Comparative Study on Reactions and Self-Directed Growth

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Langmuir 2006, 22, 3040-3048

Comparative Study on Reactions and Self-Directed Growth Mechanisms of Styrene Molecules on H-Terminated Si(111) and Si(100): Combining Quantum Chemistry and Molecular Mechanics Simulations Yong Pei and Jing Ma* Department of Chemistry, Institute of Theoretical and Computational Chemistry, Key Lab of Mesoscopic Chemistry of MOE, Nanjing UniVersity, Nanjing, 210093, P. R. China ReceiVed July 31, 2005. In Final Form: January 8, 2006 A comparative study on mechanisms of radical initiated self-directed growth of styrene molecules on the H-terminated Si(111) and Si(100) has been carried out by using quantum chemical and molecular mechanics methods. Several possible H-abstraction pathways through formations of transition states containing five-, six-, and even eight-membered ring structures are investigated with the aid of surface cluster models and density functional theory calculations. It has been demonstrated by employing periodic surface models and molecular mechanics simulations that the surface pattern and intermolecular interactions between phenyl groups play important roles in the self-directed growth processes. The formation of cluster-shaped aggregation of styrene molecules on H-Si(111) results from the undirectional chain reactions, due to the isotropic hexagonal arrangement of surface sites. On the contrary, the anisotropic style of H-Si(100) induces a strong directional preference for H-abstractions, following an order of the inter Si-Si dimer > the intra Si-Si dimer . the inter Si-Si dimer row. The one-dimensionally ordered structures of single and double lines along the Si-Si dimer row are thus formed on H-Si(100). The self-directed growths of styrene molecules on both H-Si(111) and H-Si(100) are revealed to be stage-dependent.

1. Introduction The surface chemistry of group IV semiconductors such as silicon and germanium received rapidly growing interest in recent years not only for their important technological applications in information industry but also for their fantastic surface physical and chemical properties.1-5 Modifications of silicon surfaces by attachments of various unsaturated organic molecules brought about potential applications in many fields such as molecular electronics, sensor devices, as well as the template for the biological recognition, etc.1-5 Several methods for preparing organic films on silicon surfaces have been developed, involving both wet chemical and ultrahigh-vacuum approaches.1-5 Among these, a promising way is the radical initiated reaction of unsaturated 1-alkene molecules with the hydrogen-terminated silicon surfaces. Chidsey and co-workers have made pioneering works in preparing covalently attached organic monolayers modified silicon surfaces from the hydrogen-terminated silicon surfaces.6 To date, numerous radical involved reactions have been reported for the H-terminated Si(111), H-terminated Si(100), and the porous silicon.1,7-14 A radical chain reaction mechanism, shown in Scheme 1, was frequently used to account for the thermal and radical initiated (1) Buriak, J. M. Chem. ReV. 2002, 102, 1272-1308. (2) Sieval, A. B.; Linke. R.; Zuilhof. H.; Sudho¨lter, E. J. R. AdV. Mater. 2000, 12, 1457-1460. (3) Buriak, J. M. Chem. Commun. 1999, 1051-1060. (4) Wayner, D. D. M.; Wolkow, R. A. J. Chem. Soc., Perkin Trans. 2002, 2, 23-34. (5) Wolkow, R. A. Annu. ReV. Phys. Chem. 1999, 50, 413-441. (6) Linford, M. R.; Chidsey, C. E. D. J. Am. Chem. Soc. 1993, 115, 1263112632; Linford, M. R., Fenter, P.; Eisenberger, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145-3155. (7) (a) Sieval, A. B.; Demirel, A. L.; Nissink, J. W. M.; Linford, M. R.; van der Maas, J. H.; de Jeu, W. H.; Zuilhof, H. Langmuir 1998, 14, 1759-1768. (b) Sieval, A. B.; Vleeming, V.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 1999, 15, 8288-8291. (c) Sieval, A. B.; Opitz, R.; Maas, H. P. A.; Schoeman, M. G.; Meijer, G.; Vergeldt. F. J.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 2000, 16, 10359-10368.

formations of organic films via Si-X (X ) C, O) linkages on H-terminated silicon surfaces.1-5 On the basis of this mechanism, a surface reaction self-propagates through the formation of a radical intermediate and the H-abstraction process. Experimental evidences for such radical chain mechanism were reported in reactions of a series of organic moieties including styrene, propylene, 1-decene, ferrocene, and aldehyde on H-Si(111) and H-Si(100).11,12,15-20 On the other hand, density functional theory (DFT) calculations have been performed on reactions of 1-alkene molecules with H-Si(111) and H-Si(100) on the basis of cluster (8) (a) Linford, M. R.; Chidsey, C. E. D. Langmuir 2002, 18, 6217-6221. (b) Cicero, R. L.; Linford, M. R.; Chidsey, C. E. D. Langmuir 2000, 16, 5688-5695. (c) Terry, J.; Linford, M. R.; Wigren, C. R.; Cao, Y.; Pianetta, P.; Chidsey, C. E. D. Appl. Phys. Lett. 1997, 71, 1056-1058. (9) (a) Boukherroub, R.; Morin, S.; Wayner, D. D. M.; Bensebaa, F.; Sproule, G. I.; Baribeau, J.-M.; Lockwood, D. J. Chem. Mater. 2001, 13, 2002. (b) Boukherroub, R.; Sharpe, S. M. P.; Wayner, D. D. M.; Allongue, P. Langmuir 2000, 16, 7429-7434. (10) Effenberger, F.; Go¨tz, G.; Bidlingmaier, B.; Wezstein, M. Angew. Chem., Int. Ed. Engl. 1998, 37, 2462-2464. (11) Cicero, R. L.; Chidsey, C. E. D.; Lopinski, G. P.; Wayner, D. D. M.; Wolkow, R. A. Langmuir 2002, 18, 305-307. (12) Lopinski, G. P.; Wayner, D. D. M.; Wolkow, R. A. Nature 2000, 406, 48-51. (13) (a) Stewart, M. P.; Buriak, J. M. AdV. Mater. 2000, 12, 859-869. (b) Buriak, J. M.; Stewart, M. P.; Geders, T. W.; Allen, M. J.; Choi, H. C.; Smith, J.; Raftery, D.; Canham, L. T. J. Am. Chem. Soc. 1999, 121, 11491-11502. (c) Stewart, M. P.; Buriak, J. M. Angew. Chem, Int. Ed. Engl. 1998, 37, 3257-3260. (d) Buriak, J. M.; Allen, M. J. J. Am. Chem. Soc. 1998, 120, 1339-1340. (e) Schmeltzer, J. M.; Porter, L. A.; Stewart, M. P.; Buriak, J. M. Langmuir 2002, 18, 2971-2974. (14) Dabrowski, J.; Mu¨ssig, H.-J. Silicon Surfaces and Formation of Interfaces; World Scientific: Singapore, 2003. (15) Pitters, J. L.; Wolkow, R. A. J. Am. Chem. Soc. 2005, 127, 48-49. (16) DiLabio, G. A.; Piva, P. G.; Kruse, P.; Wolkow, R. A. J. Am. Chem. Soc. 2004, 126, 16048-16050. (17) Tong, X.; DiLabio, G. A.; Clarkin, O. W.; Wolkow, R. A. Nano Lett. 2004, 4, 357-360. (18) Kruse, P.; Johnson, E. R.; DiLabio, G. A.; Wolkow, R. A. Nano Lett. 2002, 2, 807-810. (19) Tong, X.; DiLabio, G. A.; Wolkow, R. A. Nano Lett. 2004, 4, 979-983. (20) Eves, B. J.; Sun, Q.; Lopinski, G. P.; Zuilhof, H. J. Am. Chem. Soc. 2004, 126, 14318-14319.

10.1021/la052093+ CCC: $33.50 © 2006 American Chemical Society Published on Web 03/07/2006

Growth Mechanisms of Styrene Molecules on Si

Langmuir, Vol. 22, No. 7, 2006 3041 Scheme 1. Radical Chain Reaction

a 6MR, the six-membered ring structure, corresponding to pathways of H-abstraction on H-Si(111) and the inter Si-Si dimer H-abstraction on H-Si(100). 5MR, the five-membered ring structure, the intra Si-Si dimer H-abstraction on H-Si(100). 8MR, the eight-membered ring structure, H-abstraction spanning two Si-Si dimer rows on H-Si(100).

models17-19,21,22 and periodic slab models.23-27 In addition, molecular mechanics simulations on some static properties (such as packing structures) of monolayers on silicon surfaces have also been carried out, providing valuable information for experimentalists.22,28-30 Depending on experimental conditions, reactions of 1-alkene molecules with H-Si(111) and H-Si(100) have been shown to yield films with various structures, such as densely packed monolayers,8-10 islands,11,20 and even one-dimensional molecular lines12,16 through Si-C linkages. Recently, scanning tunneling microscope (STM) studies revealed two distinct behaviors of styrene molecules self-directed growth on H-Si(111) and H-Si(100), respectively.11,12 On H-Si(111), the growth of styrene molecules self-terminated within limited steps (on average, ∼20 steps) and preferred to turn back on themselves. A series of compact molecular clusters were formed on H-Si(111) with average lateral sizes of around 20 Å.11 On the contrary, a strong directional preference in the growth of one-dimensional single and double lines along the Si-Si dimer row direction was observed on H-Si(100).12 Here, we shall focus on prototype cases of radical chain reactions of styrene molecules on H-Si(111) and H-Si(100). As shown in Scheme 2, the H-Si(111) and H-Si(100) take two-dimensional rhombic and square lattices, respectively. Surface sites array in an isotropic style on H-Si(111) but adopt the anisotropic distribution on H-Si(100). The key issue of the present work is: What are roles of the surface style and intermolecular interactions playing in surface reactiVities and formations of monolayers? To date, there is still little information available about effects of substrates and intermolecular interactions on surface reactions and propagation mechanisms. Ac(21) Kang, J. K.; Musgrave, C. B. J. Chem. Phys. 2002, 166, 9907-9913. (22) Pei, Y.; Ma, J.; Jiang, Y. Langmuir 2003, 19, 7652-7661. (23) (a) Takeuchi, N.; Kanai, Y.; Selloni, A. J. Am. Chem. Soc. 2004, 126, 15890-15896. (b)Takeuchi, N.; Kanai, Y.; Selloni, J. Phys. Chem. B 2005, 109, 11967-11972. (24) Hofer, W. A.; Fisher, A. J.; Lopinski, G. P.; Wolkow, R. A. Chem. Phys. Lett. 2002, 365, 129-134. (25) Cucinotta, C. S.; Ruini, A.; Caldas, M. J.; Molinari, E. J. Phys. Chem. B 2004, 108, 17278-17280. (26) Cho, J.-H.; Oh, D.-H.; Kleinman, L. Phys. ReV. B 2002, 65, 081310. (27) Lee, J.-Y.; Cho, J.-H. J. Chem. Phys. 2004, 121, 8010-8012. (28) (a) Sieval, A. B.; van der Hout, B.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 2000, 16, 2987-2990. (b) Sieval, A. B.; van der Hout, B.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 2001, 17, 2172-2181. (c) Lee, M. L.; Guo, D.; Linford, M. R.; Zuilhof, H. Langmuir 2004, 20, 9108-9113. (29) Zhang, L.; Wesley, K.; Jiang, S. Langmuir 2001, 17, 6275-6281. (30) Yuan, S.; Cai, Z.; Jiang, Y. New J. Chem. 2003, 27, 626-633.

Scheme 2. H-Si(111) vs H-Si(100)

cording to a simple Monte Carlo simulation done by Chidsey et al., a chain reaction may take place randomly on H-Si(111) and self-terminates when there is no available neighboring H atom for the abstraction (Scheme 3a).8b In contrast, a directional preference of H-abstraction was expected to exist among three possible pathways on H-Si(100) (Scheme 3b). Musgrave et al. theoretically investigated the mechanism of styrene line formation on H-Si(100) through DFT calculations.21 They suggested that a sufficiently stable radical intermediate with respect to the initial adsorption state was essential to ensure the proceeding of H-abstractions. Similar conclusions were also drawn by Selloni et al. through investigating a series of reactions of ethene, styrene, acetylene, and phenylacetylene on H-Si(111) by using the periodic surface model and the string method.23a Moreover, they carried out a comparative study of growth mechanisms of styrene molecules on H-Si(100)-(2×1) and H-Si(100)-(3×1) by employing the same strategy.23b In the present work, we comparatively investigate Habstractions and self-directed growths of styrene molecules on H-Si(111) and H-Si(100). Possible H-abstraction pathways via formations of five-, six-, and eight-membered ring transition states on H-Si(111) and H-Si(100) are investigated through quantum chemical calculations (DFT/B3LYP) in the framework

3042 Langmuir, Vol. 22, No. 7, 2006 Scheme 3. Step by Step Self-Directed Growth of Styrene Molecules on (a) H-Si(111) and (b) H-Si(100)

of surface cluster models. On the basis of the radical chain mechanism, we further survey the step by step propagations of styrene molecules on H-Si(111) and H-Si(100) by using the molecular mechanics method and periodic surface models. The resulting cluster and line structures on H-Si(111) and H-Si(100), respectively, are in good agreement with experimental results.11,12 A stage-dependent mechanism is further suggested for the radical initiated self-propagation of styrene molecules on H-Si(111) and H-Si(100). It may provide new insights into the mechanism of self-directed growth of films on the H-terminated silicon surfaces.

2. Computational Details 2.1. Quantum Chemical (QC) Calculations. The quantum chemical calculations are carried out on SGI 3800 with the Gaussian03 package.31 Two surface cluster models, Si16H25 and Si22H35 (Scheme 2), are adopted to represent H-Si(111) and H-Si(100), respectively. The reason for using the finite cluster model in the QC calculations of surface reactions has been addressed before.32-34 Due to the (31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.03; Gaussian, Inc.: Pittsburgh, PA, 2003. (32) For example, see: (a) Mlynarski, P.; Salahub, D. R. J. Chem. Phys. 1991, 95, 6050-6056. (b) Crispin, X.; Lazzaroni, R.; Geskin, V.; Baute, N.; Dubois, P.; Jerome, R.; Bredas, J. L. J. Am. Chem. Soc. 1999, 121, 176-187.

Pei and Ma

crucial role of H-abstraction in the radical chain reaction, a model reaction involving the H-abstraction from the silane by the ethylbenzene radical, as depicted in eq 1, is investigated by the

second-order Møller-Plesset (MP2) and the density functional theory (DFT) with the three-parameter hybrid exchange functional of the Becker and the Lee, Yang and Parr correlation functional (B3LYP). The H-abstraction barriers obtained by different methods are 14.56 kcal/mol (UB3LYP/6-31g(d)), 15.28 kcal/ mol (UB3LYP/6-31+g(d,p)), and 16.15 kcal/mol (UMP2/631g(d)), respectively. In contrast to the confined H-abstraction reaction on the two-dimensional (2D) silicon surface, degrees of freedom of reactants, transition states, and reaction products in the model reaction (eq 1) are fully relaxed in the three-dimensional (3D) space. Therefore, we can approximately estimate the lower limit of H-abstraction barrier of reaction of styrene molecule with the H-terminated silicon surface. It is anticipated that the “real” energy barrier of the constrained H-abstraction reaction of styrene molecule on the silicon surface will be higher than that of the model reaction in eq 1. The unrestricted DFT/B3LYP with the all-electron basis set of 6-31g(d) is used in our QC calculations on reactions of styrene molecules with H-Si(111) and H-Si(100). All reactants, products, and transition states (TS) are obtained through partial optimizations with all Si atoms fixed. Frequency calculations are implemented at the optimized geometries of each stationary point. All energies reported in this work have taken the zeropoint energy (ZPE) corrections into account. 2.2. Molecular Mechanics (MM) Simulations. The MM calculations are performed on SGI Origin200 workstation with the Cerius2 (Version 3.5) package from the Molecular Simulation Inc.35 Optimizations by molecular mechanics are completed with the “high convergence criteria” using the “smart minimizer” routine in the Minimizer module. The polymer consistent force field (PCFF)36 is applied. It will be demonstrated from the following validation calculations that the PCFF can produce reasonable results of packing structures of styrene molecules on Si surfaces. 2.2.1. Benzene Dimer. The benzene dimer is the simplest prototype in studies of the aromatic π-π interactions.37,38 PCFF potential curves of two forms of benzene dimers, the π-stack and the T-shaped, are drawn in Figure 1a. The PCFF predicts the T-shaped conformer is slightly more stable than the π-stack one by 0.71 kcal/mol, which is in good agreement with the result of (33) Choi, C. H.; Gordon, M. S. J. Am. Chem. Soc. 1999, 121, 11311-11317. Choi, C. H.; Gordon, M. S. J. Am. Chem. Soc. 2002, 124, 6162-6167. (34) Dkhissi, A.; Este’ve, A.; Jeloaica, L.; Este’ve, D.; Djafari Rouhani, M. J. Am. Chem. Soc. 2005, 127, 9776-9780. (35) Cerius2, Molecular Simulation Inc., version 3.5, 1997. (36) (a) Sun, H. Macromolecules 1995, 28, 701-712. (b) Sun, H.; Mumby, S. J.; Maple, J. R.; Hagler, A. T. J. Phys. Chem. 1995, 99, 5873-5882. (c) Hill, J. R.; Sauer, J. J. Phys. Chem. 1994, 98, 1238-1244. (d) Hwang, M. J.; Stochfisch, T. P.; Hagler, A. T. J. Am. Chem. Soc. 1994, 116, 2515-2525. (37) (a) Sinnokrot, M. O.; Sherrill, C. D. J. Phys. Chem. A 2004, 108, 1020010207. (b) Sinnokrot, M. O.; Valeev, E. F.; Sherrill, C. D. J. Am. Chem. Soc. 2002, 124, 10887-10893. (38) Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K. J. Am. Chem. Soc. 2001, 124, 104-112.

Growth Mechanisms of Styrene Molecules on Si

Langmuir, Vol. 22, No. 7, 2006 3043 Table 1. Order Parameters of Two Packed Styrene Molecules on Surface Models III and IV Predicted by the PCFF and the B3LYP/6-31g(d) Calculations

models H-Si(111) (III) H-Si(100) (IV)

order parametersa

DFT (B3LYP/6-31g(d))

PCFF

ro-o′ (Å) θ (deg) ro-o′ (Å) θ (deg)

5.8 35.9 5.9 31.0

4.6 17.0 5.4 13.2

a The labels o and o′ represent the mass center of the phenyl groups. The B Vi and B Vj represent vectors that vertical to planes of phenyl rings, and θ is the angle between vectors of B Vi and B V j.

Figure 2. Torsion potentials calculated by the PCFF and the B3LYP/ 6-31g(d) using surface models of I, Si4H9C8H9, and II, Si9H13C8H9.

Figure 1. (a) Potential energy curves for the π-stack and T-shaped configurations of benzene dimers predicted by the PCFF. (b) Comparisons of geometries of cluster models I-IV predicted by the PCFF (in red color) and the B3LYP/6-31g(d) (in black color).

around 0.9 kcal/mol obtained by the high-level quantum chemical calculation (CCSD(T)/aug-cc-pVDZ).37a In addition, the equilibrium intermolecular distances predicted by PCFF, R ) 3.9 Å for the π-stack style and R ) 5.3 Å for the T-shaped style, are close to those evaluated by the CCSD(T)/aug-cc-pVDZ (the π-stack style, R ) 3.9 Å; the T-shaped style, R ) 5.1-5.2 Å) (Figure 1a).37a 2.2.2. Cluster Models. Besides benzene dimers, the optimized geometries from the DFT/B3LYP and PCFF methods for four surface cluster models, I-IV, attached by one (I-II) and two (III-IV) styrene molecules are compared in Figure 1b. The geometries of cluster models I and II optimized by PCFF agree fairly well with those obtained by the DFT/B3LYP, whereas one can find from Table 1 that the PCFF calculations predict relatively smaller values of incline angles (θ) between phenyl rings in cluster models III and IV in comparison with the DFT/B3LYP results. However, the nearly T-shaped stackings of phenyl groups in models III and IV are well reproduced by PCFF, as shown in Figure 1b. In fact, our previous studies on oligothiophene

systems have also demonstrated that PCFF provided reasonable predictions of packing structures and relative stabilities of oligothiophenes.39 Figure 2 displays the rotational potentials of phenyl groups in cluster models I and II predicted by PCFF and DFT/B3LYP. Encouragingly, PCFF predicts energy differences of 2.36 kcal/ mol (I) and 2.44 kcal/mol (II) for rotations of phenyl groups from the horizontal (Φ ) 0°) configuration to the perpendicular (Φ ) 90°) one, in good agreement with B3LYP/6-31G(d) results (I, 1.44 kcal/mol; II, 1.45 kcal/mol). The coplanar conformer is identified as a transition state, because an imaginary frequency is found. 2.2.3. Periodic Surface Models. In MM simulations, larger 2D periodic models of H-Si(111) and H-Si(100) are adopted to investigate the self-directed growths of styrene molecules. The H-Si(111) is modeled by a rhombic 2D surface model with dimensions of 57.6 Å × 57.6 Å, containing 225 surface H sites with four layers of surface atoms presented. For H-Si(100), a rectangular surface model with dimensions of 30.6 Å × 305.7 Å (in Si-Si dimer row direction) is employed. It contains 642 surface H sites, with five layers of surface silicon atoms present. We use the packing energy per adsorbed styrene molecule (Eav) to describe the thermodynamic stability of packed styrene molecules on silicon surfaces. The Eav is determined by removing contributions from substrate Si atoms and surface terminated H atoms from the total energy,22,28-30

Eav )

Etot. - Esurf N

(39) Zhang, G.; Pei, Y.; Ma, J. J. Phys. Chem. B 2004, 108, 6988-6995.

3044 Langmuir, Vol. 22, No. 7, 2006

Pei and Ma

Figure 3. Potential energy profiles and reaction paths for reactions of styrene molecules on (a) H-Si(111) and (b) H-Si(100). The barriers and bond lengths are in units of kcal/mol and angstrom, respectively.

where Etot. and Esurf are the total energy of a system with N adsorbed styrene molecules and the interaction energy between molecules and surface, respectively. The values of Eav are used to estimate favorable routes of self-directed growth of styrene molecules on H-Si(111) and H-Si(100).

3. Results and Discussion 3.1. Radical-Chain Reactions on H-Si(111) and H-Si(100). The spin-unrestricted DFT/B3LYP calculations are performed to study possible pathways of radical chain reaction of styrene molecules on H-Si(111) and H-Si(100). The potential energy

profiles for H-abstractions of styrene molecules on H-Si(111) and H-Si(100) are shown in Figure 3a,b, respectively. The configurations of reactants (1 and 1′), intermediates (3 and 3′), transition states (2(TS), 2′(TS), 4(TS), and 4′(TS)) and reaction products (5 and 5′) are also given in Figure 3 to make comparison among different pathways. The H-abstraction processes on H-Si(111) and H-Si(100) are shown to be composed of three main steps, which are the initial attachments of styrene molecules to silicon surfaces (1 f 2(TS) and 1′ f 2′(TS)), formations of carbon-centered radical intermediates (3 and 3′), and generations of new radical sites

Growth Mechanisms of Styrene Molecules on Si

(4(TS) f 5, 4′(TS) f 5′). On both H-Si(111) and H-Si(100), attachments of styrene molecules to surfaces experience almost barrierless processes, in agreement with other calculations.23 The calculated energy barriers for initial formations of Si-C linkages on H-Si(111) and H-Si(100) are 1.56 and 1.61 kcal/mol, respectively. After formations of surface Si-C bonds, the intermediates 3 and 3′ are stabilized by energy releases of 18.14 and 18.04 kcal/mol on H-Si(111) and H-Si(100), respectively, similar to previous theoretical predictions using cluster models21 and periodic slab surface models.23 Subsequently, a crucial step involving the abstraction of a neighboring surface hydrogen atom by the carbon-centered radical intermediate is expected, as displayed in Scheme 1. The energy barrier for the formation of a six-membered ring transition state on H-Si(111) is evaluated by 18.46 kcal/mol. On the H-Si(100), it is found that three possible pathways for H-abstractions proceeding via transition states containing five- (4′(TS)-r2), six- (4′(TS)-r1), and eightmembered (4′(TS)-r3) rings have barriers of 21.35, 18.59, and 29.35 kcal/mol, respectively. Our predictions of H-abstraction barriers on H-Si(111) and H-Si(100) on the basis of cluster models are consistent with those obtained by Wolkow et al.,17 Musgrave et al.,21 and Kleinman et al.26 However, they are much higher than those suggested by Selloni et al. (around 17∼19 kcal/mol).23 Such differences may be ascribed to different kinds of surface models and quantum chemical methods used. The examinations of geometries of local parts Si-CR-CβCPh in intermediates, transition states, and products allow us to gain detailed information of surface H-abstraction processes. Similar to those reported by others,23 in metastable intermediates, 3 and 3′, phenyl groups are coplanar with vinyl groups, as shown in Figure 3, facilitating delocalizations of the carbon-centered radical electrons into phenyl groups and thus effectively stabilizing the radical intermediates (3 and 3′). The Cβ-CPh bonds in 3 and 3′ have the same length (1.41 Å), corresponding to partial carboncarbon double bonds. The coplanarity between the phenyl group and the vinyl group vanishes when the H-abstraction occurs. The CR-Cβ and Cβ-CPh bonds in the transition states (4(TS) and 4′(TS) in Figure 3) are lengthened to different extents (0.3-0.7 Å) relative to those in intermediates 3 and 3′. In the case of the H-abstraction spanning two Si-Si dimer rows, Si-CR, CR-Cβ, Cβ-CPh, Cβ-H and H-Si bonds in the eight-membered ring transition state are lengthened by relatively larger values in comparison with those in five- and six-membered ring transition states (4(TS), 4′(TS)-r1 and 4′(TS)-r2) due to the larger distance between the inter Si-Si dimer rows. Indeed, this kind of H-abstraction is predicted to be energetically unfavorable. Turning back to energy profiles of H-abstractions and assuming an Arrhenius-type surface activation process with the usual attempt frequency of ∼1014 Hz at 298.15 K,40 we estimate the H-abstraction rates to be 2.94 s-1 on H-Si(111), 2.36 s-1 (interdimer, r1), 0.022 s-1 (intradimer, r2), and 3.06 × 10-8 s-1 (inter-Si-Si-dimer rows, r3) on H-Si(100), respectively. Most of these reaction rates are greatly larger than the rate constant of styrene polymerization in solution.41 At same time, we also evaluate the reverse desorption rates of around 0.4 s-1 for the initial attachments of styrene molecules on both H-Si(111) and H-Si(100). It should be pointed out that current evaluations of reaction rates are rather approximate, because the surface is simplified by using a cluster model. However, by comparing these reaction rates, we can still reasonably conclude that radical chain reactions on H-Si(111) and H-Si(100) proceeding by a (40) Masel, R. I. Principles of Adsorption and Reaction on Solid Surfaecs; Wiley: New York, 1996; p 607. (41) O’Driscoll, K. F.; Mahabadi, H. K. J. Polym. Sci. Chem. 1976, 14, 869881.

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series of H-abstractions should readily occur at the room temperature. Directional preference of H-abstraction is expected on H-Si(100) in contrast to H-Si(111). It is anticipated that H-abstraction along the surface Si-Si dimer direction (r1 in Scheme 3b) is favorable than the other two H-abstraction manners. H-abstraction within a Si-Si dimer (r2 in Scheme 3b) is also possible. However, the following H-abstraction spanning two surface Si-Si dimer rows (r3 in Scheme 3b) on the H-Si(100) is considered to be less favorable due to its low reaction rate (∼3.06 × 10-8 s-1). These results are in good agreement with the preferential growth of single and double lines along the surface Si-Si dimer row on the H-Si(100).12 3.2. Stage-Dependent Growth Mechanisms. It has been shown from the above discussions that propagations of styrene molecules on H-Si(111) and H-Si(100) are both step “forward”: molecules are expected to link to silicon surfaces one by one. To obtain more comprehensive insights into the selfdirected growth of styrene molecules on H-Si(111) and H-Si(100), simulations of step by step propagations are carried out on 2D periodic surfaces. 3.2.1. Cluster-Shaped Aggregation on H-Si(111). Assuming a surface dangle bond is generated on H-Si(111), the irregular propagation of the chain reaction is inevitable due to the isotropic style of surface sites (Scheme 3a). An awkward situation is thus encountered: how can we determine the favorable path for the step by step growth of molecules on H-Si(111)? Two aspects from both kinetic and thermodynamic effects should be considered. As mentioned above, the H-abstraction is considered to be the rate-determination step of the chain reaction. Theoretically, if we obtain energy profiles of various H-abstraction patterns, we may determine the most favorable propagation route. However, it is impractical due to formidable computational costs. We adopt an approximation that the probability of H-abstraction for each neighboring surface site is equivalent, on the basis of the isotropic feature of H-Si(111). Only thermodynamic effects including intermolecular and molecule-surface interactions are considered here. In fact, interactions between adjacent phenyl groups strongly influence the orientations of newly adsorbed styrene molecules, which may in turn affect the preference of H-abstraction to some extent. So, in our following discussion, the sample method shown in the Scheme 3a is applied. In each sample step, we investigate various possible modes of styrene molecule linking at each available neighboring surface site. Various orientations of the phenyl group in the newly attached styrene molecule are sampled. These configurations are further optimized to obtain local minima. The favorable site for the attachment of a new styrene molecule on the surface is judged from values of Eav, as defined in subsection 2.2. One should notice that in many cases the energy difference between two sample steps is fairly small, implying that there are many possible diffusion pathways for the chain reaction on H-Si(111). Here we only discuss one growth manner, which has the lowest Eav in each sample step. The resulting growth route of styrene molecules on H-Si(111) is displayed in Figure 4. The packing energy per adsorbed styrene molecule (Eav) decreases rapidly in the preliminary growth stage (Figure 4a), during which no more than 10 styrene molecules are linked (Nstyrene e 10, stage I). As shown in Figure 4b, phenyl groups in this stage exhibit distinctly T-shaped stacking, which are expected to stabilize the compact cluster structure of adsorbates. In stage I, the self-directed growth is thought to be both kinetically and thermodynamically favorable. Proceeding with the attachment of styrene molecules on H-Si(111) (Nstyrene > 10), an uphill tendency of packing energy is observed. We call this stage II. During this stage, π-stack configurations of adjacent

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Figure 4. (a) Packing energy per styrene molecule (Eav) in the self-directed growth process. (b) Top view of the resulting cluster-shaped structure of adsorbed styrene molecules (Nstyrene ) 23) on H-Si(111) with the lateral size of around 21.6 Å.

phenyl groups gradually increase. The desorption of linked styrene molecules is anticipated in this stage due to the rapid increase in packing energies, which competes with attachments of styrene molecules. We deduce that the termination of self-directed growth occurs in stage II, correlating well with experimental observations of ∼20 steps on average for chain reactions on H-Si(111).11 When there are 23 styrene molecules adsorbed (Nstyrene ) 23), the resulting molecular aggregation on H-Si(111) is cluster shaped with the lateral size of around 21.6 Å, which is also in line with experimental characterizations (∼20 Å).11 The exhaustion of adjacent H atoms for abstractions, suggested by Chidsey et al.,8b may be not the sole reason for the self-termination of chain reactions in limited steps. It is shown that most favorable sites for attachments of styrene molecules on H-Si(111) are concentric with the core of the cluster. The self-propagation process prefers to turn back, in agreement with experimental postulations.11 It was commonly considered that the self-directed growth of alkyl chains on the isotropic hexagonal H-Si(111) proceeded via preferred 120° turns, due to favorable intermolecular van der Waals interactions (see Supporting Information, Part I).8b,11,22 However, some 60° turns are also observed here (such as steps 1 to 3, steps 6 to 8, and steps 7 to 9, as shown in Figure 4b). In reality, these 60° turns facilitate formations of T-shaped packing configurations of neighboring phenyl groups and hence improve the stability of the cluster aggregation. 3.2.2. Lines on H-Si(100). In contrast to H-Si(111), the directional preference of H-abstractions on H-Si(100) is found to be in the order inter-Si-Si-dimer > intra-Si-Si-dimer . inter-Si-Si-dimer row. Some simulations including growths of single and double lines along one and two sides of a surface Si-Si dimer row are investigated (Scheme 3b).

For the self-directed growth of a single line (sl) along one side of a surface Si-Si dimer row, two kinds of stacking patterns with phenyl groups tilted “in” and tilted “out” relative to the substrate Si-Si dimer row are both possible. The packing energies of two kinds of molecular lines are compared in Figure 5. The self-directed growth of molecular styrene line via the tilted “in” manner is slightly more favorable than that via the tilted “out” style. For both growth manners, a rapid decrease of Eav is distinctly observed in the preliminary growth stage of a molecular line (Nstyrene e 7), during which the molecular line gradually forms and is strongly stabilized by newly adsorbed styrene molecules. After this stage, the value of Eav decreases smoothly and eventually converges to -0.55 kcal/mol and -0.38 kcal/mol for the tilted “in” and the tilted “out” patterns, respectively. The order parameters, θ and ro-o′ (cf. Table 1), of packed phenyl groups in the molecular line are analyzed in Figure 6. It indicates that the molecular line turns to an ordered structure by the successive linkage of styrene molecules. In the early stage of line formation, such as Nstyrene ) 7, the degree of π-overlap between neighboring phenyl groups is relatively small, as reflected by the less ordered packing of the phenyl groups (Figure 6). The long-range order in packed phenyl groups appears with the accumulation of styrene molecules on one side of the Si-Si dimer row. Such ordered packing structure was suggested to potentially function as an effective hole conductor.12,24 The edge effect is revealed from the distorted conformations of phenyl groups on two ends of the molecular line (Figures 5b and 6), caused by the less steric hindrances on edges of the line. In contrast, the strong π-π interactions and steric hindrances between neighboring molecules restrict free rotations of phenyl groups in the middle of the line,

Growth Mechanisms of Styrene Molecules on Si

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Figure 5. (a) Variations in packing energy per styrene molecule in the self-directed growth of single and double lines on H-Si(100). (b) Top view of styrene molecular lines. Arrows represent growth directions.

Figure 6. Order parameters, (a) angles between vertical vectors of neighboring phenyl groups and (b) distances between centers of neighboring phenyl rings, for the tilted “in” sl pattern (shown in Figure 5b). Definitions of order parameters are given in Table 1.

leading to partially torsional conformations, as shown in Figure 5b. Besides the formation of single line on H-Si(100), growths of double lines (dl) were also found in STM studies.12 In fact, our QC calculations also suggest a possibility of H-abstraction jog within a Si-Si dimer, because the energy difference between the interdimer H-abstraction (r1) and the intradimer H-abstraction (r2) is fairly small (∼2.8 kcal/mol). To explore the mechanism of dl formation on H-Si(100), we assume H-abstraction jogs

take place when there are 16 and 25 styrene molecules adsorbed on one side of a Si-Si dimer row, respectively. Two kinds of dl, with the growth of an adjacent line in the same forward direction (dlforward) and doubling back (dlbackward), are investigated (Scheme 3b). The packing energies and some representative conformations can be found in Figure 5. The growths of dlforward and dlbackward are demonstrated to be both thermodynamically favorable, because distinct drops of packing energies in the process of dl formation are found (Figure 5a). The growth of dl doubling

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back (dlbackward) is expected to be energetically more favorable than the forward manner (dlforward). It is also interesting that the optimum packing structures of two growth modes, dlforward and dlbackward, are both composed of mixtures of two single lines with tilted “in” and “out” orientations in phenyl groups. The unfavorable steric effects between adjacent lines may be minimized in this manner. It should be noted that our simulations are based on ideal silicon surfaces. Surface reconstructions and defects are ignored in simulations, which may terminate the surface reaction unexpectedly.11,12 In addition, the physical adsorptions and diffusions of free styrene molecules on the surface are also not considered.42 However, these approximate models can be applied to rationalize experimental results.11,12,20

4. Conclusions We comparatively study mechanisms of radical chain reactions and self-directed growth processes of styrene molecules on H-Si(111) and H-Si(100). Several possible H-abstraction manners proceeding via transition states containing five-, six-, and even eight-membered ring structures on H-Si(111) and H-Si(100) are theoretically surveyed. The distinct surface patterns lead to different H-abstraction manners. For the selfdirected growth of styrene molecules on H-Si(100), the naturally anisotropic surface structure induces strong directional preference for H-abstractions, which suppresses the diffusion of a chain reaction across surface Si-Si dimer rows and results in formations of one-dimensionally ordered structures of single and double lines on H-Si(100). In contrast, the formation of the clustershaped molecular aggregation on H-Si(111) is rationalized by (42) Mo, Y. W.; Kleiner, J.; Webb, M. B.; Lagally, M. G. Phys. ReV. Lett. 1991, 66, 1998-2001.

Pei and Ma

the isotropic, hexagonal arrangements of surface sites. The interactions between neighboring phenyl groups greatly affect self-directed growth processes and morphologies of molecular aggregations on the surface. A so-called stage-dependent mechanism is proposed to understand the self-directed growth of styrene molecules on both H-Si(111) and H-Si(100). In the case of cluster aggregation on H-Si(111), interactions between adjacent phenyl groups stabilize or destabilize the molecular aggregation in different growth stages, providing an alternative explanation for the self-termination of propagation of styrene molecules on H-Si(111).11 In contrast, interactions between phenyl groups facilitate the line formation on H-Si(100) throughout the self-directed growth process. Especially in the preliminary stage of line growth on H-Si(100), interactions between adjacent phenyl groups greatly lower the packing energies of the molecular aggregations, implying a preferential growth of longer lines. In addition, we also discuss favorable growths of double lines resulting from H-abstraction jogs. The growth of an adjacent line doubling back on the original single line (dlbackward) is demonstrated to be energetically more favorable than the forward manner (dlforward). These results are in good agreement with experimental observations.11,12 Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant No. 20433020, 90303020, 20420150034, 20573050). Supporting Information Available: Textual description of the difference between the self-directed growths of alkyl chains and styrene on H-Si(111) and figures of configurations of reactants, intermediates, transition states, and reaction products on H-Si(111) and H-Si(100). This material is available free of charge via the Internet at http://pubs.acs.org. LA052093+