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comment on “structures of the benzene monolayers physisorbed on the graphite basal plane” by C. Bondi and G. Taddei
L527
Surface Science 219 (1989) L527-L529 North-Holland, Amsterdam
SURFACE
SCIENCE
LETTERS
COMMENT ON “STRUCTURES OF THE BENZENE MONOLAYERS PHYSISORBED ON THE GRAPHITE BASAL PLANE” BY C. BOND1 AND G. TADDEI Milton W. COLE Physics ~e~a~i~en~,
Pennsylvania
State University,
Uniuersity Park, PA 16802, USA
Received 15 February 1989; accepted for publication 11 May 1989 I refute the claim of Bondi and Taddei [Surface Sci. 203 (1988) 5871 that a paper of Carlos and Cole [Surface Sci. 91 (1980) 3391 incorrectly calculates the anisotropic two body dispersion interaction between au adatom and a carbon atom in graphite.
Bondi and Taddei (BT henceforth) recently Carlos and Cole (CC henceforth) incorrectly body dispersion interaction V(r, R) between atom at R. CC expressed this energy in terms and the graphite surface normal z^: V(r,
R) = -B[l
f(e)
= 1+
+ ~~(1 - : cos28)]
1r-R
claimed [l] that a paper [i] of describes the anisotropic two an adatom at r and a carbon of the angle 8 between (r - R)
le6,
(1) where B and yA are coefficients evaluated from the theory of dispersion forces. BT insist that the function multiplying the anisotropy factor yA should instead be the negative of the second order Legendre polynomial. In refuting this claim here, I fill in several gaps in the derivation of CC. This seems useful because the results of CC have been frequently adopted [3-51. In the following discussion, P is the polarizability of the adatom, while P,, (PI) is the carbon polar&ability component parallel (perpendicular) to the c axis of graphite, which is the z direction. In an oscillator (Drude) model of the atoms, each polarizability has a time dependence characterized by a single energy; we take the values to be E, E,, and E, , respectively. The carbon atom is taken to be invariant to rotation about the z axis (due to its three-fold symmetry in the plane). The interaction thus satisfies [6]:
p,
2;; + ;;,
(3 cos2e - l),
(1 + E/E,,)
bEK(l+E/EJ 0039-6028/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics publishing Division)
(4)
L528
hf. W. Cole / Comment on “Benzene monolayers on the graphite
basalplane"
The function in eq. (3) may be rearranged to yield: f(f))
=
2 0 + b, 2
(l+2b)[l+YA(l-qq~
2(b - 1) ‘*=
3(b+
1) ’
These are the results reported in CC. Note that CC defined the terms in eq. (1) so that the yA term vanishes when the laterally averaged potential V,(z) is computed by summing over the substrate of area A, i.e. for the dispersion part alone I$=
-;/dxdyx,r-RJ6, i
where the carbon atoms are at lattice sites Ri. Thus V,(z) involves only one “parameter” B; the lateral variation involves yA as well. Experiments seem to be consistent with the value yA = 0.4 estimated in CC [2-51. With this choice, the bracketed factor in eq. (1) varies between 0.8 and 1.4 as 8 changes from zero to 8/2 radians. The variation is even larger (a ratio of 5/2) in the extreme anisotropic case assumed by Meyer and Deitz [7]. Their model’s 8 dependence corresponds to the b = co, yA = 2/3 limit of eq. (1). Since the preceding algebra is straightforward, how did BT come to believe that it is wrong? First, note that the bracketed factor in eq. (1) can be written as a Legendre polynomial term plus a constant. If one does this, of course, a different anisotropy parameter (yA) will ensue. More importantly, CC define the anisotropy term in eq. (1) so that eq. (8) is satisfied, i.e. the term does not contribute to the lateral average. This is just mathematical convenience! I add one point to update the discussion in CC: eq. (8) yields for large z v, -
- C3’2)r-
3
7
Cj2’ = -in cB/6 9
where nc is the number density of graphite. As discussed in refs. [8,9] the three body energy Vcs augments this value of C, by about 25% but weakens the attraction near the well minimum by about the same amount; the sign change in Vc3) occurs near z = 4 A. This magnitude suggest that Vc3) should be included in realistic calculations of the adsorption potential. I am grateful to P. Rowntree and L.W. Bruch for drawing my attention to this paper, to Hye-Young Rim for helpful discussion, and to the National Science Foundation for financial support.
M. W. Cole / Comment on “Benzene monolayers on the graphite basal plane”
L529
References [I] (21 [3] [4] [S] [6]
C. Bondi and G. Taddei, Surface Sci. 203 (1988) 587. W.E. Carlos and M.W. Cole, Surface Sci. 91 (1980) 339; Phys. Rev. Letters 43 (1979) 697. G. Vidali and M.W. Cole, Phys. Rev. B 29 (1984) 6736. A.D. CrowelI and J.S. Brown, Surface Sci. 123 (1982) 296. Y.P. Joshi and D.J. Tildesley, Mol. Phys. 55 (1985) 999. H. Margenau and N.R. Kestner, Theory of Intermolecular Forces, 2nd ed. (Pergamon, Oxford, 1969) ch. 2, eq. (53). [7] E.F. Meyer and V.R. Deita, J. Phys. Chem. 71 (1967) 1521; E.F. Meyer, J. Phys. Chem. 71 (1967) 4416. [S] H.Y. Rim and M.W. Cole, Phys. Rev. B 35 (1987) 3990. [9] D. Nicholson, in: Fundamentals of Adsorption, Ed. A.I. Liapis (Engineering Foundation, New York, 1986); Surface Sci. 184 (1987) 255.
Surface Science 219 (1989) L527-L529 North-Holland, Amsterdam
SURFACE
SCIENCE
LETTERS
COMMENT ON “STRUCTURES OF THE BENZENE MONOLAYERS PHYSISORBED ON THE GRAPHITE BASAL PLANE” BY C. BOND1 AND G. TADDEI Milton W. COLE Physics ~e~a~i~en~,
Pennsylvania
State University,
Uniuersity Park, PA 16802, USA
Received 15 February 1989; accepted for publication 11 May 1989 I refute the claim of Bondi and Taddei [Surface Sci. 203 (1988) 5871 that a paper of Carlos and Cole [Surface Sci. 91 (1980) 3391 incorrectly calculates the anisotropic two body dispersion interaction between au adatom and a carbon atom in graphite.
Bondi and Taddei (BT henceforth) recently Carlos and Cole (CC henceforth) incorrectly body dispersion interaction V(r, R) between atom at R. CC expressed this energy in terms and the graphite surface normal z^: V(r,
R) = -B[l
f(e)
= 1+
+ ~~(1 - : cos28)]
1r-R
claimed [l] that a paper [i] of describes the anisotropic two an adatom at r and a carbon of the angle 8 between (r - R)
le6,
(1) where B and yA are coefficients evaluated from the theory of dispersion forces. BT insist that the function multiplying the anisotropy factor yA should instead be the negative of the second order Legendre polynomial. In refuting this claim here, I fill in several gaps in the derivation of CC. This seems useful because the results of CC have been frequently adopted [3-51. In the following discussion, P is the polarizability of the adatom, while P,, (PI) is the carbon polar&ability component parallel (perpendicular) to the c axis of graphite, which is the z direction. In an oscillator (Drude) model of the atoms, each polarizability has a time dependence characterized by a single energy; we take the values to be E, E,, and E, , respectively. The carbon atom is taken to be invariant to rotation about the z axis (due to its three-fold symmetry in the plane). The interaction thus satisfies [6]:
p,
2;; + ;;,
(3 cos2e - l),
(1 + E/E,,)
bEK(l+E/EJ 0039-6028/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics publishing Division)
(4)
L528
hf. W. Cole / Comment on “Benzene monolayers on the graphite
basalplane"
The function in eq. (3) may be rearranged to yield: f(f))
=
2 0 + b, 2
(l+2b)[l+YA(l-qq~
2(b - 1) ‘*=
3(b+
1) ’
These are the results reported in CC. Note that CC defined the terms in eq. (1) so that the yA term vanishes when the laterally averaged potential V,(z) is computed by summing over the substrate of area A, i.e. for the dispersion part alone I$=
-;/dxdyx,r-RJ6, i
where the carbon atoms are at lattice sites Ri. Thus V,(z) involves only one “parameter” B; the lateral variation involves yA as well. Experiments seem to be consistent with the value yA = 0.4 estimated in CC [2-51. With this choice, the bracketed factor in eq. (1) varies between 0.8 and 1.4 as 8 changes from zero to 8/2 radians. The variation is even larger (a ratio of 5/2) in the extreme anisotropic case assumed by Meyer and Deitz [7]. Their model’s 8 dependence corresponds to the b = co, yA = 2/3 limit of eq. (1). Since the preceding algebra is straightforward, how did BT come to believe that it is wrong? First, note that the bracketed factor in eq. (1) can be written as a Legendre polynomial term plus a constant. If one does this, of course, a different anisotropy parameter (yA) will ensue. More importantly, CC define the anisotropy term in eq. (1) so that eq. (8) is satisfied, i.e. the term does not contribute to the lateral average. This is just mathematical convenience! I add one point to update the discussion in CC: eq. (8) yields for large z v, -
- C3’2)r-
3
7
Cj2’ = -in cB/6 9
where nc is the number density of graphite. As discussed in refs. [8,9] the three body energy Vcs augments this value of C, by about 25% but weakens the attraction near the well minimum by about the same amount; the sign change in Vc3) occurs near z = 4 A. This magnitude suggest that Vc3) should be included in realistic calculations of the adsorption potential. I am grateful to P. Rowntree and L.W. Bruch for drawing my attention to this paper, to Hye-Young Rim for helpful discussion, and to the National Science Foundation for financial support.
M. W. Cole / Comment on “Benzene monolayers on the graphite basal plane”
L529
References [I] (21 [3] [4] [S] [6]
C. Bondi and G. Taddei, Surface Sci. 203 (1988) 587. W.E. Carlos and M.W. Cole, Surface Sci. 91 (1980) 339; Phys. Rev. Letters 43 (1979) 697. G. Vidali and M.W. Cole, Phys. Rev. B 29 (1984) 6736. A.D. CrowelI and J.S. Brown, Surface Sci. 123 (1982) 296. Y.P. Joshi and D.J. Tildesley, Mol. Phys. 55 (1985) 999. H. Margenau and N.R. Kestner, Theory of Intermolecular Forces, 2nd ed. (Pergamon, Oxford, 1969) ch. 2, eq. (53). [7] E.F. Meyer and V.R. Deita, J. Phys. Chem. 71 (1967) 1521; E.F. Meyer, J. Phys. Chem. 71 (1967) 4416. [S] H.Y. Rim and M.W. Cole, Phys. Rev. B 35 (1987) 3990. [9] D. Nicholson, in: Fundamentals of Adsorption, Ed. A.I. Liapis (Engineering Foundation, New York, 1986); Surface Sci. 184 (1987) 255.