Molecular Understanding of the Adhesive Force between a Metal

ARTICLE pubs.acs.org/JPCC

Molecular Understanding of the Adhesive Force between a Metal Oxide Surface and an Epoxy Resin Takayuki Semoto, Yuta Tsuji, and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering and International Research Center for Molecular System, Kyushu University, Fukuoka 819-0395, Japan

bS Supporting Information ABSTRACT: A mechanism of the adhesion between an aluminum oxide surface and an epoxy resin is investigated by using density functional theory (DFT) calculations. Force field simulations are carried out for a better understanding of the dynamic behavior of the resin on the surface and for constructing models for DFT calculations. Stable structures of a resin
surface complex, adhesion energies, and details about interaction sites are obtained from geometry optimizations for some models based on DFT calculations with a plane-wave basis set and periodic boundary conditions. DFT calculations reveal that hydroxyl groups of the epoxy resin interact with the surface of aluminum oxide to form hydrogen bonds, which work as a main force for the adhesion. Plots of energy versus vertical distance of the resin from the surface are nicely approximated by the Morse potential. The force required for detachment of the resin from the surface can be estimated from the maximum value of the force
distance curve, which is obtained from the derivative of the potential energy curve. Obtained results demonstrate that hydrogen bonds play a central role for the adhesion between an aluminum oxide surface and an epoxy resin.

1. INTRODUCTION Adhesion is one of the most important phenomena in the field of science and technology.1
5 The technology of adhesion has found widespread applications ranging from aerospace to automotive engineering. In the aeronautical industry, for instance, epoxy adhesive is widely used to joint aluminum alloys, which compose the structural skeleton of aircrafts.6 The adhesive joining with the resin eliminates the need for a welding process and boring of screw holes, which makes a metal composite material lighter than that fabricated by the traditional method using screws and bolts. Resins generally excel in water resistance, chemical resistance, and insulation performance. Thus, the adhesion technology plays an important role in the production of lighter and stronger composite materials. A lot of experimental and theoretical studies on the adhesion mechanism have been carried out during the last two decades.7
24 Various experimental techniques have been developed to elucidate the mechanism of adhesion in the polymer
metal interface,7
13 polymer
polymer interface,14 and polymer
inorganic interface.15 Wedge tests7
11,14 and tensile tests12,13 based on fracture mechanics provide useful information on mechanical properties, such as the stress
strain curve, crack-growth kinetics, and adhesion durability. Several surface analysis methods, such as scanning electron microscopy (SEM),7,8,11,14 X-ray photoelectron spectroscopy (XPS),7
11,14,15 and secondary ion mass spectroscopy (SIMS),9 have been employed for the characterization of the fracture surface. Most experimental studies focus on the mesoscopic characteristics of the surface, for instance, morphology, r 2011 American Chemical Society

topography, and roughness. Such experimental views are likely to lack a molecular understanding of the adhesion mechanism. To yield a better insight into adhesion phenomena, a lot of theoretical studies have been carried out on the basis of force field simulation,16
19 semiempirical quantum chemistry,20,21 density functional theory (DFT),22 and the density functional based tight-binding (DFTB) method.23,24 However, the basic mechanism of adhesion on the atomic scale has not yet been fully elucidated. The following four mechanisms have been proposed so far to explain the adhesion phenomena.1
3 (1) Mechanical interlocking theory: More than 80 years ago, McBain and Hopkins25 proposed a theory that adhesion is a result of the mechanical interlocking of adhesive materials into the pores, holes, and crevices of an adherend. The mechanical interlocking is effective on porous or rough substrates, such as wood, textile, and paper.1
3,25,26 However, the adhesion strength of adhesives used on polished and smooth metallic surfaces does not strongly depend on the surface roughness. At least in the adhesion on metallic surfaces, it is difficult to regard the mechanical interlocking as a general mechanism. (2) Diffusion theory: This theory of adhesion has been mainly supported by Voyutskii.27 Polymeric materials in intimate contact can merge at the interface by the interpenetration of the chains of the superficial Received: March 25, 2011 Revised: May 9, 2011 Published: May 25, 2011 11701

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Figure 1. Chemical structure of (a) DGEBA and (b) epoxy resin.

layers.1
3,27 The diffusion theory is validated when the molecules of both adhesive and adherend are mobile and soluble in each other. The applicability of the diffusion theory is limited to the adhesion of compatible polymers and welding of thermoplastics. (3) Electronic theory: This theory has been developed by Derjaguin and Smilga.28 If adhesive and adherend have different electronic band structures, electron transfer should occur across the interface to balance the Fermi levels, which results in the formation of an electrical double layer at the interface.1
3,28,29 The adhesion force can be assigned to the electrostatic interaction between the partially charged adhesive and adherend in this theory. However, it is reported that the electrostatic contribution to the adhesion force is usually very small.30,31 (4) Adsorption theory: This theory of adhesion is likely to be most generally accepted, where adhesive and adherend can adhere through the forces acting between the atoms in the interface region when the sufficiently intimate intermolecular contact is achieved at the interface.1
3 The interaction between adhesive and adherend can be classified into two classes, that is, primary bond and secondary bond.1 Covalent, ionic, and metallic bonds resulting in chemisorption are assigned to the primary bond, whereas van der Waals force, hydrogen bond, and acid
base interaction that can result in physisorption are assigned to the secondary bond in general. It is controversial with respect to which bond is more important to adhesion.32
39 The primary bonds have considerably high interaction energies ranging from 15 to 250 kcal/mol in comparison to the secondary bonds, whose energies are generally less than 10 kcal/mol.1,3 Among the primary bonds, ionic and metallic bonds are relatively nondirectional because ions involved in ionic and metallic bonds are approximately spherical, whereas covalent bonds are strongly directional because the orbitals involved are typically nonspherical. In nature, mixtures of these bonding types occur frequently, and many adsorption systems should include bonding characteristics that resemble more than one type. This hybrid bond situation produces some characteristics of directional covalent bonds along with nondirectional metallic or ionic bonds.40 Therefore, adsorbates that are chemisorbed stick at specific sites, and they exhibit a binding interaction that depends strongly on their exact position and orientation with respect to the substrates.41 On the other hand, secondary bonding systems do not experience such strongly directional interactions. Therefore, they bond more tenuously to specific sites and experience an attractive interaction with the surface that is much more uniform across the surface.41 The adsorption theory of adhesion based on the secondary bond formation has broad utility because the secondary bond, which has little directional constraint, is applicable to many systems and is relatively more independent of the morphology of the surface than the primary bond. In this study, we have investigated the adhesion interaction between an aluminum oxide surface and an epoxy resin. Because

aluminum is characterized with the lightness and strength, aluminum materials play an essential role in various industrial fields,6,42 which need a detailed understanding of adhesion phenomena on the aluminum surface. Pure aluminum is readily oxidized in air at room temperature to form an aluminum oxide layer.43,44 γ-Alumina is the first of a series of transition aluminum oxides, formed from an amorphous or boehmite precursor. The series is followed by δ-, θ-, and R-alumina at higher temperatures.45 R-Alumina (R-Al2O3) is a thermodynamically stable phase of coarsely crystalline aluminum oxide; however, γ-alumina (γ-Al2O3) has a lower surface energy than R-alumina. It is energetically stable at the surface region because γ-alumina has greater entropy than R-alumina as a result of the presence of tetrahedral and octahedral sites in its spinel-type structure and the fairly random distribution of Al3þ and vacancies over these sites.46 Therefore, it is adequate to model the surface layer of aluminum oxide using γ-alumina, which is of considerable significance in a variety of industries, such as structural composites for spacecraft, miniature power supplies, and catalyst.45,47 Despite its great industrial importance, there is still controversy in the literature concerning the crystallography and surface of γ-alumina.48,49 In a moist environment, water molecules easily adsorb to the alumina surface to form hydroxyl groups. The surface hydration of γ-alumina is experimentally and theoretically investigated by Peri.50,51 The surface hydroxyl group can make the theory of adhesion based on hydrogen bonds a plausible mechanism of adhesion. Epoxy resin, which is one of the most common structural adhesives, particularly in automotive and aircraft industries, has a good affinity for aluminum alloy surfaces and oxide layers produced during surface preparation.52 As shown in Figure 1, epoxy resin is usually produced by polymerization of the diglycidylether of bisphenol A (DGEBA), containing hydroxyl groups and ether groups, which can form hydrogen bonds with the hydrated aluminum oxide surface. Rider and co-workers have extensively studied the adhesion between an aluminum surface and the epoxy adhesive using wedge tests and surface analysis methods.7
10 They shed light on the influence of water pretreatment of the aluminum surface and hydroxyl group concentration on the adhesion strength and durability, which provides an important clue for the nature of the adhesion mechanism. Knaup et al. have investigated the adhesion mechanism of the epoxy adhesive components, DGEBA, the curing agent diethyltriamine (DETA), and the adhesion promoter 3-aminopropylmethoxysilane (AMEO) on a hydrated γ-alumina (0 0 1) surface with the self-consistent charge-density functional based tight-binding (SCC-DFTB) method,24 which is a semiempirical method based on DFT.53 They reported that the covalent-bond formation of AMEO between its silane group and the hydroxyl group on the surface is favorable over the adsorption of the other two examined adhesive components, DGEBA and DETA. The 11702

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Figure 3. Structure of a fragment of epoxy adhesive used in geometry optimization (green, C; red, O; white, H). The hydrogen and oxygen atoms of the hydroxyl group are labeled as H1 and O1, respectively. Figure 2. Periodic model of (a) the γ-alumina (0 0 1) surface and (b) optimized structure of the hydroxylated γ-alumina (0 0 1) surface (silver, Al; red, O; white, H). Bonds crossing the periodic boundaries are not shown.

reaction energy of the covalent-bond formation of AMEO with the surface is estimated to be nearly
45 kcal mol
1, which indicates a strong exothermicity characteristic of the primary bond. In this article, we investigate the adhesion mechanism of the polymerized DGEBA with a hydrated γ-alumina surface, focusing on the secondary bond, that is, hydrogen bond, using DFT calculations. Calculated adhesion forces are in good agreement with experiment.

2. METHOD 2.1. Model Preparation for the Metal Oxide Surface. The crystallographic data for the γ-alumina bulk structure used in the present study was taken from a model proposed by Toulhoat and co-workers,54,55 who theoretically investigated the structure of γ-alumina using DFT calculations. The model contains 16 Al atoms and 24 O atoms in a unit cell. Their minimal model serves as the basis for larger supercells in subsequent steps. The determined lattice parameters are a = 5.587 Å, b = 8.314 Å, c = 8.068 Å, and β = 90.59°, which are in good agreement with experimental data. The adhesion surface was modeled by the γ-alumina (0 0 1) surface because the surface is well known as a cleaved surface of γ-alumina and numerous studies have been performed on the (0 0 1) surface of γ-alumina.56,57 We employed a model of the γ-alumina (0 0 1) surface shown in Figure 2, where they include a 15 Å vacuum slab over the surface. To obtain a structure of the hydroxylated γ-alumina surface, molecular dynamics (MD) simulations were performed on the model surface covered by a 10 Å thick layer of water molecules. The total dynamics time was set to be 3 ps. The simulation temperature was set at 300 K for the first 1 ps, 600 K for the second 1 ps to remove the nonadsorbed water molecules, and 300 K for the last 1 ps to cool down the system. The MD simulation showed that several water molecules are physisorbed on the surface. However, the procedure cannot describe the chemisorption. We performed ab initio molecular dynamics (AIMD) simulations for the physisorbed structure obtained after the MD simulation. We observed chemisorption of water molecules, in which the oxygen atoms of water molecules are strongly bonded to the surface aluminum atom and one hydrogen atom of a water molecule migrated to the neighboring Al
O
Al bridge to form an O
H bond. We manually split the water molecule into hydroxyl group and proton, forming a hydroxylated aluminum and protonated oxygen in a neighboring Al
O
Al bridge on the basis of Knaup’s procedure to prepare the hydroxylated aluminum oxide surface.24 All four Al atoms of

the top layer are hydroxylated, as shown in Figure 2. The unit cell totally contains 52 atoms (Al16O24 3 4H2O). Geometry optimizations of the hydroxylated aluminum oxide surface were performed with the Perdew
Burke
Ernzerhof (PBE)58 form of generalized gradient approximation (GGA) with plane-wave basis functions implemented in the CASTEP software package59,60 of Materials Studio 4.4.61 Electron
ion interactions were treated with ultrasoft pseudopotentials, the plane-wave cutoff energy being set to be 380 eV. A k-point set of (4  3  1) was used. In the optimization process, atoms were frozen in their bulk positions except for the top and second layers. An optimized structure of the hydroxylated aluminum oxide surface is shown in Figure 2b. The concentration of hydroxyl groups on the optimized surface is 8.61 per nm2, which is fully consistent with experimental values for γ-alumina51 and aluminum62 surfaces. 2.2. Model Preparation for the Resin
Surface Complex. To look at the dynamic behavior of the adhesive on the hydroxylated γ-alumina surface, we performed force field simulations. An oligomer containing three units of DGEBA (n = 3 in Figure 1b) was placed on a 5  3 supercell of a hydroxylated γ-alumina (0 0 1) surface, and a vacuum slab of 31.9 Å was added over the surface to adjust the size of the supercell to 27.9  24.9  40.0 Å3. The terminating glycidol groups of the adhesive molecule were removed and substituted by hydrogen atoms to exclude effects of the terminating groups. In the MD simulations, we used the Discover force field simulation program63 with the COMPASS force field64
66 via Materials Studio 4.2. The system was simulated at a constant temperature of 300.0 K in the NVT ensemble with a Nos
e
Hoover thermostat for 100 ps, where the time step was set to be 1.0 fs. During the simulations, all atoms of the surface, containing the surface hydroxyl groups, were frozen to save computational efforts. The simulation time of 100 ps is long enough for the system to reach a steady state. We performed the MD simulations to exclude arbitrariness on the adhesion site selection. The MD simulations cannot yield the detailed nature of the adhesion interaction. The distortions and relaxations of the surface hydroxyl groups in the adhesion process can be taken into account in subsequent DFT calculations. 2.3. Geometry Optimization of the Resin
Surface Complex. For an essential understanding of the adhesion interaction at the atomic level, calculations based on quantum mechanics are indispensable. We performed geometry optimizations for some models of the adhesion complex based on DFT. Because the system obtained from the MD simulation is too large to perform geometry optimization by DFT, we partitioned the system into smaller parts with the periodic boundary condition. We considered two small slab models named models A and B. The adhesive molecule also becomes fragmented, as shown in Figure 3, where two benzene rings, two ether groups, and a hydroxyl group are included. Model A consists of the fragment of adhesive 11703

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over a 2  1 supercell of the hydroxylated γ-alumina surface, and model B consists of the fragment of adhesive over a 1  2 supercell of the hydroxylated γ-alumina surface. Geometry optimizations of models A and B were performed with the PBE form of GGA with plane-wave basis functions implemented in the CASTEP software package of Materials Studio 4.4. Electron
ion interactions were treated with ultrasoft pseudopotentials. The plane-wave cutoff energy was set to be 380 eV. A 2  3  1 k-points sampling was used for model A and a 4  1  1 k-points sampling was used for model B. In the optimization process, atoms of adherend were frozen in their bulk positions except for the top and second layers of γ-alumina and surface hydroxyl groups. All lattice parameters were fixed to save computational efforts. The adhesion energy between the epoxy adhesive and the γ-alumina surface can be calculated according to the following equation Eadhesion ¼ Eadhesive þ Eadherend
EðadhesiveþadherendÞ

ð1Þ

Figure 4. Final configuration obtained after the MD simulation described in section 2.2. The system contains three units of DGEBA and a 5  3 supercell of the hydroxylated γ-alumina (0 0 1) surface. Bonds crossing the periodic boundaries are not shown.

where E(adhesiveþadherend) is the total energy of the resin
surface complex and Eadhesive and Eadherend are the energies of the fragments of epoxy adhesive and the hydroxylated γ-alumina surface separated in vacuum, respectively. The value of the adhesion energy should be a good indicator about how much the system is stabilized via adhesion. 2.4. Adhesion Force Calculation. The force resulting in adhesion can be calculated as follows67 F ¼

dE dΔr

ð2Þ

where Δr is the displacement of the adhesive molecule from the position of stable equilibrium and E is the total energy of the system. Our model assumes that detachment does not occur at the inside of the epoxy adhesive, but at the interface between the adhesive molecule and the hydroxylated γ-alumina surface, which is consistent with the result of the finite element method (FEM) study performed by Tsiafis et al.12 We changed Δr in a direction perpendicular to the γ-alumina (0 0 1) surface from
0.5 to 2.0 Å at an interval of 0.1 Å and repeated single-point energy calculations at each step of Δr. We plotted the calculated single-point energies as a functional of Δr. Obtained plots of energy versus distance were approximated by a Morse potential curve by using the least-squares method in the range from 0.0 to 2.0 Å, where the Morse potential is written as follows: E ¼ De ð1
e
aΔr Þ2

ð3Þ

Here, De is the binding energy and a is a constant specific to a system. According to eq 2, the differentiation of eq 3 by Δr gives a force
distance curve. The adhesion force, Fad, is considered to depend on the maximum value of the force, Fmax, and the density of the interaction sites at the interface between the adhesive molecule and the hydroxylated γ-alumina surface, θ, as shown in the following equation: Fad ¼ Fmax θ

ð4Þ

We performed MD simulations to estimate the value of θ. The condition for the MD simulations was set to be same as that noted in section 2.2. We saturated the surface with five oligomers of the epoxy adhesive and performed 100 ps MD simulations. Subsequently, energy minimization was done.

Figure 5. Optimized structures of models A and B of the resin
surface complex, including the fragment of epoxy resin described in Figure 3. The 2  1 and 1  2 supercells of the hydroxylated γ-alumina (0 0 1) surface are used for models A and B, respectively. The lengths of hydrogen bonds are shown in Å. Bonds crossing the periodic boundaries are not shown.

3. RESULTS AND DISCUSSION 3.1. Model Preparation for the Resin
Surface Complex. The final configuration obtained after the MD simulations is shown in Figure 4. The adhesive molecule, which showed a random coil structure during early stages of the simulation, was finally stretched and spread over the surface. The hydroxyl groups of the adhesive molecule oriented toward the surface to form hydrogen bonds. Other functional groups, such as the ether groups, alkyl groups, and benzene rings, do not play an important role in the adhesion interaction. 3.2. Geometry Optimization of the Resin
Surface Complex. Optimized structures of models A and B described in section 2.3 are shown in Figure 5. Computed adhesion energies per DGEBA unit for models A and B are 0.682 eV (15.7 kcal/mol) and 0.671 eV (15.5 kcal/mol), respectively. In both models, the hydroxyl group of the adhesive molecule nicely interacts with the surface, which is very similar to the model for a configuration of epoxy resin on a hydrophilic surface proposed by Glazer.68 The hydroxyl group of the adhesive molecule forms three hydrogen bonds with the surface: one is formed between atom H1 of the adhesive molecule and the O atom of a hydroxyl group on the surface, and the other two are formed between atom O1 of the 11704

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Figure 6. Panels A-1 and B-1 are the top views of optimized geometries of the hydroxylated γ-alumina (0 0 1) surface before adhesion for models A and B, respectively. Panels A-2 and B-2 are the top views of optimized geometries of the hydroxylated γ-alumina (0 0 1) surface and the hydroxyl group of the epoxy resin after adhesion for models A and B, respectively. The bulk atoms of γ-alumina and the atoms of the epoxy resin except for the hydroxyl group are not shown for clarity. Bonds crossing the periodic boundaries are not shown.

adhesive molecule and H atoms in a protonated Al
O
Al bridge. The distances of the hydrogen bonds are in the range of 1.8
2.2 Å. The benzene rings and ether groups cannot make significant contributions to the adhesion interaction. They can play a crucial role in the mechanical aspect, such as rigidity of the resin. To better understand the adhesion site of the epoxy resin, we concentrated on the uppermost layer of the surface. The top view of the optimized geometry of the hydroxylated γ-alumina (0 0 1) surface before adhesion and that after adhesion are shown in Figure 6, where only the uppermost layer of the surface and the hydroxyl group of the epoxy resin are shown for clarity. The only difference between A-1 and B-1 is the size of the supercell, A-1 and B-1 being essentially identical structures. Optimized lengths of hydrogen bonds in each model are shown in Table 1. In model A, the adhesion site is composed of atoms O2, H2, and H3 labeled in Figure 6. Before the adhesion, in Figure 6A-1, atoms H2 and H3 are stabilized by forming hydrogen bonds with atoms O2 and O3, respectively. After the adhesion, in Figure 6A-2, these hydrogen bonds are dissociated. Subsequently, atoms H2 and H3 form hydrogen bonds with atom O1 and atom H1 is oriented to form a hydrogen bond with atom O2. In model B, the adhesion site is composed of atoms O4, H4, and H5. Before the adhesion, in Figure 6B-1, atoms H4 and H5 are stabilized by forming hydrogen bonds with atoms O4 and O5, respectively, where the hydrogen bond between atoms H5 and O5 is working beyond the supercell, due to the periodic boundary condition. After the adhesion, in Figure 6B-2, these hydrogen bonds are dissociated. Subsequently, atoms H4 and H5 form hydrogen bonds with atom O1, and atom H1 is oriented to form a hydrogen bond with atom O4. Although models A and B are optimized by using different initial geometries and sizes of supercells, the adhesion manner of the hydroxyl group of the epoxy resin to the hydroxylated γ-alumina (0 0 1) surface has no significant difference between models A and B. The adhesion site is a triangle composed of two adjacent hydrogen atoms belonging to protonated Al
O
Al bridges and one oxygen atom in a vicinal hydroxyl group. To look at the role of hydrogen bonds in the adhesion mechanism, we investigated the adhesion between the nonhydroxylated

Table 1. Selected Bond Lengths (Å) for Models A and B in Figure 6 H2
O2

H3
O3

H1
O3

H2
O1

H3
O1

A-1

1.530

1.497

A-2

2.156

2.385

1.916

2.197

1.855

H4
O4

H5
O5

H1
O4

H4
O1

H5
O1

B-1

1.530

1.497

B-2

2.299

2.316

2.221

2.000

1.841

γ-alumina (0 0 1) surface and the epoxy adhesive in accordance with the same procedure for models A and B. This model is named as model C in Figure 7. It contains the fragment of epoxy resin shown in Figure 3 and the 1  2 supercell of the nonhydroxylated γ-alumina (0 0 1) surface. Although the benzene rings and ether groups do not make significant contributions to the adhesion interaction, the hydroxyl group of the epoxy resin interacts with an oxygen atom of the surface, forming only one hydrogen bond. A calculated adhesion energy is 0.411 eV (9.48 kcal/mol), which is much lower than those for models A and B. This result demonstrates that an increase in the density of hydroxyl groups on the aluminum surface has an important impact on the adhesive interaction. 3.3. Adhesion Force Calculation. Obtained energy
distance plots are shown in Figure 8a. The plots are nicely approximated by Morse potential curves in the range from 0.0 to 2.0 Å. The derivatives of the approximated potential curves provide force
distance curves, as shown in Figure 8b. Table 2 summarizes data regarding the adhesion for models A, B, and C. The maximum forces for models A and B are nearly twice larger than that for model C. The obtained ΔrF, which is the distance Δr that leads to the maximum force Fmax, for model C is larger than ΔrF for models A and B. These results also demonstrate that the adhesion force is enhanced by the hydration of the surface and that the density of hydrogen bonds plays a crucial role in the adhesion energy and force. Results of the calculations clearly revealed that hydrogen bonds serve as a main force of the adhesion between the 11705

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aluminum oxide surface and the epoxy resin. We defined θ as the density of interaction sites at the interface, that is, the density of hydroxyl groups of the epoxy adhesive trapped by the surface. According to the MD simulations, the number of hydroxyl groups trapped by the hydrated γ-alumina surface is estimated to be six per supercell, which corresponds to 0.86 per nm2. The average area occupied by a repeating unit of the epoxy resin, AEP, is calculated as follows69 AEP ¼ Mn =ðNA FtÞ

ð5Þ

where Mn is the molecular weight of a repeating unit of the epoxy resin, NA is Avogadro’s number, F is the density of the epoxy resin, and t is the thickness of the surface atomic layer of the epoxy resin on the aluminum surface. According to Figure 1, Mn is calculated to be 284.3 g/mol. F and t are reported to be 1.13 g/cm3 and 0.4 nm, respectively.9 A calculated value of AEP is 1.04 nm2. Given that all hydroxyl groups of the epoxy resin interact with the hydroxylated γ-alumina surface at the interface, the density of hydrogen bonds is estimated to be 0.96 per nm2

because one hydroxyl group is included per repeat unit of the epoxy resin. The value of θ obtained from the MD simulations is fully consistent with that calculated from eq 5. Adhesion forces calculated from eq 4 are 6.2  108 and 6.1  8 10 Pa for models A and B, respectively. The calculated adhesion forces are 1 order of magnitude larger than the value of the adhesion strength measured by using the experimental tensile test,12 in which the adhesion strength is reported to be 2.3  107 Pa. In a real adhesion system, surface asperity, impurity contamination, internal stress, blister formation, and solvent retention can reduce the adhesion strength. Of course, it is difficult to characterize the density of the hydroxyl group on the γ-alumina surface well. We assumed maximum hydroxyl group density at the surface, but in reality, the hydroxylation density will probably be lower than that. Even when assuming a maximum hydroxylation density, the density of available surface sites favorable for hydrogen bridge bond formation with hydroxyl groups of the epoxy resin will be considerably lower because a lot of the available surface sites should already be occupied by physisorbed water molecules. Some part of the epoxy chain must extend perpendicular to the surface into the bulk polymer, which will sterically hinder the formation of hydrogen bonds in some areas of the surface, leading to a lowering of the effective adhesion force per surface unit. Our model assumes ideal interface conditions, that is, maximum hydroxyl group density, absence of physisorbed water molecules, and no curving of parts of the epoxy chain into the bulk polymer. Relaxations of the adhesive molecule and surface in the peeling process can be also a factor in reducing adhesion energies and forces. We calculated the adhesion energy and force of model A by performing partial relaxations. The Table 2. Adhesion Properties by DFT Calculations for Models A, B, and C

Figure 7. Optimized structure of model C of the resin
surface complex, including the fragment of the epoxy resin described in Figure 3. A 1  2 supercell of the nonhydroxylated γ-alumina (0 0 1) surface is used. The length of the hydrogen bond is shown in Å. Bonds crossing the periodic boundaries are not shown.

a

model

Eadhesion/eV

Fmax/nN

ΔrFa/Å

Fad/MPa

A

0.682

0.726

0.570

6.2  102

B

0.671

0.706

0.555

6.1  102

C

0.411

0.352

0.735

ΔrF is the distance Δr that leads to the maximum force Fmax.

Figure 8. (a) Energy
distance plots and (b) force
distance curves for models A, B, and C. 11706

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The Journal of Physical Chemistry C detailed description of the calculation is given in the Supporting Information. The theoretical calculation is considered to predict the maximum value of adhesion strength. Incorporation of the factors resulting in a reduction of the adhesion strength into the theoretical calculation will be addressed in our future work.

4. SUMMARY AND CONCLUSIONS We have analyzed the mechanism of the adhesion between an aluminum oxide surface and an epoxy adhesive using DFT as well as MD simulations. The force field simulation that showed the microscopic and dynamic behavior of the epoxy resin on the aluminum oxide surface provided initial geometries for DFT calculations. We constructed three small models: models A and B are composed of the fragment of the adhesive molecule and the hydroxylated γ-alumina surface, and model C is composed of the fragment of the adhesive molecule and the nonhydroxylated γ-alumina surface. Geometry optimizations performed on the models provided stable structures of the resin
surface complex. DFT calculations for models A and B revealed details about the adhesion site, where the hydroxyl group of the epoxy adhesive forms hydrogen bonds with the surface hydroxyl groups and protonated Al
O
Al bridges. The hydrogen bonds are considered to serve as a main force of the adhesion. The comparison of models A and B with model C demonstrates that the surface water pretreatment of the adherend, resulting in surface hydroxyl groups and hydrogen bond formation at the interface between the adhesive and the adherend, is important. The DFT calculations yielded not only stable structures of the resin
surface complex but also the adhesion energy and adhesion force. The adhesion energies for models A, B, and C are 0.682, 0.671, and 0.411 eV, respectively. The adhesion force can be obtained from the maximum value of the force
distance curve, which is calculated from the derivative of the energy
distance curve. The adhesion forces for models A and B are 6.2  102 and 6.1  102 MPa, respectively. The theoretical calculations are in good agreement with experiment, considering surface asperity, impurity contamination, internal stress, blister formation, solvent retention, lower hydroxyl group density, physisorbed water molecules, and curving of parts of the epoxy chain into the bulk polymer in the real system. Relaxations of the adhesive molecule and surface in the peeling process can be also a factor in reducing adhesion energies and forces. We propose a methodology of quantum chemical investigation on adhesion systems. The result of the present study will contribute to the molecular understanding and design of effective adhesive and adherend materials. ’ ASSOCIATED CONTENT

bS

Supporting Information. Atomic Cartesian coordinates for the optimized geometries of a model for the hydroxylated γ-alumina surface and models A, B, and C. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT K.Y. acknowledges the Grants-in-Aid for Scientific Research (Nos. 18GS0207 and 22245028) from the Japan Society for the

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Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), the Kyushu University Global COE Project, the Nanotechnology Support Project, the MEXT Project of Integrated Research on Chemical Synthesis, and CREST of the Japan Science and Technology Cooperation.

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