pubs.acs.org/Langmuir © 2009 American Chemical Society
Colloidal Gold-Catalyzed Reduction of Ferrocyanate (III) by Borohydride Ions: A Model System for Redox Catalysis Susana Carregal-Romero,† Jorge Perez-Juste,† Pablo Herves,*,† Luis M. Liz-Marzan,† and Paul Mulvaney*,‡ †
Departamento de Quı´mica Fı´sica, Universidade de Vigo, E-36310, Vigo, Spain, and ‡School of Chemistry & Bio21 Institute, University of Melbourne, VIC, 3010 Australia Received July 7, 2009. Revised Manuscript Received September 10, 2009
We report results on the large catalytic effect of spherical gold nanoparticles on the rate of reduction of hexacyanoferrate (III) by sodium borohydride in aqueous solution. Because the gold nanoparticles remain stable and no aggregation takes place during the reaction, it can be monitored until completion. The presence of colloidal gold leads to a considerable increase in the observed reaction rate and to a change in the order of reaction. The reaction is first-order with respect to the hexacyanoferrate (III) concentration and gold particle concentration, but the reaction order with respect to borohydride ion is more complex. The activation energy is found to be 15 kJ/mol for 15 nm gold particles. The redox reaction is activation-controlled under most conditions, but the rate of reaction approaches the diffusion limit for higher borohydride concentrations and is over 104 times faster than in the absence of the gold catalyst.
Introduction Because of the increasing urgency to develop efficient methods for the fixation of atmospheric N2, chemical reduction of CO2, generation of hydrogen from water, and for the elimination of environmental pollutants, research into redox catalysis1 has remained an active topic for over half a century.2,3 Pt, Pd, and Rh remain the most common metal catalysts, particularly for hydrogenation reactions, and are usually prepared in situ as nanoparticles supported on ceramic carriers such as silica or alumina,4,5 or dispersed in organic solvents.6 However, more recently, gold and silver nanoparticles of different sizes have been used to catalyze electron transfer7-10 and oxidation reactions11 and both Ag and Au have recently been found to exhibit catalytic effects on some important reactions, such as CO oxidation and desulfurization reactions.12,13 Catalytic activity is strongly affected by particle size and shape, and consequently, the synthesis of colloidal nanoparticles which have well-controlled size and shape has become very important.14 The recent advent of protocols for synthesizing platinum, gold, and silver nanocrystals with different morphology has opened up the possibility of doing systematic morphology studies to answer these questions. For example, studies using platinum *Corresponding author. (1) Sinfelt, J. H. Acc. Chem. Res. 1977, 10, 15–20. (2) Turkevich, J.; Miner, R. S., Jr.; Babenkova, L. J. Phys. Chem. 1986, 90, 4765–4767. (3) Bond, G. C.; Turkevich, J. Trans. Faraday Soc. 1953, 49, 281–291. (4) Sinfelt, J. H.; Via, G. H. J. Catal. 1979, 56, 1–11. (5) Nakao, Y.; Kaeriyama, K. Chem. Lett. 1983, 949–950. (6) Toshima, N.; Yonezawa, T. New J. Chem. 1998, 22, 1179–1201. (7) Freund, P. L.; Spiro, M. J. Phys. Chem. 1985, 89, 1074–1077. (8) Kamat, P. V. J. Phys. Chem. B 2002, 106, 7729–7744. (9) Hirakawa, T.; Kamat,, P. V. J. Am. Chem. Soc. 2005, 127, 3928–3934. (10) Sau, T. K.; Pal, A.; Pal, T. J. Phys. Chem. B 2001, 105, 9266–9272. (11) Rodrı´ guez-Fernandez, J.; Perez-Juste, J.; Mulvaney, P.; Liz-Marzan, L. M. J. Phys. Chem. B 2005, 109, 14257–14261. (12) Haruta, M. Chem. Rec. 2003, 3, 75–87. (13) Mohr, C.; Claus, P. Sci. Prog. (St. Albans, U.K.) 2001, 84, 311–334. (14) (a) Hao, E.; Schatz, G. C.; Hupp, J. T. J. Fluoresc. 2004, 14, 331–341. (b) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668–677. (c) Germain, V.; Brioude, A.; Ingert, D.; Pileni, M. P. J. Chem. Phys. 2005, 122, 124707/1–124707/8.
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nanoparticles of various shapes have been reported by El-Sayed and co-workers, and the catalytic activity has been found to correlate with the fraction of surface atoms located on corners and edges.15 Gold provides an even better system for examining shape effects because gold nanocrystals can now be synthesized with a wide range of morphologies including rods, cubes, octahedral, prisms and decahedra.16 Furthermore, gold nanoparticles can be prepared as monodisperse spherical colloids (s.d. < 10%) with sizes ranging from 3 nm up to 100 nm in diameter. However, in order to carry out systematic studies on the role of particle size, shape, surface roughness, and faceting on catalytic rates of redox catalyzed reactions, it would be useful to have a standard redox reaction as a benchmark. In this paper we report on a model system for redox catalysis: the colloidal gold catalyzed reduction of hexacyanoferrate (III) ions by borohydride ions in alkaline, aqueous solution. The gold nanoparticles remain colloidally stable, and no aggregation takes place during catalysis. The advantage of this system is that the whole reaction can be monitored spectroscopically,7,15,17 and, consequently, the catalytic effects of different metals can be readily compared. We demonstrate that the catalyzed reaction can be up to 4 104 times faster (under our experimental conditions) than the uncatalyzed one18,19 and can be controllably shifted between activation-control and diffusion-limited reaction kinetics. The intrinsic rate constants and transfer coefficient can be extracted from the kinetics and the issue of maintaining stable redox potentials during nanoscale redox catalysts is discussed. Finally, the perplexing problem of colloid coagulation during catalysis can be largely circumvented, because both the reagents and the colloidal gold catalyst particles are negatively charged, as are most noble metal nanocatalysts in aqueous solution. (15) (a) Narayanan, R.; El-Sayed, M. A. Nano Lett. 2004, 4, 1343–1348. (b) Narayanan, R.; El-Sayed, M. A. J. Am. Chem. Soc. 2004, 126, 7194–7195. (16) Grzelczak, M.; Perez-Juste, J.; Mulvaney, P.; Liz-Marzan, L. M. Chem. Soc. Rev. 2008, 37, 1783–1791. (17) Jiang, Z.-J.; Liu, C.-Y.; Sun, L.-W. J. Phys. Chem. B 2005, 109, 1730–1735. (18) Freund, T. J. Inorg. Nucl. Chem. 1959, 9, 246–251. (19) Bhattacharjee, M.; Bhattacharjee, A. K.; Mahanti, M. K. Bull. Chem. Soc. Jpn. 1981, 54, 3566–3569.
Published on Web 10/14/2009
DOI: 10.1021/la902442p
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Experimental Details Materials and Methods. Tetrachloroauric acid (HAuCl4 3 3H2O), trisodium citrate dihydrate, sodium borohydride, and sodium hydroxide were purchased from Aldrich, and potassium hexacyanoferrate (III) was purchased from Scharlab and used as received. Milli-Q water with a resistivity higher than 18.2 MΩ cm was used in all experiments. Synthesis of Au Nanoparticles. Gold sols were prepared by boiling 5 10-4 M HAuCl4 in the presence of 1.6 10-3 M sodium citrate for 20 min.20 This results in a stable dispersion of gold particles with an average diameter around 15 nm and 10% polydispersity. Au colloids with higher concentration but similar size were prepared by a modification of this method recently described by Pan et al.21 Nanoparticle Characterization. Transmission electron microscopy (TEM) was carried out with a JEOL JEM 1010 transmission electron microscope operating at an acceleration voltage of 100 kV. For TEM preparation, a drop of the particle solution was placed on a Formvar-coated copper grid and dried at room temperature. Kinetic Measurements. Fast reactions were carried out in an Applied Photophysics SX-18MV Stopped-Flow Reaction Analyzer while slower reactions were monitored in an Agilent 8453 UV-vis diode-array spectrophotometer, both thermostatted with an accuracy of 0.2 C. NaCl was used to keep the ionic strength of the medium at 0.085 M. Kinetic data were always satisfactorily fitted to first-order integrated rate equations, and therefore, in what follows, kobs denotes the pseudofirst order rate constant. The rate constants were reproducible to within 5%. Electrochemistry Measurements. Electrochemistry data were obtained using a standard three-electrode electrochemical cell with a TEQ-Argentina potentiostat. A small gold flag electrode was used as a working electrode. A Ag/AgCl electrode in 3 M KCl was employed as a reference, and all electrode potentials were referred to it; a platinum gauze auxiliary electrode of large area was employed. All electrochemical measurements were carried out at room temperature. All experiments were carried out at pH = 11.5, and this value remained constant during the time required to complete the reaction.
Results The reduction of hexacyanoferrate (III) by borohydride ions in aqueous solution can be written as18 BH4 - þ 8FeðCNÞ6 3 - þ 3H2 O f H2 BO3 þ 8FeðCNÞ6 4 - þ 8H þ
ð1Þ
The advantage of using hexacyanoferrate ions for this redox study is that in both oxidation states (+2 and +3), iron ions are stable with respect to dissociation, do not hydrolyze and possess the same geometry and chemical composition.18 The redox potential corresponding to the reaction being studied, E0 (Fe(CN)63-/ Fe(CN)64-) is +0.44 V versus a normal hydrogen electrode (NHE). The standard reduction potential for borate ion reduction is H2 BO3 - þ 5H2 O þ 8e - f BH4 - þ 8OH E0 ¼ -1:24 V vs NHE Hence there is an enormous free energy change associated with the reaction. During the reduction of Fe(III) by BH4-, the (20) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday Soc. 1951, No.11, 55–75. (21) Pan, B.; Gao, F.; Ao, L.; Tian, H.; He, R.; Cui, D. Colloids Surf., A 2005, 259, 89–94.
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Figure 1. Spectral evolution of a mixture of hexacyanoferrate (III) and Au nanoparticles upon borohydride addition. [Fe(CN)63-] = 8.33 10-4 M, [BH4-] = 0.01 M, [Au]NP = 2.28 10-10 M. T = 15 C, pH = 11.5. t1/2 = 7.48 s. The inset shows that the Au surface plasmon band remains unchanged during the reaction. The total reaction time is 50 s.
hydrolysis of the borohydride ions (represented by eq 2), also occurs and thus competes with eq 1: BH4 - þ 2H2 O f 4H2 þ BO2 -
ð2Þ
Fortunately, this chemical decomposition of the reducing agent can be strongly inhibited by working at high pH.22 For this reason, the pH was maintained at 11.5 for all of the experiments reported here, and we can therefore neglect this side reaction, which is slow on the time scale of the catalyzed reactions. To further avoid side reactions and thus obtain cleaner kinetic traces, the reactions were carried out under anaerobic conditions. I. Influence of Hexacyanoferrate (III) Concentration. The experiments were carried out under pseudo-nth-order conditions such that [Fe(CN)63-] , [NaBH4]. Under these conditions, the reaction of the ferrocyanide ion obeys -
d½FeðCNÞ36 - ¼ k obs ½FeðCNÞ36 - n dt
ð3Þ
where kobs is the pseudo-nth-order rate constant for the reaction. The rate of reaction was monitored spectrophotometrically, following the decrease of the hexacyanoferrate (III) absorption band at 420 nm. From the spectra shown in Figure 1, it can be clearly observed that, during the period required for complete reduction of hexacyanoferrate (III), the absorbance band at 520 nm due to the surface plasmon resonance of gold nanoparticles remains totally unchanged, proving that the gold particles remain colloidally stable and that no aggregation takes place during catalysis.23 The stability of the gold nanoparticles was also checked by TEM. Figure 2 shows representative TEM images of the gold nanoparticles before and after the reaction; the size as well as the shape of the nanoparticles remains unchanged. Furthermore, there is no chemical reaction between the reactants and the nanoparticles. It is worth noting that this has been reported to occur with Pt nanoparticles,15,24 where it is proposed (22) Chatenet, M.; Micoud, F.; Roche, I.; Chainet, E. Electrochim. Acta 2006, 51, 5459–5467. (23) Pastoriza-Santos, I.; Gomez, D.; Perez-Juste, J.; Liz-Marzan, L. M.; Mulvaney, P. Phys . Chem. Chem. Phys. 2004, 6, 5056–5060. (24) (a) Narayanan, R.; El-Sayed, M. A. J. Phys. Chem. B 2003, 107, 12416– 12424. (b) Narayanan, R.; El-Sayed, M. A. J. Phys. Chem. B 2004, 108, 5726–5733.
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Figure 2. Representative TEM images and size distributions of gold nanoparticles acquired before (left) and after (right) performing the reaction.
that hexacyanoferrate (III) ions react with surface Pt atoms, resulting in Pt dissolution in the form of cyanide complexes, thus leading to a gradual reduction in nanoparticle size. The colloidal stability of the gold nanoparticles during the time needed to complete the reaction25 (typically between 0.15 and 50 s) makes this system very attractive for detailed studies of their catalytic activity. The gold nanoparticles dramatically increase the reaction rate, but more significantly, they also change the order of the reaction with respect to the reactants. While the direct reduction of hexacyanoferrate (III) to hexacyanoferrate (II) with borohydride ions has been reported to follow zero-order kinetics with respect to [Fe(CN)63-],18,19 with a half-life around 5000 s, when gold nanoparticles are present, first-order kinetics were consistently observed, and the half-lives were typically much shorter than those observed for the uncatalyzed reaction under the same conditions (pH = 11.5, T = 15 C, and inert atmosphere) and the same starting reactant concentrations. As an example, for a gold colloid concentration of 2.28 10-10 M, the measured halflife was of just 7.48 s (see Figure 1). Figure 3 shows a typical time trace of the absorbance, which highlights the high-quality, firstorder kinetics of the reaction. The rate constant for reduction of Fe(CN)63- has been studied for [Fe(CN)63-] ranging between 0.21 10-3 and 1.26 10-3 M at a fixed Au nanoparticle concentration. We found that the kobs values are independent of the ferricyanide concentration, as predicted by eq 3. In all cases, the experimental results can be fitted perfectly to eq 4, and conform to strictly first-order kinetics under all the experimental conditions used, often for over 6 halflives (see Supporting Information, Figure S1). (25) We observed Au nanoparticle degradation after 30 min, when all the reactions studied were complete.
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Figure 3. Kinetic trace of the absorbance at 420 nm during the reduction of Fe(CN)63- and linearized data for first order analysis according to eq 4. [Fe(CN)63-] = 8.33 10-4 M, [BH4-] = 0.01 M, [Au]NP = 2.28 10-10 M. kobs = 9.22 10-2 s-1, t1/2 = 7.48 s.
-ln
At -A¥ ¼ kobs t Ao -A¥
ð4Þ
II. Influence of Catalyst Concentration. The effect of the amount of catalyst on the reaction rate was studied at three different NaBH4 concentrations (0.050, 0.010, and 0.002 M). The results are summarized in Figure 4, showing that there is linear dependence of kobs on [Au]NP. The gold nanoparticle concentration was calculated from the concentration of gold ions, using ½HAuCl4 3Vm ½HAuCl4 ¼ ð5Þ ½AuNP ¼ Nagg NA 4πR3 DOI: 10.1021/la902442p
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Figure 4. Influence of the amount of catalyst on the observed pseudo-first-order rate constant at different borohydride concentrations: (b) 0.05 M, (O) 0.01 M, (9) 0.002 M, [Fe(CN)63-] = 4.16 10-4 M, pH = 11.5, T = 15 C. (Lower x-axis) in terms of moles of nanoparticles per liter, (upper x-axis) in terms of total gold surface.
where Nagg is the number of gold atoms per nanoparticle, R is the particle radius, NA is Avogadro’s number, and Vm is the molar volume of gold metal (10.3 cm3/mol). The catalytic effect of the nanoparticles depends upon both the number concentration and the surface area per particle. In Figure 4 (lower x-axis), kobs is plotted as a function of the gold particle concentration at different borohydride concentrations. There is a linear relationship between the observed rate constant and the concentration of gold particles, which indicates that the nanoparticles are indeed involved in the rate-determining step of reaction 1. To highlight the surface effect, we have plotted the values of the observed rate constant, kobs, versus the total surface area at different constant borohydride concentrations. We can see in Figure 4 (upper x-axis) that there is a linear relationship between the observed rate constant and the surface area of the metal nanoparticles. Equation 3 can thus be written as -
d½FeðCNÞ36 - dt
¼ k obs ½FeðCNÞ36 - ¼ k s ½AuNP A½FeðCNÞ36 -
ð6Þ
where A is the surface area per particle and ks is the rate constant normalized to the total surface area of gold per unit volume of solution. (Values of 7.5 nm and 19.2 g/cm-3 for the gold nanoparticle radius and gold density were used.) Equation 6 predicts the linear dependence of the observed rate constant on the available surface area observed in Figure 4. Moreover, we have found that the observed rate constant normalized to the unit gold surface area is constant over a wide range of reaction conditions (see Figure 5). All these findings confirm the reproducibility of the rate constant data, and more importantly, demonstrate conclusively that the gold nanoparticles are acting as the true catalyst for reaction 1. Moreover, these data indicate that the catalysis takes place on the surface of nanoparticles and that the catalytic activity depends on the total surface area of the gold nanoparticles. III. Influence of Borohydride Concentration. To study the effect of borohydride concentration on the reduction of 1274 DOI: 10.1021/la902442p
Figure 5. Values of kobs normalized by total surface area, averaged for different nanoparticle concentrations at the same NaBH4 concentration. The dashed lines represent the mean value in each case. Borohydride concentrations: (b) 0.05 M, (O) 0.01 M, (2) 0.002 M; [Fe(CN)63-] = 4.16 10-4 M, pH = 11.5, T = 15 C, ionic strength = 0.085.
Figure 6. Influence of NaBH4 concentration on the observed rate
constant at different gold nanoparticle concentrations: (0) 1.50 10-9 M, (9) 1.13 10-9 M, (b) 7.50 10-10 M, (O) 3.80 10-10 M. [Fe(CN)63-] = 4.16 10-4 M, pH = 11.5, T = 15 C, ionic strength = 0.085. The lines are guides to the eye.
ferricyanide, experiments were conducted at different gold nanoparticle concentrations (between 3.8 10-10 and 1.6 10-9 M) while varying the BH4- concentration, (see Figure 6). The observed rate constant does depend on borohydride concentration, but the dependence is complex, being approximately linear at low borohydride concentrations but the rate of reaction asymptotes to a maximum value, which depends on the amount of gold nanoparticles, as the concentration of BH4- is increased. IV. Influence of Temperature. The temperature dependence of the reaction rate was studied over the temperature range of 5-30 C. All solutions were thermostatted for at least 5 min prior to starting the reaction within the stopped-flow spectrometer. The results are summarized in Figure 7, where ln kobs (s-1) is plotted versus T-1 at two different borohydride concentrations. The activation energy for the catalyzed reaction (mean value of 15.6 ( 1.1 kJ mol-1) is half the activation energy of the noncatalyzed reaction reported by Freund,18 (30 kJ mol-1). From the intercept of Figure 7, we derived a value for the activation entropy (ΔS‡) of -180 J mol-1 K-1. Langmuir 2010, 26(2), 1271–1277
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Figure 7. Arrhenius plot of the temperature dependence of the electron transfer reaction in the presence of Au nanoparticles ([Au]NP = 1.22 10-9 M) at two different borohydride concentrations; (O) 0.007 M and (9) 0.0025 M. [Fe(CN)63-] = 4.16 10-4 M, pH = 11.5, ionic strength = 0.085. Scheme 1
studies by Freund18 and Bhattacharjee et al.,19 which were also carried out under basic conditions (pH = 9-13) but with no catalyst, the reaction was found to be first-order with respect to both borohydride ion and hydrogen ion but independent of hexacyanoferrate (III) concentration. Under these conditions, these authors proposed that the slow step is the formation of H+BH4 as an intermediate, which reacts with ferricyanide in subsequent, rapid steps. We have found that when gold nanoparticles are present, the reaction is first-order with respect to the hexacyanoferrate (III) ion concentration. The presence of nanoparticles makes the formation of the postulated intermediate H+BH4 unnecessary and provides a new and extremely reactive pathway for the reaction. This scheme also predicts the linear dependence on the amount of catalyst (or surface area) on the reaction rate observed in Figure 4. Nevertheless, the nonlinear influence of borohydride on the reaction rate observed in Figure 6 must be also explained. For this purpose and in order to have a more complete scenario for the reaction, we applied the generalized formulation of the mixed potential model developed by Miller et al.28 The colloidal metal is considered to couple the two halfreactions; one is the oxidation of borohydride ions BH4 - þ 8OH - þ Aun f H2 BO3 - þ 5H2 O þ 8e - ðAun Þ
Discussion Systematic studies of redox catalysis in aqueous solutions were first carried out and modeled by Spiro and colleagues,26 while Henglein used the microelectrode model to demonstrate that metal nanocrystals store electrons during redox catalysis.27 In our reaction, the metal nanoparticles act as a reservoir for electrons and become cathodically polarized. In an initial step, borohydride can inject electrons onto gold nanoparticles. The reaction is completed (see Scheme 1) in a second, slow step whereby ferricyanide ions diffuse to the nanoparticle surface and are reduced by excess surface electrons. This scheme explains the change in the reaction order of ferricyanide in the presence of gold nanoparticles. In previous
-d½BH4- ¼ ½AuNP 4πNA R2 dt -d½FeðCNÞ36 - ¼ ½AuNP 4πNA R2 dt
(
(
ð7aÞ
and the other is the reduction of hexacyanoferrate (III) ions by stored electrons on the gold colloid -
8e - ðAun Þ þ 8FeðCNÞ6 3 f 8Aun þ 8FeðCNÞ6 4
-
E0 2
ð7bÞ
In the absence of precipitation at the surface, and in the absence of adsorption equilibria, the Butler-Volmer equation can be applied to each half-cell. It can be shown (see Supporting Information and ref 28) that the specific rates of electron injection into the gold particles by borohydride ions and their extraction by Fe(CN)63- are
½H2 BO3- bulk expð -R1 Z1 Þ -½BH4- bulk exp½ð1 -R1 ÞZ1 h 1 R expð1 -R Þ R exp½ð1 -R ÞZ i 1 1 1 þ þ DH2 BO3DBH4k01
)
½FeðCNÞ36 - bulk expð -R2 Z2 Þ -½FeðCNÞ46 - bulk exp½ð1 -R2 ÞZ2 h 1 R expð -R Z Þ R exp½ð1 -R ÞZ i 2 2 2 2 þ þ DFeðCNÞ3 DFeðCNÞ4 k02 6
where Z1 = f(Εmix - Ε01), Z2 = f(Εmix - Ε02), f = F/RT, Εmix is the mixed potential, R is the particle radius, R1 and R2 are the cathodic transfer coefficients for the respective electron transfer reactions, and k10 and k02 are the standard electrochemical rate constants (cm/s) at the equilibrium (26) (a) Spiro, M. J. Chem. Soc., Faraday Trans. 1 1979, 75, 1507–1512. (b) Freund, P. L.; Spiro, M. J. Chem. Soc., Faraday Trans. 1 1983, 79, 481–490. (c) Freund, P. L.; Spiro, M. J. Chem. Soc., Faraday Trans. 1 1983, 79, 491–504. (d) Freund, P. L.; Spiro, M. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2277–2282. (27) (a) Henglein, A.; Lilie, J. J. Phys. Chem. 1981, 85, 1246–1251. (b) Westerhausen, J.; Henglein, A.; Lilie, J. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 182–189. (c) Henglein, A.; Lilie, J. J. Am. Chem. Soc. 1981, 103, 1059–1066.
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E0 1
ð8aÞ ) ð8bÞ
6
redox potential of the two couples. This general model accounts for back reactions and mass transfer limits on reactions involving simple electron transfer. Under steady state conditions, the rates of electron injection into the gold particles by borohydride ions and their extraction by Fe(CN)63- via eqs 8a and 8b are equal. The particles adopt a mixed potential Εmix that must be solved by numerical solutions to eqs 8a and 8b. For colloid catalyzed reactions, (28) Miller, D. S.; Bard, A. J.; McLendon, G.; Ferguson, J. J. Am. Chem. Soc. 1981, 103, 5336–5341.
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Table 1. Measured Open Circuit Potential of a Gold Flag Electrode versus Ag/AgCl at 20 C in the Absence and Presence of Ferricyanide Ions [NaBH4] (M)
[NaCl] (M)
[NaOH] (M)
[K3Fe(CN)6] (M)
ionic strength
E (V)
0.075
0
0.01
0.050
0.025
0.01
0.025
0.050
0.01
0.010
0.065
0.01
0.005
0.070
0.01
0 4.16 10-4 0 4.16 10-4 0 4.16 10-4 0 4.16 10-4 0 4.16 10-4
0.085 0.0875 0.085 0.0875 0.085 0.0875 0.085 0.0875 0.085 0.0875
-0.99 ( 0.0141 -1.11 ( 0.07 -0.94 ( 0.0071 -0.91 ( 0.04 -0.91 ( 0.0071 -0.83 ( 0.05 -0.81 ( 0.00 -0.81 ( 0.01 -0.75 ( 0.00 -0.76 ( 0.03
we assume that the diffusion coefficient of Fe(CN)63- (D ∼ 10-6 cm2/s), equilibrium redox potentials (E01 = -1.24 V, E 02 = þ0.44 V vs NHE) and particle radii (R = 7.5 nm) are all known, while the transfer coefficients, R1 and R2, and standard rate constants, k01 and k02, are fitting parameters. Two important simplifications are possible. First, because there is no Fe(CN)64- present in solution, the second term in eq 8b can be neglected. Second, the rate of reaction is unambiguously first-order in Fe(CN)63- concentration. This strongly suggests that the reduced acceptor, Fe(CN)63-, and the product H2BO3- do not have any effect on Emix and are effectively fixed throughout the reaction. This is primarily due to the fact that the borohydride ions are present in great excess. However, to confirm that the mixed potential on the gold colloid particles is not influenced by Fe(CN)63- ions, the open-circuit or mixed potential of a small gold flag electrode was measured for different borohydride concentrations in the presence and absence of ferricyanide. The results are shown in Table 1 and prove unambiguously that the mixed potential is determined solely by the concentration of BH4-. Consistent with this, the steady state value lies reasonably close to the Nernst potential of the borohydride couple. These data confirm that the ferricyanide does not influence the gold particles under the reaction conditions employed. This considerably simplifies the analysis. The mixed potential, Emix, is close to the value of E01 and is effectively fixed during any one run. RT ½BH4 - ln Emix ¼ E 0 1 ð9Þ zF ½H2 BO3- Inserting this value for the mixed potential into eq 8b and neglecting the second term we obtain -d½FeðCNÞ36 - ¼ ½AuNP 4πNA R2 dt expð -R2 f ΔE10, 2 Þ 1 R expð -R2 f ΔE1, 2 Þ ½BH4- þ ½H2 BO3- DFeðCNÞ3 k2 0
3!R2 ½FeðCNÞ6
½BH4- ½H2 BO3-
! R2
6
ð10Þ ΔE 01,2
Figure 8. The second-order rate constant for reduction of ferricyanide ions in the presence of different gold colloid concentrations (squares 0.75nM, circles 1.13nM, triangles 1.51nM) as a function of the NaBH4 concentration. The solutions were degassed; pH = 11.5, ionic strength = 0.085. The dotted line indicates the calculated diffusion limit assuming D = 2.6 10-6 cm2/s. Fits to eq 10 with R2 = 0.8; for three different values of k02; ΔE01,2 = þ0.7 V.
The unknown parameters in eq 10 are ΔE 001,2, D, k02, and R2. Bortels reported a value29 of D = 6.7 10-6 cm2/s, but this drastically overestimates the limiting rate constant for all gold catalyst concentrations. A slightly lower value of D = 2.6 10-6 cm2/s was chosen for the diffusion coefficient of the Fe(III) ions, which yields the plateau values shown in Figure 8. The value of ΔE 01,2 = þ1.5 V is based on tabulated values;30 however, from the experimental values of the mixed potential in Table 1, the overpotential lies closer to ΔE 01,2 = þ0.7 V. This leaves k02 and R2 as the only parameters to be fitted to the data in Figure 8. Linear leastsquares fitting yields a best fit of k02 = 1 10-7 cm/s and R2 = 0.8. We mentioned above that the rate of the reduction clearly plateaus at high borohydride ([NaBH4] ∼0.1M). At higher borohydride concentrations, the gold particles accumulate a large number of electrons (several thousands) and the overpotential for electron transfer to the ferrocyanide becomes large enough that the rate of reduction becomes limited by the rate of diffusion of ferricyanide ions to the gold particles. Therefore, the second term of the denominator of eq 10 becomes much higher than 1/k02, and then the observed rate becomes independent of [BH4-]. We identify this plateau with the diffusion limited rate of reaction, given by eq 11:
Here is the difference in standard redox potentials between the donor and acceptor redox couples. This equation predicts a linear dependence on the gold colloid concentration and the ferricyanide ion concentration, as observed experimentally. In Figure 8, we show plots of the second-order rate constant for electron transfer as a function of log10[NaBH4] and [Au], for [Fe(CN)63-] = 4.16 10-4 M. As can be readily observed, there is a drastic rise in the rate constant as the NaBH4 concentration is increased. However, in all cases, the rate of reduction clearly plateaus at about [NaBH4] ∼0.1 M. We identify this plateau with the diffusion limited rate of reaction.
-d½FeðCNÞ36 - ¼ ½AuNP 4πNA RDFeðCNÞ3 - ½FeðCNÞ36 - ð11Þ 6 dt From the values in Table 1 the gold particle mixed potential during the transition to diffusion control is about -0.8 V vs Ag/AgCl.
(29) Bortels, L.; Van den Bossche, B.; Deconinck, J.; Vandeputte, S.; Hubin, A. J. Electroanal. Chem. 1997, 429, 139–155.
(30) Latimer, M. Oxidation Potential, 2nd ed.; Prentice-Hall/Academic Press: New York, 1959.
1276 DOI: 10.1021/la902442p
Langmuir 2010, 26(2), 1271–1277
Carregal-Romero et al.
Article
This is about 1 V cathodic of the Nernst potential for the hexacyanoferrate (II,III) redox couple, E 02. This implies that an enormous overpotential is required to drive the reduction of the hexacyanoferrate (III) ions at the diffusion limited rate. Hence the value of the standard electrochemical rate constant k02 must be very small. For lower [BH4-], the overpotential is too low to drive the reaction at the diffusion limited rate. Under these conditions, the reaction is activation controlled rather than mass-transferlimited, and the value of 1/k02 is much higher than the second term of the denominator of eq 10, and then the order with respect to the borohydride ion is equal to the cathodic transfer coefficient (R2) for the reduction of Fe(CN)63-. The obtained value for R2 = 0.8 explains the nonlinear dependence of the observed rate on [BH4-]. The dependence of kobs on borohydride concentration observed in Figures 6 and 8 implies a change from a surface-controlled reaction to a diffusioncontrolled one. It is important to recognize that the observed rate is linearly dependent on the gold particle concentration, irrespective of whether the reaction is diffusion limited or activation controlled. Only the magnitude of the second-order rate constant indicates which regime is operative. Increasing the borohydride ion concentration increases the rate constant by increasing the steady state concentration of electrons on the gold catalysts. However at higher borohydride concentrations, the increase of the observed rate constant is lower and tends to reach a plateau, indicating a change from surface-controlled to a diffusioncontrolled process at higher [BH4-]. The experimental data suggest the diffusion limit is reached when the gold colloid redox potential is about -0.8 V vs Ag/ AgCl. Only a few reductants are likely to drive the mixed potential to such cathodic values. For our system, the diffusion-controlled rate constant kd = 4πDRNA would be ca. 1.5 1010 M-1 s-1 taking R = 7.5 10-9 m, D = 2.6 10-6 cm2/s, and NA being Avogadro’s constant. The value of the bimolecular rate constant for the reaction can be easily obtained from the slopes of Figure 4 using eq 6. Table S1, in the Supporting Information, shows the obtained values. They range from about 3.5 times smaller than the predicted diffusion limit (for low borohydride concentrations) to a very close value to the diffusion-controlled rate constant for high borohydride concentrations. From the limiting values of kobs reached at high concentrations of borohydride in Figure 6, we obtain values for the bimolecular rate constant ranging from (0.82-1.5) 1010 M-1 s-1, in very good agreement with the theoretical diffusion-controlled rate constant for our system. To calculate the diffusion limited rate constant, we have assumed a diffusion coefficient for the Fe(CN)63- ion of ∼2.6 10-6 cm2/s, within a factor of about 2.5 of the value of Bortels and colleagues29 of 6.7 10-6 cm2/s. Since both the colloid and the acceptor ion are strongly negatively charged, there will be a reduction in the rate of mass transfer due to migration, which we have not included.31 Hence this should be considered as a very good agreement. Finally, we note that metal nanoparticles in solution are prone to coalescence due to their high surface energy and the correspondingly large dispersion forces, and thus they show a tendency to aggregate during the catalytic processes, unless they are properly protected. Consequently, polymers, complex ligands, and surfactants are often used as stabilizers
for metal catalysts.32,33 Alternatively, polyelectrolyte brushes34 may serve as steric coatings to prevent flocculation or aggregation, while particle supports, such as silica shells35 and carbon nanotubes36 have been used more recently to study the catalytic properties of metallic nanoparticles. However, these stabilizers also reduce the effective area of the catalyst and hence its efficacy. In this work we have used citrate-stabilized gold nanoparticles. Atomic force microscopy (AFM) studies have revealed that citrate ions form an electrosteric barrier at the gold surface, reducing its active surface area. The negative charge from the ionized carboxyl groups minimizes aggregation during catalysis, but this also affects the rates of both mass transfer and electron transfer across the Helmholtz layer at the gold particle surface.30 It was observed that citrate addition led to a lower rate of reaction compared to the addition of chloride ions, presumably because of its higher adsorption to the gold surface. In aqueous redox catalysis, it is essential to maintain a constant ionic strength when possible, but of course aggregation is higher as the ionic strength is increased. The activation energy for the reaction was measured under conditions where the rate of reaction was less than diffusionlimited and found to be 15.6 kJ/mol for 15 nm gold particles. The activation energy can be attributed to the electron transfer step to the acceptor ion. We conclude that, if the mixed or steady state potential is controlled purely by the concentration of NaBH4, then the particles acquire an extremely negative potential, which enables the reduction of ferricyanide to be driven extremely fast and enables catalytic enhancements of more than 104 over the uncatalyzed rate. Finally, we note that for 4 10-4 M Fe(III), and 1 nM Au nanoparticles, each nanoparticle reduces 400 000 Fe(III) ions during catalysis. Also, at -0.7 V, the steady state number of electrons on each gold particle can be estimated to be about 2500 during catalysis.37 This is only 0.6% of the total number of electrons transferred to Fe(III).
(31) Mulvaney, P.; Swayambunathan, V.; Grieser, F.; Meisel, D. Langmuir 1990, 6, 555–559. (32) Pal, T.; Sau, T. K.; Jana, N. R. Langmuir 1997, 13, 1481–1485. (33) Schmid, G. Chem. Rev. 1992, 92, 1709–1727. (34) (a) Mei, Y.; Sharma, G.; Lu, Y.; Ballauff, M.; Drechsler, M.; Irrgang, T.; Kempe, R. Langmuir 2005, 21, 12229–12234. (b) Mei, Y.; Lu, Y.; Polzer, F.; Ballauff, M.; Drechsler, M. Chem. Mater. 2007, 19, 1062–1069.
(35) Pastoriza-Santos, I.; Perez-Juste, J.; Carregal-Romero, S.; Herves, P.; Liz-Marzan, L. M. Chem. Asian J. 2006, 1, 730–736. (36) Sanles-Sobrido, M.; Correa-Duarte, M. A.; Carregal-Romero, S.; Rodrı´ guez-Gonzalez, B.; Alvarez-Puebla, R. A.; Herves, P.; Liz-Marzan, L. M. Chem. Mater. 2009, 21, 1531–1535. (37) Calculated from the double layer capacitance of C = 80 μF/cm2 and using Q = C*A*V = 6.2 1018 0.7V 80 10-6 F/cm2 4π(7.5 10-7)2.
Langmuir 2010, 26(2), 1271–1277
Conclusions In summary, we have demonstrated that gold nanoparticles act as a very efficient catalyst for the reduction of ferricyanide ion to ferrocyanide by sodium borohydride. We have observed not only an enormous increase in the reaction rate, but also a change in the mechanism, from zeroth-order in hexacyanoferrate (III) concentration for the noncatalyzed reaction to first-order for the catalyzed reaction. This system appears to be a useful model for the study of redox catalysis in aqueous solution. Further studies related to the influence of particle size and shape on the catalytic activity of gold nanoparticles are currently underway and will be reported elsewhere. Acknowledgment. Financial support from the Ministerio de Educacion y Ciencia/FEDER (Projects CTQ2007-64758 and PCI2005-A7-0075) is gratefully acknowledged. S.C.-R. acknowledges receipt of a FPI fellowship. J.P.-J. is the recipient of a Ram on y Cajal fellowship. P.M. acknowledges support through ARC Grant FF0561486. Supporting Information Available: Influence of Fe(CN)6-3 concentration on the observed reaction rate, values of the slope obtained from Figure 4 by fitting the data to eq 6 and derivation of eqs 8a and 8b from the Butler-Volmer equation. This material is available free of charge via the Internet at http://pubs.acs.org.
DOI: 10.1021/la902442p
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