J. Phys. Chem. 1992,96, 8538-8544
8538
dential Young Investigator R o g ” (DMR-89-57236).We thank Prof. F. Zaera for preprints of submitted papers. Registry No. Cu,7440-50-8; Mg,7439-95-4; bromomethane, 74-83-9; bromoethane, 74-96-4; 1-bromopropane, 106-94-5; 1-bromobutane, iodomethane, 74-88-4; iodoethane, 109-65-9; 1-bromopentane, 110-53-2; 75-03-6; 1-iodopropane,107-08-4; 1-chloropropane, 540-54-5; l-chlorobutane, 109-69-3; 1-chloropentane, 543-59-9; 1-chlorohexane,544-10-5; 1-chloroheptane,629-06-1.
References and Notes (1) Walborsky, H. M. Acc. Chem. Res. 1990, 23, 286. Garst, J. F. Acc. Chem. Res. 1991, 24, 95. Walling, C. Acc. Chem. Res. 1991, 24, 255. (2) Voorhoeve, R. J. H. Organosilanes: Precursors to Silicones; Elsevier: New York, 1967.
(3) Henderson, M. A.; Mitchell, G. E.; White, J. M. Surf.Sci. 1987. 184. L325. Costello, S.A,; Roop, B.; Liu, Z.-M.; White, J. M: J. Phys. Chem. 1988, 92, 1019. (4) Henderson, M. A.; Mitchell, G. E.; White, J. M. Surf. Sci. 1991, 248, 219. ( 5 ) Zaera, F. Submitted for publication. (6) Sanderson,R. T. Chem. Bonds and Bond Energy; 2nd 4.;Academic: New York. 1976. (7) Bent, B. E.; Nuzzo, R. G.; Zegarski, B. R.; Dubois, L. H. J . Am. Chem. SOC.1991, 113, 1137. (8) Chiang, C.-M.; Wentzlaff, T. H.; Bent, B. E. J. Phys. Chem. 1992,96,
1836.
(9) Mate, C. M.; Kao, C.-T.;Somorjai, G. A. Surf. Sei. 1986, 176, 505. (10) Kirstein, W.; Kruger, B.; Thieme, F. Surf. Sci. 1988, 206, 145.
(1 1) Jenks, C. J.; Paul, A.; Bent, B. E. Manuscript in preparation. (12) Nuzzo, R. G.; Dubois, L . H. J . Am. Chem. SOC.1986, 108, 2881. (1 3) Shimanouchi, T. Tables of Molecular Vibrational Frequencies; NSRDS, National Bureau of Standards 39, 1972; Vol. 1. (14) Magrini, K. A.; Gebhard, S.C.; Koel, B. E.; Falconer, J. J. Surf. Sci. 1991, 248, 93. (15) Zaera, F.; Hoffmann, H.; Griffiths, P. R. J . Electron Specfrosc.Rel. Phenom. 1990, 54, 705. (16) Lin, J.-L.; Bent, B. E. In Catalytic Control of Air Pollution, Mobile and Stationary Sources; Silver, R. G., Sawyer, J. E., Summers, J. C., Eds.; ACS Symposium Series 495; American Chemical Society: Washington, DC, 1992; p 153. (17) Hayashi, M.; Ohno, K.; Murata, H. Bull. Chem. Soc.Jpn. 1973,46, 2332. Ogawa, Y.; Imazeki, S.; Yamaguchi, H.; Matsuura, H.; Harada, I.; Shimanouchi, T. Bull. Chem. SOC.Jpn. 1978, 51, 748. Shimanouchi, T.; Matsuura, H.; Ogawa, Y.; Harada, I. J. Phys. Chem. Ref. Data 1980,9, 1149. (18) Ibach, H.; Mills, D. L. Electron Energy Loss Spectroscopy and Surface Vibrations; Academic: New York, 1982. (19) Lin, J.-L.; Bent, B. E. Chem. Phys. Len. 1992, 194, 208. (20) Anger, G.; Winkler, A.; Rendulic, K. D. SUI$ Sci. 1989, 220, 1. (21) Jenks, C. J.; Chiang, C.-M.; Bent, B. E. J . Am. Chem. Soc. 1991,113, 6308. (22) Dinardo, N. J.; Plummer, E. W. Surf. Sci. 1985, 150, 89. (23) Lin, J.-L.; Bent, B. E. J. Vac. Sci. Technol. A 1992, 10 (4), 2202. (24) Lin, J.-L.; Bent, B. E. Manuscript in preparation. (25) Zhang, R.; Gellman, A. J. J . Phys. Chem. 1991, 95, 7433. (26) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982,33, 493. (27) This analysis neglects entropic effects; Le., all preexponential factors have been taken to be 10” s-’. (28) Lin, J. L.; Bent, B. E. Manuscript in preparation.
Molecular Dynamics Studies of Elementary Surface Reactions of C2H2and C2H in Low-Pressure Diamond-Film Formation James Peploski,+Donald L. Thompson, and Lionel M. RafP Department of Chemistry and Diamond Research Group, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: May 4, 1992; In Final Form: July 9, 1992)
Molecular dynamics studies of some of the important elementary reactions involved in the low-pressure synthesis of diamond films are reported. The C( 1 1 1) surface is modeled with an ensemble of 127 atoms and a velocity reset procedure to incorporate the thermal effects of the bulk. The hydrocarbon potential developed by Brenner [Phys. Rev. B 1990,42,9458]is employed in all calculations for both the surface and the incident gas-phase molecules. The principal results are as follows: (1) The sticking coefficients for acetylene on a clean C( 1 1 1) surface lie in the range 0.17-0.45 for incident translational energies between 1.5-2.0eV with surface temperatures in the range 1OOO-1500 K. (2)Chemisorption of acetylene most frequently involves the formation of two C-C3, single bonds to adjacent adsorption sites on the C( 1 1 1) surface. (3) Surface chemisorption of acetylene via the formation of one C-C,,, single bond to yield an ethenyl radical is observed, and the subsequentdesorption of this species from a clean C( 1 1 1) surface does not appear to be a high probability process. (4) The addition of a second acetylene molecule to form an ethenyl radical is a very low probability process for all surface structures investigated. When such chemisorption does occur,the probability of subsequent desorption is large unless the ethenyl radical is able to subsequently with a much higher form a second C-C bond. (5) Addition of a ‘C=CH radical to a chemisorbed acetylene group pr&s probability than is the case for CzH2. The ethynyl radical is also chemisorbed readily to other surface structures with a low probability of subsequent desorption. It therefore appears likely that C2H is an important diamond-growth species even in experiments where its concentration is 1 or 2 orders of magnitude less than that of acetylene.
I. Introduction It is now well established that diamond films may be grown at low pressures by using microwave and radio frequency plasmas, hot filament, or UV-assisted chemical vapor deposition or by combustion methods.’-5 Reviews of the synthesis of diamond under metastable conditions have been presented by DeVries,4 by Angus and Hayman: and by Spear.’ Formation of diamond at low pressure is kinetically controlled. Therefore, detailed knowledge of the reaction mechanism is essential in devising processing schemes for the growth of diamond. Measurements and models designed to estimate the concentration of gas-phase species present in a filament-assisted diamond-growth experiment suggest that the two most likely growth species are Current address: Department of Chemistry, Clarkson University, Potsdam, NY 13699-5810.
methyl radicals and a ~ e t y l e n e . The ~ * ~precise reactions of these species or others that are involved in low-pressure diamond growth
are, however, unknown. There have been several hypothetical mechanisms suggested for the overall process. Zhu and Whitelo suggested that the growth sequence involves (1) the chemisorption of aceytlene, (2) the decomposition of acetylene to ethylidyne, acetylide, and surface hydrogen, (3) the decomposition of ethylidyne to form acetylide, methylidyne, and surface hydrogen, and (4) the decomposition of methylidyne and acetylide to surface solid carbon and gas-phase hydrogen. Tsuda et a1.”J2 have proposed that methyl radicals are the primary growth species. They have carried out semiempirical quantum calculations to determine the lowest energy path for a mechanism that involves a diamond plane covered with methyl groups via methylene insertion or hydrogen abstraction followed by methyl radical addition. In this mechanism, three
0022-365419212096-8538$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 0539
Surface Reactions in Diamond-Film Formation
42-Le + H2
Abstraction
Atom Transfer C-C Bond Formation
I
R2H2
VH2 Abstraction C2H2Addition
&
VR2 H: '
I
H Addition
%F-eH Ring Closure
6
E
Atom Transfer C-C Bond Formation
6
F
1. Schematic of the diamond-film growth mechanism suggested by Huang, Frenklach, and Maroncelli, (refs 13 and 14). The closed circles represent carbon atoms. Open circles denote hydrogen atoms. The asterisk (*) is used to represent an unpaired electron, radical site. Figure
neighboring methyl groups on the (111) surface plane become bonded to form the diamond surface. Huang, Frenklach, and Maroncelli (HFM)13 assumed that acetylene is the principal growth species, as would be expected in a combustion synthesis using an oxy/acetylene torch, and suggested that a mechanism involving (1) surface activation via hydrogen-atom abstraction, (2) addition of acetylene molecules to the surface via the formation of one C-C single bond at the radical site, and (3) a series of hydrogen-atom migrations from lower to upper layers coupled with the formation of more C-C bonds via successive addition of acetylene molecules. Frenklach and Spear14have proposed a similar growth mechanism for vapor deposited diamond films. More specifically, HFM suggest that diamond-film growth involves the reactions shown in Figure 1. Reaction A B involves the activation of a surface site via hydrogen-atom abstraction. This is followed by addition of an acetylene molecule leading to structure C. An important part of the HFM hypothesis is that the newly added C2H2molecule is bonded to the surface via a single C-C bond as shown in Figure 1. Diamond-film growth is now postulated to proceed by a hydrogen-atom transfer either with simultaneous C-C bond formation or followed by C-C bond formation. This produces structure D which possesses a radical to which a second acetylene molecule is presumed to add to form structure E. Another hydrogen-atom transfer and a C-C bond-formation process produces the hexagonal ring structure characteristic of diamond. In support of this mechanism, HFM13have reported the results of a series of semiempirical quantum calculations that suggest that all of the proposed steps in the growth sequence, except the hydrogen-atom abstractions, proceed without any activation energy. This mechanism is attractive because it not only provides a model for diamond growth but also for the formation of sp2 carbon. Hams and Beltonls have critized the HFM mechanism on the basis of a thermochemical analysis that suggests that the reverse reaction +
C,,)--CH--LH
-
C(S) + HC=CH(,,
[C,,) = diamond surface]
BR VE Figure 2. Schematic of the diamond-film growth mechanism suggested by Belton and Harris (ref 16). The closed circles represent carbon atoms. Open circles denote hydrogen atoms. Carbon atoms are present at each vertex of the C(110) lattice. The asterisk (*) is used to represent an unpaired electron, radical site.
proceeds at a rate so fast that acetylene will desorb in preference to incorporating into the diamond lattice. They have therefore suggested an alternative pathway for the formation of diamond (110) from acetylene that involves the sequence of reactions shown in Figure 2.16 The figure utilizes the nomenclature introduced by Harris and Belton.16 The initial step in this and all other proposed mechanisms is surface activation via hydrogen-atom abstraction. However, here abstraction at two adjacent surface sites is required. This is shown as the reaction sequence H4 RH3 R2H2in Figure 2. This is followed by addition of acetylene to form structure VH2. The significant difference here from the HFM mechanism is that acetylene is assumed to be bound by two C-C bonds. The growth then proceeds by the repetition of steps 1-3 to yield two adjacent ethylene groups, structure Vz. A gas-phase hydrogen atom is then assumed to add across the ethylene double bond to yield structure VE which then undergoes ring closure to form the six-membered carbon ring characteristic of the diamond structure as shown by structure BR. This mechanism is atrractive in that the chemisorption of acetylene is more exothermic due to the formation of two C-C bonds and C2H2 is consequently less likely to desorb. The mechanism involves no atom rearrangements on the surface, which are likely to be processes with substantial activation barriers. However, it does not provide a mechanism for the formation of sp2 carbon. Belton and Harris16 have utilized the above mechanism along with rate coefficients estimated from gas-phase thermodynamic and kinetic data to provide a phenomenological description of diamond-growth kinetics. The ratdetermining step in the process is the addition of the second acetylene molecule. The calculations yield a predicted growth rate of 0.03 pm/h, which is about 1 order of magnitude less than those observed experimentally. Each of the proposed mechanisns has some attractive features. Each could conceivably lead to the formation of diamond films. However, there is little direct experimental evidence that can be used to decide between them. In the present paper, we report the results of molecular dynamics simulations of the interaction of
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acetylene and acetylene-derived radicals with diamondlike structures. In section 11, we describe the model and potentialenergy surface used in the calculations. The results are given in section 111. A summary is presented in section IV.
11. Molecular Dynamics Calculations and Potential-Energy Surface IIA. Potd-Energy Hypemuface. The molecular dynamics calculations simulate an open system in which the number of atoms present, N, is an increasing function of time. At time t = 0, the system consists of an ensemble of carbon atoms arranged in a geometry corresponding to the C( 111) plane of diamond plus one gas-phase molecule, which may be either C2H2,C2H, or a hydrogen atom. Trajectories are computed in the usual manner by solution of the classical Hamiltonian equations of motion. If scattering occurs, the scattered molecule is removed from the calculation and another molecule is allowed to collide with the surface. Upon chemisorption, the size of the system increases by the number of atoms in the chemisorbed molecule. Consequently, subsequent collision events occur from a diamond surface containing all molecules chemisorbed in previous trajectories. We therefore require a potential-energy hypersurface that accurately represents all statistically significant configurations of a C,H, system where n and m are arbitrary. The empirical hydrocarbon potential # 2 developed by BrennerI7 has been employed in all of the calculations reported in this paper. This potential is based on Tersoffs covalent bonding formalism18with additional terms that correct for overbinding of radicals and nonlocal environmental effects. Nonlocal effects are included using an analytic function that defines conjugation in terms of the coordination of carbon atoms that neighbor carbon-carbon bonds. Brenner has employed this potential to compute atomization energies for 12 alkanes, 13 alkenes, 4 alkynes, 7 aromatics, and 12 radicals." The average absolute deviation of the results from the experimental values were 0.133 eV (alkanes), 0.546 eV (alkenes), 0.275 eV (alkynes), 0.557 eV (aromatics), and 0.18 eV (radicals). In terms of the average absolute percent error, the results were 0.30%, 1.31%,0.73%, 0.74%, and 0.61%, respectively. In terms of bond energies, errors of this magnitude translate into errors on the order of 3-9 kcal/mol, which compares well with typical results from multireferenced CI calculations. II.B. Surface Model. The C( 111) surface is modeled with an ensemble of N carbon atoms arranged in the tetrahedral configuration characteristic of the (1 11) plane. The N lattice atoms are partitioned into three subsets comprising Np, NQ,and NB atoms, which are designated as the P-zone, Q-zone, and B-zone, respectively. P-zone atoms have no chemical bonds to B-zone atoms. Lattice atoms in the Q-zone have at least one bond to a B-zone atom. The motions of the P-zone atoms are determined solely by the forces produced by the interaction potential and the direct solution of the classical Hamiltonian motion equations. The motions of the Q-zone atoms calculated from the solution of Hamilton's equations are modified by the presence of velocity reset functions associated with each atom in the Q-zone. The B-zone atoms are fmed in position. These sites serve to reduce edge effects and maintain the proper symmetry of the lattice. The velocity reset functions used to modify the Q-zone motion are designed to simulate the thermal effects of the bulk which are not explicitly included in the lattice model. We employ the method developed by Riley, Coltrin, and Die~t1er.l~In this procedure, the velocity components of the peripheral Q-zone atoms are reset at periodic intervals, At, by random selection of velocities from a Boltzmann distribution at the lattice temperature T,. For example, the reset function for the x velocity component of the ith Q-zone lattice atom is
U"xi(tn)= [ 1 - W ] '/2~oxj(t,) + w'/~u'([;TJ
(1)
where unxi(t,)is the new x component of velocity for atom i at time t, and voxi(t,)is its old velocity; U'([;T,)is a random velocity selected from a Boltzmann distribution at temperature Tsby the random number E; w is a parameter that controls the strength of
Figure 3. Top view of the C(111) surface model. The carbon atoms within one C-C bond length of the outer carbon ring constitute the Pand Q-zonesof the lattice. These atoms are those within the circle. The outer ring of carbon atoms are in the B-zone.
Figure 4. Side view of the C(11 1) surface model showing 25 of the 37 P- and Q-zone atoms. The remaining 12 P- and Q-zone atoms along with the 90 B-zone atoms are omitted for the sake of visual clarity.
the reset. Analogous equations are used for the y and z components of velocity. This reset procedure is applied to every peripheral atom in the Q-zone at equally spaced time intervals, At. In the present calculations, we have taken N = 127, N p = 7, NQ = 30, and NB= 90. Figures 3 and 4 show top and side views of portions of the model lattice, respectively. The 37 atoms shown within one C-C bond length of the outer carbon ring in Figure 3 constitute of the P- and Q-zone of the lattice. The remaining 90 atoms comprise a fixed boundary zone (B-zone). Figure 4 illustrates the relative positions of 25 of the 37 P- and Q-zone atoms. These atoms and the 90 B-zone atoms are in the lower layers of the lattice. They provide the expected rigidity to the lattice. The reset parameters in eq 1 are w = 0.329 and At = 0.48 X s. The latter value is one-fifth of the Debye period for the lattice, which is thi value suggested by Riley et al.19 1I.C. Initial Conditions and Numerical Procedures. Each trajectory is initiated with the incident gas-phase molecule sufficiently far from the surface to be effectively outside the interaction range. In some trajectories, the initial orientation of the incident molecule, the surface aiming point, and the incidence angle the initial relative velocity vector makes with the surface normal are all selected randomly from the appropriate distribution functions.20 Aiming points on the surface were randomly chosen to lie within a radius of 5.0 A of the center atom. The size of the lattice model made it necessary to restrict the initial incidence angles to the range 0-45O. In some calculations, the aiming point and initial molecular orientation were selected to permit an assessment of the influence of steric effects and the directional character of carbon bonding. In all calculations, the incident molecule was assumed to be rotationally cold (J = 0). The initial zerqoint vibrational energy was partitioned into the appropriate normal modes using previously described projection methods.21 The initial translational energy, E,, was generally fixed at a desired value in the range 1.09 eV I E, I2.06 eV. These energies are larger than the average energy generally expected to be present in the experiments.22 We have chosen to employ higher translational energies in the initial studies in order to enhance the reaction probabilities and make the detection of important reaction pathways easier. At lower energies, we would expect the reaction probabilities for processes with an
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The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8541
activation barrier to decrease significantly. Reactions involving radicals will be much less affected since such processes usually have very low or zero activation energies. The thermal energy of the diamond surface is introduced by placing the lattice in its equilibrium configuration and inserting a kinetic energy of kT, into each degree of freedom. The sign of the various momentum components are chosen randomly. That is, the a momentum component of the ith atom is taken to be
TABLE I: Average Sticking Coefficients ((fs))for Acetylene Incident on a Clean, C(111) Diamond Surface as a Function of Surface Temperature (T,) and Initial C2H2Translational Energy ( E , ) (Error Limits Represent One u Limit of Statistical Uncertainty) 1000 1250 1500
for a = x, y , or z. Subsequent to the introduction of the thermal energy, the equations of motion for the lattice are integrated for a period to sufficiently long to achieve a randomization of the lattice energy. In practice, to was taken to be 50.0 tu [1 tu = 1.019 X s]. The resulting phasespace point describing the lattice was stored and denoted as the initial lattice configuration, b(to). At the start of a trajectory, Lo(to) is retrieved and this initial phase-space point is evolved for an additional period 7i,where 7i is randomly chosen so as to lie in the range 10 tu I q I 20 tu. The new lattice configuration, L ( f O + T i ) , is used as the initial lattice state for the ith trajectory. Vibrational phase averaging on the lattice is achieved by repetition by this procedure for each trajectory so that the initial lattice configuration for the ith trajectory is L ( t O + Z ~where i ) , the summation runs over all trajectories from 1 toj. The Hamiltonian equations of motion for the N-atom system are integrated using a variable-order, variable-step-size predictor-corrector procedure.23 This method produces energy conservation to about four significant digits throughout the integration. Chemisorption is assumed to occur when the center of mass of the incident molecule or radical experiences four inner turning points of vibrational motion relative to the surface plane (2= 0). In effect, we monitor the time variation of the distance between the center-of-massof the incident molecule and the surface plane, dCM.If the interaction results in direct scattering, this distance will exhibit precisely one minimum, which we define to be an “inner turning point”. If, however, there exists sufficient attractive interaction to interrupt the outward trajectory of departure and pull the molecule or radical back toward the surface, dCM will exhibit a second inner turning point. If the interaction holds the molecule/radical near the surface for a protracted period, the vibrational motion will produce a series of inner turning points. Our previous experience in other similar chemisorption studies24 indicates the appearance of four such inner turning points to be a reasonble criterion for chemisorption.
III. Results The nature of the initial acetylene chemisorption on a clean C( 11 1) surface has been determined from the results of 138 collision events. In each case, C2H2was randomly oriented with respect to the surface. Incidence angles were randomly selected in the range 0 I8 I4 5 O from a distribution weighted by sin 8. Aiming points on the surface were randomly selected within the area inside the circle shown in Figure 3. At a surface temperature, T,, of 1000 K, the average total chemisorption fraction, is 0.36 for incident translational energies in the range 1.5 eV IE, I2.0 eV. There is a slight tendency for Cr,) to decrease as E, increases, but the effect is small. There is likewise a propensity for the chemisorption probability to decrease as the surface temperature is raised. At surface temperatures of 1250 and 1500 K,the nominal average chemisorption fractions are 0.20 f 0.07 and 0.17 f 0.06,respectively. The trajectory results are summarized in Table I. The most striking result of the C2H2/C(1 1 1) clean surface trajectories is the nature of bonding exhibited by chemisorbed acetylene molecules. The most probable chemisorption mode involves the formation of a surface-bound ethylene structure with two C-C,,) bonds. This was observed in 62% of the trajectories that resulted in C2H2chemisorption. The remaining 38% of the chemisorption events produced an ethenyl radical structure with a single C-C,,) bond. A typical sequence of events is shown in
us),
45 20 8 30 35
1S O 1.75 2.00 1S O 1S O
0.33 f 0.07 0.45 f 0.11 0.25 f 0.15 0.20 f 0.07 0.17 f 0.06
Total number of trajectories computed.
W
Figure 5. “Snapshot” of the C( 111) surface subsequent to the chemisorption of four acetylene molecules. Three of the chemisorptionsform a surface-bound ethylene structure with two C-C,,, bonds. The fourth forms an ethenyl radical. The acetylene molecule on the left has also incorporated an additional hydrogen atom as the result of trajectories involving incident hydrogen atoms. Solid circles represent carbon atoms. Open circules are hydrogen atoms.
Figure 5 for the chemisorption of four acetylene molecules. Here, three of the four chemisorptions result in the formation of the ethylene structure while the fourth chemisorbs via a single C-C,,, bond to form a surface-bound ethenyl radical. It is, of course, possible that if we continued to follow the dynamics for a sufficiently long period, we would observe rotation of the ethenyl radicals followed by the formation of a second C-C,,) bond. Figures 7 and 8 show an example of such an event. The principal point here, however, is that is is possible for acetylene to undergo chemisorption on a clean C( 1 1 1) surface via the formation of a single C-C,,) bond. These results lend support to the hypothesis recently advanced by Belton and Harris16that the initial C2H2 absorption forms an ethylene species bonded to two adjacent lattice sites rather than an ethenyl radical attached to the lattice via a single C-C,,) bond. The HFM m e ~ h a n i s m ’ for ~ * ~the ~ propagation of diamond growth involves the addition of acetylene molecules to radical sites on previously incorporated C2H2species. Reactions structure B structure C and structure D structure E shown in Figure 1 are typical examples. The present MD studies indicate that such propagation is unlikely in that these addition processes appear to have very small reaction probabilities. We have investigated the interaction of incident C2H2 molecules with each of the structures shown in Figure 6. The initial translational energies were varied from 0.096 to 2.0 eV for a surface temperature of lo00 K. In each case,the initial relative velocity vector was chosen so as to aim the acetylene molecule directly at the anticipated radical adsorption site. In some trajectories, the initial C2H2 orientation and velocity vector were selected so as produce the most favorable approach angle in terms of the directional character of the anticipated C-C bond formation. The result of nearly every trajectory for each of the structures shown in Figure 6 was the same; acetylene was observed to scatterfrom the surface without the formation of a new C-C bond. Although acetylene bonds readily to a clean C( 1 1 1) surface, it exhibits little propensity to form similar C-C bonds to other chemisorbed radical sites. We have also found that when acetylene does “bond” (exhibit more than four inner turning points of the C-C motion) to chemisorbed moieties on the diamond surface, the desorption probability is large. For example, in two trajectories we observed acetylene chemisorption at the radical ledge site shown in structure S6, Figure 6. These chemisorption events initially formed ethenyl radicals bound by a single C-C bond as shown in Figure 7 where
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0542 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 H
h ?
s1
n
s2 H
s3
s4
s5
S6
Figure 8. "Snapshot" of the same system shown in Figure 7 at a time subsequent to internal rotation of the chemisorbed acetylene molecule about the newly formed C-C bond. This rotation has resulted in the formation of a second C-C,,, bond that prevents desorption of the molecule. Solid circles represent carbon atoms. Open circles are hydrogen atoms.
H
s7
Representsthe Diamond Surface = Radical Site
Figure 6. Various diamond surface structures investigated in the present study. The moiety denoted with the letter "S" represents the 127 atom, C(111) surface. Radical sites on the chemisorbed species are denoted by the large square dot.
F v 7. "Snapshot" of the chemisorption of acetylene (indicated by the arrow) at a radical ledge site. The picture shows the structure of the system shortly after chemisorption occurs. Solid circles represent carbon atoms. Open circles are hydrogen atoms. the ethenyl radical is seen at the right of the ledge structure. In one case, this ethenyl radical lived for several C-C vibration periods after which C2H2desorption occurred. In the second case, internal rotation about the newly-formed C-C bond permitted the unbound end of the ethenyl radical to approach a surface radical site where it formed a second C-C(s)bond that stabilized the system and prevented desorption. This structure is shown in Figure 8. Belton and H a d 5 have suggested that the unfavorable entropy change associated with the chemisorption of acetylene in the form of an ethenyl radical, coupled with a relatively small chemisorption exothermicity, should lead to rapid desorption of the species. On this basis, they conjectukd that formation of such ethenyl surface structures would not be an important step in diamond-film growth. The present calculations lend support to this view. However, in this context, it should be noted that the chemisorption of C2H2 via ethenyl radical formation proceeds readily on a clean C(111) surface. Furthermore, the propensity for such structures to desorb is very low. In fact, we have observed no such desorption events in any of the clean surface, acetylene/C( 111) trajectories. Apparently the interaction of the ethenyl radical with adjacent unpaired electrons on the C(111) surface tends to stabilize the structure and thereby impede desorption. The above results indicate that if diamond growth proceeds via the HFM mechanism,13*14the growth species must be something
Figure 9. "Snapshot" of the C( 111) system subsequent to the chemisorption of an ethynyl radical on the surface configuration shown in Figure 5. The arrow in the figure shows the newly incorporated C2H radical. Solid circles represent carbon atoms. Open circles are hydrogen atoms.
other than acetylene itself. A similar conclusion is suggested by the growth-rate calculations reported by Belton and Harris.16 In their phenomenological modeling study of diamond growth rates, Belton and Harris16 obtained a value of 0.03 rm/h, whereas the experimentally measured growth rates are 1 order of magnitude larger. This difference could be due to inaccuracies in the assumptions made in the Belton/Harris16 calculations or it could indicate that acetylene addition plays a minor role in diamond-film growth. The latter possbility is suggested by the fact that the ratelimiting step in the Belton/Harris mechanism is the addition of the second acetylene molecule. Consequently, the possibility that the proposed mechanism omits propagation reactions of greater importance than those considered cannot be discounted. Matsui et al.25have measured the flame composition of an oxy/acetylene flame as a function of the C2H2/02ratio. Their results show that for C2H2/02ratios in the range 1.0 I C2H2/02 I1.2, the mole fraction of unburned acetylene remaining in the flame is nearly identical to that for the ethynyl radical (C2H). For larger ratios up to C2H2/02= 1.5, the mole fraction of acetylene exceeds that for C2H, but by less than a factor of 2. These data suggest that the ethynyl radical could be an important growth species in the combustion synthesis of diamond film. If this radical is substantially more reactive than acetylene, it could play a significant role in diamond growth even in experiments where its concentration is 2 or more orders of magnitude less than that of acetylene. We have investigated this possibility by examining a few trajectories in which a C2H radical collides with structures S1, S2, S3,S4, and S6 shown in Figure 6. Overall, we observe a chemisorption probability significantly larger than the near-zero result obtained for acetylene collisions. Roughly, one-third of the trajectories result in C2H chemisorption. However, the statistical accuracy of the present calculations is too low to permit to be determined. We estimate that the reaction probability of C2H radical is at least 1 order of magnitude larger than that of acetylene at the elevated translational energies employed in the present calculations. Since there is a significant activation barrier for the addition of acetylene but probably not for ethynyl radicals, the ratio of the reaction probabilities, Pethynyl/Paatykne, is likely to exceed
vs)
Surface Reactions in Diamond-Film Formation
C
W
Figure 10. (A) A radical ledge site containing an sp2 bonding site denoted by the arrow in the figure. Other carbon bonds of the ledge carbons are saturated with hydrogen atoms. Solid circles represent carbon atoms. Open circles are hydrogen atoms. (B) ‘Snapshot” showing the chemisorption of an ethynyl radical at the radical ledge site shown in part A. (C) “Snapshot” of the system shown in parts A and B after internal rotation of the C2H moiety about the newly formed C-C bond. The rotation results in the formation of a second C-C,,, bond.
lo2 at the lower thermal energies characteristic of CVD experiments. As noted above, this means C2Hcould be a major growth species even at very low concentrations. Figure 9 shows the final result of a ‘ m H collision with a surface structure of the type shown in Figure 6, S3. The initial surface configuration is that shown in Figure 5. As can be seen, the C2H radical bonds readily to the sp2carbon of the H2C-CH moiety. No subsequent C2H desorption was observed. The sequence of trajectory “snapshots” shown in Figure 10, parts A-C show a similar ethynyl chemisorption at a radical ledge site (structure S6, Figure 6). It is interesting to note that the chemisorption occurs via C-C bond formation from the CH carbon rather than the bare carhon atom of the ethynyl radical (see Figure 10B). Subsequent to chemisorption, the ethynyl radical rotates and forms a second bond to a surface radical site as seen in Figure 1OC. This process is very similar to that shown in Figure 8 for acetylene. Obviously, the C2H radical is capable of forming any bonds that acetylene might theoretically form. However, the reaction probabilities for an ethynyl radical are significantly greater than those for the corresponding reactions of acetylene. Consequently, C2His a much more probable candidate as a diamond-film growth species. The absence of such reactions in the phenomenological mechanism proposed by Belton and HarrisI6 may well account for the low growth rates predicted by the model. In addition, the much larger exothermicity associated with chemisorption of C2H compared to that for acetylene makes desorption of C2Hless likely. Hence, the HFM mechanism13J4with C2Has the principal growth species may play a significant role in diamond-film growth.
IV. Summary We have carried out molecular dynamics studies of various elementary reactions involving C2H2and C2H that are likely to be involved in low-pressure diamond-film growth. The C( 111)
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8543 surface is modeled with an ensemble of 127 lattice atoms. The P-and Q-zones of the lattice contain 7 and 30 atoms, respectively. A fixed boundary zone comprises the remaining 90 atoms. The thermal effects of the bulk are simulated using a velocity reset procedure.19The hydrocarbon interaction potential #2 developed by Brenner” is employed in all calculations. The results indicate the following: (1) The sticking coefficients for acetylene on a clean C( 111) surface lie in the range 0.17-0.45 for incident translational energies between 1.5-2.0 eV with surface temperatures in the range 1000-1500 K. (2) Chemisorption of acetylene most frequently involves the formation of two C-C(slsingle bonds to adjacent adsorption sites on the C( 111) surface. (3) Chemisorption of acetylene via the formation of one C-C(s) single bond to yield an ethenyl radical is observed and the subsequent desorption of this species does not appear to be a high probability process on the clean C( 111) surface. (4) The addition of a second acetylene molecule is a very low probability process for all surface structures investigated except the clean C( 111) surface. When such chemisorption does occur, the probability of subsequent desorption of the acetylene molecule is large unless the ethenyl radical is able to subsequently form a second C-C bond. (5) Addition of a ‘ m H radical to a chemisorobed acetylene group proceeds with a much higher probability than is the case for C2H2. The ethynyl radical is also chemisorbed readily to other surface structures with a low probability of subsequent desorption. At the translational energies used in the present calculations, we estimate the chemisorption probability for C2H to be 1 order of magnitude greater than that for acetylene. At the lower energies characteristic of thermal CVD experiments, we would expect the ratio of chemisorption probabilities for C2H and C2H2to exceed lo2. The ethynyl radical therefore appears likely to be an important diamond-growth species even in experiments in which its concentration is 1 or 2 orders of magnitude less than that of acetylene.
Acknowledgment. We are indebted to Dr. Donald W. Brenner for making the details of his hydrocarbon potential surface available to us in advance of publication and for discussions with Dr.Brenner related to various details of the potential. The authors express their appreciation to Dr. Stephen Harris for his many valuable suggestions and comments on the work which resulted in significant improvement of the manuscript. We are pleased to acknowledge financial support from the Air Force Offiice of Scient& Research (AFOSR) under Grants AFOSR-89-0085 and F49620-92-5-0011. We are also indebted to the Oklahoma State University Center for Energy Research (UCER) for financial support to the O.S.U. Diamond Research Group. Registry NO.H m ,2122-48-7;H-H, 74-86-2; C,7440-44-0; CH,=CH, 2669-89-8.
References and Notes (1) Derjaguin, B. V.; Fedoseev, D. V. Sci. Am. 1975,233, 102. (2)Fedoseev, D. V.; Derjaguin, B. V.; Varshavskaya, I. G.; SemenovaTyan-Shanskaya,A. S. Crystallization of Diamond; Nauka: Moscow, 1984. (3) Derjaguin, B. V.; Fedoseev, D. V. Russ. Chem. Reu. 1984,53,435. (4)DeVries, R. C.Ann. Rev. Mater. Sci. 1987,17, 161. (5) Messier, R.;Badzian, A. R.; Badzian, T.; Spear, K. E.; Bachmann, P.; Roy, R. Thin Solid Films 1987,153, 1. (6)Angus, J. C.;Hayman, C. C. Science 1988,241,913. (7)Spear, K. E. J. Am. Ceram. Soc. 1989,72, 171. (8) Good-win, D. G.; Gavillet, G. G. J. Appl. Phys. 1990,68,6393. (9)Harm, S.J.; Weiner, A. M.; Perry, T. A. Appl. Phys. Lett. 1988,53,
Zhu, X. Y.; White, J. M. Surf Sci. 1989,214,240.‘ Tsuda, M.; Nakajima, M.; Oikawa, S. J. Am. Chem.Soc. 1986,108, Tsuda, M.; Nakajima, M.; Oikawa, S. Jpn. J. Appl. Phys. 1987,26, Huang, D.; Frenklach, M.; Maroncelli, M. J. Phys. Chem. 1988.92, Frenklach, M.; Spear, K. E. J. Mater. Res. 1988,3, 133. Harris, S. J.; Belton, D. N. Jpn. J. Appl. Phys., to be published. Belton, D. N.; Harris, S. J. J. Chem. Phys. 1992,96,2371. Brenner, D. W. Phys. Rev. B 1990,42,9458.
J. Phys. Chem. 1992, 96, 8544-8548
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(18) Tersoff, J. Phys. Reu. Lett 1986, 56, 632; Phys. Rev. B 1988, 37, 6991. (19) Riley, M. E.; Coltrin, M. E.; Diestler, D. J. J. Chem. Phys. 1988,88, 5934. (20) Raff, L. M.; Thompson, D. L. The Classical Trajectory Approach to Reactive Scattering. In Theory of Chemical Reaction Dynamics; Brier, M., Ed.; CRC Press Inc.: Boca Raton. FL, 1985; Vol. 111, p 1. (21) Raff, L. M. J . Chem. Phys. 1988,89, 5680. (22) Harris, S. J., J. Appl. Phys. 1989, 66, 5353.
(23) Shampine, L. F.; Gordon, M. K. Computer Solutions of Ordinary Differential Equations, The Initial Value Problem; W. H.Freeman: San Francisco, 1975. (24) For example, see: Agrawal, P. M.;Thompson, D. L.; Raff, L. M.J . Chem. Phys. 1989, 91, 5021. Agrawal, P. M.; Raff, L. M.; Thompson, D. L. Surf.Sci. 1987,188,402. Rice, B.M.; Raff, L. M.; Thompson, D. L. Surf. Sei. 1988, 198, 360. (25) Matsui, Y.; Yuaki, A.; Sahara, M.; Hirose, Y. J . Appl. Phys. 1989, 28, 1718.
The Nature of 4-AmlnophthaIitnide-Cyclodextrin Inclusion Complexes T. Soujanya, T. S. R. Krishna, and A. Samanta* School of Chemistry, University of Hyderabad, Hyderabad 500134, India (Received: May 6, 1992; In Final Form: June 29, 1992)
The complexation between Caminophthalimide and cyclodextrin has been investigated in aqueous solution using steady-state and time-resolved fluorescencetechniques. While 1:l complex formation with a-or B-cyclodextrin is evident from the presence of the isosbestic point in absorption and analysis of fluorescence spectral data, the binding is rather weak with y-cyclodextrin and more than one type of complex are indicated. The complexes of a-and hyclodextrins have been characterized through the measurement of fluorescence spectra, quantum yields, and lifetimes. On the basis of the available experimental data and the results of AM1 calculation on the probe molecule, possible structures of these complexes are suggested.
1. Introduction The guest-host interaction in cyclodextrin (CD) inclusion compounds has been a subject of considerable interest in recent years for the fact that these complexes serve as excellent model systems for complex enzymatic reactions.'-22 Study of a large variety of complexes of a-,8-, and y-CDs has revealed that the complexation process, driven mainly through hydrophobic interaction, requires a good match of size between the host and the guest molecules. Thus, for benzene derivatives, the ideal host is a-CD (cavity diameter, d 5 A); for naphthalene derivatives, 8-CD (d = 6 A) is preferred. While the inclusion process could be monitored through UV-vis absorption studies, the measurement of fluorescence provides a more sensitive technique. This is particularly true for emitting compounds with intramolecular charge-transfer states where encapsulation results in a shift of spectral "aand fluorescence enhancement.l2-Is From a study of photophysical properties in different solvent media and in aqueous 8-CD solutions, we have demonstrated, in an earlier workZZthe usefulness of a dye molecule, eaminophthalimide (AP) in probing the microheterogeneity of the media. Because of the charge-transfer nature, the lowest excited state of AP is extremely sensitive to solvent polarity.23The fluorescence maximum exhibits a shift as large as 115 nm on changing the solvent from ether to water; Qf is decreased from 0.6 to 0.01 for the same change of solvent. On the basis of the photophysical data in homogeneous media and in 8-CD added solutions, we could conclude in that preliminary communication that AP binds to B-CD.22 However, due to a lack of sufficient data, we were unable to make any comment on the possible arrangement of the probe in the host cavity: also we have not examined the inclusion phenomenon in a- and y-CDs. As the specificity with which an encqpsulated molecule will react depends on the particular arrangement of the molecule in the host cavity, a knowledge of the structure of these complexes is extremely important. In view of this, we have undertaken further studies on this aspect. It is interesting to note that barring few cases3s4detailed structural information of the complex has not been obtained from photophysical data. Though it has been possible to identify in a few cases the existence of different types of complexes through the measurement of fluorescence excitation spectra,l3JSthe structural arrangement of the guest molecule inside the host cavities was not examined.
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Fluorescence enhancement on complexation, which is so common with probts such as (dimethylamino)benzonitrile,12J3Js does not necewady mean that the probe is completely inside the host cavity. In this paper, we have examined the photophysical behavior of the probe molecule, AP,in a-and y-CDs through steady-state and time-resolved studies of fluorescence. In addition, further experiments involving AP and B-CD are carried out. Analysis of these results, supported by semi-empirical calculation of the geometry of the probe molecule, provides fairly good detail of the arrangement of AP into cyclodextrin cavities. The work is of significance for the fact that structures of these complicated systems could not be ascertained in most cases by the conventional spectroscopic techniques. 2. Experimeatal Section AP (Eastman)was recrystallized twice from water prior to the spectral investigations. CDs, received from Aldrich, were used without any futher purification. Triply distilled water was used for all measurements. All other solvents were purified following standard procedures. The polarities of the solvents were verified by measuring E ~ ( 3 0values ) using betaine dye molecule.24 The absorption and fluorescence spectra were measured in a Perkin-Elmer Lambda 3B spectrophotometer and in a Hitachi F 3010 spectmfluorimeter,respectively. The fluorescence lifetimes were recorded in a Photon Technology International LS-100 fluorescence spectrophotometer using stroboscopic technique. A nanosecond flash lamp of pulse width 1.6 ns was used for excitation. The goodness of the fit was estimated from xz, a plot of weighted residuals, and autocorrelation functions. The fluorescence quantum yields in homogeneous media were measured by comparing the fluorescence intensities on excitation of optically matched solutions at 390 nm. Quinine sulfate was used as reference (Qr = 0.55 in 1 N H2S04).25CD solutions of the probe molecule were obtained by adding solid CD to an already prepared dilute aqueous solution of the probe. The fluorescence spectrum of the complex was obtained in the following manner. An aqueous solution of known concentration of AP was prepared, and a known amount of CD was added to it. The fluorescence spectrum of the resulting solution was recorded. Using the relations K = [complex]/[AP]~,,[CDJ and [API,,,, = [APlfrm+ [complex], [APIfr, was determined. An@ 1992 American Chemical Society
