4590
J . Phys. Chem. 1986, 90, 4590-4599
is quite constant in the various zeolites studied, namely, X, mordenite, and ZSMS. Our data clearly indicate that it is more difficult to reduce Ni2+ to the metallic phase in calcium-X than in sodium-X zeolite, although with both cocations partial reduction to monovalent nickel is readily achieved. This conclusion is similar to that of Olivier et al.,I7 who used ESR and ferromagnetic resonance studies. However, there is evidence in Y zeolites, which have about a twofold greater silicon to aluminum ratio than do X zeolites but with the same structure, that NiCa-Y zeolite reduced easier than NiNa-Y zeolite. These results were obtained by chemical studies of hydrogen r e d u c t i ~ nand ~ ~indicate ~ that the nature of the cocation can have drastically different influences on the reducibility of nickel depending upon the silicon to aluminum ratio. This may be related to differences in the population of exchanged cation sites in X vs. Y zeolites and it appears that more comprehensive studies of both cocation effects and zeolite structure effects may allow one to achieve a substantial degree of control over the reducibility of Ni2+ and perhaps other metal ions in zeolites.
Conclusions ESR and XPS analyses of dehydrated and hydrogen-reduced NiNa-X and NiCa-X zeolites have been carried out. XPS indicates that reduction at 600 K is sufficient to reduce some of the Ni2+ in NiNa-X to the metallic form. Deconvolution of the broad XPS peak shape indicates three components assignable to Ni*+, Ni+, and Nio. The center component with a binding energy of 854 eV is assigned to Ni+ by correlation with ESR data. Both XPS and ESR indicate that hydrogen reduction of Ni2+to Ni+ and Nio occurs at lower temperatures in NiNa-X than in NiCa-X. This observation of nickel in the sodium form of X zeolite being easier to reduce than in the calcium form contrasts with Y zeolites, in which the opposite has been reported. Thus both the cocation and the zeolite structure can control the reducibility of nickel cations. Acknowledgment. This research was supported by the Robert A. Welch Foundation and the National Science Foundation. Registry No. Ni2+, 14701-22-5.
Adsorption and Aggregation Kinetics and Its Fractal Description for Chromate, Molybdate, and Tungstate Ions on Colloidal Silver from Surface Raman Spectra Hannah Feilchenfeldt and Olavi Siiman* Department of Chemistry, Clarkson University, Potsdam, New York I3676 (Received: November 15, 1985: In Final Form: April 21, 1986)
Surface-enhanced Raman scattering (SERS) from chromate, molybdate, and tungstate ions on colloidal silver in aqueous media was observed once the silver particles had been induced to aggregate with sufficientlyhigh concentrations of the oxoanion. Chemisorption was indicated by a 30-50-~m-~shift to lower energy in the frequency of the totally symmetric stretching mode. The Raman bandwidths of surface species were about 5-6-fold greater than their solution counterparts. This was attributed to heterogeneous broadening on the silver surface due to differences in the adsorption sites or in the orientation of the ions with respect to the surface. Polyoxoanions were sometimes detected in the SERS spectra but relatively weakly as minor adsorbed species. The time evolution of surface Raman and absorption band intensities of Cr042-and W042- on colloidal silver was measured as a function of oxoanion concentration. At concentrationsgreater than 1.0 X M the overall kinetics of Cr04” and WO,*- adsorption and aggregation of silver particles showed a pseudo-first-orderrate dependence. To account for the first-order behavior of an otherwise bimolecular process, aggregation, it is proposed that the rate of adsorption and the rate of aggregation reach a steady state after some initial induction period. The first-order rate constant, k l , for this process with chromate ion was 1.5 X lo-* M-I s-I For tungstate ion the pseudo-first-order rate constants, 1.5 X lo4 and M concentrations of W042-,respectively. The resulting 2.1 X 10” s-l, were widely different at 5.0 X lO-’and 3.5 X twelfth-order dependence of the rate on tungstate concentration was, however, consistent with the much greater tendency of W042- to polymerize into clusters. In addition, a power law dependence of surface Raman band intensity of W04’- on time was found at both slow and fast aggregation limits. As a result, a fractal dimension was associated with the SERS active surface probed on aggregates of silver particles that were formed in the fast aggregation limit. This agrees with the value expected for diffusion-limited aggregation in which the aggregates are highly branched and randomly distributed in space. For slow aggregation a significantly lower value, consistent with the formation of mostly linear chain aggregates, was obtained.
Introduction The series of tetracoordinate group VIB (6)39transition-metal oxoanions, chromate, molybdate, and tungstate, constitutes a group of highly symmetrical potential adsorbates for surface Raman studies. They are structurally analogous and therefore allow facile comparison between the chromophoric chromate and the nonchromophoric molybdate and tungstate adsorbates. In addition, they are sorbed directly onto a metal particle surface in contrast to the azo dye, dabsyl aspartate (dabsyl = N-[[4-[[4-(dimethy1amino)phenyllazo]phenyl]sulfonyl]), that was recently used to investigate the extent of coupling between surface resonance Raman scattering (SRRS) and surface-enhanced Raman scattering (SERS) and in which the chromophoric group was relatively ‘On leave from the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel.
far removed from the surface of the silver] or gold2 particles on which the molecule was adsorbed. The coordination chemistry of these oxoanions as mono- and bidentate ligands in transitionmetal complexes has been de~cribed,~ and some of their vibrational spectra have been assigned. Oligomerization of the monoanions, especially those of molybdate and tungstate, has been extensively studied4 since their isopoly and heteropoly derivatives form an important class of soluble polyoxoion salts. Formation of polymers in solution can usually be avoided by maintaining near neutral or basic conditions of hydrogen ion concentration. Like other soluble salts in sufLepp, A.; Siiman, 0. J. Phys. Chem. 1985, 89, 3494. Siiman, 0.; Hsu,W. P.J . Chem. Soc., Faraday Trans. 1 1986.82, 851. Coomber, R.; Griffith, W. P. J . Chem. SOC.A 1968, 1128. Pope, M. T.Heteropoly and Isopoly Oxometalates;Springer-Verlag: Heidelberg, 1983. (1) (2) (3) (4)
0022-365418612090-4590$0 1.5010 0 1986 American Chemical Society
Aggregation Kinetics of Cr042-,
MOO^^-, and W042-
ficiently large concentrations, the dianions CrOZ-, MOO^^-, and W042-are expected to be effective agents for the coagulation of colloidal size silver particles, i.e., they are good salting-out agents. In contrast to noncoordinating anions of low charge, such as the perchlorateS ion, that have previously been used to study coagulation of gold sols, these dianions should form coordinate bonds directly with the silver particle surface. As a consequence the kinetics of coagulation of metal particles may be simpler than the bimolecular rate dependence previously observed, especially when the total concentration of adsorbate in the colloidal suspension is much larger than its saturation concentration on the available surface. In order to analyze the relationship between the positions and intensities of the SERS bands of structurally well-defined adsorbates on colloidal silver and the extent of aggregation6 of the silver particles, we have examined the behavior of the chromate ion and its nonchromophoric counterparts, molybdate and tungstate, on colloidal silver. The time evolution of SERS band intensity of adsorbed Cr042-or WO2- and of the visible absorption band intensity of aggregated silver particles was measured, and the kinetics of aggregation of silver particles induced by the addition of chromate or tungstate were analyzed. It was found that a fractal dimension might be associated with the surface of aggregated silver particles that was probed by SERS intensity measurements for adsorbed tungstate. Moreover, the resonance Raman spectra and excitation profiles of alkali-metal salts of chromate in solution and in the solid state have been thoroughly examined by several groups.'-'' The lowest energy charge transfer absorption band and corresponding RRS profile maximum are located at 370 nm in aqueous solution. This is far-removed from the 500-600-nm absorption band of aggregated colloidal silver that we found to coincide with a maximum in the SERS excitation profile. Thus, SRRS and SERS profiles should be well resolved.
Experimental Section The silver sol was prepared and purified according to previously described procedures.12 It was kept in the dark in a 1.0 X M solution of sodium citrate at a silver concentration of -2 g/L. A light-scattering measurement showed the particles to have a mean diameter of 25 nm and to be uniform in size. Before it was used, the sol was diluted 10-fold with doubly distilled water and treated with an ion exchanger (Bio-Rad analytical grade mixed-bed (H+, OH- form) resin AG 501-X8) in order to remove excess sodium citrate from the suspension and to displace some of the adsorbed citrate and compensating sodium ions. The progress of the ion exchange was followed by conductivity measurements with a Cole-Parmer digital conductivity meter (Model 148 1-00) and a platinum dip cell. The conductivity of the diluted sol before treatment was about 400 pR-' cm-'; that of doubly distilled water was 3 pR-' cm-I. Raman measurements of the Ag sol at conductivities of 40, 8, and 4 pR cm-' all yielded SERS spectra of citrate, showing that some citrate always remained adsorbed on the sol. From then on the treated sol was kept at a conductivity of 30-40 pR-' cm-I in order to avoid spontaneous coagulation. For chromate adsorption studies this sol was further diluted to a silver concentration of about 0.02 g/L. Its pH was then about 6.5. The first mixtures of silver sol and potassium chromate prepared contained rather high concentrations of chromate, typically 5.0 X M. They were unstable; their color changed from yellow ( 5 ) Enustun, B. V.; Turkevich, J. J. Am. Chem. SOC.1963, 85, 3317. (6) Blatchford, C. G.; Campbell, J. R.; Creighton, J. A. Surf.Sci. 1982, 120, 435. (7) Carter, R. L.; Bricker, C. E. Spectrochim. Acta, Part A 1971, 27A, 569. ( 8 ) Kiefer, W.; Bernstein, H. J. Mol. Phys. 1972, 23, 835. (9) Homborg, H. Z . Anorg. AIlg. Chem. 1983, 498, 25. (10) Campani, E.; Ferri, F.; Gorini, G.; Polacco, E.; Masett, G. Chem. Phys. Lett. 1984, 107, 91. (11) Weinstock, N.; Schulze, H.; Muller, A. J . Chem. Phys. 1973, 59, 5063. (12) Siiman, 0.; Bumm, L. A.; Callaghan, R.; Blatchford, C. G.; Kerker, M. J . Phys. Chem. 1983,87, 1014.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4591 at the time of preparation to a dark green hue, and silver precipated within a few days. The intensity of the Raman bands first increased and then decreased as some of the coagulated silver precipitated together with the adsorbed chromate. The stability was improved by adding poly(vinylpyrro1idone) (PVP) with an average molecular weight of 10000 at a concentration of 0.6 mg/mL and by decreasing the concentration of the chromate ion. After preparation, the mixtures went through a period (varying from a few hours to several days) of rapid change characterized by an increase in the intensity of the Raman bands as well as by changes in color and visible absorption spectra. These variations correspond to the formation of aggregates of various sizes in the mixture. This was confirmed by a light-scattering measurement on a red-colored mixture, which showed a mean particle diameter of 250-300 nm with a wide dispersion of values. Since it was found that the silver sol treated with ion exchanger and the chromate mixtures prepared with this treated sol were slightly acidic (pH -6.5), the influence of the pH on the SERS spectra was checked. Two mixtures containing silver sol, PVP, and chromate at concentrations of 1.0 X lo4 M and 2.5 X M were prepared; a few drops of 0.1 NaOH were added to obtain a pH of about 8.5. The Raman spectra of these mixtures, measured after several days, were in no way different from those of similar mixtures prepared without addition of NaOH. No NaOH was added in later experiments. Mixtures of silver sol with the sodium salt of tungstate at M or less behaved in a similar fashion concentrations of 5.0 X but were much more stable and did not require the addition of PVP. If the concentration of tungstate were reduced to 1.O X lo4 M or less, no aggregation of the sol and no SERS bands were detected. The lowest concentration of tungstate at which SERS bands were seen was 5.0 X M. On the other hand, if the tungstate concentration was increased to 1.0 X M, silver particles precipated within a few hours. Absorption spectra were recorded with a Hewlett-Packard 8450A diode array spectrophotometer. The Raman instrumentation has previously' been described. A 1-cm path length stationary quartz fluorescence cell at ambient temperature was used for sampling. The dynamic light scattering measurements were madeI3 with a 12-W Model 171 Spectra Physics Ar+ laser as the source of illumination, a goniometer, and a digital correlatormicroprocessor (Brookhaven Instruments).
Results and Discussion Surface Raman Spectra of CrO:-, and W042- on Colloidal Silver. Several observations described in this section were made to distinguish surface Raman bands of the oxoanions from their solution counterparts. These include (1) different Raman band positions and relative intensities for M 0 2 - stretching and bending modes on colloidal silver, (2) much larger bandwidths of surface Raman bands, (3) depolarization of Raman bands of the surface species that were otherwise polarized for the solution species, and (4) the presence of additional bands in the surface Raman spectra due to chemical changes in M042- units on the surface. Raman spectra of Cr042-, and W042- on colloidal silver are compared with the Raman spectra of the respective solution species in Figure 1. Also, a series of Raman spectra of Cr042-on colloidal silver without the addition of PVP are given in Figure 2 for comparison. Each of the solution spectra shows a single dominant intense Raman band in the 85C-950-cm-' region, which has been assigned to the totally symmetric v,(M-O) stretching mode, as well as weaker bands assigned to the v,(M-O) asymmetric stretch and to the bending modes. In the surface Raman spectra these vibrational bands are both shifted and broadened as well as considerably intensified when compared with their solution counterparts. The most intense enhanced Raman band in the spectrum of Cr04" on colloidal silver is assigned to v,(Cr-O) at 800 cm-I. This (13) Reed,W.; Guterman, L.; Tundo, P.; Fendler, J. H. J . Am. Chem. Soc. 1984, 106, 1897.
4592
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
I I
Feilchenfeld and Siiman
#
'A
\
C
1500
I \
I
RAMAN SHIFT, cm-'
zw
Figure 2. Time dependence of Raman spectra of chromate (5.0 X M) on colloidal silver in absence of PVP (spectra A-F) and Raman spectrum of chromate (5.0 X lo-' M) in aqueous solution (G). Elapsed time (min): (A) 5 ; (B) 35; ( C ) 65; (D) 125; (E) 185; (F) 1235. Experimental conditions: excitation wavelength, 488.0 nm Art; incident laser power, 100 mW; spectral slitwidth at 1000 c d , 7 c d ; photon counting time interval, 0.10 s; scan speed, 2 cm-'/s. v4 (368-cm-l) bands observed for Cr042- in solution.
1
I
1200
1 1000
I
1 I I 800 600 RAMAN SHIFT, cm-'
1
I 400
I 200
Figure 1. Raman spectra of oxoanions on colloidal silver (A, C, E) and in aqueous solution (B, D, F) with the following total anion concentrations and photon counting time intervals (5): (A) 1.0 X lo4 M CrOZ-, 0.050; (B) 0.20 M CrOZ-, 0.030;( C ) 5.0 X M Mood2-,0.80; (D) 0.20 M MOO:-, 0.030;(E) 5.0 X lo-' M WOZ-, 0.050; (F) 0.20 M WOl-, 0.030.Top spectra in B, D, F were taken with a 3.3-fold greater counting time inveral. Experimental conditions: excitation wavelength, 488.0 nm Art; incident laser power, 60 mW; spectral slitwidth at 1000 cm-', 7.0 cm-I; scan speed, 1 cm-l/s. The chromate on colloidal silver sample of spectrum A contained 0.6 mg/mL PVP band has been shifted by 50 cm-I from its position at 850 cm-I for Cr042-in solution. A bent bridge coordination for Cr042-on the silver particle surface gives three most probable geometrical arrangements: (1) monodentate coordination of to silver, assuming a C, overall point symmetry and a C3,local point symmetry for Cr042-;(2) bidentate coordination, assuming a C2? point symmetry; and (3) tridentate coordination, assuming a C3, point symmetry. Symmetry considerations alone should then give rise to multiple totally symmetric v(Cr0) bands for Cr042-on the surface. All three modes of surface coordination will give two Cr-O stretching bands. These bands are expected to be intense according to the surface Raman selection which stipulate that modes transforming like the radial polarizability component, azz,or having a part that transforms as a,, will be the surface active ones. Because of these selection rules, part of the asymmetric mode at 886 cm-' in Td CrOd2-is also observed as a medium-intensity band at 917 cm-' for Cr042-on Ag. In the surface Raman spectra of Cr042-on Ag the band at 353 cm-I assignable to the bending modes was observed as a single broad band similar in position to the closely spaced u2 (349-cm-l) and (14) Moskovits, M. Reu. Mod. Phys. 1985, 57, 783 (1 5 ) Creighton, J. A. Surf. Sci. 1983, 124, 209.
Enhanced Raman spectra of M004~and W042-on colloidal silver were also observed. The Raman spectrum of molybdate in aqueous solution is characterized by two relatively weak bands at 317 and 841 cm-I and a strong one at 898 cm-I. The fwhm (full width at half-maximum) of the strongest band is about 14 cm-I. When molybdate is added to silver sol, only one enhanced Raman band at 865 cm-l can be detected. This band is broader by a factor of 5.5 than the corresponding Raman band of the solution species and has a fwhm of about 77 cm-l. The Raman spectrum of tungstate in aqueous solution has two weak bands at 320 and 839 cm-I and an intense band at 936 cm-l. The fwhm of the strongest band is about 11 cm-'. When tungstate is added to silver sol, only one strong enhanced Raman band is observed at 895 cm-' with a shoulder, or weaker band, at 790 cm-l. The strong band is broader than the corresponding solution band by a factor of 6.5 and has a fwhm of 74 cm-l. This band appears first at 910 cm-l and then its position slowly decreases to about 895 cm-'. The solution Raman spectra of Mood2-and W042- show a reversal in the positions of v1 and v3 as compared to 00:- spectra, i.e., 1 9 occurs at higher frequency while v3 occurs at lower frequency. In the surface Raman spectra on colloidal silver, only a single broad band at 876 cm-I for MOO^^- and at 912 cm-' for W042-was observed. Thus, it appears that vI decreases in all three oxoanions upon adsorption on silver: in Cr042-from 853 to 800 cm-'; in MOO^^-' from 898 to 876 cm-I; and in W04*- from 936 to 9 12 cm-'. Since v3(Cr04*-) increased from 890 to 9 15 cm-I with adsorption, it seems probable that V3(M0042-) at 841 cm-] and u ~ ( W O ~ at~839 - ) cm-I have also increased to 876 and 912 cm-I, respectively, on Ag. Although the separation between v I and v, increased for Cr042-on Ag, the reversal in the positions of v1 and v3 in the solution spectra of MOO^^- and W042-, added to a similar trend for these anions, gives a decrease in the separation of v, and v3, so that the two bands are not resolved for MOO^^- and W041- on colloidal Ag. The bandwidths, fwhm, of the Raman bands at 915, 800, and 353 cm-' for Cr042-on colloidal silver are all about 5 times greater than those of the equivalent Raman bands for CrO," in solution. The Raman spectra of nonchromophoric Moo4*-and W042-show a very similar broadening of Raman bands at 876 and 912 cm-I to fwhm of 77 and 74 cm-I as compared to 96 cm-' for the most intense band at 800 cm-I for Cr042-on Ag. Since and WOq2-will give only SERS spectra with the 488.0-nm excitation
Aggregation Kinetics of Cr042-, MOO^^-, and W042(the lowest energy absorption bands16of MOO:- occur at 234 and 210 nm), their bandwidth broadening can be explained in two different ways: (1) by a large spread in frequencies of M04'vibrational modes on the surface due to heterogeneity in the types of adsorption sites or in the orientation of the ions with respect to the surface; (2) by a coverage effect on the surface, whereby the shorter average distances and therefore stronger interactions between adjacent anions on a particle surface favor fast vibrational relaxation and thus large bandwidths. Since Raman spectra taken at various surface coverages of MOO^^- (ctotal= 1.0 X to 5.0 X M) on colloidal silver did not show any change in the fwhm of SERS bands of MOO^^-, the latter explanation was discarded. Further, the fwhm of SERRS bands of C1-02- remains constant as a function of time (during which adsorption of GO4" on Ag and further aggregation of Ag particles occur), showing that the increasing intensity of SERS bands is not a function of Cr042coverage on colloidal silver which might change the fwhm by preferential and sequential filling of certain adsorption sites. There is also no shift in the C r 0 2 - SERRS band frequencies with time, which might be expected if coverage effects were operative; Le., expect higher frequencies at higher coverage due to less average interaction with Ag surface. Depolarization ratios, p, = ZL/Z,,, of the most intense SERS band in Cr04*-, MOO^^-, and W042- on colloidal silver were determined to be 0.45, 0.46,and 0.48,respectively. These observations are in agreement with previous results that have shown that totally symmetric A I modes of molecules in the gas phase or in solution, which gave depolarization ratios near zero, will become depolarized when the molecule is adsorbed on a surface. Additional bridge vibrations of I on the colloidal silver surface
I might also be observed for adsorbed Cr042- and the other oxoanions. In both monodentate and bidentate modes of coordination, the single symmetric stretch v,(I) of the bent bridge, which transforms as polarizability components ayy azzinstead of ayz, should be surface active. This mode might at first sight be assigned to a very weak to medium weak band at 558 cm-' in the enhanced Raman spectra of Cr042- on colloidal silver. A similar band, v,(Cr-O-Cr) is found17 at 565, 554 cm-' in the Raman spectrum of sodium dichromate. Also, a band at 601 cm-' in [Co(NH3),CrO4]C1 and at 551 cm-' in [ C O ( N H ~ ) ~ C ~ O ~has ] Nbeen O~ assigned3 to the monodentate I1 and to the bidentate I11 bridge
+
co
co
I11 us modes
in the respective chromate complexes. However, the SERS band at 558 cm-' was only observed when PVP was also present in the colloidal silver suspension. In the absence of PVP (Figure 2) no surface Raman band was detected at or near 558 cm-'. Since poly(4-vinylpyridinium dichromate), wherein the dichromate ion electrostatically bridges two adjacent and protonated pyridine side groups of the polymer chain, is available commercially as a polymeric oxidizing agent, it is not inconceivable that an analogous situation can develop when poly(vinylpyrro1idone) side groups are protonated. For chromate'* in basic solutions above pH 6 Cr0:- is the dominant species, but between pH 2 and pH 6, HCr04- and dichromate, Cr20T2-,are in equilibrium. At pH 6.5 of the silver sols a substantial population (20%) of protonated species, HCrO;, will therefore exist to allow partial dimerization to occur. The presence of dichromate on the surface of silver particles might also be detected from the higher position of an intense (16) Lever, A. B. P. Inorganic Electronic Spectroscopy, 2nd ed.; Elsevier:
Amsterdam, 1984. (17) Brown, R. G.; Ross, S. D. Spectrochim. Acta 1972, 28, 1263. (18) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 4th 4.; Wiley: New York, 1980; p 733.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4593 terminal Cr-0 stretching frequency at 902 m-'and much weaker band at 932 cm-l that occur in the resonance Raman spectrum M) taken of aqueous solutions of potassium dichromate (5.0 X with 488.0-nm excitation. However, the dichromate ion produced from chromate ion in our colloidal silver suspension is only a minor species as suggested by the relatively low intensity of the 558-cm-I surface Raman band. Under these circumstances any weak surface Raman bands assignable to Cr2072- in the 950-750-cm-' region would be eclipsed by the much stronger bands of the dominant adsorbed species, in the same spectral region. A 220-cm-l symmetric bending mode of the bridge that was observed17 for Cr2072-in solution and in the solid state was not resolved in our surface Raman spectra. It is well-known4 that the tendency of MOO^^- and W042- to form oligomers in aqueous solution is much greater than that of Cr02-. In the SERS spectra of WO2- on colloidal silver (Figure 1E and vide infra) it is apparent that there are many more weak bands in the 300-8OO-cm-' range than can be explained by the adsorption of the monomeric tungstate ion alone on the silver surface. All of these bands at 310, 388, 560, 671, and 800 cm-' grew with the same relative intensity as aggregation proceeded. These bands might be assignable to intermediates or products in the formation of isopolytungstate clusters. One mechanism4 for their formation in solution is thought to be the simple and successive addition of WOOtetrahedra. This process might be facilitated or even catalyzed by the adsorption and therefore concentration of W 0 4 units on a colloidal silver surface. Similar Raman bands in the 300-800-~m-~region were detectedIg from a polymeric molybdenum oxide layer on small silver particles that were prepared by evaporation of silver from a molybdenum boat into a reduced-pressure atmosphere of argon and oxygen. Polyoxoanion clusters of Mo(V1) or W(V1) invariably exhibit20J a very intense Raman band toward higher frequency of the vl(M-O) band of the parent monomer, M042-. Since this is not observed as an intense Raman band in our surface-enhanced Raman spectra of molybdate or tungstate on colloidal silver, we conclude that the polymeric species are only minor ones on the surface. Time Evolution of Surface Raman and Absorption Bands as a Function of Chromate Concentration. The effects of stabilizing polymer (PVP), residual citrate, and adsorbing chromate concentrations on the rate of coagulation of colloidal silver particles were initially noted. Two distinct regions of kinetic behavior appeared to exist. In region I with total chromate concentrations 1 .O X M or lower, the rate of coagulation of silver particles increased as the concentration of chromate ion was decreased. In region I1 for total chromate concentrations greater than 1.0 X loW3 M, the coagulation rate increased as the chromate concentration was raised. Surface Raman spectra for a typical measurement as a function M) on colloidal silver in the of time for chromate (5.0 X absence of PVP are shown in Figure 2. Since the sols without PVP were not stable, Le., they rapidly showed sedimentation of some silver particles, further investigation of the adsorption of chromate on colloidal silver as a function of adsorbate concentration was done in the presence of PVP. A series of mixtures was prepared, all of which contained the same amount of silver (about 0.02 g/L) treated with ion exchanger to a conductivity of about 40 @ cm-' and the same amount of PVP (0.6 mg/mL). The concentrations of chromate in the mixtures and their visible and SERS spectral characteristics are given in Table I. Mixtures 1-5 became red, the time needed to reach stability decreasing from several days to a few hours with decreasing chromate concentration. In the visible region the single particle absorption band at 400 nm decreased from an absorbance of 3.0 to about 1.5, and a new band appeared at 540 nm and reached an absorbance of (19) Schwab, S. D.; McCreery, R. L.; Cummings, K. D. J . Appl. Phys. 1985, 58, 355. (20) Rocchiccioli-Deltcheff, C.; Thouvenot, R.; Fouassier, M. Inorg. Chem. 1982, 21, 30. (21) Rocchiccioli-Deltcheff, C.; Fournier, M.; Franck, R.; Thouvenot, R. Inorg. Chem. 1983, 22, 207.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
4594
TABLE I: Adsorption of Chromate on Colloidal Silver'
silver sol-chromate mixture 1
total absorbance chromate concn, M at 400 nmb at 550 nm 0.92 1.0 x 10-3 >3.5 3.0 x 10-4 1.0 x 10-4 3.0 x 10-5 1.0 x 10-5 3.0 X 10" 1.0 x 10-6 3.0 x 10-7 1.0 x 10-7
2.5 1.75
1.so 1.65 >3.0 >3.0 >3.0 >3.0
0.95 1.08 1.15 1.oo
SERS band'
intensity, ISo5 100 118 119 116 118
"40 fin-' cm-I. bSumof absorbances of single particles of silver and chromate. Corrected for absorption.
TABLE II: Adsorption of Chromate on Colloidal Silver"
silver sol-chromate mixture 1 2d 3d
4d 5d
6 7 8 9
total chromate absorbance concn, M at 400 nmb at 560 nm >3.5 0.70 1.0 x 10-3 2.3 0.92 3.5 x 10-4 I .20 0.88 1.0 x 10-4 0.90 0.88 3.5 x 10-5 0.95 0.95 1.0 x 10-5 2.4 0.70 3.5 x 10-6 >3.0 1.0 x 10" 3.5 x 10-7 1.0 x 10-7
SERS band'
intensity, IBM) 1330
540 545 257 196
>3.0 >3.0
'4 pn-l cm-I. bSum of absorbances of single particles of silver and chromate. CCorrectedfor absorption. dMixtures 2, 3, 4, and 5 flocculated almost immediately. about 1.0 while the position of its maximum slowly moved to 560 nm. During this period the intensity of chromate SERRS bands increased to a constant maximum, having approximately the same value for all mixtures. Mixtures 6-9 showed no reaction whatsoever. All of these mixtures were stable for several weeks after their preparation. Since the previous measurements seemed to indicate that citrate still adsorbed on silver particles successfully competes with the chromate ion for adsorption sites when the chromate concentration M, a parallel series of experiments was made is below 1 .O X with silver sol containing a lower amount of citrate. In the second run the silver sol was treated with ion exchanger until the concm-'. Again, nine mixtures ductivity reached a value of 4 were prepared, all containing the same amounts of silver sol and PVP as before, but with the concentrations of chromate and results noted in Table 11. In addition, a blank containing no chromate was also prepared. Mixture 1 changed color from yellow to red very slowly, over a period of several days. This was accompanied by an increase in the intensity of the SERRS bands of chromate and of the visible absorption band appearing in the vicinity of 550 nm. No Raman bands of citrate were detected. In mixture 2 the color turned to red much faster than in the first experiment. Within a few hours the SERRS and visible absorption bands reached their maximum intensities. The sol coagulated and precipitated completely in less than 15 h. The sol mixtures 3, 4, and 5 all behaved in the same fashion: on addition of chromate, a strong red color appeared instantly and the solutions became turbid. The absorption band of single silver particles at 400 nm had an absorbance of about 1.O, much weaker than in the previous experiment. The band appearing in the visible also had a lower absorbance than previously (about 0.9), and its maximum was at about 560 nm from the beginning, showing the aggregates to be larger immediately. The SERRS signals, measured about 1 h after preparation, were of the same order of magnitude as in the last experiment, decreasing, however, from mixture 3 to mixture 5. No citrate bands were detected. These three mixtures coagulated and precipitated completely within 2-3 h. Mixture 6, which had shown no reaction in the previous series, now turned slowly to a deeper yellow color, and a shoulder appeared at 475
&-'
Feilchenfeld and Siiman nm on the single-particle absorption band. This shoulder later moved toward longer wavelengths up to 500 nm, while the overall absorption between 550 and 800 nm increased markedly. The Raman spectrum showed strong bands of citrate, enhanced by a factor of about 10 with respect to the blank, while the chromate bands could no longer be seen. The sol mixtures 7, 8, and 9 did not react to the addition of chromate. The mixtures of 1, 6, 7, 8, and 9 were stable for several weeks. From a comparison of the two series of obervations, it would seem that chromate has at least two different effects: one is to displace the adsorbed citrate from the silver surface, the other is to cause aggregation of the particles into increasingly larger clusters. When the concentration of the chromate is lower than 3.5 X lo4 M, it can no longer displace the citrate or cause further aggregation. In the 40 ~ f i - l cm-I sol, there was no effect of M or less; chromate on the sol at concentrations of 3.0 X in the 4 pfi-l cm-' sol, there was no effect at concentrations of 1.0 X M or less, but at a concentration of 3.5 X M (mixture 6) the chromate, through not displacing the citrate, was still able to cause further aggregation, strongly enhancing the intensity of the citrate SERS bands. The increased rates of coagulation of mixtures containing lower M) of coagulating amounts (from 1.0 X lo" M to 1.0 X agent, especially noticeable in the second run, can be understood if the silver particles experience a change in formal electrostatic charge from positive to negative upon addition of chromate ion. After exchange of excess and easily displaceable citrate and sodium ions with hydroxyl and hydrogen ions, the initial sol was left with a deficiency of charge originating from surface silver ions. As the point of zero charge of the silver particles was approached with ever smaller amounts of chromate ion addition (to 1 .O X M, mixture 5), the rate of coagulation increased. To avoid the complicating effects of particle charge on the kinetics of aggregation of these silver particles, further work on kinetics was restricted to the use of relatively high concentrations (>1.0 X M) of the adsorbing oxoanion. At these high initial oxoanion concentrations the characteristics of oxoanion adsorption on the surface and coagulation of the particles were considerably simplified. Kinetics of Adsorption and Aggregation of Chromate on Colloidal Silver. The kinetics behavior of mixtures with a concentration of 5.0 X M (A) and 2.5 X M (B) of CrO,*was more thoroughly investigated. The appearance of SERRS bands of Cr042-on silver and the disappearance of R R S bands of Cr042-in solution together with changes in visible absorption spectra of the sols were followed over several days, until the system stabilized or led to separation of some particles from the sol phase. Representative changes in Raman and absorption spectra are shown in Figures 3 and 4 for run A. Relative Raman intensity (Z) of the 800-, 915-, and 353-cm-I bands of adsorbed Cr042-and of the 850-cm-' band of Cr04*- in solution as well as the absorbance ( A ) of the silver sol at 550 nm are shown as a function of the time elapsed after mixing of Cr042-with Ag sol in Figures 5 and 6 for runs A and B, respectively. The kinetics plots in Figures 5 and 6 appear to show that step 1, adsorption of the chromate ion onto the silver surface by displacement of water, citrate ion, or PVP units represented by adsorbed citrate
+ X2- in solution Z= ki
k-i
adsorbed Xz-
+ citrate in solution
and step 2, aggregation of particles that contain adsorbed chromate ion to form clusters of n-mers, go through an initial induction stage. The evidence for this lies in the steeper slopes at the beginning of kinetics runs A and B for IRamnSO' vs. elapsed time as compared to the initial slope of the A550501 vs. elapsed time curve. In the interval of 0 to 100 min surface Raman band intensities are increasing rapidly while absorbance due to formation of aggregates of silver particles is increasing very slowly. In addition, there is a discontinuity in both curves after 100 min. Since log (AD vs. elapsed time plots (supplementary Figures 1' and 2'), where AI = I , - I , and I , was the maximum band
-
-
The Journal of Physical Chemistry, Vol. 90, No. 19, I986 4595
and W04z-
Aggregation Kinetics of Cr042-,
0.90 0.60 0.70 0.60
0.50
FI
0.40
0.30 0.20 0.10
3500 ELAPSED TIME, min
Figure 6. Time evolution of surface Raman band intenisty at 805 (O), 915 (O),and 350 (A) cm-I, solution Raman band intensity at 850 cm-’ (X), and absorption band intensity at 550 nm ( 0 )for chromate (2.5 X M) on colloidal silver in the presence of PVP. RAMAN SHIFT. cm“
Figure 3. Time dependence of Raman spectra of chromate (5.0 X lo-’ M) on colloidal silver in the presence of PVP. Elapsed time (min): (A) 35; (B) 79; (C) 127; (D) 180; (E) 240; (F)390. Experimental conditions: excitation wavelength, 488.0 nm Ar’; incident laser power, 60 mW; spectral slitwidth at 1000 cm-’, 7.0 cm-I; photon counting time interval, 0.10 s; scan speed, 1 cm-’/s.
0.00 w
a
0.40
00.0 400
450
500 .
550
600
650 2
700
750
000 0
WAVELENGTH, nm
Figure 4. Time dependence of absorption spectra of chromate (5.0 X IO-’ M) on colloidal silver in the presence of PVP. Elapsed time (min): (A) 10; (B) 220; (C) 370; (D) 640; (E) 1320; (F) 2225; (G) 3085.
where D is the particle diffusivity, r is the particle radius, and N i s the number of each particle. Since the hydrosol is dominated by singlets, we expect singlet-singlet aggregation to dominate over cluster-cluster aggregation and singlet addition to clusters. Also, the development of an absorption band of constant position and width at 550 nm after an initial induction period suggests that the aggregates formed are of similar structure and size. This is in accord with previous observationsz4 that size distributions in coagulated sols were “self-preserving” after some initial period of time for systems that were initially either homogeneous or heterogeneous in size distribution. The results of this similarity theory24have been shown to satisfy Smoluchowski’s equations of ~ coagulation by Brownian motion. Since our Raman and absorption measurements were used to follow the formation of aggregates of primary silver particles, whose cluster size distributions sometimes showed a “selfpreserving” form, the kinetics of the reaction can be described by a generalized Smoluchowski equation of the form2s-27
1
2oc
\
X
0.70 0.60 g
0.40 0.30 0.20 0.10
O
lecular rate equations, there appear to be conditions under which a pseudo-first-order rate law is obeyed. We have previously shown12 that the parent silver sol consists mainly of single particles and a few small clusters. The collision frequency of two particles, i and j, of different size, under Brownian diffusion conditions, was shown by Smoluchowski to be J i j = 4a(Q + D,)(r, + r,)N,Nj
T
I
500
1000
2000 I500 ELAPSED TIME, min
2500
3000
3500
Figure 5. Time evolution of surface Raman band intensity at 805 ( O ) , 915 ( O ) , and 350 (A) cm-l, solution Raman band intensity at 850 cm-l (X), and absorption band intensity at 550 nm ( 0 )for chromate (5.0 X lo-’ M) on colloidal silver in the presence of PVP.
intensity at the end point and I, was the band intensity at time t , were linear in the intermediate time range, the data for runs A and B followed apparent first-order kinetics in this time regime. Even though colloid aggregation is a bimolecular process and its dynamics have been d e s ~ r i b e d * by ~ s ~Smoluchowski ~ with bimo(22) Von Smoluchowski, M. Phys. Z . 1916, 17, 557, 5 8 5 .
The concentration of clusters of size n, c,, will change according to a bimolecular rate law with rate constants a. The first set of terms in the equation represents the rate of formation of n-mers from all combinations of clusters which together contain n units. The second term represents the rate of disappearance of n-mers by their pairing with all other possible n’-mers. To account for the observed overall pseudo-first-order rate process, we propose that the rate of adsorption of X2- on the silver particles and the rate of aggregation of these particles with adsorbed Xz- reaches a steady state after some initial induction period. With this assumption the functional form of the size distribution in the clusters formed need not be specified to analyze the kinetics of their formation. Further, desorption of X2- from the silver surface is assumed to be a very slow process. This is understandable since the residual concentration of citrate for a specific conductivity of 40 p W cm-’ (23) Von Smoluchowski, M. Z . Phys. Chem., Stoechiom. Verwandtschaftsl. 1917, 92, 129. (24) Swift, D.L.; Friedlander, S. K. J . Colloid Sci. 1964, 19, 621. (25) Drake, R. L. In Topics in Current Aerosol Research, Part 2; Hidy, G. M., Brock, J. R., Eds.; Pergamon: New York, 1972; Vol. 3. (26) Cohen, R. J.; Benedek, G. B. J . Phys. Chem. 1982, 86, 3696. (27) Bowen, M. S.; Broide, M. L.; Cohen, R. J. J . Colloid Interface Sci. 1985, 105, 617.
4596
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
Feilchenfeld and Siiman
-
is estimated to be 1 X M and water and PVP units are weakly bonding adsorbates. Also, for the high concentrations of X” M) used, the solution concentration of X2- is effectively M represents the maximum amount constant since -3-4 X of adsorbed X2- for the silver concentrations used. Under these conditions adsorption28 on a nonporous substrate will be a pseudo-first-order rate process with
t v)
2
w t-
rateads= k , [ads] [X2-l0
f
a
and a pseudo-first-order rate constant k‘ = kl [X2-l0; [ads] is the concentration of available SERS active adsorption sites. Thus, the overall rate process that was followed by changes in either surface Raman band intensity ( r ) or absorption band intensity ( A ) can be expressed in the form
z
U
m
z 4
I
4
a
I, = I , [ 1 - e-kr]
or -
log AI = log I , -
2.303
where A I = I , - I,. The rate constants k’, derived from the slope vs. time plots (Figures 1’ and 2’) in the linear region of log (us@,) of the curves, were 7.6 X and 3.7 X s-l from data for the 800-cm-I SERRS band of CrOd2-on colloidal silver in run A (5.0 X M = [X*-],) and run B (2.5 X M = [X2-],), M-I S-I in respectively. Therefore k l = k’/[X2-], = 1.5 X this chromate concentration range. Half-lives, tIl2values, obtained by inspection of Ivs. time curves in Figures 5 (run A) and 6 (run B) were -250 and -400 min. These are -100 min longer and show that the first-order rate process begins after an initial period of 100 min in both runs with chromate ion. Rate constants for the same process derived from kinetic data (Figures 1’ and 2’) of the absorbance increment (AA = A , - A,) of aggregates at 500 nm were 5.7 X and 3.0 X s-I for runs A and B, respectively. These constants are about 20% lower than the ones determined from surface Raman spectra and might reflect the fact that not all aggregates contribute equally to the growth of the surface Raman signal from chromate. Part of the growth in the chromate surface Raman bands may originate from clusters of primary particles that do not absorb at the main satellite peak in adsorption at 550 nm. The tracking between Raman band and absorption band intensities with time was then further exvs. Asm2,shown for runs A amined graphically in a plot6 of IBoo and B in Figure 7. Both curves are very similar, showing an initial steep rise in Raman band intensity followed by a smaller growth in Raman signal but more rapid increase in absorption band intensity. This may indicate more cluster-cluster aggregation, which does not influence the growth of SERS signal as much as the absorbance from larger particles at longer times. The RRS intensity at 850 cm-I from chromate in solution (5.0 X or 2.5 X M) should be constant for the small amount of (-3-4 X M) that adsorbs to the silver particle surface. However, because of the increasing broad inelastic continuum29that accompanies the SERS from discrete vibrational modes of the adsorbed Cr042-the RRS band intensity of Cr0:in solution shows an apparent decrease with time. The rate of decrease in this band can then be equated with the rate of increase in the intensity of the continuum. This also shows pseudofirst-order kinetics behavior from log AI vs. time plots and gives rate constants 4.2 X IOW4and 1.1 X s-* for 5.0 X and M total Crop” concentrations, respectively. The higher 2.5 X rate constants for the rise in the intensity of the continuum imply that Raman spectra taken with a single wavelength of excitation and absorption measured at a single wavelength do not probe the entire active surface. Time Dependence of SERS and Absorption Band Intensities of Tungstate Ion on Colloidal Silver. Molybdate and tungstate
-
(28) Boyd, G. E.; Adamson, A . W.; Myers, L. S., Jr., J . Am. Chem. SOC. 1941,69, 2836.
(29) Chang, R. K.; Laube, B. L. CRC Crit. Reu. Solid State Mater. Sci. 1984, 12, 1 .
0 0
k t
0.2 0.4 0.6 (ABSORBANCE 1 2
0.8
Figure 7. Raman band intensity (IBooor 19,*) vs. (absorbance)2,ASoo2, for chromate and tungstate on colloidal silver: CrO?-, 5.0 X M, (El), and 2.5 X 10-3 M (0); WO?-,5.0 X IO-’ M (A) and 3.5 X loT3 M (0).
mixtures with colloidal silver (conductivity of 40 p0-I cm-I) showed similar kinetic behavior in the appearance of surface Raman bands and development of absorption spectra. The addition of PVP as a stabilizer to prevent sedimentation of silver particles was not required in the presence of these ions. Differences in the solution chemistry of Cr042-vs. M 0 0 ~ ~ - ’ a nW042d appear to influence the aggregation kinetics of silver particles in their presence. In contrast to Cr04*-in aqueous solution, for W0:- upon addition of acid the equilibria30 are
+ H+ G HW04HW04- + H+ 9 H2W04 W042-
K = lo3.’ K = 104.6
Since the second reaction has such a high value for its equilibrium constant relative to the first one, the dimerization reaction of HWO, does not occur for Wvl. Rather, only polynuclear species4 of seven or more W(V1) ions are detectable in equilibrium studies. Thus, this polymerization of tungstate as well as the aggregation of silver particles with adsorbed WO2- may easily be hampered at low concentrations of WOd2-mixtures with silver sol at pH 6.5 since the average number of protonated species, HW04-, will be relatively lower (smaller equilibrium constants) than in the chromate mixtures. Moreover, unlike the chromate ion which absorbs maximally at 370 nm and thus overlaps extensively with the singlet absorption band of colloidal silver at 400 nm, molybdate and tungstate ions absorb at wavelengths e 3 0 0 nm, so that their absorption bands do not overlap with the absorption band of single particles of silver at 400 nm. Raman and absorption spectra for a typical run with M total concentration of W042-are shown in Figures a 5.0 X 8 and 9, respectively. Relative SERS band intensity of W042on colloidal silver at 9 12 cm-’ and absorption band intensity of aggregates of silver particles at 500 nm and singlets at 400 nm were monitored as a function of time. The results are shown for two different total concentrations of tungstate in Figures 10 (3.5 X M) and 11 (5.0 X M). Kinetic plots of log (AI912),log (AAsw), or log (AA,,) vs. elapsed time shown in supplementary Figures 3’ and 4’ again showed linear behavior in the intermediate time domain. Thus, pseudo-first-order rate constants, derived in the same way as for M W042- were chromate ion on colloidal silver, for 5.0 X 1.5 X 1.3 X and 6.6 X s-I from AI912,A&, and AA4,o data, respectively. At the lower W04*- concentration of 3.5 X IO-) M the same constants were 2.1 X lo”, 4.2 X lo”, and 3.2 X lo6 s-l. Correlation between surface Raman intensity with (30) Schwarzenbach, G.;Geier, G.; Littler, J . Helu. Chim. Acta 1962, 45, 2601.
Aggregation Kinetics of Cr042-, MOO^^-, and WOd2I
I
I
I
I
I
I
1 2 1-
I
1
1
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4597
1
1
4100min.
1
~
1400
1
1
1200
1
1
1000
1
l
1
1
so0
800
1
400
1
1
200
RAMAN SHIFT, cm-l Figure 8. Time dependence of SERS spectra of tungstate (5.0 X M) on colloidal silver. Experimental conditions: same as in Figure 3. 4.0
I
I
I
I
I
i
tionship between SERS intensity from molecules adsorbed on colloidal metal particles in aggregates and the size of such aggregates is lacking. Thus, it is not possible, with certainty, to say, for example, that SERS intensity scales linearly as the mean radius, R , of the aggregates, surface area ( -R2), volume (-It3), or the number of primary particles that the aggregate contains. In what follows, we indirectly infer such a relationship by experimentally determining the rate law for SERS intensity and using an appropriate rate law (classical or fractal) for the size of aggregates in the diffusion-limited regime. In recent ana lyse^^',^^ of kinetically formed colloidal gold aggregates containing monodisperse single particles by transmission electron microscopy, a power law dependence of mass on the size of various aggregates was found. The clusters of gold particles were shown within limits to exhibit a scale invariance which described them as fractal objects with a fractal dimension, D,in RD,between their mass and size. D was the relationship, M found to be 1.75, in agreement with theoretical predictions for cluster-cluster aggregation in the diffusion-controlled limit. The method was also extended to the results of dynamic light scattering studies32on kinetically evolving clusters of gold particles. In this work, fast and slow aggregation showed different functional forms in the dependence of R H ,the mean effective hydrodynamic radius of clusters, on time. In the fast or diffusion-limited regime the shape of the growth curve was hyperbolic and appeared to reach a limiting radius at long times. Modeling of this curve suggested a scaling law of the type R H t i l D . In the slow regime, an exponential cluster growth curve was found and a different “sticking time” limited regime was modeled to reproduce the divergent behavior in RH with time. Since the silver surface represented by the SERS active sites on kinetically formed aggregates of silver particles is probed in the Raman scattering experiments of the present work, this surface of fractal objects (aggregates of silver particles) may also manifest fractal behavior and thus a fractal dimension. The intensity (Z) of the SERS bands of Cr042-and W042-that were measured in the kinetics runs is proportional to the number of these scatterers on the surface active sites of aggregates of silver particles or, in turn, to the surface area represented by the occupied active sites. Therefore, we have first constructed log-log plots of I vs. time (Figure 12) for the kinetics runs with both Cr04*- and W042to detect any power law dependence of I on time. The curves with Cr0,2- were not linear and may reflect the influence of PVP on the aggregation process. However, both runs with WO>- showed extensive regions of linearity in the log I vs. log t curves. Also, the I vs. time curves of Figures 10 and 11 for W0,2- in both slow and fast aggregation regimes showed the same functional form, making facile comparison of the kinetics of aggregation at the two limits possible. The classical rate law for diffusion-limited a g g r e g a t i ~ ngives ~ ~ R;(t) - t , R, being the radius of gyration of the aggregate. If the entire surface area in aggregates of silver particles were coated with W042-and if all adsorption sites were R2 t . Alternatively, if I surface Raman active, then I R , then I til2. Neither scaling law was observed in our kinetics results with W042-on colloidal Ag. Rather, the exponent fl in I to was found to be 0.56 in the fast aggregation limit and 0.78 in the slow limit. In recent simulation^^^-^^ of the fractal growth of diffusion-limited aggregates a rate law, R3I2(t) t , was predicted in three dimensions. If this relationship were used with I R2, an I t4I3 dependence would be obtained. However, a more reasonable value of fl = 2/3 is predicted when it is assumed that I scales as R . This latter value of the power law exponent lies within the range of our observed values. In both cases, it appears necessary that SERS intensity, I a (perimeter in clusters) 0: R rather than I a (total surface area of particles in clusters)
- -
-
WAVELENGTH, nm Figure 9. Time dependence of absorption spectra of tungstate (5.0 X lo-’ M)on colloidal silver. Elapsed time (min): (1) 70;(2) 190;(3) 590;(4)
1190;(5) 4080.
488.0-nm excitation and absorbance at 500 nm for W042- on colloidal silver as shown in a plot of IgI2vs. ASm2in Figure 7 showed linear behavior over a wide time range. At the higher tungstate concentration the agreement between rate constants determined from Raman and absorption data for the formation of aggregates was very good; however, the rate constant for the disappearance of primary singlet particles was lower by a factor of 2. This may imply that some cluster aggregates are forming or some rearrangement of primary particles in aggregates already formed is occurring. These processes do not affect the absorbance of singlets at 400 nm but would influence the surface Raman band intensity and the absorbance of aggregated particles. In contrast to the results with chromate ion, an increase in total tungstate ion concentration by a factor of 1.4 leads to a very large increase in the pseudo-first-order rate constant by a factor of 71. This suggests a very high order dependence on tungstate concentration in the adsorption and subsequent aggregation process. Using the ratio of pseudo-first-order rate constants, k’ = k,[WO>-lo, at two different tungstate concentrations but with an nth-order tungstate concentration dependence, we have
-
k1(5.0 x k1(3.5 x 10-3)”
- 1.5 x 10-4 s-i
[
= 71, n = 12 2.1 x 10-6 s-i or It appears that adsorption of about 12 tungstate monomers is required before aggregation proceeds. This is consistent with the tendency of tungstate to form clusters of this size in solution under some conditions. In fact, several isopoly tungstates that are dodecamers of composition [W12042H12]1b and [Wi2040H2J6 have been isolated from s o l ~ t i o n . ~ Fractal Description of the SERS Active Surface of Colloidal Silver Aggregates. Direct information on the functional rela-
-
-
- -
-
-
-
-
(31) Weitz, D. A.; Oliveria, M. Phys. Reu. Letr. 1984, 52, 1433. (32) Weitz, D. A.; Huang, J. S. In Kinetics of Aggregation and Gelation; Family, F., Landau, D. P., Eds.; Elsevier/North-Holland: Amsterdam, 1984. (33) Deutch, J. M.; Meakin, P. J . Chem. Phys. 1983, 78, 2093. (34) Hentschel, H. G . E.; Deutch, J. M.; Meakin,P.J . Chem. Phys. 1984, 81, 2496. (35) Witten, T. A,; Sander, L. M. Phys. Reu. Lett. 1981, 47, 1400.
4598 The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
Feilchenfeld and Siiman
3.8
3.6
D 1.4g
%m P
L2
t 0 m
B
ELAPSEC1
TIME
, min.
I 12.000
I
I
14,000
16,000
I
Figure 10. Time evolution of SERS band intensity of 912 cm-' (0)and absorption band intensity at 500 nm (0) for tungstate (3.5 X
silver. "
I
"0
,
,
5w
1000
,
,
,
zow ELAPSED TIME, min ,500
- -
--
, 3
2500
1.1 m
35woo
Figure 11. Time evolution of SERS band intensity at 9 1 2 cm-I (0)and absorption band intensity at 500 nm (0)for tungstate (5.0 XlO" M) on colloidal silver.
-
0
0 0
I^
I
I
I
I
2
3
4
5
LOG t Figure 12. Power law dependence of surface Raman band intensity, I , with time, t , for aggregation of silver particles induced by Cr0,2- 5 . 0 X lo-' M (0)and 2.5 X lo-' M (A)and by WOd2- 5.0 X lo-' M (0) and 3.5
X 10-3 M
M) on colloidal
be obtainable at present; however, as long as the same scaling law is used we feel justified in comparing D values since the functional forms of the I vs. time curves were the same in the fast and slow R t'IDscaling and aggregation regimes. D is 1.8 from I R t'/(*+&d)~ c a l i n g in ~ ~our - ~fast ~ aggregation 2.8 from I M. The first limit at a total tungstate concentration of 5.0 X value is very similar to the one obtained in p r e v i o u ~analyses ~~*~~ of mass and size of clusters ( M RD)as well as size and time of kinetically evolving clusters (RH tilD) in the diffusion-limited aggregation regime. At this limit every collision between two particles leads to a sticking together of the particles. Since there is little time to examine the most favored orientations for the sticking together of two particles, this situation gives highly branched clusters of particles with the branches distributed randomly in space. This was observed in transmission electron micrographs when aqueous gold sols were aggregated3I with the addition of a small amount of pyridine and when red Carey Lea silver sols were similarly analyzed by us.12 At the lower W042-concentration the rate constant was about tlID 102-foldlower and the fractal dimensions, D = 1.3 from I and D = 2.3 from I t1/(2eo-d), were also considerably smaller. We propose that the lower value of D might be expected for a particular case of slow aggregation in which all collisions between two particles are not productive. Only collisions between particles that are most favorably oriented give aggregates that stick together. Since repulsions between particles are minimized when single particles add on to produce linear chains6 rather than add on to the belly of a doublet or any other multiplet and thus experience the repulsions from two or more particles, this situation would give preference to the formation of linear chains by adding on singlets. A preponderance of linear chains would explain the much lower fractal dimension in the slow aggregation case as the favored formation of linear chain aggregates would give a fractal dimension close to d = 1. Moreover, recent36high-resolution electron micrographs of silver particles from the parent Carey Lea sol with adsorbed citrate, which we have used in the present work, have shown that the particles are predominantly pentagonal biprisms or decahedra with triangular faces. Where aggregation into clusters of silver particles was observed under the microscope, it was mainly limited to short chains of individual particles. Catalytically active sites37on typical metal surfaces consist of energy-rich sites, namely, steps, ridges, terraces, kinks, edges, corners, etc. However, for many chemical
- -
.*;e
).O
(0).
0: R2 for agreement with our power law depencence of I on time. Similar arguments made with a dependence of I on the number of particles, N , or volume show that the exponent, p, will be greater than unity. We tentatively suggest that the exponent in our observed power law dependence of surface Raman intensity on time, I t@,might also be equated in the same way, @ = 1/D, as in the diffusionlimited regime of the dynamic light scattering experiments with gold colloids. A correct value of the fractal dimension may not
-
-
( 3 6 ) Heard, S. M.; Grieser, F.; Barraclough, C. G.; Sanders, J. V. J . Colloid Interface Sci. 1983, 93, 545. (37) Taylor, H. S. Proc. R.SOC.London, A 1925, A108, 105.
J. Phys. Chem. 1986, 90, 4599-4603 reactions on the surface of metal colloids all the adsorption sites were shown3*to be catalytically active. This is probably not true of SERS active sites on colloidal metal particles. Single and primary metal particles have the same edges, corners, etc. that occur in clusters of particles, but do not exhibit any detectable SERS enhancements. We have examined a model in which a chain aggregate was constructed by sharing faces, edges, or corners of decahedra. Between each pair of adjacent particles in the chain there are wedge-shaped cavities of variable apical angle in which faces, edges, and/or corners form parts of the wedge cavity. This particular set of shared faces, edges, and corners may represent the SERS active surface and also form a fractal curve. This is not inconceivable since the boundary of the face in a multifaceted (38) Turkevich, J. In Heterogeneous Catalysis: Selecied American Histories; Davis, B. H., Hettinger, W. P., Jr., Eds.; ACS Symposium Series 22; Amercian Chemical Society: Washington, DC, 1983. (39) 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 groups 3 through 12, and the pblock elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.&, I11 3 and 13.)
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4599
crystal does form a fractal structure. The edges and corners do not represent discontinuities; rather they are smoothed over on the atomic scale by silver atoms of finite surface area. Much of the heterogeneity in adsorption of Cr042-, MOO^^-, and W042on aggregates of silver particles, as reflected in the large bandwidths of SERS bands, probably arises from adsorption on different types of SERS active sites, Le., faces, edges, and corners. For example, tridentate coordination of the oxoanion may be the preferred mode on a face, bidentate, on an edge, and monodentate, on a corner. Acknowledgment. This work was supported by Army Research Office Grant DAAG29-85-K-0102, by N I H Grant GM-30904, and by N S F Grant CHE-801144. We thank Dr. Lee Guterman, who carried out the light-scattering measurements. Registry No. PVP, 9003-39-8; AG 501-X8, 75444-61-0; CrO:-, 13907-45-4; Mood2-, 14259-85-9; WO:-, 1431 1-52-5; Ag, 7440-22-4; sodium citrate, 994-36-5.
Supplementary Material Available: Figures 1r-4r (4 pages) showing first-order rate dependence of surface Raman band intensity (AI) and absorbance (AA)on time in intermediate time range. Ordering information is given on any current masthead page.
Reaction of N20, with H20 on Carbonaceous Surfaces L. Brouwer; M. J. Rossi,* and D. M. Golden Department of Chemical Kinetics, Chemical Physics Laboratory, SRI International, Menlo Park, California 94025 (Received: December 6, 1985; In Final Form: March 24, 1986)
The heterogeneous reaction of N2O5 with commercially available ground charcoal in the absence of H 2 0revealed a physisorption process (y = 3 X together with a redox reaction generating mostly NO. Slow H N 0 3 formation was the result of the interaction of N 2 0 Swith H 2 0 that was still adsorbed after prolonged pumping at lo4 Torr. In the presence of H20, the same processes with y = 5 X lo-' are observed. The redox reaction dominates in the early stages of the reaction, whereas the hydrolysis gains importance later at the expense of the redox reaction. The rate law for HNO, generation was found to be d[HNO,]/dt = kbi[H20][N2O5]with kbi, the effective bimolecular rate constants, for 10 mg of carbon being (1.6 & 0.3) X cm3/s.
Introduction The chemistry of the atmosphere is generally thought of in terms of gas-phase reactions and photoprocesses, but given the presence of various particles and liquid droplets, the importance of certain competing heterogeneous processes has also been postulated.' In the stratosphere, the collision frequency of a gas molecule s-', and thus very few with an average particle is about processes, even if unit efficient, can compete with the gas-phase chemistry. However, it has been suggested* that some heterogeneous reactions of N2O5 might account for observed inconsistencies in the measured seasonal NO, variations. In the troposphere, there are considerably more collisions between gas molecules and particles. The collision frequency in a highly polluted urban environment is about 1 s-I, and loss processes with efficiencies of even lo4 can compete with gas-phase processes. Dinitrogen pentoxide, N2O5, is mainly formed through recombination of NO2 and NO3 radicals throughout the atmosphere, that is, from the lower troposphere to the stratosphere. However, the homogeneous reaction of N205 with H 2 0is slow due to the closed-shell nature of both reaction partners. An interesting possibility for the potential importance of the N2O5 hydrolysis to nitric acid in the atmosphere would be its catalysis on small 'Postdoctoral Research Associate. Present address: Institut fur Physikalische Chemie, Universitiit Gtittingen, West Germany.
aerosol particles with surfaces like carbonaceous material or sulfuric acid. A sufficiently rapid effective bimolecular rate constant for reaction 1 could make this process an important sink for NO,. N2O5
+ H20
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2HN03
In this work we investigate the interaction of gaseous N2O5 with a carbonaceous surface, in both the absence and presence of H20. Two questions were of prime interest to us: First, what is the nature of the products that result from this interaction? Second, if HNO, is a major product, what is its effective rate of formation due to a heterogeneous mechanism? Due to the fact that in this phase of our research we were primarily interested in the chemical aspect of this gassurface interaction, we did not attempt detailed surface characterization. A simple commercially available carbon substrate was used. It was inevitable that the surface condition of the carbon sample changed over time, and therefore small changes in the quantitative parameters of the gas-solid interaction had to be expected. However, in no instance did this uncertainty affect the conclusions, and in general the self-consistency of the data is surprisingly good. ( 1 ) Heikes, B. G.; Thompson, A. M. J . Geophy. Res. A 1983, 88, 883. (2) Ridley, B. A.; et al. J . Geophys. Res., A 1984, 89, 4191.
0022-3654/86/2090-4599!$01 .50/0 0 1986 American Chemical Society
