J . Phys. Chem. 1989, 93, 8080-8089
8080
parallel their gas-phase diatomic values. Since the difference of metal-oxygen bond is larger than metal-carbon bond for M o and Rh, the relative values of the metal-carbon bonds appear to be less important. Conclusions Phenol undergoes 0-H bond cleavage to form a phenoxy intermediate at temperatures below 300 K on Rh( 111). The C-O bond of the phenoxy remains intact at all coverages and temperatures. Thermal decomposition of the phenoxy yields adsorbed CO which desorbs into the gas phase near 500 K. The kinetic
stability of the phenoxy depends on its coverage. Specifically, C-C bond cleavage to form CO is more rapid at low coverage than at saturation. Such self-stabilization of intermediates containing phenyl rings has been observed on Mo( 1 lo), suggesting a general trend for this class of molecules. Acknowledgment. We acknowledge support from the donors of the Petroleum Research Fund, administered by the American Chemical Society. Registry No. C6H50H, 108-95-2; Rh, 7440-16-6; C6H50,2122-46-5; "C6H5OH, 89059-34-7.
co, 630-08-0;
Diffusion of Ethylene and Xenon in Thin Pyrazine Layers Douglas Blue: Kate Helwig,t and Martin Moskovits* Department of Chemistry, University of Toronto, and the Ontario Laser and Lightwave Research Centre, Toronto, Ontario, Canada M5S 1Al (Received: March 6, 1989; In Final Form: May 26, 1989)
The rate of diffusion of C2H4 and Xe through thin pyrazine films condensed on coldly deposited silver films was studied by following the time evolution of the surface-enhanced Raman intensity of the diffusant, as a measure of its accumulation at the silver-pyrazine interface. The form of the intensity versus time curve was reproduced well by solving the diffusion equation with the appropriate boundary conditions and including, in addition, contributions from depolarization effects that become significant at high diffusant surface concentration. The temperature dependence of the diffusion coefficient of C2H4 through the pyrazine film was found to be of the form D = 6 X lo-" exp[-0.7 kcal/RT] cm2/s, indicating that the pyrazine films deposited on cold surfaces (40-60 K) have an amorphous structure. In addition to diffusion data, SERS spectra were measured at various silver film deposition temperatures for the mixed C2H4-pyrazine layer adsorbed on the silver surface after C2H4 diffusion through the pyrazine film occurred. The spectra showed evidence for two different types of SERS-active sites on these rough Ag films, with the relative numbers of each type of site depending on the surface preparation temperature of the Ag film. Since the diffusion coefficient was apparently independent of the Ag surface preparation temperature, these studies also indicate that neither of these SERS-active sites are located at the bottom of long narrow pores as postulated by the pore model of Albano et al.' Comparison between diffusion coefficients determined for C2H4 and Xe shows that the diffusion coefficient follows a M-Il2 mass dependence as predicted by simple kinetic theory treatments of diffusion.
1. Introduction Thin films play an important role in semiconductor technology, and diffusion processes (particularly the interdiffusion of two films in contact with each other) are of special interest in the fabrication of electronic devices.* Diffusion is also an important process in thin polymer films, playing a key role in understanding the kinetics of dyeing3 and the aging process of polymers such as polyethylene and polypropylene! While much work has been done on diffusion through thin films of organic polymers,5 little has been done on nonpolymeric organic thin films. In this paper, surface-enhanced Raman spectroscopy (SERS) is used as a probe of the diffusion of ethylene and xenon through thin (several hundred angstroms thick) pyrazine films that are adsorbed on a SERS-active silver film. The dominant mechanism of diffusion through a thin film depends upon the film's s t r ~ c t u r e , ~which - ~ may be broadly classified as belonging to one of three crystallinity regimes: single crystal, polycrystalline, or amorphous. The regime into which a film falls depends on its mode of growth.IO Single-crystal thin films are virtually impossible to grow unless the substrate itself is a single crystal and the film grown epitaxially," so that most thin films have either polycrystalline or amorphous structures. Two methods that are used in determining thin film diffusion coefficients are depth profiling and surface accumulation techniques.12 Depth profiling involves the measurement of the concentration of a tracer (which may be radioactively labeled) as a 'Present address: Research Department, Esso Petroleum Canada, P.O. Box 3022, Sarnia, ON.
:Present address: Department of Chemistry, Stanford University, Stanford, CA.
0022-3654/89/2093-8080$01.50/0
function of penetration depth into the thin film of interest. The tracer concentration profile in the film may be determined by one of several different sectioning techniques, including mechanical sectioning: electrochemical serial sectioning," and radio frequency argon ion back-sputtering? The last two methods have a sectioning resolution of a few nanometers but are not suitable techniques for use with organic films. Mechanical sectioning has been used for bulk organic crystals, but the sections used in determining concentration profiles must be several micrometers thick for re( I ) Albano, E. v.; Daiser, s.;Miranda, R.; Wandelt, K. Surf. Sci. 1985,
150, 367.
(2) Rosenburg, R.; Sullivan, M. J.; Howard, J. K. Effect of Thin Film Interactions on Silicon Device Technology. In Thin Films-Interdiffusion and Reactions; Poate, J. M., Tu, K. N., Mayer, J. W., Eds.; Wiley-Interscience: New York, 1978; p 13. ( 3 ) McGregor, R. Diffusion and Sorption in Fibres and Films; Academic Press: London, 1974. (4) Guillet, J. E. Mass Diffusion In Polymers. In Photophysical and Photochemical Tools in Polymer Science; Winnik, M. A,, Ed.; NATO AS1 Series; D. Reidel: Dordrecht, The Netherlands, 1986; p 467. ( 5 ) Crank, J.; Park, G. S. Diffusion in Polymers; Academic Press: London, 1968. (6) Peterson, N. L. Int. Mer. Reu. 1983, 28, 65. (7) Gupta, D.; Campbell, D. R.; Ho, P. S. Grain Boundary Diffusion. In Thin Films-Interdiffusion and Reactions; Poate, J. M., Tu, K. N., Mayer, J. W., Eds.; Wiley-Interscience: New York, 1978; p 161. (8) Girifalco, L. A. Atomic Migration in Crystals; Blaisdell Publishing Co.: N e- w York. 1964 .-..., .~ (9) Gupta, D. Thin Solid Films 1975, 25, 231. (IO) Bauer, E.; Poppa, H. Thin Solid Films 1972, 12, 167. ( 1 1 ) Thun, R. E. Phys. Thin Films 1963, I , 187. (12) Mayer, J. W.; Poate, J. M. Depth Profiling Techniques. In Thin Films-Interdiffusion and Reactiom; Poate, J. M., Tu, K . N.,-Mayer, J. W., Eds.; Wiley-Interscience: New York, 1978; p 119. (13) Pawel, R. E.; Lundy, T. S. J . Phys. Chem. Solids 1965, 26, 937.
0 1989 American Chemical Society
Diffusion of C2H4and Xe in Thin Pyrazine Layers producible results to be obtained, making this sectioning method inappropriate for thin organic films. The surface accumulation method determines the diffusion flux passing through a thin film, in contrast to the depth profiling technique, which determines the tracer distribution within the film. Experimentally, a thin layer of the diffusant is deposited on one side of the film, and the sample temperature is raised sufficiently highly to cause a significant fraction of the tracer to diffuse to the other side of the thin film in a reasonable time. The concentration of tracer at the accumulation surface may be detected by monitoring the growth of signal such as the Auger intensity14 of the tracer at this surface. The ability of Auger to detect small surface concentrations allows experiments to be carried out at much lower temperatures than those typically used in depth profiling experiments. However, Auger spectroscopy is not particularly well suited to the study of diffusants in organic films, due to surface charging. In this paper, a variation of the surface accumulation experiment is proposed that uses surface-enhanced Raman spectroscopy (SERS). Experimentally, a thin film of the organic molecule of interest is deposited on a SERS-active silver film. The organic diffusant is then introduced at the vacuum interface of the thin film, and the arrival of the diffusant at the thin filmsilver interface is observed by monitoring changes in the SERS spectrum a t the Ag surface. 11. Experimental Section
Experiments were carried out in an ultrahigh-vacuum (UHV) system15 equipped with Auger, electron energy loss, mass, and surface-enhanced Raman (SERS) spectroscopies. The base pressure in the system during experiments was (1-2) X Torr. Silver films were deposited by evaporating previously outgassed 99.99% Ag (Aldrich, gold label) from a resistively heated tantalum boat onto an electrically isolated, polished copper substrate. The copper substrate was mounted on an x-y-2-0 manipulator and thermally coupled to an Air Products DISPLEX closed-cycle helium refrigerator with a heavy copper braid. By use of the DISPLEX refrigerator and a tungsten wire heater embedded in the copper substrate, the substrate temperature could be varied between 35 K and room temperature during the deposition of the Ag film. The substrate temperature was monitored during Ag deposition to within f0.5 K by use of a temperature sensing diode. To obtain SERS spectra, samples were excited with 50 mW (at the sample) of 514.5-nm radiation from a Spectra Physics Model 171 Ar+ laser. The scattered radiation was collected and collimated with an f/2 lens mounted on a linear feedthrough inside the vacuum chamber and focused onto the slits of a SPEX 1403 double-pass Raman monochromator with an external achromat. The detection system was either an RCA 31034 or a Hamamatsu R955 photomultiplier tube with standard photon-counting electronics, which was interfaced to a Commodore 8032 microcomputer. Silver films were deposited on the copper substrate, which was held at a constant temperature (Ts)during deposition. The sample was then cooled to temperature TD,where a SERS spectrum was taken of the bare Ag surface to ensure that it was free of surface contaminants such as CO or carbonaceous deposits. The pyrazine overlayer was then dosed onto the Ag film by back-filling the chamber through a precision leak valve with thoroughly degassed pyrazine (Aldrich, 99%+ gold label). During the pyrazine dosing and the recording of the SERS spectrum of the pyrazine overlayer after dosing, the substrate temperature was held at TD.Next, the temperature of the sample was adjusted to TE, the temperature at which the diffusion coefficient of the ethylene through the pyrazine overlayer was to be determined. In all experiments, the
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8081
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RAMAN SHIFT (cm-1) Figure 1. S E R S spectrum of (a) 100-A-thick film of C2H4 on a Ag film prepared a t Ts = 40 K and (b) the same sample as in a, but the C2H4 film has now been covered by a 2300-A-thick pyrazine film.
upper limit of TEwas the lower limit of TD or Ts, so as to ensure that no structural changes would occur in either the pyrazine layer or the silver film. The monochromator was set at 1320 cm-I (the position of the u3 SERS peak of C2H4), the UHV system was Torr of CzH4 (Matheson, back-filled to a pressure of 5 X research purity), and the intensity of the v3 SERS signal (from the C2H4reaching the Ag surface) was monitored as a function of time. Finally, a SERS spectrum was taken of the mixed pyrazine/ethylene overlayer remaining on the rough Ag film after the diffusion was complete. The relationship between the pyrazine dose on the Ag surface and the pyrazine film thickness was determined by using interference fringes.I5 The major uncertainty in this procedure arises from the uncertainty in the refractive index of coldly deposited films.I6 A value of n = 1.4953 was assumed, the value for liquid pyrazine. l 7 Three types of experiments were performed, in which one of (1) the thickness of the pyrazine overlayer, (2) the Ag surface preparation temperature, or (3) the temperature a t which the diffusion occurred as varied while all other experimental parameters were kept constant. As well, experiments were performed in which xenon was used as the diffusant. In this case, the disappearance of the pyrazine v1 SERS band at 1015 cm-I was monitored as a function of time as Xe displaced pyrazine at the Ag surface. 111. Results and Discussion
A . Evidence for Ethylene Diffusion through Pyrazine Films. Figure 1 shows the spectrum obtained when pyrazine is dosed on a Ag surface previously covered by a 100-A overlayer of CzH4. It shows that the SERS spectrum of 100 A of ethylene covered by 2300 A of pyrazine (Figure lb) is virtually identical with the spectrum obtained with ethylene alone (Figure la). In both cases the spectrum is the previously assigned SERS spectrum of ethylene,18and no bands belonging to pyrazine are present. This
~
(14) Hwang, J. C. M.; Balluffi, R. W. Auger Electron Spectroscopy Technique For Measuring Grain Boundary Diffusion At Low Temperatures. In Proceedings of the Symposium on Thin Film Phenomene-lnterface and Interactions; Baglin, J. E., Poate, J. M., Eds.; Electrochemical Society: New York, 1978; p 471. (15) Blue, D. W. Ph.D. Dissertation, Department of Chemistry, University of Toronto, 1988.
(16) Gibson, E. P.; Rest, A. J. Chem. Phys. Lett. 1980, 73, 294. (17) CRC Handbook of Chemistry and Physics, 49th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1969. (18) Moskovits, M.; Dilella, D. P. Vibrational Spectroscopy of Molecules Adsorbed on Vapour Deposited Metals; In Surface Enhanced Raman Scattering, Chang, R. K., Furtak, T.E., Eds.; Plenum Press: New York, 1982; p 243.
8082 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989
Blue et al.
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Figure 3. Time evolution of SERS signals during the diffusion process: (a) disappearance of the u, totally symmetric ring breathing mode of pyrazine at 1015 cm-'; (b) appearance of the u3 scissoring mode of C2H4 at 1320 cm-I.
Figure 2. SERS spectrum of (a) 165-&thick pyrazine film on a Ag film prepared at Ts = 40 K and (b) the same sample as in a, but with an amount of C2H4 equivalent to a 100-A film added. Note that in b the SERS spectrum of C2H4 is observed.
is expected, since the Raman enhancement decreases rapidly as the adsorbate-surface separation increase^.'^ The Raman spectrum of C2H4, which occupies the monolayers directly adjacent to the surface, is strongly enhanced, while that of the pyrazine adsorbed on top of the C2H4 layer is enhanced to a much smaller extent. Figure 2b shows the spectrum obtained when ethylene is dosed onto a Ag surface previously covered by a 165-A overlayer of pyrazine. For comparison the SERS spectrum previously assigned to pyrazine adsorbed on a rough, coldly deposited Ag film'* is shown in Figure 2a. The addition of enough C2H4 to this sample to form a 100-A-thick C2H4 film produces a spectrum identical with that shown in Figure la, the SERS spectrum of C2H4. The ethylene added to this sample has obviously diffused through the pyrazine overlayer to the Ag surface and has, moreover, displaced the pyrazine adsorbed on the Ag surface. A detailed monitoring of the diffusion process by following the time evolution of the SERS signal is possible as shown in Figure 3 (with Ts = T D = TE = 40 K). Either the disappearance of pyrazine as indicated by the decrease of the intensity of the totally symmetric u , ring breathing mode at 1015 cm-' (Figure 3a) or the appearance of ethylene as shown by the increase. in the intensity of its u3 scissoring mode at 1320 cm-' (Figure 3b) may be measured as a function of time. In both cases there is a characteristic lag time ( f ~ before ) a change in the intensity of the peak being monitored is noted. For most of the experiments performed, it was the growth of the ethylene uj SERS band that was monitored as a function of time. The lag time might be caused by one or a combination of the following processes: (1) a delay between the opening of the precision leak valve, which admits the CzH4 to the UHV system, and the CzH4reaching the vacuumsample interface; (2) the time required for a measurable quantity of the CzH4 to dissolve into the pyrazine overlayer; (3) the diffusion of the CzH4 through the pyrazine overlayer; (4) a slow rate of interchange between C2H4 and pyrazine at sites on the Ag surface. To determine which of these steps is responsible for the time lag, a series of experiments (1 9) Murray, C. A. Molecule-Silver Separation Dependence. In Surface Enhanced Raman Scattering; Chang, R. K., Furtak, T. E., Eds.; Plenum Press: New York, 1982; p 203. (20) Hall, P. M.; Morabito, J. M. Surf. Sci. 1976, 59, 624.
/
4 .r
c
?
n
i
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I
m u l o 6 o o m 1 O O 0
T I M E (sec) Figure 4. Time evolution of the v3 SERS signal of C2H4 for 5 X lo4 Torr of C2H4 being added to a Ag surface (Ts = 42 K) covered by pyrazine overlayers of (a) 0, (b) 315, and (c) 760 A.
were performed in which the thickness of the pyrazine overlayer on the Ag film was changed. When no pyrazine overlayer was present (see Figure 4a), no lag time was observed between the time C2H4 was admitted to the chamber and the increase in C2H4 SERS intensity. Hence, process 1 can be neglected. Increasing the pyrazine overlayer thickness, on the other hand, did cause the lag time to increase (see Figure 4b,c), eliminating processes 2 and 4 as major contributors to the time lag. The lag time is, therefore, largely due to the diffusion of C2H4 through the pyrazine overlayer. A strong contribution from photoassisted diffusion was also eliminated. The spectrum of a sample in which diffusion was carried out in the dark was similar to that measured for a sample continuously illuminated for an equal length of time. B. Model of the Diffusion Process. An estimate of the diffusion coefficient may be obtained by using the Einstein-Smoluchowski relationship4 L2 = 6DtL (1) where L is the thickness of the pyrazine overlayer, D is the diffusion coefficient, and t, is the time lag. The estimate is very approx-
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8083
Diffusion of C2H4 and Xe in Thin Pyrazine Layers imate, since it is difficult to determine tL appropriately, especially when tL is small. Most importantly, it fails to make proper use of all the data. The approach taken to determine the diffusion coefficient is similar to one suggested for the analysis of Auger surface accumulation data used to determine grain boundary diffusion coefficients in thin metallic films." The pyrazine overlayer is assumed to be of uniform thickness L (in the region 0 < x < L) that covers a flat Ag surface completely. Silver is found at all x I 0, and a constant flux of C2H4 is assumed at x = L. A solution is then obtained to Fick's second law:
ac -- D -a2c _
0
at ax2 where C = C(x,t) is the concentration of the C2H4 at time t and at any point x in the pyrazine film, using the following the initial and boundary conditions: C(x,t = 0) = 0 for 0 < x < L (3a) Le., the initial concentration of C2H4 everywhere in the pyrazine overlayer at t = 0 is zero. J =
'.,I%[
E
i.e., there is a constant flux of C2H4 across the boundary at x = L into the pyrazine overlayer.
[2]x=0 O =
Le., there is no molecular flow of C2H4 past the Ag surface at x = 0. The solution for the concentration of C2H4 at any point in the pyrazine film at time t was determined, by using standard Laplace transform techniques,21 to be C(x,t) =
where ( = n r / L . Since only C2H4 that is in direct contact with the silver surface produces significant SERS, the SERS signal that is being measured experimentally is almost entirely due to the concentration of ethylene adsorbed a t the Ag surface (x = 0). In this case, eq 4 simplifies to 1-2 --
-(-1)"
exp(-Dtt2)
It
(5)
Figure 5a shows a plot of eq 5 as a function of time. C(0,t) is found to be virtually zero for a length of time before it begins to increase. Eventually, C(O,r)increases linearly with time without reaching a limiting value. This is due to the assumption that the diffusant was composed of point particles capable of infinite concentration. The first monolayer next to the Ag surface can only accommodate a finite number of C2H4 molecules, however, before complete ethylene coverage is reached. The SERS signal from C2H4 should, therefore, level off as the first monolayer next to the Ag surface saturates with ethylene molecules. There is an isotherm that relates the concentration of the molecules adsorbed on the surface to those near the surface. Since its form is unknown, a Langmuir form is assumed: e = bC(O,t) (6) 1 + bC(0,t) where 0 is the fractional surface coverage and b a function of the heat of adsorption. A plot of eq 6 as a function of time is given in Figure 5b. It is similar to Figure 5a, except that the function now levels off and (21) Crank, J. Ma?hematics ojDiffusion; Oxford Press: London, 1956.
(.c .)
0 '
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TIME (sec) Figure 5. Plots of equations (a) 5, (b) 6, and (c) 7. Parameters chosen were D = 7.0 X cm2/s and a pyrazine film thickness of 760 A. approaches an asymptotic value as a monolayer coverage of C2H4 on the Ag surface is reached. This equation does not yet reproduce the experimental data (see Figure 4 for example). The measured SERS intensity of the v3 band does not level off monotonically with increasing time; rather it reaches a maximum before a monolayer of ethylene has been added to the sample and then decreases in intensity, so that a partial monolayer of CTH4gives a more intense SERS signal than a full monolayer. This type of behavior has been reported before for CN- on Ag island films22 and C2H4 adsorbed on rough, coldly deposited Ag films.23 In the former case it was successfully explained in terms of a local electric field at the surface that consists of the incident field and the polarization induced by the surrounding adsorbed C2H4. Since the polarization for field components normal to the surface is opposed to the incident field, this phenomenon is usually referred to as a depolarization effect. The SERS intensity depends on both the number of molecules at the surface and the strength of the local electric field exciting them. The initial increase in SERS intensity with dose is due, then, to the increasing number of scatterers, while the following decline is due to the decrease in the local electric field strength at the surface at a point where the surface coverage changes slowly with dose. Murray and BodofP4 determined an expression relating the SERS intensity to the surface coverage 0 as follows: ~ E R S=
e [1 + ,3914
(7)
where ,3 is given by
Here, a, is the polarizability relating the normal component of the dipole moment induced in the adsorbed molecule to the local electric field, a is the lattice parameter of the two-dimensional array of adsorption sites, and t is the dielectric constant of the Ag substrate at the excitation wavelength. The two-dimensional lattice sums of the planar layer of adsorbate and its lattice of image dipoles found a distance d inside the silver substrate are toand &, respectively. Substituting eq 6 into eq 7 yields an expression whose dependence on time is shown in Figure 5c. This expression reproduces the experimental data very well if is treated as an adjustable parameter. The experimental data was fit to eq 7 by using five ~~~
~
~~~
~
(22) Murray, C. A,; Bcdoff, S. Phys. Reu. 1985,832, 671. (23) Pockrand, I. Surf. Sci. 1985, 126, 192. (24) McGregor, R.; Mahajan, I. Y. Trans. Faraday SOC.1962,58,2484.
Blue et al.
8084 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989
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TIME ( S K I Figure 6. Experimental data (noisy line) and the fitted data (smooth curve) using eq 7. Data is for CzH4diffusion through pyrazine films of thickness (a) 760 and (b) 165 A. Experimental conditions are Ts = TD = TE = 42 K.
TABLE I: Fitted DiHusion Coefficient ( D ) for Pyrazine Films of Various Thicknesses' diffusion coeff ( D X 10l5),cm2/s pvrazine film thickness, 8, 3.5 165 4.3 315 5.9 465 7.9 760 8.5 1460
OThe experimental data are fit to eq 7. adjustable parameters with a nonlinear least-squares routine that utilizes a Fletcher-Powell minimization algorithm. One of the parameters being fit to the experimental data was the diffusion coefficient. The other parameters were as follows: (1) a parameter that consists of the product of the flux of C2H4across the pyrazine-vacuum interface (4 and the constant in the Langmuir isotherm equation (b); (2) the depolarization parameter 8; (3) a scaling factor that relates surface coverage to SERS intensity; (4) an additive background value to account for the fact that even when the concentration of ethylene is zero at the Ag surface, there is still significant light scattering by the Ag surface. Typical fits of eq 7 to the experimental data (using a Gould 32-9705 minicomputer) are shown in Figure 6. A change of 10% in the assumed pyrazine film thickness results in a change of about 20% in the fitted value of the diffusion coefficient. Thus, a small uncertainty in the pyrazine film thickness does not produce a large change in the value determined for the diffusion coefficient. C . Film Thickness Dependence of the Diffusion Coefficient. The diffusion coefficient was determined at T E= 42 K for C2H4 diffusing through pyrazine overlayers of 165, 315, 465, 760, and 1460 A from fits to experimental data using eq 7. The fitted diffusion coefficients as a function of pyrazine overlayer thickness are given in Table I and plotted in Figure 7. The diffusion coefficient is found to increase with pyrazine film thickness. The model assumed so far predicts no film thickness dependence for the diffusion coefficient. The observed film thickness dependence suggests a shortcoming in the simple model developed in section IIIB. Two possible flaws in the model are, first, the assumption that the pyrazine film is of uniform thickness ( L ) and, second, that the flux into the pyrazine film is at all times. The consequences of relaxing these two assumptions will now be considered. If the pyrazine overlayer is assumed to be formed by ballistic aggregation, then a rough film will be formed with approximately a normal distribution of thicknesses about an average thickness
1
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PYRAZINE FILM THICKNESS (A) Figure 7. Plot of the effective diffusion coefficient (DF) fit by using eq 7 as a function of film thickness for concentration values calculated from eq 11. The best fit values from the experimental data of D = 8.73 X cm2/s and k = 2.24 X lO-'s-' are used. The experimental data are also plotted. Solid points are calculated data; open points are experimental data.
do, the value determined in the light interference experiment. The root mean square deviation in the film thickness from the average thickness would be given by u = (pdO)'l2
(9)
where p is the average molecular diameter. Model calculations were performed to ascertain if the variability in the film thickness due to ballistic aggregation could be the cause of the observed dependence of the fitted diffusion coefficient on the pyrazine film thickness. These produced the opposite trend in the pyrazine film thickness dependence of D from that observed. Thus, inclusion of film thickness nonuniformity in the model cannot explain the observed dependence of the experimentally determined diffusion coefficient on the mean pyrazine film thickness. However, the nonconstancy of the diffusion constant with pyrazine film thickness may be due to the finite rate at which ethylene molecules cross the vacuum-film interface. A complete treatment of the diffusion through a film of uniform thickness with barriers at both film surfaces has been derived.24 However, the complexity of the solution prompted us to use the alternative approach given in the Appendix. In it we assume that C2H4crosses the pyrazine-vacuum interface with a rate constant k in the forward direction and k-, in the reverse direction. The forward flux of molecules (in units of molecules/(cm2 s)) is found to be
Here N ( t ) is the number of C2H4molecules that have already crossed into the pyrazine film after time t and F is the condensation rate of C2H4 at the pyrazine-vacuum interface. The limiting values for eq 10 are 4 = 0 at t = 0 and 9 = Fk/k_, at very long times. The assumption of a time-dependent flux crossing the pyrazine-vacuum interface should actually be incorporated in the boundary condition (eq 3b) used in obtaining eq 2. Because we are dealing with an effect that makes a minor contribution to the observed dynamics, we adopt the simplified approach in which the constant flux ( J in eq 5 ) is replaced with time-dependent flux @ ( t ) . Replacing J in eq 5 by +(r) leads to the expression
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8085
Diffusion of C2H4 and Xe in Thin Pyrazine Layers TABLE 11: Values of the Effective Diffusion Coefficient (DF) Obtained by Fitting Eq 7 to Data Generated with Eq 11 with cm3/s and k = 2.24 X s-l Parameters D = 8.73 X effective diffusion coeff (DFX lo”), cm2/s, for different film thicknesses (A) 165 A 315 A 465 A 760A 1460A 5.54 6.54 7.52 8.42 calcd 2.92 exptl
3.50
4.53
5.92
7.93
c
a
8.47
TABLE 111: Diffusion Coefficients Determined at Different Temperatures diffusion coeff ( D X cm2/s
temp of exptl run, K 39 45 50 55
60
run result 8.33 8.28 12.0 13.0 36.2 48.0 71.9 117 153 206
av 8.30
12.5 42.0
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94.5 179
With this expression, the observed film thickness dependence of the value of the diffusion coefficient of C2H4 in pyrazine derived from our data can be accounted for. This is demonstrated as follows. The expected time evolution of the SERS intensity corresponding to pyrazine films of varying thicknesses was calculated by using eq 7 (into which eq l l was incorporated rather than eq 5) and using the values D = 8.73 X cm2/s and kl = 2.24 X s-l. The pyrazine film thicknesses chosen corresponded to those for which the experiments were carried out. The calculated curves were then fit to eq 7 assuming a constant C2H4 flux, J, across the pyrazine-vacuum interface, thereby yielding an effective diffusion coefficient DP The values of DFso calculated are tabulated in Table I1 and plotted as a function of pyrazine film thickness in Figure 7. The values are in remarkably good agreement with those obtained from the experimental data. This leads us to believe that the time dependence associated with crossing the pyrazine-vacuum interface (or an equivalent process in which pyrazine is displaced by ethylene at the pyrazinesilver interface) is indeed responsible for the apparent pyrazine film thickness dependence of the diffusion coefficient. The values of D and k-l used above were obtained by taking the experimental data from all five experiments at different film thicknesses and simultaneously fitting them as one data set to a two-parameter ( D and LI)fit of eq 7. Values of other parameters used were those that gave the best fit to individual data sets. D. Temperature Dependence of the Diffusion Process. The temperature dependence of the diffusion coefficient for the diffusion of C2H4 through thin pyrazine films was determined with Ts = 100 K, TD = 60 K, and TEranging from 39 to 60 K. The Ag surfaces were prepared at 100 K to ensure that there would be no morphology changes in the surface upon varying the temperature. Likewise, the pyrazine overlayer was dosed at TD = 60 K, the maximum temperature used in the determination of the diffusion coefficient, in order to avoid problems of pyrazine desorption and annealing if the sample temperature is raised from TD to TE. The results of the experiments at various values of TE are given in Figure 8. As TE is increased, the lag time decreases, and the diffusion coefficient consequently increases. Two runs were done at each of the following temperatures: 39,45, 50, 55, and 60 K. The results for the fitted diffusion coefficients are given in Table 111. The agreement between two runs done at the same TEis best for experiments done at TE= 39 K and becomes progressively worse at higher TEvalues, likely due to the shorter lag times at higher temperatures. While the absolute uncertainty in the lag time remains the same (regardless of temperature), the relative uncertainty increases as the temperature and diffusion coefficient
Figure 8. Time evolution of the v, SERS signal of C2H4for diffusion through a 760-Apyrazine film for experiments performed at various Tis. The experimental conditions for all runs were Ts = 100 K and TD = 60 K. The TEvalues plotted are (a) 39, (b) 50,and (c) 60 K.
I
-29
-11 -_.
1
I
015
I
I
*
,023
019
,027
(*K-l)
Figure 9. Arrhenius plot of the average values of the fitted diffusion coefficients versus 1 / T for data given in Table 111. The fitted kinetic parameters are ED = 0.7 kcal/mol and a preexponential factor of Do = 6 X lo-” cm2/s, with a correlation constant of r = 0.971. increase and the lag time decreases. This manifests itself in poorer reproducibility for higher temperature diffusion experiments. The diffusion coefficients were found to fit the Arrhenius expression (see Figure 9) D = DOeXp(-ED/RT) (12) with values of ED = 0.7 kcal/mol and Do= 6 X lo-” cm2/s and a correlation coefficient of 0.971 (for the linearized form). In all experiments performed in this section a pyrazine film thickness of 760 8,was used and the model derived in section IIIB was used to fit the experimental data to determine the diffusion coefficient. This method of finding the diffusion coefficient does not take into account the effect of a time-dependent flux at short times discussed in section IIIC. This process would be especially important at higher TE values. An analysis using a plausible range of temperature dependencies for Ll suggests that the neglect of its temperature dependence results in, at most, a factor of 2 uncertainty in the value of the calculated diffusion coefficient. The values of ED and Do obtained are unusually small for bulk diffusion. The structure of the pyrazine films may be polycrys-
8086 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989
talline, nanocrystalline, or amorphous. In polycrystalline metallic thin films, the activation energies for grain boundary diffusion are typically 40-70% of those found for lattice diffusion in the same metal,25 so that grain boundary diffusion is the dominant mechanism in polycrystalline solids and lattice diffusion makes little or no contribution. Typical Dovalues for grain boundary diffusion are of the order lo-’ to In one of the few investigations of diffusion in an organic crystal, a value of Do= 1X cm2/s for grain boundary diffusion of phenanthrene in anthracene was obtained.26 The extremely low preexponential factor of Do= 6 X IO-” cm2/s obtained in this study makes a polycrystalline structure for the pyrazine films unlikely. Another possibility is that the pyrazine film has a nanocrystalline structure, implying that it is a solid with “gaslike” disorder.27 These materials are composed of randomly oriented nanocrystals with sizes below 100 A. The large density of interfaces between the nanocrystals (typically on the order of 1019grain boundaries per cubic centimeter of material) results in the volume fraction of the interfacial component becoming comparable to that of the nanocrystals.28 The self-diffusion of radioactive 67Cuin nanocrystalline Cu was found to be approximately 3 orders of magnitude larger than that of the corresponding polycrystalline substance,29 while the activation energy was approximately half that for self-diffusion in polycrystalline Cu and about one-quarter that for self-diffusion in a Cu single crystal. Likewise, Dowas found to be 3 X IO-$ cm2/s for 67Cuself-diffusion in nanocrystalline C U . While ~ this is lower than a typical value for grain boundary diffusion (Dois on the order of 1 X 1O4 cm2/s for grain boundary self-diffusion of Cu), it is still several orders of magnitude larger than the Doobtained for the diffusion of C2H4 through pyrazine films. The nanocrystalline structure may likely also be rejected for our pyrazine films. The pyrazine films are therefore probably amorphous. Much work has been done on the diffusion of atoms in amorphous metal and metal alloy films in the past dozen years.30 In many of the systems studied, kinetic parameters were impossible to determine due to the curvature in the Arrhenius plots arising from the fact that several diffusion mechanisms occur in the temperature range being studied. In the systems for which an evaluation of these parameters was possible values of Doranging from lo-’’ to 1 cm2/s were measured. For example, Au diffusion in the metallic glasses Ni59.5Nb40,5 and Pd77.5cU6Si16.5 has Dovalues of 3 X and 2 X 1O-Io cm2/s, re~pectively.~’In addition, the activation energy for diffusion in amorphous materials is also lower than that found for the analogous crystalline material. For example, annealing Pd77.5CU6Si16.5glass to a temperature that allowed its relaxation toward a more crystalline structure increased the activation energy for Au diffusion by a factor of 2. The low value of Dofound in this study suggests an amorphous structure for our deposited pyrazine films. This is not unexpected. Water films deposited at TD = 77 K, for example, are known to be amorphous.32 Likewise, the mechanism of diffusion in amorphous solids remains s p e ~ u l a t i v e . ~In ~ the free volume the amorphous solid is thought to contain cavities that (25) Balluffi, R. W. Phys. Status Solidi 1970, 42, 1 1 . (26) Reucroft, P. J.; Kevorkian, H. K.; La&, M. M. J . Chem. Phys. 1966, 44, 4416. (27) Birringer, R.; Gleiter, H.; Klein, H.; Marquardt, P. Phys. Lett. 1984, 102A, 365. (28) Zhu, X.; Birringer, R.; Herr, U.; Gleiter, H. Phys. Reu. 1987, 8 3 5 , 9085. (29) Horvath, J.; Birringer, R.; Gleiter, H. Solid State Commun. 1987, 62, 3 19. (30) Limonge, Y.;Brebec, G.; Adda, Y. Diffusion In Metallic Glasses. In DIMETA-82 Diffusion In Metals And Alloys; Kedves, F. J., Beke, D. L., Eds.; Trans Tech Publications: Aedermannsdorf, Switzerland, 1983; p 283. (31) Chen, H. S.;Kimerling, L. C.; Poate, J. M.; Brown, W. L. Appl. Phys. Lett. 1978, 32, 461. (32) Schmitt, B.; Ocampo, J.; Klinger, J. J . Phys., Colloq. CI 1987, 48, 519. (33) Cantor, B.; Cahn, R. W. Atomic Diffusion In Amorphous Alloys. In Amorphous Metallic Alloys; Luborsky, F. E., Ed.; Butterworths: London, 1983; p 487.
Blue et al.
i
- 1
n L
zj
l
I I
0
400
I
I
800
1200
I 1600
TIME (sec)
Figure 10. Time evolution of the v3 SERS signal of C2H, for 5 X 10” Torr of CzH4being dosed when only the surface preparation temperature ( Ts) is changed. Other experimental conditions are T, = TE= 4 2 K for values of (a) Ts = 4 2 K, (b) Ts = 100 K, and (c) Ts = 200 K. TABLE I V Diffusion Coefficient of Ethylene Determined for a 760-APyrazioe Film Deposited on an Ag Substrate Prepared at Various Temperatures and with T, = Tn = 42 K surface prepn temp, K diffusion coeff ( D X lo’$), cm2/s 42
6.8 7.9 5.6 7.6 7.5 4.6 7.2
70 100
150 200
are larger than those in the analogous crystalline material. Diffusant that is incorporated in these cavities moves about rather freely; hence the activation barrier associated with its motion is very low. Diffusion occurs due to infrequent, correlated events in which the diffusant is at an extremity of the void at the same time as one or more of the molecules of the cage collapse behind it. Hence the “attempt frequency” is also small?5 In the process studied in this paper the attempt frequency of diffusion is very low, but this is compensated for by a very low activation barrier that the diffusant must surmount. It is even not clear that the use of the Arrhenius expression to obtain kinetic parameters is justified for an amorphous film. In a crystalline lattice, the preexponential factor of the diffusion coefficient is often written as33
Do = av& exp{AS/R}
(13)
where a is a geometric factor, Y is an “attempt frequency“, d is the diffusion jump distance, and A S is the activation entropy of a single diffusion jump. In an amorphous substance, on the other hand, the values of a,v, d, and A S and also of ED are all likely to vary from one diffusion step to another. Hence, the temperature dependence of the diffusion coefficient need not follow the Arrhenius expression. Nevertheless, in some cases, the Arrhenius equation does describe the temperature dependence of the diffusion coefficient in amorphous solids, implying that a single mechanism is a t play over a significant range of temperatures. According to eq 13, the low value of Do obtained in this study could arise in two ways. Either A S has a large negative value (34) Cohen, M. H.; Grest, G. S. Phys. Rev. 1979, E20, 1077. (35) Gupta, D.; Tu, K. N.; Asai. K. W. Phys. Reu. Lett. 1975, 35, 796. (36) Wagman, D. D.; Evans, W. H.; Halow, I.; Dudley, R. M. American Institute Of Physics Handbook; John Wiley: New York, 1963; pp 4-170.
Diffusion of C2H4 and Xe in Thin Pyrazine Layers (due to an extremely ordered transition state) or the diffusion jump attempt frequency u is very low. Assuming that u has a typical value of 1Ol3 s-I,* and that d is of the order of 5 A, then AS = -34.9 cal/(K mol) (assuming unity for a). This is an unreasonable value. The entropy of fusion for C2H4at T = 104 K is only ASF = -19.1 cal/(K mo1).j2 Hence, it is unlikely that our low value of Dois due to the entropy term alone. Taking the other extreme, and assuming that AS = 0, then eq 13 yields a value of u = 2.4 X lo4 s-’ for the attempt frequency. Although much smaller than the typical value of v = 1013s-I, it is a plausible number in the free volume model, which predicts a lowering of the attempt frequency by several orders of magnitude. E . Surface Preparation Temperatures and the Pore Model of SERS. In the final set of diffusion experiments, only the surface preparation temperature ( Ts) during the Ag deposition was varied. The other experimental conditions were T D = TE = 42 K, with a pyrazine overlayer thickness of 760 8, for all samples. Typical results are shown in Figure 10. The lag time observed is independent of the surface preparation temperature, and not unexpectedly, the diffusion coefficients extracted from the data are independent of Ts. These are summarized in Table IV. It should be noted that the diffusion experiment on the 200 K Ag film was carried out by monitoring the intensity of the scattered radiation at a Raman shift of 1345 cm-I. This is due to the fact that the u3 scissoring band of C2H4 has almost entirely shifted to this higher frequency on the Ag film prepared at the highest temperature (see Figures 1 1 and 12). These results may have an impact upon the pore model of SERS suggested by Albano and co-workers.IJ7 Silver films prepared by vapor deposition onto a cold substrate are known to be rough. The pore model envisions the roughness to be in the form of long narrow pores, 5-1 5 8,in width and approximately 150 8,in depth, which are separated by rather flat plateaus. The pore model postulates that the SERS-active sites are regions with small radii of curvature situated at the bottom of these pores and molecules adsorbed on the plateaus between the pores do not contribute to SERS.37 This model ascribes the irreversible loss of SERS intensity observed upon annealing the films to the progressive “healing” of these fine pores. Complete healing occurs with annealing at 250 K or above. However, strong SERS signals are still observed from molecules on films that had been annealed to temperatures up to Tan= 170 K. In fact, the SERS signal increases with this degree of annealing. Within the framework of the pore model, the increase in SERS signal with mild annealing was ascribed to an increase in adsorbate concentration in the pores, due to the increased mobility of adsorbed molecules with increased temperature. If it is assumed that the annihilation of the pores above Tan= 170 K is a gradual rather than an instantaneous process, then the healing mechanism for the pore may be envisioned as a stepwise narrowing of the pore until it has eventually closed at approximately Tan= 250 K. If this is the case, the effective diffusion coefficient observed for C2H4 diffusing through a pyrazine film prepared at Ts = 200 K is expected to be lower than that for Ag films prepared at lower temperatures, since the C2H4 will have greater difficulty in reaching the SERS-active sites at the bottom of the pore as the pore narrows. The inward diffusion of ethylene would also be impeded by the reduced rate of outward diffusion of pyrazine as the pores narrow. It is clear from the observation of a strong pyrazine SERS signal that there must originally have been pyrazine at the bottom of the pores. Since the diffusion coefficient of ethylene is found to be independent of the film preparation temperature, the fine pore model of Albano and co-workers is probably not a correct description of the structure of coldly deposited silver films. This is not to say that most SERS-active sites are not found in valleys among silver surface roughness features; it simply indicates that the valleys need not (37) Albano, E.V.; Daiser, S.; Ertl, G.;Miranda, R.; Wandelt, K.; Garcia, N. Phys. Rev. Lett. 1983, 51, 2314.
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8087
m Ln
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C
3
n L
a
lrx)
1350
1 4 a
RAMAN SHIFT (cm-1) Figure 11. High-resolution SERS in the 1300-1400-~m-~region after 5X Torr of C2H4has been added to 760-1( pyrazine for 1600 s on Ag films prepared at (b) Ts = 42 K, (c) Ts = 100 K, and (d) Ts = 200 K. The case where no CzH4has been added is shown in (a) for a Ts = 42 K film. be smaller in average size than the metal surface features themselves. In the Albano model, however, the active pores are assumed to be much smaller than the size of the average silver surface feature. While the diffusion coefficient obtained is independent of the surface preparation temperature, the mixed pyrazine-ethylene SERS spectrum that was observed after the diffusion experiment was complete shows a gradual change as a function of Ts. Figure 11 shows a series of high-resolution scans of the ethylene u3 band region of the mixed CzH4-pyrazine SERS spectrum that is obtained after the completion of the diffusion experiment and after a dose of CzH4 equivalent to a 160-21 film had been deposited onto the sample. Figure 1l a shows that the region of the spectrum between 1300 and 1400 cm-’ contains no peaks when only pyrazine is dosed onto a Ag film. Clearly the peaks shown in Figure 1lb-d must belong to ethylene. Moreover, the spectra indicate that there are two types of v3 bands of CzH4: a high- and low-frequency band. As the surface preparation temperature of the Ag film is increased, the high-frequency component of the u3 band at 1345 cm-’ becomes more intense at the expense of the low-frequency component at 1320 cm-I. However, neither the high- or lowfrequency component of this band completely disappears, regardless of T,. A series of SERS spectra showing the full vibrational spectral range from 200 to 3200 cm-’ and taken under the same conditions as those in Figure 11 are shown in Figure 12. Aside from the changes to the v3 mode of the C2H4, there are several other differences in the mixed C2H4-pyrazine spectra that occur as a function of surface preparation temperature. The most dramatic change is found in the C-H stretching region. As the surface preparation temperature increases, the intensity of the u1 C-H stretching mode at 2996 cm-’ increases from being virtually absent in films prepared at Ts = 42 K to being the strongest peak in the SERS spectrum for films deposited at Ts = 200 K. At the same time, the broad peak consisting of the overlap of the two outof-plane bending modes, u7 and us (950-980 cm-’), decreases in intensity with increasing Ts. The changes in the intensity of the C2H4peaks of the spectrum might signal a change of the surface geometry of the CzH438 The spectrum obtained on silver films deposited at the lowest Ts value is consistent with CzH, “lying down” ( r bonding) to the silver (38) Moskovits, M. J . Chem. Phys. 1982, 77, 4408.
Blue et al.
8088 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 400 t
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RAMAN SHIFT (cm-1) Figure 12. Mixed C,H,-pyrazine spectra observed after 5 X Torr of C,H, has been added to 760-A pyrazine for 1600 s on Ag films prepared at (a) Ts = 42 K, (b) Ts = 100 K, (c) Ts = 150 K, and (d) Ts = 200 K. The various C2H4bands described in the text are denoted with arrows.
surface. The spectrum observed with the highest Ts surface is most consistent with an ethylene molecule that binds edge-on or end-on to the surface. It is also consistent with randomly oriented CzH4molecules on the silver surface. This indicates that there are at least two types of bonding sites on a cold-deposited surface: chemisorption sites and physisorption sites. While chemisorption sites abound on surfaces prepared at the coldest temperatures, their number decreases with increasing surface preparation temperature. This type of behavior has previously been reported in a surface IRAS of CO adsorbed on coldly deposited silver films.39 Other spectral details are consistent with this interpretation. The shift of u3 toward the gas-phase value and the disappearance of the normally weak u, and us bands with increasing surface preparation temperature are what is expected as the molecule changes its bonding from chemisorption to physisorption. It must be emphasized that according to this interpretation, a mixture of chemisorbed and physisorbed ethylene is found on all silver surfaces produced, with the relative contribution to the SERS signal from each type of site varying with Ts. The time evolution of the intensities of both the high- (200 K Ag film) and low- (40 K Ag film) frequency components of the v3 mode of C2H, as it diffuses through a pyrazine film was found to be identical, implying that the diffusion coefficient is independent of the type of surface site that the ethylene ultimately occupies (Figure 10). This implies that both the chemisorption and physisorption SERS-active sites are in the same region of the surface. Hence neither the chemisorbed molecules nor the physisorbed molecules need necessarily be at the bottom of long narrow pores. Finally, it may also be noted that as the surface preparation temperature increases, the relative SERS intensity of the pyrazine not displaced by ethylene also increases. This result indicates that CzH, is better able to displace chemisorbed pyrazine than physisorbed pyrazine. F. Diffusion of Xenon fhrough Pyrazine Films. Diffusion experiments were also performed with xenon, which is similar in size to ethylene but has 5 times the mass. The changes brought about in the SERS spectra of a 165-Athick pyrazine film deposited on a Ag surface, as a result of dosing Torr (uncorrected) and with Ts = TD= TE= 40 Xe at 5 X K, are shown in Figure 13. The intensity of the pyrazine SERS decreases with time, presumably as a result of the displacement of the pyrazine at the Ag surface by Xe. No new bands appear (39) Dumas, P.; Tobin, R. G . ;Richards, P. L. Surf. Sci. 1986, 171, 5 5 5 .
I
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m 3000
RAMAN SHIFT (cm-1) Figure 13. Change in the S E R S spectrum of a 165-A-thick pyrazine overlayer as 5 X lo* Torr of xenon is added to the sample. Experimental conditions are Ts = TD = TE.= 40 K. The spectra are taken after Xe has been added for the following time periods: (a) t = 0 s, (b) f = 1000 s, and (c) t = 3000 s.
I
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i
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1000
2000
3000
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T I M E (sec) Figure 14. Plot contrasting the results for CzH4 and Xe diffusion through a 760-A-thick pyrazine film: (a) time evolution of the u, S E R S signal of pyrazine for a dose of 5 X lo4 Torr of Xe; (b) time evolution of the u3 signal of CzH4 for a dose of 5 X lo4 Torr of CzH4. Experimental conditions are Ts = TD = TE = 42 K.
in the SERS spectrum since the xenon-silver vibration (if it can be observed at all) would be too low in frequency to be easily detected. In order to obtain the diffusion coefficient from the decrease in pyrazine SERS intensity, eq 14 (which is the complement of eq 6) is used:
where Io is the initial intensity of the u I SERS band of pyrazine at time f = 0, 0 is the fractional surface coverage of Xe on the Ag surface, C(0,t) is the concentration of Xe on the Ag surface as a function of time (given by eq 5 ) , and b is the constant of the Langmuir isotherm, which describes the Xe coverage of the surface as a function of dose. A plot of the decrease in intensity for the ul SERS band of Torr of Xe pyrazine when an uncorrected pressure of 5 X is admitted into the UHV chamber is shown in Figure 14a. For
Diffusion of C2H4 and Xe in Thin Pyrazine Layers TABLE V Comparison of the Diffusion Coefficient of Ethylene and Xe through a 766-A Pyrazine Film diffusion coeff ( D X loi5).cm2/s tvDe of diffusion exDmt C2H4 C2H4
xenon
6.83 7.93 3.59
comparison, the increase in SERS intensity for the vj band of CzH4 is presented in Figure 14b for an experiment performed under exactly the same conditions (Ts = TD= TE= 42 K) and for the same film thickness (760 A). The lag time is longer for xenon diffusion than for ethylene diffusion. Both sets of experimental data were fitted by using the respective models described in this section and section IIIB. The fitted diffusion coefficients obtained for the two types of diffusants were D = 6.83 X cm2/s and D = 7.93 X cm2/s for duplicate runs with ethylene and D = 3.59 X cm2/s for Xe (see Table V). Thus, ethylene diffusion through the pyrazine film is roughly twice as fast as Xe diffusion under identical conditions. All theories of diffusion predict a dependence of the diffusion coefficient on the mass of the diffusing species.40 For an ideal gas, kinetic theory suggests that D 0: M-'/z.41 The diffusion coefficient also scales as M-'/2 in more elaborate treatments of gaseous diffusion,42 as well as in several theoretical treatments of diffusion processes in solids.40 Xenon has roughly 5-fold the mass of ethylene; a Mi/zdependence of the diffusion coefficient would imply that the diffusion coefficient of C2H4 in a pyrazine film should be 2.16 times larger than that of xenon. The average diffusion coefficient of C2H4 is found to be 2.06 times greater than that of Xe, well within the tolerance of experimental error. Although very preliminary, this result implies a diffusional mechanism that does not involve complex formation and, as a result, follows a M-Il2 dependence.
IV. Summary and Conclusions Using SERS as a molecule specific surface accumulation technique, we found the diffusion coefficient of C2H4 through pyrazine films to be of the form D = 6 X IO-" exp[-O.7 kcal/RT] cm2/s. The extremely low values of these parameters indicate that the pyrazine films deposited at low temperatures are probably amorphous. The fitted diffusion coefficient for this process is independent of the surface preparation temperature ( Ts) of the Ag film. This result is inconsistent with the pore model of SERS postulated by Albano and co-workers, which suggests that the SERS-active sites in coldly deposited Ag films are at the bottom of long, narrow pores. Evidence was also presented that confirmed reports by other groups indicating that there are two different types of SERS-active sites on rough, coldly deposited Ag films, one probably associated with chemisorbed C2H4 and the other with physisorbed molecules. The relative abundance of the two types of sites varies with the surface preparation temperature of the Ag film. Xe was found to have a 2-fold smaller diffusion coefficient than C2H4, possibly suggesting that the diffusion coefficient scales as M-II2. A possible further application of this technique could be in the determination of diffusion coefficients for the diffusion of small molecules through polymer or Langmuir-Blodgett films deposited on SERS-active Ag island films. Acknowledgment. We thank NSERC and Exxon for financial support. One of us (D.B.) thanks the University of Toronto for a scholarship. K.H. thanks NSERC for a summer scholarship. (40) Satterfield, C. N . In Mass Transfer In Heterogeneous Catalysis; M.I.T. Press: Cambridge, MA, 1970; Chapter 1 . (41) Atkins, P. W. In Physical Chemistry, 2nd ed.; W. H. Freeman and Company: New York, 1982; Chapter 25. (42) Hirschfelder, J. 0.; Bird, R. B.; Spotz, E. L. Chem. Reu. 1949, 64, 205.
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 8089 We acknowledge the valuable discussions with Professor R. W. Balluffi, Professor Koichi Itoh, Dr. Jung-Sang Suh, and Tom Haslett. We are grateful to Dr. Mike Peterson for a copy of the VAO5A minimization program. Appendix. Model of Dissolution into a Film In this appendix, the consequencesof partitioning of the ethylene molecules across the pyrazine-vacuum interface are considered. This mechanism is referred to as process 2 in section IIIA. Assume F to be the rate of condensation of C2H4 at the pyrazine-vacuum interface per unit area (cm2) per second. If (as in our case) the condensation rate (F)is small enough that multilayers of C2H4do not form on the surface of the pyrazine film, the surface concentration of CzH4 (molecules/cm2) after a time t is
If the ethylene molecules can cross the pyrazine-vacuum interface, then the rate of crossing into the film is
where k and k-, are the forward and backward rate constants for the crossing process, N(t) is the number of C2H4molecules that have already dissolved into the pyrazine film, and [Ns - N(t)] is the number of C2H4 molecules remaining on the surface of the pyrazine film. Substituting for Ns from eq A-1 into eq A-2 yields
This is a linear, first-order differential equation with the following solution: F N(t) = -[k-,t - 11 + c e~p[-k-~t] (A-4) k-1 The constant of integration (c) is now evaluated by using the boundary condition that no molecules have dissolved into the pyrazine film at time t = 0, i.e. N(0) = 0
64-51
c = F/k-l
(A-6)
This yields which, substituted into eq A-5, gives kFt F N(t) = - - -(1 - exp[-k-,t]) k-l k-1
('4-7)
The short and long time limits of eq A-7 are N(t) = 0 when t = 0 and N(t)=Fkt/k-, when t is very large. The rate of C2H4 crossing the surface into the pyrazine film per unit area is therefore given by dN(t) kF - - -(I dt
k-,
- exp[-k-,t]) = $(t)
(A-8)
The limiting values of the rate of crossing the film surface are 4(t) = 0 at t = 0 and 4(t)=Fk/k-' at very large values of time (or if k-I is very large, 4(t) may equal Fklk-, at short times). A series of calculations were performed to determine if the time dependence of the rate of crossing the pyrazine-vacuum interface alone could be responsible for the observed experimental lag times. It was concluded that it could not. However, it could be contributing in a minor way to the evolution of the SERS intensity, and indeed, the observed dependence of the diffusion coefficient on pyrazine film thickness may result from this process. Registry No. C2H4.74-85-1; Xe, 7440-63-3; Ag, 7440-22-4; pyrazine, 290-37-9.
