Molecular Origin of Adhesion at Epoxy Resin–Titania Composite Interfaces: Crystal Phase and Hydroxylation Effects

Abstract

Polymer nanocomposites composed of polymer matrices and inorganic fillers are widely used in structural materials, coatings, and electronics. Bisphenol A epoxy resins are commonly employed as matrix materials, and the incorporation of various inorganic nanoparticles has been investigated to impart additional functionalities. Titanium dioxide (TiO₂) with anatase (A), brookite (B), and rutile (R) crystal phases has attracted attention as a promising nanofiller, but molecular understanding of the interfacial adhesion mechanism with epoxy resins remains limited. In this study, we performed density functional theory (DFT) calculations to analyze the interfacial interactions between a fragment model of bisphenol A epoxy resin and three TiO₂ crystal surfaces. Both pristine surfaces and hydroxylated surfaces, considering the chemisorption of atmospheric moisture, were examined. The results revealed that adhesion performance depends on the crystal structure. The pristine R-TiO₂ surface exhibited the highest adhesive strength, attributed to the highly active titanium atoms exposed on the surface. On hydroxylated surfaces, A-TiO₂ also showed strong adhesion, which was explained by the formation of multiple hydrogen bonds induced by its sawtoothed surface structure. In contrast, B-TiO₂ exhibited low adhesion performance for both pristine and hydroxylated surfaces. These findings provide molecular insights into the interfacial adhesion mechanism between epoxy resins and TiO₂ nanoparticles, offering theoretical guidelines for the design of nanocomposites with adjusted interfacial properties.

1. Introduction

Polymer composite technology plays a vital role in modern society, with widespread applications in structural materials, protective coatings, and electronic substrates. − Composite materials are generally composed of two main components: a polymer matrix and a nanofiller. Bisphenol A epoxy resin is one of the most typical polymer matrices, and its chemical structure is shown in Figure . Although epoxy resins have high chemical stability and heat resistance, − their inherent brittleness leads to low impact and fracture strength. , To overcome these limitations, recent research has focused extensively on the development of composite materials incorporating nanofillers. Nanofillers, when dispersed in the matrix, significantly modify the mechanical, optical, thermodynamic, and electronic properties of the composites, enabling functionalities beyond the intrinsic capabilities of epoxy resin.

1.

Chemical structures of bisphenol A epoxy resin and its fragment model (FER).

One of the most promising nanofillers for enhancing the performance of epoxy resins is titania (TiO₂) nanoparticles. TiO₂ particles have excellent ultraviolet (UV) shielding ability, corrosion resistance, and biocompatibility, enabling a wide range of applications. For example, incorporating TiO₂ nanoparticles into epoxy resin–based anticorrosive coatings for carbon steel has been shown to suppress UV-induced degradation of the coating. Furthermore, when epoxy resin-TiO₂ nanocomposites are used as admixtures in mortar, the tensile strength increases with higher TiO₂ particle concentrations.

TiO₂ exists mainly in three crystal polymorphs: anatase (A-TiO₂), brookite (B-TiO₂), and rutile (R-TiO₂). The thermodynamically stable phase of TiO₂ particles depends on their size. As illustrated in Figure a, previous studies have shown that A-TiO₂ is stable below 11 nm, B-TiO₂ between 11 and 35 nm, and R-TiO₂ above 35 nm. Despite extensive research, the interfacial interactions between epoxy resin and the various crystal surfaces of TiO₂ remain insufficiently understood. Since the long-term durability of composites is largely determined by the interfacial adhesion between the polymer matrix and nanofillers, much attention has been devoted to clarifying how the TiO₂ crystal structure influences interfacial interactions. In recent years, adhesion has increasingly been recognized as a typical multiscale phenomenon, encompassing both macroscopic structural and mechanical responses as well as microscopic factors such as intermolecular interactions at interfaces. In fact, it has been demonstrated that as the particle size of nanofillers decreases, the specific surface area increases, resulting in a larger number of interfacial interaction sites and consequently enhancing the tensile strength of composite materials. Thus, in optimizing the functional properties of nanocomposites, not only the type of nanofiller but also the selection of particle size is important. However, direct experimental observation of adhesive interfaces is hindered by their being buried within the constituent materials, leaving the molecular understanding of adhesion mechanisms still limited. Consequently, theoretical clarification of the interactions contributing to adhesion between epoxy resins and TiO₂ particles is required.

2.

(a) Three TiO₂ crystal structures. (b) Most stable surfaces (1a, 2a, and 3a) of A-TiO₂, B-TiO₂, and R-TiO₂. (c) Hydroxylated surfaces (1aw, 2aw, and 3aw) of A-TiO₂, B-TiO₂, and R-TiO₂.

In recent years, theoretical approaches such as density functional theory (DFT) calculations and molecular dynamics (MD) simulations have been increasingly employed to elucidate adhesion mechanisms. − These methods have been extensively applied to analyze chemical interactions between adhesives and adherends, covering a wide range of systems from industrial and dental applications to advanced functional materials. In this work, we conducted DFT-based analyses of the adhesion mechanism at the interface between epoxy resin and TiO₂ surfaces. The findings deepen the molecular understanding of interfacial interactions in epoxy resin/TiO₂ composite materials and provide theoretical guidelines for optimizing particle sizes and surface structure to achieve enhanced adhesion performance.

2. Materials and Methods

2.1. Modeling of Adherend Surfaces

The crystal structures of A-TiO₂, B-TiO₂, and R-TiO₂ were optimized using DFT calculations. The optimized bulk structures are presented in Figure a. For surface modeling, the most stable surface of each structure was cleaved, and a vacuum region of approximately 20 Å was added to avoid unintentional interactions across periodic boundaries. Subsequent DFT optimization yielded the surface models 1a, 2a, and 3a, as shown in Figure b. During optimization, the topmost and bottommost atomic layers were allowed to relaxed, while the middle layers were fixed. These surfaces correspond to the (101), (210), and (110) surfaces of A-TiO₂, B-TiO₂, and R-TiO₂, respectively. Their unit cells were expanded to A-TiO₂―p(1 × 4) (10.24 × 15.14 Ų), B-TiO₂―p(2 × 1) (10.98 × 19.13 Ų), and R-TiO₂―p(2 × 2) (11.84 × 12.99 Ų) supercells. These supercell sizes were chosen to provide sufficient space for the FER molecule.

All structures were visualized using the VESTA software. To account for the chemisorption of atmospheric moisture, hydroxylated surface models (1aw, 2aw, and 3aw) were also constructed, as illustrated in Figure c. It should be noted that most titania surfaces exhibit high affinity for water molecules, resulting in high coverage, and water molecules readily undergo dissociative adsorption on titania surfaces. , Thus, under typical experimental conditions where moisture is present in air, such a fully hydroxylated surface can be a plausible candidate. Hydroxylation was introduced by placing OH groups on the surface Ti atoms and H atoms on the neighboring O atoms of models 1a–3a, followed by DFT optimization. Although the reactivity for dissociative adsorption may change depending on the degree of water coverage, a systematic investigation of coverage dependence is beyond the scope of this study and will be addressed in future studies.

All periodic DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP 5.4.4). − The generalized gradient approximation was employed with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional. To account for dispersion interactions, the Grimme D3BJ scheme was applied. The Kohn–Sham (KS) equations were solved using the projector augmented wave (PAW) method , with a plane-wave basis set. The plane-wave cutoff energy was set to 500 eV, and the self-consistent field (SCF) convergence criterion was set to 1.0 × 10^–5 eV. Geometry optimizations were performed until the forces on each atom were less than 0.03 eV Å^–1. The Brillouin zone was sampled using a Γ-centered k-point mesh with a spacing of 2π × 0.05 Å^–1.

2.2. Modeling of Adhesive Interfaces

A fragment molecule representing epoxy resin (Figure ), referred to as the fragmented epoxy resin (FER), was used as the adhesive model. The FER model has been extensively used in previous theoretical studies to investigate microscopic interfacial interactions. − ,, It has also been demonstrated that differences in fragment termination have only a minor impact on the computed adhesive strength. To explore the stable geometries of the FER molecule on each TiO₂ surface, initial configurations were generated by randomly placing the FER molecule on the surfaces, followed by molecular dynamics (MD) simulations using the Forcite module in Materials Studio. Each TiO₂ surface was extended into a supercell sufficiently large to accommodate the FER molecule. To adequately sample the conformational space, MD simulations were performed in the NVT ensemble at 500 K using the Nosé–Hoover thermostat with the Dreiding force field. The time step was 1.0 fs, and the trajectories were propagated for 20.0 ns. During the simulations, all TiO₂ atoms were fixed, while the FER molecule was fully relaxed. Snapshots were extracted every 200.0 ps, and each was subsequently optimized to obtain 100 locally stable geometries. Among these, 10 energetically stable geometries were selected for DFT optimizations. In the DFT calculations, the FER molecule and the topmost TiO₂ layer were allowed to relax, while the remaining layers were kept fixed. The most stable structure was adopted as the interfacial model.

By applying this workflow to both pristine (1a–3a) and hydroxylated (1aw–3aw) surfaces, the optimized interfacial structures 1b–3b and 1bw–3bw were obtained, as shown in Figure . These models contained 178, 178, 178, 226, 250, and 226 atoms, respectively. The workflow was designed to prevent trapping in local minima and allows sufficient exploration of the conformational space, using an elevated temperature (500 K) and relatively long time-evolution (20 ns). The obtained metastable structures, shown in Figure S1, are similar to the global minimum, with energy differences of approximately 0.1 eV. In all low-energy structures, the hydroxyl group of the FER molecule interacts in a qualitatively similar manner with surface Ti atoms or hydroxyl groups. It should be noted that the present interfacial models do not include the effects of polymer chain entanglement and curing agents. For example, previous experimental and theoretical studies have suggested that low molecular weight amine curing agents can aggregate at filler interfaces. , In contrast, the primary purpose of this study is to elucidate the molecular origins of how differences in crystal phase affect the interfacial affinity with epoxy resins. Accordingly, we adopt the simplified FER model to focus on the interfacial interactions between the functional groups of the epoxy resin and the crystal surfaces. While this model does not capture all aspects of real composite interfaces, the trends obtained here can be fundamental atomistic insights into the intrinsic affinity between the epoxy resin and the filler surface. While the effects of polymer chain entanglement and curing agents are important for understanding realistic adhesive interfaces, the investigation is beyond the scope of this study. First-principles studies considering curing agents have previously been conducted for carbon materials and copper surfaces.

3.

Adsorption structures of fragmented epoxy resin (FER) molecules. (a) A-TiO₂, (b) B-TiO₂, and (c) R-TiO₂. Adsorption structures for pristine surfaces are 1b, 2b, and 3b, and for hydroxyl surfaces are 1bw, 2bw, and 3bw. The FER molecule is surrounded by purple lines.

2.3. Calculation of Adhesive Strength

The tensile adhesive stress of the FER molecule was evaluated by differentiating the potential energy curve with respect to vertical displacement during detachment from the surface. The energy curves were obtained for the six interfacial structures (1b–3b and 1bw–3bw) by incrementally separating the FER molecule from the surface in 0.2 Å steps up to 8.0 Å, followed by a single-point energy calculation at each step. Each curve was plotted with the equilibrium adsorption position defined as Δr = 0.0 Å, and fitted to a Morse potential function of the form:

$$E=E_{\mathrm{ad}}{(1-e^{-a\mathrm{\Delta }r})}^2$$ 1

Here, E _ad denotes the adhesion energy, and a is a parameter characterizing the potential width. The fitted energy curve was differentiated with respect to displacement (Δr) to obtain the adhesive stress (S), which is expressed as

$$S=\frac{1}{A_{\mathrm{cell}}}·\frac{\mathrm{d}E}{\mathrm{d}\mathrm{\Delta }r}$$ 2

where A _cell denotes the surface area of the cell. The maximum value of S was defined as the adhesive strength S _ad, which can be analytically obtained as the product of E _ad and a, given by

$$S_{\mathrm{ad}}=\max (S)=\frac{a{E}_{\mathrm{ad}}}{2A_{\mathrm{cell}}}$$ 3

The total energy E can be decomposed into the dispersion correcti on term (E _dispersion) and the Kohn–Sham DFT energy (E _DFT):

$$E=E_{\mathrm{dispersion}}+E_{\mathrm{DFT}}$$ 4

The E _DFT term was fitted to a Morse potential shifted by α and β along the x and y axes:

$$E=E_{\mathrm{ad}}(1-e^{-a(\mathrm{\Delta }r-\alpha )}{)}^2+\beta$$ 5

The E _dispersion term was then obtained as the difference between E and E _DFT. Differentiating eq with respect to displacement yields the total adhesive stress S as the sum of its dispersion and DFT contributions (S _dispersion and S _DFT):

$$S=S_{\mathrm{dispersion}}+S_{\mathrm{DFT}}$$ 6

This decomposition enables identification of the origin of adhesive stress based on the magnitudes of the dispersion and DFT components.

2.4. Visualization of Interfacial Interactions Based on Charge Density

To visualize the interfacial interactions accompanied by changes in charge density between the FER molecule and the TiO₂ surface, the difference of charge density was calculated as follows:

$$\mathrm{\Delta }{\rho }_{\mathrm{ad}}={\rho }_{\mathrm{complex}}-({\rho }_{\mathrm{surface}}+{\rho }_{\mathrm{adhesive}})$$ 7

Here, ρ_interface denotes the charge density of the FER/TiO₂ interface, and ρ_surface and ρ_FER represents that of the TiO₂ surface and the isolated FER molecule. The ρ_surface and ρ_FER were calculated separately, with their atomic coordinates fixed to those in the optimized interfacial complex.

To quantify the strength of the interactions between specific atomic pairs at the adhesive interface visualized by the charge density difference analysis, integrated crystal orbital Hamilton population (ICOHP) analysis was performed using LOBSTER v4.1.0. The ICOHP value represents the bond energy between two atoms. , The more negative the ICOHP value, the stronger the interaction.

3. Results and Discussion

3.1. Adhesive Stress Curves and Decomposition Analysis

Figure a presents the adhesive stress curves between the FER molecule and the pristine TiO₂ surfaces. The adhesive stress curves of 1b (A-TiO₂), 2b (B-TiO₂), and 3b (R-TiO₂), are rep resented by black, blue, and red lines, respectively. Their maximum values, the adhesive strengths (S _ad), are summarized in Figure b. The result clearly demonstrate that S _ad depends on the crystal structure, with values of 1137, 411, and 1536 MPa for 1b, 2b, and 3b, respectively (3b > 1b > 2b). The R-TiO₂ surface (3b) exhibits the highest S _ad, while the B-TiO₂ surface (2b) shows a remarkably low value. The Morse potential parameters (E _ad, a) related to S _ad for 1b, 2b, and 3b, as shown in Table , were (1.96 eV, 1.12 Å^–1), (1.05 eV, 1.01 Å^–1), and (2.62 eV, 1.13 Å^–1), respectively. The order of the adhesion energy E _ad (3b > 1b > 2b) is consistent with that of S _ad. These results indicate that the E _ad plays a crucial role in the S _ad at the pristine TiO₂ surfaces.

4.

(a, b) Adhesive stress curves and adhesive strength for pristine TiO₂ surfaces. (c, d) Adhesive stress curves and adhesive strength for hydroxylated TiO₂ surfaces.

1. Morse Potential Parameters for 1b –3b and 1bw – 3bw .

	1b	2b	3b	1bw	2bw	3bw
E ad (eV)	1.96	1.05	2.62	2.07	1.81	1.79
a (Å–1)	1.12	1.01	1.13	1.14	1.12	1.21

^a E _ad and a are the adhesive energy and parameter characterizing the potential width, respectively.

Figure c shows the adhesive stress curves for 1bw, 2bw, and 3bw. The black, blue, and red lines correspond to 1bw, 2bw, and 3bw, respectively. The S _ad was 1223, 772, and 1127 MPa, respectively (Figure d). Surface hydroxylation affected S _ad by +8%, +88% and −27% for A-TiO₂, B-TiO₂ and R-TiO₂, respectively, resulting in an increase for A-TiO₂ and B-TiO₂ and a decrease for R-TiO₂. The corresponding Morse potential parameters (E _ad, a) were (2.07 eV, 1.14 Å^–1), (1.81 eV, 1.12 Å^–1), and (1.79 eV, 1.21 Å^–1). The order of E _ad (1bw > 2bw > 3bw) differs from that of S _ad (1bw > 3bw > 2bw). This result indicates that not only E _ad but also a contributes to adhesion. Since S _ad is expressed as the product of E _ad and a in eq , both the depth (E _ad) and the width (a) of the potential energy well contribute to adhesive strength. Interestingly, S _ad for the A-TiO₂ surface (1bw) increased while S _ad for the R-TiO₂ surface (3bw) decreased, making 1bw the most adhesive performance among the hydroxylated surfaces. Although S _ad also increased for the B-TiO₂ surface (2bw), its adhesive strength remained lower than those of the other surfaces.

What causes the effects of the crystal structures and the hydroxylated surfaces? To clarify these reasons, the energy and adhesive stress curves were decomposed into dispersion and DFT components. In Figure , the gray, red, and blue bars correspond to the maximum total, DFT, and dispersion components of the adhesive stress curves, respectively. Here, since the shown DFT and dispersion values correspond to the maximum on each curve, their simple sum does not match the total value (S _ad). As shown in Figure a, the dispersion contribution is dominant for 1b, 2b, and 3b, with values of 981, 460, and 1043 MPa, respectively. However, as shown in Figures S1 and S2, the dispersion component rapidly decays with increasing displacement. The DFT contribution, which reflects electrostatic and charge transfer interactions, is significant to the overall adhesive strength. The DFT component values were 373, 82, and 553 MPa for 1b, 2b, and 3b, respectively. Both the dispersion and DFT components follow the same trend as S _ad. These results suggest that the differences in crystal structure affect both the dispersion and DFT contributions to adhesion. Here, the values of the DFT and dispersion components at the displacement giving each S _ad are shown in Figure S3.

5.

Maximum values of DFT and dispersion components obtained by decomposition of the adhesive stress curve. (a) Pristine surfaces and (b) hydroxylated surfaces.

For the hydroxylated surfaces (Figure b), the dispersion components for 1bw, 2bw, and 3bw are 798, 536, and 655 MPa, respectively, and their order corresponds to that of the total adhesive strength. The DFT components are 637, 340, and 495 MPa, respectively, which also follow the same trend as the total adhesive strength. This indicates that the dispersion and DFT components provide the important contribution to adhesion. Notably, the DFT component increases for 1bw and 2bw compared to 1b and 2b, while it decreases for 3bw compared to 3b. These results suggest that surface hydroxylation enhances the DFT contribution for A-TiO₂ and B-TiO₂ but reduces for R-TiO₂. What kind of interfacial interactions underlie these changes? In the following section, we discuss the interfacial interactions contributing to these differences in adhesive strength based on the adsorption structures and charge densities.

3.2. Interfacial Interactions at FER/Pristine TiO₂ Surface Systems

To visualize the interfacial interactions on the pristine TiO₂ surfaces (1b, 2b, and 3b), charge density difference analysis was performed. Figure a,c,e show the changes of charge density for 1b, 2b, and 3b, respectively, where yellow and cyan regions represent charge accumulation and depletion. For clarity, only the surface layer is displayed, and the isosurface value (ISV) was set to 0.003 e/ų. Figure b,d,f present magnified views of the regions exhibiting pronounced interactions in 1b, 2b, and 3b, respectively.

6.

(a, c, e) Charge density differences for 1b, 2b, and 3b. (b, d, f) Magnified views of the interaction sites of 1b, 2b, and 3b. Ti_5c and O_2c represent the five-coordinated titanium and two-coordinated oxygen atoms, respectively.

For 1b (Figure b), two main interaction sites are observed. The hydroxyl group of the FER molecule forms interaction (1), and the phenyl group forms interaction (2) with the surface. For interaction (1), (1A) corresponds to a hydrogen bond between the hydrogen atom of the hydroxyl group in the FER molecule and an oxygen atom on the surface, where electron donation occurs from the surface oxygen atom. (1B) corresponds to the interaction between the oxygen atom of the FER hydroxyl group and a titanium atom on the surface, in which the oxygen atom of the FER molecule donates electrons to the surface titanium atom. The ICOHP values for (1A) and (1B) are −0.17 and −0.96 eV, respectively, indicating that the (1B) interaction is stronger. This can be attributed to the high Lewis acidity of the five-coordinated titanium (Ti_5c) atom. Additionally, the two-coordinated oxygen (O_2c) atoms possess relatively high Lewis basicity, which also contributes to the formation of interfacial interactions. As for (2), (2A) corresponds to the metal-π interaction between the phenyl group of the FER molecule and the titanium atom on the surface, and its ICOHP value is −0.17 eV. (2B) corresponds to the interaction between the phenyl group and the oxygen atom on the surface, and its ICOHP value is −0.07 eV. Although these interactions are weaker than (1B), it can still be significant because the repeating unit of the epoxy resin contains two benzene rings, and curing agents often include phenyl groups as well.

For 2b (Figure d), only the hydroxyl group of the FER molecule is involved. This interaction (1) consists of (1A) between the oxygen atom of the FER hydroxyl group and a titanium atom on the surface, and (1B) between the hydrogen atom of the FER hydroxyl group and an oxygen atom on the surface. The corresponding ICOHP values are −0.07 and −0.48 eV, respectively, giving a small total |ICOHP| value of 0.55 eV. This result confirms the weak interfacial interaction in B-TiO₂. The low S _ad value for 2b compared with the other surfaces can be attributed to the weak interaction between the surface titanium atoms and the FER molecule at site (1A). The 2b surface structure features protruding surface OH groups and recessed titanium atoms, which prevents the formation of strong interactions with the titanium atoms. This structural characteristic is considered the main reason for the low S _ad value of 2b.

For 3b (Figure f), two interaction sites are observed, similar to those in 1b. These correspond to (1) the structure around the hydroxyl group and (2) the phenyl group of the FER molecule. Interaction (1) involves three atom pairs: (1A) an interaction between the hydrogen atom of the carbon chain in the FER molecule and titanium atoms on the surface, (1B) a hydrogen bond between the hydrogen atom of the hydroxyl group in the FER molecule and a surface oxygen atom, and (1C) an interaction between the oxygen atom of the hydroxyl group in the FER molecule and a surface titanium atom. The ICOHP values are −0.17, −0.13, and −1.37 eV, respectively. The strong interaction with the titanium atom is common to both 1b and 3b. The titanium atoms on the R-TiO₂ surface are also five-coordinated and Lewis acidic, with a higher acidity than those on the A-TiO₂ surface. Consequently, the interaction energy is more negative on R-TiO₂ (−1.37 eV) than on A-TiO₂ (−0.96 eV). This difference is also reflected in the interatomic distances: the corresponding atomic distances (d) in 1b and 3b are 2.46 Å and 2.31 Å, respectively. In other words, the smaller d in 3b indicates a stronger interaction. Interaction (2) involves two atom pairs, (2A) and (2B). These interactions are weak, with ICOHP values of −0.14 and −0.09 eV, respectively.

These results reveal that the adhesion of the epoxy resin to pristine TiO₂ surfaces is primarily governed by the interaction between the hydroxyl group of the resin and the highly active titanium atoms on the surface, where the strong Lewis acidity of the titanium atoms plays an important role. Table lists the total |ICOHP| values, which are 1.37, 0.55, and 1.50 eV for 1b, 2b, and 3b, respectively. This trend (3b > 1b > 2b) agrees with that of S _ad, indicating that charge transfer interactions contributing to the DFT component play an important role in interfacial adhesion.

2. Total |ICOHP| Values for All Interfaces (1b– 3b and 1bw – 3bw).

total |ICOHP| (eV)
A-TiO2	1b	1bw
	1.37	3.43
B-TiO2	2b	2bw
	0.55	1.47
R-TiO2	3b	3bw
	1.90	3.02

3.3. Interfacial Interactions at FER/Hydroxylated TiO₂ Surface Systems

As in the case of the pristine surfaces (1b, 2b, and 3b), charge density difference analysis was also applied to the hydroxylated surfaces (1bw, 2bw, and 3bw). Figures a and a,c show the charge density differences for 1bw, 2bw, and 3bw, respectively. The regions exhibiting significant changes in charge density are indicated by dotted lines. Enlarged views of these regions from different angles are presented in Figures b and b,d. Here, ISV was set to 0.003 e/ų, the same as for the pristine surfaces.

7.

(a) Charge density difference of 1bw. (b) Enlarged interaction sites of 1bw. (c) Sawtoothed structure of the hydroxylated A-TiO₂ surface (1aw).

8.

(a, c) Charge density differences for 2bw and 3bw. (b, d) Magnified views of the interaction sites of 2bw and 3bw.

For 1bw (Figure b), three interaction sites originating from (1) the hydroxyl group, and (2) and (3) the phenyl group of the FER molecule are observed. The hydroxyl group of the FER molecule forms three hydrogen bonds with the surface hydroxyl groups, with the ICOHP values of −0.93, −0.83, and −0.92 eV, respectively. Each of hydrogen bonds is comparable in strength to the interaction between the hydroxyl group of the FER molecule and the surface titanium atom observed in 1b (Figure b). Furthermore, the phenyl group of the FER molecule forms OH−π interactions with the surface hydroxyl groups at (2) and (3), with their ICOHP values of −0.06 (2A), −0.20 (2B), −0.16 (3A), −0.07 (3B), −0.16 (3C), −0.10 eV (3D). The total |ICOHP| value reaches 3.43 eV, which is more than twice that of 1b. The formation of the three hydrogen bonds, which contributes to the total |ICOHP|, is attributed to the sawtoothed structure of the hydroxylated A-TiO₂ (1aw) surface. As shown in Figure c, the hydroxy group of the FER molecule is inserted into the concave site indicated by the black triangle on the 1aw surface and interact with the three hydroxy groups on the surface. These charge transfer interactions mediated by hydrogen bonds are considered to have increased the DFT component from 373 to 637 MPa (1b → 1bw), thereby enhancing S _ad.

For 2bw (Figure b), similar to 2b, only the hydroxyl group of the FER molecule forms interactions (A) and (B) with the surface. Their ICOHP values are −0.51 and −0.96 eV, respectively, indicating that both hydrogen bonds are stronger than those of 2b. These hydrogen bonds thus contribute to the enhancement of S _ad associated with the surface hydroxylation. As shown in Table , the total |ICOHP| value increases from 0.55 to 1.47 eV. On the hydroxylated surface, these charge transfer interactions increase the DFT component from 82 to 340 MPa (2b → 2bw), leading to an increase in S _ad.

For 3bw (Figure d), the hydroxyl group of the FER molecule forms strong hydrogen bonds (A) and (B) with the hydroxyl groups on the surface. Their ICOHP values are −1.59 and −1.43 eV, respectively, which are stronger than the hydrogen bonds (1A), (1B), and (1C) of 1bw. Meanwhile, as shown in Table , the total |ICOHP| values for 1bw (3.43 eV) and 3bw (3.02 eV) are comparable. This is because 3bw forms two hydrogen bonds, whereas 1bw forms three. Upon hydroxylation (3b → 3bw), the DFT component decreases (553 MPa → 495 MPa) while the total |ICOHP| value increases (1.90 eV → 3.02 eV). This suggests that the direct electrostatic interaction between the strongly Lewis acidic titanium atoms on the R-TiO₂ surface and the hydroxyl group of the FER molecule is replaced by hydrogen bonds involving charge transfer interactions.

These results indicate that the adhesion performance for hydroxylated TiO₂ surfaces is influenced by the formation of hydrogen bonds involving charge transfer interactions. In particular, for A-TiO₂, the sawtoothed surface structure enables multiple hydrogen bonds, leading to a remarkable increase in adhesive strength. For B-TiO₂, hydrogen bonds formed by surface hydroxylation are stronger than those on the pristine surface, thereby enhancing adhesive strength. In contrast, for R-TiO₂, the dominant adhesion mechanism shifts from direct electrostatic interactions with Lewis acidic titanium atoms on the pristine surface to hydrogen bonding with the surface hydroxyl groups, causing a decrease in adhesive strength. These results indicate that charge transfer interactions play an important role at the adhesive interface. This is difficult to describe using classical force fields, suggesting the need for analysis by quantum chemical calculations.

The insights obtained in this study provide a guideline for selecting the appropriate TiO₂ particle size in the design of composite materials. Under conditions where moisture in the atmosphere can be thoroughly removed and an ideal clean surface can be achieved, R-TiO₂, which exposes highly Lewis acidic titanium atoms, is advantageous. R-TiO₂ is thermodynamically favored at particle sizes larger than 35 nm. Accordingly, the result of this study is consistent with the previous studies, reporting that the tensile strength of TiO₂/epoxy composites increases for relatively large (>50 nm) particles prepared under sufficiently degassed conditions. , In contrast, when complete drying is difficult and surface adsorption of water molecules is unavoidable, A-TiO₂ is preferable because it can effectively utilize a hydrogen bonding network. Meanwhile, B-TiO₂, which is stabilized at intermediate particle sizes, exhibits weaker interfacial interactions and should be avoided from the viewpoint of adhesive strength. For A-TiO₂ and B-TiO₂, which are thermodynamically favored at smaller particle sizes, a direct comparison with experimental data is currently difficult due to the formation of mixed crystal phases and particle aggregation. , The results in this study suggest that controlling particle size to preferentially obtain either the A-TiO₂ or R-TiO₂ phase, depending on the moisture conditions during composite fabrication, can be an effective strategy for maximizing adhesion performance between epoxy resin and TiO₂ particles.

4. Conclusions

Based on first-principles calculations, we systematically analyzed the adhesive interactions between the FER molecule and both pristine and hydroxylated TiO₂ surfaces of different crystal structures. Each surface exhibited distinct characteristics depending on its crystal phase. On the clean R-TiO₂ and A-TiO₂ surfaces, direct interactions with highly Lewis acidic Ti_5c atoms played a key role in adhesion. In contrast, the pristine B-TiO₂ surface, where titanium atoms are recessed, showed significantly lower adhesion performance. For the hydroxylated surfaces, the formation of hydrogen bonds involving charge transfer was found to change the adhesion behavior. In the case of A-TiO₂, multiple hydrogen bonds were formed due to its characteristic sawtoothed surface structure, leading to a pronounced increase in adhesive strength. In B-TiO₂, the adhesive strength also increased through the formation of hydrogen bonds. In R-TiO₂, the direct interaction with the Ti_5c atoms was replaced by hydrogen bonding, resulting in a decrease in adhesive strength. These findings highlight the important role of charge transfer interactions in determining adhesion at the molecular interface.

From an application perspective, the results indicate that controlling the particle size of TiO₂ has a significant impact on interfacial adhesion performance. When moisture can be sufficiently removed to stabilize a pristine surface, R-TiO₂ is the most effective. Under humid conditions where complete drying is difficult, a particle size range in A-TiO₂ is preferable because it can form hydrogen bond network. In contrast, particle sizes that favor the B-TiO₂ formation should be avoided in terms of adhesion performance. The insights obtained in this study provide not only molecular design guidelines for adhesive interfaces but also valuable implications for materials design through particle size control.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c05322.

• Metastable interfacial structures for A-TiO₂, B-TiO₂, R-TiO₂. Adhesive stress curves for 1b–3b and the decomposition. Adhesive stress curves for 1bw–3bw and the decomposition. The value of DFT and dispersion components at the displacement giving maximum adhesive stress for 1b–3b and 1bw–3bw. Glossary of terms and abbreviations (PDF)

The authors declare no competing financial interest.