ARTICLE pubs.acs.org/JPCA
Modeling Reaction Pathways of Low Energy Particle Deposition on Polymer Surfaces via First Principle Calculations Michelle Morton,† Joseph Barron,† Travis Kemper,‡ Susan Sinnott,‡ and Nedialka Iordanova*,† † ‡
Department of Chemistry, Georgia Southwestern State University, Americus, Georgia 31709, United States Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611-6400, United States ABSTRACT: The chemical processes that lead to polystyrene surface modification via low energy deposition of C2Hþ, C2Fþ, CH2, CH2þ, and Hþ radicals and ions are examined using first principles calculations. Specifically, the reaction mechanisms responsible for products identified in classical molecular dynamics with reactive empirical bond-order potentials are examined using density functional theory. In addition, these calculations consider how the presence of charges on the incident particles changes the result for the CH2 system through the comparison of barriers, transition states, and final products for CH2 and CH2þ. The structures of the reaction species and energy barriers are determined using the B3LYP hybrid functional. Finally, CCSD/6-31G(d,p) single point energy calculations are carried out to obtain optimized energy barriers. The results indicate that the large variety of reactions occurring on the polystyrene surface are a consequence of complex interactions between the substrate and the deposited particles, which can easily be identified and characterized using advanced computational methodologies, such as first principle calculations.
I. INTRODUCTION Polystyrene (PS) is one of the four most common thermoplastics used worldwide.1 It is low cost, easy to process, and has low density, high electrical resistivity, and relatively high modulus. These properties have led to its use in a myriad of applications ranging from toys and disposable dinnerware to biomedical implants.14 Surface modification via plasma or ion-beam treatment is an inexpensive and efficient way of altering the surface properties of polymers such as PS.37 For example, in the case of biomedical applications, plasma modification is often used to increase the biocompatibility of PS for use as implants, antifouling surfaces, biosensors, and barrier coatings.4,5 Similarly, ion beam deposition has been used to improve its surface properties, including hardness and resistance to friction and wear in applications such as bearings, gears, and guides.6,7 Fundamental to all these approaches is the change in bonding at the surface due to energetic particle bombardment. Molecular dynamics (MD) simulations have been carried out of particle bombardment on PS surfaces in order to elucidate the reactions that occur during surface modification.811 In this work, ab initio methods are used to determine the reaction pathways and energy barriers associated with the chemical reactions identified in the MD studies that are likely to occur during ion-beam deposition or plasma treatments. The results provide important insights into these reactions that cannot be otherwise obtained.
radicals and ions were examined using first principle calculations. MD simulations using the second generation reactive empirical bond order (REBO) potential10 were first used to identify likely products as a result of the interactions between radicals (C2H, CH2, and H) and the surface of polystyrene. The current form of the REBO potential does not allow for the inclusion of explicit charges, so only radicals could be considered. Due to the variety of particles used, a large number of products were identified as a result of the attachment of particles to the benzene ring and the backbone chain. The reaction mechanisms to obtain the identified products were then examined using DFT methods. In addition, the DFT calculations considered how the presence of charge changed the result for the CH2 system through the comparison of barriers, transition states, and final products for CH2 and CH2þ. In particular, the structures of the reaction species and energy barriers were determined using the B3LYP hybrid functional.12 Due to the relatively large size of the systems (more than 22 atoms), only subsequent single point energy calculations using the CCSD (coupled cluster singles and doubles) method13,14 were performed on each optimized structure to obtain more accurate energetics. A. Reactive Empirical Bond Order (REBO) Simulations. To isolate the most frequently formed products on the surface of polystyrene, a series of MD simulations were performed with the REBO potential where particles were deposited with kinetic energies of 4 or 10 eV on β00 syndiotactic polystyrene
II. COMPUTATIONAL METHODS The chemical processes that lead to PS surface modification via low energy deposition of C2Hþ, C2Fþ, CH2, CH2þ, and Hþ
Received: December 14, 2010 Revised: March 18, 2011 Published: April 28, 2011
r 2011 American Chemical Society
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Figure 1. Crystalline polystyrene where the black and white atoms are thermostated and the blue and gray atoms are active: (a) side view along the backbone and (b) top view.
Table 1. Percent Reactivity of Deposited Ions with Substrate H
CH2
C2H
4 eV
10 eV
4 eV
10 eV
4 eV
10 eV
in substrate
24.67
48.33
39.67
70.89
53.00
74.67
bonded
15.00
33.67
24.00
58.33
30.67
58.33
bonded to ring
12.67
24.67
17.50
42.00
19.00
35.50
C(2)
2.67
6.67
4.17
12.00
4.00
7.50
C(3)
2.67
3.67
5.67
9.17
5.33
7.83
C(4)
1.33
5.00
5.00
10.50
7.33
9.67
C(5)
2.00
4.67
2.67
6.67
2.00
7.33
C(6)
4.00
4.67
0.00
3.67
0.33
3.17
(Figure 1).15 The reactivity of the ions with the substrate is summarized in Table 1. Separate simulations were carried out for each deposited particle species and kinetic energy. In each simulation, particles were randomly oriented and positioned within the surface plane and deposited in continuous beams impacting every 1.5 ps. Each beam contained 300 particles corresponding to fluencies of 97.6 1018 atom/cm2. Following continuous deposition, the systems were evolved for an additional 25 ps until the fluctuations in the potential energy were less than 0.0033 eV/ atom. The surface was then analyzed to identify the products of the deposition process. B. Density Functional Theory Calculations. The MD trajectories that yield products observed with high frequency (>5%) were subsequently examined using DFT. The reactant species, including the deposited particle and the PS monomer, as well as the REBO predicted product were optimized using the B3LYP hybrid functional and a 6-31G(d,p)16 basis set. Transition states and intermediates were identified along the reaction pathways using the above level of theory. Frequency analysis was performed as well, to confirm a single imaginary frequency along the reaction coordinate for each transition state and one real frequency for each minimum. Since two minima on a potential energy surface may have more than one reaction pathway to connect them, involving different transition state structures, IRC
Figure 2. Optimized geometries of PS monomer, CH2þ/•, C2Hþ, C2Fþ, Hþ, and PS monomer with a longer chain.
(intrinsic reaction coordinate)17 calculations were performed to verify that a particular transition structure connects the starting and ending species of interest. The IRC calculation starts at the saddle point and follows the path in the forward and reverse directions, optimizing the geometry of the system at each point specified along the path. Using this procedure one can be certain that two minima are definitely connected through the transition state between them, which is essential to characterize the details of a reaction path. All geometry optimizations, frequency, and IRC calculations were performed using the Gaussian 0318 package. C. Coupled Cluster Calculations. In general, the optimization of reaction structures using DFT leads to reliable geometries, but the energy barriers are not necessarily predicted with high accuracy. To determine more precisely the energy barriers for the reaction pathways considered, single point CCSD/6-31G(d,p) calculations were performed on the B3LYP/6-31G(d,p)-optimized reaction structures. For each case involving open shell systems, unrestricted DFT and CCSD calculations were performed within the Gaussian 03 package.
III. RESULTS A. C2Hþ and C2Fþ Deposition. MD simulations of C2H mole-
cule deposited onto a PS surface resulted in a majority of deposited molecules, 17% and 25% at deposition energies of 4 and 10 eV, respectively, bonding to the C2, C3, and C4 positions of the phenol ring (Table 1). The primary product formed during 4977
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Figure 3. Reaction profile of the interaction of C2Hþ with the polystyrene monomer. The barriers are presented in Table 2.
Figure 4. Reaction profile of the interaction of C2Fþ with the polystyrene monomer. The barriers are presented in Table 3.
the C2H reaction with the phenol carbons was the addition of the C2H to the carbon with the carbonhydrogen bond remaining intact (Figure 3). The addition reaction of C2H to C2, C3, or C4 occurred during 68% and 55% of the bonding reactions of C2H with PS for 4 and 10 eV deposition energies, respectively. Therefore, the reaction mechanisms of the addition of C2H were further studied with quantum chemical methods. The first step of the characterization was to optimize the structures of the reactant species using DFT. The optimized geometries of the PS monomer where the backbone carbon chain is capped with H atoms and the deposited species are shown in Figure 2. In the case where the deposition of a CH2•/þ particle on the backbone chain was investigated, a longer chain (Figure 2) was used comprised of five carbon atoms instead of three carbon
atoms, as used for all other reactions. In addition to the DFT calculations, an optimization of the deposited particles was performed using different levels of theory and basis sets in order to obtain the lowest energy structure with the most accurate geometry for each particle. Due to the good agreement between the different methods in regard to the geometry parameters and for consistency, in this work, we used the B3LYP/6-31G(d,p)-optimized geometries of the deposited particles and the PS monomer to examine the various surface reaction mechanisms. The results from the DFT calculations are presented in blue in all of the energy diagrams and the ones from the CCSD calculations in purple; for all tables, the energy differences on the left-hand side are denoted by capital letters, and those on the right-hand side are denoted by capital letters and a prime symbol. 4978
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The first set of reactions investigated in the present study involves the interaction of a C2Hþ particle with the polystyrene Table 2. Reaction Barriers (kcal/mol) for the Interaction of C2Hþ with the Polystyrene Monomer C2Hþ
B3LYP/
CCSD/
B3LYP/
CCSD/
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
B
10.87
12.08
B0
11.49
13.06
A
12.46
14.16
A0
15.90
17.51
C
11.13
12.56
C0
11.47
12.74
D
16.12
18.84
D0
16.63
18.56
Table 3. Reaction Barriers (kcal/mol) for the Interaction of C2Fþ with the Polystyrene Monomer B3LYP/
CCSD/
B3LYP/
CCSD/
C2Fþ
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
A
10.35
12.44
A0
13.98
15.93
B
9.35
10.68
B0
9.81
11.61
C D
9.54 14.83
11.18 17.25
C0 D0
9.58 14.71
11.20 16.98
Table 4. Reaction Barriers (kcal/mol) for the Interaction of Hþ with the Polystyrene Monomer Hþ
B3LYP/
CCSD/
B3LYP/
CCSD/
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
6-31G(d,p)
A
15.46
14.17
A0
15.30
14.32
B C
15.95 11.47
15.43 11.08
B0 C0
16.09 12.17
15.75 11.92
D
11.50
11.25
D0
11.87
11.45
E
17.10
17.26
E0
16.97
16.99
monomer. The overall charge of the system is þ1 and the multiplicity considered here is a singlet. As given in Figure 3, the reaction pathway shows that the interaction leads to various product minima where the C2Hþ particle is attached on one of the benzene carbon atoms. The minima are connected via transition states corresponding to bridged structures where the C2Hþ particle is interacting with two neighboring carbon atoms of the benzene ring. The reactant species and each minimum are directly connected, since the interaction between the C2Hþ and the styrene benzene ring is proven to be barrierless, as shown on Figure 3. The reaction profile shows the single point CCSD calculations as well. The latter are in accordance with the B3LYP calculations and give consistent relative energies between the minima and transition states. In Figure 3, as well as on all other figures in this work that illustrate a reaction mechanism, the zero is considered to be the sum of the reactants energies. The calculations indicated above were performed for the deposition of the C2Fþ particle on the polystyrene chains as well (see Figure 4). Due to the similar properties of the deposited C2Hþ and C2Fþ particles, the reaction profiles are alike, although the relative energies between the minima and transition structures are different. The numerical values of the reaction barriers calculated using the DFT and the CCSD methods for both deposited species (C2Hþ and C2Fþ) are summarized in Tables 2 and 3. The formation of a similar barrierless adduct was observed by Landera et al.,19 who studied the reactions of the ethynyl radical (C2H•) with benzene. In our case, the addition of the C2Hþ particle to the benzene ring of the PS monomer occurs with a much higher exothermicity of 196 kcal/mol, compare to the 42.2 kcal/mol for the interaction of the ethynyl radical with benzene. Other groups also studied the interaction of the C2H• radical with a series of small molecules.2026 This radical attracts scientists’ attention due to its importance in interstellar space and planetary atmospheres. Similar to our work, the results from these studies show a variety of reaction mechanisms when highly
Figure 5. Reaction profile of the interaction of Hþ with the polystyrene monomer. (Note the minimum where the H atom is attached to the C1 carbon atom could not be localized due to steric hindrance of the C1 carbon atom by the side chain.) The barriers are presented in Table 4. 4979
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Figure 6. Reaction pathways for CH2 triplet radical on (1) C3, (2) C4, (3) C5. The barriers are presented in sections a, b, and c of Table 5, respectively. 4980
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Table 5. Reaction Barriers for the Interaction of CH2 Triplet Radical with the Polystyrene Monomer C3, C4, and C5 Positions reaction barriers, kcal/mol B3LYP/6-31G(d,p)
CCSD/6-31G(d,p)
(a) Polystyrene Monomer C3 Position A
4.95
10.51
B C
26.59 40.66
29.87 47.14
D
39.71
43.78
(b) Polystyrene Monomer C4 Position A
4.84
10.52
B
26.69
29.90
C
40.83
44.19
D
40.11
40.99
(c) Polystyrene Monomer C5 Position A B
5.07 26.10
10.66 29.43
C
40.58
47.14
D
40.16
42.98
reactive particles such as the ethynyl radical interacts with other species. B. Hþ Deposition. MD simulations of atomic hydrogen deposited on PS were conducted with kinetic energies of 4 and 10 eV. Of the 300 H particles deposited at energies of 10 eV, 14.7% remained in molecular form, 9% bonded to the backbone carbons, and 24% bonded to the phenol carbons, while molecules deposited at 4 eV resulted in 75% that does not penetrate the substrate. Of the 25% that penetrated the substrate, a majority (14%) bonded to the phenol carbons, while only 1% bonded to the backbone. While there was some apparent favored bonding to the C6 carbon of the 35 molecules that bonded to the phenol carbons for the 4 eV deposition, the relatively few reactions occurring did not produce statistically viable probabilities. Therefore, according to the MD simulations, H exhibits nonpreferential bonding to PS. The gas-phase study of the low energy deposition of Hþ particles on the polystyrene surface was performed as for the C2Hþ and C2Fþ deposition. All minima and transition state structures were optimized using the methods described above (see Table 4). A single imaginary frequency was found for each transition state along the reaction pathway by performing frequency analysis calculations. In addition, the connection of each two neighboring minima to a specific transition state was confirmed via IRC calculations. As illustrated in Figure 5, the reaction profile was found to be very similar to those of the C2Hþ and C2Fþ particle depositions. When in the vicinity of the PS monomer, the Hþ attaches directly to one of the carbon atoms of the benzene ring, forming a positively charged nonaromatic product. The product can isomerize to another one by a migration of the proton to another carbon atom via a triangularshaped transition state (see Figure 5). C. CH2 Deposition. 1. Triplet (charge = 0, multiplicity = 3) and Singlet (charge = 0, multiplicity = 1) Radicals. The REBO simulations used to model the deposition of CH2 particles on the PS surface showed that bonding to the C2, C3, and C4 positions on the styrene ring was more probable than bonding to the C5 or C6 positions. Further, the products are a combination
of two processes: (i) attachment of the CH2 particle on one of the benzene carbon atoms and breaking the aromaticity of the ring and (ii) attachment of the CH2 particle on one of the benzene carbon atoms and subsequent transfer of the hydrogen atom from the benzene ring to the CH2 particle to form a methyl group, restoring the aromatic structure of the ring. The molecular dynamic simulations performed with REBO do not take into account explicitly the charge of the incident particle and they do not distinguish between ionic or radical particles. Depending on the electronic structure of the incident particle, singlet and triplet states with neutral charge were considered, as well as a doublet cation. The first case that is discussed in the current study concerning the deposition of the CH2 particle is the deposition of a CH2 radical particle with two unpaired electrons—a triplet. As a result of the performed gas-phase DFT calculations, it was determined that the two reaction pathways i and ii identified in the molecular dynamic simulations can be considered as two processes that are part of one reaction profile and are connected through a transition state structure. The CH2 triplet radical was allowed to interact only with the carbon atoms on positions 3, 4, and 5 in the benzene ring of the polystyrene, since the MD simulations indicated that the reaction predominantly occurs there. The reaction pathways resulting from the CH2 triplet radical deposition and the corresponding barriers are given in Figure 6 and Table 5. As a result of the quantum mechanical characterization of the reaction of the CH2 singlet radical with the polystyrene benzene ring, it was determined that a concerted mechanism is more preferable for the formation of a methyl product on the C3, C4, and C5 positions (Figure 7). The energy barriers for this reaction using the DFT and CCSD methods are summarized in Table 6. 2. CH2 Doublet Cation (charge = þ1, multiplicity = 2). As illustrated in Figure 8, the reaction pathway that was initially determined for the deposition of the CH2þ particle using the B3LYP/6-31G(d,p) level of theory involves the formation of stable structures where the CH2 cation forms bonds with two carbon atoms of the benzene ring (C4 and C5). The first optimized intermediate was found to be more stable than the reactant complex by approximately 128 kcal/mol. Then the reaction proceeds through the formation of a transition state for which the barrier was calculated to be ∼73 kcal/mol, which further evolves to another minima corresponding to CH2 bonded to an adjacent pair of carbon atoms of the benzene ring (C5 and C6). The last structure was found to be ∼76 kcal/mol more stable than the transition state structure. Since the reaction occurs with a significant stabilization of the first intermediate, we expect to observe similar pathways if the CH2 cation is initially situated in the vicinity of another pair of carbon atoms of the benzene ring undergoing a consequent hop along the benzene ring through the formation of a transition structure similar to the one depicted on Figure 8. Although this reaction was identified by our calculations, the high activation energy required for the formation of the transition state indicates a relatively low probability of occurrence. Similar to the formation of methyl derivative products for the interaction of the CH2 singlet and triplet radicals with the benzene ring, in this case we also investigated the possibility of the formation of the same product when the CH2 cation interacts with the benzene ring. The current calculations did not provide a viable mechanism for this particular case, and the formation of a methyl derivative as a result of the cation deposition is not considered further in our study. 4981
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Figure 7. Reaction pathway of CH2 singlet radical on (1) C3, (2) C4, (3) C5. The barriers are presented in sections a, b, and c of Table 6, respectively. 4982
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Table 6. Reaction Barriers for the Interaction of CH2 Singlet Radical with the Polystyrene Monomer C3, C4, and C5 Positions reaction barriers, kcal/mol B3LYP/6-31G(d,p)
CCSD/6-31G(d,p)
(a) Polystyrene Monomer C3 Position A
76.60
78.44
B C
68.96 110.83
75.62 112.71
(b) Polystyrene Monomer C4 Position A
76.41
B
61.13
78.09 70.77
C
103.14
108.09
(c) Polystyrene Monomer C5 Position A
75.99
B
61.44
77.83 70.54
C
103.88
108.23
D. CH2 Deposition on the Backbone Chain. 1. CH2 Triplet Radical. In addition to all reactions studied in the current work
that involve the interaction of the small reactive particle with the benzene ring of the polystyrene monomer, some reactions of the deposited particles with the backbone chain were also investigated. In order to consider these reactions, a PS monomer with a longer backbone chain was constructed as illustrated in Figure 2. The longer backbone allows the deposited particle to interact with one of the carbon atoms from the chain to form the product. The first reaction that was investigated here involves the deposition of a CH2 triplet radical. All the structures localized along the reaction pathway were optimized using the B3LYP/6-31G(d,p) level of theory. Vibrational analysis was performed to confirm the single imaginary frequencies for the transition structures and one positive frequency for the reactant and product minima and intermediates. IRC calculations were carried out to confirm the connection of each transition state to the corresponding preceding and subsequent minima. The results from the calculations performed for the deposition of the CH2 triplet radical are summarized in Figure 9 and the energy barriers are given in Table 7. 2. CH2 Singlet Radical. A similar pathway was determined when a CH2 singlet radical was deposited, and its interaction with the backbone chain was observed. The calculations were performed on the HF level of theory using the 6-31G(d,p) basis set for consistency. This particle, although technically a ground-state radical, was not run as such due to the default settings of the Gaussian 03 program; instead, the calculations were run with the assumption that the particle was a closed shell species, leaving it in an excited state. The same holds true for C2Hþ and C2Fþ described in a previous section. As indicated in Figure 10 the first step of the profile is the formation of the reactant complex, which is more stable than the sum of the isolated reactants by ∼1 kcal/ mol (Table 8). For this reaction, the formation of the transition state requires significantly larger activation energy (∼16 kcal/ mol) than what was observed in the previous case discussed. Another major difference between the singlet and triplet radical interaction with the backbone was that when the CH2 singlet radical was deposited, its interaction with the backbone led to the
Figure 8. Reaction pathway of CH2þ doublet that does not involve the formation of a methyl derivative.
formation of the methyl side chain polystyrene derivative product, avoiding the formation of the intermediate that was observed in the reaction described above. The product was found to be significantly more stable than the transition state. Its energy is 114 kcal/mol lower than the calculated transition state energy. IRC calculations were performed to confirm that the transition state connects the reactant complex and the product. In addition, for each structure localized along the reaction pathway, vibrational analysis calculations were performed as well to determine if a true first-order saddle point and reaction minima are isolated. The pathway described above was unachievable using B3LYP/6-31G(d,p). When using B3LYP, the IRC calculations from the transition state both led to the same product. In particular, it can be seen that the two directions take a different path, but in the end they finish at the same point with the same energies. This pathway was also attempted using BMK with a 6-31G(d,p) basis set for consistency, and this approach also gave the product in both directions. Apparently the B3LYP and BMK functional are not sufficiently adequate to describe the reaction profile, or the observed behavior can be attributed to the fact the product is significantly more stable than the reactant complex and the IRC calculation diverts to it.
IV. DISCUSSION A. C2Hþ and C2Fþ Deposition. As indicated in Table 2, the
reaction profile clearly indicates that the most favorable attachment of the C2Hþ particle occurs on the para-position, as expected from the effect of the backbone chain on the benzene ring reactivity. In addition, the calculations predict relatively close barriers for the formation of the C4C5 and C3C4 transition states as well as for the C5C6 and C2C3 transition states pair. As shown on the left-hand side of the reaction pathway, the slight differences can be attributed to the steric hindrance of the carbon atoms of the benzene ring due to the backbone chain. The C2Fþ particle is more reactive than the C2Hþ due to the presence of the fluorine atom, and as a result, as indicated in Table 3, all the barriers are lower for the C2Fþ particle migration on the benzene ring. As for the C2Hþ deposition, the C2Fþ deposition is most preferable on the para-position of the benzene ring, but since the gas-phase attachment of the C2Fþ 4983
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Figure 9. Reaction pathway of CH2 triplet radical with the backbone chain. The barriers are presented in Table 7.
Table 7. Reaction Barriers (kcal/mol) for the Interaction of CH2 Radical Triplet with the Backbone Chain of the Polystyrene Monomer B3LYP/6-31G(d,p)
CCSD/6-31G(d,p)
A
0.75
0.78
B
4.77
12.51
C
19.10
20.86
D
0.96
2.65
particle on the PS ring is barrierless for any carbon position of the ring, each of the minima is accessible, depending on the orientation of the C2Fþ particle with respect to the benzene ring when deposited. Using the DFT method and the above-described combination of charge and multiplicity, no additional structures were isolated for the C2Hþ and C2Fþ deposition on the PS surface, and no other reaction pathways were examined in the current study. The interactions of these cations as well as other positively charged particles considered in this study with the PS surface are of great interest to us because the gas-phase energy profiles can be used to refine and improve the REBO potential, which currently does not allow the use of charged particles in the simulations. B. Hþ Deposition. The data in Table 4 indicate that, as expected for electrophilic addition of alkyl-activated benzene ring, the ortho- and para-products are more stable than the meta ones. The para-product is 1.12 kcal/mol more stable than the C6 ortho-product and 1.19 kcal/mol more stable than the C2 orthoproduct. Due to the orientation of the isopropyl group and its steric effect on the benzene ring, it would be expected that the C6 is less stable than the C2 minimum. Our calculations show a slightly opposite effect. The C6 minimum is more stable than the C2 minimum. After analyzing the structures of the optimized products, it was determined that the isopropyl group rotated significantly to accommodate the incoming Hþ particle only when the proton was attaching on the C6 position. Apparently, this rotation leads to enough stabilization of the product that the
C6 minimum has lower energy than the C2 minimum. The slight variations of the transition barriers on the left- and right-hand side of the reaction profile are also attributed to the presence of the isopropyl group and its rotation during the reaction. If the addition occurred on a methyl-activated benzene ring, we would expect perfectly symmetric barriers for the ortho- and metapositions, respectively. C. CH2 Deposition. 1. Triplet (charge = 0, multiplicity = 3) and Singlet (charge = 0, multiplicity = 1) Radicals. As mentioned above in the Results section, as indicated from the MD simulations, only three attachment reactions were considered for the deposition of the CH2 triplet radical: on C3, C4 and C5 carbon atoms of the PS benzene ring. In all three cases, the formation of the final product occurs through a mechanism that involves the formation of two transition states (TSs) connected by an intermediate structure. The first TS is characterized by the CC stretch between the carbon atom of the incident particle and the carbon atom of the benzene ring. In all three cases the formation of the first TS is preceded by the formation of a weak molecular complex between the reactants. The complex is ∼0.5 kcal/mol more stable than the reactants, and since its formation does not affect significantly the reaction rate and mechanisms, it is omitted on the diagram for simplicity. Additionally, in all three cases the rate-limiting state is the formation of the second TS structure corresponding to the transfer of the H atom from the benzene ring to the attached CH2 particle. The intermediate that connects the two TS states corresponds to a stable nonaromatic structure resulting from the attachment of the CH2 particle to the ring. As the diagrams and Table 5 illustrate, the formation of the second transition state requires a barrier of ∼2 eV to be overcome for all three cases. Both DFT and coupled cluster calculations indicated similar barriers, and the results are consisted within each method as well. The second TS evolves to the product of the reaction where the H atom from the benzene ring has transferred to the CH2 particle to form a methyl group. The final product is slightly less stable compared to the intermediate, but the overall reaction describing the interaction of the CH2 triplet radical with the 4984
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Figure 10. Reaction pathway of CH2 singlet radical with the backbone chain (HF).
Table 8. Reaction Barriers (kcal/mol) for the Interaction of CH2 Radical Singlet with the Backbone Chain of the Polystyrene Monomer (HF level of theory) HF/6-31G(d,p) A
0.984
B
15.97
C
114
benzene ring of the styrene monomer is exothermic. As the diagrams show in all three cases, the CCSD calculations result in larger barriers compared to the DFT data, but the mechanism of the process does not change. Both the DFT and the coupled cluster calculations clearly indicate that the gas-phase reactions studied here require relatively large activation energies to be overcome for the formation of the second transition state. Although the process in a gas-phase is predicted to be relatively slow, the MD simulations indicated that the formation of the methyl derivatives of the polystyrene is a frequent process resulting in a variety of products. Since neither MD nor gasphase ab initio calculations can provide a complete description of the surface modification of polystyrene via small particle deposition on its own the two methodologies are utilized in conjunction to ensure a complete and detailed description of the process. For the deposition of the CH2 singlet radical, both the DFT and CCSD calculations showed a large energy barrier for the reaction (see Table 6). The results were consistent with HF calculations that were performed in addition as a comparison. The HF calculations showed that the intermediate is 62.83 kcal/ mol more stable than the reactants for attachment at the C3 position. As predicted in the calculations performed for the other small particles discussed previously, the reactions proceed with similar barriers for the C3, C4, and C5 positions on the benzene ring. The concerted reaction profile determined for the
interaction of CH2 singlet with the benzene ring clearly indicates that the sequential mechanism to obtain the methyl derivative of the PS monomer involving the triplet radical might be energetically more preferable. 2. CH2 Doublet Cation (charge = þ1, multiplicity = 2). Similar to the results obtained for the deposition of the CH2 singlet radical, the formation of the products when a CH2þ particle was deposited required a large activation energy of ∼73 kcal/mol. This is again an indication that this particular reaction where the product contains the deposited particle bonded to two carbon atoms of the benzene ring is energetically unfavorable. D. CH2 Deposition on the Backbone Chain. 1. CH2 Triplet Radical. For the deposition of the CH2 triplet radical, Figure 8 illustrates that the first step of the reaction involves the formation of a reactant complex that is 0.75 kcal/mol more stable than the isolated reactants (Table 7). In this complex, the deposited radical is in the vicinity of the backbone chain, which allows the reaction to proceed easily through a TS where an H atom from the backbone is shared between the CH2 radical and the PS side chain. The activation energy for the formation of this transition structure is relatively low, 4.77 kcal/mol. The next step in the reaction involves the formation of an intermediate that is approximately 19 kcal/mol more stable than the transition structure. The intermediate contains a CH3 particle that is separated from the PS monomer. The formation of the reactant complex and the intermediate was confirmed by running IRC calculations in the reverse and forward directions. A product structure was also localized along the pathway where the CH3 particle is attached to the backbone chain, forming a methyl side chain derivative of the initial PS monomer used. The energy difference between the intermediate and the final product is very small; the intermediate is more stable than the product by 0.96 kcal/mol, and that was attributed to the electron density in the intermediate being such that there is charge separation between the CH3 particle and the monomer which stabilizes the structure. 4985
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The Journal of Physical Chemistry A In general, the CCSD calculations give similar results but, as can be seen from Table 8, the barrier for the formation of the TS is around 7.5 kcal/mol higher than was predicted by DFT. In addition, instead of having another low barrier to go from the intermediate to the product, the CCSD method predicts that the product is more stable than the intermediate by 2.65 kcal/mol. The minor discrepancies are attributed to the correlation effects taken into account explicitly by the CCSD method compared to the empirical correlation embedded in the DFT.
V. CONCLUSIONS In the work presented, a series of reactions between a PS monomer and small reactive particles has been studied using ab initio methods. Two different structures of the PS monomer were used in order to be able to observe not only the interaction of the deposited small particles with the PS benzene ring, but the reactions with the PS hydrocarbon backbone chain as well. After determining the most frequently observed products of the interaction of the PS with C2Hþ, C2Fþ, Hþ, CH2 radical (triplet and singlet), and CH2þ using MD simulations, the ab initio calculations were initiated. The first step of the calculations involved identification of all reaction structures along a certain reaction pathway leading to a particular product using DFT (B3LYP/6-31G(d,p)) as a fast and reliable method to determine structures with relatively large number of atoms. To identify reaction minima and transition states, frequency calculations were performed for each localized structure, and additional IRC calculations were carried out to relate two minima with the transition structure found between them. To obtain a more accurate energetic profile, a single point CCSD calculation was performed on each optimized structure using the same basis set. The calculations showed a large variety of reactions to obtain the products found as a result of the MD simulations, and each reaction was analyzed in detail. In summary, the interactions of the C2Hþ and C2Fþ particles with the benzene ring of PS monomer occur as a barrierless reaction of attachment of the particle on the ring, breaking the aromaticity of the ring. After the particle was attached, it was observed that it can further migrate along the carbon atoms of the ring, forming stable products through a series of transition states. The processes required moderate activation energies (CCSD ∼1019 kcal/ mol). The deposition of a proton on the PS surface led to a similar reaction profile. The proton easily attaches to one of the benzene carbon atoms and was shown to be able to migrate to other adjacent carbon atoms, overcoming moderate reaction barriers (∼1117 kcal/mol) corresponding to transition structures where the hydrogen atom was shared between two carbon atoms of the PS benzene ring. When a CH2 triplet radical particle was deposited on the PS surface, the most frequently observed product in the MD simulations was a methyl derivative of the PS monomer. The meta- and para-products were mainly investigated since the ortho-product was observed much less frequently in the MD simulations due to the hindrance of the reaction by the backbone chain. For both meta- and para-positions of the benzene ring, the reaction profiles observed were similar, involving the formation of two transition states and an intermediate. The barrier for the formation of the second transition state was relatively high for all three cases (>44 kcal/mol), while the activation energy required for the formation of the first transition structure was only ∼5 kcal/mol. The reactions of the CH2 triplet radical were significantly different from the interaction of the CH2 singlet radical with the
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PS monomer. The latter involved the formation of only one transition state, and the mechanism of the formation of the methyl product was concerted. The formation of reactant complex led to a significant stabilization (>78 kcal/mol) in comparison to the isolated reactants, but the activation energy for this reaction was really too high (>75 kcal/mol) to be considered as a competitive channel to obtain the product. The interaction of the CH2 cation with the PS benzene ring was also determined to be energetically unfavorable according to our calculation. The formation of a cyclic product where the CH2þ particle is attached to two adjacent carbon atoms of the benzene ring required a large activation energy (>72 kcal/mol) to overcome the barrier for the formation of the transition state connecting the reactant complex and the product. The last type of reaction investigated in the current work involved the deposition of CH2 radicals (singlet and triplet) on the backbone of the PS monomer. In both cases a methyl derivative was localized as a final product of the reaction where the methyl group was formed by the attachment of the CH2 particle on the backbone chain and a subsequent migration of a hydrogen atom from the chain to the CH2 carbon atom. The barrier for the formation of the transition state was found to be relatively small, ∼5 kcal/mol, so the reactions were identified as energetically favorable. The calculations performed in the present investigation allowed us to study the mechanism of the reactions in great detail and to determine which of the interactions are energetically more favorable. The results obtained were used to characterize the mechanism of the reactions. The calculated reactions barriers will be used in our further investigations related to improvement of currently existing potentials utilized in MD simulations to study surface reactions of various materials.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We gratefully acknowledge the support of the National Science Foundation (CHE-0809376). We thank Prof. K. Morokuma for the stimulating discussions and the Cherry L. Emerson Center for Scientific Computation at Emory University for providing computational resources partly funded by NSF MRI-R2 grant (CHE0958205). ’ REFERENCES (1) Harper, C. A. Handbook of Plastics, Elastomers, and Composites; New York: McGraw-Hill, 2002. (2) Nicholson, J. W. The Chemistry of Polymers; Royal Society of Chemistry Paperbacks; Royal Society of Chemistry: Cambridge, UK, 2006. (3) Hanley, L.; Sinnott, S. B. Surf. Sci. 2002, 500, 500–522. (4) Chu, P. K.; Mater. Sci. Eng., R 2002, 36, 143–206. (5) Siow, K. S.; Britcher, L.; Kumar, S.; Griesser, H. J. Plasma Process. Polym. 2006, 3, 392–418. Lee, E. H. Nucl. Instrum. Methods Phys. Res. B 1999, 151, 2941. (6) Lee, E. H.; Rao, G. R.; Lewis, M. B.; Mansur, L. K. J. Mater. Res. 1994, 9 (4), 1043. (7) Dong, H.; Bell, T. Surf. Coatings Technol. 1999, 111, 29–40. (8) Jang, I.; Ni, B.; Sinnott, S. B. J. Vac. Sci. Technol., A 2002, 20, 564–568. 4986
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