Langmuir 1985,1,557-564 triaquo complex at SII* in KX zeolite and a hexaaquo complex in the a-cages in TlX ~ e o l i t e . ~In~ the J ~ last case, the high affinity of T1+for the SI’ and SII sites was thought to be a prime factor resulting in Cu2+forming hexaaquo complexes in the a-cage. There is no crystal structure data available for CdX zeolite. From the close similarities of Cu2+behavior in CaX and CdX we conclude that in CdX, Cd2+is most probably in SI’ sites thus preventing Cu2+ from occupying the SI’ or SI sites. Thus Cu2+ends up in SI1 sites. The decrease in the g, value of Cu(A’) relative to that of Cu(A) is indicative of an increase in the in-plane Cu-0, bond lengths, which is reasonable to expect as Cu2+ moves further into the P-cages from the plane of the sixring window. That Cu2+has moved into the @-cageson dehydration is evident from the weak interaction observed with adsorbed methanol. Methanol molecules are too bulky to enter the P-cage via the six-ring window. It is interesting to note that the ESR parameters in fully dehydrated Cu-CdX are similar to those in dehydrated CuNaX and different from those in dehydrated Cu-CaX. In previous studies5 Cu2+in dehydrated X and Y zeolites was suggested to be in SI and SI’ sites. However, rehydration of Cu-NaX does not result in formation of the trigonal-
557
bipyramidal Cu(A) while it does in Cu-CdX. Thus we suggest that in dehydrated Cu-CdX, Cu2+is most likely in ,511’ sites so that it can move back into the SI1 sites on rehydration to form the trigonal-bipyramidal complex.
Conclusions The ESR and ESEM studies on Cu2+in fully cadmium exchanged X zeolites reveal the formation of an unusual trigonal-bipyramidal complex CU(O,)~(OH)~ which is observed in CaX zeolite and not in any other monovalent or divalent ion exchanged X zeolites. The stability of this complex in CdX was found to be less than than in CaX. However, unlike in CaX, this complex could be completely recovered on rehydration after dehydration of the zeolite at 500-700 K. Such regeneration seems to be due to the fact that Cu2+is at different sites in the dehydrated CuCdX and Cu-CaX. Acknowledgment. This research was supported by the National Science Foundation and the Robert A. Welch Foundation. We are grateful to the University of Houston Energy Laboratory for equipment support. Registry No. Cu, 7440-50-8; Cd, 7440-43-9.
Coverage Dependence of Gas-Surface Energy Transfer Daqing Zhao and John E. Adams* Department of Chemistry, University of Missouri, Columbia, Missouri 65211 Received February 22, 1985. I n Final Form: M a y 31, 1985 The energy transfer occurring when an energy-selectedargon atom beam impinges on a tungsten(ll0) surface is examined via a classical trajectory simulation. Of special interest here is the enhancement of energy exchange observed when a submonolayer coverage of the argon test gas is adsorbed on and equilibrated with the metal surface. The computed scattering distributions are found to be in agreement with the limited experimental data available at present and are interpretable in terms of the adsorbate’s effect on the surface roughness.
I. Introduction The energy transfer accompanying the scattering of rare gases from metal surfaces has been the subject of numerous investigations, the earliest work coming shortly after the turn of the century. In these older studies the principal focus was on the determination of thermal accommodation coefficients, with the pioneering work of Roberts’ and the subsequent results by Thomas and co-workers2constituting some of the more significant contributions to the field. Accommodation coefficients (hereafter, AC’s) have been reported not only for gases in contact with clean metallic surfaces (although the presence of adsorbed atoms identical with those of the test gas could not be ruled out) but also for surfaces deliberately dosed with an adsorbate (for example, an alkali metal).3 Some of the more recent work, however, has involved the use of techniques that permit a somewhat greater control over the experimental conditions. Both Yamamoto and Stickne9 and also Weinberg (1) Roberta, J. K. Proc. R. SOC.London, Ser. A 1930, 129, 146. (2) See, for example: Thomas, L. B. In “Fundamentals of Gas-Surface
Interactions”; Saltsburg, H., Smith, J. N., Jr., Eds.; Academic Press: New York, 1967; p 346. (3) Thomas, L. B. In “Rarefied Gas Dynamics”; Fisher, S. S., Ed.; American Institute of Aeronautics and Astronautics: New York, 1981; p 83. (4) Yamamoto, S.; Stickney, R. E. J. Chem. Phys. 1970, 53, 1594.
0743-7463/85/2401-0557$01.50/0
and Memills have directed atomic beams at single-crystal W(ll0) surfaces and have determined angular distributions for the scattered rare gas atoms. Additional detail is revealed in the experiments of Janda, Hurst, and co-workwho reported time-of-flight distributions for a beam of argon atoms scattered from a polycrystalline tungsten or platinum(ll1) surface.* The appearance of these experimental results for welldefined systems has sparked a renewed interest in theoretical studies of gas-surface energy transfer, with the contributions made to date ranging from the simple dy(5) Weinberg, W. H.; Merrill, R. P. J. Chem. Phys. 1972, 56, 2881. (6) Janda, K. C.; Hurst, J. E.; Becker, C. A,; Cowin, J. P.; Auerbach, D. J.; Wharton, L. J. Chem. Phys. 1980, 72,2403. (7) Hurst, J. E.; Wharton, L.; Janda, K. C.; Auerbach, D. J. J . Chem. Phys. 1983, 78,1559. (8) For studies of inelastic scattering from insulator surfaces, see:
Brusdeylins, G.; Doak,R. B.; Skofronick, J. G.; Toennies, J. P. Surf. Sci. 1983, 128, 191. Several groups recently have also addressed questions concerning the nature of inelastic molecule-surface scattering, with rotational state distributions and state-to-state rotational transition probabilities being reported for diatomics scattered from single-crystal surfaces. See, for example: Cowin, J. P.; Yu, C. F.; Sibener, S. J.; Hurst, J. E. J. Chem. Phys. 1981, 75,1033. Cowin, J. P.; Yu, C. F.; Sibener, S. J.; Wharton, L. J. Chem. Phys. 1983, 79,3537. Frenkel, F.; Hager, J.; Krieger, W.; Walther, H.; Campbell, C. T.; Ertl, G.; Kuipers, H.; Segner, J. Phys. Rev. Lett. 1981, 46, 152. McClelland, G. M.; Kubiak, G. D.; Rennagel, H. G.; Zare, R. N. Phys. Rev. Lett. 1981,46,831. Brusdeylins, G.; Toennies, J. P. Surf. Sci. 1983, 126,647.
0 1985 American Chemical Society
558 Langmuir, Vol. 1, No. 5, 1985
namical models such as the hard-cube and soft-cube theoriesgto the rigorous but cumbersome quantum treatments of Wolken’O and Tsuchida.” One here finds a number of interesting approaches, notably those that consider sudden or impulsive dynamical assumptions,12those that treat collisional inelasticity as a perturbation of the elastic scattering problem,13 and those that apply such well-known scattering approximations as DWBA14 to the study of gas-surface collisions. Nearly absent, however, are inquiries into the role played by an adsorbate in a gassurface collision event. Since in both thermal AC measurements and atomic beam scattering experiments the collision processes occurring with and without the influence of trapped test gas atoms are usually not easily distinguished, it seems clear that a characterization of the adsorbate effect on energy accommodation can represent an important step toward understanding the results obtained for “clean” surfaces as well as for those that are intentionally dosed. Those existing studies that do address the modification of collision dynamics accompanying the interposition of adatoms15 have on the whole only yielded a qualitative description of the scattering, although a notable exception to this situation is to be found in the work of Lorenzen and Raff.lG They proposed a classical dynamical model for scattering from a collection of fixed and movable centers arranged so as to represent a crystal lattice and adsorbed atoms and calculated not only energytransfer coefficients and angular scattering distributions but also velocity distributions for the reflected particles (the systems examined being He/Ni(lll) and He/Ar/ Ni(ll1)). The present work is very much in the spirit of the investigations by Lorenzen and Raff, but the model described in the following section does in our view permit a more realistic representation of the system dynamics. We should note that in trying to model gas-surface collisions (or for that matter other condensed phase events), one is faced with the practical necessity of reducing the number of degrees of freedom of the system. The simplest way to handle the problem would be to use a truncated array of solid atoms and to hope that the range of the interactions influencing the collision dynamics does not extend beyond the limits of the array. More desirable, however, is a model that affords a better description of the lattice motion, such as the generalized Langevin equation approach17J8in which one follows the dynamics of a small number of atoms (the primary zone) exactly while treating the remaining solid as a heat bath. In practice such a model is most useful when the system being studied in(9)Logan, R. M.;Stickney, R. E. J. Chem. Phys. 1966,44,195.Logan, R. M.; Keck, J. C. J. Chem. Phys. 1968,49,860. (10)Wolken, G. J. Chem. Phys. 1973.58,3047;1973,59,1159;1974, 60,2210. (11)Tsuchida, A. Surf. Sci. 1969,14,375. (12)See, for example: Gerber, R. B.; Yinnon, A. T.; Murrell, J. N. Chem. Phys. 1978,31,1.Kouri, D. J. Chem. Phys. Lett. 1979,64,139. Gerber, R.B.;Yinnon, A. T.; Shimoni, Y.; Kouri, D. J. J. Chem. Phys. 1980,73,4397.Adams, J. E.;Miller, W. M.Surf. Sei. 1979,85,77.Adams, J. E.Surf. Sci. 1980,97,43. (13)Metiu, H. I. J . Chem. Phys. 1978, 67,5456. Hubbard, L. M.; Miller, W. H. J. Chem. Phys. 1983,78,1801. (14)Stutzki, J.; Brenig, W. 2.Phys. B: Condens. Matter 1981,45,49. (15)See, for example: Goodman, F. 0. Surf. Sci. 1968,11,283. Shin, Feuer, P. J. Chem. Phys. H. J. Chem. Phys. 1965,42,3442.Allen, R. T.; 1965,43,4500. Oman, R. A. AIAA J. 1967,5,1280. (16)Lorenzen, J.; Raff, L. M. J. Chem. Phys. 1970,52, 1133,6134. (17)Adelman, S. A.; Doll, J. D. Acc. Chem. Res. 1977,IO,378. Tully, J. C. Acc. Chem. Res. 1981,14, 188. (18)In recent work DePristo has coupled the GLE approach to lattice dynamics with a semiclassical description of the gaseous species, thereby obtaining what he refers to as the “semiclassical stochastic trajectory“ method. See, for example: Richard, A. M.; DePristo, A. E. Surf. Sci. 1983,234,338. Clary, D. C.;DePristo, A. E. J , Chem. Phys. 1984,81, 5167.
Zhao and Adams
volves a clean crystal surface, since the inclusion of a submonolayer adsorbate necessitates the adding of many more atoms to the primary zone. An alternate way of rendering the collision events amenable to theoretical treatment makes use of a template model of the surface. Here one describes the surface in terms of a rectangular slab that is replicated in two dimensions through the imposition of periodic boundary conditions. Previous studies, both of adsorbate diffusionlg and also of atomic and molecular sticking,20have indicated that such a model can be getlerally useful and that very little additional effort is required in order to account for the presence of adsorbed species.21 Consequently, it is this template model that we have chosen to adopt for the present study.
11. Simulation of Ar/W(llO) Scattering We take as our prototypical system for the evaluation of adsorbate coverage effects a collimated, monoenergetic beam of argon atoms incident on the (110) face of a tungsten single crystal. As indicated in the Introduction, the surface description adopted here is that of a template model,1!+21which in the present implementation consists of three layers of tungstens atoms with 24 atoms per layer. (The area of the slab is thus 12(21/2)u2, where a is the cubic bcc lattice dimension. For tungsten this area is approximately equal to 170 A2. Since previous calculations of sticking probabilities have suggested that an expansion of the model lattice by about 25% leads to no appreciable change in the values obtained, we feel that the size of the slab is adequate for the study described here.) The atoms comprising the lower two layers in this model are held fixed in their equilibrium lattice positions (thereby defining the solid template), while the atoms in the top layer are permitted to move according to the appropriate classical equations of motion. By allowing motion of the top layer only, we are assuming that the movement of these atoms adequately represents the thermal deformation of the surface lattice, i.e., that the surface phonon modes couple only weakly with the bulk modes. Adams and Do1121 previously showed the inclusion of the motion of only a single layer to be sufficient for describing the dynamics of a xenon surface, which appears substantially more strongly corrugated to an impinging rare gas atom than does the present tungsten surface. We thus expect the assumption that only a single layer of moving atoms need be considered also to be reasonable in this case. Note that an important consequeiice of ignoring energy exchange between the first and second layers is an implicit assumption that surface energy dissipation into the bulk is slow when compared to the time scale over which the collision of the incident species occurs. One should certainly not conclude, though, that energy flow perpendicular to the surface will be negligible over longer time intervals. The interactions among tungsten atoms (either within the uppermost solid layer or between atoms in this top layer and the atoms in the lower layers) are taken as being sums of pairwise potentials. Although Lennard-Jones 6-12 potential parameters for tungsten have been given by Halicioglu and Pound,22such a functional form provides a poor description of the forces between atoms crystallizing in a bcc lattice. In fact, our random walk calculations indicated below reveal that the assumption of a 6-12 PO(19)See, for example: Doll, J. D.; McDowell, H. K. J. Chem. Phys. 1982,77,479;Surf. Sci. 1982,123,W.Valone, S.M.; Doll, J. D. Surf. Sci. 1984.139. 478. (20) Adams, J. E.; Doll, J. D. J. Chem. Phys. 1984,80,1681. Adams, J. E. Chem. Phys. Lett. 1984, 110,155. (21)Adams, J. E.; Doll, J. D. J. Chem. Phys. 1982,77,2964. (22)Halicioglu, T.; Pound, G. M. Phys. Status Solidi A 1975,30,619. ~~
Coverage Dependence of Gas-Surface Energy Transfer
tential for tungsten will lead to an attempted reconstruction of the (110) face, with this observation contradicting both e ~ p e r i m e n t aand l ~ ~ theoretical results.% (It is known that a 6-12 potential does correctly predict the equilibrium structure of an fcc crystal.26) We thus have chosen instead to use a potential form suggested by Weber and StillingeP that yields a stable bcc crystal lattice, V w d r ) = 3.81Oc,[(~,/r)~ - (r/u,)I expl[(r/u,) 2.0]-'), 0 < r < 2u8 = 0, r 1 2u, where the range parameter, us,is chosen so as to give the correct interlayer spacing (us= 2.257 A here) and the well depth, G,is assumed to be the same as in the corresponding Lennard-Jones potential (q/kB = 12391 K, kB = Boltzmann's constant). A particularly advantageous feature of such a function is that the forces deriving from this POtential go smoothly to zero at a distance r = 2u,, and so we avoid encountering discontinuities in the forces due to truncation of the potential at a finite range. To describe the interaction between an argon atom, whether it be incident or adsorbed, and the tungsten surface we adopt the function proposed by Tully2' where Ti is the coordinate vector of the ith argon atom, {gj)is the set of solid atom coordinate vectors, and ziis the component of iilying in the direction normal to the surface plane (the average position of the top layer of solid atoms being z = 0). The first of these two terms consists of a sum of two-body Lennard-Jones 6-12 potentials describing the van der Waals interactions between isolated argon and tungsten atoms
rij = 17;- gjl The second term, the one depending only upon the vertical distance between the argon atom and the surface, then corrects this pairwise additive potential so as to account for the metallic nature of the solid, since it represents an interaction with the delocalized electron density of the tungsten surface. Specifically, we have Vz(zj) = C((2/15)[D/(zi + z0)19 - [ D / ( z i + z0)131 The parameter values chosen for the present study are actually those that Tully has reported for the Ar/Pt(lll) cp/kB = 25.17 K, bps= 2.93 A, C/kB = 929.72 K, D = 4.30 A, and zo = 0.90 A. We feel justified in adopting these quantities without further refinement for two reasons, the first being that the experimental binding energy used by Tully in fitting the Ar/Pt potential was actually a binding energy which was measured for Ar/W, and the second being that the angular distributions observed for argon atoms scattered from a tungsten surface appear to be nearly the same as those seen in argon scattering from platinum (the distributions in the former case being slightly narrower6). Although we cannot be sure that the potential seleded is of sufficient accuracy that our results will agree quantitatively with those obtained from experiments, we do nonetheless expect that the results will reflect the correct qualitative description of the role played by an adsorbate in energy transfer and of the principal mechanisms of these processes. One should note in par(23) Stem, R. M.; Sinharoy, s. Surf. Sci. 1972,33,131. Van Hove, M. A.; Tong, S. Y. Surf. Sci. 1976, 54, 91. (24) Bourdin, J. P.; Treglia, B.; Desjonqueres, M. C.; Ganachaud, J. P.; Spanjaard, D. Solid State Commun. 1983,47, 279. (25) Broughton, J. Q.; Gilmer, G. H. J. Chem. Phys. 1983, 79, 5095. (26) Weber, T. A.; Stillinger, F. H. J. Chem. Phys. 1984, 81, 5089. (27) Tully, J. C. Surf. Sci. 1981, 111, 461.
Langmuir, Vol. 1, No. 5, 1985 559
ticular that the scattering dynamics will depend very strongly on the value of zo, since it is this parameter that, effectively, establishes the position of the argon-surface repulsive wall and consequently determines the degree of corrugation of the tungsten crystal surface. The total potential energy of the system is calculated by using the various functional forms indicated above plus a 6-12 potential describing the two-body rare gas-rare gas interaction ( c k / k B = 119.8 K, uA, = 3.405 A28)via a summation consistent with the imposed periodic boundary conditions. Argon-argon interactions are truncated at a distance equal to twice the unit cell dimension of the tungsten bcc crystal (and thus half the length of the shorter side of the crystal slab). We also truncate the 6-12 contribution to the argon-tungsten potential at this same distance but retain the longer range z-dependent term, so that for this part of the potential we have what amounts to a cylindrical range cutoff. Initial conditions for trajectories involving this surface (whether clean or with a number of adatoms present) must be selected so as to reflect the thermal fluctuations appropriate to the given system temperature. As in previous workz0r2lwe generate the set of atomic positions at time equal to zero on the basis of a thermally biased random walk of those particles in the system for which motion is allowed. Such a procedure, representing just a Monte Carlo calculation with Metropolis sampling,29yields instantaneous "snapshots" of the system characteristic of the chosen temperature and the various interaction potentials. The initial momenta, which are not determined in the random walk, can then be set by random sampling from the appropriate Boltzmann distribution. The initial lateral position for the impinging atom is selected at random on a plane 12.5 A above the average position of the uppermost solid layer, just beyond the range of the interaction with any argon atoms adsorbed in equilibrium binding sites. Because we wish to model the scattering of a velocity-selected, collimated beam, the initial momentum of the incident atom is taken to be the same for each trajectory of a given set, and thus each group of trajectories may be labeled by a specific incident energy and a pair of incident angles as well as an equilibrium surface temperature and adsorbate coverage. In all the calculations described in the present paper, the argon atoms were incident in the [IlO] direction at the angle of 30" with respect to the surface normal. (We plan to explore the changes in the amount of energy transferred arising due to an alteration of the angles of incidence in future work.) The actual classical trajectories are generated via the numerical integration of Hamilton's equations of motion for the incident atom, the 24 atoms of the uppermost solid layer, and any adsorbed argon atoms. An individual trajectory is then stopped whenever either the impinging atom returns to the plane where it was found initially or the totaltime exceeds some maximum value, usually 10-15 ps. While the particular choice of the maximum time admittedly seems rather arbitrary, our results indicate that (28) Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. 'Molecular Theory of Gases and Liquids"; Wiley: New York, 1954; p 1110. (29) Valleau, J. P.; Whittington, S. G . In "Modern Theoretical Chemistry"; Berne, B. J., Ed.; Plenum Press: New York, 1977; Vol. V. (30) The angles cited here are defined so as to correspond to the experimental ones described in ref 7. The angle 0 refers to an "in-plane" scattering angle, namely, the angle between the surface normal and the l i e representing the projection of the outgoing trajectory onto the plane of incidence. p, on the other hand, represents an "out-of-plane"scattering angle and is measured in a plane containing both the outgoing asymptotic trajectory and the corresponding projection of that trajectory onto the incident plane.
A 171
Zhao and Adams
560 Langmuir, Vol. 1, No. 5, 1985
..........
i
,
,
:
I
.......
~
I----
$1
.
u
4 p:
E (f inal)/E (inciden t) Figure 1. Energy distributions of argon atoms scattered from a clean W surface at incident energies of 0.15 (the broken line), 0.25 (the solid line), and 1.00 eV (the dotted line).
,. ......
,
,
-55
-33
0.15
0.25 1.00
(Et)lEi 0.87 (0.13)b 0.85 (0.13) 0.86 (0.10)
(0): deg 34 (14) 34 (13) 33 (12)
deg 1.8 (26) 1.4 (25) 1.8 (27)
for the conditions chosen here very few trajectories involving the direct reflection of the impinging atom from the surface will in fact need to be followed for times longer than 5-7 ps, while nearly all of the adatoms that are collisionally ejected from the surface will have reached this same plane within 10 ps. Since the probability of an incident atom sticking to the surface decreases as ita initial translational energy is increased, we have selected incident energies that greatly exceed the average thermal energy of an atom of the solid. The fraction of the trajectories in which the impinging atom has sufficient final momentum to escape from the surface even when the amount of energy transferred is appreciable will thus be large enough for us to obtain statistically significant final energy and scattering angle distributions. 111. Results A. Clean Surface. All calculations described here have been carried out for a surface temperature of 77 K, with the impinging argon atom being incident at an angle of 30” with respect to the surface normal and in the [TlO] direction. Prior to considering the role of an adsorbate in the gas-surface energy transfer, we examined the scattering from a perfectly clean tungsten surface at incident energies of 0.15,0.25, and 1.00 eV (200 trajectories were generated at each energy). In Figure 1 we give the distributions of reflected atom energies in terms of a fraction of the incident energy for these three cases. One sees immediately that the dependence of the fractional energy transfer on the initial energy is essential negligible over the range considered here, with the average final energies given in Table I attesting to the absence of statistically significant differences among the three distributions. This same insensitivity to the initial energy may also be observed in the distributions of scattering angles30 found in Figures 2 and 3 (the lowest order moments of the distributions again being listed in Table I). A direct examination of the individual trajectories reveals the scattering here to be dominated overwhelmingly by “direct” trajectories, i.e., those primarily involving single atom-surface collisions.
....... ....
30
0
I._..
60
9c
0
Figure 2. B dkkributions correspondingto the energy distributions of Figure 1.
.....
(P)”,
Angle definitions corresponding to those of Hurst et al.? bThe value in parentheses corresponds to one standard deviation.
\
,
Table I. Scattering Distributions, Clean Surface E;, eV
I tI _ _ _ _
.........
b
O-9C
,
:
:i
.........
,
I
,Ti n ........
E v, u 4 0.2 /
. _ _ _ I
z
........ ....
,....... (.
g 0,l !? p:
......... ___,
: . : . : . :a
-60
-7C
0
70
50
93
P Figure 3. p distributions corresponding to the energy distributions of Figure 1. The observed peak widths may be shown to vary as one adjusts the zo parameter that determines the surface corrugation; as zo decreases, the surface appears progressively smoother and the angular scattering distributions narrower. While in principle we could improve our results by matching our peak widths to those given by experimenta via the alteration of this parameter, we are currently not aware of experiments involving the exact same surface conditions that are described here (namely, a single crystal at 77 K). But more importantly we fully expect that a further refinement of our assumed potential function will not be necessary in order for us to acquire a qualitative picture of adsorbate coverage effecta, particularly inasmuch as we do have some evidence concerning the accuracy of the gross energy transfer predicted by our model. Janda et have reported an empirical formula obtained by fitting kinetic energy data for directly scattered atoms which were originally incident at 45” on a polycrystalline tungsten surface, with this study being repeated for a number of incident energies and surface temperatures. Specifically, they found the average kinetic energy of the scattered beam to be described well by the expression (111.1) (E,) = 0.83(Ei) + 0.20(E,) where (E,) (=2kBT,)is the average energy that a gas atom would possess if the scattered beam left the surface with the Boltzmann energy distribution characteristic of the surface temperature (i.e., if the beam were fully accommodated). A comparison of the predictions of eq. III.1 with our own calculated values can be found in Table 11. Even though the initial conditions are certainly not identical for
Langmuir, Vol. 1 , No. 5, 1985 561
Coverage Dependence of Gas-Surface Energy Transfer n ,,n>
Table 11. ComDarison of Average Final Kinetic Energies 0.15 0.25 1.00
0.127 0.210 0.833
0.13 0.21 0.86
"Experimental values of ref 6 obtained from eq 111.1. bResults obtained in the present work.
r'cI
Table 111. Scattering Distributions, Three Adatoms Ei, eV
(Ef)lEi
(e), deg
(P),
I....
deg
Incident Atom 0.15 0.25
0.66 (0.26) 0.66 (0.24)
22 (24) 25 (24)
-1.3 (22) -0.4 (21)
0.48 (0.24) 0.49 (0.24)
a Ei refers to the energy of 0.01 eV.
13 (34) 16 (31)
.0-90
Ejected Adatoms 0.15" 0.25"
4
p:
1.6 (29) -0.9 (27)
the incident argon atom, (Ei)adatom =
E( f inal)/E( inciden t) Figure 4. Energy distributionsof argon atoms directly scattered from a W crystal slab on which three adatoms are adsorbed. The incident energies are 0.15 (broken line) and 0.25 eV (solid line). the two studies and thus too much should not be made of the numerical agreement, we do note that in either case a linear relationship between (Ef) and ( E i ) will be observed when the surface temperature (and thus ( E , ) )is held constant. B. Partially Covered Surface. Two different adsorbate concentrations have been considered in the present study, one in which three argon adatoms are found on the surface of our crystal (corresponding to a concentration of 1.79 X 1014cm-? and another in which five adatoms are located within that area (2.97 X 1014cm? Let us begin with the results from the three-adatom case. In Figure 4 we give the distribution of final energies (again, expressed as fractions of the incident energy) for reflected argon atoms having initial energies of 0.15 and 0.25 eV. From the basic forms of these histograms as well as from the moments of the distributions found in Table 111, one can see that while increasing the incident energy has no noticeable effect on the distribution of final energies of these atoms, there has been a very significant increase in the average energy transfer as a result of the introduction of an adsorbate. In fact, only 82% of the 0.25-eV incident atom trajectories can now be said to represent direct scattering (77% at 0.15 eV), while the remaining trajectories involve trapping. We find that when trapping of the impinging atom occurs, one will nearly always observe the eventual ejection of one or more of the previously adsorbed argon atoms. At 0.25 eV the 54 (of a total of 300) trajec-
..___-30
,___._ ,....
0
-60
30
60
90
8 Fmre 5. 6' distributions corresponding to the energy distributions of Figure 4.
T
E( f inal)/E( inciden t) Figure 6. Energy distribution of argon adatoms ejected by the collision of 0.25eV argon atoms. The initial adatom concentration for each trajectory is three per slab area. tories that result in trapping also describe 91 adatoms leaving the surface, while at 0.15 eV the trapping of 46 incident atoms (of 200 total) results in the ejection of 62 adatoms. The overall increase in the energy transfer is also reflected in the change in the distributions of scattering angles for the direct trajectories, these distributions being given in Figure 5. Although still clearly peaked about the specular, the 0 distributions are found to be broadened considerably over those seen when the surface is perfectly clean; the 0 standard deviations listed in Table I11 are approximately twice as large as the corresponding values from Table I. We have also examined the energies and scattering angles of those adatoms the desorption of which was stimulated by the argon-surface collision event. Even though the limited number of trajectories reported here causes these results to be less reliable statistically than are the analogous quantities describing the more numerous directly scattered atoms, some features of these distributions do seem to be emerging. The final ejected adatom energies obtained when the argon is incident at 0.25 eV can be seen in Figure 6 (the results from the 0.15-eV collisions are quite similar and so are not displayed here), where one finds a fairly flat energy distribution throughout the range 0.00-0.25 eV, with an average final energy of 0.12 eV and a standard deviation of 0.06 eV. A similar lack of structure characterizes the distribution of angles at which the adatoms leave the surface (Figure 7). While the scattering is still primarily at positive values of 0, one does not observe
562 Langmuir, Vol. 1, No. 5, 1985
Zhao and Adams Table LV. Scattering Distributions, Five Adatoms (E, = 0.25 eV)
(&)I4 incident atoms ejected adatoms
0.48 (0.28) 0.37 (0.22)
(e), deg 18 (29) 5.6 (29)
(P), deg -2.2 (25) 3.0 (27)
"'I F
i \
I
l
e
-
1
Figure 7. 8 distribution corresponding to the energy distribution of Figure 6.
8 Figure 9. 8 distribution corresponding to the energy distribution of Figure 8.
L
02
04
0 6
08
10
1 2
- 4
E(final)/E( incident) Figure 8. Energy distribution of argon atoms directly scattered from a crystal slab on which five adatoms are adsorbed. The incident energy is 0.25 eV.
the same specular angle peaking that would be expected for the directly scattered incident species. (The average value of 0 is now reduced to 16O, with a standard deviation of 31O.) Thus, the collisionally induced desorption does not strongly reflect the incident atom dynamics in the sense that there does not appear to be an appreciable residual memory of the direction of the impinging argon atom. As indicated above, we have also examined a higher coverage case in which five argon atoms are adsorbed within the area of our crystal slab. The incident argon atoms again impinge at an angle of 30" with respect to the surface normal and in the [IlO] direction, but we now consider only a single initial translation energy of 0.25 eV. (The results with three adatoms were remarkably insensitive to changes in this incident energy, and we would expect a similar independence to be observed here also.) A comparison of the energy distribution as depicted in Figure 8 of the directly scattered argon atoms at this higher surface coverage with the lower coverage result of Figure 4 attests to the enhancement of energy exchange accompanying an increase in the adatom concentration. (The parameters characterizing the fiveadatom distribution can be found in Table IV.) The distribution no longer shows the peaking at higher energies, but instead appears rather flat, presumably as a consequence of a decreased probability of a collision event occurring in which the scattered argon atom does not encounter an adatom. This increase in the likelihood of a strong incident atom-adsorbed atom
4
E( f inal)/E( incident) Figure 10. Energy distribution of argon adatoms ejected by the collision of 0.25eV argon atoms. The initial adatom concentration for each trajectory is five per slab area.
1
n
1
z l
8 Figure 11. 0 distribution corresponding to the energy distribution of Figure 10.
interaction may also be deduced from the 6 scattering angle distribution found in Figure 9, one which is shifted to lower angles than are the three-adatom or clean-surface distributions described above.
Coverage Dependence of Gas-Surface Energy Transfer
Again we have obtained scattering data for the adatoms ejected from the surface as a consequence of the collision, the appropriate energy and angular distributions being given in Figures 10 and 11. (Of a total of 300 trajectories, 205 result in direct scattering, with the remaining 95 describing argon atom trapping; these collisions lead to the subsequent ejection of 191 adatoms.) In contrast to the relatively featureless energy distribution found when three adatoms were present on the crystal slab, we now observe there to be a definite preference for the adatoms to leave the surface with relatively low translational energies. It is likely that this result derives from the increase in the frequency of incident atom-adatom and adatom-adatom collisions so that the initial energy is eventually distributed over a larger number of adatoms, thereby diminishing the amount of energy carried along by any one of the desorbing atoms. As before, little structure is evident in the angular distribution of desorbing adatoms; albeit the histogram appears suggestive of a cosine distribution, too few trajectories have been included to be able to make a definitive judgment.
IV. Discussion From our simulations of an argon beam scattering from a tungsten surface “contaminated” with a submonolayer coverage of argon, we are able to divide the observed collision events into three principal categories. Though the divisions between collision types are admittedly somewhat arbitrary and imprecise, this categorization nonetheless yields a useful physical picture of the system dynamics. (1) If the coverage is sufficiently low, some of the incident atoms will be reflected from the surface without experiencing a strong interaction with the adsorbate, the result being a scattering distribution essentially identical with that for reflection from a perfectly clean surface. The lower the coverage, the larger the fraction of the trajectories that will be of this sort. Angular scattering distributions for these trajectories are characteristically fairly narrow and are peaked in the specular direction inasmuch as the metal surface appears smooth to the incoming atoms. (2) As long as adatoms are present, there is a chance that the impinging atom will come sufficiently close to one or more of them that a fraction of the incident kinetic energy will be converted into (mainly lateral) kinetic energy of the adspecies. The amount of energy transferred, however, is not so much that the incident atom cannot escape the attractive physisorption well at the surface. For these trajectories one observes angular distributions that are broader than those obtained for clean-surface scattering yet that are still peaked at the specular angle, indicating that the impinging atoms upon reflection still retain some memory of the initial conditions. Overall the surface behaves as if it were rougher due to the presence of the adsorbate. Increasing the surface coverage leads to a larger fraction of the total number of trajectories being found in this category. It is conceivable that a few adatoms may pick up enough energy in collisions with the incoming species that they will eventually desorb, but not before the directly scattered atom has returned to the counting surface at z = 12.5 A and the trajectory has been stopped. We recognize that we therefore may be missing that part of the experimentally observed scattering distributions contributed by these atoms. Since part of the energy transferred to the adatoms will be expended in escaping from the argon-surface attractive well, the presence of these desorbing species will be manifested as an increase in the numbers of low-energy
Langmuir, Vol. 1, No. 5, 1985 563
atoms scattering from the surface, with their average energy increasing as the collision energy is increased. Unfortunately, the expense of running trajectories renders the following of these adatoms for longer times prohibitive. (3) Adsorbate coverages approaching half of a monolayer enhance the prospect of the incident atom interacting at close range with an adatom or with a group of adatoms and collisionally stimulating the desorption of the adspecies. In most of the encounters of this type, we find that the incident atom becomes trapped for a minimum of 10-15 ps (which is the maximum length of a trajectory considered here). At the incident energies of the present study there are in fact no trajectories resulting in trapping that do not also involve ejection of adatoms, although at lower energies trapping without concurrent adspecies ejection should become increasingly likely. Multiple collisions clearly play an important role in the dynamics in this regime. It is really not surprising that a significant change in the efficiency of gas-surface energy transfer due to the presence of an adsorbate is observed even at the low coverages examined in this study since the radius of an argon atom appears relatively large when compared with the interatomic spacing of the tungsten atoms. Consequently, even with only a few adatoms present on the crystal slab, we find the probability that collisions will fall into the first category above to be significantly less than one. A more gradual change in energy with coverage might be anticipated as one approaches a monolayer, since the probability of a direct atom-adatom collision occurring will already be quite high in that adsorbate concentration regime. (A more important consideration there could well be an increase in the overall rigidity of the argon overlayer lattice as the monolayer is completed.) If one indeed has a monolayer of adsorbed argon present, then the observed scattering should be characteristic of a rare gas-rare gas solid system for which simple 6-12 potential forms presumably give adequate descriptions of the interactions (the metal surface being effectively screened by the adsorbate). Peaking would thus again be seen in the final energy and scattering angle distributions. We concur with the analysis of Lorenzen and RafflG suggesting that a good way of evaluating the effect of an adsorbate is in terms of an alteration of the effective surface corrugation. In the two limits, one being the perfectly clean surface and the other a surface covered by a monolayer of adatoms, the scattering is sharply peaked in the specular direction and energy transfer is characteristically rather inefficient. However, the interposition of a submonolayer adsorbate coverage yields a considerably rougher surface. The probability of multiple collisions by the impinging atom and thus of significant energy transfer rises as the surface roughness is increased and should, we conclude, reach a maximum at about a half monolayer coverage. Experimental determinations of AC’s for rare gases incident on partially covered polycrystalline tungsten surfaces indeed indicate that energy transfer is greatest when roughly a half of a monolayer of adspecies is p r e ~ e n t . ~ An important caveat should be noted here, namely, that one needs t o be very careful when trying to determine gas-surface interaction potentials on the basis of scattering data. If parameters F i g the degree of surface corrugation are adjusted so as to reflect the experimental width of a scattering angle distribution, then one must keep in mind that any adsorption of the test gas itself will necessarily lead to a broadening of those peaks. Incomplete surface cleaning can thus result in the extracted corrugation parameters being too large, with this problem being particularly troublesome inasmuch as it is the adsorption of the
564
Langmuir 1985, 1,564-567
impinging species that is causing the values to be in error. Experiments employing a surface that is hot relative to the incident gas atoms should minimize any errors here as a consequence of the fact that sticking probabilities typically drop with an increase in the surface temperature.
Acknowledgment. We are pleased to acknowledge support of this work by the Research Corporation, the
donors of the Petroleum Research Fund, administered by the American Chemical Society, and the University of Missouri’s Weldon Spring Endowment Fund. We also would like to thank J. C. Tully for helpful comments on the surface model and C. L. Krueger for discussions concerning experimental results. Registry No. Ar, 7440-37-1; W, 7440-33-7.
Semiequilibrium Dialysis: A New Method for Measuring the Solubilization of Organic Solutes by Aqueous Surfactant Solutions Sherril D. Christian,* George A. Smith, and Edwin E. Tucker Department of Chemistry, The University of Oklahoma, Norman, Oklahoma 73019
John F. Scamehorn School of Chemical Engineering and Materials Science, The University of Oklahoma, Norman, Oklahoma 73019 Received February 25, 1985. I n Final Form: May 7, 1985 An experimental method is described for determining equilibrium constants for the solubilizationof organic solutes by aqueous surfactant solutions. One side of an ordinary equilibrium dialysis cell is loaded with a solution containing a surfactant (largely in micellar form) and a solute that is present both as the free monomer and in solubilized form in the micelles. The other side of the cell initially contains distilled water. After approximately 1day, the permeate (dilute solution) side of the cell is analyzed to determine the concentrations of the surfactant and of the organic solute that have passed through the membrane. Although the surfactant in the permeate is not at equilibrium with that in the retentate (concentrated solution) side of the cell, the organic solute diffusesthrough the membrane rapidly enough to be in equilibrium simultaneously with the solutions on both sides of the membrane. Because the concentration of surfactant in micellar form is extremely small on the permeate side of the membrane, the concentration of organic solute in the permeate is nearly equal to that of the unbound organic solute in the retentate solution. By using information about the concentrations of organic solute and surfactant on both sides of the membrane, one may calculate the equilibrium constant for solubilizationof the solute in the surfactant micelles in the concentrated solution. Results are given for aqueous solutions of the solute phenol and the cationic surfactant n-hexadecylpyridinium chloride. results have shown that solubilization equilibrium conIntroduction stants inferred at saturation may differ by at least a factor Only a few experimental techniques are capable of of 2 from those obtained when the same surfactant soluyielding reliable solubilization data for organic solutes in tions contain the organic solute at low ~oncentrations.~-~ surfactant solutions. In systems containing solutes of Ultrafiltration and molecular sieve techniques7 have been sufficient volatility,vapor pressure methods’ have provided the most accurate and extensive results yet a ~ a i l a b l e , ~ - ~ applied to obtain solubilization data at solute concentrations less than saturation, but these methods have not but there have been few careful, systematic studies of the found extensive use. Because an understanding of solusolubilization of solutes of low volatility, throughout wide bilization phenomena is essential in many areas of colloid ranges of activity or concn. Several groups of workers have science, we sought to devlop a general experimental meused a maximum solubility (phase equilibration) method6 thod for determining solubilization constants for surfactant to determine the extent of solubilization of liquid or solid solutions containing solutes of almost any type. organic solutes at saturation. However, our vapor pressure In practical applications of solubilization, an organic solute (e.g., a contaminant) may be present in surfactant (1) Taha, A. A.; Grigsby, R. D.; Johnson, J. R.; Christian, S. D.; Affssolutions at concentrations well-below saturation. We have prung, H. E. J. Chem. Educ. 1966,43,432. Tucker, E. E.; Christian, S. recently reported the use of micellar-enhanced ultrafilD. J. Chem. Thermodyn. 1979,11, 1137. trations to remove a solute from an aqueous stream. A (2) Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. Soc. 1982, 17, 11; J. Colloid Interface Sci. 1985, 104, 562. surfactant is added to the aqueous stream to give a final (3) Christian, S. D.; Tucker, E. E.; Lane, E. H. J. Colloid Interface Sci. concentration well above the critical micelle concentration 1981, 84, 423. (4) Christian, S. D.; Smith, L. S.; Bushong, D. S.; Tucker, E. E. J . (cmc) and the resulting solution is passed through an ul-
Colloid Interface Sci. 1982,89, 514. (5) Christian, S. D.; Scamehom, J. F., presented at the Symposium on Interfacial and Colloidal Systems, The 1984 International Chemical Congress of Pacific Basin Societies, Honolulu, HI, Dec 16-21, 1984. (6) Elworthy, P. H.; Florence, A. T.; MacFarlane, C. B. ‘Solubilization by Surface Active Agents”; Chapman and Hall: London, 1968; Chapter 2.
(7) Aboutaleb, A. E.; Sakr, A. M.; El-Sabbagh, H. M.; Abdelrahman, S. I. Arch. Pharn. Chemi, Sci. Ed. 1977,5, 105; Pharm. Ind. 1980,42, 940. (8) D u n , R. 0.; Scamehorn, J. F.; Christian, S. D. Sep. Sci. Technol. 1985, 20, 257.
0743-7463/85/2401-0564$01.50/0 0 1985 American Chemical Society
