J . Phys. Chem. 1988, 92, 2957-2960
2957
New Technique for the Determination of Metal Particle Size in Supported Metal Catalysts Carolyn K. Preston and Martin Moskovits* Department of Chemistry, University of Toronto, Toronto, Ontario, Canada MSS 1Al (Received: November 30, 1987)
A technique for determining the particle size of noble metals deposited on an alumina/aluminum-supportedcatalyst is presented. The particle size of goldalumina catalysts (on an aluminum substrate) is determined from the plasmon in the visible reflectance spectrum for the catalyst by computer fitting the measured spectrum with spectra calculated from Maxwell Garnett (Philos. Trans. R . SOC.London, A 1904,203,385; Philos. Trans. R. SOC.London, A 1906, 205, 247) colloidal particle theory and reflectance theory. This new technique for calculating reflectance spectra involves correcting the complex refractive index of gold to account for conduction electron wall collisions within the gold particles. The consequences of this new technique to produce reproducible particle sizes for supported metal catalysts are considered.
Introduction The study of the effect of metal particle size on the catalytic activity of supported metal catalysts is a relatively unexplored topic in the characterization of these catalysts. This is due to the paucity of reliable techniques that provide reproducible particle size distributions for supported metal catalysts. Often the particle size determined for a catalyst by one technique can be very different from the particle size of the same catalyst sample determined by another technique. A case in point is the study of Parravano et a1.2 of the gold particle size in alumina, silica, and magnesia supported catalysts by wide-angle X-ray scattering and by transmission electron microscopy techniques. The sizes determined by both techniques for a particular catalyst sample could differ by up to 300%. The particle size in alumina/aluminum gold-supported catalysts can be determined from the surface plasmon observed in the visible reflectance spectrum for these gold-alumina catalysts. This technique for metal particle size determination is outlined in this paper. The gold catalysts prepared by Moskovits and Goad3 consist of small gold metal particles in the pores of an anodic aluminum oxide film that is on the surface of aluminum foil. The aluminum oxide film consists of an approximately hexagonally close-packed s t r u ~ t u r ewith ~ * ~a base of thin, nonporous oxide whose thickness is proportional to the applied anodization voltage. A more porous oxide is obtained if a moderately aggressive electrolyte, such as phosphoric acid, is used in the anodization process rather than a highly aggressive electrolyte such as sulfuric acid. A particular applied voltage leads to a constant pore diameter in the oxide layer since the oxide film formation occurs at a constant rate that is determined by the average field in the oxide layer. The gold metal used in the preparation of the catalysts is applied to the alumina/aluminum substrate electrochemically in a buffered aqueous gold(II1) chloride solution (pH 1.3). The resulting catalyst consists of an aluminum oxide film, whose lower portion contains gold metal particles concentrated at the oxide pore bases (Le., near the metal/oxide interface), which coats the aluminum metal (see Figure 1). The gold metal is just a few weight percent of the anodic oxide film with a considerable amount of oxide pore volume left unoccupied. Reflectance calculations for “colored” anodized aluminum are based upon colloidal metal particle theory which was developed by J. C. Maxwell Garnett’ at the beginning of this century. The (1) (a) Maxwell Garnett, J. C. Philos. Trans. R. SOC.London, A 1904, 203,385. (b) Maxwell Garnett, J. C. Philos. Tram. R. Soc. London, A 1906, 205, 247. (2) (a) Parravano, G.; Galvagno, S.J . Catal. 1978,55, 178. (b) Parravano, G., et al. J . Phys. Chem. 1979, 83, 2527. (3) Goad, D. G. W.; Moskovits, M. J . Appl. Phys. 1978, 49, 2929. (4) Keller, F.; Hunter, M. S.; Robinson, D. L. J . Electrochem. SOC.1953, 100, 41 1. ( 5 ) OSullivan, J. P.; Wood, G. C. Proc. R. Soc. London, A 1970,317,511.
theory of reflectance calculations, neglecting metal particle size, has been discussed in some detail in a previous papers3 While this approach for reflectance calculations provided good fits of experimental data for nickel and molybdenum catalysts, the fits were poor for copper, silver, and gold experimental reflectance spectra. One approach to modifying the calculation of reflectance spectra for copper, silver, and gold, to obtain better matches between calculated and experimental data, is to consider the effect of the average size of the deposited metal particles on the reflectance spectrum. This is the improvement made to the calculations of gold reflectance spectra in this paper. Another modification might be to introduce interference effects that may occur when the particle-free alumina (see Figure 2, film B) on the surface of the catalyst is smooth and/or its thickness is less than the wavelength of the incident light beam. Interference effects are caused by multiple reflections within the goldalumina film, before refraction back into the air at the surface of the alumina-thus causing a phase shift in the reflected beam, which is related to the thickness of the gold-alumina film, the complex refractive index of the gold-alumina film, and the wavelength of the incident beam. The calculation of the reflectance of the gold catalysts can be made by simplifying the catalyst structure by assuming that the catalyst consists of three parallel layered films (see Figure 2). Since the gold deposited on the alumina is deposited at the pore bases, the top portion of the alumina structure may be considered gold-free and of nonuniform thickness (film B). Film A consists of alumina containing randomly distributed gold colloids (this is an oversimplification since the gold is concentrated at the pore bases). The third layer is the substrate, aluminum metal. If the complex refractive index is defined as r) = n + ik, where n is the refractive index and k is the absorption coefficient, then the reflectance for polarized light for the given, simplified, system is3 R, = ( P ] : + P~:U
- 2P1: COS w v ) e x ~ ( - 4 ~ ) ) / ( 1 P l 2 P 2 V Z exp(-4P))
(1)
where v is s- or p-polarized light, /3 is the imaginary part of the complex phase difference suffered by the light in one complete passage through the film, plvand pZvare the moduli of the complex Fresnel coefficients for s- or p-polarized light where 1 denotes the air-film interface and 2 signifies the film-substrate interface, and \klv is the argument of the complex Fresnel coefficient denoted by lv. This expression for the reflectance of the gold catalyst suppresses the effect of multiple reflections within the gold-alumina film by averaging the reflectance over all possible phase lags of the reflected light. This, in effect, mimics the behavior of the light due to the rough oxide overlayer, film B (see Figure 10 in ref 7 for the roughness of the oxide). ~
~~
(6) Goad, D. G. W.; Moskovits, M., private communication.
(7) McBreen, P. H.; Moskovits, M J . Cutal. 1987, 103, 188.
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The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
Preston and Moskovits TABLE I: Gold Catalyst Preparation Conditions (0.27 g/L AuCI,) time, curr density, sample min mA/cm2 color Au4 1 4.1 light mauve Au5 4 4.1 mauve-pink Au6 10 4.7 mauve-pink 601
Figure 1. Schematic representation of gold/alumina/aluminum catalyst ~tructure.~
t
3Ot
400
Film A
1
I
I
I
v 1
I
500
I
1
A
I
measured
o calculated (VAO4Al
calculated (=radius)
I I I I 600 700 WAVELENGTH ( n m )
I
800
Figure 3. Measured and calculated Au4 reflectance spectra: one calculation with infinite radius and the other using optimized S,q, d, radius, and nA data.
\ Aluminum substrote
Figure 2. Schematic representation of the simpler film system used in the optical model for reflectance calculations of metal particle/alumina/aIuminum catalysts.6
For a natural, unpolarized light source the average reflectance R is R = (RP R , ) / 2 . To take into account intensity losses suffered by the light when it passes through film B, the above average reflectance, R , is multiplied by the spectral fraction, S. Hence the average reflectance is R = S ( R , + R , ) / 2 . However, the average reflectance must take into account the effect of the average gold colloid size. The complex refractive index of film A is affected by the gold particle size if the particle is of the order of the mean free path of a conduction electron, approximately 100 A. In this case the effective optical absorption is decreased due to surface scattering, thus affecting the complex refractive index for gold vB as follows
+
where vB’ is the new vB affected by the radius of the metal particles r, uF is the Fermi surface velocity for the gold metal particles, wp is the plasma frequency, ye is the bulk metal electron relaxation rate of the particles, w is the frequency of the incident light, and y is the electron relaxation rate taking into account both bulk and surface scattering. The effect of including particle size upon reflectance spectrum calculations for copper, silver, and gold is to add a resonance absorption in the visible region. This absorption depends upon the refractive index of alumina, the volume fraction of metallic colloids in film A, the plasma wavelength, and contributions in the visible region due to electronic absorptions in the ultraviolet region. The cases of copper, silver, and gold are unique since these are the only transition metals with strong resonance absorptions in the visible due to d-to-s interband transitions close to the visible region. The calculated reflectance can be fitted to experimental data by varying S, the spectral fraction, q, the volume fraction occupied by the metal particles in film A, d, the mean thickness of film A, and r, the radius of the metal particles, and by introducing interference effects.
;201
\ p
A
\d
n
I 500
1
measured
o calculated (VAO4A)
I
calculated I
I
600 700 WAVELENGTH ( n m )
(=radius) I
800
Figure 4. Measured and calculated Au5 reflectance spectra: one calculation with infinite radius and the other using optimized S, q, d, radius, and nA data.
The theory described here and in the previous paper3 has been based upon a simplified model of the prepared catalysts. In reality the theory is limited by the following: 1. The actual shape of the particles is unknown, whereas it was assumed to be spherical. 2. The optical constants for the bulk metal are not appropriate for particles whose size is of the order of the mean free path of an electron, which is approximately 100 A. 3. The particles are not randomly distributed in the lower portion of the anodic oxide layer as this simplified model suggests, but they are concentrated in the bases of the pores of the alumina. These limitations can be reduced by taking particle size and interference effects into account when calculating reflectance spectra.
Method The gold-alumina catalysts were prepared by Moskovits and Goad3 by the method outlined in their paper. The preparation conditions are listed in Table I. The visible reflectance data for these catalysts were also obtained from this paper. The measured reflectance data for the three gold catalysts are shown in Figures 3-5. Calculations of reflectance spectra for the gold catalysts were made by using Fortran 77+ on a Gould MPX-32 mainframe
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2959
Metal Particle Size in Supported Metal Catalysts
9 I
40
A
measured
t
o calculated ( V A 0 4 A )
calculated (-radius1
I 01
i
I
i
c
400
I
I I
I
I
500
I
600
WAVELENGTH
1
I
I
TABLE 11: Initial Variables Used To Fit Reflectance Data 4
d, nm
Au4 Au5 Au6
6.8 X lo4 3.1 x 10-3 1.1 x 10-2
639 615 414
500
800
700
S 0.61 0.56 0.50
qd 0.44 2.1 4.5
computer* with the reflectance theory derived above and a library minimization routine, VA04A.
Results and Discussion Initially it was decided to computer fit the measured gold reflectance data in the same manner as Moskovits and Goad,3 Le., with no particle size effect taken into account, by using eq 1 and the average reflectance, including the spectral fraction, as described above, to check that the same calculated spectrum was obtained by using the identical variables S, q, and d (see Table II).9 The same reflectance spectra were obtained which were poor fits of the well-defined plasmons in the measured reflectance spectra. The effect of the particle radius on the reflectance plasmon was introduced into the calculation of the gold reflectance spectra by using eq 2. Reflectance spectra for 25-, SO-, 7 5 , and 100-Agold particle radii were calculated from the S , q, and d values given for Au5 in Table 11. The resulting Au5 spectra are shown in Figure 6. It can be seen that as the particle size is increased, the plasmon well gets deeper and narrower. However, the plasmon minimum at 550 nm in these calculated spectra is not at the same wavelength as the measured reflectance plasmon, which is at 525 nm. The location of the plasmon in the calculated reflectance spectrum can be moved by varying q and d or essentially the product qd, which is the total volume occupied by the gold particles in the alumina film. Since the calculated Au5 spectra appear at higher percent reflectance values than the measured Au5 spectrum, the value of S, the spectral fraction, needed to be adjusted for a better fit of the measured data. The particle radius in the calculated spectra also had to be adjusted in order to get a correct match for the measured spectra. The calculations were therefore further modified to include a minimization routine VA04A, which calculated and minimized a variance function F for the measured and calculated data by adjusting the values of S, q, d, and r to get the best fit of the measured spectrum. The values that were initially chosen for S, q, and d are shown in Table 11. A particle radius of 30 A was chosen since the 25-A radius plasmon in the calculation of Au5 appeared to most closely match the measured Au5 data. A moderately good fit of the Au5 data was obtained with a variance value of 0.8 X lo-* and a plasmon minimum at 550 nm. (8) (a) Wagener, J. L. Fortran 77-Principles of Programming; Wiley: Toronto, 1980. (b) "Fortran 77+ Release 4.2 Reference Manual", July 1985; Gould Inc., Computer Systems Division. (9) n and k data were obtained from: (a) Schulz, L. G. J . Opt. Sot. Am. 1954, 44, 357; (b) Schulz, L. G. J . Opt. Sac. Am. 1954, 44, 362.
1
1
600 WAVELENGTH
(n m I
Figure 5. Measured and calculated Au6 reflectance spectra: one calculation with infinite radius and the other using optimized S, q, d, radius, and nA data.
sample
v
I
I
1 700 (nml
IOOH 75a I
iI
800
Figure 6. Calculated Au5 gold reflectance spectra using the particle size effect for 25-, 50-, 75-, and 100-A gold particles. TABLE 111 VA04A Best Fit Variables for Reflectance Data sample u d, nm S qd radius, A nA F ( X 1 0 4 ) 19.4 1.29 1.8 1715.9 0.65 2.3 Au4 1.33 X Au5 Au6
2.97 X 3.82 X
1194.5 0.64 3.56 261.4 0.54 9.99
31.3 32.4
1.40 1.27
6.7 6.2
In order to obtain a very good fit with a plasmon minimum at 525 nm, the refractive index for alumina, nA, was introduced as an adjustable variable in the VA04A routine, since the exact value of this is not known for the prepared catalysts. The value initially chosen for nA was 1.59, which is the value for nonporous alumina. Calculations using n A as an adjustable variable gave very good fits for all three measured gold reflectance data, with the plasmon minimum at 525 nm for both the measured and the calculated spectra. The resulting variance functions, F, which indicate the goodness of fit, were 1.8 X lo-", 6.7 X and 6.2 X for samples Au4, Au5, and Au6, respectively. The resulting calculated spectra are shown in Figures 3-5 along with the measured spectra and the calculated spectra obtained without introducing the particle size effect into the calculation (i.e., the spectra obtained at infinite particle radius), using the S, q, d, and nA values obtained in the fitting calculations (see Table 111), as a comparison. The data in Table 111 show that the volume fraction occupied by the gold metal in the alumina, the product qd, increases with the electrochemical deposition time, as one might expect. Indeed, the particle size of the gold deposited in the alumina pore structure also increases with deposition time as one might also expect. It appears from these data that there is an initial surge in average particle radius (Au4 to Au5) which levels off with time (Au5 to Au6). However, the amount of gold deposited increases steadily with electrochemical deposition time. In addition, the data in Table I11 show that the refractive index of alumina, nA, which was included as an adjustable variable in the calculations, varied only slightly between the three catalyst samples while remaining fairly close to the value of 1.40 for y-alumina, the form of alumina expected to be present in these catalysts. It is reasonable for the refractive index to change among samples since the pore size in each of the samples will not be identical and hence the volume fraction of oxide will vary from sample to sample. A second calculation for the Au4 sample was made with a much lower initial value for q and a very large value for d. The final values of S, q, d, nA, and the particle radius which were obtained in the best fit (which had a variance of 1.8 X lo4, identical with the other Au4 calculation) were 0.65, 7.24 X lo4, 3182 nm, 1.29, and 19.4 A, respectively. It is interesting to note that the product qd and the particle radius for this calculation were identical with the values obtained for the other Au4 calculation. This result shows that the fitting results are independent of the initial values chosen for S, q, d, nA,and the particle radius. The independence of the reflectance spectrum on the individual values of q and d and its dependence on the product qd, as predicted by the theory described above, is also shown by this result.
J. Phys. Chem. 1988, 92, 2960-2969
2960 TABLE IV: Standard Deviations for samde a d. nm 1.5 X 10’ Au4 0.11 0.18 7.4 X lo4 Au5 Au6 0.43 3.1 X lo3
Data in Table 111 S radius, A 0.02 2.8 0.04 5.5 0.07 14.8
as wide-angle X-ray scattering, a comparison with other standard methods for determining particle sizes cannot be made. However, it is known from electron microscopy studies that the pore diameter obtained under the electrochemical conditions used is about 250 A.5 This indicates that the particle sizes obtained for these catalysts are within the range that can be expected, since the average particle radii are limited by the radii of the alumina pores within which they are embedded (see Figure 1). Normally the particle sizes obtained could be compared with the particle sizes found by adsorption/AAS techniques. However, gold surface areas are difficult to determine by adsorption techniques since an appropriate adsorption gas, whose adsorption stoichiometry is known and which adsorbs on the entire metal surface, is not readily available. The results of this approach for calculating supported metal particle radii also reveal the expected trend of particle size growth, as well as the increasing volume of metal deposited in the alumina, with increasing electrochemical deposition time. Finally, one could obtain the conditions for ensuring a required particle size for the metal particles in a supported catalyst with the aid of this method for determining particle size. Therefore, the effect of varying the particle size on the activity and selectivity of the catalyst in a structure-sensitive reaction such as the formation of ammonia and nitrogen by the reduction of nitric oxide, especially in the range of 5-40 A where the most interesting effects of particle size are observed,2J2could be determined.
nd 0.06 0.07 0.06
A rigorous nonlinear least-squares adjustment was made to the obtained parameters found in Table 111 to determine the errors in the fitted values for each of the samples. This adjustment followed the method of WentworthloJ1using partial derivatives of the reflectance with respect to each adjustable variable used in VA04A to calculate the standard deviation for each of these variables. Table IV contains the standard deviations that were obtained in the error analysis routine. For samples Au4 and Au5 the errors are low for S , r, and but very high for q and d. Large errors for q and d a r e expected since the reflectance depends upon the product of q and d with only a slight dependence upon each individual value.3 The data for Au6 show small errors for S and nA with smaller errors for q and d than in the other two cases. However, the error in the fitted value for the average radius of the gold particles in catalyst Au6 is quite significant. This is undoubtedly due to the lower percent reflectance values obtained for sample Au6, making its analysis more prone to error than those of samples Au4 and Au5.
Conclusions The results of fitting gold-alumina catalyst reflectance spectra by the procedure outlined above show that this method for obtaining the average particle radius of a noble metal catalyst with a nonabsorbing support, such as alumina, is quick (the whole procedure is completed within a few minutes) and efficient and provides reliable results. Since results of the average particle radii for these catalysts have not been obtained by another method such
Acknowledgment. This paper was presented at the Tenth Canadian Symposium on Catalysis which was held at Queen’s University in Kingston, Ontario, Canada, in June 1986. We thank the National Sciences and Engineering Research Council of Canada (NSERC), the Ontario Graduate Scholarship program, and the Ontario BILD program for financial support.
(10) Wentworth, W. E. J . Chem. Educ. 1965, 42, 96. (1 1) Bevington, P. R.Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: Toronto, 1969; Appendix B.
(!2) (a) van Hardeveld, R.; Hartog, F. Ado. Catal. 1972, 22, 75. (b) O’Cinmeidi, A. D.; Clarke, J. K. A. Catal. Rev. 1972, 7, 213. (c) Slinker, A. A.; Fedorovskaya, E. A. Russ. Chem. Reo. 1971, 40, 660.
Thermodynamics of Alkanol-Alkane Mixtures Constantinos G. Panayiotou Chemical Process Engineering Research Institute and Department of Chemical Engineering, University of Thessaloniki, 54006, Thessaloniki, Greece (Received: July 22, 1987; In Final Form: November 20, 1987) A new theoretical approach is presented for the description of the thermodynamic behavior of systems containing associated compounds. A continuous linear association model is implemented in the lattice-fluid theory of Sanchez and Lacombe as modified recently by the author. The apparent equilibrium association constant, widely used in the various theories of associated solutions, is density dependent in the present model. The model can be applied to both liquids and gases at any external conditions down to the critical point. A single set of association enthalpy, association entropy, and association volume is used for all 1-alkanols; these association properties are pure-component properties. The theory is used to calculate vapor pressures, orthobaric densities, and heats of vaporization of 1-alkanols. New lattice-fluid scaling constants for these compounds are presented which are now close to the corresponding constants of their homomorph hydrocarbons. The theory is, subsequently, extended to mixtures and used to calculate the basic thermodynamic quantities of mixing for a number of alkanol-alkane systems. In its present form the theory is an approximate one since it does not take into account, besides others, the cooperative character of association phenomena in dilute liquid solutions and gases, but because of its simplicity it may form the basis for more refined treatments.
Introduction Alkanol-alkane mixtures is a class of mixtures remarkably deviating from ideal solution behavior, which attracted particular attention in recent years. For the thermodynamic description of these systems there prevails the relatively simple picture wherein the alkanol is self-associated and interacts with alkane only by physical forces.’ This picture was corroborated, besides other (1) Prigogine, T. (with the collaboration of A. Bellemans and V. Mathot) The Molecular Theory of Solutions; North-Holland: Amsterdam, 1957.
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studies,’ by recent spectroscopic studies by Kleeberg et al.? who also pointed out the significance of the nonpolar van der Waals interaction energy in alcoholic liquids. Division between physical and chemical interactions in these systems remains, however, a matter of considerable controversy in the l i t e r a t ~ r e . Statistical ~ thermodynamics, when applied to these systems, requires as(2) Kleeberg, H.; Kocak, 0.; Luck, W. A. P. J . Solution Chem. 1982, 1 1 , 611. (3) Marsh, K.; Kohler, F. J . Mol. Liq. 1985, 30, 13.
0 1988 American Chemical Society
