J . Phys. Chem. 1992,96, 8700-8702 Miyasaka, H.; Mataga, N . J . Phys. Chem. 1990, 94, 5834. (3) (a) Brun, A. M.; Harriman, A.; Hubig, S.J . Phys. Chem. 1992, 96, 254. (c) Vergeldt, F. J.; Koehorst, R. B. M.; Schaafsma, T. J.; Lambry, J.-C.; Martin, J.-L.; Johnson, D. C.; Wasielewski, M. R. Chem. Phys. Lett. 1991, 107, 182. (4) Gould, 1. R.; Ege, D.; Moser, J. E.; Farid, S.J . Am. Chem. Soc. 1990, I 12,4290. (5) Zhou, J. S.; Rodgers, M. A. J. J . Am. Chem. Soc. 1991, 113, 7728. (6) Hubig, S. M.; Rodgers, M. A. J. In Handbook of Organic Chemistry; Scaiano, J. C., Ed.; CRC Press: Boca Raton, FL, 1989; Vol. 1, Chapter 13. (7) Logunov, S.L.; Rodgers, M. A. J. J. Phys. Chem. 1992, 96,2915. (8) Tian, R.; Rodgers, M. A. J. In New Techniquesof Optical Microscopy and Microspectroscopy; Cherry, R. J., Ed.;Macmillan Press: London, 1991; Chapter 7. (9) Rougee, M.; Ebbesen, T.; Ghettl, F.; Bensasson, R. V. J . Phys. Chem. 1982,86,4404.
(IO) Okura, 1.; Aono, S.; Hoshino, M.; Yamada, A. fnorg. Chim. Acra 1984, 86, 155. (11) Nahor, C. S.; Rabani, T. J . Phys. Chem. 1985,89, 2469. (12) Rodriguez, J.; Kirmaier, C.; Holten, D. J . Am. Chem. Soc. 1989, I 11, 6500. (13) (a) Cation radicals of por hyrins have structureless spectra with maxima between 650 and 700 nm;IPbanion radicals of viologens have broad
maxima near 600 nm and maximum below 400 nm, where the picosecond spectrometer has weak continuum and absorbance masked by a Soret band of the porphyrin. (b) Fuhrhop, J.-H.; Mauzerall, D. J. Am. Chem. Soc. 1969. 91,4174. (c) Kalyanasundaram, K.; Meumann-Spllart, M. J . Phys. Chem. 1982, 86, 5163. (d) Gill, R.; Stonehill, H. I. J . Chem. Soc. 1952, 1845. (14) The reason why the CS reaction is faster than CR is not clear, but it may be because different molecular orbitals are involved in the CS and CR processes thereby implying different electronic coupling factors. (15) Shelnutt, J. A. J . Phys. Chem. 1984, 88, 6121. (16) Shelnutt, J. A. J . Phys. Chem. 1983, 87, 605. (17) Asahi, T.; Mataga, N . J . Phys. Chem. 1989, 93, 6375. (18) Segawa, H.; Takehora, C.; Honka, K.; Shimidzu, T.; Asahi, T.; Mataga, N . J . Phys. Chem. 1992, 96, 503. (19) Gould, I. R.; Young, R. H.; Moody, R. E.; Farid, S.J . Phys. Chem. 1991, 95, 2068. (20) Jortner, J.; Bixon, M. J . Chem. Phys. 1988, 88, 167. (21) Rips, 1.; Jortner, J. J . Chem. Phys. 1987, 87, 2090. (22) The average frequency of 1500 cm-I was chosen in accordance with
resonance Raman data for porphyrins, the internal reorganization energy of a porphyrin is 0.1 eV?* and the same value was chosen for the pyridinium acceptors. (23) Kakitani, T.; Kakitani, H. Biochim. Biophys. Acra 1981, 635, 498. (24) We are grateful to a referee for pointing this out to us.
Fermi Level Equlllbration between Colloidal Lead and Silver Particles in Aqueous Solutlon Arnim Henglein,* Arnold Holzwartb, and Paul Mulvaney Hahn- Meitner-Institut Berlin, 1000 Berlin 39, Germany (Received: August 18, 1992;
In Final Form: September 15, 1992) Colloidal solutions of lead and silver were mixed under the exclusion of air. The equilibration of the Fermi levels in the two different types of metal particles took place over a few days at room temperature. The equilibrationtook place by the transfer of lead atoms from lead to silver particles until the latter carried a lead mantle of one to two monolayers. This could be concluded from the observed changes in the optical spectrum of the silver particles. The results are discussed in terms of two mechanisms: (1) Pb atom transfer following heterocoagulation of the lead and silver particles and (2) electron transfer during Brownian encounters, followed by Pb2+desorption from the lead particles and subsequent Pb2+reduction on the silver particles carrying the transferred electrons. Traces of methylviologen, MV2+,in the solution drastically increase the rate of equilibration;this is explained by a relay mechanism in which electrons in the lead particles are first picked up by MV2+ and are then transferred from MV+ to the silver particles.
Introduction The optical spectra of colloidal silver and lead in aqueous solution are well-known. They contain intense absorption bands at 380 and 2 15 nm, respectively. The changes in the position of the silver band upon chemical modification of the surface of the colloidal particles have been studied in detail in this laboratory. For example, when lead ions are reduced on the surface of silver particles, the band is blue-shifted; after deposition of one to two monolayers of lead, the band peaks close to 340 nm.' In the present paper, the following problem is addressed. Let an aqueous solution contain both silver and lead particles. Both types of particles are stabilized toward coagulation by a suitable polymer. An elecrronic instability will still exist, the Fermi level in the lead particles (a base metal) lying at a more negative potential than the Fmni level in the silver particles (a noble metal). The question which arises is, how much time is required for the equilibration of these two levels and what is the chemical mechanism by which the equilibration takes place? Experimental Section
Figure 1 shows the glass vessel used to prepare the colloidal solutions of lead and silver and to mix them. Parts 1 and 2 were filled with the solutions of the metal salts: (1) 1 X lo4 M Pb(C104)2,0.1 M propanol-2, and 1 X lo', M poly(ethy1enimine); (2) 2 X M AgClO,, 0.1 M propanol-2, 2 X lo4 M poly(ethylenimine). The solutions were deaerated by triple freezethaw cycles on a high-vacuum line. The vessel was then put into the 0022-36S4/92/2096-8100$03.00/0
field of a 6oco y-source for 2 h (dose rate 8.7X 10" rad/h). This irradiation time was sufficient to reduce all the metal ions to yield the corresponding co1loids.l The solutions were then mixed. The absorption spectrum could be determined as the vessel camed side arms with cuvettes of different thicknesses. In some experiments, a small volume of a methylviologen solution, which was first deaerated, was sucked into the evacuated vessel.
Results and Discussion In the inset of Figure 2, the absorption spectra of separate 5 X M lead and 1 X lo4 M silver sols are shown. Both sols were stabilized by 1 X lo" M poly(ethy1enimine). Equal amounts of the two solutions were mixed, and the spectrum was recorded after various periods of aging. The main part of Figure 2 shows the spectra obtained. Immediately after mixing, the spectrum is the superposition of the spectra of the separated colloids. Changes take place over hours and days. The 21 5-nm band of lead slightly decreases in intensity, whereas the silver band shifts gradually to shorter wavelengths and becomes broadened. These changes occur until the silver band is located at 337 nm; i.e., the position of the band at this point corresponds to one or two monolayers of lead on the silver particles. The overall reaction consists of the transfer of lead atoms from the lead particles to the silver particles. One could suppose that a second reaction occurs: the silver catalyzes the oxidation of lead by H+ ions: 2H+ Pb H2 Pbz+. This would lead to a loss of lead. To measure this possible
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Figure 3. Relay mechanism for Fermi level equilibration in the presence of methylviologen.
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Figure 1. Vessel for the preparation and mixing of lead 2.0 1
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A Inml Figure 2. Absorption spectrum of the solution at various times after M Pb after mixing. The solution contained 1 X lo4 M Ag and 5 X mixing. pH = 4.5. Inset: absorption spectra of the separate lead and silver sols. loss, the lead concentration was determined shortly after mixing and after reaching the final state (after 4 days) by adding 10" M methylviologen, MV2+,and 0.05 M NaOH to the solution (to reach a pH of about 11). MV2+ oxidizes finely dispersed lead, 2MV2+ Pb 20H- 2MV+ + Pb(OH)2,and the amount of lead can be determined by measuring the concentration of the blue radical cation MV+. Lead adatoms do not react with MV2+.I It was found that the lead concentration had decreased by less than 1096, when the band had shifted to 337 nm, which means that the silver-catalyzed oxidation of lead does not play an important role. The Pb atom transfer from lead to silver particles could be explained in two ways: (1) Lead and silver particles undergo heterocoagulation, followed by the transfer of lead surface atoms to the silver surface, the driving force being the stronger binding energy of lead adatoms to silver than to lead. This driving force would disappear, when the silver particles are coated with one or two monolayers of lead. (2) Lead and silver particles undergo Brownian encounters, during which the metal particles do not actually come into contact with each other. According to the DLVO (Deryaguin, Landau, Verwey-Overbeek) theory, the repulsion generally reaches a maximum when the interparticle
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i o 2 10) 10' 105 t [mid Figure 4. Wavelength of the silver plasmon band as a function of time in the absence and presence of various amounts of methylviologen. Inset: double-logarithmicplot of the "half-life" for Fermi level equilibration vs MV2+ concentration.
0.1 1 I
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separation is about 10%of the particle radiw2 For the colloids with radii 30-60 A used here, the distance of closest approach is about 5 A. Alternatively, the particles may only be able to resist coagulation due to the stability afforded by the steric repulsion between polymer chains. The particles may approach to within a distance dictated by the polymer coating which is probably of the order of 5 A. At this distance, electrons may tunnel from the lead to the silver particles, and simultaneously Pb2+ions are emitted from the lead particles into the solution. These Pb2+ions are then reduced on the silver particles which have excess electrons. That Pb2+can be reduced on silver particles carrying excess electrons has been shown previous1y.I The Fermi level is shifted to more negative potentials as the silver particles are coated with more and more Pb atoms, until the driving force for electron transfer from the lead to the silver particles disappears. A clear distinction between the two mechanisms cannot be made. One can, however, realize an electronic mechanism by using methylviologen, MV2+,as an electron-transfer relay. Figure 3 illustrates the mechanism: the lead and silver sols are mixed, and a small amount of MVZ+is added. MVZ+oxidizes finely dispersed lead to yield the stable radical cation MV+;' this leads to the detachment of Pb2+ ions from the lead particles. MV+ then transfers an electron to a silver particle. Thus, the electron transport is achieved via the relay, MV2+. The Pb2+ ions formed are finally reduced on the cathodically polarized silver particles. It was found that extremely small amounts of methylviologen strongly accelerate the rate of Fermi level equilibration. This can be seen from Figure 4 where the wavelength of the maximum of the absorption band of silver is plotted versus the time of aging. In the absence of MVZ+,about 4 days is required until the equilibration is complete. Only about 1 min is needed in the M MVZ+. Just M MV2+ is sufficient to presence of accelerate the reaction by a factor of 10. The inset of Figure 4 shows the "half-life" for the band shift, 1 , (when the maximum has shifted to 358 nm), as a function of the MV2+concentration in a double-logarithmic plot. From the slope of the straight line obtained one finds that t l / 2 is not proportional to [MV*+]-' but to [MV2+]-".'.
J . Phys. Chem. 1992, 96, 8702-871 1
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In the presence of MV2+,spectra as in Figure 2 were obtained, Le., spectra which did not possess either of the characteristic absorption bands at 395 and 600 nm of MV+. This means that the stationary MV+ concentration was always very low, from which one concludes that the electron transfer from MV+ to the silver particles was much faster than from the lead particles to MV2+. This latter electron transfer is rate determining at the pH of 4.5 at which the experiments were carried out. Thus, one has to conclude that the Fermi level in the lead particles must lie close to -0.445 V, Le., the potential of the redox system MV2+/MV+. Pulse radiolysis experiments were also carried out to test this assumption. When MV+ was generated in solutions of colloidal Ag (in the absence of Pb), the half-life for the reaction with the
silver particles was found to be 0.2 s. Since the equilibration reaction in the mixed leadsilver solutions containing MV2+takes place on a much longer time scale, the oxidation of Pb by MV2+ has again to be considered as the rate-determining step. The fact that the overall rate of the equilibration reaction is proportional to [MV2+]4,3possibly reflects an adsorption phenomenon, the limiting concentration of MV2+adsorbed on the Pb particles being reached at rather small MV2+concentrations.
References and Notes (1) Henglein, A.; Mulvaney, P.;Holzwarth, A.; Sosebee, T. E.; Fojtik, A. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 154. (2) Hunter, R. J. Foundations of Colloid Science; Oxford University Press:
London, 1986; Vol. 1, p 444.
FEATURE ARTICLE Simple and Complex Propagating Reaction-Diff usion Fronts Stephen K. Scott* School of Chemistry, University of Leeds, Leeds LS2 9JT. U.K.
and Kenneth Showalter* Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506 (Received: June 2, 1992; In Final Form: August 13, 1992)
Chemical waves are common features of many reactions in which there is autocatalysis. These waves typically travel at a steady velocity and with a particular, constant waveform. The speed and waveform reflect the coupling of the autocatalytic reaction to diffusion. For some autocatalytic systems, waves can be initiated with ease, no matter how small the initiation stimulus. In other cases, however, depending on the exact form of the kinetics, the shape of the reaction zone, or the Occurrence of competing reactions that remove the autocatalybt, waves may develop only for certain ranges of the rate constants and only when a sufficiently large initial stimulus is applied. The analogous phenomenon for flame propagation is known as quenching and gives rise to the existence of flammability limits and minimum ignition energies. Depending on relative diffusivities, chemical waves propagating in two or three dimensions may spontaneously develop patterned fronts analogous to the appearance of “cellular” flames.
1. Introduction Imagine a chemical reaction starting at a point and spreading through a reactant medium like a burning f i r e b u t with no heat. Just such “isothermal flames” arise in chemical systems when autocatalytic reaction couples with diffusion. A front or moving zone of reaction propagates into fresh reactants and leaves behind final products, typically with constant velocity and a constant waveform. The front itself is the spatial realization of the reaction event. Reaction-diffusion fronts may also exhibit complex behavior arising from inherent instabilities, behavior reminiscent of destabilized flames. In this article we consider fundamental types of propagating fronts, how they are related, and how they may exhibit complex behavior. Propagating reactiondiffusion fronts were first studied around the turn of the century as models for wave behavior in biological systems.’-* However, as recently as 10 years ago they fell into the category of “exotic phenomena”, as only a few experimental examples were known and their mechanisms were poorly understood. Today, many autocatalytic reactions are known to support propagating fronts? and more complex wave behavior is of widespread interest for modeling excitable media in biological system^.^ The theoretical treatment of reactiondiffusion fronts,
while first addressed over a half-century ago,$’ has also advanced in recent years. Many features are now well understood, and in addition, new theoretical challenges are apparent. All chemical waves, simple or complex, reflect the basic features of their fronts: propagation velocity and waveform are directly linked to the chemical kinetics of autocatalysis and its coupling with diffusion. We consider the two simplest forms of autocatalysis, quadratic and cubic, which we contrast and then join together to illustrate the general features of propagating reaction-diffusion fronts. These forms have long been thought tg be fundamentally different in character; we describe here their similarities and how one transforms into the other as the form of autocatalysis varies. Propagating fronts with quadratic kinetics have a long history, first formally studied in 1937 by Fisher’ and, independently, by Kolmogorov et a1.6 While this type of front has been considered the generic prototype for chemical waves (and propagating waves in biological systems), its mathematical description has remained an enigma-a simple one-variable reactiondiffusion equation without a general analytical solution. Propagating fronts with cubic kinetics were first considered by Semenov et al.’ in 1939; however, these fronts have received less attention over the years.
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