Simulation Study of the Effects of Nanoporous Structures on

J. Phys. Chem. B , 2019, 123 (5), pp 1161–1170. DOI: 10.1021/acs.jpcb.8b10556. Publication Date (Web): January 24, 2019. Copyright © 2019 American ...
0 downloads 0 Views 7MB Size
Download PDF
Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

pubs.acs.org/JPCB

Simulation Study of the Effects of Nanoporous Structures on Mechanical Properties at Polymer−Metal Interfaces Toshiaki Miura,*,† Maki Funada,‡ Yukihiro Shimoi,† and Hiroshi Morita† †

National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Innovative Structural Materials Association (ISMA), AIST Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan

J. Phys. Chem. B Downloaded from pubs.acs.org by OPEN UNIV OF HONG KONG on 01/28/19. For personal use only.

‡

ABSTRACT: We investigated the effect of nanopores on the adhesion behavior at polymer−metal interfaces by molecular dynamics simulation. The effects of shear and extension behavior were examined. In the shear mode, samples with porous substrates showed larger shear forces than those with flat substrates. Meanwhile, the breaking strengths in the extension mode were almost the same for systems with flat and porous substrates. The similar behavior in the extension mode was ascribed to the formation of voids in the polymer layer, which was related to the increase of total system volume and not affected by the presence of pores. We also investigated the relationship between the mechanical properties of polymer−metal interfaces in the shear mode and pore size in detail. Even a very shallow pore with a depth of 0.5 nm produced a large shear force comparable to that of a pore with a depth of 2.0 nm. The shear force increased gradually as the pore diameter became wider. These simulation results revealed that the adhesion forces between polymers and rough metal surfaces are not simply related to the interface area but depend on the pulling mode, pore size, and polymer chain length in a complicated manner.

1. INTRODUCTION In recent years, adhesion between polymers and metals has attracted much attention, especially for application to lightweight devices and transport bodies. Although the strength of polymers has been improving, metals still play an important role as the structural framework. As a result, heterojunction technology is essential for the development of lightweight products. Various methods to strengthen the adhesion have been examined, such as flame treatment, plasma treatment, and chemical treatment at adhesion layers.1,2 It has been reported that interconnected surface structures with sponge-like morphologies can be formed by chemical processing.3,4 Such structures are considered to be effective to increase the adhesive force and thus the reliability and durability of adhesion between polymer and metal surfaces. Transmission electron microscopy observation revealed that the metal surfaces in these systems contained complicated porous structures with diameters of 10−100 nm. Therefore, the sizes of the nanopores and polymer chains were comparable. Rough metal surfaces can also be obtained by physical processing, such as laser exposure.5−10 However, the pore or dip sizes obtained by laser exposure are usually several micrometers, which are far greater than the size of polymer molecules. In the present paper, we focus our attention on the effects of nanostructures at the interfaces between polymers and metals on adhesion. This is because the detailed relationships between the shape of nanopores and mechanical properties of polymer−metal interfaces are not obvious. First, adhesion behavior has fundamentally two modes, which are the © XXXX American Chemical Society

extension and the shear modes. It is currently unclear whether the surface nanostructure affects both adhesion modes in a similar manner. Second, in the case of nanopores, the motion and conformation of each polymer chain would strongly influence the mechanical properties of the polymer−metal interface. The polymer region in the nanopores cannot be regarded as simple elastic bulk. Simulation is a useful tool to study these complicated microscopic phenomena.11−13 We can systematically change the structure of polymers, shape of interfaces, and strength of molecular interactions in simulation models. There have been multiple attempts to study the adhesion mechanisms of polymers using simulations.14−30 Because adhesion phenomena are essentially multiphysics and multiscale problems, many different simulation approaches can be implemented depending on the focus of the study. The microscopic adhesion energies between surface metal atoms and functional groups of resin monomers are often estimated by quantum calculations.14,15 To model the interaction between surface and long polymer molecules as a whole, molecular dynamics (MD) simulation is an effective method. MD simulation of the adhesion behavior of polymer systems has been studied using relatively small system sizes with flat substrates. In addition, to shorten calculation times, coarse-grained models have often been used in the simulations. These simulation studies include Received: October 30, 2018 Revised: January 9, 2019

A

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B investigations of the effects of connector chains at polymer− polymer interfaces,16,17 grafted polymers on the surface,18−20 thermal welding at polymer interfaces,21,22 and cross-linker functionality23 on adhesion behavior. The acceleration of computation speed has recently allowed MD simulations of full atomistic models to be attempted. Examples of such simulations include an epoxy compound on a copper substrate26,27 and polyimides on silica glass.28,29 These simulation studies on the adhesion properties of polymer systems have provided many insights on the microscopic behavior in adhesion and breaking processes. However, no detailed simulations with porous surfaces have yet been reported. In this study, we carry out MD simulations of the adhesion behavior of polymer−metal interfaces with different porous structures. We elucidate the detailed relationship between the porous structures and mechanical properties of polymer−metal interfaces for both the extension and shear modes of adhesion.

Figure 1. Typical examples of the simulation models of porous metal substrates. Red spheres indicate metal atoms. Gray lines indicate polymer molecules. (a) Overview. (b) Vertical cross section. The size of PEO-20 (shown in blue) and pore depth are similar. (c) Horizontal cross section of a cylindrical pore.

2. MODEL In our simulation model, polymer molecules were sandwiched between two metal substrates. We used poly(ethylene oxide) (PEO) as the model polymer. The molecular structure of PEO was [−O−CH2−CH2−]n, and the polymer ends were terminated by hydrogen atoms. Because each PEO molecule consisted of a main chain without large side groups, it was suitable to investigate the basic polymer chain behavior during the breakdown. The lack of large side groups would also accelerate the whole polymer dynamics, resulting in a decrease of simulation time. The degrees of polymerization, n, of PEO were 10, 20, and 30: we call these polymers PEO-10, PEO-20, and PEO-30, respectively. The number of polymer molecules in the simulation box was 456, 228, and 152 for PEO-10, PEO20, and PEO-30, respectively. We changed the number of polymers depending on the chain length so that the number of total monomer units in the simulation box was the same. We used aluminum (Al) as the metal substrate. Although the surface of Al is usually transformed to aluminum oxide or aluminum hydroxide in the atmosphere, we used Al metal in this simulation to simplify the detailed surface structures and parameters. Because there is no permanent polarization in systems that consist of a single kind of atom, the electric charge of all Al atoms was set to zero. Thus, only the Lenard-Jones (LJ) interaction was considered for the interaction between the polymers and metal surfaces. To shorten the calculation time, we approximated the substrates as two layers of metal atoms. Our main interest was how the porous structures at the metal surface affect adhesion behavior between the metal surface and polymers. To model the porous structures, we prepared a cylindrical pore on each metal surface as shown in Figure 1. We placed the two porous substrates opposite each other in a symmetric manner in the initial state. The pore diameter was changed from 1.0 to 4.0 nm, and their depth was changed from 0.5 to 2.0 nm. We investigated both the extension and shear mechanical adhesion properties of the polymer−metal interfaces by MD simulations. We used GROMACS 5.1.4 with the general AMBER force field for polymers.31 For nonbonded LJ parameters of Al, we used those of the universal force field.32 The neighboring Al atoms were bonded with a harmonic potential with the equilibrium bond length, r0 = 0.2405 nm and spring constant, k = 4.0 × 105 kJ/mol/nm2. The electric charges were calculated by Gaussian 09 using the restrained

electrostatic potential.33 The cutoff distance for the nonbonded LJ interactions was 1.0 nm, and the long-range Coulomb interactions were calculated using the particle mesh Ewald (PME) method. There are some reports that the longrange part of the dispersive forces was sensitive to quantitative predictions in the interfacial systems.34 Because we focused on the basic mechanism, we used the conventional method in this study. The size of the box was 10.1010 × 9.9974 × 50.0 nm3, and periodic boundary conditions were applied. During the process of extension and shear deformations, we applied external pull forces to the center of mass of each metal substrate. This was equivalent to applying external forces uniformly to each atom of the metal substrates and preventing large deformation of the substrates themselves during the pulling simulations. The k values of the harmonic potential for the pulling force were 40 000 and 1000 kJ/mol/nm2 for the extension and shear modes, respectively. The pulling rate was 0.002 nm/ps; that is, 2 m/s. The pulling simulations were carried out under NVT conditions. Temperatures were controlled by the Nosé−Hoover method for polymers and substrates separately. The time constant for temperature coupling was 0.1 ps. For the study of mechanical properties, it is important to consider the frictional heat during simulations.35 Because our sliding simulation was carried out at the relatively slow speed of 2 m/s, temperatures of both the polymer layer and metal substrates were well kept at room temperature and the effect of local heating by friction can be ignored in our simulation conditions. We investigated the adhesion behavior at the polymer− metal interfaces in the solid state. To determine the simulation temperature, we first examined the liquid−solid transition point of model PEO samples. In Figure 2, we show the simulation results for the volume and self-diffusion coefficient of a bulk sample of PEO-20 at various temperatures. The number of polymer molecules was 256, and periodic boundary conditions were applied to the cubic box shape. The slope of the plot of volume against temperature changed around T = 337 K. Above this temperature, the diffusion coefficient increased rapidly. Thus, we confirmed that the model polymer PEO-20 was in the solid state at room temperature (300 K). The molecular weight (Mw) of PEO-20 is 882. In experiments, it is reported that the melting point of PEG with Mw ∼1000 is around 308−313 K, which is roughly consistent with our simulation results. We also calculated the liquid−solid B

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

3. RESULTS AND DISCUSSION First, we present the results for the shear behavior at PEO-20− metal interfaces with and without pores. Figure 4 shows typical

Figure 2. Temperature dependence of the volume and self-diffusion coefficient of PEO-20 in the simulation. Blue squares and red circles indicate the volume and self-diffusion coefficient D, respectively. Dotted lines indicate the fitting lines for volume change.

Figure 4. Snapshots of a pulling simulation in the shear mode for flat substrates and PEO-20. (a) t = 0.0 ns. (b) t = 1.2 ns. (c) t = 2.3 ns.

examples of snapshots of a pulling simulation in shear mode for the flat metal substrates. During this process, the substrates moved horizontally, while the polymer conformation did not change much. In Figure 5a, force curves are plotted as a

transition points of PEO with other chain lengths in the same way; the transition points of PEO-10 and PEO-30 were 325 and 340 K, respectively. Therefore, the simulations were carried out at a constant temperature of 300 K, which corresponds to the rubbery amorphous solids of all model polymer samples. When constructing the initial structures, it is important to distribute polymers uniformly between the metal substrates because regions with low polymer density or defects might become the origins of fractures. Therefore, we repeated the following two steps to fill the pores uniformly with polymer chains: (1) apply high temperature (600 K), which is above the liquid−solid transition points of the polymers, while keeping the positions of metal substrates fixed to prevent volume expansion. (2) Apply low temperature (300 K) without fixing the position of the metal substrates to allow the volume to decrease as the polymer filled the pores. An example of the preparation of porous samples is shown in Figure 3. Because the breaking of adhesion depends on the random formation of cracks or friction with various neighboring chains, it is important to observe average behaviors. In this simulation, we prepared five initial states with different chain allocations to ensure that average behaviors were observed.

Figure 5. Force curves in the shear mode for flat substrates and PEO20. (a) Force curves of three different samples. (b) Average of five simulation runs.

function of the displacement of the substrates for three MD samples with different initial structures. To aid visibility, we showed only three examples of the total of five simulation runs. Here, sample 1 corresponds to the snapshots in Figure 4. Figure 5a reveals that the metal substrate moved with a stick− slip motion: at first, the metal substrates were pinned by static friction forces and they accumulated shear stress. Then, the substrates jumped suddenly to lower the stress. Such processes occurred repeatedly in the simulation. In each curve in Figure 5a, data points were connected on the basis of temporal sequence. Because there were large fluctuations in the shear

Figure 3. Preparation of porous samples. Polymers penetrated into pores at 600 K. (a) t = 0 ns. (b) t = 25 ps. (c) t = 775 ps. (d) Final structure obtained by repeated heating and cooling. C

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B modes, the substrates moved back and forth and passed the same distance several times. In the earlier time of such processes, when the substrate was ahead of the equilibrium pulling position, the pull force became smaller. In the later time, it was behind the equilibrium pulling position and the pull force became larger. These processes repeated continuously, which resulted in the asymmetric counterclockwise patterns in Figure 5a. Figure 5b is the force curve obtained by averaging the five MD simulation runs. Using the ensemble average, we can estimate the mean force to pull the substrates. In Figure 5b, the average forces were plotted as a function of displacement. We then examined the effects of pores in the metal substrates on polymer−metal adhesion in the shear mode. Figure 6 shows a typical example of the MD snapshots for the

Figure 7. Force curves in the shear mode for porous substrates and PEO-20. (a) Force curve of each sample. (b) Average of five simulation runs. Error bars are shown for displacements of 2 and 5 nm.

from the pores or dragged into the pores. We calculated the temporal change of number of each polymer segments in the pores during the shear simulations in Figure 6e. This result indicated that most polymers in the pores showed small changes in the fraction located in the pores. In the case of amorphous polymer solids, the movements of polymer chains were limited and the complete replacement of polymer chains during the shear process hardly occurred. Thus, high stress accumulated in these porous samples mainly by chain deformation. Although, these behaviors are obvious in general, the correlation between the porous structure and shear force might be rather complicated. It is not clear whether the shear force is simply proportional to the surface area of the pores. We will address this issue below again. Next, we simulated the extension behavior at PEO-20−metal interfaces with and without pores. In Figure 8, we show snapshots of the pulling behavior in the extension mode for the flat metal substrates. Molecules are displayed in different colors to clearly distinguish them from each other. During substrate separation, small voids first appeared inside the polymer layer and then grew into large cracks. As the substrates separated further, polymer strings remained in the middle region and then the polymer layer eventually divided. Figure 9 presents the force curves as a function of displacement of the substrates. The extension force increased rapidly before destruction of the adhesion layer. After formation of very small voids, the extension force decreased rapidly for a while and then the force curves showed very long tails until the complete breakage of the polymer layer. As depicted in Figure 9a, the extension behavior shows less variation between samples than the shear behavior.

Figure 6. Snapshots of a pulling simulation in the shear mode for porous substrates and PEO-20. (a) t = 0.0 ns. (b) t = 1.2 ns. (c) t = 3.0 ns. (d) t = 4.0 ns. (e) Evolution of the number of atoms located in the pores for each polymer chain.

porous substrates. The diameter and depth of the pores was 4 and 2 nm, respectively. In contrast to their behavior on the flat substrates, the polymer chains change their positions and conformations considerably around the pores. The force curves for five MD simulation runs are shown in Figure 7a. We displayed the displacement up to 6 nm so as to avoid the effect of interaction with another mirror pore arising from the periodic boundary conditions in our systems. The averaged force curve for the porous substrates is shown in Figure 7b, as well as that for the flat substrates for comparison. The presence of pores increases the average pulling force by about ten times compared with that for flat substrates. The large shear force for the porous substrates originates from the anchoring of the polymer chains around the pores, as depicted in Figure 6b. Here, the polymers that spanned both the porous and bulk regions are highlighted. As the displacement of the porous substrates increased, conformations of polymer chains were largely deformed. Some polymer segments were pulled out D

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 8. Snapshots of a pulling simulation in the tensile mode for flat substrates and PEO-20. (a) t = 0.0 ns. (b) t = 0.65 ns. (c) t = 1.2 ns. (d) t = 2.0 ns. (e) t = 2.5 ns. (f) t = 3.0 ns.

Figure 10. Snapshots of a pulling simulation in the tensile mode for porous substrates and PEO-20. (a) t = 0.0 ns. (b) t = 0.65 ns. (c) t = 1.2 ns. (d) t = 2.0 ns. (e) t = 2.5 ns. (f) t = 3.0 ns.

bulk polymer layer. These voids grew into large cracks in a similar manner to that observed for the flat substrates (Figure 8). Meanwhile, few voids appeared inside the pores. The configuration of polymer molecules inside the pores was almost unchanged during the fracture induced by the extension force. Figure 11 shows the force curves as a function of substrate displacement. The overall shape of the force curves for the porous samples was similar to that of the force curves for the flat samples (Figure 11a). The variation between the force curves for different samples was relatively small in the initial period before crack formation. In contrast, the variation between samples became larger in the late period. Figure 11b compares the force curves for the porous and flat substrates that were each obtained by averaging the force curves of the five samples. In the case of extension, the adhesion behavior of the flat and porous samples was almost the same under the simulation conditions used here. Unlike the shear behavior, the breakdown occurred through the formation of small voids. The probability of void formation would be related to the increase of system volume. In the case of vertical pores like those in our samples, the increase of system volume on extension was the same for both flat and porous samples. Therefore, the difference in extension behavior became almost negligible during the initial extension period. So far, we have described the overall features of the shear and extension modes of adhesion at polymer−metal interfaces, mainly focusing on the effects of pores on the adhesion behavior, with fixed pore size and polymer chain length. Hereafter, we move to more detailed analysis. First, we consider the relationship between the pore sizes and mechanical properties at PEO-20−metal interfaces. In this case, we confined our attention to the shear mode because the pores mainly affected the shear behavior as shown previously. We changed the depth and diameter of pores independently.

Figure 9. Force curves in the tensile mode for flat substrates and PEO-20. (a) Force curve of each sample. (b) Average of five simulation runs.

The effects of pores in the metal surface on the extension behavior at PEO-20−metal interfaces were then examined. Snapshots of the pulling behavior in the extension mode for porous metal substrates are provided in Figure 10. The diameter and depth of each pore was 4 and 2 nm, respectively. As shown in Figure 10b, small voids appeared mainly in the E

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 13. Force curves in the shear mode for systems with various pore depths. Force curves were obtained by averaging five simulation runs. For comparison, error bars are shown for displacements of 2 and 5 nm.

just inside the pores mainly contribute to the adhesion behavior in the shear mode. Next, we examined the effects of the pore diameter on adhesion at polymer−metal interfaces. Figure 14 shows

Figure 11. Force curves in the tensile mode for porous substrates and PEO-20. (a) Force curve of each sample. (b) Average of five simulation runs. Error bars are shown at both breaking points and a displacement of 3 nm.

Figure 12 shows examples of the initial configurations with pore depths of 0.5, 1.0, 1.5, and 2.0 nm. Here, the pore

Figure 14. Examples of initial configurations with pore diameters of (a) 1.0, (b) 2.0, (c) 3.0, and (d) 4.0 nm. Some PEO-20 molecules are depicted in blue to aid comparison.

examples of the initial configuration of systems with various pore diameters and a fixed depth of 2 nm. When the pore diameter was 1.0 nm, only a few polymer molecules penetrated into the pores and they extended in these narrow pores because the pore diameter was smaller than the polymer size. Figure 15a compares the average force curves for the systems with different pore diameters under the shear force. Looking at the steady states (after a displacement of about 4 nm in this figure), the shear forces increased gradually with pore diameter from 1 to 3 nm. This behavior is in sharp contrast to the dependence of shear force on pore depth shown in Figure 13, in which the steady shear forces increased suddenly at a certain threshold of pore depth. Our findings suggest that the number of polymer molecules intersecting the pore and flat regions strongly affects adhesion behavior. Meanwhile, the increase of steady shear force was far smaller than the increase of pore area, which is proportional to the square of pore diameter. We have calculated the mean bond force by skeletal bonds (C−C and C−O bonds of PEO main chains) as a function of distance from pore center for samples with the pore diameter of 4.0 nm (Figure 15b). Here, we divided the pore entrance region into five regions by the distance from the centers of cylindrical

Figure 12. Examples of initial configurations with pore depths of (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0 nm. Some PEO-20 molecules are depicted in blue to aid comparison.

diameter was fixed to 4 nm, which is a little larger than the polymer radius. In Figure 12, some polymer molecules in the pores are shown in blue to aid comparison of the sizes of the pores and polymer molecules. As seen in Figure 12a, only the first layers of polymer atoms were located within the pores when the pore depth was 0.5 nm. Figure 13 displays the average force curves during the shear simulations with different pore depths. This figure indicates that even the shallow pores generated a large shear force. In addition, the shear force did not strongly depend on the pore depth in the range between 0.5 and 2.0 nm. This suggests that the polymer atoms located F

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 15. (a) Force curves in the shear mode for systems with various pore widths. Force curves were obtained by averaging five simulation runs. For comparison, error bars are shown for displacements of 2 and 5 nm. (b) Distribution of mean bond force from pore center. Error bars are shown in black lines.

pores and they were represented by the middle values of each radius range (e.g., 0.6 nm for radius range 0.4−0.8 nm). For vertical range (z direction), we considered the area within 0.5 nm above and below the pore entrance. As bond forces fluctuated largely, we averaged them for 1.0 ns (displacement from 3.7 to 5.7 nm). This result suggests that the mean bond stretching force in the pore center is smaller than that in the peripheral region. Meanwhile, the region just adjacent to the pore wall was not the place where the polymer chains were mostly stretched. Because the polymer bonds were not uniformly deformed in pores, contribution to the shear resistance was not simply proportional to the number of polymer molecules intersecting the pore and flat regions. The effects of chain length on the adhesion behavior at polymer−metal interfaces were then analyzed in detail. Although the size of pores and length of polymer chains have a somewhat relative relationship from the viewpoint of geometry, the observed mechanical properties at polymer− metal interfaces cannot be simply scaled by the ratio of these two parameters. This is because the mechanical strength of the polymer layer changes with polymer length, whereas the interaction between the polymer atoms and surface atoms does not change much with polymer length. Figure 16a,b displays the average force curves for polymers with different chain lengths (PEO-10, PEO-20, and PEO-30) in extension simulations with flat and porous substrates, respectively. The diameter and depth of the pores were 4 and 2 nm, respectively. These force curves show that longer polymer chains led to larger breaking strength. On the other hand, the displacement at the peak force did not strongly depend on the chain length. In Figure 16c, we examined the free volume of the polymer

Figure 16. Force curves in the extension mode for systems with various polymer lengths (PEO-10, PEO-20, PEO-30). (a) Flat surfaces. (b) Porous surfaces. Force curves were obtained by averaging five simulation runs. For comparison, error bars are shown around the breaking points and a displacement of 3 nm. The width and depth of the pores are 4 and 2 nm, respectively. (c) Free volume of PEO-10, PEO-20, and PEO-30 before fracture for flat surfaces.

layer for flat substrates during extension processes until the fracture. This result suggested that the amounts of free volume are almost the same regardless of chain length in our simulation range, although PEO-30 was slightly smaller than PEO-10 and PEO-20. We supposed that the systems with longer polymer chains have more interconnectivity of strong covalent bonds than that with shorter polymer chains, which resulted in the larger breaking strength for longer chains. In the large displacement region (1−6 nm), the force curves of longer polymer chains showed longer tails than the force curves of the shorter polymer chains. In the case of long polymer chains, chain connectivity suppresses the separation of polymers in fibrils, which resulted in the long tails in their force curves. These simulation results of cohesive fracture for flat substrates have features common to cavitation phenomena in bulk polymers.36,37 In the case of a bead-spring model, it was G

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

when the imprint shape was vertical. Another experiment suggested that the imprint depth contributes little to the adhesion strength in the case of a patterned metal surface attached to a polyamide.7 In our simulation results, the extension mode was not strongly affected by the presence of nanopores (see Figures 9 and 10). Reference 6 also reported that the samples imprinted with a pattern with an undercut larger than 25° showed increased tensile strength. If we consider that such an undercut induces an additional contribution from the shear mode, their experimental results may qualitatively correspond to the effects of nanopores on the shear mode behavior obtained from the simulations (Figure 7). Thus, our simulation results share common features with these experimental results even though the scales of these simulated and experimental systems are different. In the case of nanostructures prepared by chemical treatment, the nanopores are often not a simple vertical hole like those in our simulation model; they may have a more complicated interconnected structure or sponge-like structure.4,5 In such cases, the adhesion force is related to both the tensile and shear modes. Because the shear forces for rough surfaces are considerably larger than those for flat surfaces, the total adhesion force would be high for such interconnected porous surfaces. In this study, we investigated the mechanical properties of interfaces between linear polymers and metal surfaces with nanopores. The effects of crosslinking in polymers on polymer−metal adhesion were not considered here but would be an interesting future topic. The crosslinks would suppress the fracture or sliding of polymer chains, which change the system behavior from cohesive fracture to adhesive fracture. Another interesting topic is the effects of homogeneous polymer dispersion in the nanopores on adhesion behavior. When the polymer chains do not sufficiently penetrate into the nanopores, the pore might become a weak point in the bonding between the polymer and metal, which might weaken the adhesion strength. However, the relationship between polymer density in nanopores and mechanical properties has not been clarified systematically. Further simulation studies along with experimental investigations should lead to comprehensive understanding of the adhesion mechanisms at polymer−metal interfaces.

reported that the longer polymer chains showed a longer stress plateau, whereas the peak in the force curves occurred at similar displacement.36 Therefore, our results in a full atomistic model are consistent with the results in a bead-spring model. The force curves for polymers with different chain lengths in shear simulations with flat and porous substrates are provided in Figure 17a,b, respectively. The pore sizes are the same as

Figure 17. Force curves in the shear mode for various polymer length (PEO-10, PEO-20, PEO-30). Force curves were obtained by averaging five simulation runs. (a) Flat surfaces. (b) Porous surfaces. The width and depth of the pores are 4 and 2 nm, respectively. For comparison, error bars are shown for displacements of 2 and 5 nm.

those in Figure 16b. Figure 17b reveals that longer polymer chains showed larger shear forces for the porous substrates. Although the same dependence of force on chain length was observed for both the extension and shear modes, it arises from different origins. At the steady stage in the late period in the shear mode, shear forces are induced by the friction between polymer chains. Because the friction is larger for longer polymer chains, the shear force becomes larger for longer polymer chains. Note that clear dependence of shear force on chain length was not seen for the flat substrates (Figure 17a). Another interesting feature is the amount of fluctuation in the force curves. As shown in Figure 17b, PEO-30 showed large fluctuations in shear force. In the case of longer polymers, the segment inclusion in pores or exclusion from pores would cause large stress generation and release. We next consider the relationship between our simulation results and reported experimental results. Because there are almost no systematic experiments on the effect of nanostructures in metal surfaces on polymer adhesion, a direct comparison is not easy. With regard to the extension mode, an experiment that compared the behavior of a flat interface with one with imprinted patterns with a depth of 500 μm in adhesive-polypropylene systems has been reported.6 In their experiments, the tensile strengths of the interfaces were similar

4. CONCLUSIONS We investigated the adhesion behavior at polymer (PEO)− metal (Al) interfaces with different surface roughness by MD simulations. The pore diameter was varied from 1.0 to 4.0 nm and the pore depth from 0.5 to 2.0 nm in the simulations. The degrees of polymerization of PEO used in the simulations were 10, 20, and 30. In the case of shear behavior, the systems with pores showed larger shear forces in the steady states than those with flat surfaces. In the case of flat polymer−metal interfaces, the conformations of polymer chains did not change much during shear simulations. Conversely, in the case of porous polymer−metal interfaces, they were gradually deformed with increasing shear strain. The large increase in the shear forces mainly resulted from the deformation of polymer chains near the pore edges and their subsequent exclusion from or inclusion in the pores. Unlike the shear mode, the behavior in the extension mode was almost the same for both flat and porous polymer−metal interfaces. The breaking strength in the extension mode was determined by a different mechanism to that for the shear strength. In the case of extension mode, H

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

(4) Kimura, F.; Kadoya, S.; Kajihara, Y. Effects of molding conditions on injection molded direct joining using a metal with nano-structured surface. Precis. Eng. 2016, 45, 203−208. (5) Suzuki, A.; Arai, Y.; Takata, N.; Kobashi, M. Effect of layer thickness on bonding strength of Al/epoxy resin joints via interpenetrating phase layer. J. Mater. Process. Technol. 2018, 254, 338−345. (6) Matsuzaki, R.; Tsukamoto, N.; Taniguchi, J. Mechanical interlocking by imprinting of undercut micropatterns for improving adhesive strength of polypropylene. Int. J. Adhes. Adhes. 2016, 68, 124−132. (7) Rodríguez-Vidal, E.; Sanz, C.; Soriano, C.; Leunda, J.; Verhaeghe, G. Effect of metal micro-structuring on the mechanical behavior of polymer-metal laser T-joints. J. Mater. Process. Technol. 2016, 229, 668−677. (8) Byskov-Nielsen, J.; Balling, P. Laser structuring of metal surfaces: Micro-mechanical interlocking. Appl. Surf. Sci. 2009, 255, 5591−5594. (9) Kim, W.-S.; Yun, I.-H.; Lee, J.-J.; Jung, H.-T. Evaluation of mechanical interlock effect on adhesion strength of polymer-metal interfaces using micro-patterned surface topography. Int. J. Adhes. Adhes. 2010, 30, 408−417. (10) Kleffel, T.; Drummer, D. Investigating the suitability of roughness parameters to assess the bond strength of polymer-metal hybrid structures with mechanical adhesion. Composites, Part B 2017, 117, 20−25. (11) Miura, T.; Seki, K. Effects of surface affinity on the ordering dynamics of self-assembled monolayers of chain molecules: Transition from a parallel to a perpendicular structure. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2015, 91, 052604. (12) Miura, T.; Seki, K. Diffusion influenced adsorption kinetics. J. Phys. Chem. B 2015, 119, 10954−10961. (13) Ito, T.; Shimomura, T.; Miura, T. Simulation study of the effect of the side-chain structure on the initial nucleation process of polythiophene derivatives. J. Phys. Chem. B 2017, 121, 1108−1117. (14) Semoto, T.; Tsuji, Y.; Tanaka, H.; Yoshizawa, K. Role of edge oxygen atoms on the adhesive interaction between carbon fiber and epoxy resin. J. Phys. Chem. C 2013, 117, 24830−24835. (15) Semoto, T.; Tsuji, Y.; Yoshizawa, K. Molecular understanding of the adhesive force between a metal oxide surface and an epoxy resin. J. Phys. Chem. C 2011, 115, 11701−11708. (16) Solar, M.; Van der Giessen, E. Polymer-polymer adhesion via connector chains: An MD study of the competition between bulk dissipation and connector pull-out. Comput. Mater. Sci. 2012, 64, 187−191. (17) Zhang, B. Polymer-polymer adhesion with mobile promoters: Connector areal density dependence. AIP Adv.. 2013, 3, 012104-1 012104-10. DOI: 10.1063/1.4775350 (18) Sides, S. W.; Grest, G. S.; Stevens, M. J. Large-scale simulation of adhesion dynamics for end-grafted polymers. Macromolecules 2002, 35, 566−573. (19) Sides, S. W.; Grest, G. S.; Stevens, M. J.; Plimpton, S. J. Effect of end-tethered polymers on surface adhesion of glassy polymers. J. Polym. Sci., Part B: Polym. Phys. 2003, 42, 199−208. (20) Morita, H.; Miura, H.; Yamada, M.; Yamaguchi, T.; Doi, M. Molecular Dynamics Study of the Adhesion between End-Grafted Polymer Films II -Effect of Grafting Density-. Polym. J. 2006, 39, 73− 80. (21) Baljon, A. R. C.; Vorselaars, J.; Depuy, T. J. Computational studies of contact time dependence of adhesive energy due to redistribution of the locations of strong specific interfacial interactions. Macromolecules 2004, 37, 5800−5806. (22) Ge, T.; Grest, G. S.; Robbins, M. O. Tensile fracture of welded polymer interfaces: Miscibility, entanglements, and crazing. Macromolecules 2014, 47, 6982−6989. (23) Tsige, M.; Stevens, M. J. Effect of cross-linker functionality on the adhesion of highly cross-linked polymer networks: A molecular dynamics study of epoxies. Macromolecules 2004, 37, 630−637.

overall conformation of each polymer chain did not change largely before fracture. Because fracture in the extension mode occurs through the formation of large voids or cracks, it is related to the increase of total volume of the system during the extension process. This resulted in the similar behavior of the system in the extension mode regardless of the presence of vertical pores in the metal surfaces. We analyzed the correlation between the pore sizes and shear forces in detail by examining the dependence of shear force on pore depth and diameter and polymer chain length. Shallow pores with a depth of 0.5 nm showed comparable shear strength to those with a depth of 2.0 nm. This result suggested that the polymers inside the pores have little influence on the shear strength of the polymer−metal interface, whereas those near the pore surface played an important role in the generation of the shear stress. The shear force in the steady state increased gradually with the pore diameter. The simulation results also suggested that the shear force was not simply proportional to the number of polymer molecules in the horizontal pore cross section because the number of polymer molecules increased by the square (exponent of two) of hole diameter, whereas the shear strength increased by an exponent of one or smaller. This might be because the polymer molecules near the central part of the pores do not contribute to the shear stress as much as those near the pore peripherals. Systems with longer polymer chains showed larger adhesion strength in both tensile and shear modes. In the case of the tensile mode, fracture occurred at almost the same displacement regardless of chain length. With regard to the shear mode, longer polymer chains transmit the deformation stress to a larger region in bulk layer and increase the resistance to pull out chains from the pores compared with the situation for shorter polymer chains. These mechanisms resulted in the increased adhesion strength of longer polymer chains in the shear mode. These simulation results revealed that the adhesion forces between polymers and rough metal surface are not simply related to the surface area but show complicated relationships with the pulling mode, pore size, and polymer chain length.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (+81)-29-861-3460. ORCID

Toshiaki Miura: 0000-0002-1538-0224 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported in part by a grant from the New Energy and Industrial Technology Development Organization (NEDO).

■

REFERENCES

(1) Awaja, F.; Gilbert, M.; Kelly, G.; Fox, B.; Pigram, P. J. Adhesion of polymers. Prog. Polym. Sci. 2009, 34, 948−968. (2) Baldan, A. Adhesion phenomena in bonded joints. Int. J. Adhes. Adhes. 2012, 38, 95−116. (3) Fabrin, P. A.; Hoikkanen, M. E.; Vuorinen, J. E. Adhesion of thermoplastic elastomer on surface treated aluminum by injection molding. Polym. Eng. Sci. 2007, 47, 1187−1191. I

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B (24) Yew, Y. K.; Minn, M.; Sinha, S. K.; Tan, V. B. C. Molecular simulation of the frictional behavior of polymer-on-polymer sliding. Langmuir 2011, 27, 5891−5898. (25) Higuchi, Y.; Saito, K.; Sakai, T.; Gong, J. P.; Kubo, M. Fracture process of double-network gels by coarse-grained molecular dynamics simulation. Macromolecules 2018, 51, 3075−3087. (26) Yang, S.; Gao, F.; Qu, J. A molecular dynamics study of tensile strength between a highly-crosslinked epoxy molding compound and a copper substrate. Polymer 2013, 54, 5064−5074. (27) Yang, S.; Cui, Z.; Qu, J. A coarse-grained model for epoxy molding compound. J. Phys. Chem. B 2014, 118, 1660−1669. (28) Min, K.; Kim, Y.; Goyal, S.; Lee, S. H.; McKenzie, M.; Park, H.; Savoy, E. S.; Rammohan, A. R.; Mauro, J. C.; Kim, H.; et al. Interfacial adhesion behavior of polyimides on silica glass: A molecular dynamics study. Polymer 2016, 98, 1−10. (29) Jiang, N.; Sen, M.; Zeng, W.; Chen, Z.; Cheung, J. M.; Morimitsu, Y.; Endoh, M. K.; Koga, T.; Fukuto, M.; Yuan, G.; et al. Structure-induced switching of interpolymer adhesion at a solidpolymer melt interface. Soft Matter 2018, 14, 1108−1119. (30) Ogata, S.; Uranagase, M. Unveiling the chemical reactions involved in moisture-induced weakening of adhesion between aluminum and epoxy resin. J. Phys. Chem. C 2018, 122, 17748−17755. (31) Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701−1718. (32) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 1992, 114, 10024−10035. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (34) Sgouros, A. P.; Vogiatzis, G. G.; Kritikos, G.; Boziki, A.; Nikolakopoulou, A.; Liveris, D.; Theodorou, D. N. Molecular simulations of free and graphite capped polyethylene films: estimation of the interfacial free energies. Macromolecules 2017, 50, 8827−8844. (35) Berro, H.; Fillot, N.; Vergne, P.; Tokumasu, T.; Ohara, T.; Kikugawa, G. Energy dissipation in non-isothermal molecular dynamics simulations of confined liquids under shear. J. Chem. Phys. 2011, 135, 134708. (36) Baljon, A. R. C.; Robbins, M. O. Simulations of crazing in polymer glasses: effect of chain length and surface tension. Macromolecules 2001, 34, 4200−4209. (37) Morozinis, A. K.; Tzoumanekas, C.; Anogiannakis, S. D.; Theodorou, D. N. Atomistic simulations of cavitation in a model polyethylene network. Polym. Sci., Ser. C 2013, 55, 212−218.

J

DOI: 10.1021/acs.jpcb.8b10556 J. Phys. Chem. B XXXX, XXX, XXX−XXX