water system, however, a clear minimum in the water density profile cannot be identified because silica and water molecules coexist near the interface. Therefore, based on the correspondence observed in the crystalline systems, the boundaries of the local regions were defined using the local maxima in the potential energy profile of water molecules.

As shown in Figure d, three regions were identified according to the potential energy distribution near the amorphous silica 1 surface. Below z = 0 nm, the potential energy of water molecules decreases markedly, corresponding to trapped water molecules that appear as discrete points in the density map. A local minimum in the potential energy (−11.4 kcal mol^–1) is observed between z = 0 and 0.23 nm, which differs from the position of the density peak at z = 0.28 nm. This potential energy minimum corresponds to water molecules located within the concave regions of the amorphous silica surface. Another local minimum is found between z = 0.23 and 0.59 nm, corresponding to the density peak. In this region, water molecules are present both near convex surface features, where strong wall interactions occur, and near concave regions, where interactions are weaker, as shown in Figure d.

Based on these observations, the first local region (LR₁, z = 0–0.23 nm) and the second local region (LR₂, z = 0.23–0.59 nm) in the amorphous silica 1–water system were defined to exclude the influence of the trapped water molecules on the diffusion analysis and to distinguish the effects of concave and convex surface features. The LRs for the amorphous silica 2 and 3–water systems were also defined using a similar procedure. The width of the local regions from LR₃ toward the bulk was fixed at 0.4 nm for all systems. The definitions of the local regions for each silica–water system are summarized in Table S3 of the Supporting Information.

The local self-diffusion coefficients parallel to the interface for each LR _k are shown in Figure and Table S4. In all silica–water systems, the local self-diffusion coefficients in LR₄ and LR₅, which are sufficiently far from the wall surface, are approximately 2.7 × 10^–9 m²/s. This value agrees with the self-diffusion coefficient of bulk SPC/E water reported in previous studies (2.72 × 10^–9 m²/s at 298 K). The local self-diffusion coefficient decreases as the distance from the wall decreases, with the largest reduction of approximately 70% relative to the bulk values observed in LR₁, where water molecules interact most strongly with the silica surface. In a previous study, the bulk water diffusion coefficient was reported as 5.46 × 10^–9 m²/s in the TIP3P water model, whereas the interfacial value was not explicitly given but can be estimated to be approximately 1.5 × 10^–9 m²/s, corresponding to a reduction of approximately 72.5%. Although different water and silica models were employed, this comparable order-of-magnitude reduction supports the robustness of the observed suppression of water mobility in LR₁.

4.

Local self-diffusion coefficients parallel to the interface in various SiO₂–water systems. Red circles, green squares, purple inverted triangles, blue triangles, orange diamonds, and brown pentagons represent the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, amorphous silica 3–water systems, respectively. The black dashed line indicates the self-diffusion coefficient of bulk water. Error bars represent the standard deviation of the local self-diffusion coefficients obtained from five independent simulations. The solid–liquid interface is defined at z = 0.

In LR₁, the local self-diffusion coefficients of water are similar for the α-cristobalite (0.87 × 10^–9 m²/s) and amorphous silica 1 and 2 (0.85 and 0.82 × 10^–9 m²/s) surfaces, whereas the value for the α-quartz surface is slightly higher (1.06 × 10^–9 m²/s), despite α-quartz having the highest silanol density among the six surfaces. Furthermore, the lowest values are observed for the β-cristobalite (0.60 × 10^–9 m²/s) and amorphous silica 3 (0.56 × 10^–9 m²/s) surfaces. Notably, although α-cristobalite and β-cristobalite have similar silanol group densities, the diffusion coefficient is lower in the β-cristobalite–water system than in the α-cristobalite–water system.

This difference can be attributed to the more pronounced penetration of water molecules into the gaps between silanol groups in the β-cristobalite system, as discussed in the density profile analysis. These results suggest that, in crystalline systems, the arrangement of silanol groups may influence the extent of water penetration into the silanol gaps, which in turn affects the diffusion of water molecules parallel to the interface. In contrast, on the α-quartz surface, penetration of water molecules into the wall does not occur because of the high silanol density. Although the motion of water molecules parallel to the interface remains restricted, it is less constrained than in the α-cristobalite and β-cristobalite systems. Consequently, the local self-diffusion coefficient near the α-quartz surface is slightly higher than the corresponding values for α-cristobalite and β-cristobalite. The reduction in diffusivity due to penetration into these silanol gaps has also been discussed in previous studies.

A similar relationship between water penetration and reduced diffusivity is also observed in the three amorphous silica–water systems, where water molecules partially penetrate the surface because of the lower silanol density and surface roughness, thereby suppressing their motion parallel to the interface. Overall, these results indicate that diffusivity cannot be determined by a single factor such as silanol density but instead arises from surface structural characteristics and their influence on the extent of water penetration.

Figures , , and present the LD values, water density maps, and the spatial distribution of water molecules hydrogen-bonded to silanol groups on the x–y plane in LR₁, respectively. The LD maps shown here were obtained using t ₀′ = 0.95 ps. Analyses using alternative t ₀′ values of 0.5 and 1.9 ps yielded qualitatively similar spatial distributions (Figures S5 and S6 of the Supporting Information). In the LD maps, red, blue, and white indicate LD values higher than, lower than, and equal to the bulk value (1.03), respectively. In Figures , , and , black regions correspond either to areas occupied by silica wall atoms, where water molecules are absent, or to areas near silica wall atoms, where fewer than 40 statistical samples were available for the LD analysis. This threshold was adopted because previous studies have demonstrated that statistical reliability is not ensured below this sample count. Note that this criterion is based on the sample count used for LD averaging and is not directly related to the local time-averaged density. Therefore, even regions with low average density may be retained in the analysis if sufficient samples are available for the LD calculation. Hydrogen bonds were identified according to the criteria reported previously and illustrated in Figure S14 of the Supporting Information, namely an O–O distance (|r _oo|) of ≤3.5 Å and an H–O···O angle (β) of ≤30°.

5.

Local diffusivity of water in the first local region (LR₁). Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. Black regions indicate areas where LD values were not evaluated because water molecules were absent due to the presence of silica wall atoms or because fewer than 40 statistical samples were available.

6.

Density distribution in the first local region (LR₁). Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. Black regions indicate areas occupied by silica wall atoms or areas excluded from the LD analysis because fewer than 40 statistical samples were available.

7.

Spatial distribution of water molecules hydrogen-bonded to silanol groups in the first local region (LR₁). Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. Black regions indicate areas occupied by silica wall atoms or areas excluded from the LD analysis because fewer than 40 statistical samples were available.

In LR₁ of the α-quartz, α-cristobalite, β-cristobalite systems, spatial fluctuations in LD reflecting the underlying crystalline surface structure are observed. Regions with a high water density generally exhibit relatively low LD values, whereas regions with lower water density tend to show higher LD values. In the adsorption regions, water molecules form hydrogen bonds with silanol groups, which reduces their mobility and consequently lowers the LD. These results indicate that the mobility of water near the interface does not decrease uniformly but instead shows periodic spatial variations associated with the crystalline surface structure.

In contrast, all three amorphous silica–water systems consistently exhibit non-periodic LD fluctuations owing to the irregular surface structure of amorphous silica. In the region enclosed by the black dashed line in Figure d, the LD value is relatively high (approximately 0.95). This behavior can be attributed to the lower surface height (Figure S13), which increases the distance from the wall and results in weaker solid–liquid interactions. Near the black regions associated with convex surface features, the LD of water is consistently reduced across all amorphous silica surfaces. These results suggest that, in the vicinity of amorphous silica, water mobility is strongly influenced not only by interactions with local silanol groups but also by geometric factors, such as local variations in the distance from the interface arising from surface height variations and the degree of confinement imposed by the surrounding surface features.

To quantitatively examine the relationship between the reduction in LD and both the water density distribution and the spatial distribution of water molecules hydrogen-bonded to silanol groups, correlation coefficients were calculated, as shown in Figure . The correlation analysis included only local regions with valid LD values and excluded regions with insufficient sampling for LD evaluation. The scatter plots used to compute these correlations are presented in Figures S15 and S16 of the Supporting Information. The corresponding analyses using alternative t ₀′ values are provided in Figures S7–S12 of the Supporting Information and show only minor changes in the correlation coefficients.

8.

Correlations between LD and the water density distribution, and between LD and the spatial distribution of water molecules hydrogen-bonded to silanol groups.

For the α-quartz, α-cristobalite, β-cristobalite and three amorphous silica (models 1–3)–water systems, the correlation coefficients between LD and the water density distribution are −0.88, −0.91, −0.73, −0.67, −0.77 and −0.57, respectively. The crystalline systems exhibit strong negative correlations, whereas the amorphous systems show a moderate negative correlation overall, with variability depending on surface structure. These results indicate that water mobility decreases in regions with higher water density, a trend that is particularly pronounced for crystalline surfaces.

Similarly, the correlation coefficients between LD and the spatial distribution of water molecules hydrogen-bonded to silanol groups are −0.84, −0.86, −0.72, −0.63, −0.68, and −0.53 for the α-quartz, α-cristobalite, β-cristobalite and three amorphous silica systems, respectively. These results suggest that, in the amorphous silica–water systems, factors other than hydrogen bonding with silanol groups may also contribute to the reduction in water mobility.

These smaller correlation coefficients observed in the amorphous systems, compared with the crystalline silica–water systems, may be attributed to (i) the presence of regions with nearly uniform water density within LR₁ and (ii) reduced diffusion caused by direct interactions with bulk Si and O atoms exposed on the wall surface. A more detailed investigation of the influence of amorphous silica surface conditions is therefore required; however, this topic is beyond the scope of the present study and will be considered for future work.

Figures and show the LD and water density maps on the x–y plane in the LR₂. In the α-quartz and α-cristobalite systems, the weak spatial dependence of LD in LR₂ is attributed to hydrogen bonding with low-diffusivity water molecules located in LR₁, which mitigates the local influence of the wall surface structure. In contrast, the LD of water in LR₂ of the β-cristobalite and three amorphous silica–water systems exhibits clear spatial variation. In the β-cristobalite–water system, water molecules penetrate closer to the wall compared to the other crystalline systems. As a result, water molecules in LR₂ are partially subject to direct interactions with silanol groups, leading to enhanced spatial heterogeneity in LD. In the amorphous silica systems, LD decreases in regions with higher surface height because of stronger surface interactions (indicated by red dashed rectangles), whereas it increases in regions with lower surface height owing to weaker interactions (indicated by black dashed rectangles).

9.

Local diffusivity of water in the second local region (LR₂). Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. The red dashed rectangles indicate regions with strong surface interactions, while the black dashed rectangles indicate regions with weak surface interactions.

10.

Density distribution in the second local region (LR₂). Panels (a–f) correspond to the α-quartz (100)–, α-cristobalite (101)–, β-cristobalite (111)–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. The red dashed rectangles indicate regions with strong surface interactions, while the black dashed rectangles indicate regions with weak surface interactions.

These observations are further supported by the probability distributions of the spatial LD values provided in the Supporting Information (Table S5 and Figure S17). The probability distributions in LR₁ show relatively large standard deviations, indicating that LD in LR₁ varies substantially depending on the spatial location. In contrast, the standard deviation of LD in LR₂ is small for all systems considered, indicating that spatial variations in LD are smaller in LR₂ than in LR₁. Among these systems, the α-quartz–water system exhibits the smallest standard deviation (0.014), whereas the amorphous silica 3–water system shows the largest value (0.041). The β-cristobalite–water system also exhibits a relatively large standard deviation (0.031), and its probability distribution is characterized by a bimodal profile. This indicates the presence of distinct regions where water molecules experience either strong or weak interactions near the β-cristobalite surface. Consequently, the β-cristobalite and amorphous silica–water systems exhibit large spatial variations in LD, which is consistent with the above observations.

These results indicate that LD varies significantly depending on the spatial location, even when the diffusion coefficient is approximately the same in the region closest to the wall (LR₁). Regions with reduced LD correspond to adsorption regions where water molecules form hydrogen bonds with silanol groups. However, in the amorphous silica–water systems, the observed behavior cannot be explained solely by hydrogen bonding with silanol groups. It is likely influenced by the presence of regions with near-bulk-like water density and interactions with exposed Si and O atoms at the surface. Furthermore, the decrease in LD observed in LR₂ is mainly caused by indirect interactions with the wall mediated by water molecules in LR₁ for α-quartz (100) and α-cristobalite (101) surfaces. In the β-cristobalite–water system, water molecules penetrate closer to the wall than in other crystalline systems, causing partial interactions with silanol groups and resulting in enhanced spatial heterogeneity in LD. In the amorphous silica–water systems, the reduction in LD is likely attributable to direct interactions with the convex regions of the wall, as evidenced by the decrease in LD in regions with higher surface height (Figures and S13).

The mobilities of water molecules in LR₁ vary depending on the spatial location, and hydrogen bonding with silanol groups plays an essential role. To further clarify how hydrogen bonding contributes to the reduced diffusivity in LR₁, we examined the effect of each wall surface on the velocity autocorrelation function (VACF) of the water near the interface. Figure shows the VACF of water in the direction parallel to the interface. The deviation from the bulk value around t ≈ 0.1 ps depends on the type of silica wall and decreases in the order β-cristobalite, amorphous silica 3, α-cristobalite, amorphous silica 2, amorphous silica 1, and α-quartz. Previous studies have suggested that the feature observed around t ≈ 0.1 ps in the VACF of bulk water originates from changes in the direction of hydrogen bonds between water molecules. − Accordingly, the orientation of hydrogen bonds formed between water molecules and silanol groups in LR₁ may also play an important role in the present systems.

11.

Velocity autocorrelation function (VACF) of water oxygen atoms. Red, green, purple, blue, orange, and brown lines represent the α-quartz–, α-cristobalite–, β-cristobalite–, amorphous silica 1–, amorphous silica 2–, and amorphous silica 3–water systems, respectively. The black dashed line represents bulk SPC/E water.

Figure shows the distribution of hydrogen bond orientations between silanol groups and water molecules in LR₁. In this representation, cos θ = −1, 0, and 1 indicate that water molecules are located above, adjacent to, and below the silanol groups, respectively. In the vicinity of the amorphous silica 3 and β-cristobalite walls, which exhibit the largest deviations from the bulk VACF at t = 0.1 ps, the hydrogen bond orientations are broadly distributed around cos θ ≈ −0.25. In comparison, in the vicinity of the amorphous silica 1 and amorphous silica 2, and α-cristobalite walls, which exhibit the next largest deviations from the bulk VACF at t = 0.1 ps, the hydrogen bond orientations are broadly distributed around cos θ ≈ −0.4.

12.

Distribution of the angle between the hydrogen bond vector (water–OH group) and the interface normal vector.

These distributions suggest that systems exhibiting larger deviations in the VACF tend to have a higher fraction of water molecules located laterally adjacent to silanol groups at the interface. In contrast, near the α-quartz wall, the distribution is centered around cos θ ≈ −0.75, indicating that water molecules preferentially occupy positions above the silanol groups. These results suggest that the change in hydrogen bond orientation associated with the parallel motion of water near the interface is most pronounced in the β-cristobalite and amorphous silica 3 systems, followed by the α-cristobalite and other amorphous silica systems, whereas it is least pronounced in the α-quartz system. This enhanced reorientation is consistent with the more pronounced deviation in the VACF at t = 0.1 ps and contributes to the reduced diffusion observed in LR₁ (Figure ).

Conclusion

In this study, the effects of different silica surface states on the local structure and diffusion properties of water molecules near silica walls were evaluated by analyzing the mass density profile, local self-diffusion coefficient, local diffusivity (LD), and hydrogen-bonding characteristics.

The adsorption structures of water near the interface were found to be strongly influenced by variations in surface structure and silanol group density. Water density maps on the x–z plane reveal that, for crystalline silica surfaces, adsorption layers form uniformly across the entire wall surface. In contrast, for amorphous silica, regions of high and low water density coexist near the surface because of local variations in surface roughness. Consequently, the density profile along the direction normal to the interface exhibits multiple pronounced peaks in the crystalline silica–water systems, whereas in amorphous silica–water systems, at most a single density peak is observed near the wall, and in some cases, no distinct peak can be identified. In amorphous silica systems, water penetration into the surface is primarily induced by geometrical factors such as surface roughness and local concave features. In contrast, in crystalline silica systems, water penetration may be influenced by the density and spatial arrangement of surface silanol groups.

To characterize diffusion behavior near the wall, the local self-diffusion coefficients were evaluated. The local self-diffusion coefficient of water decreases as the distance from the wall decreases, with the most significant reduction observed in the region closest to the surface (LR₁). In LR₁, the lowest local self-diffusion coefficients are observed near the β-cristobalite (0.60 × 10^–9 m²/s) and amorphous silica 3 (0.56 × 10^–9 m²/s) surfaces. These are followed by comparable local self-diffusion coefficients observed near the amorphous silica 2 (0.82 × 10^–9 m²/s), amorphous silica 1 (0.85 × 10^–9 m²/s) and α-cristobalite (0.87 × 10^–9 m²/s) surfaces but slightly higher near the α-quartz surface (1.06 × 10^–9 m²/s), despite its highest silanol density among the six surfaces. Among the crystalline systems, the diffusivity is lowest for the β-cristobalite–water system, where the overlap between the silica and water density distributions is most pronounced. These results indicate that diffusivity cannot be determined by a single factor such as silanol density alone, but instead arises from the interplay of multiple factors, including density overlap and surface structural characteristics.

The spatial distribution of LD near each silica surface exhibits strong local variation. Even for crystalline silica surfaces with relatively flat structures, LD does not decrease uniformly but instead displays periodic fluctuations reflecting the periodic surface structure. In contrast, such periodicity is absent near amorphous silica surfaces because the surface height varies spatially. The LD is enhanced in concave regions due to the increased separation from the surface, whereas it is suppressed in regions directly above and surrounding convex surface features because of stronger solid–liquid interactions. Significant correlations were observed between LD and both the water density distribution and the spatial distribution of water molecules hydrogen-bonded to silanol groups. Strong negative correlations were found near crystalline silica surfaces, whereas a moderate negative correlation was observed near the amorphous silica surface. These results indicate that, consistent with previous studies, hydrogen bonding between water molecules and silanol groups plays a key role in governing water diffusion near crystalline silica surfaces. The smaller correlation coefficients observed in the amorphous systems, compared with coefficients observed in the crystalline silica–water systems, may be attributed to (i) the presence of regions with nearly uniform water density within LR₁ and (ii) reduced diffusion caused by direct interactions with bulk Si and O atoms exposed on the wall surface. These findings suggest that factors other than hydrogen bonding with silanol groups may also contribute to the reduction of water diffusivity near amorphous silica surfaces. Consequently, insights obtained from crystalline systems cannot be directly applied to amorphous systems. Further investigation is needed to clarify the respective roles of hydrogen bonding and other possible surface-interaction mechanisms in reducing water diffusivity near amorphous silica surfaces.

To further clarify the influence of hydrogen bonding on the reduction of water diffusivity in LR₁, the effects of each wall surface on the velocity autocorrelation function (VACF) of water and on the orientation of hydrogen bonds between silanol groups and water molecules were examined. The deviation of the VACF from the bulk value around t ≈ 0.1 ps depends on the silica surface type and decreases in the order β-cristobalite, amorphous silica 3, α-cristobalite, amorphous silica 2, amorphous silica 1, and α-quartz. In the β-cristobalite, α-cristobalite and amorphous silica systems (all three models), water molecules forming hydrogen bonds with silanol groups are predominantly located laterally adjacent to the silanol sites, whereas in the α-quartz system they are preferentially located above the silanol groups. Consequently, the change in hydrogen bond orientation induced by molecular motion parallel to the interface is greater for the β-cristobalite, three amorphous silicas and α-cristobalite systems than for the α-quartz system. This difference explains the variation in the magnitude of the VACF feature observed around t ≈ 0.1 ps and contributes to the reduced diffusion observed near the interface.

The results of this research provide a fundamental understanding of water behavior that will be useful for interface design in nanofluidic devices and semiconductor manufacturing processes where interface influences are dominant.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.6c02123.

• Radial distribution functions of amorphous silica; silica–water force-field parameters; definitions of local regions in all solid–liquid systems; local self-diffusion coefficients for all systems; standard deviations of the spatial distributions of local diffusivity in each local region; structural models of silica walls; slab-thickness dependence of local self-diffusion coefficients; effects of the Langevin damping coefficient on local self-diffusion coefficients; surface height maps; definition of hydrogen bonds; scatter plots of local diffusivity versus water density and the probability density of water molecules hydrogen-bonded to silanol groups; and LAMMPS input settings for intermolecular interactions (PDF)

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.