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Molecular Modeling of a Thin Film of Polybenzoxazine Won-Kook Kim and Wayne L. Mattice* Maurice Morton Institute of Polymer Science, The University of Akron, Akron, Ohio 44325-3909 Received April 24, 1998. In Final Form: September 1, 1998 Atomistic polybenzoxazine (PBO) thin films of thickness ∼28 Å were constructed in a vacuum from the bulk amorphous PBO by increasing one edge (the z-axis) of the cubic cell enough, 100 Å, so that the atoms cannot interact with periodic images in this direction. The density profile with respect to the distance from the center of mass was obtained. The density drops rapidly at the distance of ∼7 Å from the surface, and the density in the interior (1.05 g/cm3) is slightly lower than the bulk density (1.1 g/cm3). The average location of chain ends is ∼5 Å from the surface. In the composition distribution profile, polar atoms are rich in the interior of the film while the nonpolar atoms are slightly enriched near the surfaces. The fraction of hydrogen bonds in the thin film was found to be slightly higher than that in the bulk. The predicted surface tension from the internal energy contribution is 46 ( 6 dyn/cm.
Introduction Polymer thin films play an important role in various technologies such as adhesion, coatings, paints, and microelectronics. Thin films experience directional asymmetry in the interaction with their surroundings, and the properties and structures of films are different from those of the bulk state. Molecular modeling techniques, as well as other experimental techniques such as surface force apparatus,1 grazing incidence X-ray scattering,2 and neutron reflectivity,3 are useful for studying the thin film or interface. Compared to experimental methods, molecular modeling can attain very detailed atomistic information using only the chemical constitution and interatomic force parameters. With current computational power, fully atomistic simulation of polymer films with several nanometer thickess is accessible4-8 and has been successfully applied for polyethylene, polypropylene, polybutadiene, and styrene-butadiene and styrene-butadiene-acrylonitrile copolymers. To study larger size systems, simulations have been performed on a lattice9-11 or in continuous space with coarse graining12-16 as well. These methods * To whom correspondence should be addressed. (1) Christenson, H. K.; Gruen, D. W. R.; Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1987, 87, 1834. (2) Factor, B. J.; Russell, T. P.; Toney, M. F. Macromolecules 1993, 26, 2847. (3) Russell, T. P. Mater. Sci. Rep. 1990, 5, 171. (4) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1990, 23, 4430. (5) Zhan, Y.; Mattice, W. L. Macromolecules 1994, 27, 7056. (6) Misra, S.; Fleming, P. D.; Mattice, W. L. J. Comput.-Aided Mater. Des. 1995, 2, 101. (7) He, D.; Reneker, D. H.; Mattice, W. L. Comput. Theor. Polym. Sci. 1997, 7, 19. (8) Natarajan, U.; Tanaka, G.; Mattice, W. L. J. Comput.-Aided Mater. Des. 1997, 4, 193. (9) ten Brinke, G.; Aussere, D.; Hadziioannou, G. J. Chem. Phys. 1988, 89, 4374. (10) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1989, 22, 3143. (11) Smith, G. D.; Yoon, D. Y.; Jaffe, R. L. Macromolecules 1992, 25, 7011. (12) Kumar, S. K.; Vacatello, M.; Yoon, D. Y. J. Chem. Phys. 1988, 89, 5209. (13) Vacatello, M.; Yoon, D. Y.; Laskowski, B. C. J. Chem. Phys. 1990, 93, 779. (14) Thompson, P. A.; Grest, G. S.; Robbins, M. O. Phys. Rev. Lett. 1992, 68, 3448. (15) Yoon, D. Y.; Smith, G. D.; Matsuda, T. J. Chem. Phys. 1993, 98, 10037. (16) Matsuda, T.; Smith, G. D.; Winkler, R. G.; Yoon, D. Y. Macromolecules 1995, 28, 165.
sacrifice somewhat the detailed chemical geometry and covalent bonds in order to achieve equilibration of the large size system. The recent development of a “mapping and reverse mapping approach” permits the construction of the films with thickness exceeding 10 nm, but this technique is currently limited to polymers with simple repeat units, such as polyethylene.17 Several methods have been applied to study polymer thin films, using fully atomistic molecular modeling techniques such as molecular mechanics or molecular dynamics. In an earlier atomistic simulation by Mansfield and Theodorou,4 the initial atactic polypropylene thin film was generated in an orthorhombic box (17.04 × 17.22 × 61.17 Å3) containing multiple parent chains, using a steep repulsive potential at the cell faces normal to the longest direction in order to confine the chains within the box. The microstructure of the thin film was obtained by potential energy minimization of the initial guess structure using multiple stages of potential representation. These authors observed that (i) the density drops very rapidly within ∼5 Å of the surface region but that, in the interior region, the film reproduced bulk density, (ii) backbone bonds in the surface region (within ∼10 Å of the free surface) tended to orient parallel to the plane of the surface, (iii) the conformation distribution in this region also deviated from that in the interior region, and (iv) for the chains whose centers of mass were located near the surface region, the average chain width parallel to the surface plane was remarkably larger than that for the chains located in the interior region. More recently, in the work of Misra et al.,6 poly(cis-butadiene) thin films were prepared from the bulk structure by extending one of the periodicities to be long enough (100 Å) so that the parent chains do not have interatomic interactions with their periodic images in that direction. The final equilibrated thin films of ∼25 Å thickness were obtained by subsequent relaxation of this “pseudo-2-D” cell. The predicted surface tension is 26 ( 10 dyn/cm, which is close to the experimental value of 31 dyn/cm at 300 K.6 In the present work, the surface properties of polybenzoxazine (PBO) thin films were studied, motivated by the technological importance of the surfaces, since PBO has (17) Doruker, P.; Mattice, W. L. Macromolecules 1998, 31, 1418.
10.1021/la9804738 CCC: $15.00 © 1998 American Chemical Society Published on Web 10/09/1998
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Figure 1. Comparison of the bulk structure in a 3-D periodic box and the thin film in a pseudo-2-D periodic box. The 2-D thin film was obtained from the 3-D bulk structure by extending one of the periodicities
a potential for application in adhesives or electronics.18 The energetics of the thin film as well as the surface structure can play an important role in these industries. Compared to previous molecular models of polymer thin films, PBO is more complicated in modeling due to the structural constraints of the bulky phenyl ring and the directional constraints of the hydrogen bonding. Recently, amorphous PBO molecular models were obtained at the
bulk density 1.1 g/cm3 and the hydrogen bonds, radial distribution function, free volume size and shape distribution, and solubility parameter were studied.19 Since the bulk structures are available, the method of Misra et al.6 was employed to build the PBO thin films. On the basis of the PBO thin film molecular models, the energetics of the thin film, the hydrogen bonding, the density distribution profile, the bond orientational order param-
(18) Ishida, H.; Allen, J. D. J. Polym. Sci., Polym. Phys. Ed. 1996, 34, 1019.
(19) Kim, W.-K.; Mattice, W. L. Comput. Theor. Polym. Sci., in press.
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Figure 2. Potential energy evolution during NVT dynamics at 500 K for one of the thin films.
eter, and the composition distribution profile as functions of distance from the center of mass were studied. Simulation Method and Details As starting structures, the static bulk PBO molecular models at the bulk density 1.1 g/cm3 with the cubic periodic boundary conditions of periodicity 20.075 Å were employed.19 One of the periodicities (z-axis) was chosen and extended long enough (100 Å) while fixing the other two periodicities (x and y). As a result, parent chains cannot have interactions with their periodic images in this direction and only can have interactions in x and y directions. Relaxation with this “pseudo-two-dimensional” condition can successfully imitate the thin film environment. A schematic description of this process is illustrated in Figure 1. The times required for the relaxation of the system in two-dimensional periodicity are relatively faster than those of the bulk structure, since the density occupied by the parent chain within the “pseudo-two-dimensional” volume is much less than the bulk density under 3-D cubic continuity conditions. The initial structures formed by conversion from the bulk to the thin film environment were further relaxed by employing NVT molecular dynamics at 500 K, which is slightly above the glass transition temperature of PBO bulk (450 K).18 To relax the structure within a short time interval, the choice of a relatively high temperature was essential. For this reason, 500 K was chosen although the initial density of the amorphous cell is that at room temperature. During the simulation, the cutoff distance 9.5 Å was employed for the nonbonded energy calculation. The potential energy drops during the first 100 ps and then reaches a steady state, as shown in Figure 2. On the basis of this information, more than 100 ps of NVT dynamics was applied for the rest of the independent pseudo-twodimensional initial structures. The lowest energy snapshots among the trajectories were chosen and minimized further with the energy convergence criteria 0.1 kcal mol-1 Å-1. The resultant four independent equilibrated film structures, with energy lower than the energy of the initial amorphous cell and a symmetric density distribution with respect to the distance from the center of mass, were employed for further analysis.
Figure 3. Density profile as a function of the distance from the center of mass plane. The arrow indicates the location of the methyl chain ends. Ortho and para positions are relative to OH.
Results and Discussion 1. Mass Density Profiles. The density profile in the films as a function of the distance from the center of the mass plane is shown in Figure 3. The density was calculated by slicing the z-axis (normal to the surface plane) with the thickness 2 Å. As expected, sigmoidal density profiles are obtained near the surface. The density in the interior of the film is ∼1.05 g/cm3, which is slightly lower than the bulk density, 1.1 g/cm3. The difference in the density between the bulk state and the interior of the film may be because (i) the film simply is not sufficiently thick so that the interior perfectly recovers the bulk structure and (ii) the thermal history of the NVT dynamics at 500 K may affect the density of the relaxed equilibrium film obtained by subsequent energy minimization. The employment of a thicker film (starting from a larger amorphous cell) may help to retain the bulk density at the mass center of the film but would require enormous computer time for generation of the initial amorphous cells.19 Also the relaxation temperature of NVT dynamics at 500 K can affect the density at the interior as well as relax the initial pseudo-two-dimensional structure, although the choice of the temperature 500 K for dynamics, which is above the glass temperature, was essential to achieve the relaxation of the system within feasible computational time. The density drops very rapidly at the distance ∼7 Å from the surface, and the thickness of the surface region is around 8 Å. Due to the entropic reason, the chain ends prefer to be located near the surface. The averaged locations of the carbon atoms in methyl groups attached para and ortho to the hydroxyl group in the chain ends are 10.25 and 9.18 Å, respectively, from the midplane. In the polyethylene thin film atomistic simulation study,7 the discrepancy of the density between the bulk and the interior of films was observed because the films were very thin. The authors employed a method similar
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Figure 4. Orientational order parameter for (a) backbone bonds and (b) phenyl rings.
to that of the current study to construct the equilibrium thin film structure, except for the thickness (∼48 Å) of the film and relaxation with the NVT dynamics at 400 K. More recently, Natarajan et al.8 reported, in the density profiles of the styrene-butadiene (SB) copolymer and the styrene-butadiene-acrylonitrile (SBA) copolymer films of comparable thinness, the discrepancy of the density between the bulk structure (0.97 g/cm3, SB; 0.99 g/cm3, SBA) and the interior of thin films (0.94 g/cm3, SB; 0.95 g/cm3, SBA) when NPT molecular dynamics was performed at 300 K to relax the initial “pseudo-two-dimensional” cells. In the study of Misra et al.6 on polybutadiene and the study of Mansfield et al.4 on atactic polypropylene of thickness ∼65 Å films, the density of the interior films can reproduce the bulk density. 2. Bond Orientational Order and Composition Distribution Profile. Since the particles near the free surface experience vacuum on one side and the film on the other side, orientational ordering of bonds due to the anisotropic energetic contribution in the direction normal to the surface may be expected. The orientation of bonds can be studied using the order parameter defined as
SB )
3〈cos2 θ〉 - 1 2
(1)
where θ is the angle between the bond vector and the normal to the surface plane, and the angle brackets denote the ensemble average. The SB with respect to the distance from the plane of the mass center of the film to the midpoint of the bonds is shown in the top panel of Figure 4. Note that SB ) 1 when the bonds are all normal to the surface and SB ) -1/2 when the bonds are all parallel to the surface. In the case of the phenyl rings (bottom panel of Figure 4), order parameters of the unit vector normal to the planar phenyl ring and the normal to the thin film were considered to describe the orientation. As a consequence, SB ) 1 when the phenyl rings are all parallel to
Figure 5. Composition distribution profile of PBO thin film. The polar atoms are slightly rich in the interior, and the nonpolar atoms are slightly rich near surface. Table 1. Number of Hydrogen Bonds in PBO Thin Filmsa structure
no. of donors (H(O))
no. of acceptors (N)
no. of acceptors (O(H))
film 1 film 2 film 3 film 4 avg avg(RIS) avg(bulk)
25 24 24 25 24.5 ( 0.5 35.4 ( 3.9 22.8 ( 3.3
20 18 18 20 19 ( 1 30.6 ( 1.9 15.8 ( 2.9
5 6 6 5 5.5 ( 0.5 4.8 ( 2.3 7 ( 0.9
a
The results in the last two columns are from ref 19.
the surface, and SB ) -1/2 when the phenyl rings are all normal to the surface. In the figure, the orientational order parameters of bonds and phenyl rings in the interior of the films are indistinguishable from zero, which is characteristic of the bulk material. Bonds close to the free surface (>8 Å) exhibit a slight tendency to be parallel to the surface. This tendency is also observed for bonds in PE,7 PP,4 poly(cisbutadiene),6 and the SB/SBA8 copolymer. The atoms can have maximum contacts with each other when the bonds are parallel to the surface, which is energetically favored. Since PBO is much stiffer than PB or PE, the tendency of orientation of bonds parallel to the surface plane is much weaker. PBO contains polar atoms (H(O), O, and N) and nonpolar atoms (C and H). These two types of atoms can experience dissimilar interactions with a vacuum, which can result in distinct local composition fluctuation along the direction normal to the surface direction. The composition profile parameter can be characterized by
C0(z) ) N ×
Fi(z) F(z)‚ni
(2)
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Table 2. Components of the Internal Energy (kcal/mol) of the Four Independent Bulk Structuresa and the Corresponding Thin Films with the Ensemble Average Surface Energy (〈γE〉) 46 ( 6 γE ) 50.9 dyn/cm total bond angle torsion oop cross nonbond vdW Coulombic a
γE ) 52.9 dyn/cm
γE ) 39.7 dyn/cm
γE ) 40.8 dyn/cm
cell 1
film 1
cell 2
film 2
cell 3
film 3
cell 4
film 4
-694.9 123.1 119.0 -333.6 1.1 -226.7 -377.9 -6.9 -371.0
-636.1 113.8 99.3 -351.0 0.7 -219.0 -280.0 70.3 -350.3
-669.0 128.2 126.8 -323.7 1.0 -232.7 -368.6 4.9 -373.5
-607.9 117.4 106.0 -341.9 0.5 -222.2 -267.6 86.2 -353.8
-516.2 161.6 170.0 -277.6 1.5 -247.0 -324.6 27.8 -352.4
-470.4 157.4 146.3 -319.2 0.9 -237.0 -218.9 124.7 -343.6
-667.3 124.1 121.2 -316.8 1.5 -234.2 -363.1 -9.6 -353.5
-620.1 116.9 100.1 -347.0 0.7 -220.1 -270.7 62.5 -333.2
The bulk structures are from ref 19.
where N is the number of atoms in the system, F(z) is the number density at distance z, ni is the number of atoms of i type in the system, and Fi(z) is the number density of i at the distance z. In this expression, when elements of type i are relatively rich compared to the random distribution, the value is higher than 1, and when elements of type i are relatively poor, then the value is less than 1 at the given distance z from the plane of the mass center. In the composition distribution profile as shown in Figure 5, the polar atoms are slightly rich in the interior of the film, and nonpolar atoms such as H and C(C3) are relatively rich near the surface. The interaction of the vacuum with polar atoms is unfavorable; therefore, the polar atoms prefer to be located in the interior of the film. The number of hydrogen bonds for each film is listed in Table 1. Whenever the distance between donors (H(O)) and acceptors (O(H), N) is shorter than 2.5 Å and the absolute angle of H-O‚‚‚N or H-O‚‚‚H(O) is greater than 120°, the hydrogen bond was defined. The same definition for the hydrogen bonds was applied in both the bulk structure and RIS Monte Carlo initial chains for the bulk structures.19 About 74% of the hydroxyl groups participated in the hydrogen bonds, and ∼78% of the acceptors were provided by nitrogen atoms. The number of hydrogen bonds in PBO thin films (24.5) is marginally higher than that in the PBO bulk but definitely less than that in the single chain subject to short-range interactions, including the interaction between nearest neighbor hydroxyl groups but ignoring interactions of longer range. The fraction of nitrogen atoms as the acceptors of hydrogen bonds in PBO thin films is higher than that in the PBO bulk state (69%) but less than that in the PBO single chain subject to shortrange interaction (86%). The observed number of hydrogen bonds in the three systems becomes smaller as the density of the system increases. This seemingly counterintuitive result can be rationalized by considering the conformational requirements for the shortest range intramolecular hydrogen bond, which is from a phenolic hydroxyl group to a nearest neighbor nitrogen atom. Formation of the hydrogen bond places strong constraints on the dihedral angles at the Car-CH2 and CH2-N bonds, where Car denotes a carbon atom in the six-membered ring. This restriction causes a rather large portion of the chain, corresponding to the structure CH2-C6H2(OH)(CH3)-CH2-N(CH3)-CH2, to approximate a single rigid unit. This large rigid unit can be accommodated without difficulty in an isolated chain, but it presents important problems when multiple chains must be packed together in a dense amorphous structure. An efficient packing at high density is more easily obtained if the rigidity of the unit is reduced, which requires disruption of the intramolecular hydrogen bond between OH and the nearest N. Therefore the amorphous structure
at high density contains fewer hydrogen bonds than does the isolated chain. 3. Surface Energy. The particles near the free surface experience an anisotropic environment, and the cohesive attractive interaction is weakened in the surface region. As a result, there is excess free energy in the surface region which is equivalent to the amount of work applied to bring the molecules from bulk to surface states. Technically, the free energy cannot be measured easily due to the entropic contribution, arising from the elasticity of chains exposed to the two different environments of surface and bulk states as well as from chain end segregation and so forth. When the entropic contribution is neglected, the surface energy can be calculated from the internal energy of the thin films. Hence, hereafter, the surface energy is used as the potential energy difference between the bulk structure and the thin film, normalized with total surface area. This can be described as
γE )
〈E2D - E3D〉 2A
(3)
where E2D is the energy of the thin film, E3D is the energy of the bulk structure, A is the surface area of one surface, and the prefactor of 2 in the denominator arises because each thin film has two surfaces. The ensemble average, indicated by 〈...〉, is calculated from the difference in energy between an amorphous cell and its corresponding thin film cell, for all available pairs. In this simulation, four independent thin films were obtained. The surface area A is 20.0752 Å2. In Table 2, the details of the energy in the amorphous cells and the film cells are listed. The averaged surface energy from four independent sets of systems is 46 erg/cm2 with the standard deviation of 6 erg/cm2. The nonbonded energy parts, including van der Waals and Coulombic energy, are the major part of the surface tension. But the torsional, bending, and bond stretching energies of films are lower than those of amorphous cells. Because the density of the surface layer is lower than those of the bulk or interior of the film, the surfaces of the films have less steric hindrance from the surroundings and can have lower bond, bending, and torsional energies than bulk structures. The experimental value of the surface energy of PBO is not available yet. The predicted surface tension of PBO is comparable to the surface tension of several other polymers which have hydrogen bonds or high electrostatic interaction, such as Nylon 6,6 (46.5 erg/cm2),20 poly(vinyl chloride) (41.5 erg/cm2),20 and poly(methyl methacrylate) (41.1 erg/ cm2).21 (20) Dann, J. R. J. Colloid Interface Sci. 1970, 32, 302. (21) Wu, S. J. Polym. Sci. 1971, C34, 19.
Thin Film of Polybenzoxazine
Summary PBO thin films of thickness ∼28 Å were constructed in a vacuum from the bulk amorphous cell by extending one edge (the z-axis) of the cubic cell long enough, 100 Å, so that the chain cannot have interactions with its periodic image in this direction. In the density profile of the films with respect to the distance from the plane of the mass center, a fairly symmetric profile was obtained and the density of the interior of the film is found to be 1.05 g/cm3, which is a little less than the bulk density 1.1 g/cm3. This might result from insufficient thickness of the film (i.e., the interior of the thin film may not reproduce the bulk property) or the effect of the thermal history of 500 K employed during molecular dynamics to relax the initial structure within a feasible time period, since PBO has fairly stiff units and directional constraints of hydrogen bonds. The density drops very rapidly around 8 Å, and the estimated surface thickness is about 7 Å from the density
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profile. The average chain end location was found to be ∼5 Å from the free surface. The bonds near the surfaces are slightly oriented to be parallel to the surface plane. In the composition distribution profile, polar atoms are rich in the interior of the film while the nonpolar atoms are slightly rich near the free surface. The number of hydrogen bonds in the thin films is predicted to be higher (24.5) than that in the bulk structures (22.8) and less than that in the single chain at the Θ condition (35.4). The predicted surface tension from the potential energy difference between surface cells (2-D) and the amorphous cells (3-D) was 46 erg/cm2 with the standard deviation 6 erg/cm2. Acknowledgment. This work was supported by the Federal Aviation Administration. LA9804738
