J. Phys. Chem. 1996, 100, 1779-1785
1779
Reduction of Silver Ions to a Colloid by Eriochrome Black T X. Zhai and S. Efrima* Department of Chemistry, Ben Gurion UniVersity of the NegeV, P.O.B. 653, Beer SheVa, Israel 84105 ReceiVed: July 6, 1995; In Final Form: October 11, 1995X
2-Hydroxy-1-(1-hydroxy-2-naphthylazo)-6-nitronaphthalene-4-sulfonic acid sodium salt (Eriochrome Black T, EBT) dye reduces silver ions in an aqueous solution, producing a stable colloidal suspension. The kinetics of the initial stage, monitored by UV-visible absorbance spectroscopy, are characterized by kinetic equations of a complex form, consisting of at least two distinct rate reactions. The reaction order for the dye in the partial reactions is 2-3, consistent with its involvement in the reduction as well as in the stabilization of the colloidal nuclei. The reaction order for silver ions is ∼1, indicating that the silver-dye interaction is the main factor determining the nucleation. The activation barriers are found to be in the range 73-120 kJ/mol, excluding diffusion as the controlling mechanism. The activation energy is interpreted in terms of the formation of silver nuclei of a critical size consisting of 50-80 silver atoms. Raman spectroscopy shows that the EBT molecules break in the process into smaller fragments which adsorb on the colloidal particles.
Introduction The production of metal colloids by the reduction of their ions in solution involves two distinct stages: nucleation and growth.1 The former requires relatively high activation energies associated with the high area/volume ratio of the embryo particles, while the latter is usually characterized by lower potential energy barriers and is often diffusion controlled. The relative rates of these two processes determine the final size distribution of the colloid. An increase of the nucleation rate relative to the rate of growth generally results in a higher number concentration of a finer dispersion. The relative rates of nucleation and growth can be affected by many of the control parameters of the system: the concentration of the reactants, the potency of the reductant, the pH, and the temperature. They can be influenced also by other constituents of the system. For instance, molecules may adsorb onto the colloidal particles, at various stages of the entire process, and modify the rate of the reaction at that specific stage. Additives may also form complexes with the reacting metal ions, effectively reducing the concentration of the free ions, on the one hand, and opening new channels for reaction, on the other. As a group, organic dye molecules can be especially effective due to the highly extended π system they usually possess. Also, the presence of ionic or polar functional groups, or groups containing nonbonding electron pairs (amines, sulfides, etc.), that may be active ligands, makes them especially active. In a recent report2a we discussed the effect of Alizarin Yellow 2G (AY) on the reduction of silver ions by hydrazine, giving a silver colloid confined to the water/chlorobutane interface. This was in a macroemulsion, metal liquidlike film (ME-MELLF3,4). We have seen that AY, by adsorption at the very early stages of nucleation, accelerates this stage compared to the subsequent growth. A similar effect was seen also for dithizone.2b These studies were facilitated by using Raman spectroscopy, especially surface-enhanced Raman spectroscopy (SERS) to monitor the dye. Here we report on the effect of 2-hydroxy-1-(1-hydroxy-2naphthylazo)-6-nitronaphthalene-4-sulfonic acid sodium salt (Eriochrome Black T, EBT) dye (Figure 1) on the production of a silver colloid. The main point here is that EBT is, in itself, an efficient reductant of silver, and no additional reductant is required. Thus, in addition to the indirect role of the dye X
Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1779$12.00/0
Figure 1. Molecular formula of EBT and its resonance structures: (a) pH < 5; (b) 7 < pH < 10; (c) pH > 12.
described above, EBT is active in the reduction process itself. We focus on the initial stages of the reaction, when nucleation is the dominant process, and follow the reaction kinetics. The complexity of this stage suggests that the chemical rate equations will not be of a simple form. Also one should expect the activation barriers to be considerably higher than that of diffusion-controlled processes. These expectations are borne out by the experiment, as will be described below. Raman spectroscopy and SERS were used here to monitor the adsorbed dye. UV-visible absorption spectroscopy was applied to follow the production of the colloid. Experimental Section Silver nitrate solutions were made basic with ammonia to the point immediately after the silver oxide becomes soluble, at pH ∼10. EBT (Merck) solutions at pH 5 were freshly prepared for every set of experiments and were kept in the dark. The water is purified using an E-Pure Barnsted system, giving 18 MΩ resistivity. The temperature was controlled within 0.1 © 1996 American Chemical Society
1780 J. Phys. Chem., Vol. 100, No. 5, 1996
Figure 2. UV-visible absorption spectra of 1.57 × 10-4 M EBT at pH (a) 5.1, (b) 9, and (c) 12.5.
°C during the reaction and the UV-visible measurements. Usually the temperature was set to 25 °C, except when stated otherwise. The absorption spectra were taken with a 8452A HP diode array spectrophotometer in the range 190-820 nm, with a resolution of 2 nm. Generally, we used 0.5 s exposure times and a cycle of 2 s. A 1 cm quartz cuvette was used. Raman spectroscopy was taken with a coherent Innova 90/4 argon ion laser operating at 514.5 nm, typically with a power 200 mW. The dispersion system was a Spex 1403 double monochromator equipped with 300 groove/mm ruled gratings. The entrance slit was set at 500 µm, and the two intermediate slits were kept at 1 cm. The detector was a Princeton Instruments OSMA multichannel analyzer with a 1024G IRY intensified diode array and a ST-120 controller interface with a PC microcomputer. The resolution was 1.5 cm-1 per diode, i.e. an effective resolution of 5 cm-1, taking into account diode cross-talk. Mass spectrometry was carried out on an AutoSpec E HRMS Fisions-VG machine using a FAB+ (gun Cs+) ionization mode. The matrix was glycerol and the mass range was 100-1500 Da. Results The EBT molecule has two acidic protons in addition to that of the sulfonic group. Utilizing spectrophotometric titrations, we found the corresponding pKa values to be 6.44 ( 0.15 and 11.11 ( 0.25. The possible main electronic resonance structures are given in Figure 1. The first ionization is stabilized by molecular resonance structures involving a decrease in the bond order of the nitrogen-nitrogen bond. This rationalizes the reduction of the pKa from 9.85 found for R-naphthol and 9.63 for β-naphthol5 to 6.44 found here. The negative electrical charges on both sides of the molecule most probably exert a strain on the nitrogen-nitrogen bond and weakens it further. The second ionization does not contribute any new resonance structures but will tend to impart a lower weight to the structures that concentrate the charges near the sulfonic group (Figure 1b,c). The weakening of the nitrogen-nitrogen bond due to the repulsion of the charges should be more significant. The UV-visible absorbance spectra associated with the three ionization states of EBT are shown in Figure 2. The acidic form has an absorption maximum at 538 nm with an extinction coefficient of 6547 cm-1 M-1. This wavelength also happens to be an isosbestic point for the two more basic forms. At intermediate pH values, between the two pKa given above, there
Zhai and Efrima
Figure 3. UV-visible absorption spectra of ammoniacal solutions of silver nitrate (2.5 × 10-3 M) and EBT (7.8 × 10-5 M) 5 min after mixing: (a) initial pH 5.1 of dye solution, pH of mixture 8.8; (b) pH 9; (c) pH 12.5. (d) is (a) above with 1 × 10-2 M cyanide added, and the concentrations of silver nitrate and EBT are 1.9 × 10-3 and 5.9 × 10-5 M, respectively (calculated on the basis of the parent solutions).
is a shift of the maximum to 612 nm ( ) 1 × 104 cm-1 M-1), reflecting the molecular resonance structures (Figure 1). Correspondingly, the color of the solution goes from red to blue. At the higher pH the maximum of absorption reverts to 518 nm ( ) 7 × 103 cm-1 M-1) and appears as a very broad feature extending all the way to the near-UV. Time progressions of the reaction were monitored by UVvisible spectra of an ammoniacal silver ion solution following the addition of EBT (at initial pH of 5.1), at the final pH 8.8 in which the reaction occurs. A feature gradually grows at 400 nm. It is the characteristic extinction of a silver hydrosol which is formed by a reaction with the dye. The concomitant decrease in the signal of the dye is also clearly seen in the 600 nm region. At higher pH values (10.3 and above) the reaction was faster than we could follow conveniently using UV-visible spectrometry, and copious aggregation of the colloid smeared out most of the spectroscopic features (Figure 3). At these pH values the reaction probably involved the high-pH species of EBT. We therefore limit this study to the reaction at pH 8.8 where the dye is predominantly that shown in Figure 1b. We only note here that also when the reaction mixture is maintained at pH 5.1 throughout the reaction, there is a fast reaction between the dye and silver in the presence of ammonium ions. As this involves the acidic form of the dye (Figure 1a), it will be a matter for a separate study. Figure 4 shows the time development of the optical densities at 400 and 612 nm at pH 8.8. The rate is not constant in time, as is expected of a complex process involving nucleation, growth, and perhaps also some aggregation. However, there is a clear linear region in the first 10 s or so of the reaction. From our analysis we find that during this initial stage only approximately 10% of the dye reacts and much less so of the silver (which is taken in a large excess). Thus, in terms of concentrations this is a nearly stationary region. At these early times we do not see in the UV-visible spectra any sign for aggregation. Aggregation would be manifested by an asymmetric broadening of the 400 nm feature toward long wavelengths, as seen in Figure 3b, for instance. The linearity of the kinetics in the initial period of the reaction suggests that this early time should be associated predominantly with the formation of small silver nuclei of approximately equal sizes, rather than with the growth stage of the colloid. In the latter stage the optical density should grow in the Rayleigh limit as the second power of the rate of
Reduction of Ag Ions to a Colloid by Eriochrome Black T
J. Phys. Chem., Vol. 100, No. 5, 1996 1781
Figure 5. Temperature dependence of the reaction rate. The silver concentration is 0.0022 M. The EBT concentration is 7.1 × 10-5 M.
reactant concentrations. At low reagent concentrations such that, k2[Ag+]β′[dye]γ , 1,
rate ) k1[Ag+]β[dye]R
(2)
and at high reagent concentrations, k2[Ag+]β′[dye]γ . 1,
1/rate ) (k2/k1)[Ag+]β′-β[dye]γ-R Figure 4. Change in time of the optical density at 400 and 612 nm, following the addition of 6.1 × 10-5 M EBT to an ammoniacal 6.7 × 10-3 M silver nitrate solution at pH 8.8. Insert: the first 10 s.
reaction, as the extinction is second order in the volume. Indeed, such behavior is seen in Figure 4 for times between 20 and 40 s. For these reasons we focus in this report on the initial rates, the linear region in the first 10 s of the reaction. Reaction Orders and the Rate Equation. Reaction orders with respect to the silver ion concentration and the dye concentration were measured with a large excess of silver ions; its concentration was 15-550 times higher than that of the dye. The EBT concentration was varied in the range 1.2 × 10-5 to 8.2 × 10-5 M and that of silver nitrate from 1.3 × 10-3 to 6.6 × 10-3 M. The reaction rates are given in terms of the rate of increase of the optical density (OD) at 400 nm (i.e., we monitor here the production of the colloid), with the units au/s. We measured the dependence of the rate on the silver ion concentration for various EBT concentrations. The reaction becomes independent of the silver concentration at the higher concentrations of the dye. At lower concentrations of the dye the rate increases with the silver concentration. We found the following rate equation to agree well with the entire kinetic data we have measured:
rate ) k1[Ag+]β[dye]R/(k2[Ag+]β′[dye]γ + 1)
(1)
with β ∼ β′ ) 1.15 ( 0.05, R ) 3.27 ( 0.01, and γ ) 2.26 ( 0.05. These parameters gave an average 4% deviation between the calculated rates and the experimental ones. In these ranges of parameter uncertainties k1 varied from 1.6 × 1016 to 7.8 × 1016, and k2 from 3.1 × 1013 to 2.2 × 1014, in the proper units derived from those of the total rate (au/s) and the molar concentrations of the reactants. The treatment of the kinetic data was repeated also using the decrease of the signal at 612 nm (i.e., monitoring the dye). This gave similar results as the above, with β ∼ β′ ) 1.1 ( 0.1, R ) 3.18 ( 0.1, and γ ) 2.16 ( 0.2. The analysis was facilitated by the fact that the rate equation attains particularly simple forms at two limiting cases of the
(3)
These limiting forms were also used in the measurement of the activation energies, as we now describe. Activation Energies. Measurements of the reaction rates in the temperature range 10-45 °C, at ∼5 °C intervals, were carried out in order to obtain the activation parameters. The silver nitrate was kept at a concentration of 0.0022 M, and the concentration of the dye was set at three different concentrations. The first concentration, 1.2 × 10-5 M, corresponds to the low reagent concentration limit when eq 2 is valid. In this case the usual log(rate) versus 1/T analysis, with T the temperature in the kelvin scale, gives the activation energy, E1, for the process represented by k1. The linear plot gives an activation energy of E1 ) 77.4 ( 0.3 kJ/mol. On the basis of the dye absorption peak we obtained E1 ) 73.9 ( 0.4 kJ/mol. The second EBT concentration we used was 7.1 × 10-5 M, corresponding to the high reagent concentration limit when eq 3 is valid. Here the activation energy analysis yields E2 - E1, where E2 is associated with the process represented by k2. We find two linear sections with the slope changing at 30 °C (Figure 5). The results are summarized in Table 1. The third dye concentration we used in the measurements as a function of temperature was 3.6 × 10-5 M, corresponding to an intermediate reagent concentration. This set of experiments was carried out in order to verify the accuracy of the kinetic parameters we have derived. Using all the kinetic parameters given above, R, β, β′, γ, k1, k2, derived for 25 °C, and E1 and E2, we calculated the expected rates at all the temperatures which have been measured, and the deviations from the measured rates were averaged. The average ratio between the experimental rate and the calculated one was found to be 1.01-1.04, with a standard deviation of 4%. Repeating this calculation for other kinetic parameter ranges gave larger rate ratios, larger deviations, or both. We take this as an indication that the kinetic parameters we derived are trustworthy. Raman Scattering. Raman scattering was utilized in order to obtain some molecular information about the state of the molecules before and after the reaction. It is expected to be particularly useful in the case at hand, because it involves dye molecules which are right on resonance with the exciting light
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TABLE 1: Activation Energies Measured in the Redox Reaction of EBT and Silver Ions E1, kJ/mol of colloid E1, kJ/mol of dye E2 - E1, kJ/mol of colloid E2 - E1, kJ/mol of dye E2, kJ/mol of colloid E2, kJ/mol of dye under 30 °C over 30 °C
77.4 ( 0.3 77.4 ( 0.3
73.9 ( 0.4 73.9 ( 0.4
41.9 ( 1.6 11.7 ( 0.8
49.1 ( 3.9 7.1 ( 0.8
119.3 ( 1.9 89.4 ( 1.2
123.0 ( 4.3 81.0 ( 1.2
(A)
(B) Figure 7. Schematic structure of Eriochrome Black T with hydrogen bonds: (A) formation of five-member rings; (B) formation of sixmember rings.
Figure 6. Raman spectra with 514.5 nm excitation. (a, top) 1.74 × 10-4 M EBT in solution: (1) pH 4.7, exposure 66.7 s; (2) pH 9.3, exposure 56.6 s; (3) pH 12.8, exposure 60 s. (b, bottom) 8.8 × 10-5 M EBT and 0.025 M silver nitrate, taken 5-15 min after mixing: (1) pH 4.7; (2) pH 10.
(at 514.5 nm). The molecules might also be adsorbed on the silver particles and exhibit surface-enhanced Raman scattering (SERS) or perhaps even surface-enhanced resonance Raman scattering (SERRS).6 Figure 6a shows the Raman spectra from EBT in solution in three different pH environments: 4.7, 9.3, and 12.8, corresponding to the three dissociation regions of the molecule. The concentration is low, 1.74 × 10-4 M, so the spectra are definitely resonatively enhanced. A strong fluorescence background (note that the spectra in Figure 6 are shifted along the intensity axis) is further evidence for the resonance condition. The intensities of the spectra are very similar, in spite of the fact that at pH 9 the maximum of absorption is shifted to 612 nm. Perhaps the isosbestic point near the excitation wavelength is responsible for this behavior. The major bands in the spectra of the three forms appear in the region 1300-1400 cm-1. At pH 12.8 there is a clear and strong structure (with two peaks at 1319 and 1359 cm-1). Probably another band is present at about 1390 cm-1, indicated by the strongly asymmetric broadening of the 1359 cm-1 band. At pH 4.7 there is a wide band with a maximum at ∼1338 cm-1, a band that appears as a shoulder at ∼1270 cm-1, and an indication of another band around 1390 cm-1. In pH 9.3 there
are also two bands that are not very well resolved, at 1313 and 1342 cm-1, and probably a feature at ∼1390 cm-1 is hidden in the 1342 cm-1 broad band. The 1318-1360 cm-1 region can be attributed to the symmetric stretch of the NO2 group,7 while the range 1360-1390 cm-1 is associated with naphthalene tworing structure.7 Thus, though the different dissociation stages affect the charge distribution throughout the molecule, that, in turn, affects the vibrational spectrum of the NO2 group and the fused-ring system; the spectrum in this region retains its general appearance. Stronger pH effects are seen at 1400-1600 cm-1. We assign this region predominately to vibrations of the five- and sixmember ring formed by internal hydrogen bonding, as shown in Figure 7.8 Indeed at pH 4.7, when both hydroxyl groups can form such six-member rings, the 1598 cm-1 feature is very apparent. At pH 9.3 when one of the hydroxyls lost its proton, the 1598 cm-1 band is weaker, and at pH 12.8 it is virtually absent. The residual signal at this position is due to water. A similar behavior is exhibited by the 1465 and 1480 cm-1 bands that appear in the low-pH spectrum. At pH 9.3 only a weaker feature at 1449 cm-1 is present, and it disappears completely at pH 12.8. This band is also related to five-member ring vibrational modes.8 Other differences are seen in the range 1100-1200 cm-1. At pH 4.7 a clear signal at 1155 cm-1 is present. At pH 12.8 the band is shifted to 1129 cm-1, and a new band appears at 1207 cm-1. The behavior at pH 9.3 seems to be intermediate between the two extreme pH values. The range 1130-1160 cm-1 can be assigned to vibrations in the group C6H5-N-.9 This group is expected to be affected by the dissociation of EBT, as the contribution of the various resonance structures (Figure 1) should vary. Thus, using Raman spectroscopy, one can readily distinguish between the various dissociation forms of EBT. Figure 6b shows the Raman spectra obtained from the reaction mixture of EBT and silver nitrate. At the two pH values presented here, and also at 12.5, which is not shown here, the spectra are essentially identical to each other, regardless of the pH. The 1300-1400 cm-1 region is rather similar to that of the EBT molecule at acidic pH values. Recall that this region reflects vibrational modes of the naphthyl, fused-ring system and the NO2 group. Nevertheless, the spectral regions 1100-1200 and 14001600 cm-1 are very different than those exhibited by EBT itself.
Reduction of Ag Ions to a Colloid by Eriochrome Black T The bands around 1130-1160 cm-1 (the C6H5-N- vibrations) are totally absent. A new feature appeared 1237 cm-1. The 1400-1600 cm-1 region has changed completely and has now two strong and broad bands centered at 1528 and 1580 cm-1. Obviously, the five-member rings have transformed or disappeared entirely. In fact, it seems that the whole molecule has changed totally. This, of course, is consistent with the observation that a redox reaction occurs between silver ions and EBT. When we add cyanide to the colloidal solution produced by the reaction of silver ions and EBT, the metallic silver is oxidized by oxygen dissolved in the water and the suspension clears up. Figure 3d shows that the 400 nm colloidal silver extinction totally disappeared; yet the dye absorption is still missing. Even in the presence of the silver colloid one would expect to see the absorption of the dye, if it still existed as a dye in solution or adsorbed on the silver particles, but there is no sign of it in Figure 3a-c. In comparison, a solution composed of EBT that is added to a silver colloid prepared with sodium borohydride, exhibits the 612 nm band of the dye in the UV-visible absorption spectrum. Also, the Raman spectrum of this solution shows (weak but clear) spectral features of the dye at the ambient pH, rather than that of the product of the reaction of EBT and silver ions. Thus, the reaction of EBT with silver ions oxidizes it to a colorless form. These colorless products from the EBT are seen in the Raman spectrum from the colloid only due to the SERS phenomena. At least some of the products of the redox reaction adsorbed onto the silver cores and are seen by SERS. In order to identify the products of the reaction, we reacted large (1 g) quantities of EBT with silver nitrate and analyzed the products mass spectrometrically. We found that the parent peak, or those corresponding to their sodium salts, were completely missing from the spectrogram. These peaks were the major peaks seen in the spectrogram of control samples of EBT, whether that directly supplied by the manufacturer or recrystallized from a basic aqueous solution. The mass spectrogram of the EBT/ silver product was dominated by peaks at 291, 199, and 201 that were practically absent from the spectrogram of the controls. The former can be associated with 2-hydroxy-6-nitronaphthalene-4-sulfonic acid sodium salt. The latter two peaks correspond to an additional lose of the sodium sulfonic group with a capture of protons. Weaker peaks at 185, 202, and 207 corroborate these assignments. Signals below 170 were too weak to detect. The conclusion from these measurements is that the reaction between EBT and silver ions fragments the dye into separate naphthalenic moieties. The azo bridge is severed and nitrogen is probably released. Indeed, during the course of the reaction we see gas evolution. We checked that it was not ammonia evolution (from the ammoniacal solution that we use). In any event ammonia is not expected to evolve from the system, as the solutions are rather dilute. Discussion From the experiments described here we see that EBT reacts with silver ions in a redox reaction yielding a silver colloid and products which are essentially fragments of the dye. It seems that the azo bridge is severed, accompanied by nitrogen evolution. Silver ions are well-known reagents used in synthetic routes requiring the oxidation of hydroxy aromatic compounds to the corresponding quinoid systems.10 However, we found little evidence, or discussion, of the mechanism of these reactions. In particular, no regard has been given to the precise chemical events involving the silver moieties. Also, we did not find previous work involving an azo substitution as is present in EBT. We do not take upon ourselves here to solve this
J. Phys. Chem., Vol. 100, No. 5, 1996 1783
Figure 8. (A) An outline of the redox reaction between silver ions and EBT. (B) Oxidation of dihydroxynaphthalene by silver ions.
mechanistic problem, which merits a study by itself. Instead, we limit ourselves to general suggestions that seem to agree with the results of the present study. Figure 8A shows an outline of a possible reaction scheme. Most probably important stages and details are missing here, for this scheme to be considered as a mechanism. First the silver ions form complexes with the dyesprobably a π-complex. The molecule becomes more susceptible to a nucleophilic attack. Obviously, the equilibrium is expected to be strongly affected by the pH. Next, the molecule breaks down with the evolution of nitrogen and silver is reduced. In fact, preliminary ZINDO calculations showed extensive charge transfer between the dye conjugated π-system and the silver ion. Several intermediates and products can form, including metal-organic compounds. Some of them, such as (substituted) dihydroxynaphthalenes, can reduce additional silver ions, yielding quinoide structures (Figure 8B). The reduced silver atoms can combine to form metal nuclei. If the initial reduction occurs in an aggregate of the dye molecules, the formation of the silver nuclei will be achieved more readily. The fragments, or even their precursors, can remain attached to the silver metal core and form the stabilizing adsorption layer. These species should then be the species seen in the Raman spectra from the colloid. Reactive or nonreactive desorption of the fragments will free the surface of the growing silver particles for further adsorption of dye molecules and silver ions, which will continue the reduction process. The pH dependence of the rate of the reaction can also stem from the pH effect on the reducing power of the naphthol moieties, as well as on its influence on the stability of the azo bridge. At the high pH values the nitrogen-nitrogen bridge comes under strain, due to the repulsion between the negatively charged groups on the two naphthalenic moieties. This should facilitate the breakage of the bonds which connect the azo group to the ring systems. We would like to reemphasize: We do not imply here that Figure 8A represents the detailed mechanism of the redox reaction. This is only an outline which shows some of the ways by which the reaction could proceed and yield the products indicated by our experiments.
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The early stage of the reaction, this is the stage we investigated, involves the formation of small silver metal nuclei stabilized by the fragments from the dye molecule. The reaction can continue by dye molecules attaching to a small silver embryo. Then a silver ion from the solution joins into this complex (or surface aggregate of dye molecules) and is reduced. This process should be characterized by rather high activation energies. The experimental activation energies (70-120 kJ/ mol) are certainly much larger than typical activation energies of diffusional processes that are responsible for the later stage of growth. The values of the activation energy that were found are consistent with what is estimated for a silver colloid, based on a very simple, perhaps even naive, model. In this model the nucleation stage is characterized by a high activation energy stemming predominately from the high surface energy of small particles (per mole of silver atoms). In the very early phase of nucleation, when clusters of only a few atoms are formed, the coordination of the atoms is very low indeed. Only the interaction of these clusters with molecules in the environment (EBT and its fragments, for instance) can compensate, in part, for the “surface” energy and lower the effective barrier to a sufficiently low level. We have recently demonstrated such an effect in the production of silver colloids in the presence of Alizarin Yellow and dithizone.2 However, when the nuclei grow beyond a few atoms, there are not enough dye molecules in our system to effectively lower the surface energy. In fact, because of the large excess of silver ions, practically all of the dye eventually reacts. Therefore, the surface energy, i.e., the barrier to the reaction, can be estimated from simple surface energy considerations. Once the nuclei grow to a stage when an additional silver atom can be accommodated in the bulk of the particle, the surface energy per mole of atoms will start to decrease. We identify the end of the nucleation with this stage. There is a critical size of (spherical) nuclei which corresponds to having all the atoms in the surface, and beyond which atoms will be also fully coordinated, which is energetically similar to a bulk situation. Thus, the activation energy can be approximated by the surface energy per mole of silver atoms of an ensemble of “critical” nuclei. As soon as the particle becomes large enough, additional atoms will be added more and more into the “bulk” and will not contribute to the extra energy required for the formation of the exposed surface. Let us denote the volume of the critical nuclei by Vc, the number of atoms in the nuclei Nc, the critical radius by rc ) (3Vc/4π)1/3, the surface area of the critical nucleus by Ac ) 4π(3Vc/4π)2/3, and the number of atoms at the surface of the particle, Ns. The volume of a silver atom is given by Vat ) Mw/(FNa), with the atomic mass Mw, the density F, and Avogadro’s number Na. The atomic radius is given by ra ) (3FvVat/4π)1/3, and the area covered by an atom Aa ) πFar12. Here Fv is the fraction of the volume occupied by the atoms (0.74 for a fcc structure). Fa is the reciprocal fraction of the area occupied by an atom, 1.273 and 1.103 in a two-dimensional square and hexagonal packing, respectively. In this simple model of close-packed spheres one has in each particle Nc ) Vc/Va atoms, and Ns ) Ac/Aa ) (4/Fa)(Vc/FvVa)2/3 surface atoms. In the critical nuclei these two numbers are equal. Thus, we obtain for a critical nucleus
Nc ) 43/(Fv2Fa3)
(4)
Using values for silver, F ) 10.5 g/cm3 and Mw ) 108 g/mol, we obtain the following parameters for the critical nucleus for a 2D square (hexagonal) packing: Ns ) 54 (83), rc ) 0.60 (0.70) nm, Vc ) 0.92 (1.4) nm3. The value we obtained for Ns is consistent with the value obtained using a fcc model and simply
counting atoms as a function of distance from a reference atom. One can easily count the total number of atoms and the number of surface atoms. Approximately two layers of atoms are required to reach a situation such that an additional layer completely covers almost all of the atoms present in the cluster. Two complete layers consist of 87-111 atoms, of which 7498 are exposed at the surface. The surface tension of silver is 903 dyn/cm at 961 °C, at the melting point.11 Using this value, we obtain the surface energy of 1 mol of silver atoms arranged in an ensemble of “critical” particles. It is in the range 46-54 kJ/mol. Considering the crudeness of this model, it gives values of energy barriers that are suprisingly in the range of those we report here for the activation energies E1. One should also consider that the reduction reaction involves also the breakage of two nitrogencarbon bonds and the evolution of nitrogen gas into water (accompanied by the lose of water-water interactions). Both of these should also contribute to the activation energy. The rate equation we found for the reaction at the nucleation stage is of a high order in the reactants and is of a complex form. This reflects the complexity of this stage and its multimolecular nature. The order of reaction for the dye suggests that several dye molecules are required, per silver ion. Probably one EBT is needed for the reduction and one or two more for stabilizing the small silver metallic cores or forming an aggregate in which the reduction proceeds more readily. The high order of reaction for EBT is further evidence that this is not a simple diffusion-controlled reaction, as expected for the final growth stage. From the process represented by the term with k2 it seems that the growth from an embryo particle (of a few atoms) to a nucleus (of a few dozen atoms), which can then continue to grow in a more regular fashion, can be hampered by the adsorption of the dye molecules. The very same dye molecules that stabilize the embryo metal cores by adsorption and enable their formation block their surfaces and slow down a further expansion. An interesting feature of the rate equation is the approximately unity order of reaction found for silver ions. Normally one would expect a high order of the depositing ions, reflecting the extremely high energy of a single reduced atom. Thus, a lower barrier path of the nucleation is expected for a cooperative reaction of several ions. However, in our case, the EBT-silver interaction seems to provide a more efficient pathway, involving only a single silver ion at a time. It seems that EBT adsorbs onto a silver embryo particle, most probably sitting in a flate adsorption conformation on the surface. Then a single silver ion attaches to this EBT molecule in a π-complex. Preliminary ZINDO calculations show that in such a complex the silver ion is practically neutralized. This is facilitated by the delocalization of the negative charge throughout the naphthalenic system. Irreversibility is brought in by nitrogen evolution. If this is the slow process, a low reaction order for silver ions is expected. The very strong interaction between EBT and silver is manifested in several ways. First, the mere fact that a fast redox reaction between these two species occurs is strong evidence for the interaction. Note that at pH 12 the reaction was completed within a few seconds, while at pH ∼9 it took only a few dozen seconds. Second, in this reaction the EBT molecule breaks into smaller fragments. The characteristic absorption of the molecule around 612 nm is absent in the colloidal solution, even after cyanide is added and the silver colloidal particles are oxidized back to ions. In fact, the product does not exhibit any absorbance in the visible or near-UV regions, indicating that the conjugate electronic
Reduction of Ag Ions to a Colloid by Eriochrome Black T
Figure 9. Optical density of a silver colloid solution. Comparison of an experimental spectrum to spectra calculated theoretically for two different sets of dielectric constants for silver (JC, ref 13; MC, ref 14).
system of the molecule has been severed. Also, the mass spectrometry of the product showed the fragmentation of the large dye molecule into naphthalenic compounds. The Raman spectra of the dye in the presence of the colloid retain the signature of the naphthyl and nitro groups but lack the spectral features associated with hydrogen bonding in five-member rings or with nitrogen azo groups conjugated to an aromatic ring. This is another piece of molecular information showing the strong chemical interaction of EBT and silver. The linear increase in the optical density of the silver colloid suspension, in itself, is not sufficient evidence for the nature of the molecular process. However, it does give an indication for the nature of the reaction. For small particles (the Rayleigh limit) and low extinction, one has12
OD ∼ Nrp3
(5)
Here OD is the measured optical density of an ensemble of N particles of radius rp. The third power comes from the cross section (power of 2) and the linear dependence of the efficiency of extinction, usually denoted by Qext, on the size of the particle.12 Thus, the measured OD should be proportional to the total amount of reduced silver. Only for particles equal or larger than the wavelength of the light divided by 2π does this relation break down. For such particles the shape of the spectrum depends on the size (and not the number, as long as the concentration is low). We calculated the silver concentration at specific times during the reaction from the decrease of the dye absorption at 612 nm. Combining these data with a calculation of the extinction of a silver colloid at the Rayleigh limit (small, unaggregated particles), we calculated the optical density that is expected of the colloid under the conditions of our experiment.
OD ) NCextL/2.3
(6)
where L is the path (1 cm), N is the number concentration of the particles, and
Cext ) Qext/πrp2 Qext ) 4x Im{(m2 - 1)/(m2 + 1)} and x ) 2πm′rp/λ
(7) (8)
m is the complex frequency-dependent refractive index of the silver core divided by the refractive index of the ambient solvent (water), m′ is its real part, and λ is the wavelength. Figure 9 shows the results of this calculation for two different sets of dielectric data for silver, that of Johnson and Christy13 and that of Morriss and Collins.14 The experimental spectrum
J. Phys. Chem., Vol. 100, No. 5, 1996 1785 is also shown for our system 60 s from the beginning of the reaction. As is quite usual, the calculated spectra are much narrower than the observed one. This is probably due to some aggregation as well as nonspherical shapes of the silver colloidal particles. A small number of large aggregates can dominate the entire spectrum due to the rp3 dependence we discussed earlier. Notwithstanding this, the integrated band intensities are very similar. For instance, from the experiment we find the integral to be 24.0 and 34.8 nm‚au for 60 and 100 s, respectively. The calculation gives an integral of ∼23 and 46 nm‚au, assuming a dye/silver ratio of 1:2 and 1:4, respectively. This may be taken as an indication that, after all, there is a full quantitative correspondence between the dye disappearance and the appearance of the colloid. Also, it seems safe to infer from the agreement between the Rayleigh limit calculation and the experimental results that the majority of the colloidal particles are small (radius < 20 nm) and that most are unaggregated (at that stage of the reaction). In summary, we have discussed here the production of a silver colloid by the reduction of silver ions and a strongly reducing dye, Eriochrome Black T. We focused on the nucleation stage and found it to be characterized by a complex reaction rate equation, with a high reaction order for the dye. The rate equation reflects the complex nature of the nucleation stage. The activation energies were found to be high and are associated, at least in part, to the surface energy of the small silver nuclei. The dye adsorbs on the silver particles. This allows continuing growth and stabilizes them at the long run, but it also interferes with the reactions at the earlier stage of the production of the colloid. In the reaction the dye fragments into naphtholenic moieties together with the evolution of nitrogen from the azo group of the dye. Acknowledgment. We acknowledge the partial support of the Wolfson Foundation administered by the Israeli Academy of Sciences and Humanities and the Israeli Ministry of Science. Thanks are due to M. Cojocaru for the mass spectrometry and to V. Khodorkovsky for helpful discussions. References and Notes (1) Heicklen, J. Colloid Formation and Growth; Academic Press: New York, 1976. (2) (a) Zhai, X.; Efrima, S. SilVer Colloids and Interfacial ColloidssAdsorption of Alizarin Yellow 2G and its effect on Colloidal Nucleation, submitted. (b) Zhai, X.; Efrima, S. SilVer Colloids and Macroemulsions of Metal Interfacial Colloidal FilmssInteraction with Dithizone, submitted. (3) Efrima, S. CRC Crit. ReV. Surf. Chem. 1991, 1, 167. (4) Yogev, D.; Rostkier-Edelstein, D.; Efrima, S. J. Colloid Interface Sci. 1991, 147, 167. (5) Albert, A.; Serjeant, E. P. Ionization Constants of Acids and bases; Methuen & Co.: London, 1962. (6) Efrima, S. In Modern Aspects of Electrochemistry; Conway, B. E., White, R. E., Bockris, J. O’M., Eds.; Plenum Press: New York, 1985; Vol. 16, p 253. (7) Robinson, J. W. CRC Handbook of Spectroscopy; CRC Press: Boca Raton, FL, 1980; Vol. II. (8) Dollish, F. R.; Fateley, W. G.; Bentley, F. F. Characteristic Raman Frequencies of Organic Compounds; John Wiley & Sons: New York, 1974. (9) Pemberton, J. E.; Buck, R. P. J. Phys. Chem. 1981, 85, 248. (10) Schafer, W.; Leute, R.; Schlude, H. Chem. Ber. 1971, 104, 3211. (11) Smithells, C. J. Metals Reference Book, 5th ed.; Butterworth: London, 1976. Metals Handbook; 9th ed.; American Society for Metals: Metals Park, OH, 1979; Vol. 2. (12) Bohren, C. F.; Huffman, R. Absorption and Scattering of Light by Small Particles; John Wiley: New York, 1983. (13) Johnson, P. B.; Christy, R. W. Phys. ReV. B 1972, 6, 4370. (14) Morriss, R. H.; Collins, L. F. J. Chem. Phys. 1964, 41, 3357.
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