Langmuir 1997, 13, 1773-1782
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Spectroelectrochemistry of Colloidal Silver Thearith Ung, Michael Giersig,† David Dunstan,‡ and Paul Mulvaney* Advanced Mineral Products Research Centre, School of Chemistry and Department of Chemical Engineering, University of Melbourne, Parkville, Victoria, 3052, Australia Received September 4, 1996. In Final Form: November 25, 1996X The spectroelectrochemical response of small silver particles was studied in aqueous solution using an optically transparent, thin layer electrode. The position of the surface plasmon band of the colloidal silver was found to depend on the applied electrode potential. It varied from 400 nm in air, corresponding to a redox potential of +0.15 V vs Ag/AgCl, to about 392 nm at -0.6 V vs Ag/AgCl. A value of 80 ( 10 µF cm-2 for the double-layer capacitance of the silver-water interface was obtained on the basis of the spectroelectrochemical shift. The equilibration kinetics of the particles with the electrode obeyed the Cottrell equation. However, the number of electrons transferred at each particle-electrode encounter was found to be potential dependent and reached 1600 ( 300 at potentials more negative than -0.4 V vs Ag/AgCl. The evidence suggests that this particle charging current occurs via electron tunneling across the particle and electrode double layers and not by contact electrification. Changes in the redox potential of the particles due to added chemical reductants could also be directly monitored by laser doppler electrophoresis.
Introduction Theories of the electrical double layer around colloid particles are largely based upon the classical electrochemical models used to explain the properties of the mercury-water interface.1-5 Although these models can adequately explain the electrokinetic properties of colloidal metal oxides6 and silver halides,7 they are generally not applied to metal particles themselves. The primary reason for this is the lack of control over the chemical potential of electrons on metal particles in solution. Whilst the surface potential of most semiconducting or insulating particles is determined by ionic adsorption of potential determining ions from solution (normally the lattice ions), in the case of metal particles both ionic adsorption and electron transfer between particle and solution may determine the overall particle charge and hence its electrophoretic mobility. In order to characterize the electrical double layer around metal particles, it is necessary to be able to measure the electronic and ionic surface charge density and the surface potential of the particles on an electrochemical scale. To date such simultaneous measurement of both charge and potential in one experiment has not been possible. In this paper we explore a spectroscopic method for determination of both particle redox potential and electronic charge density. The technique relies on the fact that, for some metals, the transfer of electronic charge to the particle results in optical changes to the absorption spectrum of the metal colloid.8-10 Quantitative analysis of the spectral shift allows the excess electronic charge to † Permanent address: Abt. Kleinteilchenforschung, HahnMeitner Institut, Glienickerstrasse 100, Berlin 15109, Germany. ‡ Department of Chemical Engineering. X Abstract published in Advance ACS Abstracts, February 1, 1997.
(1) Grahame, D. C. Chem. Rev. 1941, 41, 441. (2) Parsons, R. Mod. Aspects Electrochem. 1954, 1, 103. (3) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, 1989; Vol. 1. (4) Gouy, L.-G.C. R. 1909, 149, 654. (5) Chapman, D. L. Philos. Mag. 1913, 25, 475. (6) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci. 1978, 9, 303. (7) Lyklema, J.; Overbeek, J. Th. G. J. Colloid Sci. 1961, 16, 595. (8) Mulvaney, P. In Electrochemistry of Colloids and Dispersions; Mackay, R. A., Texter, J., Eds.; VCH: New York, 1992; p 345. (9) Henglein, A.; Mulvaney, P.; Linnert, T. Faraday Discuss. 1991, 92, 31. (10) Ung, T. Honours Thesis, University of Melbourne, 1995.
S0743-7463(96)00863-3 CCC: $14.00
be calculated. It is important to note that only the electronic charge is detected this way and that any ionic adsorption that may take place is not included. The absorption changes also allow the kinetics of electron transfer to and from an immersed electrode to be monitored directly. As a result, it is possible to demonstrate that electrochemical equilibration of particles of a metal colloid with a bulk electrode does occur. It should be noted that Bard and co-workers have previously shown that equilibrium can be achieved in the presence of a redox mediator to shuttle electrons between the particles and the immersed electrode.11 It will be shown in this paper that the process of direct electrode-to-colloid electron transfer obeys normal electrode kinetics but is characterized by the transfer of a large number of electrons, rather than a small, integral number as in conventional molecular electrode kinetics. Experimental Section (I) Colloid Preparation. AgClO4‚H2O and methyl viologen were procured from Sigma, and sodium borohydride and NaClO4 were obtained from BDH. The polyacrylic acid (PAA) (M.W. 2000) was a product from Aldrich. Solutions were made up using Milli-Q water. Silver sols were prepared by two techniques. For small quantities, a slightly modified version of the preparation described by Creighton was used.12 Ice-cold solutions of AgClO4 (0.100 mM) containing various concentrations of PAA (10 µM, 40 µM, 400 µM, 3 mM, and 5 mM) were added rapidly to freshly prepared, ice-cold, rapidly stirred, solutions of NaBH4 (∼1 mM). The solutions turned transparent yellow upon mixing. For larger syntheses used in the OTTLE cell, a 400 mL solution of AgClO4 (1.3 mM) and PAA (4.0 mM) was added dropwise from a buret to an aqueous, ice-cold, rapidly stirred solution of NaBH4 (4.0 mM). The transparent yellow solution was then concentrated by rotary evaporation at 30 °C for about 7 h to yield a more concentrated sol (0.4 µM particle concentration equivalent to 12 mM Ag ions). This sol appeared dark brown and transparent. Sols containing PAA:Ag ratios greater than 5 could be concentrated to form translucent, waxy solids, which could be redissolved in distilled water. NaClO4 (0.10 M) was added dropwise as a supporting electrolyte to the stirred sol immediately before use in electrochemical experiments. (II) Electrochemical Measurements. The OTTLE cell was prepared by standard literature techniques,13-16 using a gold (11) Miller, D. S.; Bard, A. J.; McLendon, G.; Ferguson, J. J. Am. Chem. Soc. 1981, 103, 5336. (12) Creighton, J. A.; Blatchford, C. G.; Albrecht, M. G. Trans. Faraday. Soc. 1979, 75, 790.
© 1997 American Chemical Society
1774 Langmuir, Vol. 13, No. 6, 1997 100 wires/inch mesh from Buckbee Mears Co., St. Paul, MN, and Teflon tape spacers. Diagrams of the cell are available in these references. Epoxy resin was applied along the vertical edges and part of the top to prevent leaking. Part of the grid was folded over onto the outside of the glass walls and bound with Al foil, which served as an electrical contact. The thickness of the cells was determined using 0.10 M K3Fe(CN)6 solutions and assuming 420 ) 1000 M-1 cm-1. The thicknesses of such cells were found to be 47-50 µm. The colloid solution was held in a small bath under the OTTLE cell and was drawn into the cell by capillary action. A Ag/AgCl reference electrode with a thin capillary tube was placed immediately under the OTTLE cell (distance 1.5 mm) to minimize the iR drop. The auxiliary electrode was a Pt flag. The whole assembly was placed in an Hitachi 150-20 UV-vis spectrophotometer. Spectra were collected with 0.5 nm wavelength resolution (slit width 0.2 nm) and stored on computer. The potential of the working electrode was controlled by a MacLab digital potentiostat and a MacLab 2e controller. The system was software driven using the Echem software. The OTTLE cell was not degassed by bubbling, as this was found to be unreliable with the thin cells. Instead, prior to making electrochemical measurements, the gold mesh was cathodically biased at -0.6 V for several minutes to consume any oxygen in the cell and was then repolarized at the open circuit potential. After such pretreatment, reproducible and stable absorption spectra of the air-sensitive methyl viologen monocation radical could be obtained, and this was taken as evidence for quantitative oxygen removal. Inward diffusion of oxygen through the head of the OTTLE cell was found to be too slow to interfere with subsequent experiments. In some cases, open circuit potentials of the sol were recorded by simply connecting the gold mesh and Ag/AgCl electrodes to a high impedance Keithley voltmeter. The potentials of the Ag/ AgCl reference electrodes were checked against Zobell’s solution and found to be accurate to within 2-5 mV.17 Voltammograms on a rotating disk electrode were measured using either 9 or 3.5 mm Pt disks. The solution volumes were 75 mL, and the solutions were purged with nitrogen. (III) Particle Characterization. Electrophoretic mobilities of the concentrated silver sols were determined using a Coulter Delsa 440 electrophoresis apparatus. Dynamic light scattering was used to measure the particle size of the silver particles, using a commercial Malvern 4700 system equipped with an Ar ion laser operating at 488 nm. Analysis of the correlation function, measured at θ ) 90°, was carried out using the CONTIN algorithm. Diffusion coefficients were then converted into hydrodynamic radii using the Stokes-Einstein equation. Results used here are derived from two sols and were measured with dilute sols, where D was independent of particle concentration. Particle sizing was also carried out by TEM with a Philips CM10 microscope. To ensure good particle adhesion, polylysinecoated carbon grids were used as detailed elsewhere.18 TEM images of particles of Ag sol 2 are shown in Figure 1. The particles are seen to be round with angular faces and crystalline with a mean diameter of 11.3 nm. The inset shows a high-resolution image of a single particle. The preparation described above yields very spherical, monocrystalline particles. All particles yielded electron diffraction patterns consistent with the normal fcc modification. The dense packing is due to the presence of the cationic polymer on the TEM grid. In addition, a more monodisperse gold colloid reference was examined by both TEM and light scattering to demonstrate that the two methods yielded concordant data for small particles. Accurate values of the mean radius are necessary for the interpretation of the chronoamperometry data. In Figure 2, the two independently determined (13) Kuwana, T.; Darlington, R. K.; Leedy, D. W. Anal. Chem. 1964, 36, 2023. (14) Kuwana, T.; Winograd, N. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1974; Vol. 7. (15) Murray, R. W.; Heineman, W. R.; O’Dom, G. W. Anal. Chem. 1967, 39, 1666. (16) Heineman, W. R.; Norris, B. J.; Goelz, J. F. Anal. Chem. 1975, 47, 79. (17) Zobell, C. E. Bull. Am. Chem. Assoc. Petrol. Geol. 1946, 30, 477. Zobell’s solution is 1/300 M in potassium ferrocyanide, 1/300 M in potassium ferricyanide, and 0.1 M in KCl. It has a redox potential of +0.430 V vs NHE at 25 °C. (18) Giersig, M.; Mulvaney, P. Langmuir 1993, 9, 3408.
Ung et al. particle size distributions are shown. Because the light scattering in the Rayleigh regime varies as the sixth power of the radius, the presence of even a small number of larger particles causes a pronounced tail to be observed in the size distribution when DLS is used. Although the gold sols could be fitted to Gaussian distribution functions, these were very unsatisfactory for silver sols, which possessed asymmetric size distributions as measured by both TEM and DLS. The mean particle sizes for sols 1 and 2 used in all calculations were obtained by fitting the DLS data to a log-normal distribution function. The mean particle sizes and aggregation numbers found by the fitting procedures are summarized in Table 1.
Results and Discussion The primary aims of this study were to demonstrate that the optical properties of colloidal silver are dependent upon the surface charge density on the particles and to see whether a quantitative relationship could be found between the position of the surface plasmon band and the particle charge or redox potential. To do this, it was necessary to determine firstly whether the colloid particles could exchange charge directly with an electrode and secondly whether an impressed electrode potential resulted in electrochemical equilibration of the particles with the electrode. Initial attempts to observe a voltammetric peak using a standard RDE and citrate-stabilized silver particles failed because of the low particle concentration and slow precipitation of the colloid at the high ionic strengths necessary for stable electrochemical behavior. Polymeric stabilization enabled concentrated silver sols to be prepared. Low molecular weight PAA is known to be an excellent stabilizer of silver colloids.19,20 The presence of the polyelectrolyte on the particle surface clearly complicates the interaction between particles and the electrode but was necessary for the preparation of concentrated, electrolyte-stable, reproducible silver colloids. We start by presenting the experimental results obtained with silver sols using the OTTLE cell in section I. In section II, we discuss the effects of electronic charge on the particle mobility, and then in section III, we use simple modifications to the Mie-Drude equations to account for the spectroelectrochemical effects observed in this work. In section IV, we address the adverse effects and limitations introduced by the polymeric stabilizer, and finally, in section V, we consider the actual mechanism of electron transfer from electrode to particle. (I) RDE and OTTLE Voltammetry. Open circuit potentials (Voc) of the silver colloid, both before and after concentration by rotary evaporation, consistently yielded values of +0.15 V vs Ag/AgCl for the colloid at pH 9. This value is very close to the open circuit values normally found for Pt electrodes immersed in aerated aqueous solutions.21 It arises from the irreversibility of oxygen reduction at metal surfaces. The potentiostat was always set at this open circuit potential prior to cathodic degassing cycles or colloid measurements. In Figure 3, a cyclic voltammogram of colloidal silver is shown taken with the OTTLE cell. As can be seen, a cathodic peak associated with electron transfer from the gold mesh to the colloid occurs at +0.15-0.20 V vs Ag/AgCl and an anodic peak occurs at much more positive potentials, around +0.70 V vs Ag/AgCl. The scan was started at +0.20 V in a negative (19) Henglein, A.; Mulvaney, P.; Linnert, T. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 1449. (20) Mostafavi, M.; Keghouche, N.; Delcourt, M.-O.; Belloni, J. Chem. Phys. Lett. 1990, 167, 193. (21) Garrels, R. M.; Christ, C. L. Solutions, Minerals and Equilibrium; Jones and Bartlett Publishers: Boston, 1990. In the presence of a clean Pt electrode, most solutions show a redox potential of Voc ) +(0.70 0.059)pH vs NHE. This value is well below the thermodynamic value of +(1.23 - 0.059)pH and is due to the irreversibility of oxygen reduction.
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Figure 1. Electron micrograph of the colloidal silver particles of sol 2. The average size is 11.3 nm. Grid prepared by electrophoresis at 0.5 V cm-1 of sol onto polylysine-coated grids.
Figure 2. (a and b) Size distributions of the two silver sols used in the experiments as determined by TEM and DLS. (c) Reference sample of colloidal gold. The silver samples are fitted to log-normal functions, and the gold sample is fitted to a Gaussian distribution function. Results are summarized in Table 1.
direction. The voltammogram of the blank solution showed no faradaic peaks in this potential regime. The cathodic peak in the voltammogram is close to the open circuit potential whereas the oxidation peak appears to be drastically shifted. We attribute this shift to competitive adsorption of the polymer onto the electrode at positive potentials. The adsorbed anionic polymer blocks the electrode surface, thereby inhibiting electron transfer to the electrode from the particles. Consequently, most of the data presented in this paper have been obtained from experiments on electrode-to-particle electron transfer. In Figure 4, UV-vis spectra of the colloid are shown before and after a potential step to -0.6 V. Initially, the absorption band maximum of the sol was located at 400 ( 0.4 nm. After application of the potential step, the
absorption spectrum changed, and the band blue-shifted to a new position with a maximum at 392 nm. This spectrum was quite reproducible for minutes at a time. After about 5 min, the absorption of the solution began to decrease. It was found that this was due to very slow migration of particles out of the OTTLE cell due to the iR drop between the mesh and reference electrodes. Although the reference electrode was located within 1.5 mm of the mesh, this slow electrophoresis of solute was found to be unavoidable, as noted by other workers.15,16 As can also be seen from spectrum c in Figure 4, when the potential was then stepped back to +0.15 V, the absorption spectrum again changed. The absorption band red-shifted and broadened until it resembled that of the silver sol before the initial potential step had been imposed. To demonstrate that the optical shifts are caused entirely by electron transfer between the working electrode and the colloid particles, the absorbance was monitored directly at 393 nm as the potential step was applied. The results are shown in Figure 5. The potential of the mesh was held at the open circuit value, and after steady absorbance readings were obtained from the silver sol, a potential step to -0.6 V was applied. The absorbance of the sol changed immediately, with rapid increases in absorption being seen which leveled off after some 150 s in the experiment shown. When this new steady absorbance value was achieved, the potential was stepped back to the original value. Immediately, the absorbance decreased again at almost the same rate, until the original
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Table 1. Particle Parameters determined by TEM and DLS colloid
dTEM (nm)
sda
Ag sol 1 Ag sol 2 au ref
9.81 11.27 18.5
1.4 1.6 2.10
dDLSb (nm)
sda
104Nagg
[Ag] (mM)
[particles]c or [Au] (µM)
10-7D (cm2 s-1)
9.11 14.4 19.3
2.57 2.42 6.15
2.90 4.40 19.14
12 12 0.4
0.413 0.273 2.089
5.38 3.41 2.56
a Standard deviations for TEM and DLS data based on Gaussian fits to the gold size distribution and log-normal fits to silver size distributions. b Using Stokes-Einstein equation with η ) 0.89 cP. c [particles] ) [Ag]/Nagg.
Figure 3. Cyclic voltammogram of a 12 mM silver sol (0.41 µM particle concentration) in 0.1 M NaClO4, 2 mM PAA (MW 2000) at pH 9 using an OTTLE cell. The solution was degassed by a cathodic prepolarization cycle.
Figure 5. Change in absorbance of a silver sol at 393 nm (continuous line) as a function of time after application of a potential step to -0.6 V from +0.15 V, and then reversal of the potential step back to +0.15 V (dashed line). Conditions as per Figure 3.
Figure 4. Spectra of the silver sol obtained (a) at the open circuit potential of +0.15 V, (b) after a potential step to -0.6 V, and then (c) after stepping the potential back to +0.15 V vs Ag/AgCl. Solution as per Figure 3.
value was attained about 200 s later. Since the measured absorption is due to all the particles in the OTTLE cell between the cell walls and the electrode, all the silver particles in the OTTLE cell must have equilibrated with the mesh on the time scale of the absorbance changes seen in Figure 4. Not only did the silver particles in the 50 µm wide cell diffuse to the gold mesh on this time scale but they also collected the necessary charge for electrochemical equilibrium to be attained. Using the value of D ) 5 × 10-7 cm2 s-1, obtained directly by DLS, a silver particle will diffuse a distance of x2 ∼ Dt ∼ 80 µm in 150 s, which corresponds well to the thickness of the OTTLE cell. Thus the observed absorption transients are exactly those required to deplete the cell of “unreacted” particles. These spectroelectrochemical kinetics clearly indicate not only that the absorption spectrum of the sol depends on the potential applied to the mesh but also that equilibrium can be achieved by applying both positive and negative potential steps to the electrode.
Figure 6. Equilibrium position of the colloidal silver surface plasmon absorption band as a function of the gold mesh electrode potential. Peaks recorded at least 300 s after equilibration at each potential. Also shown is the number of electrons per particle required to reach any particular potential starting at +0.4 V vs Ag/AgCl calculated using eq 10.
In Figure 6, the position of the silver colloid surface plasmon absorption band is shown after application of different potential steps to the sol. The peak positions are accurate to within 0.4 nm. All potentials are measured relative to Ag/AgCl. As can be seen, starting from an open circuit potential of +0.15 V vs Ag/AgCl and a surface plasmon band position at 400 nm, it was possible to blueshift the band to about 392 nm by application of potentials of up to -0.8 V to the gold mesh. At more negative potentials hydrogen evolution from both the mesh and the particles prevented further shifts from occurring, or at least being measured accurately, due to bubble accumulation in parts of the OTTLE cell. Application of a more positive potential to the gold mesh resulted in a
Spectroelectrochemistry of Colloidal Silver
Figure 7. Equilibrium spectra of the12 mM silver sol (0.41 µM particle concentration) in 0.1 M NaClO4, 2 mM PAA (MW 2000) at pH 9 at various gold mesh electrode potentials vs Ag/ AgCl.
red-shift of the colloid absorption band, and this attained a value of 404 nm at potentials greater than +0.4 V vs Ag/AgCl. The limiting factor in this case was particle oxidation. From the Nernst potential for bulk silver,
E (vs Ag/AgCl) ) +0.577 + 0.059 log10 [Ag+] (1) we see that a silver sol will show noticeable dissolution (1-10% absorbance decrease) when the electrode potential is maintained in the region +0.34-0.40 V, as was observed. When the potential of the working electrode was maintained at values any more positive than this, total dissolution of the colloid was observed. This rate of electrochemical particle oxidation was much faster than the migration out of the cell. The equilibrium spectra of the silver particles at several potentials are shown in Figure 7. Note not only that the surface plasmon band blue-shifted as the potential was made more negative but also that the maximum absorption increased, and the band became much sharper at more negative redox potentials. This is in accordance with earlier qualitative trends observed when electrons were injected by solution phase reductants.8,9 In the experiments with the RDE, mass-transfer-limited currents were found for potentials more negative than -0.4 V vs Ag/AgCl. As is obvious, the spectral changes to the silver colloid do not obey Beer’s Law and therefore cannot be used to quantitatively measure the rate of electron transfer, as is common practice in spectroelectrochemistry. Nevertheless, qualitatively some dependence of the rate of charge transfer on the applied potential is expected. In Figure 8, we show how the absorbance of the sol was observed to change with time after application of steps to different cathodic potentials. The absorbance was measured at the wavelength where the peak was after equilibration at the new potential. (The peak positions were established from the experiments of Figure 7.) As can be seen, when the potential was maintained at +0.15 V, no discernible change to the absorption spectrum was observed in the presence of the mesh, and no current was observed to flow. As the potential step size was increased, the rate of increase of the absorbance increased drastically, as did the final equilibrium absorbance at each potential. At potentials more negative than -0.4 V, the rate of change of the absorbance after the potential step was almost constant. These kinetic traces support the fact that at potentials more negative than -0.4 V vs Ag/AgCl the rate of electron transfer from the electrode to the particles is
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Figure 8. Absorbance vs time curves for silver sols after application of potential steps to various potentials from the open circuit value. The rate becomes almost constant at potentials more negative than -0.4 V vs Ag/AgCl. 12 mM silver sol (0.41 µM particle concentration) in 0.1 M NaClO4, 2 mM PAA (MW 2000) at pH 9. Solution was degassed by prepolarizing at -0.6 V and then anodic polarization at +0.15 V vs Ag/AgCl.
independent of electrode potential, i.e. is mass-transferlimited. Under these conditions, n, the number of electrons transferring during each encounter, can be extracted from the current-time response after application of a large potential step. According to the Cottrell equation, the transient current obeys the equation22
ilim )
nFAD1/2[Agm] π1/2 t1/2
(2)
where A is now the area of the gold mesh. To obtain the effective electrochemical surface area of the mesh, Cottrell plots for MV2+ were measured after cathodic oxygen degassing cycles. Good linearity was obtained at times >2-3 s. Heineman et al. have previously shown that the mesh behaves as a macroscopic electrode at times greater than λ2/2D where λ is the mesh spacing and D the diffusion coefficient of the reactant.16 Knowing n ) 1, D ) 9 × 10-6 cm2 s-1, and [MV2+] ) 5 mM, we obtained 0.28 cm2 for the effective area of the mesh, very close to the geometric area of 0.31 cm2 exposed to solution. The experiment was then carried out with a silver colloid in the same OTTLE cell. In Figure 9a, the current time response is shown for the sols after application of different cathodic potential steps. The current transients lasted about 100 s, which is similar to, but shorter than, the time scale for the absorbance changes under identical reaction conditions, as shown in Figure 5. Cottrell plots for both methyl viologen and colloidal silver reduction are shown in Figure 9b. The linearity of the plot for the silver colloid is not nearly as good as that obtained from analysis of the methyl viologen reduction data, but a slope of -7.4 ( 1.0 µA s1/2 was obtained from several runs, for data collected in the time period 5-100 s after the applied pulse. Taking A ) 0.28 cm2 and D ) 5 × 10-7 cm2 s-1, we find that n ) 1600 ( 200. To obtain an independent value for n, cyclic voltammetry of the same sol was carried out using a rotating disk electrode (RDE). The Levich equation predicts that, at potentials where the reduction of a molecular redox couple becomes mass-transfer-limited, the current dependence on the electrode rotation rate is given by22 (22) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980.
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Figure 10. Levich plot of the limiting current vs square root of the RDE angular rotation rate. Solution conditions as per Figure 3. Solution was N2-saturated.
Figure 9. (a) Current vs time after application of various potential steps to the silver sols. Conditions as per Figure 3. (b) Plots of the gold mesh electrode current as a function of the inverse square root of the time both for 5 mM MV2+ in 0.1 M KCl and for Ag sol 2.
ilim ) 0.620nFAD2/3ω1/2ν-1/6[Agm]
(3)
where n is the number of electrons transferred, A the electrode area, D the particle diffusion coefficient, ν the kinematic viscosity, and ω the electrode rotation rate (rad s-1). A plot of the limiting current vs ω1/2 is shown in Figure 10. The linearity demonstrates that the Levich equation can be applied to small particles and further supports the idea that, for concentrated nanoparticle dispersions, direct electrochemical measurements are possible. The limiting current was found to be proportional to particle concentration within experimental error over the small range 1-12 mM Ag.10 From the plot shown, a value of n ) 1650 ( 500 was obtained. The excellent agreement is partly fortuitous, since the total error in the experimental slopes, diffusion coefficient, and colloid concentration is estimated at 2530%. The fundamental point is that both values are orders of magnitude greater than unity and prove that electron transfer from electrode to particles is a multielectron process. A third method of analysis, again using cyclic voltammetry with the RDE, is possible on the basis of a plot of the limiting cathodic current as a function of the scan rate. This yielded a further value of n ) 530 for the same silver sol. Generally, when cathodic potentials were applied to sols in the OTTLE cell, the currents decayed to nonzero steady-state values. This background current was due both to hydrogen evolution from the gold mesh and to the steady state current due to electron transfer to colloid particles. This steady state current arises because as a particle diffuses away from the electrode after accepting charge, it too begins to discharge via proton reduction. On
Figure 11. Open circuit potential of the gold mesh electrode in a silver sol (as per Figure 8) as a function of time after disconnection of the potentiostat at a potential of -0.6 V vs Ag/AgCl.
colloidal silver particles, this process is quite slow, with first-order discharge times in the region 50-300 s at -0.4 V vs NHE.23 The charge on the colloidal silver must be continuously replenished. We found that a blue-shift further than 393 nm, at a potential of -0.6-0.8 V was not possible. We know that it takes about 150 s for all particles to collect charge from the electrode; thus, the limiting position is achieved once proton reduction at the silver particle surface takes place much faster than this. To observe surface plasmon bands at even shorter wavelengths, either faster diffusion (smaller particles) or a thinner OTTLE cell is required. In Figure 11, the open circuit potential of the Au mesh is recorded as a function of time after disconnecting the potentiostat. It instantly dropped from the applied potential of -0.60 to -0.10 V (2-3 s) and then slowly drifted over 30 min toward the usual open circuit value of +0.15 V. The absorption spectrum of the sol was likewise monitored after disconnection of the potentiostat. The colloid absorption shifted to longer wavelengths, as was shown in Figure 4, but the response was much slower. The initial, fast discharge of electrons to form hydrogen on the gold mesh was too rapid for particle equilibrium to be maintained. When the position of the plasmon band in an open-circuited gold mesh OTTLE cell was monitored 10 or more min after disconnection of the potentiostat, (23) Henglein, A.; Lilie, J. J. Am. Chem. Soc. 1981, 103, 1059.
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the values were close to those obtained more directly by equilibration with a mesh held at a fixed potential. This highlights the importance of time scales for convection, diffusion, and charge transfer when making open circuit measurements on particulate systems. The advantage of the OTTLE measurements is that there is no need to rely purely on the current to demonstrate charge transfer between the electrode and the particles. II. Electrophoretic Mobility. We now briefly consider the electrophoretic mobility of charged particles. This measurement is important for an understanding of the electron transfer mechanism. Unfortunately, we cannot measure the particle mobility in the OTTLE cell directly, so there is no possibility to monitor electron transfer to the particles via their changing electrophoretic mobility. Instead, the mobility was measured by laser light scattering prior to electron transfer. The values obtained were averaged over four angles and at both stationary layers in the cell. To simulate the effects of cathodic polarization, sodium borohydride was then added to the sol. This leads to the following reactions:
a
b
3H2O + BH4- + Agm w Agm10- + BO3- + 10H+ (4) Agm10- + 10H+ w Agm + 5H2
(5)
The second reaction is much slower, so that a considerable steady state charge builds up and a strong plasmon band blue-shift occurs upon hydride reaction with the sols. Borohydride also reacts with water directly to form hydrogen, so the rate of reaction is difficult to monitor. In Figure 12, the measured mobility of the silver particles is shown before and after addition of 0.1 M NaBH4. Prior to addition, a mobility of -2.3 µm s-1 cm V-1 was found for the silver sol at Voc. The mobility was found to be independent of the particle concentration; dilution of the sol by a factor of 5 in 0.1 M NaClO4 did not lead to a perceptible change in mobility. Since Voc is positive of the silver pzc (-0.7 V vs NHE for polycrystalline Ag), the particles are positively charged due to adsorbed silver ions, and there must be superequivalent adsorption of PAA, giving rise to a net negative charge. Addition of borohydride causes the open circuit potential of the sol to jump to about -0.6 V vs Ag/AgCl as measured with both the gold mesh and a platinum flag electrode. This may cause some desorption of polyacrylic acid from the silver surface, but the major effect is a drastic increase in the magnitude of the particle mobility. Over a period of 2 h, the sol mobility then decreased again back to a value of about -2.4, as reactions 4 and 5 ran to completion. As far as we are aware this is the first direct measurement of reductant induced mobility changes on metal particles. Direct conversion of the mobility values into surface potentials or net surface charge densities is complicated by the fact that the particles are in the small κa regime.24 κa has a value of about 7-10 depending on the exact particle size and solution composition assumed. Exact conversion of the mobility to surface potential using the MOBLTY program of O’Brien and White24 showed the particles initially had a surface potential of about -30 ( 5 mV. At κa ) 10, colloid particles can only ever achieve a mobility of about -4.7 before retardation effects force a reduction in mobility. The observed value of -5.0 after addition of BH4- is close to the predicted limit. However, as is clear from the calculated values shown in Figure 12b, this mobility could correspond to a ζ potential (24) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607.
Figure 12. (a) Electrophoretic mobility of a concentrated silver sol in 0.1 M NaClO4, 2 mM PAA at pH 9 before and at various times after addition of 0.01 M NaBH4. (b) Conversion curve for electrophoretic mobility into ζ potential for κa ) 4, 10, and 20 in 0.1 M NaClO4. Calculations carried out using MOBLTY.24
anywhere between -100 and -300 mV with respect to the bulk solution. III. Mie-Drude Model. In this section, we now explain the origins of the surface plasmon band blue-shift and attempt to derive some values for double-layer parameters from the observed dependence of the band position on electrode potential. The measured attenuation of a solution, A, is given by
A ) log10 Io/Id ) NCextd/2.303
(6)
where N is the number concentration of particles, d the optical path length, and Cext the extinction cross section per particle. Io and Id refer to the initial and final beam intensities. For nanosized, spherical particles in a nonabsorbing medium of dielectric function m, Cext at a wavelength λ is given by
Cext )
24π2R3m3/2 ′′ λ (′ + 2 )2 + ′′2
(7)
m
where R is the particle radius and (λ) ) ′ + i′′ is the dielectric function of the material. For silver, the conduction electrons dominate the response at optical wavelengths, and Drude theory gives accurate values of (λ) throughout the visible part of the spectrum; however, it is much easier to express in terms of the angular frequency ω ) 2πc/λ.
(ω) ) ∞ - ωp2/(ω2 + iωg)
(8)
The plasma frequency ωp ) Ne2/mo, and g the damping parameter is 1.44 × 1016 s-1 for bulk Ag; for Ag ∞ ) 5.0
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( 0.2.25 Importantly, the dielectric function depends on the conduction electron concentration, N. Changes to the particle charge alter N and thereby the dielectric function, which in turn leads to a shift in the position of the surface plasmon absorption band. Hansen and McIntyre used similar arguments to explain electroreflectance effects at bulk Ag electrodes, though the effects were much smaller.26,27 McIntyre proposed that the dielectric function is altered only over the Fermi screening length, ∼1-2 Å, and so he introduced a bulk metal coated with a surface layer with an adjusted electron density. Siiman et al. showed that when such a double-layer construction is used for small metal particles, two surface plasmon bands result, due to excitation of two distinct modes in the particle core and in the surface layer.28 An exact solution to the electrical properties of the particles also requires that one take into account the fact that the compensating cation for the excess charge is not part of the lattice but is a solution cation, H+ or Na+ in our case. Thus the normal and added conduction electrons may have different responses to applied electric fields, but this should not be important at optical frequencies. From eqs 7 and 8 and the resonance condition ′ ) -2m, it follows that the peak positions are related directly to the relative electron concentration through
λf2 ) λi2Ni/Nf
(9)
where N is the conduction electron concentration and i and f refer to initial and final states, respectively. It is then readily shown that, for nanosized particles, the capacitance of the electrical double layer, K, is related to the electrooptical shift by
K ) ∆σ/∆E )
(λf2/λi2 - 1)aF 3Vm∆E
(10)
Inserting λi ) 404 nm and λf ) 392 nm, a ) 5.65 nm, F ) 96487 C mol-1, and Vm ) 10.26 cm3 mol-1, for which E varied from +0.4 to -0.7 V, we obtain K ) 80 µF cm-2, a result in close agreement with direct capacitance measurements for polycrystalline silver.29 Our spectroelectrochemical results do not allow us to state what the potential of zero charge is. Therefore, in Figure 6, where we have shown the number of electrons per particle being transferred in order to shift the redox potential to any arbitrary value, we have simply taken +0.4 V vs Ag/AgCl as a reference point, since this is the most positive potential at which stable spectra could be obtained. From the spectral shift, 1790 electrons are needed to alter the position of the surface plasmon band from 404 to 392 nm or to raise their electrochemical potential from +0.4 to -0.7 V, which corresponds to a charge density increase of 6.2%. This is in very good agreement with the direct electrochemical value of n ) 1600. Thus the electrochemical and electrooptical results both demonstrate that significant changes in charge density are required to polarize nanosized metal particles. Clearly, since the double-layer capacitance of a particle should scale with the surface area, the amount of charge transferring to (25) Johnston, P. B.; Christy, R. W. Phys. Rev. B 1972, 8, 4370. (26) Hansen, W. N.; Prostak, A. Phys. Rev. 1967, 160, 600; 1968, 174, 500. (27) McIntyre, J. D. E. Surf. Sci. 1973, 37, 658. (28) Siiman, O.; Bumm, L. A.; Callaghan, R.; Blatchford, C. G.; Kerker, M. J. Phys. Chem. 1983, 87, 1014. (29) (a) Bockris, J. O’M.; Khan, S. U. M. Surface Electrochemistry; Plenum Press: New York, 1993; p 160. (b) Hamelin, A. In Modern Aspects of Electrochemistry; Conway, B. E., White, R. E., Bockris, J. O’M., Eds.; Plenum Press: New York, 1985; Vol. 16.
Figure 13. Position of the surface plasmon band of 0.10 mM silver sols immediately after preparation using 1 mM NaBH4 and after various periods of aging as a function of the added PAA concentration.
individual silver particles during each encounter will scale as the square of the particle radius. The value of 1600 is a weighted average over the total colloid surface area. If the double-layer capacitance remained independent of size for particles down to 1 nm in diameter, we can see from eq 10 that a similar potential jump would entail charge density changes of around 50%. IV. Optical Effects of Polymer Adsorption. The initial surface plasmon band positions of the colloidal silver samples were found to be increasingly red-shifted at higher PAA concentrations. The effects of polymer concentration on peak position are shown in Figure 13, where silver sols were prepared under identical conditions using a fixed concentration of NaBH4 as reductant, but with variable PAA concentrations. There is a clear shift to longer wavelengths at higher polymer concentrations. This is attributed to the creation of a dielectric coating around the particles. The condition for surface plasmon resonance will shift with coating thickness to longer wavelengths.30 A shift of 10 nm corresponds to a shell layer of refractive index 1.50 having a thickness of about 10-14 Å. This thickness is similar to the thickness measured by AFM for adsorbed PAA on ZrO2 particles.31 The actual band position also changes with time after sol preparation because of the changing Fermi level in the particles as borohydride ion is continually consumed, producing hydrogen (eqs 4 and 5). Consequently, the particle charge becomes more positive after preparation. As the positive charge density increases, the plasmon band red-shifts, but simultaneously adsorption of the anionic polymer becomes more favorable and this induces an even stronger red-shift, as well as some damping. Unfortunately, allowance for the presence of the dielectric layer is impossible without independent adsorption data for PAA on colloidal silver as a function of the particle charge. These effects are shown schematically in Figure 14 and stress the interplay between the electrooptical shift induced by the changing conduction electron concentration after an encounter with the electrode and the resultant change in polymer configuration, which alters the refractive index of the coating around the particle and also results in spectral shifts. V. Mechanism of Charge Transfer. We now address two final, contentious points concerning the actual mechanism of electron transfer in these systems. The main question is that of the mechanism for charge transfer from (30) Mulvaney, P. Langmuir 1996, 12, 788. (31) Biggs, S.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1994, 90, 3415.
Spectroelectrochemistry of Colloidal Silver
Figure 14. Diagram illustrating the effect of charge transfer on the optical properties of polymer-stabilized silver sol particles. Small surface charge promotes chemisorption of carboxyl groups from the polyelectrolyte and a denser, thicker stabilizer layer. A layer with a refractive index greater than that of the solvent red-shifts the surface plasmon band.30 The shift is greater for thicker films or for denser films because they have higher refractive indices. Transfer of electrons from reductants such as borohydride ions or from a mesh electrode causes a blue-shift of the surface plasmon band due to the increased metal plasma frequency. However, the charge may also induce some desorption of the polymer from the surface (i.e. thinner dielectric layer) or for smaller charge densities simply a polymer swelling (thicker layer but lower refractive index). For any particular PAA concentration, reproducible, equilibrium peak positions vs electrode potential are obtained, but the absolute values depend on the thickness of the dielectric layer and its effective refractive index.
mesh to particle. Three mechanisms can be envisaged. The first is contact electrification, where the colloid particles adsorb to the surfacesdespite the electrostatic repulsionsand then make direct metal-metal contact with the electrode. The second mechanism is dielectric breakdown, where the intense electric field existing between the mesh and particles at closest approach (estimated at 10-20 Å) causes a breakdown in the solvent layers between the metals and a nanospark of charge flows across the gap. The 0.5 V difference in Fermi levels between electrode and particles implies fields of >108 V m-1, easily enough to cause electrical breakdown in water over macroscopic distances. The third mechanism is direct tunneling through both the solvent and polymer layers between the metals. In order to decide which mechanism is more likely, we need to calculate the interaction energy for the particles with the mesh during approach of the particles to the surface. In principle, this can be calculated with the sphere-plate geometry used in classical DLVO theory for particle coagulation. The primary problem is that the electrostatic potentials of the particle and electrode cannot be measured on the same electrochemical scale, so exact values cannot be used. The following qualitative results can be used to indicate the effects involved. The potential of zero charge of gold is about -0.4 V vs Ag/AgCl,29 so that at -0.6 V, where the particle reaction is diffusion controlled, the surface potential is at least -200 mV with respect to the solution. For the silver colloid, we have a total electric potential with respect to the bulk solution of -30 mV from the mobility measurements. This potential is due to both carboxyl groups on the adsorbed polymer and residual silver ions. The Hamaker constants for both gold and silver are 2.5 × 10-19 J.32 The ionic strength is 0.10 M, and the particle radius is 55 Å. The (32) Biggs, S.; Mulvaney, P. J. Chem. Phys. 1994, 100, 8501.
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Figure 15. Calculated interaction energies for spheres of radius a ) 5.5 nm and ζ potentials of -30 and -200 mV with a flat plate of surface potential -200 mV. κ ) 109 m-1. A ) 2.5 × 10-19 J.32 No retardation of the van der Waals interaction included. Mixed boundary conditions assumed, with plate at constant potential and sphere at constant charge: (curve A) sphere -200 mV, plate -200 mV, van der Waals plane offset by 4 nm; (curve B) as per curve A but sphere at -30 mV; (curve C) as per curve B but van der Waals term not offset.
calculated interaction curves are shown in Figure 15.33 The sphere energy was obtained by integration of the equivalent flat-plate interaction energy curves. The lower curve, curve C, was calculated with both the surface charge and the van der Waals plane located at the respective metal surfaces. The curve predicts strong attraction at all separations, because the Debye length is just 10 Å in the presence of the supporting electrolyte. This implies that the silver sol itself is unstable and that the particles should also aggregate spontaneously with the electrode. In fact the sol is stable for months. To resolve this, we need to account for the steric effects of the poly(acrylic acid) stabilizer. Recent AFM work on PAA (MW 2000) adsorption at metal oxides shows that a 2-3 nm steric barrier is created even at very low concentrations on each surface.31 We can simulate this by offsetting the plane of charge due to the polymer from the metal surface. Incorporation of a 4 nm steric barrier (equivalent to offsetting the plane of charge on each surface by just 2 nm) leads to curve B, which now shows that although there is still a substantial van der Waals attraction between the two surfaces down to about 2 nm separation (or 6 nm between the actual metal surfaces), the electrostatic charge creates a substantial barrier to coalescence at separations between about 1 and 2 nm. The model then predicts that the particles will not coagulate on the gold electrode surface but that diffusion to the mesh is probably enhanced at small separations by van der Waals forces. The calculations are very sensitive to the offset used, but any offset greater than about 3 nm is sufficient to create an electrostatic barrier to coalescence. Curve A shows the interaction curve after the silver particle is polarized. It shows that, after electron transfer, an even greater electrostatic barrier is present, as expected. This will cause the particles to move away from the electrode after charging, though the calculations still indicate a very strong secondary minimum some 4-6 nm away from the electrode surface. In view of (a) the observed colloid stability, (b) the repeptizability of the dried silver sol, and (c) the calculated stability of the mesh-particle system in the presence of a thin, 2 nm PAA layer, we contend that no direct metal-metal contact occurs during the electrochemical processes described in this paper. Contact (33) As boundary conditions for the solution of the force between the electrode and the sphere, we assume that the gold mesh is at constant potential, since this electrode is potentiostated, but that the silver particle surface charge remains constant during approach to the electrode. The force is then integrated using the Derjaguin approximation, valid since κa ) 7-10.
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electrification, i.e. particle adsorption followed by transient metal-metal contact, is excluded as a charge transfer mechanism. The second possible electron transfer mechanism is through dielectric breakdown. Szklarcyk has recently reviewed the mechanisms for breakdown of liquids.34 There are some six basic physical models, but electrochemical mechanisms are perhaps most useful, since they can also explain the effects of electrode material on the breakdown voltage. Electrochemical models require that the Fermi energy of the electrode be sufficiently high that electrons can be emitted directly into the solvent conduction band. For water, this would imply electrode potentials of at least -3 V vs Ag/AgCl. We observe charge transfer at potentials of just -40 mV vs Ag/AgCl. Other mechanisms also generally invoke strong acceleration of emitted electrons by the field between the two electrodes. Whilst the absolute value of the electric field between the particles and the gold mesh is extremely high, the separation is extremely small, and field-enhanced liquid dissociation and collision ionization are not energetically feasible. For these reasons, we believe that dielectric breakdown does not occur during the experiments described in this paper. Instead, we believe direct Fowler-Nordheim tunneling from the electrode to the particles is sufficient to explain the experimental data. Whilst the tunneling process requires the simultaneous transfer of hundreds, or even thousands, of electrons across the double layers between the two metal surfaces, the DLVO calculations suggest that the polymer-coated silver particles approach the gold mesh to within 1-2 nm at the high ionic strength employed in the experiments, and this is close enough for tunneling to be significant. (The colloid particles are no different from STM tips in this sense, except that they are interacting under open circuit conditions.) Direct electrode-particle tunneling opens up the possibility of a second interesting phenomenon during particle electrochemistry. It is clear that once a silver particle is cathodically polarized, it is then capable of transferring charge directly to a second unreacted particle. Charge could then migrate through the OTTLE cell by a sort of relay system, driven by the different redox potentials on each silver particle, without the necessity for each particle to diffuse the entire distance to the electrode. The probability of electron tunneling between charged and uncharged silver particles should be similar to the electrode-particle case; however, since the donor particle charge would not be replenished during Fermi level equilibration of two particles in solution, the tunneling probability would decrease rapidly as charge transferred (34) Szklarczyk, M. In Modern Aspects of Electrochemistry; Conway, B. E., White, R. E., Bockris, J. O’M., Eds.; Plenum Press: New York, 1993; Vol. 25, p 253.
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from one particle to the other. Since the donor redox potential would become more positive too, each particle would need many such equilibration encounters before all particles reached the mesh potential. Direct, spontaneous Fermi level equilibration between polymer-coated silver and lead colloid particles has recently been reported.35 Equilibration was found to take several hours. Conclusions Direct electrochemical equilibration with a gold mesh electrode on a time scale as short as 150-200 s has been demonstrated.36 The optical properties of colloidal silver are systematically affected by changes to the surface charge density on each particle. The spectral shifts can in principle be calculated from Mie-Drude theory. However, the presence of dielectric layers and the potential dependent chemisorption of stabilizer molecules may present insurmountable difficulties when reconciling peak positions exactly with theory. We have shown by chronoamperometry, steady state absorption measurements, linear sweep voltammetry, and laser doppler electrophoresis that the surface plasmon band position is blueshifted during electron accumulation, and we have attempted to quantify the relationship between peak position and surface charge density. A value of 80 µF cm-2 for the silver-water double-layer capacitance in 0.1 M NaClO4 adds credibility to the method of analysis. On the basis of both electrochemical and electrooptical data, some 1600 ( 300 electrons are transferred simultaneously during a single particle-electrode encounter when large negative potentials are applied to the electrode. The most exciting point, and one that remains unanswered, is the actual method of equilibration and whether the electron current that flows is due to contact electrification, to nanosparking, or to multielectron tunneling across the Helmholtz layers between the two metal surfaces. The results here point indirectly to tunneling, and this aspect is being investigated by STM studies at present underway. Acknowledgment. P.M. acknowledges the receipt of an ARC QEII Research Fellowship. The continued support of the Advanced Mineral Products Research Centre, an ARC Special Research Centre is gratefully acknowledged. M.G. is the recipient of an ARC International Research Fellowship. We thank Derek Chan for useful discussions as well as access to his “dissimilar surfaces” program. Useful advice from Paul Duckworth of AD Instruments is also appreciated. LA960863Z (35) Henglein, A.; Holzwarth, A.; Mulvaney, P. J. Phys. Chem. 1992, 96, 8700. (36) During the course of this study, a series of papers involving voltammetry of metal oxide colloids and suspensions was published by Heyrovsky and co-workers (Langmuir 1995, 11, 4288). They also showed that multielectron transfer occurred in semiconductor dispersions.
