- Email: [email protected]
Gas-solid energy transfer: effect of internal vibrational energy
GAS-SOLID
ENERGY TRANSFER:
George WOLKEN Jr. and Jane Hylton Battelle.
15 February 1978
CHEMICAL PHYSICS LETTERS
Volume 54, number 1
EFFECT OF INTERNAL
VIBRATIONAL ENERGY *
McCREERY
Columbus Laboratories. Columbus. Ohio 43201.
USA
Received 5 September 1977
Clasc~cal trajectories were run simulating the collision of a diatomic molecule with a sohd surface on a realistic potential energ+ surf.~cc. Previous model potentials have been gcnerslizcd to include I.Wicc dynzurucs in the solid surface snd, hence, the possibility of gas-solid energy tranGx. This energy transfer is cvamincd as .I functmn of the vibrational state of the diatomic molcculc and is found to be rather insenritivc to added vibrational energy. h means is suggcstcd to utilize this
effect to separate vlbrdtionally excited molecules
from unexcited
1. Introductiun We have developed a model potential to describe the interaction of diatomic molecules with solid surfaces [I]. Using this potential, we have integrated classical equations of motion to simulate the dynamics of adsorption [2,3] , recombir Ation (41 as well as collisions of atoms [5] and molecules [G] with previously adsorbed species. All studies cited assumed that the solid surface remains rigid throughout the collision, providing a static background potential in which the atoms move but playing no role in the dynamics of the process. The purpose of this note is to relax this rigid-surface approximation and to rcFort preliminary investigations for the relative efficiency of gas-surface energy transfer for various vibrational states of the incident gids molecule. The results of this calculation lead us to propose selective adsorption on a solid surface (where the adsorption proceeds over an activation barrier) as a possible method for separating isotopes following selective laser-excitation of vibrational states. As is well known, highly monochromatic laser radiation can be used to excite definite molecular energy states of a specific isotopic species**. In order to effect a physical separation of the selectively excited * This research WIFsupported by the Battcllc Institute. Grant l
B 1333-1180. * For a rec42ntreview, set ref.
171.
ones by adsorption
ou ,I surface.
isotope, a second step is needed. For example, the mixture of excited and unexcited moIecu1es can be caused to react with an additional reagent under conditions where the excited molecule reacts appreciably faster than the uncxcitcd one 1891. Thcrc arc two possible reasons for this occurrcncc. (I) If the reaction proceeds with an activation barrier, the laser excited molcculc will react more rapidly simply because it has more energy available than the unexcited spccics to use in surmounting the barrier. (2) It is well known in gas-phase chemical dynamics [IO] that certain kinds of energy can promote a reaction more efficiently than equal amounts of other kinds of energy. Laser cxcitation can selectively populate those modes most efficient in accelerating the desired reaction. It has recently been reported that titanium metal powder added to a mixture of BCl, and Hz effected a 10% enrichment of l”B when irradiated by a 10.55 pm CO, laser [ 1 l] _ This seems to bc the first demonstration of laser isotopc separation in which a heterogeneous catalyst is used. It is well docurneuted that specks often experience an activation barrier to adsorption on a solid surface [ 121 and recent cxpcriments hzve observed pronounced isotope effects for dlc adsorptim of Cl-i4 and CD4 on tungsten [ l3J _ We have previously reported classical trajectory calculations for the adsorption of HD on a rigid solid surface, for potential energy contours both with and without activation barriers [2] _As expected, 35
CHEhiICAL PHYSICS LEITERS
Volume 54. number 1
as irwcased vibrational excitation was present in the incident HD, the probability for surmounting the barrier and adscrbing also increased. The activation barrier appeared to he ncccssary for an efficient separation to occur. Therefore, if a mixture of vibrationally excited and unexcited molecules (as produced by a suitable laser) impinges on such a solid, the excited molecule would preferentially adsorb, effecting a physical separation. However, the approximation of a rigid solid surface may bias the results. If the process of cncrgy transfer between the gas and the solid shows an appreciable dependence on vibrational state, the efficiency of*isotopc separation would also be appreciably affected. The effect could either enhance the adsorption sclectivity (if higher vibrational states transferred more energy to the solid, enhancing sticking) or may diminish the selectivity (if the converse were true). To test this, we computed classical trajcctorics for the system reported previously [2] but aIlowing the surface atom to oscillate about its lattice site (Einstein model). The modifications necessary to introduce lattice motion and the results obtained are discussed in section 2. The present suggestion for isotope separation should be compared with a recent proposal to separate isotopes by selective adsorption in which the crucial mechaIIISI~ is the transfer of vibrational energy to the surface from the incident gas (apparently in the absence of an activation barrier) 1141. ‘I his depends on a heterogeneous V-V energy transfer process which is resonant for certain vibrational states but off-resonance for others. Given the continuous phonon spectrum of the substrate, and the perturbing influences of adsorhates and contaminants, this process may be hard to control in detail in practical situations. In contrast, selective adsorption via an activation barrier (as proposed here) has two simple requirements: an activation barrier to adsorption must be present and gassolid energy transfer strongly favoring lower vibrational states of the molecule must nut bc present. The first rcquircment has often been observed experimentally and the computations reported below indicate that the second requirement is aiso likely to obtain in practice.
2. Description
of the method
As a prototype 36
and results
system we consider
the adsorption
15 February 1978
I--a+
Y
-x
z
t
Fig. 1. Surface geometry and coordinate system for the W(OO1) surface. The ICN, 2CN. XN sites aa indicated (and named according to the number of tungsten atoms to which an adsorbed hydrogen at that site is coordinated). The lattice spacing, u, is 5.97 au and the origin of coordinates is at a ICN site.
of HP in various vibrational states on the (001) face of tungsten. The geometry of the W(OO1) face is given in fig. l_ We are chiefly concerned with the cast of adsorption when an activation barrier is present. As discussed previously [3], the London-Eyring-Polanyi-Sato (LEN) potential can be adjusted to model a variety of activation barriers. The equipotential contours for the approach of HD to the solid surface is shown in fig. 2 for that geometry leading to the lowest activation barrier. The potential shown in fig. 2 assumes a rigid surface and, hence, depends only on the 6 spatial coordinates of the II and D atoms. We denote this rigid surface potential by SLEPT- Following work to be presented in detail elsewhere 115 ] , we briefly describe ho-w VLsps can be simply modified to account for the motion of the surface atoms. In addition to describing the gas rigid-surface potential, VLEPs can also be considered as the interaction of a gas molecule with the lattice sites of the solid. If we allow motion of the solid atoms, at any instant those atoms may or may not be at a lattice site. Therefore, we modify VL~s by introducing correction terms (1) VR, the restoring force on each atom of the solid, tending to return it to its lattice site; (2) VcoRR, to account for the change in the gassurface interaction when the solid atom is displaced from its lattice site. Then we have V totat = vLEPS + vR + VCORR -
(1)
V, and V=ORR must vanish when all the solid atoms occupy their lattice positions reducing the total poten-
Volume 54, number
CHEMICAL
1
PHYSICS
LETTERS
IS February
1978
where N is the number of gas atoms, N, is the number of so-I-id atoms that are free to move, R,_, is the distance between the gas atom and the solid atom and R g_-e is the distance between the gas atom and the lattice site of the solid atom. In the present case, W was taken to bc an exponential repulsion. If the solid
atom s is at its equilibrium lattice site the contribution to VcORR from s is zero. The total gas-solid potential for the nonrigid surface case is then
+c c z,=zz
(au)
Fig. 2. Equipotentiaf contours (in cl/) for the approach of HD to the solid surface. The H-D bond is parallel to the plane of the surface. One atom is Perpendicularly approaching a ICN site and the second is varying in the direction of a neighboring 1 CN site. The coordinates of the two atoms are (XI .y t , ZI), (x2,y2,22). For this potentl;ll. adsorption proceeds WIUI a classical activation barrier of 0.15 eV. The dctaded formula for the potential surface io glvcn in refs. [ 1.21.
tial to VLEps. lvc use pair-potcnti& for YR and VcoRR to correct VLEfi - in an approximate way to allow for motion of the solid atoms. For the restoring force rrR we use an harmonic potential binding an atom of the solid to its (fixed) lattice site. This constitutes an Einstein model of the solid. It has been shown [ 161 that the Einstein desctiption of the lattice dynamics is reasonably good for the rather short, impulsive collisions of the sort we have in the present case. To account for the change in the gassolid potential due to displacement of the surfice atom from its lattice site, WC use a pair-potential for V&RR connecting each gas atom with each surface atom. V,,, already contains the interaction of each gas atom with each lattice site, so to avoid including it twice, this lattice site interaction must be subtracted from VCORR. SO we take
[W(Rg-s) - WR6_,)I
where Vk is the harmonic restoring atom s. In the present case, we assume W(R
(3)
9
5
g
force for solid
j = D exp(-a@
(44)
and D = 3.0 eV, Q = 0.5 123 au-l. The D and or parameters are the same as those used for the Morse curve obtained when a single isolated H atom approaches perpendicularly a ICN site (see fig. 1 and ref. [l]). This is a crude estimate of the required correction term and, hopefully, bettor approximations will be possible 2s gas-surface
iuteraction
potentials
become
bcttcr
known, especially for solid atoms displaced from their lattice sites. To derive the harmonic restoring force we need an estimate of the Einstein temperature of the surface. The Einstein temperature can be estimated from the Debye temperature either by requiring the best single-oscillator approximation to the Debye mode density [ 161 or by expanding the high temperature Dcbye and Einstein heat capacities and matching terms through Tm2. In both casts, one finds the Dcbye temperature to be smaller than the Einstein temperature by a factor of (O.6)1/2. Also, in order to correct approximately for the smaller Debyc temperature of the surface compared to the bulk, an extra factor of 213 is used [ 171. Hence, f~&gf;z)
= ;(0_6)t/2@$
_
(5)
(Wfiacc) = 210 K. This Using O$Fb? * ye = 400 K yields oE,_..h gives a harmonic force constant for a tungsten solid atom of 0.074 au. The solid atoms were assumed ini37
CHEMICAL PHYSICS LETTERS
Volume 54, number 1
TabIe 1 Energy transfer from IED to the (001) face of tungsten. In all cases, the translational kinetic encr@y of HD, and the internal rotational energy were hetd fiI?ed at 0.10 CV and 0.066 eV (j = 3) respectively U
Vibrational energy above zero point (eV)
Total colhsion energy (eV)
Total collision energy (in ‘I&;) tranGxrcd to the solida)
2.82(00.33) 2.53 (0.34) 2.84(0.36) -a) The standard deviation of each sampIe is given in parentheses.
cl 1 2
0.000 0.450 0.876
0.166 -0.613 1.036
tially to be at their equilibrium positions and at rest, approximating a solid at 0 K. We assume that only a single surface atom occupying a 1 CN site could move about its lattice site and all trajectories were aimed within a unit square centered about that arom. Trajectories were run and the mean energy twnsferred to the solid was calculated as we11as the standard deviation of the distribution_ The results are shown in
table 1. Overall, the net energy transferred to the solid is small, which is expected due to the large mass difference between the gas and surface atoms. More important than the magnitlIde of the energy transfer is the observation that it is nearly constant for the various vibrationai states of the HD. One might expect that if the net energy transfer is small (as it is here) it may be particularly sensitive to the small changes due to vibrationaf excitation in HD. However, that seems not to be the case. ~~0~~ the vibrations energy constittites a major part of the total collision energy, the relative energy transfer seems to be reasonably constant. If HD
vibration were particularly efficient at transferring energy to the solid compared to rotation or translation, one would expect much larger fractional energy transfer at u = 2 since vibration constitutes a major share of the total collision energy. Conversely, we expect a much lower fractional energy transfer at u = 2 if vibration were comparatively inefficient. Neither of these results were observed. CIearfy, further work is needed to refine the details of this caI~uIation for other potential surfaces, other mass combinations and other gas-surface coupling potentials [eq. (4)]. However, the present results do suggcst that gas-surface energy transfer is not likely to be a strong function of the vibrational state in the absence 38
15 February 1978
of some special resonance effect. (Note, the selective adsorption method in ref. [ 141 depends on the existence of just such a resonance. The method proposed here depends on the absence of such resonance effects which may be simpler to achieve in practice.) Given an activation barrier to adsorption, and the absence of strong resonance effects in gas-surface vibrational energy trans fer, a method for separating vibrationaliy excited moiecules from unexcited ones may be possibie and should merit an experimental test. The USCof added cnergi (in this case, vibration) to surmount an activation bar- . ricr is a general phenomenon throughout chemistry. In the absence of special resonant V-V energy transfer. the practical applications should extend well beyond the simpfe illustration of HD presented here.
References [if J.M. McCrccry and G. WolkcnJr., J. Chem. Phys. 63 (1975) 2340. [2] J.H. McCrccry and G. Wolken Jr.. C%c:m.Phys. Letters 39 (1976) 478.
[3] J.H. McCreery and G. Wolken Jr., J. Chem. Phys. 65 (1976) 1310. [4] J.H. M&&cry and G. Wolken Jr., J. Chcm. Phyn 63 (1975) 4072; 64 (1976) 2845. [5J A.B. Elkowitz, J.ff. hfdrcery and G. Wolken Jr., Chem. Phys. 17 (1976) 423. 161 J.H. McCreery and G. Wotken Jr., J. Chem. Phys. 66 (1977) 2316. [ 7 ] J-1. Steinfeld, Molecules and radiation (Harper and Row, New York, 1974). [S] S. Datta. R-W. Anderson and R.N. Zarc, 5. Chcm. Phys. 63 (1975) 5503; D. Luci, S. Datta and R.N. Zare, J. Am. Chcm. Sot. 97 (1975) 2557. [9] D. Arnoidi, K. Kaufmann and J. Wolfrum, Phys. Rev. Letters 34 (1975) 1597. [IO] J.C. Polanyi, Accounts Chem. Res. 5 (1972) 161. f Ii] C.T. Lin, T.D.Z. Atvars and F.B.T. Pessine. J. Appl. Pfiys. 48 (1977) 1720. 1121 CN. Stewart and G. Ehrfich, Chem. Phys. Letters 16 (1972) 203. and references therein; T.L. Bradley and R.E. Stickney, Surface Sci. 38 (1973) 313, and references therein; M. Bzdooch, hf.J. Cardillo, D.R. Miller and R.E. Stickney, Surface Sci. 46 (1974) 358. and refarences therein. ll3] H.F. Winters, J. Chem. Phys. 62 (1975) 2454; 64 (8976) 3495. jI4] N.F. Basov, E.M. Belenov,V.A. Isakov, Y.S. Lenox, E.P. Markin. A.N. Oracvskii, V.I. Romanenko and N.B. Ferapontov, Soviet Phys. JETP Letters 22 (1975) 102; K.S. Gochelashvili, N.V. Karbv, A.I. Ovchenkov, A.N.
Volume 54, number 1
CHEMICAL PHYSICS LETTERS
Orlov. R.P. Petrov. Y.N. Petrov and A.M. Prokohorov. Sovbt Phys. JETP 43 (1976) 274. [ 151 J.H. McCreery and G. Wolken Jr., Atomic Recombination Dynamics on Solid Surfaces: Effect of Various Potentials, J. Chem. Phys.. to bc published.
15 February 1978
[ 161 B.J. Garrison and S.A. Adelman, Generalized Langevin Theory for Gas-Solid Processes: Inelastic Scattering Studies, Surface Sci.. to be pubiishcd. [17] R.F. WaUis, Progr. Surface Sci. 4, part 3 (1973).
39
ENERGY TRANSFER:
George WOLKEN Jr. and Jane Hylton Battelle.
15 February 1978
CHEMICAL PHYSICS LETTERS
Volume 54, number 1
EFFECT OF INTERNAL
VIBRATIONAL ENERGY *
McCREERY
Columbus Laboratories. Columbus. Ohio 43201.
USA
Received 5 September 1977
Clasc~cal trajectories were run simulating the collision of a diatomic molecule with a sohd surface on a realistic potential energ+ surf.~cc. Previous model potentials have been gcnerslizcd to include I.Wicc dynzurucs in the solid surface snd, hence, the possibility of gas-solid energy tranGx. This energy transfer is cvamincd as .I functmn of the vibrational state of the diatomic molcculc and is found to be rather insenritivc to added vibrational energy. h means is suggcstcd to utilize this
effect to separate vlbrdtionally excited molecules
from unexcited
1. Introductiun We have developed a model potential to describe the interaction of diatomic molecules with solid surfaces [I]. Using this potential, we have integrated classical equations of motion to simulate the dynamics of adsorption [2,3] , recombir Ation (41 as well as collisions of atoms [5] and molecules [G] with previously adsorbed species. All studies cited assumed that the solid surface remains rigid throughout the collision, providing a static background potential in which the atoms move but playing no role in the dynamics of the process. The purpose of this note is to relax this rigid-surface approximation and to rcFort preliminary investigations for the relative efficiency of gas-surface energy transfer for various vibrational states of the incident gids molecule. The results of this calculation lead us to propose selective adsorption on a solid surface (where the adsorption proceeds over an activation barrier) as a possible method for separating isotopes following selective laser-excitation of vibrational states. As is well known, highly monochromatic laser radiation can be used to excite definite molecular energy states of a specific isotopic species**. In order to effect a physical separation of the selectively excited * This research WIFsupported by the Battcllc Institute. Grant l
B 1333-1180. * For a rec42ntreview, set ref.
171.
ones by adsorption
ou ,I surface.
isotope, a second step is needed. For example, the mixture of excited and unexcited moIecu1es can be caused to react with an additional reagent under conditions where the excited molecule reacts appreciably faster than the uncxcitcd one 1891. Thcrc arc two possible reasons for this occurrcncc. (I) If the reaction proceeds with an activation barrier, the laser excited molcculc will react more rapidly simply because it has more energy available than the unexcited spccics to use in surmounting the barrier. (2) It is well known in gas-phase chemical dynamics [IO] that certain kinds of energy can promote a reaction more efficiently than equal amounts of other kinds of energy. Laser cxcitation can selectively populate those modes most efficient in accelerating the desired reaction. It has recently been reported that titanium metal powder added to a mixture of BCl, and Hz effected a 10% enrichment of l”B when irradiated by a 10.55 pm CO, laser [ 1 l] _ This seems to bc the first demonstration of laser isotopc separation in which a heterogeneous catalyst is used. It is well docurneuted that specks often experience an activation barrier to adsorption on a solid surface [ 121 and recent cxpcriments hzve observed pronounced isotope effects for dlc adsorptim of Cl-i4 and CD4 on tungsten [ l3J _ We have previously reported classical trajectory calculations for the adsorption of HD on a rigid solid surface, for potential energy contours both with and without activation barriers [2] _As expected, 35
CHEhiICAL PHYSICS LEITERS
Volume 54. number 1
as irwcased vibrational excitation was present in the incident HD, the probability for surmounting the barrier and adscrbing also increased. The activation barrier appeared to he ncccssary for an efficient separation to occur. Therefore, if a mixture of vibrationally excited and unexcited molecules (as produced by a suitable laser) impinges on such a solid, the excited molecule would preferentially adsorb, effecting a physical separation. However, the approximation of a rigid solid surface may bias the results. If the process of cncrgy transfer between the gas and the solid shows an appreciable dependence on vibrational state, the efficiency of*isotopc separation would also be appreciably affected. The effect could either enhance the adsorption sclectivity (if higher vibrational states transferred more energy to the solid, enhancing sticking) or may diminish the selectivity (if the converse were true). To test this, we computed classical trajcctorics for the system reported previously [2] but aIlowing the surface atom to oscillate about its lattice site (Einstein model). The modifications necessary to introduce lattice motion and the results obtained are discussed in section 2. The present suggestion for isotope separation should be compared with a recent proposal to separate isotopes by selective adsorption in which the crucial mechaIIISI~ is the transfer of vibrational energy to the surface from the incident gas (apparently in the absence of an activation barrier) 1141. ‘I his depends on a heterogeneous V-V energy transfer process which is resonant for certain vibrational states but off-resonance for others. Given the continuous phonon spectrum of the substrate, and the perturbing influences of adsorhates and contaminants, this process may be hard to control in detail in practical situations. In contrast, selective adsorption via an activation barrier (as proposed here) has two simple requirements: an activation barrier to adsorption must be present and gassolid energy transfer strongly favoring lower vibrational states of the molecule must nut bc present. The first rcquircment has often been observed experimentally and the computations reported below indicate that the second requirement is aiso likely to obtain in practice.
2. Description
of the method
As a prototype 36
and results
system we consider
the adsorption
15 February 1978
I--a+
Y
-x
z
t
Fig. 1. Surface geometry and coordinate system for the W(OO1) surface. The ICN, 2CN. XN sites aa indicated (and named according to the number of tungsten atoms to which an adsorbed hydrogen at that site is coordinated). The lattice spacing, u, is 5.97 au and the origin of coordinates is at a ICN site.
of HP in various vibrational states on the (001) face of tungsten. The geometry of the W(OO1) face is given in fig. l_ We are chiefly concerned with the cast of adsorption when an activation barrier is present. As discussed previously [3], the London-Eyring-Polanyi-Sato (LEN) potential can be adjusted to model a variety of activation barriers. The equipotential contours for the approach of HD to the solid surface is shown in fig. 2 for that geometry leading to the lowest activation barrier. The potential shown in fig. 2 assumes a rigid surface and, hence, depends only on the 6 spatial coordinates of the II and D atoms. We denote this rigid surface potential by SLEPT- Following work to be presented in detail elsewhere 115 ] , we briefly describe ho-w VLsps can be simply modified to account for the motion of the surface atoms. In addition to describing the gas rigid-surface potential, VLEPs can also be considered as the interaction of a gas molecule with the lattice sites of the solid. If we allow motion of the solid atoms, at any instant those atoms may or may not be at a lattice site. Therefore, we modify VL~s by introducing correction terms (1) VR, the restoring force on each atom of the solid, tending to return it to its lattice site; (2) VcoRR, to account for the change in the gassurface interaction when the solid atom is displaced from its lattice site. Then we have V totat = vLEPS + vR + VCORR -
(1)
V, and V=ORR must vanish when all the solid atoms occupy their lattice positions reducing the total poten-
Volume 54, number
CHEMICAL
1
PHYSICS
LETTERS
IS February
1978
where N is the number of gas atoms, N, is the number of so-I-id atoms that are free to move, R,_, is the distance between the gas atom and the solid atom and R g_-e is the distance between the gas atom and the lattice site of the solid atom. In the present case, W was taken to bc an exponential repulsion. If the solid
atom s is at its equilibrium lattice site the contribution to VcORR from s is zero. The total gas-solid potential for the nonrigid surface case is then
+c c z,=zz
(au)
Fig. 2. Equipotentiaf contours (in cl/) for the approach of HD to the solid surface. The H-D bond is parallel to the plane of the surface. One atom is Perpendicularly approaching a ICN site and the second is varying in the direction of a neighboring 1 CN site. The coordinates of the two atoms are (XI .y t , ZI), (x2,y2,22). For this potentl;ll. adsorption proceeds WIUI a classical activation barrier of 0.15 eV. The dctaded formula for the potential surface io glvcn in refs. [ 1.21.
tial to VLEps. lvc use pair-potcnti& for YR and VcoRR to correct VLEfi - in an approximate way to allow for motion of the solid atoms. For the restoring force rrR we use an harmonic potential binding an atom of the solid to its (fixed) lattice site. This constitutes an Einstein model of the solid. It has been shown [ 161 that the Einstein desctiption of the lattice dynamics is reasonably good for the rather short, impulsive collisions of the sort we have in the present case. To account for the change in the gassolid potential due to displacement of the surfice atom from its lattice site, WC use a pair-potential for V&RR connecting each gas atom with each surface atom. V,,, already contains the interaction of each gas atom with each lattice site, so to avoid including it twice, this lattice site interaction must be subtracted from VCORR. SO we take
[W(Rg-s) - WR6_,)I
where Vk is the harmonic restoring atom s. In the present case, we assume W(R
(3)
9
5
g
force for solid
j = D exp(-a@
(44)
and D = 3.0 eV, Q = 0.5 123 au-l. The D and or parameters are the same as those used for the Morse curve obtained when a single isolated H atom approaches perpendicularly a ICN site (see fig. 1 and ref. [l]). This is a crude estimate of the required correction term and, hopefully, bettor approximations will be possible 2s gas-surface
iuteraction
potentials
become
bcttcr
known, especially for solid atoms displaced from their lattice sites. To derive the harmonic restoring force we need an estimate of the Einstein temperature of the surface. The Einstein temperature can be estimated from the Debye temperature either by requiring the best single-oscillator approximation to the Debye mode density [ 161 or by expanding the high temperature Dcbye and Einstein heat capacities and matching terms through Tm2. In both casts, one finds the Dcbye temperature to be smaller than the Einstein temperature by a factor of (O.6)1/2. Also, in order to correct approximately for the smaller Debyc temperature of the surface compared to the bulk, an extra factor of 213 is used [ 171. Hence, f~&gf;z)
= ;(0_6)t/2@$
_
(5)
(Wfiacc) = 210 K. This Using O$Fb? * ye = 400 K yields oE,_..h gives a harmonic force constant for a tungsten solid atom of 0.074 au. The solid atoms were assumed ini37
CHEMICAL PHYSICS LETTERS
Volume 54, number 1
TabIe 1 Energy transfer from IED to the (001) face of tungsten. In all cases, the translational kinetic encr@y of HD, and the internal rotational energy were hetd fiI?ed at 0.10 CV and 0.066 eV (j = 3) respectively U
Vibrational energy above zero point (eV)
Total colhsion energy (eV)
Total collision energy (in ‘I&;) tranGxrcd to the solida)
2.82(00.33) 2.53 (0.34) 2.84(0.36) -a) The standard deviation of each sampIe is given in parentheses.
cl 1 2
0.000 0.450 0.876
0.166 -0.613 1.036
tially to be at their equilibrium positions and at rest, approximating a solid at 0 K. We assume that only a single surface atom occupying a 1 CN site could move about its lattice site and all trajectories were aimed within a unit square centered about that arom. Trajectories were run and the mean energy twnsferred to the solid was calculated as we11as the standard deviation of the distribution_ The results are shown in
table 1. Overall, the net energy transferred to the solid is small, which is expected due to the large mass difference between the gas and surface atoms. More important than the magnitlIde of the energy transfer is the observation that it is nearly constant for the various vibrationai states of the HD. One might expect that if the net energy transfer is small (as it is here) it may be particularly sensitive to the small changes due to vibrationaf excitation in HD. However, that seems not to be the case. ~~0~~ the vibrations energy constittites a major part of the total collision energy, the relative energy transfer seems to be reasonably constant. If HD
vibration were particularly efficient at transferring energy to the solid compared to rotation or translation, one would expect much larger fractional energy transfer at u = 2 since vibration constitutes a major share of the total collision energy. Conversely, we expect a much lower fractional energy transfer at u = 2 if vibration were comparatively inefficient. Neither of these results were observed. CIearfy, further work is needed to refine the details of this caI~uIation for other potential surfaces, other mass combinations and other gas-surface coupling potentials [eq. (4)]. However, the present results do suggcst that gas-surface energy transfer is not likely to be a strong function of the vibrational state in the absence 38
15 February 1978
of some special resonance effect. (Note, the selective adsorption method in ref. [ 141 depends on the existence of just such a resonance. The method proposed here depends on the absence of such resonance effects which may be simpler to achieve in practice.) Given an activation barrier to adsorption, and the absence of strong resonance effects in gas-surface vibrational energy trans fer, a method for separating vibrationaliy excited moiecules from unexcited ones may be possibie and should merit an experimental test. The USCof added cnergi (in this case, vibration) to surmount an activation bar- . ricr is a general phenomenon throughout chemistry. In the absence of special resonant V-V energy transfer. the practical applications should extend well beyond the simpfe illustration of HD presented here.
References [if J.M. McCrccry and G. WolkcnJr., J. Chem. Phys. 63 (1975) 2340. [2] J.H. McCrccry and G. Wolken Jr.. C%c:m.Phys. Letters 39 (1976) 478.
[3] J.H. McCreery and G. Wolken Jr., J. Chem. Phys. 65 (1976) 1310. [4] J.H. M&&cry and G. Wolken Jr., J. Chcm. Phyn 63 (1975) 4072; 64 (1976) 2845. [5J A.B. Elkowitz, J.ff. hfdrcery and G. Wolken Jr., Chem. Phys. 17 (1976) 423. 161 J.H. McCreery and G. Wotken Jr., J. Chem. Phys. 66 (1977) 2316. [ 7 ] J-1. Steinfeld, Molecules and radiation (Harper and Row, New York, 1974). [S] S. Datta. R-W. Anderson and R.N. Zarc, 5. Chcm. Phys. 63 (1975) 5503; D. Luci, S. Datta and R.N. Zare, J. Am. Chcm. Sot. 97 (1975) 2557. [9] D. Arnoidi, K. Kaufmann and J. Wolfrum, Phys. Rev. Letters 34 (1975) 1597. [IO] J.C. Polanyi, Accounts Chem. Res. 5 (1972) 161. f Ii] C.T. Lin, T.D.Z. Atvars and F.B.T. Pessine. J. Appl. Pfiys. 48 (1977) 1720. 1121 CN. Stewart and G. Ehrfich, Chem. Phys. Letters 16 (1972) 203. and references therein; T.L. Bradley and R.E. Stickney, Surface Sci. 38 (1973) 313, and references therein; M. Bzdooch, hf.J. Cardillo, D.R. Miller and R.E. Stickney, Surface Sci. 46 (1974) 358. and refarences therein. ll3] H.F. Winters, J. Chem. Phys. 62 (1975) 2454; 64 (8976) 3495. jI4] N.F. Basov, E.M. Belenov,V.A. Isakov, Y.S. Lenox, E.P. Markin. A.N. Oracvskii, V.I. Romanenko and N.B. Ferapontov, Soviet Phys. JETP Letters 22 (1975) 102; K.S. Gochelashvili, N.V. Karbv, A.I. Ovchenkov, A.N.
Volume 54, number 1
CHEMICAL PHYSICS LETTERS
Orlov. R.P. Petrov. Y.N. Petrov and A.M. Prokohorov. Sovbt Phys. JETP 43 (1976) 274. [ 151 J.H. McCreery and G. Wolken Jr., Atomic Recombination Dynamics on Solid Surfaces: Effect of Various Potentials, J. Chem. Phys.. to bc published.
15 February 1978
[ 161 B.J. Garrison and S.A. Adelman, Generalized Langevin Theory for Gas-Solid Processes: Inelastic Scattering Studies, Surface Sci.. to be pubiishcd. [17] R.F. WaUis, Progr. Surface Sci. 4, part 3 (1973).
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