Internal fractal structure of aggregates of silver particles and its

J . Phys. Chem. 1988, 92, 453-464

453

Internal Fractal Structure of Aggregates of Silver Particles and Its Consequences on Surface-Enhanced Raman Scattering Intensities 0. Siiman* and H. Feilchenfeldt Department of Chemistry, Clarkson University, Potsdam, New York 13676 (Received: April 13, 1987; In Final Form: August 4, 1987)

Transmission electron micrograph (TEM) images of colloidal silver particles that had been induced to aggregate in the absence and presence of oxoanions of Cr(VI), Mo(VI), and W(V1) were obtained. Both monomeric, chromate and tungstate, ions and polymeric, isopolymolybdate, isopolytungstate, and phosphomolybdate, ions were used to produce aggregates of varying size, in which the oxoanions function as bridging ligands between silver particle surfaces. When electron-dense tungstate ions were used as adsorbates, the bridging tungstate was visualized directly in the TEM photographs. For a series of photographs with isopolytungstate on silver, the spatial dependence of the mass of silver particles in a large, low-density aggregate was analyzed as a fractal object in several ways. An average Hausdorff dimension, D = 1.51, was obtained. The substantially lower value of D in these silver clusters, compared to aggregates of gold particles that have been analyzed, is indicative of cluster-cluster aggregation which has been modeled in computer simulations to give D values between 1.4 and 1.6 in two dimensions. Chains of silver particles on the perimeter of some aggregates were also analyzed in terms of a fractal scaling. The average value of D thus obtained, 1.35, was very similar to the value, ,/,, that has been derived for polymer chains in dilute media and for the self-avoiding random walk on a two-dimensional lattice. Surface-enhanced Raman (SER) spectra of chromate and phosphate on colloidal silver were used to identify two types of adsorption sites: (1) oxoanions adsorbed in a double-sided mode of coordination, bridging pairs of silver particles; (2) oxoanions adsorbed in a single-sided mode on one silver particle surface. Single-sidedcoordination showed additional intense SERS bands at 558 and 915 cm-’ for chromate and at 575 and 1095 cm-’ for phosphate, which are assigned to uS(M=O) and 8,(OMO) vibrational modes involving oxygen atoms that are not directly coordinated to the surface. Changes in relative Raman band intensities of the polyoxoanions, isopolymolybdate and phosphomolybdate, in solution and on colloidal silver were interpreted in terms of orientation of the polyions on the silver surface. Data on the kinetics of aggregation of colloidal silver particles as induced by NaHPO, were obtained to further investigate the scaling of SERS intensity with time. Linear, logarithmic plots of SERS band intensity at 920 cm-l, u(P-0) of double-sided phosphate, and at 560 cm-I, S(OP0) of single-sidedphosphate, against time gave different slopes or exponents, 0.82 and 0.64, in the power law relationship, I [email protected] with similarly analyzed data for chromate and tungstate on silver, a relationship between the reciprocal of 0and the type of aggregate structure and mode of adsorbate coordination is proposed.

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Introduction the surface-enhanced Recently, we have been Raman scattering (SERS) from group VIB (group 6)50oxide coated particles of colloidal silver. Our special interest in this field stems from several significant observations. Enhanced photoemission3from the S-1 photocathode, composed of a Cs-0 overlayer on silver, was known to occur many years before the recognition of SERS. Enhanced photochemistry on silver surfaces is an established ingredient of the photographic p r o ~ e s s . ~ Other possibilities for enhanced photochemistry with photosensitive metal oxides5s6such as polytungstates remain to be explored. Interest in Mo and W oxides is widespread with respect to their ability to catalyze organic reaction^',^ such as the dehydrogenation of alcohols. Mixed W, Mo oxides are also used in the Folin phenol methodg for the quantitative determination of proteins, and some of the polytungstic acids have been widely used as nonspecific electron-dense stains for electron microscopy. Further, in devising strategies for enhancing Raman scattering intensities produced by molecules adsorbed in monolayer or submonolayer concentrations, surface resonance Raman scattering (SRRS), which involves exciting into a molecular electronic transition to give an enhanced signal, has some novel possibilities. This electronic reonance may already exist in the isolated molecule, be perturbed somewhat by adsorption unto a surface, or even be completely new. The latter case can occur from chemisorption-induced charge transfer between an adsorbate such as metal oxide and the metal substrate so that a nonlocalized form of intervalence charge transferlo (eg., Ago Wv’ for tungstate or polytungstate on Ag) can occur. This case has not been characterized thus far and may be responsible for the observation of strong Raman signals from molecules adsorbed on metalsI1J2such as Ni and Pd which are not believed to support SERS.

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‘On leave from the Institute of Chemistry, The Hebrew University, Jerusalem, Israel.

0022-3654/88/2092-0453$01.50/0

Our primary aims have been directed at more precisely defining the nature and occurrence of SERS active sites. We have found that these are intimately connected with the pattern of growth of colloidal metal aggregates and with their shape at various stages in the evolution of metal particle clusters. Our earlier work2shows that there may be a correlation between the structure of colloidal silver aggregates and the kinetics of their formation as determined by initial concentrations of metal oxide adsorbate and silver particles. In that study the aggregation of silver particles, triggered by the adsorption of M042- anions on the silver surface, was kinetically related to the appearance and increase in intensity of the SERS bands of these ions. Pseudo-first-order kinetic behavior was observed in both the Cr04”- and W042--induced aggregation of silver particles. A tentative fractal rate law of cluster growth was also suggested from a power law relationship between SERS intensity and time. At different concentrations of W O t - different slopes were found in this power law dependence, indicating different mechanisms in the aggregation. These would result in different aggregate structures: slower aggregation probably producing more open low-density structures such as chains; faster Feilchenfeld, H.; Siiman, 0. J . Phys. Chem. 1986, 90, 2163. Feilchenfeld, H.; Siiman, 0. J. Phys. Chem. 1986, 90, 4590. Sommer, A. H. Photoemissiue Material; Wiley: New York, 1968. James, T. H., Ed. The Theory of the Photographic Process, 4th ed.; MacMillan: New York, 1977. ( 5 ) Papaconstantinou, E. J . Chem. SOC.,Chem. Commun. 1982, 12. (6) Darwent, J. R. J . Chem. Soc., Chem. Commun. 1982, 798. (7) Hucknall, D. J. Selective Oxidation of Hydrocarbons; Academic: New York, 1974. (8) Misono, M. In Proceedings of the Climax Fourth International Conference of the Chemistry and Uses of Molybdenum; Barry, H. F.; Mitchell, P. C. H., Eds.; Climax Molybdenum Company: Ann Arbor, MI, 1982; pp (1) (2) (3) (4)

289-295. (9) Peterson, G. L. Anal. Biochem. 1979, 100, 201. (10) Robin, M. B.; Day, P. Ado. Inorg. Chem. Radiochem. 1967,10,247. (1 1) Loo, B. H. Solid State Commun. 1982, 43, 349. (12) Krasser, W.; Renouprez, A. J. J . Raman Spectrosc. 1981, 1 1 , 425.

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aggregation giving more globular compact clusters. In view of these results it was considered mandatory to use transmission electron microscopy (TEM) to determine the actual geometrical arrangement of silver particles in clusters obtained by aggregation under varying conditions of adsorbate size and concentration. In addition, the results of various computer simu l a t i o n ~ of ' ~ aggregation in two dimensions could be tested. A number of metal oxoanions, including the previously studied chromate and tungstate, as well as larger polyoxoanions such as isopolymolybdate, isopolytungstate, phosphomolybdate, phosphotungstate, and silicotungstate, were used.

Experimental Section As in our previous work's2 with chromate, molybdate, and tungstate ions on colloidal silver, the silver hydrosol was prepared and purified by a modified Carey Lea method.I4 The stock silver sol, prepared by the procedure described for sol 1 was stored in the dark at a silver concentration of about 2 g/L in a 1.O X M aqueous solution of sodium citrate. The sol was further diluted for all spectroscopic measurements (1/ 100) and for TEM examination (1/1000). Before addition of oxometallic ions to the silver sol, the excess sodium citrate was removed by treating the sol, diluted by 1/10 with double-distilled water, with a mixed-bed (1:l H+:-OH form) ion exchanger, Bio-Rad analytical grade AG 501-X8 resin. The ion exchange was followed by conductivity measurements with a Cole-Parmer conductivity meter and a platinum dip cell. Sols with conductivities of about 350, 35, and 6 pmho cm-' were used. Further dilutions of the ion-exchanged sol were made with double-distilled water. The compounds used were potassium chromate (K,CrO,), AR reagent, from Mallinckrodt; sodium tungstate (Na2W04),ammonium polymolybdate ((NH4)6M07024-4HZO), phosphomolybdic acid (20Mo03.2H3P04.48H20),and sodium phosphotungstate (1 2W03.H3P04.H20) from Sigma; ammonium metatungstate ((NH,),H2W12040), pract., and tungstosilicic acid (H4SiW12040).aq),p.a. grade, from Fluka. The Raman instrumentation has been previously d e ~ c r i b e d . ' ~ Ultraviolet and visible absorption spectra were recorded with a Perkin-Elmer Lambda-3 spectrophotometer. The transmission electron microscope was a JEOL JEM- 1200EX instrument, which has a nominal resolution of 1.4 %, and a resolution of 2.0-2.5 %, on focus. Samples were prepared on Fullam copper-rhodium, 3-mm-diameter, 400 mesh, grids. The grids were first covered with collodion, and then, 1 or 2 pL of the sol to be studied was evaporated on the collodion. The samples were allowed to age for several days and reach a stable condition before being examined by TEM. Results and Discussion The present new results primarily emphasize the structure of aggregates of silver particles as determined by transmission electron microscopy. The establishment of the local, spatial environment for adsorbed molecules on the surface of silver particles in the aggregates is essential for the interpretation of SERS spectra of various ions on silver, which are then presented. One series of 2-D photomicrographs of a large cluster is, next, analyzed as a fractal object. Then, a link between the fractal structure of the aggregates and the kinetics of their aggregation as measured by the temporal dependence of SERS intensity is proposed. Finally, the mechanism for SERS enhancement in the light of these new findings is discussed. (1) Preparation and Transmission Electron Microscopy of Silver Particle Clusters. Silver Sol in the Absence of Additional Zons. The stock silver sol, diluted by 1/1000 with double-distilled water, was found to contain mainly single silver particles and a few very small aggregates of single particles. Previous TEM analysisI4 of the particle size distribution in this silver sol gave ( 1 3 ) Witten, T. A.; Cates, M. E. Science (Washington, D.C.)1986, 232, 1607 and references cited therein. (14) Siiman, 0.; Bumm, L. A,; Callaghan, R.; Blatchford, C. G.; Kerker, M. J . Phys. Chem. 1983, 87, 1014. (15) Lepp, A.; Siiman, 0.J . Phys. Chem. 1985,89, 3494.

Siiman and Feilchenfeld a mean diameter of 13 nm with a standard deviation of 6.3 nm. If the sol, diluted 10-fold with double-distilled water, was treated with ion exchanger to a conductivity of 35-40 pmho cm-I, TEM examination of samples prepared immediately after treatment showed practically the same size distribution of particles. Then, over a period of 1 week, a slight amount of aggregation occurred in the suspension and produced a mixture of single particles and aggregates of varying sizes. If the sol was treated in the same way to a conductivity of about 6-8 pmho cm-l, corresponding to a much lower residual citrate concentration and even to the removal of some of the citrate adsorbed on the silver surface, some aggregation took place immediately and small aggregates appeared within hours after treatment. The size of the clusters increased rapidly and the sol precipitated after a week. TEM examination of the silver clusters usually showed the particles to be very close to each other, most of the time in actual physical contact as illustrated in Figure 1. In some cases coalescence of the particles could be observed. Chromate on Colloidal Silver. Chromate at concentrations M was added to silver sol at and 3.0 X between 3.0 X 1/100 of its stock concentration. Sols treated to conductivities of 34 and 6 pmho cm-I were both used. This time, to avoid complications and in contrast to the previous procedure,2 no poly(vinylpyrro1idone)(PVP) was added to the suspension. Since PVP stabilizes the sol and chromate mixtures, the chromate concentrations studied in its absence had to be lower than 1.0 X M. The mixtures turned red within a few hours to a few days, except for the most dilute one which became slightly grayish. M Cr042-) Thereafter, the more dilute mixtures (11.0 X remained stable for over 2 months. The most concentrated one (3.0 X lo4 M) precipitated after a few days. TEM examination of the sol and chromate mixtures (further diluted 10 times with double-distilled water) showed that most of the single silver particles had disappeared from the suspension and had been replaced by clusters of varying sizes. For sols with 10-4-10-5 M CrO.," concentrations, enormous aggregates, containing thousands of silver particles, were detected. In the less concentrated mixtures, the clusters were smaller, though still containing up to several hundred particles. A clearly visible feature in the TEM photos of these aggregates shown in Figure 2 was that the particles did not touch each other; rather, they were separated by apprently "empty" spaces, so that the surfaces of the silver particles were at distances of about 1-2 nm from each other. Tungstate on Colloidal Silver. Mixtures of silver sol with sodium tungstate at concentrations ranging from 5.0 X to 5.0 X lo4 M were prepared. Sols with two different conductivities (34 and 6 kmho cm-I) were used. The behavior of these mixtures was similar to that previously described.* The mixtures with 5.0 X and 3.5 X M W0:- turned red. The more dilute ones did not change color or became a very slightly darker yellow. The appearance in TEM photos of the clusters produced by aggregation of silver particles on addition of tungstate was similar to that for chromate. However, with the more electron dense tungstate as the adsorbate, very faint shadows could be detected around the aggregated particles, sometimes filling the spaces between particles and connecting them. Polyoxoanions on Colloidal Silver. Several Mo and W polyoxoanions (isopolymolybdate, isopolytungstate, phosphomolybdate, phosphotungstate, and silicotungstate) were added to silver sol to examine the influence of these much larger ions, typically about 9 %, in diameter, on the aggregation of silver. Anion concentrations were varied from 5.0 X to 5.0 X M. beMixtures of silver sol with isopolymolybdate ( haved similarly to those with chromate or tungstate. They turned red or orange at polyoxoanion concentrations of about 1.0 X M and remained yellow in more dilute mixtures. A small amount of an unidentified white precipitate appeared in all mixtures, even though the remainder of the silver particle suspensions were stable, Le., did not flocculate. Sols with conductivities of both 34 and 6-8 pmho cm-' were used, but no appreciable differences between their mixtures with isopolymolybdate were observed. TEM mi-

The Journal of Physical Chemistry, Vol. 92, No. 2, 1988 455

Aggregates of Silver Particles

H

H t0nm

2Onm

Figure 1. Transmission electron micrographs of parent silver hydrosol with stabilizing citrate ions removed with ion-exchange resin (6 pmho cm-').

'

crographs of a mixture with 1.O X lW3 M MqON6 showed many small clusters containing chains of less than 100 silver particles. Mixtures of silver sol with isopolytungstate (H2W120a6) behaved in a similar fashion. At 5.0 X M isopolytungstatethe suspensions turned red within 1 day and began to flocculate after about 3 days. At concentrations of 1.0 X M the mixtures turned slightly darker yellow and remained stable. Extensive TEM studies of the aggregated sols were carried out in this case. Grids were prepared after the mixtures had aged for 2 days. TEM micrographs of mixtures with 5.0 X M H2W120a6-,using stock sols with either 34 or 6 pmho cm-l conductivities, showed very large, dense clusters of silver particles, many of which were overlapping each other in the two-dimensional projection on the photographs. The aggregates that were formed at 1.O X 10-3 M H2W120aGwere much less dense, and overlap was not as severe. One characteristic, common to all TEM micrographs taken with mixtures of H2W120a6,was that the silver particles usually did not touch each other. The electron-densetungsten polyoxoanion could be detected as dark shadows between and around the silver particles. This is to be expected since polytungstates are widely used as staining agents for EM examination of macromolecules and biological tissue. Typical clusters formed in a mixture of silver M sol with a 34 pmho cm-l conductivity and 1.0 X (H2W120a)6 concentration are shown in Figure 3. Extensive chains of silver particles in a single cluster are apparent in this case. For a mixture of silver sol with a 6 pmho cm-' conductivity and the same concentration of isopolytungstate, much more extensive clustering takes place as can be seen on the TEM mi-

crographs in Figure 4. No particular drying pattern of the water is apparent in the micrograph since particles of silver, mostly singlets or small multiplets, are dispersed throughout Figure 4a. No distortion is seen in this larger cluster since there is no overlap of silver particles on top of each other. In addition, the property of self-similarity16of fractal objects is clearly evident in comparing the TEM photos at different magnifications on the left-hand side of Figure 4. The large spiderlike aggregate in Figure 4a is reproduced at about 40-fold higher magnification in Figure 4c by the dilation symmetry in the aggregate. In Figure 4b there appear to be two scales of chainlike aggregation: Le., the large ribbonlike pattern of the cross with additional loops and the chains of individual single particles of silver linked by isopolytungstate. We have further noticed the remarkable similarity between the crosslike structure in our two-dimensional TEM micrograph and some of the recent results13 of computer simulations of diffusion-limitedaggregation (DLA) in two dimensions. We believe this might be the first clear experimental evidence for fractal cluster-cluster aggregation as a result of small clusters aggregating to produce a large weblike network of connected silver particles. Electron irradiation had no effect on the aggregates at relatively low magnification or low energies. At higher magnifications,such as those in Figure 4b-d, the sample temperatures that are generated by electron irradiation are sufficient to melt the hydrated (16) Mandelbrot, B. B. The Fracfal Geometry ofNature; Freeman: San Francisco, 1983.

Siiman and Feilchenfeld

456 The Journal of Physical Chemistry, Vol. 92, No. 2, 1988

JJIW

H 8Onm

C

n

d .

H

2Onm

Figure 2. Transmission electron micrographs of typical aggregates of silver particles induced by addition of chromate (34 pmho cm-' parent sol and 3.0 X 10-5 M CrOd2-).

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salts (mp 100 "C)on the surface of the silver particles but have no effect on the silver (mp 2200 "C)or the relative positions of the silver particles. No movement or resultant loss of focus in the silver particles of the aggregates was observed even at the highest magnification. The dark smear or stain of isopolytungstate about the silver particles in Figure 4 may be due to its melting in the electron beam. Phosphomolybdate at 5.0 X and 1.0 X M concentrations immediately produced a light green or blue-green color in its mixtures with silver sol (37 pmho cm-l). Some mixtures with 5.0 X 1O-j M phosphomolybdate were examined by TEM after aging for 3 days; the photographs are presented in Figure 5. The micrographs are very different from the previous ones, and it appears that many of the primary silver particles have completely coalesced to produce particles of about double the original diameter. From previous work" on adsorption on solid surfaces these results may imply that phosphomolybdate has adsorbed to the silver surface in patches or islands and thus allowed silver-silver bonds to form more easily on collision of particles, leading to eventual coalescence. Shadows showing the presence of molybdenum could be detected between some of the particles. (17) Somorjai, G. A.; VanHove, M. A. Struct. Bonding (Berlin) 1979.38, 1.

In contrast to previous high-resolution TEM studies1*of silver sols which contain mainly decahedral, pentagonal-bipyramidal structures, the coalesced particles in Figure 5 have square profiles, indicative19 of octahedral shapes. Some of the particles in the micrographs taken at highest magnification in Figures 2-4 also show the pentagonal biprismatic structurecharacteristicof multiple twinning.*O Most of the silver particles, however, appear to have rounded corners, which suggests that they have undergone more complete multiple twinning to form the globular icosahedral structure.*O Phosphotungstate in final concentrations of 5.0 X lW3 and 1.O X M was also added to the silver sol. In contrast to all previous cases,the mixtures showed no visible signs of aggregation. No change in color or in their absorption spectra could be detected. The mixtures were not examined by TEM. Silicotungstate appeared to undergo a chemical redox reaction with silver. Its addition to the sol immediately results in noticeable turbidity. At a silicotungstate concentration of 1.0 X lW3 M the mixture remained otherwise unchanged and retained the light (18) Heard, S. M.; Grieser, F.; Barraclough, C. G.; Sanders, J. V. J . Colloid Interface Sci. 1983, 93, 545. (19) Yacaman, M. J. In Chemistry and Physics of Solid Surfaces V; Vanselow, R.;Howe, R., Eds.; Springer: Berlin, 1984; p 183. (20) Allpress, J. G.; Sanders, J. V. Surf. Sci. 1967, 7, 1.



a

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H

80nm

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d

20nm

Figure 3. Transmission electron micrographs of silver particles aggregated by isopolytungstate (34 pmho cm-'parent sol and 1.0 X

yellow color of a dilute silver sol. At a 5.0 X lW3 M silicotungstate concentration the yellow color disappeared and left a clear colorless solution in which the elemental silver had been oxidized to give a soluble Ag(1) complex. The other polyoxoanions did not show a similar reaction. (2) Structural Analysis of Aggregates. Since the appearance of the aggregate of silver particles in the TEM micrographs of Figure 4 is quite different from that of colloidal gold aggregates that have previously been experimentally ~ t u d i e d , ~we l - ~have ~ analyzed it further to determine the spatial dependenceof particle mass in the aggregate. Although the aggregates were originally formed in suspension in three dimensions, their deposition on a 2-D film of collodion on a grid gives a structurethat is very nearly two-dimensional. This is apparent from the large amounts of open space and lack of overlap between any pair of silver particles as (21) Weitz, D. A.; Oliveria, M. Phys. Rev. Lett. 1984, 52, 1433. (22) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. Rev. Lett. 1984,53, 1657. (23) Weitz, D. A.; Huang, J. S. In Kinetics of Aggregation and Gelation; Family, F.; Landau, D. P., Eds.; Elsevier/North-Holland: Amsterdam, 1984. (24) Weitz, D. A.; Lin, M. Y.; Sandroff, C. J. Surf. Sci. 1985,158, 147. (25) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. Rev. Lett. 1985, 54, 1416. (26) Dimon, P.; Sinha, S. K.; Weitz, D. A.; Safinya, C. R.; Smith, G. S.; Varady, W. A.; Lindsay, H. M. Phys. Rev. Lett. 1986, 57, 595. (27) Weitz, D. A.; Lin, M. Y. Phys. Rev. Lett. 1986, 57, 2037.

M H2WI20"9.

well as the good focus for all particles in the cluster. Further, questions related to determining the fractal dimension of a three-dimensional object in projection, as on photographic film, have been previously23addressed. It was shown that the fractal dimension, D, obtained in a two-D photomicrograph of an aggregate is the same as D in the three-dimensional object, provided the masses can be determined; i.e., there is little or no overlap of masses and D Id. An 11 2/3-foldenlargement of the micrograph negative of Figure 4a was made and then overlay4 with a square lattice of 1-mm-grid graph paper. A hand-drawn image (Figure 6) of this 1 cm = 0.714 pm photograph was then obtained by assigning each 1-mm2square with the presence or absence of a particle. Actually, each 1-mm2square contained on the average 10 primary particles. This number was obtained by comparing the number (454) of actual particles in the 1 cm = 100 nm scale micrograph (Figure 4b) with the number assigned (44)in the same region of space (lower center, framed) on the image of the enlargement. The first analysis of this image was carried out by the proced u d 8outlined for aggregates of various smoke particles condensed from the vapor phase. An origin in the square lattice was chosen near the center of the cross in the micrograph. Then, the number of particles enclosed in a series of nested squares of increasing (28) Forrest, S. R.; Witten, T. A. J . Phys. A 1979, 12, L109.

458 The Journal of Physical Chemistry, Vol. 92, No. 2, 1988

C


d

H

H

SOnm

25nm

Figure 4. Transmission electron micrographs of silver particles aggregated by isopolytungstate (6 pmho cm-' silver sol and 1.0 X

size from an edge length of 1-20 cm in integral steps was counted. Assuming that each filled 1-mm2square contained the same mass of silver, the particle number (N) versus size (L) scaling of the two-dimensional aggregate of silver particles was obtained by constructing an N versus L plot on a logarithmic scale. The analysis would yield a power law dependence of the type, N LD,for an object with a Hausdorff dimension D. We found that the slope of this curve varied with the edge length of the square. From linear regression analysis of three parts of the curve, the slope and thus D = 2.02 (5) for squares of edge 2-6 cm, D = 1.51 (2) for squares of edge 12-20 cm, and D = 0.99 ( 5 ) for those of intermediate edge 7-1 1 cm were determined. We believe that these variable results reflect our choice of origin in the micrograph. The distribution of particles about the inside central region of the structure appears by eye to be uniform in two-dimensional space, and thus a D value very nearly equal to 2 might be expected. The spatial distribution of particles further outward becomes fragmented into four specificdirections. Chains of particles in these four directions appear to produce the intermediate D value close to 1. Afterward, the chains, especially in the vertical directions, spread out and a steady pattern emerges with D = 1.51. These regional changes are more apparent on a more sensitive plot of log (N/L2)versus log L. Since N/L2 should scale as LB2, the slope obtained from the logarithmic plot is D

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M H2W,20a6-). Initially, the slope is 0.02 and D = 2.02; then it goes through a stage of rapid change (slope = -1.01; D = 0.99) to finally level off to a slope of -0.49 and D = 1.51. As the effect of the high ramification in the crosslike form becomes dominant, the scaling changes to that expected of fractal structures. A different way of analyzing the internal structure of the aggregate in the square lattice that does not depend on a choice of origin was also applied. In this a histogram was first constructed of the number of squares of edge length, L, containing n particles as a function of n. The second moment of this histogram has been shown29to scale as L2+Dfor self-similar objects. In Figure 7 we have divided the second moment by L2 and show its scaling with L in a logarithmic plot. Since the second moment/L2 should scale as LD,the slope of this curve should give the values of D directly. D = 1.51 (2) is obtained in good agreement with the weighted average (1.55) of three values of D from the first method. The substantially lower value of D obtained for our silver particle aggregates compared to the value (1.7-1.8) for aggregates of gold particles analyzed in the same way21-27are in accord with the visible differences in structure. Stringy aggregates of low density as in our micrographs rather than the more dense globular

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(29) Schlomo Alexander, cited in ref 21.


a


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.

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Figure 5. Transmission electron micrographs of typical aggregates of silver particles formed with addition of phosphomolybdate(34 pmho cm-* silver sol and 5.0 X M PW120426).

24 c

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1

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by grid method described in text.

Figure 6. Hand-drawn image of enlarged Figure 4a on l-mm2 graph paper. Every fifth box in the series of nested squares used to generate N versus L data is emphasized. The region magnified in Figure 4b is shown in a frame.

aggregates seen in the gold colloids are expected to arise over longer periods of time for cluster-cluster aggregation in which

colliding clusters are prevented by strong electrostatic repulsive forces from any large degree of interpenetration. A variety of computer simulation models for cluster-cluster aggregation have p r e d i ~ t e d l ~ *similar ~ * ~ ~low values of D between 1.4 and 1.6 in (30) (31) (32) (33)

Sutherland, D. N.; Gdarz-Nia, I. Chem. Eng. Sci. 1971,26,2071. Meakin, P. Phys. Reu. Lett. 1983,51, 1119. Kolb, M.; Botet, R.;Jullien, R. Phys. Reu. Lett. 1983, 51, 1123. Hentschel, H. G. E.; Deutch, J. M. Phys. Rev. A 1984, 29, 1609.

460



0.5

0

02 0.4 0.6 Q8 1.0 1.2 1.4 1.6 1.6

log

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Figure 8. Logarithmic plot of N(I) versus 1 for inside (0) and outside (0)perimeter of ribbonlike chain of silver particles in Figure 4b.

two dimensions. An alternative interpretation of the structure of the aggregate is that it contains regions with d = 1 and d = 2 which simply average out to give a mean value, 1.5, of the two dimensions. We, therefore, also analyzed 10 X 10 cm2 regions of the internal structure of magnified images at scales of 1 cm = 80 nm and 1 cm = 40 nm for part of the ribbonlike chain in Figure 4b and a potential candidate for a primary cluster in Figure 4c. The results are also shown in the logarithmic plot of the second moment/L2 versus L in Figure 7. Fractal dimensions of D = 1.57 (2) and D = 1.49 (3) were obtained for the chain and cluster, respectively, and agree very well with the value, D = 1.51 (2) for the larger 20 X 20 cm2, Le., 14.28 X 14.28 pmz, area of the enlarged print that was analyzed. It appears, therefore, that the internal structure of the aggregate is preserved over about three decades of length from the mean diameterI4 of primary particles of silver (0.013 Fm) obtained from previous TEM analysis to the dimensions of the large aggregate (- 14 pm) which contains over 30000 primary particles. Beyond - 1 5 pm it is apparent that the chains are beginning to curl over to form large loops as part of an overall weblike structure. Further, an analysis of the small segment of chain on a 1 cm = 80 nm scale micrograph was carried out by enumerating the number of lengths, N(I), required to map the chain with a variable has yardstick of length 1. The scaling relationship N(I) rD, been shown16to hold for self-similar objects. Both the inside and outside perimeters of the chain were considered with yardstick lengths between 2 mm, the average distance (16 nm) between centers of adjacent particles on the micrograph, and 40 mm. The results are shown in a logarithmic plot of N versus I in Figure 8, from which D values of 1.40 (2) and 1.31 (4) were derived for the inside and outside chain perimeter, respectively. The average value of 1.35 is very close to D = 4 / 3 , a value36 that has been derived from a theoretical treatment for polymer chains in dilute media and from computer simulations of the self-avoiding random walk on a two-dimensional lattice. (3) Surface-Enhanced Raman Spectra of Monomeric and Polymeric Oxoanions on Colloidal Silver. Our earlier study of chromate ion-silver hydrosol mixtures,2 which had been carried out in the presence of poly(vinylpyrrolidone), was extended to chromate concentrations between 1.0 X loT4and 3.0 X 10" M, in the absence of stabilizing polymer. Procedures already reported

-

(34) Jullien, R.; Kolb, M.; Botet, R.; Vicsek, T.; Family, F.; Hentschel, H. G. E. In Kinetics of Aggregation and Gelation; Family, F.; Landau, D. P., Eds.; Elsevier/North-Holland: Amsterdam, 1984. (35) Kolb, M. Phys. Rev. Lett. 1984, 53, 1653. (36) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, New York, 1979.

1 0

800 600 W R A B A N SHIFT,em''

200

Figure 9. SERS spectra of chromate on colloidal silver. Experimental conditions: excitation wavelength, 488.0 nm Ar', photon counting time interval, 0.10 s; spectral slit width, 7 cm-'. Conductivity of parent sol (pmho cm-I), chromate concentration (M), and incident laser power (mW): (A) 34, 1.0 X lo4, 6 0 (B) 34, 3.0 X 60; (C) 34, 1.0 X lo-', 60; (D) 34, 3.0 X lo", 55; (E) 6 , 3.0 X IO", 65; (F) 4, 3.0 X lo", 65.

were followed to prepare the mixtures. The SERS spectra of chromate on colloidal silver between 200 and 1000 cm-' are shown in Figure 9. Even at the lowest chromate concentration of 3.0 X lod M the surface Cr-O stretching bands at 800 and 917 cm-I are still clearly detected. A feature, however, that was not observed in the previous SERS spectra was an increase in the relative intensity of the 558-cm-' band for sols taken to a conductivity of 34 pmho cm-* and C r 0 2 - concentration decreasing from 1.O M. This surface Raman band was absent X lo4 to 1.0 X M Cr042- on colloidal silver in in SERS spectra for 5.0 X the absence of PVP, and we had difficulty finding the correct assignment for this vibration. To help establish the identity of this SERS band we also obtained Raman spectra of orthophosphate and monohydrogen phosphate on colloidal silver. Raman spectra of PO-: in solution and on silver in the absence and presence of PVP are shown in Figure 10. For comparison purposes similar spectra of HP04'in solution and on silver and of pyrophosphate in solution are displayed in the same figure. From the similar positions of the five surface Raman bands in spectra B, C, and F in Figure 10 at 1095, 1000, 930, 575, and 410 cm-' all bands appear to be associated with the same chemical species of adsorbed phosphate, Po43-. Similar Raman bands are observed either in the solution spectrum of Na3P04,albeit slightly shifted in position, or in the s p e ~ t r a ~ ' of ? ~the * coordinated phosphate ligand in phosphatoCo(II1) complexes. The frequency, 715 cm-', of the bridging POP group in pyrophosphate is too high to be assigned to the 575-cm-' band of a possible dimer on the silver surface. This was not clear in the assignment of the 558-cm-' surface Raman band of C r 0 2 on silver since dichromate exhibits39its symmetric CrOCr bridging mode at 565 cm-I. Moreover, in SERS spectra of both Po43-and Cr042-on silver there appear to be two sets of surface Raman bands whose relative intensities are subject to changes according to the preparation of the silver sol-oxoanion mixtures. One set includes an intense (37) Lincoln, S.F.; Stranks, D. R. Aust. J . Chem. 1968, 21, 37. (38) Coomber, R.; Griffith, W. P. J . Chem. SOC.A 1968, 1128. (39) Brown, R. G.; Ross, S . D. Spectrochim. Acta, Purl A 1972, 28A, 1263.


Aggregates of Silver Particles I

I

I

I

I

chromate ligand and the other side acts as a monodentate chromate ligand is not inconceivable. Three single-sided modes of coordination of the type

I

1

I

A

Oh,,

/o--Ag Cr

'0

\O-Ag

in which chromate behaves as either a bidentate, tridentate, or monodentate ligand are possible. In all these modes of surface coordination the original Td point symmetry of the M 0 4 units in solution is lowered to D2d or C3, in the double-sided mode and to C2,, C,,, or C,in the single-sided mode so as to split the v 3 (M-0) band into two or three components, one of which has totally symmetric A(l)character. If the coordinate bond to silver is strong enough, the single-sided mode of coordination will give two sets of either CrO or PO bonds: (1) single bond, Cr-0 or P-0; and (2) multiple bond, Cr=O or P=O, with their respective sets of symmetric and asymmetric u(Cr-0) and u( C d ) or u(P-0) and v ( M ) band frequencies. Similar sets and 6(0= of 6(0-Cr-0) and 6(O=Cr=O) or 6(0-P-0) P=O) band frequencies will also occur. Analogies for the double-sided mode of coordination exist in bidentate chelate complexes such as

2 RAMAN SHIFT,

em-!

Figure 10. Raman spectra of phosphate species in solution and on colloidal silver. Experimental conditions: excitation wavelength, 488.0 nm Ar+; spectral slit width, 7 cm-I. Species in aqueous medium, concentration (M), incident laser power (mw), and photon counting time interval (s): (A) Na3P04,0.50, 300, 0.025; (B) Na3P04and Ag sol, 5.0 X 60, 0.050; (C) Na3P04and Ag sol with PVP, 5.0 X 60, 0.050; (D) Na&O,, 0.20, 300,0.025; (E) Na2HP04,0.20, 60,O.lO; (F) Na2HP04and Ag sol, 5.0 X 60, 0.10.

symmetric M - O stretching band (930 or 800 cm-I) slightly shifted to lower frequency by sorption to silver, an asymmetric M-0 stretching band (lo00 or 917 cm-I) of low intensity at 100 cm-' higher frequency, and a symmetric 0-M-0 bending band (410 or 353 cm-I) at about the same frequency as in the solution species. The other set consists of a high-frequency band (1095 or 937 cm-I) usually associated with splitting of the asymmetric v 3 mode of tetrahedral M 0 4 species and a high-frequency bending band (575 or 558 cm-I) that would originate in the same way from splitting of the v4 mode of M04. All surface Raman bands are broadened considerably over their solution counterparts so that the chemical groups associated with these vibrational bands are expected to be intimately bound to the silver surface and be subject to changes in coordination chemistry on the surface. The TEM photos of the aggregates that are formed in mixtures of chromate and the more electron dense tungstate species with the silver sol have shown that the adsorbed molecules occupy spaces between particles as well as open areas on the particle surface. The closest distances between the surfaces of neighboring silver particles lie between 10 and 20 A for aggregates formed with chromate. The minimum distance for a single bridging chromate group of the type

-

-

Ag-O,/,,

- /O--Ag Lr

Ag-0'

\O-Ag

is estimated to be -8 A. We, thus, propose that only monomeric M 0 4 units are sorbed on the colloidal silver surface but that there exist two modes of coordination which we will refer to as single sided and double sided. The symmetric double-sided mode has already been displayed in the bidentate bridging chromate diagram above. The asymmetric double-sided mode in which one side of the bridge has a tridentate

which have a tetrahedral MI'S4 core geometry. Our previous measurement and analysis of the vibrational spectra of such complexes'"' showed that only one very intense uAI (M-S) Raman band and a much lower intensity split Raman band for vT2(M-S) could be expected. The double-sided mode of Cr0:- coordination to two silver particles is expected to give similar Raman spectra. We have found experimentally that this occurs preferably in two situations: (1) when Cr04*- in concentrations greater than 1.O X 10-3 M is added to silver sol in the absence of PVP and (2) when M is added to silver Cr0:- in concentrations lower than 1.O X sol in which sodium citrate has been removed to give conductivities below 8 rmho cm-I. The single-sided mode of coordination, which shows additional intense SERS bands, v,(Cr=O) and 6,(0=C1=0), at 937 and 558 cm-I, is preferred in the following cases: (1) when PVP is present in the colloidal silver suspensions and prevents the very close approach of pairs of silver particles, which is needed to have a bridging chromate group, and (2) when CrOd2- is added in M to silver sols that contain some concentrations below 1.0 X excess sodium citrate, as shown by their conductivities of -30-40 pmho cm-I. Similar conclusions can be reached from the SERS spectra of phosphate on colloidal silver, although the phosphate group appears to be a much weaker binder to the silver surface than chromate. The symmetric vA1 ( P a ) band at 945 cm-' for Na3P04in aqueous solution is only lowered by 15 cm-I for phosphate adsorbed to silver, whereas the symmetric uAl (Cr-0) band at 850 cm-' for chromate in aqueous solution was lowered by 50 cm-' upon adsorption on silver. Thus, single-sided Po4'- coordination is preferred in most cases: (1) when PVP is present to prevent the close approach of silver particles to one another and (2) even at high M Po43-at which at least 50% of concentrations of 5.0 X the oxoanion is adsorbed in the single-sided mode (estimated from relative intensities of the two sets of SERS bands). Double-sided Po43-coordination is preferred in case 1 when HP042-is added to silver sol. Polyoxoanionsilver sol mixtures were also examined by Raman spectroscopy, and the SERS spectra in Figure 11 were compared with the solution Raman spectra of the same anion species. Isopolymolybdate, M o ~ Ohas ~ ~been ~ ,shown by X-ray analysis41 to have a nonplanar arrangement of seven edge-shared octahedra (cyclic chain of six Mo centers with one central Mo) in the solid state. The overall point symmetry of the heptamolybdate ion is (40) Siiman, 0.Inorg. Chem. 1981, 20, 2285. (41) Lindquist, I. Ark. Kemi 1951, 2, 325, 349

462


I

!I'

I

I

'

I

I

'

I

Siiman and Feilchenfeld The Raman spectrum of phosphomolybdate in aqueous solution showed a strong, sharp band at 992 cm-' (fwhm, 5 cm-I) and a weaker one at 966 cm-l (fwhm, 19 cm-I). Several medium-toweak bands appeared from 900 to 300 cm-l. Again, upon adsorption of phosphomolybdate on colloidal silver, the Raman band positions of the two highest frequency bands (998 and 970 cm-') were shifted very little but their relative intensities were reversed and the 998-cm-' band was broadened 2-fold. The Raman spectrum of phosphotungstate in solution (not shown in Figure 11) was very similar to that of the phosphomolybdate ion between 900 and 1000 cm-l. It showed a strong band at 1002 cm-' (fwhm, 7 cm-I) and a weaker one at 985 cm-' (fwhm, 30 cm-'). The Raman spectra of silver sol-phosphotungstate mixtures only showed a small change in the relative intensities of the two bands. Both phosphomolybdate (PMO,,O,~) and phosphotungstate (PWI2Oa) ~ s s e s as globular ~~ Keggin structure in the solid state that is retained in solution. Four units of M309 are bridged together into a tetrahedral array surrounding a phosphate, PO:-, central core. Metatungstate, [(Hz)W,20a]6, the isopolytungstate for which TEM micrographs on colloidal silver were obtained, is structurally isomorphous with the corresponding heteropolytungstates having the a-Keggin structure; the two hydrogen atoms function as the heteroatom in the center of the globular structure. The minimum distances between adjacent silver particles in aggregates with adsorbed metatungstate were found to be slightly longer, -220-30 A than when chromate was the adsorbate. The molecular volume of the most compact globular W12O40 cluster with the Keggin structure is reported to be 685 A3 so that the radius of a sphere enclosing its contents is 5.47 A. Thus, an estimate of the shortest distance between silver particles with a bridging metatungstate ion is (2 X 5.47 A 2 X 2.66 %.) = 16

A.

1200

1000

800 600 COO RAMAN SHIFT, cm-'

200

Figure 11. Raman spectra of isopolymolybdate (A-D) and phosphomolybdate (E-G) in solution (A and G) and on colloidal silver (B-F). Experimental conditions: excitation wavelength, 488.0 nm Ar+ except A and G, 647.1 nm Kr+. Concentration (M), incident laser power (mw), spectral slit width (cm-I), and photon counting time interval (s): (A) 60, 7, 0.20; (C) 3.0 X 0.10, 210, 7, 0.050; (B) 1.0 X 60, 7 , 60, 7 , 0.10; (F) 5.0 0.050; (D)5.0 X 60, 7, 0.050; (E) 1.0 X X 60, 7. 0.10; (G) 0.10, 105, 2, 0.30.

,C , and all measurement^^^ indicate that its structure is unchanged in solution. In aqueous solution Mo70246- showed43one intense Raman band at 937 cm-' with a bandwidth of 29 cm-' and a weaker and broader band at 890 cm-l. Other low-frequency bands were observed below 500 cm-'. When Mo702,6- was adsorbed on silver, SERS bands appeared at approximately the same positions, 939 and 886 cm-I, in the high-frequency region as in the solution spectra. However, the relative intensities of the two bands were altered. The band at 886 cm-' became the more intense one with no appreciable change in width, while the band at 939 cm-' became weaker and was broadened about 2-fold. In addition, a series of medium-weak bands were observed between 800 and 300 cm-I, all of which were not present in the solution Raman spectra. The two high-frequency Raman bands in Mo702,6-have been assigned to v,(Mo--O) and vJMc-0) of the 12 terminal M d groups. For the more probable flat orientation of M0702,~- with respect to the silver surface, the Mo=O bonds would lie at 4 5 O to the surface. Thus, v,(Mo=O) would have a large change in the polarizability component parallel to the surface, whereas vas(Mo=O) would have a large component perpendicular to the surface, and by surface selection r ~ l e s show ~ ~ la ~more ~ intense SERS band intensity, in agreement with the observed band intensities.

-

(42) Pope, M. T. Heteropoly and Isopoly Oxometalates; Springer-Verlag: Berlin, 1983. (43) Aveston, J.; Anacker, E. W.; Johnson, J. S. Inorg. G e m . 1964,3,735. (44) Moskovits, M. Rec. Mod. Phys. 1985, 57, 783. (45) Creighton, J . A. Surf, Sci. 1983, 124, 209.

+

The infrared and Raman spectral data of polyoxometalates with the Keggin structure have been analyzed46 by normal mode calculations. Many features, including the relationship between the stretching vibrations of the twelve Mo=O bonds, can be explained in terms of the C3, local symmetry of the Mo309units. v,(Mo=O) was assigned to the highest frequency Raman band at 985 cm-I, and v,,(Mo=O) was assigned to a weaker Raman band and strong infrared band at 962 cm-'. Two favored orientations of the clusters on surfaces because of multiple oxygen atom chemisorption possibilities are with a C3axis of one of the Mojo9 units perpendicular to the surface or with the C4axis of the overall Td structure perpendicular to the surface. In the first case, Mo=O bonds would be oriented at -53O with respect to the normal to the silver surface, and thus displacements due to v,(Mo=O) would have a large change in the polarizability component in the direction parallel to the surface. Displacements due to vas(Mo=O) would have a large perpendicular component and thus give rise to a more intense SERS band as observed. Similar arguments can be made for the other orientation (C, axis normal to surface). For all polyoxoanions no large increases in the bandwidths of SERS bands relative to the widths of the solution Raman bands were observed, in contrast to what was detected for monomeric M042- species. The larger surface area occupied per molecule and the more rigid structure of the polyoxoanions probably does not allow the flexibility of different modes of coordination to various surface sites such as edges and corners. Further, exhaustive deionization of the silver sols with mixed-bed ion-exchanger resin was not capable of removing all surface-adsorbed ions since a weaker SERS signal was always still observed from bridging ion sites in the aggregates. As new aggregates were formed in the absence of additional ions, the SERS intensity increased very slightly. ( 4 ) Scaling of SERS Intensity with Time. The kinetics o f aggregation of colloidal silver particles induced by the addition of 5.0 X M NaHPO, was followed by SERS and absorption spectroscopy in the same way as previously reported2 with chro(46) Rocchiccioli-Deltcheff, C.; Fournier, M.; Franck, R.: Thouvenot, R. Inorg. Chem. 1983, 22, 207.



TABLE I adsorbed species

wo,*w0;-

Po?Po:Cr0:- and PVP Cr0:- and PVP Cr0:-

I

00

1.0

re1 rate of aggregn fast slow

total concn, M 5.0 X IO-' 3.5 x 10-3 5.0 x 10-3 5.0 x 10-3 5.0 x 10-3 2.5 x 10-3 5.0 x 10-3

1

I

2.0

3.0

I

4.0

slow

SERS band. cm-I. and mode of'coordn 895, double sided 895, double sided 920, double sided

slow fast fast fast

560, single sided 800, double sided 800, double sided 800, double sided

5.0

LOG t

Figure 12. Power law dependence of surface Raman band intensity, I , with time, 1, for aggregation of silver particles by 5.0 X lo-' M NaHPO,. I920

(0); I560 (0).

mate and tungstate ions. The rate of aggregation was slow in this case even at relatively high adsorbate concentrations. An end point was reached after 3 X lo4 min. Pseudo-first-order kinetics were observed at intermediate times following an induction period of about 1400 min. Rate constants, k', derived from the slope of log (AZ920) and log (AZ560) vs time plots in the linear region of and 6.4 X s-l from data for the the curves, were 8.6 X 920- and 560-cm-' SERS bands of phosphate on colloidal silver. This has suggested a mechanism in which adsorptionaggregation assumes a steady state2at relatively high ion concentrations. This has been verified for chromophoric ions by ultracentrifuging the ion-particle mixtures and showing that, in the slow aggregation limit, adsorption of ions was also slow. Of particular relevance here is again the observation of a power law dependence of SERS intensity, Z, on elapsed time, t , in the intermediate time range, 1400-26 000 min. Logarithmic plots of 1920 (intensity of 920-cm-l SERS bands for v(P-0) of double-sided phosphate coordination) and 1560 (intensity of 560-cm-' SERS bands from 8(O=P=O) of single-sided phosphate coordination) against time (minutes) are shown in Figure 12. Regression analysis in the linear regions of the plots gave for the tp, values of 0.82 and 0.64 exponent @ in the relationship, Z for 1920 and Z560,respectively. No other Z versus t plot such as a semilog plot of In Z versus t showed a linear relationship in the intermediate 1400-26 000-min interval. Similarly analyzed kinetic data2 are assembled in Table I for the aggregation of silver particles with tungstate and chromate. There appears to be a correlation between the magnitude of the exponent @ or its reciprocal and the type of aggregate structure that can be associated with the SERS band and the mode of coordination that it implies. As pointed out and discussed in the previous article2the reciprocal of fl will provide a measure of the fractal dimensionality of the aggregates that are kinetically formed if the total surface-enhanced Raman intensity scales as the mean radius, R , of the clusters instead of their total surface area or number of adsorbed scatterers which is proportional to R2. Since the mean radius scales as t p with 8' related to the fractal dimension, we have tentatively proposed that the total SERS intensity also scales as fl, and thus a power law dependence of SERS intensity on elapsed time is observed. Therefore, fast aggregation in the absence of PVP, observed by following evolution of a SERS

-

expt, B 0.56 0.78 0.82

0.64 1.02 1.12

0.64

'18

1.8 1.3 1.2 1.6

0.98 0.89 1.6

band assigned to the double-sided mode of coordination of M 0 4 to two silver particles, gave relatively high /3-' values of 1.8 and 1.6. TEM micrographs of clusters of silver particles formed by fast aggregation have shown the presence of more globular, compact clusters, in which bridges between pairs of particles are formed in all directions. On the other hand, slow aggregation also observed by tracking the intensity of a SERS band assigned to the double-sided mode of MO, coordination gave low /3-' values of 1.3 and 1.2. At this limit, our TEM micrographs have shown more ramified cluster structures containing many linear chains. In both the above cases, the particle-bridging M 0 4 mode that is followed by surface Raman scattering appears to reflect the dimension of the cluster. Slow aggregation leads to lower dimensionality structures, such as chains, with fewer of the nearestneighbor interactions per particle that would require M 0 4 bridging groups. However, when slow aggregation is observed by tracking the evolution in SERS band intensity of a single-sided M 0 4 mode, a high 8' value, 1.6, was again obtained. Thus, even though mostly linear chains might be formed in slow aggregation, the single-sided mode reflects a spatial orientation of M 0 4 on particles in clusters that is not as highly directional as the double-sided mode of coordination. Furthermore, when PVP was added to silver sols, subsequently induced to aggregate by Cr042-,relatively fast aggregation was observed upon following the 800-cm-' SERS band of double-sided Cr042-coordination. The very low 8' values of 0.98 and 0.89 reflect a low fractal dimensionality for the clusters of silver particles as they are bridged by chromate. The presence of PVP as a competing and stabilizing adsorbate for the colloidal silver surface appears to allow only the minimum number of nearestneighbor interactions between chromate-bridged silver particles, which corresponds to the formation of linear chains. ( 5 ) Effect of Aggregation on SERS Enhancements. In previous work with ~ i l v e r ' ~and ' ~ ~gold4' ' ~ sols at various stages of aggregation we have determined SERS enhancements in the 103-106 range. Little or no enhancement was observed by excitation into the single-particle resonances of silver and gold peaked at 400 and 520 nm, respectively. The very large absorption at the singleparticle peak precludes an accurate measure of enhancements in this region; however, some aggregated sols show similarly high extinction toward the red and this has not prevented observation of SERS spectra. To investigate this further we have used pulsed, excimer-pumped dye laser (Lambda-Physik) excitation at 385 nm to probe both the silver particle Mie resonance at 400 nm and the chromate ion charge-transfer absorption band and resonance Raman peak at 370 nm. Oblique angle scattering (-30' to quartz cell window) was used to overcome the large absorption by the sol-chromate mixture in this wavelength region. Under these M chromate solution gave observable conditions a 1.0 X resonance Raman bands; however, no bands were observed in the sol mixtures even though the same silver sol-chromate mixtures gave the intense SERS bands shown in Figure 9 with excitation in the 450-550-nm range. Increases in SERS enhancements that accompany aggregation of silver and gold sols were estimated to be -103-104-fold. Mie scattering calculations, recently revised48for small single spheres (47) Siiman, 0.; Hsu, W. P.J. Chem. SOC.,Faraday Trans. 1 1986, 22, 851. (48) Kerker, M. J . Opt. SOC.Am. E : Opr. Phys. 1985, 2, 1327.

J . Phys. Chem. 1988,92, 464-461

464

of silver with the use of more recent experimental data on the optical constants of silver, put the maximum SERS enhancement figures at lower values than the IO6 figure initially calculated. The 103-104 enhancements for single spheres of silver are more in line with observations that have shown similar enhancements for both silver and gold. With the uncertainty in the purity of silver on and in colloidal silver particles due to the presence of oxide and other silver ion complexes, these ideal estimates almost certainly need to be revised downward. The electrodynamic theory for two interacting silver spheres is not complete. At the small particle limit, calculations have been made that give larger enhancements for multiplets than for single spheres as in the calculations for ellipsoidal single particles.49 For the two-sphere case, however, the assumption of point dipoles for the spheres necessarily gives peak resonance SERS intensities located at the single-sphere absorption maxima instead of the coupled sphere frequency. Additional diple-dipole coupling terms that become important only when pairwise interaction occurs between neigh-

-

(49) Kerker, M.;Siiman, 0.;Wang, D.4. J . Phys. Chem. 1984,88, 3168. (SO) In this paper the periodic group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise group 3-12, and the p-block elements comprise groups 13-18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., I11 3 and 13.)

-

boring particles in aggregates include

in which p / ' ) (pi(2))in the equivalent dipole at the center of particle 1 (2) and himol(2)(himo1(')) is the induced dipole of a molecule on the surface of particle 2 (1). As a crude first approximation, we tentatively suggest that the net SERS enhancement for molecules on the surface of particles in aggregates may be expressed as a product of enhancements from adjacent single particles

normalized to a per adsorbed molecule basis, and summed over all adjacent pairs. Some compensation factor, a,also needs to be made for the number of neighboring particles about any particular reference particle. In any case, the product of calculated enhancements for single particles of silver with an upper limit of 106-108 is more in agreement with observed enhancements of lo6 or greater for nonchromophoric adsorbates on silver. Acknowledgment. This work was supported by Army Research Office Grant DAAG29-85-K-0102. Registry No. Ag, 7440-22-4; GO:-, 13907-45-4; WO?-, 14311-52-5; M O , O ~12274-10-1; ~~, HzW120406,12207-61-3; PW,,O,'-, 12534-77-9; PO,)-,14265-44-2; P2OTe,14000-31-8; HPO?-, 14066-19-4; H4SiW,,0 4 0 , 12027-38-2; PMol2O4o3-,12379-13-4.

Discovery of Reversible Photochromism in Titanium Dioxlde Using Photoacoustic Spectroscopy. Implications for the Investigation of Light-Induced Chargeseparation and Surface Redox Processes in Titanium Dioxide James G. Highfield* and Michael Gratzel Institut de Chimie Physique, Ecole Polytechnique Fgdgrale de Lausanne, Lausanne, Switzerland, CH- 101 5 (Received: April 29, 1987; In Final Form: July I , 1987)

Utilizing a conventional photoacoustic spectrometer in a pump-probe arrangement, band-gap excitation of powdered titanium dioxide in a moist, oxygen-free atmosphere results in a strong photochromic response, characteristic of small polaron formation. The reactivity and remarkable lifetime of such excited species are demonstrated in their subsequent dark reduction of methylviologen. Results from two independent methods indicate carrier densities in the range 10'9-1020 ~ m - Electron-hole ~. recombination follows first-order kinetics, suggesting that detrapping of surface-trapped holes is rate controlling. The presence of water vapor delays the recombination process, extending decay constants from seconds to minutes.

Introduction In recent years, the search for efficient catalysts for light-driven endergonic chemical reactions has been actively pursued in this laboratory and elsewhere,' with the ultimate objective of developing an economically viable process of solar energy conversion and storage. While investigations of semiconductor photocatalysts in colloidal, Le., transparent, form by techniques such as laser flash photolysis and transmission spectrophotometry have yielded valuable information on the efficiency and dynamics of interfacial charge transfer and the optical absorption characteristics of transient excited species,2 there is a need for complementary techniques for in situ studies of such systems in more readily available form, and under typical screening conditions, e.g., as opaque powders in contact with gaseous reactants and product^;^ or suspended in liquid reactant^^,^ under continuous illumination. * Present address: Laboratoire de Chimie Technique, Ecole Polytechnique FCdCrale de Lausanne, Lausanne, Switzerland CH-1015. 0022-3654/88/2092-0464$01.50/0

In the past 10 years, photoacoustic spectroscopy (PAS) has found increasing application in the study of light-absorption and deexcitation processes in condensed-phase media, and its advantages over alternative optical methods, such as reflectance spectroscopy, in the UV-visible-near-infrared region are well documented? In its most popular (dispersive) configuration, utilizing an intensity-modulated broad-band exciting source, with synchronous gas-coupled microphonic detection, PAS is probably the most versatile "parent" of a growing family of techniques based (1) Energy Resources Through Photochemistry and Catalysis; Gratzel, M., Ed.; Academic: New York, 1983. (2) Kalyanasundaram, K.; Gratzel, M.; Pelizzetti, E. Coord. Chem. Rev. 1986, 69, 57. (3) Yamaguti, K.; Sato, S . J . Chem. Soc., Faraday Trans. 1 1985, 81, 1237. (4) Kiwi, J.; Gratzel, M. J . Phys. Chem. 1984, 88, 1302. ( 5 ) Pichat, P.; Herrmann, J.-M.; Disdier, J.; Courbon, H.; Mozzanega, M.-N. Nouu. J . Chem. 1981, 5 , 627. (6). Rosencwaig, A. Photoacoustics and Photoacoustic Spectroscopy; Chemical Analysis, Vol. 57; Wiley-Interscience: New York, 1980.

0 1988 American Chemical Society

Internal fractal structure of aggregates of silver particles and its

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