Electron Hopping Dynamics in Monolayer ... - ACS Publications

Electrons are transported within polymeric films of al- kanethiolate monolayer-protected Au clusters (MPCs) by electron hopping (self-exchange) betwee...
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Anal. Chem. 2004, 76, 5611-5619

Electron Hopping Dynamics in Monolayer-Protected Au Cluster Network Polymer Films by Rotated Disk Electrode Voltammetry Jennifer L. Brennan,† Matthew R. Branham, Jocelyn F. Hicks,‡ Andrea J. Osisek,§ Robert L. Donkers,| Dimitra G. Georganopoulou,⊥ and Royce W. Murray*

Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290

Electrons are transported within polymeric films of alkanethiolate monolayer-protected Au clusters (MPCs) by electron hopping (self-exchange) between the metal cores. The surrounding monolayers, the molecular linkers that generate the network polymer film, or both, presumably serve as tunneling bridges in the electron transfers. This paper introduces a steady-state electrochemical method for measuring electron hopping rates in solvent-wetted and swollen, ionically conductive MPC films. The films are network polymer films of nanoparticles, coated on a rotated disk electrode that is contacted by a solution of a redox species (decamethylferrocene, Cp*Fe). Controlling the electrode potential such that the film mediates oxidation of the redox probe can force control of the overall current onto the rate of electron hopping within the film, which is characterized as the apparent electron diffusion coefficient DE. DE is translated into an apparent electron hopping rate kET by a cubic lattice model. The experiment is applied to MPC network polymer films linked by r,ωalkanedithiolates and by metal ion-carboxylate connections. We evaluate the dependencies of apparent hopping rate on Cp*Fe concentration, film thickness, electrode potential relative to the Cp*Fe formal potential, filmswelling solvent, and temperature. The apparent hopping rates are in the 104-105 s-1 range, which is slower than those for the same kind of MPC films, but in a dry (nonswollen) state measured by electronic conductivities. Significant research interest has been directed at nanoscale materials such as nanotubes,1 nanowires,2 and nanoparticles,3 owing to the challenge of understanding the properties of small* To whom correspondence shoud be addressed. E-mail: [email protected]. † Present address: Department of Chemistry and Centre for Nanoscale Science, University of Liverpool, Liverpool, L69 7ZD, U.K. ‡ Present address: Space and Airborne Systems, Raytheon Co., 2000 E. El Segundo Blvd., E0/E01/F150, El Segundo, CA 90245. § Present address: 200 Olde Eastwood Village Blvd., Asheville, NC 28803. | Present address: Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, K1A 0R6, Canada. ⊥ Present address: Department of Chemistry, Northwestern University, Evanston, IL 60208-3133. (1) (a) Derycke, V.; Martel, R.; Appenzeller, J.; Avouris, Ph. Nanoletters 2001, 1, 453-456. (b) Bachtold, A.; Hadeley, P.; Nakanishi, T.; Dekker, C. Science 2001, 294, 1317-1320. (2) Cui, Y.; Leiber, C. M. Science 2001, 291, 851-853. 10.1021/ac049289j CCC: $27.50 Published on Web 08/24/2004

© 2004 American Chemical Society

dimensional materials and to their supposed potential applications in, for example, chemical sensors,4 diagnostics,5 nanofluidics,6 and catalysis,7 as well as in nanoscale electronics components for computing and communications, e.g., “molecular electronics”.8 In almost all of these applications, it is important to understand how, and how fast, electronic charge can be transported within and through thin films on experimentally addressable surfaces,9 how to measure the rate of charge transport, whether and how the rate depends on solvent swelling or counterion motions, and indeed how to fabricate the nanoparticle films. While progress has been made in the preparation of metal nanoparticle films, there as yet exists no completely satisfactory scheme for making highly uniform films in which the neighbor surfaces of nanoparticles are separated by well-defined and controllable distances. Nonlinked films containing multilayers of nanoparticles have been prepared by simple drop-casting10 and spray-coating,11 and by electrophoretic deposition.12 The chemistry of linked multilayer nanoparticle films of “monolayer-protected (3) (a) Templeton, A. C.; Wuelfing, W. P.; Murray, R. W. Acc. Chem. Res. 2000, 33, 27-36. (b) Brown, L. O.; Hutchison, J. E. J. Am. Chem. Soc. 1997, 119, 12384-12385. (c) Shen, Y.; Lihua, B.; Liu, B.; Dong, S New J. Chem. 2003, 27, 938-941. (d) Condorelli, G. G.; Costanzo, L. L.; Fragala, I. L.; Guiffrida, S.; Ventimiglia, G. J. Mater. Chem. 2003, 13, 2409-2411. (e) Lee, D.; Donkers, R. L.; DeSimone, J. M.; Murray, R. W. J. Am. Chem. Soc. 2003, 125, 1182-1183. (4) (a) Vo-Dinh, T.; Cullum, B. M.; Stokes, D. L. Sens. Actuators, B 2001, B74, 2-11. (b) Liu, J.; Lu, Y. J. Am. Chem. Soc. 2003, 125, 6642-6643. (5) (a) Jain, K. K. Expert Rev. Mol. Diagn. 2003, 3, 153-161. (b) Perez, J. M.; Simeone, F. J.; Saeki, Y.; Josephson, L.; Weissleider, R. J. Am. Chem. Soc. 2003, 125, 10192-10193. (6) Heuberger, M.; Zaech, M. Langmuir 2003, 19, 1943-1947. (7) (a) Jaramillo, T. F.; Baeck, S.-H.; Cuenya, B. R.; McFarland, E. W. J. Am. Chem. Soc. 2003, 125, 7148-7149. (b) Henry, C. R. Appl. Surf. Sci. 2000, 164, 252-259. (c) Takeda, S.; Ueda, K.; Ozaki, N.; Ohno, Y. Appl. Phys. Lett. 2003, 82, 979-981. (8) Adams, D. M.; Brus, L.; Chidsey, C. E. D.; Creager, S.; Creutz, C.; Kagan, C. R.; Kamat, P. V.; Lieberman, M.; Lindsay, S.; Marcus, R. A.; Metzger, R. M.; Michel-Beyerle, M. E.; Miller, J. R.; Newton, M. D.; Rolison, D. R.; Sankey, O.; Schanze, K. S.; Yardley, J.; Zhu, X J. Phys. Chem. B 2003, 107, 6668-6697. (9) (a) Shenhar, R.; Rotello, V. M. Acc. Chem. Res. 2003, 36, 549-561. (b) Brust, M.; Kiely, C. J. Colloids Surf., A 2002, 202, 175-186. (10) (a) Kiely, C. J.; Fink, J.; Brust, M.; Bethell, D.; Schiffrin, D. A. Nature 1998, 396, 444-446. (b) Wuelfing, W. P.; Murray, R. W. J. Phys. Chem. B 2002, 106, 3139-3145. (c) Evans, S. D.; Johnson, S. R.; Cheng, Y. L.; Shen, T. J. Mater. Chem. 2000, 10, 183-188. (11) (a) Wohltjen, H.; Snow, A. W. Anal. Chem. 1998, 70, 2856-2859. (b) Cai, Q.-Y.; Zellers, E. T. Anal. Chem. 2002, 74, 3533-3539. (12) (a) Giersig, M.; Mulvaney, P. J. Phys. Chem. 1993, 97, 6334-6336. (b) Giersig, M.; Mulvaney, P. Langmuir 1993, 9, 3408-3413.

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clusters” (MPCs) includes the use of R,ω-alkanedithiolates13 and metal ion-carboxylate connections.14 The linkages can also be electrostatic as in “layer-by-layer” grown films.15 MPC films have been prepared using poly(propyleneimine) dendrimers,13d.6 for the purpose of creating organic vapor sensors, and a recent report describes the “wiring” of MPCs via linking with redox-active viologen dithiols.17 Significantly less progress has been made in developing reliable ways to measure the rates of electron hopping transport through nanoparticle films, particularly in regard to ionically conductive films that are wetted and swollen by electrolytecontaining solvent. Potential step chronoamperometry is thus far the only method applied to electron hopping rates, in solventwetted MPC network polymers18 and in molecular melts of MPCs.19 Further, neither of those previous chronoamperometry studies examined the dependency of electron hopping rate on structural factors such as linker chemistry or monolayer or linker chain lengths. The chronoamperometry experiment has a number of liabilities, notably a transient finite diffusion geometry and possible iRUNC effects (due to slow counterion migration) on electron migration.20 These problems are mitigated in methods where a steady current rather than a transient current flows, because the ionic content of the film also reaches a steady state.21,22 In the course of investigating electron hopping through redox (13) (a) Maye, M. M.; Luo, J.; Lin, Y. H.; Engelhard, M. H.; Hepel, M.; Zhong, C. J. Langmuir 2003, 19, 125-131. (b) Joseph, Y.; Besnard, I.; Rosenberger, M.; Guse, B.; Nothofer, H. G.; Wessels, J. M.; Knop-Gericke, A.; Schlogl, R.; Yasuda, A.; Vossmeyer, T. J. Phys. Chem. B 2003, 107, 7406-7413. (c) Trudeau, P. E.; Escorcia, A.; Dhirani, A. A. J. Chem. Phys. 2003, 119, 52675273. (d) Joseph, Y.; Krasteva, N.; Besnard, I.; Guse, B.; Rosenberger, M.; Wild, U.; Knop-Gericke, A.; Schlogl, R.; Krustev, R.; Yasuda, A.; Vossmeyer, T. Faraday Discuss. 2004, 125, 77-97. (e) Wessels, J. M.; Nothofer, H. G.; Ford, W. E.; von Wrochem, F.; Scholtz, F.; Vossmeyer, T.; Schroedter, A.; Weller, H.; Yasuda, A. J. Am. Chem. Soc. 2004, 126, 3349-3356. (f) Joseph, Y.; Guse, B.; Yasuda, A.; Vossmeyer, T. Sens. Actuators, B 2004, 98, 188195. (14) (a) Zamborini, F. P.; Hicks, J. F.; Murray, R. W. J. Am. Chem. Soc. 2000, 122, 4514-4515. (b) Templeton, A. C.; Zamborini, F. P.; Wuelfing, W. P.; Murray, R. W. Langmuir 2000, 16, 6682-6688. (c) Wuelfing, W. P.; Zamborini, F. P.; Templeton, A. C.; Wen, X.; Yoon, H.; Murray, R. W. Chem. Mater. 2001, 13, 87-95. (d) Zamborini, F. P.; Smart, L. E.; Leopold, M. C. Anal. Chim. Acta 2003, 496, 3-16. (15) (a) Hicks, J. F.; Seok-Shon, Y.; Murray, R. W. Langmuir 2002, 18, 22882294. (b) Cant, N. E.; Critchley, K.; Zhang, H. L.; Evans, S. D. Thin Solid Films 2003, 426, 31-39. (c) Ruiz, V.; Liljeroth, P.; Quinn, B. M.; Kontturi, K. Nano Lett. 2003, 3, 1459-1462. (d) Jiang, C. Y.; Markutsya, S.; Tsukruk, V. V. Langmuir 2004, 20, 882-890. (e) Kariuki, N. N.; Luo, J.; Maye, M. M.; Moussa, L.; Patterson, M.; Lin, Y. H.; Engelhard, M. H.; Zhong, C. J. Electroanalysis 2004, 16, 120-126. (f) Song, W.; Okamura, M.; Kondo, T.; Uosaki, K. Phys. Chem. Chem. Phys. 2003, 5, 5279-5284. (16) (a) Krasteva, N.; Besnard, I.; Guse, B.; Bauer, R. E.; Mullen, K.; Yasuda, A.; Vossmeyer, T. Nano Lett. 2002, 2, 551-555. (b) Vossmeyer, T.; Guse, B.; Besnard, I.; Bauer, R. E.; Mullen, K.; Yasuda, A. Adv. Mater. 2002, 14, 238. (c) Krasteva, N.; Krustev, R.; Yasuda, A.; Vossmeyer, T. Langmuir 2003, 19, 7754-7760. (17) Haiss, W.; Nichols, R. J.; Higgins, S. J.; Bethell, D.; Hobenreich, H. Schiffrin, D. J. Faraday Discuss. 2004, 125, 179-194. (18) Hicks, J. F.; Zamborini, F. P.; Osisek, A. J.; Murray, R. W. J. Am. Chem. Soc. 2001, 123, 7048-7053. (19) Lee, D.; Donkers, R. L.; DeSimone, J. M.; Murray, R. W. J. Am. Chem. Soc. 2003, 125, 1182. (20) (a) Andrieux, C. P.; Saveant, J. M. J. Phys. Chem. 1988, 92, 6761-6767. (b) Saveant, J. M. J. Phys. Chem. 1988, 92, 1011-1013. (21) Saveant, J. M. J. Phys. Chem. 1988, 92, 4526-4532. (22) (a) Feldman, B. J.; Ewing, A. G.; Murray, R. W. J. Electroanal. Chem. 1985, 194, 63-81. (b) Zhang, H. H.; Murray, R. W. J. Am. Chem. Soc. 1991, 113, 5183-5187. (c) Zhang, H. H.; Murray, R. W. J. Am. Chem. Soc. 1993, 115, 2335-2340. (d) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Am. Chem. Soc. 1981, 103, 7422.

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Scheme 1. Cartoon Depicting Mediated Electron-Transfer Oxidation of Decamethylferrocene (Cp*Fe) by a Multilayer MPC Film Assembled on an Electrode

polymer films on electrodes,22,23 a number of transient and steadystate measurements on solvent-wetted films emerged, among which is rotated disk voltammetry.22d,23b Electron hopping through nanoparticle films has many parallels to the chemistry of charge transport through redox polymer films, and methods and theory used for the latter should be adaptable to the former. This paper introduces rotated disk electrode voltammetry (RDE) as a steadystate method for measuring electron hopping rates in solventwetted, ionically conductive MPC films. For a rotated electrode coated with a nanoparticle film, application23-25 of a potential can cause electron transfers at the electrode/film interface and subsequently hopping transport through the nanoparticle film. This current will cease when the film’s electron content equilibrates with the Fermi level of the electrode. If, however, the other side of the film is in contact with a solution of a redox speciesssuch as decamethylferrocene (Cp*Fe) as used here (E°′ ) -0.050 V vs Ag/AgCl)sthat reacts with the electrode-charged film and that is steadily replenished by hydrodynamic mass transport, the rate of electron hopping within the nanoparticle film can be forced to become the currentlimiting process.24,25 In other words, the nanoparticle film is made to be an electron-transfer mediator between the redox species and the electrode, as illustrated in Scheme 1. The rotated disk method has a number of requirements, known from previous work22,23 on redox polymer films. In Scheme, 1 ideally (a) the redox probe does not permeate into the nanoparticle film, but instead is oxidized at the nanoparticle film/solution interface, (b) the electron-transfer oxidation of the redox probe at the outermost nanoparticle/solution interface is fast compared to electron hopping within the film, (c) the degree to which mass transport of the redox probe to the film/solution interface controls the current can be analyzed by its dependency on electrode (23) (a) Leddy, J.; Bard, A. J. J. Electroanal. Chem. 1983, 153, 223-242. (b) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Electroanal. Chem. 1982, 138, 343-365. (c) Shigehara, K.; Anson, F. C. J. Electroanal. Chem. 1982, 132, 107-118. (24) (a) Andrieux, C. P.; Dumas-Bouchiat, J. M.; Saveant, J. M. J. Electroanal. Chem. 1982, 131, 1-35. (b) Leddy, J.; Bard, A. J.; Maloy, J. T.; Saveant, J. M. J. Electroanal. Chem. 1985, 187, 205-227. (c) Andrieux, C. P.; Saveant, J. M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; Wiley: New York, 1992. (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001.

rotation rate, and (d) the film thickness is uniform so that mixed control circumstances are avoided. These features are tested by choices of redox probe concentration, nanoparticle film thickness, and reaction driving force as governed by the oxidizing state of the film, which in turn is determined by the applied electrode potential. While, as noted above, the focus of this report is to introduce the method of rotated disk electrode voltammetry for measuring electron hopping in solvent-swollen and -wetted nanoparticle polymer films, we also present early data on the effects of monolayer linking chemistry on electron hopping rates in such films. Two different linkers are employed: R,ω-alkanedithiolates and metal ion-carboxylate-metal ion linkers. Despite substantial differences in chain length of the two kinds of linkers, the apparent electron hopping rates proved to be similar. Obtaining further results on solvent-swollen films as a function of film structure will be desirable, since the data presented here are limited; further experiments are planned. The low sensitivity of hopping rate to linker chain length effect is crudely reminiscent of results26 derived from electronic conductivities of dry and ionically nonconductive films resting on interdigitated array electrodes, but the present results show that the dry film electronic conductivities correspond to hopping rates that are much larger than obtained from the same kind of MPC film but immersed in an electrolyte/solvent system. EXPERIMENTAL SECTION Materials. Chemicals purchased from Aldrich were used as received, except for bis(pentamethylcyclopentadienyl)iron (decamethylferrocene, Cp*Fe, which was purified by sublimation). Tetrabutylammonium hexafluorophosphate is abbreviated Bu4NPF6. MPC Syntheses. Pentanethiolate (C5 MPC) and hexanethiolate (C6 MPC) coated nanoparticles were prepared using a modified Brust synthesis,27 in which a 3:1 mole ratio of alkanethiol and HAuCl4 were reacted in toluene and then reduced at 0 °C with a 10-fold molar excess of aqueous NaBH4. The details of this synthesis have been described elsewhere.28 The procedure produces clusters that have, on average, the composition Au140(C6)53. Transmission electron microscopy (not shown) confirms an average core diameter of 1.6 nm. Of the two MPC fractions obtained by solvent fractionation, those soluble in ethanol are more monodisperse in core size,28a as reflected in more regular quantized double layer charging voltammetry, than ethanolinsoluble MPCs. C6 MPCs with mixed monolayers of hexanethiolate and mercaptoundecanoic acid (MUA) were prepared by stirring solutions of ethanol-insoluble C6 MPCswith selected concentra(26) (a) Zamborini, F. P.; Leopold, M. C.; Hicks, J. F.; Kulesza, P. J.; Malik, M. A.; Murray, R. W. J. Am. Chem. Soc. 2002, 124, 8958-8964. (b) Leopold, M. C.; Donkers, R. L. Georganopoulou, D. G.; Fisher, M.; Zamborini, F. P.; Murray, R. W. Faraday Discuss. 2003, 125, 63-76. (c) Branham, M. R. unpublished results, University of North Carolina, 2004. (27) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. Chem. Commun. 1994, 801. (28) (a) Hicks, J. F.; Miles, D. T.; Murray, R. W. J. Am. Chem. Soc. 2002, 124, 13322-13328. (b) Hicks, J. F.; Templeton, A. C.; Chen, S.; Sharan, K. M.; Jasti, R.; Murray, R. W.; Debord, J.; Schaaff, T. G.; Whetten, R. L. Anal. Chem. 1999, 71, 3703. (c) Chen, S.; Murray, R. W.; Feldberg, S. W. J. Phys. Chem. B 1998, 102, 9898-9907. (d) Chen, S.; Ingram, R. S.; Hostetler, M. J.; Pietron, J. J.; Murray, R. W.; Schaaff, T. G.; Khoury, J. T.; Alvarez, M. M.; Whetten, R. L. Science 1998, 280, 2098-2101. (e) Miles, D. T.; Murray, R. W. Anal. Chem. 2003, 75, 1251-1257.

tions of MUA thiol in dry tetrahydrofuran.29 This procedure prepares MPCs with average formulas Au140(C6)53-N(MUA)N where N ) 26-33. The mixed monolayer composition is determined by NMR of the disulfides liberated upon decomposition of the MPCs by adding a crystal of iodine.29a The average core size, as determined by TEM, is unchanged after MUA exchange. MPC Film Electrode Coating. MUA-linked network polymer MPC films were formed, as described previously,14,26a,b on glass slides (for spectrophotometric monitoring of film growth and determination of film thickness using surface profilometry) and on 3-mm-diameter Au disk electrodes (for rotated disk electrode voltammetry). Pretreatment and cleaning of the Au disk electrode involved 1-µm diamond paste polishing followed by electrochemical cleaning by repetitive potential cycling in 0.1 M H2SO4 (resulting roughness factor 1.1-1.2, by gold oxide reduction wave)30 and formation of a MUA SAM by 30-min immersion in a 20 mM ethanolic solution of MUA. The MUA-linked nanoparticle network polymer was formed by sequential exposure to ethanolic solutions of copper ion and mixed monolayer C6/MUA MPCs (prepared from non-ethanol-soluble MPCs), as previously described.14,26a,b These films are abbreviated as C6/MUA films. Dithiol-linked network polymer MPC films were formed via a modification of a method described by Chen,31 on glass slides and 3-mm-diameter gold electrodes, and also on interdigitated array electrodes (IDAs) (for measurement of film electronic conductivity).26c Cleaning and presilanization of the glass slides with (3-mercaptopropyl)trimethoxysilane, and pretreatment of the IDAs (50 interdigitated 4800 µm long × 15 µm wide × 0.1 µm high gold fingers, gap-facing Au finger area 2.3 × 10-4 cm2, deposited on glass) were as described before.26b The glass slide and IDA electrode were placed overnight in a 10 mL of n-heptane solution containing 20 mg of C5 or C6 MPC and 10 µL of C8 or C10 (respectively) dithiol. Alternatively, the solution of MPCs and (6 µL in this case) dithiol was first stirred for 2 h to effect place exchange of the dithiol into the MPC monolayer, followed by immersion of the glass slide and IDA. A typical procedure deposits a ∼100 nm film; for thicker films, the modified IDA and glass slide are reimmersed in a fresh MPC-dithiol solution. Films were washed with 2-propanol and dried under an argon stream prior to use. Films prepared from pentanethiolate-coated MPCs and linked with C8 dithiol are abbreviated as C5/C8DT films, whereas those made form hexanethiolate-coated MPCs using C10 dithiol are abbreviated C6/C10DT films. Instrumentation. Electrochemical measurements were carried out using a Bioanalytical Systems (BAS) 100B electrochemical analyzer coupled to a BAS RDE-1 rotated disk electrode system. The working and counter electrodes were a 3-mm-diameter Au disk and a Pt flag, with potentials referenced to a Ag/AgCl reference electrode (except that in low-temperature measurementss acetone/ice bath (274 K) and acetone/dry ice bath (218 K), where a Ag wire quasi-reference electrode calibrated versus ferrocene/ ferrocenium (+ 0.463 V vs the AgQRE) was utilized. Spectrophotometry was done with a two-beam UV-visible Shimadzu UV1601). The quantities of MPC deposited on glass (29) (a) Song, Y.; Murray, R. W. J. Am. Chem. Soc. 2002, 124, 7096-7102. (b) Hostetler, M. J.; Templeton, A. C.; Murray, R. W. Langmuir 1999, 15, 37823789. (30) Trasatti, S.; Petrii, O. A. J. Electroanal. Chem. 1992, 327, 353-376. (31) Chen, S. J. Phys. Chem. B 2000, 104, 663-667.

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slides film were determined at λ520 nm based32 on  ) 4 × 108 cm2 mol-1, i.e., ΓΜPC (mol/cm2) ) A520 nm/520 nm. Film thicknesses (d) were determined with a Tencor Alpha Step 100 surface profilometer, combining determined d values with ΓMPC to evaluate MPC concentration in the film, CMPC (mol/cm3). The MPC core centerto-center distance, δ, was evaluated as CMPC ) NAδ3, where NA is Avogadro’s number. Electronic conductivities, σel (Ω-1 cm-1) of dithiol-linked films on IDAs were measured from the linear segments of current-potential curves as described before.26a,b RESULTS AND DISCUSSION Theory. The sought mode of current control in Scheme 1 can be described by24

1/iLIM ) 1/iA + 1/iE

(1)

where iA is the mass transport limited current of Cp*Fe, given by the Levich equation: 2/3 -1/6

iA ) 0.62nFACA0DA

ν

ω1/2

(2)

where C0A and DA are respectively solution concentration and diffusion coefficient of Cp*Fe, ν is the solution hydrodynamic viscosity (0.003 09 cm2/s at 298 K for CH2Cl2),33 ω is the electrode rotation rate (in s-1), n is the number of electrons per redox probe, and F and A have their usual significance.24,25 The electron hopping limiting current iE is given by

iE )

nFADECMPC d

(3)

where n corresponds to the charge state of the MPC film and DE is the apparent electron diffusion coefficient, which is related by a cubic lattice model to kET (s-1) the apparent first-order electron hopping rate constant, by

DE ) kETδ2/6

(4)

in which δ is the MPC core-to-core separation distance and thus the effective length of the electron “hop”. CMPC is the concentration of MPCs in the film, and d is the film thickness. Equation 1 indicates that a plot of iLIM-1 versus ω-1/2 should exhibit a slope consistent with the redox probe concentration and its diffusion coefficient, and an intercept reflecting the rate of the electron hopping reaction within the nanoparticle film, kET (s-1). Such a plot is called a Koutecky-Levich plot.25 Results for Dithiol-Linked Multilayer MPC Films. Voltammetry of dithiol-linked MPC network polymers has not been previously described. A typical cyclic voltammogram of a 300-nmthick film of C6 MPCs linked with C10 dithiol (C6/C10DT film) is shown in Figure 1. The quantized double layer charging peaks of the MPCs in the film are clearly visible;14a,28 in the charging pattern, each “valley” represents an individual MPC charge state and the average of the oxidation and reduction potentials of each (32) Hicks, J. F. unpublished results, University of North Carolina, 2003. (33) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents: Physical Properties and Methods of Purification, 4th ed.; Wiley: New York, 1986.

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Figure 1. Cyclic voltammogram of a 300-nm-thick C6/C10DT film grown on a 3-mm-diameter gold working electrode. Scan rate is 200 mV s-1 and the supporting electrolyte 0.1 M Bu4NPF6 in CH2Cl2. Potentials are vs Ag/AgCl, with a Pt flag as counter electrode. Indicated on the chart are the positions of the MPC film charge states.

current peak is the “formal potential” of a charge-state change. The underlying background current envelope reflects the MPC sample’s polydispersity as mentioned previously.18 The global minimum of the MPC charging currents occurs at or near the potential of zero MPC charge,14a,34 so the “0” charge state for this film is assigned as that at -350 mV versus Ag/AgCl. The other charge states are spaced by roughly 250-mV intervals28a,e (consistent with the anticipated quantized capacitance) as indicated in the figure. The current peaks for the MPC1+/0 charge-state change are not well-resolved in Figure 1. This was also the case for previously reported14a,18 MUA-linked films, but the effect is more dramatic in the present case. An appearance of well-defined peaks for each of the MPC core charge-state changes requires that the film’s composition of core charge states remain in near-equilibrium with the applied electrode potential scan. Film-electrode disequilibrium could occur for the MPC1+/0 charge-state change either from an overpotential for the first electron-transfer step or from uncompensated resistance within the initially neutral, hydrophobic film. Larger potentials and counterion penetration into the film would diminish these effects in the MPC2+/1+ charge-state change, the current peaks for which are better defined. That the phenomenon probably arises from uncompensated resistance is supported by the fact that ∆EPEAK values in Figure 1 decrease with increasingly positive charge states, which signals that the film’s ionic conductivity is significantly increasing. The Figure 1 experiment is a transient one, whereas the rotated disk electrode experiment involves steady-state currents that should be less influenced by the above effects. Equation 1 is compared to experimental data by observing how the current at the rotated MPC film-covered disk changes with rotation rate in the redox probe solution. A fixed potential is applied, at a value corresponding to one of the valleys in Figure 1 (i.e., a fixed MPC core charge state), while the rotation rate is varied. Figure 2A gives an example for measuring the current for a C6/C10DT film that is potentiostated at the potential for the MPC4+ state, in a 20 mM Cp*Fe redox probe solution. Figure 2B presents the currents as a Koutecky-Levich plot.24,25 It is apparent (34) Chen, S.; Murray, R. W. J. Phys. Chem. B 1999, 103, 9996-10000.

Figure 2. (A) Single-potential time base (SPTB) graph for a 300nm-thick C6/C10DT film grown on a 3-mm-diameter gold working electrode. The solution-phase redox probe was 20 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. Throughout the SPTB measurement, the electrode potential was held at +620 mV, which corresponds to the “+4” charge state of the film. Potentials are vs Ag/AgCl, with a Pt flag as counterelectrode. The rotation rates, from left to right, are 500, 750, 1000, 1500, and 2000 rpm. (B) Koutecky-Levich plot of the limiting currents determined from the SPTB graph depicted in (A). ω is the electrode rotation rate.

that, in this case, the currents are rotation rate-independent, as expected if Cp*Fe oxidation and mass transport are much faster than charge transport in the film; i.e., the second, iE term in eq 1 is dominant. Use of eq 3 gives DE ) 4.9 × 10-9 cm2 s-1, and eq 4 yields kET ) 3.9 × 105 s-1. This result is given in Table 1 with others for different film measurements that are more systematically discussed below. Discussion of structural aspects of the films and chain length effects is deferred to the end of the paper. Effect of Cp*Fe Concentration, MPC Charge State, and Film Thickness on RDE Response. Equations 1-3 represent a competition for current control by mass transport and film electron hopping. Increasing the redox probe concentration from 2 to 20 mM Cp*Fe, i.e., increasing the mass transport flux of probe, tilts control in a C5/C8DT film from the former to the latter, as shown in Figure 3A, where the film potential was chosen at the MPC3+ state. The slopes of the plot decrease as expected from eq 1 and yield Cp*Fe diffusion coefficients of 0.6 × 10-5, 2 × 10-5, and 2 × 10-5 cm2 s-1, respectively, that are reasonable in comparison to a literature value25,35 1.6 × 10-5 cm2 s-1. The kET results are presented in Table 2. Based on the evident suppression

Figure 3. (A) Koutecky-Levich plot demonstrating the effect of solution-phase redox probe (Cp*Fe) concentration on the limiting currents determined from the SPTB graphs of a 160-nm-thick C5/ C8DT film grown on a 3-mm-diameter gold working electrode. The solution-phase redox probe concentrations were 2 (closed circles), 5 (open circles), and 20 mM (closed triangles), in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. Throughout the SPTB measurement, the electrode potential was held at +310 mV, which corresponds to the “+3” charge state of the film. (B) Koutecky-Levich plot demonstrating the effect of DT film charge state on the limiting currents determined from the SPTB graphs of the film described in (A). The applied potentials were 0, +310, and +514 mV, at the CV peak valleys corresponding to the “+2”, “+3”, and “+4” charge states, respectively. In all cases, the solution-phase redox probe was 20 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. Potentials are vs Ag/AgCl, with a Pt flag as counterelectrode. ω is the electrode rotation rate.

of mass transport control in Figures 2B and 3A, subsequent experiments were carried out at Cp*Fe concentrations of 20 mM or above. The results in Figures 2B and 3A were for film potentials at the MPC4+ and MPC3+ states, respectively. The effect of the choice of nanoparticle charge state is shown in Figure 3B and by further results in Table 1. The formal potential of the Cp*Fe redox probe is -50 mV versus Ag/AgCl, so all of the chosen film states (0 V for MPC2+; 0.31 V for MPC3+; 0.51 V for MPC4+ ) should mediate the Cp*Fe oxidation. The results in Table 1 indicate a smaller rate constant from the MPC2+ charge state while the reactions of (35) The value of DA in acetonitrile given in ref 14, p 813, has been adjusted here to take into account the different hydrodynamic viscosities of acetonitrile and CH2Cl2.

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Table 1. Summary of Apparent Electron-Transfer Diffusion Coefficients and Apparent Electron-Transfer Rate Constants between Nanoparticles in the MPC Films

film type

d (nm)

film charge state

iLIM (× 10-4 A)

DE (× 10-9 cm2 s-1)a

kET from RDE (× 10 s5 -1)b

kET from σel (× 108 s-1)c

75 163 163 163 118 308 308 308 312 437

+3 +2 +3 +4 +3 +2 +3 +4 +3 +3

2.6 ((0.04) 0.46 ((0.01) 2.1 ((0.01) 3.6 ((0.01) 2.3 ((0.01) 0.8((0.01) 2.8 ((0.03) 3.6 ((0.01) 0.42 ((0.02) 0.22 ((0.02)

1.8 ((0.02)f 0.65 ((0.01) 2.0 ((0.01) 2.6 ((0.01) 1.2 ((0.05) 2.3 ((0.02) 5.1 ((0.05) 4.9 ((0.02) 2.3 ((0.02) 1.7 ((0.02)

0.9 ((0.01) 0.5 ((0.01) 1.6 ((0.02) 2.1 ((0.01) 1.2 ((0.05) 1.8 ((0.01) 4.0 ((0.04) 3.9 ((0.02) 1.1 ((0.08) 0.8 ((0.01)

0.4 0.7 0.7 0.7 4.0 7.1 7.1 7.1 0.04 0.04

C5/C8DTd

C6/C10DTd

C6/MUAe

a The MPC concentration used was calculated from the film thickness (profilometry) and surface coverage (UV-visible spectroscopy) data. Values are 3.5 × 10-5 and 8.3 × 10-5 mol cm-3 for MUA film and DT film, respectively. b δ, the center-to-center distance was determined from the film surface coverage using the cubic lattice model (eq 3) and was 3.6 ( 0.1 nm for MUA film and 2.7 ( 0.1 nm for DT film. c kET determined from conductivity measurements of the films deposited on IDAs, without charging from the as-prepared state. For DT film, these data will be presented in a future publication.26c For MUA film, data are from ref 26b. d Solution-phase redox probe for DT films was 20 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. e Solution-phase redox probe for MUA films was 2 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. f Error bars reflect the error in determining the value of the baseline current for the iLIM determination from the SPTB graph. Data for 25 s prior to rotation are averaged and the standard deviation used to calculate uncertainties in DE and kET.

Table 2. Effect of Solution-Phase Redox Probe Concentration, Solvent, and Temperature on the Apparent Electron-Transfer Diffusion Coefficients and Apparent Electron-Transfer Rate Constants between Nanoparticles in a 160-nm C5/C8DT Film film charge state

Cp*Fe concn (mM)

+3 +3 +3 +3 +3 +4 +4 +4

solventa

T (K)

iLIM (× 10-4 A)

DE (× 10-9 cm2 s-1)b

kET from RDE (× 105 s-1)c

2 5 20 20 20

CH2Cl2 CH2Cl2 CH2Cl2 CH2Cl2 2:1 (v/v) CH2Cl2/hexane

298 298 298 298 298

4.8 ((0.01) 2.1 ((0.01) 2.2 ((0.08) 0.7 ((0.02)

4.6 ((0.01)d 2.0 ((0.02) 2.3 ((0.08) 0.6 ((0.02)

3.6 ((0.01) 1.6 ((0.02) 1.7 ((0.06) 0.5 ((0.01)

20 20 20

CH2Cl2 CH2Cl2 CH2Cl2

218 274 298

0.7 ((0.02) 1.8 ((0.01) 2.3 ((0.05)

0.76 ((0.02) 1.7 ((0.01) 2.2 ((0.05)

0.6 ((0.02) 1.4 ((0.01) 1.8 ((0.04)

a Unless otherwise stated, solution-phase redox probe was 20 mM Cp*Fe, with 0.1 M Bu NPF as supporting electrolyte. b The MPC concentration 4 6 was calculated from film thickness (profilometry) and surface coverage (UV-visible spectroscopy) data and was 8.32 × 10-5 mol cm-3. c δ, the center-to-center distance was determined from the film surface coverage using the cubic lattice model (eq 3) and was 2.75 ( 0.05 nm. d Error bars reflect the error in determining the value of the baseline current for the iLIM determination from the SPTB graph. Data for 25 s prior to rotation are averaged and the standard deviation determined and used to calculate the errors in DE and kET.

MPC3+ and MPC4+ films give very similar rate constants. The films are ideally expected to produce a similar rate constant at all charge states where the electron hopping current iE controls the overall RDE current, since the same reaction, i.e.,

MPC+N + MPC+(N+1) f MPC+(N+1) + MPC+N occurs in all iE-controlled cases. The hopping rate was not observed18 to depend on charge state in chronoamperometric measurements. Experiments at higher nanoparticle film charge states are not reported since potentials above ∼0.7 V produced some instability in the film-mediated current response. The first and third, and fifth and seventh, entries in Table 1 represent cases where the charge state (MPC3+) was the same but the network polymer film thicknesses were quite different. In both cases, the thinner film produced a slower apparent electron hopping rate constant. The effect of film thickness was examined 5616

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further in experiments reported in Table 3, where again the thinner film produced slower electron hopping rate constants. (An overlay of the cyclic voltammograms recorded after each day of growth, along with the KL plots for the SPTB data, may be found in the Supporting Information, Figures S-3 and S-4.) The KouteckyLevich intercepts indicate a diminished current with thicker films, qualitatively as expected, but the diminution is not as large as the inverse film thickness dependency predicted by eq 3. The origin of the nonideal thickness dependency is not fully understood. It may arise from the film being rougher when thick than when thin, which would cause a trend of the kind observed. We suspect that the effect is a manifestation of the film properties as opposed to the methodology, but further study is obviously needed to resolve the effect. The uncertainty introduced into the rate data, according to Table 3, is of the order of a factor of 2-fold, which for kinetic data is a relatively minor concern. Effects of Temperature and Solvent. The CH2Cl2 solvent employed is useful at lowered temperatures, and we carried out

Figure 4. Arrhenius plot of the electron-transfer rate constants determined at various temperatures for a 160-nm C5/C8DT film using 20 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. Data are taken from Table 2. Table 3. Effect of Film Thickness on Apparent Electron-Transfer Diffusion Coefficients and Apparent Electron-Transfer Rate Constants between Nanoparticles in a C6/C10DT Filma growth film kET time d charge iLIM DE from RDE (days) (nm) state (× 10-4 A) (× 10-9 cm2 s-1)b (× 105 s-1)c 1 2 3

104 188 313

+4 +4 +4

4.9 ((0.02) 3.9 ((0.07) 3.2 ((0.09)

2.3 ((0.02)d 3.3 ((0.07) 4.5 ((0.10)

1.8 ((0.02) 2.6 ((0.07) 3.6 ((0.10)

a Growth and k ET values were monitored at daily intervals over a 3-day period. Solution-phase redox probe was 20 mM Cp*Fe, with 0.1 M Bu4NPF6 as supporting electrolyte. b The MPC concentration was calculated from film thickness (profilometry) and surface coverage (UV-visible spectroscopy) data and was 8.0 × 10-5 mol cm-3. c δ, the center-to-center distance was determined from the film surface coverage using the cubic lattice model (eq 3) and was 2.75 ( 0.05 nm. d Error bars reflect the error in determining the value of the baseline current for the iLIM determination from the SPTB graph. Data for 25 s prior to rotation are averaged and the standard deviation determined and used to calculate the errors in DE and kET.

a brief inspection of the thermal activation of the electron hopping reaction in the nanoparticle films. The Koutecky-Levich plot is shown in Supporting Information, the activation plot in Figure 4, and the data in Table 2. Although the data are quite limited, an activation barrier energy of ∼8 kJ/mol is indicated for the electron hopping (self-exchange) reaction in the C5/C8DT nanoparticle film. There are no previous activation data in solvent-wetted nanoparticle films available for comparison to this result. The protecting and linking thiolates in the nanoparticle monolayers in the film are hydrocarbon and correspondingly hydrophobic. The film would qualitatively be expected to imbibe hydrocarbon from the solvent bath. Table 2 shows that changing one-third of the solvent volume to hexane decreases kET by a factor of 3. This effect is analogous to previous experiments in which alkanethiolate-coated Au140 MPCs that had been linked into a network polymer film (using MUA and coordinated metal ions as linkers) were exposed to pure, ion-free organic solvents26a and to organic vapors.26b The partition of the organic compound into the film (verified by quartz crystal microbalance measurements in the vapor experiments) diminished the rate of electron hopping

Figure 5. Cyclic voltammogram depicting growth of a C6/MUA film made using multiple dipping cycles, on a 3-mm-diameter gold working electrode modified with a self-assembled monolayer of mercaptoundecanoic acid. Scan rate is 50 mV s-1, and the supporting electrolyte is 0.1 M Bu4NPF6 in CH2Cl2. Potentials are vs Ag/AgCl, with a Pt flag as counterelectrode. Curve 1, MUA; curve 2, dip cycle 2 (coverage, 1.4 × 10-10 mol cm-2); curve 3, dip cycle 4 (coverage, 6.4 × 10-10 mol cm-2); curve 4, dip cycle 6 (coverage, 1.5 × 10-9 mol cm-2). Surface coverages were determined as described in the text.

as measured by the film’s electronic conductivity. One of the effects of the in-partitioning is swelling of the films, which increases the MPC core-to-core separation distance,26a,b but a full explanation has to consider other factors and is likely to be much more complex. Results for MUA-Linked Multilayer MPC Films. The rotated disk experiment was also applied to hexanethiolate-coated MPCs that had been linked into films using mercaptoundecanoic acid ligands joined by coordination to Cu2+ ions (C6/MUA films). Figure 5 depicts the differential pulse voltammetry seen during growth of the Cu2+-linked C6/MUA film. The single-electron charging peaks can be seen but are not as well defined as those in the dithiolate-linked films above, or in previous MUA-linked films,18 owing to the use of the less-monodisperse ethanol-insoluble fraction of synthesized MPCs.28a Figure 6A shows the currents measured at different rotation rates at an electrode potential corresponding to the MPC3+ form of the nanoparticle film and immersed in a 2 mM solution of Cp*Fe in CH2Cl2. It is evident that for these films the 2 mM concentration suffices to yield independence of the current of rotation rate, which is emphasized in the Koutecky-Levich plot of these data (“76 monolayers”) in Figure 6B. Figure 6 also shows a plot of data taken on the same film but at an earlier (thinner) stage of film growth; there is again no rotation rate dependencescurrents are dominated by the rate of electron hopping through the film. Rate constant results are given in Table 1 (bottom); the rate constants at the two thicknesses are in good agreement for these relatively thick films. Electron hopping rates within a Zn2+-linked version of this film has been previously explored18 using potential step chronoamperometry on CH2Cl2-wetted films, and the electronic conductivity of dry Au140-based MPC films on IDAs has been investigated for a number of different linker ions and ligands.26a,b The Zn2+-linked films gave a hopping rate of 2 × 106 s-1, which is higher than the 1 × 105 s-1 result in Table 1. However, the electron hopping rate Analytical Chemistry, Vol. 76, No. 19, October 1, 2004

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Figure 6. (A) SPTB graph for a C6/MUA film grown on a 3-mmdiameter gold working electrode, determined after dip cycle 6 (surface coverage, 1.5 × 10-9 mol cm-2 = 76 monolayers). The solution-phase redox probe was 2 mM Cp*Fe in CH2Cl2 with 0.1 M Bu4NPF6 as supporting electrolyte. Throughout the SPTB measurement, the electrode potential was held at +361 mV, which corresponds to the “+2” charge state of the film. The rotation rates, from left to right, are 500, 750, 1000, 1500, and 2000 rpm. (B) Koutecky-Levich plot of the limiting currents determined from the SPTB graph depicted in Figure 2A and the SPTB graph for the same film after dip cycle 5 (surface coverage, 1.1 × 10-9 mol cm-2 = 55 monolayers). For (A) and (B), potentials are vs Ag/AgCl, with a Pt flag as counterelectrode. ω is the electrode rotation rate.

in Cu2+-linked films determined from conductivity measurements is consistently largersfor unknown reasonssthan that in Zn2+linked films, judging from lower electronic conductivities observed in the latter in comparisons.26b Comments on Electron-Transfer Rates Determined Using the Rotated Disk Method. We noted above that this investigation mainly aims at validating rotated disk electrode voltammetry for measuring electron hopping in solvent-swollen and -wetted nanoparticle polymer films. The results nonetheless do represent (Table 1) early data on the effects of monolayer linking chemistry on electron hopping rates in such films. Neither of the previous chronoamperometry studies18,19 involved any comparative structural variations in the nanoparticles, either monolayer chain length or linker chain length. Table 1 shows that, first, there are no clear correlations between the hopping rates and the structural components of the present films. Shorter dithiol linkers do not yield higher hopping 5618 Analytical Chemistry, Vol. 76, No. 19, October 1, 2004

rates; in fact, the apparent electron hopping rate constants in Table 1 for the C6/C10DT film are not very different from those for the C5/C8DT films. A slightly slower hopping rate would have been expected were the tunneling barrier between the MPC cores determined strictly by the length of the dithiol linkers or by nonbonded contacts between the nonlinking pentanethiolate and hexanethiolate ligands. Second, the C6/MUA films do exhibit slower hopping rates than the C6/C10DT films, but again by only a small factorsmuch less than would be expected were a 25-atomlong MUA-Cu2+ MUA linker to constitute the electron-transfer tunneling bridge. One must conclude that these different chain length constructs fail to spatially control the electron tunneling pathway in the precise manner that has been achieved with twodimensional self-assembled monolayers on Au electrodes.36 It is significant (perhaps) that, while in studies of electronic conductivities of dry MUA-linked films in which the nonlinker ligands were systematically varied, the classic exponential change of hopping rate with nonlinker chain length was observed, no such correlation is found when the length of the linker was varied.26b The structural motifs of these alkanethiolate-based films seem to be dominated by the hydrophobic collapse and interdigitation of the nonlinker ligands; the linker chains do not command the structural spacing of the nanoparticle cores that act as the locus of the electron transfers. In this sense, the solvent-swollen and dry nanoparticle films behave roughly similarly. On the other hand, the striking results of Table 1 are that the electronic conductivity measurements on dry films give hopping rates ranging from 40- to 2000-fold larger than the solvent-wetted rotated disk measurements. The dry (nonionically conductive) film results for electron hopping rates refer to films that are similarly prepared, but on interdigitated array electrodes, and that are derived from measurements of electronic conductivity and converted into hopping rates by a relation analogous to eq 4. As noted above, the electronic conductivity measurements are accomplished by a previously described procedure.26a,b The alkanedithiolatelinked MPC films are part of an ongoing study that will be described in a separate paper.26c The large wet-dry difference noted above is not understood but emphasizes that the environment of the nanoparticlenanoparticle electron hopping reaction is a major factor in its rate. We first should comment on the validity of the methods used. Some time ago, this laboratory compared37 electron hopping rates in poly(vinylferrocene) films that had been derived from concentration gradient-based measurements (analogous to the solventwetted rotated disk ones used here) and voltage gradient-based measurements (analogous to the dry-film electronic conductivity data). The rates were in reasonably good agreement, so we have some confidence that the basic principles of the methodology are generally correct. We look instead then at characteristics of the nanoparticle film structures and chemistry as more likely sources of the rate differences. The possibilities can be only speculatively outlined. (A) The linked films may contain a sufficient quantity of structural (36) (a) Finklea, H. O.; Liu, L.; Ravenscroft, M. S.; Punturi, S. J. Phys. Chem. 1996, 100, 18852-18858. (b) Weber, K.; Hockett, L.; Creager, S. E. J. Phys. Chem. B 1997, 101, 8286-8291. (c) Smalley, J. F.; Feldberg, S. W.; Chidsey, C. E. D.; Linford, R.; Newton, M. R.; Liu, Y.-P. J. Phys. Chem. 1995, 99, 13141-13149. (37) Sullivan, M. G.; Murray, R. W. J. Phys. Chem. 1994, 98, 4343-4351.

gaps and holes as to be sensitive to changes in the electrontransfer barriers of a relatively small fraction of the MPC-MPC electron hops; i.e., there are “bottleneck” sites as in a percolation situation.13c,38 A minor extent of swelling by solvent could then provoke a severe diminution of rate. This notion is supported by the decreases in dry-film electronic conductivity caused by the partition of organic solvent vapors into them. The ensuing swelling can be argued to cause an increase in nanoparticle separation and a consequent decrease in electron hopping rate. We have argued,26b however, that the actual physical situation is much more complex than this simple explanation. (B) Previous investigations39 of electron transport in molecular redox melts have identified a correlation between electron-transfer rates and the diffusion coefficient of the supporting electrolyte counterion. This form of rate control has been termed ion atmosphere relaxation. Since ionic transport rates may be slow in the nanoparticle films, this mechanism must be included as a possibility; we have at this time, however, no ionic conductivity data with which to explore it. In conclusion, the central purpose of this paper was to introduce the steady-state rotated disk electrode method to the measurement of electron hopping rates in films of nanoparticles (38) Trudeau, P. E.; Orozco, A.; Kwan, E. J. Chem. Phys. 2002, 117, 39783981. (39) (a) Lee, D.; Hutchison, J. C.; Leone, A. M.; DeSimone, J. M.; Murray, R. W. J. Am. Chem. Soc. 2002, 124, 9310-9317. (b) Lee, D.; Harper, A. S.; DeSimone, J. M.; Murray, R. W. J. Am. Chem. Soc. 2003, 125, 1096-1103. (c) Harper, A. S.; Lee, D.; Crooker, J. C.; Wang, W.; Williams, M. E.; Murray, R. W. J. Phys. Chem. B 2004, 108, 1866-1873.

on electrodes. The methodology is experimentally simple to implement and with care in selection of redox probe and its concentration, and the film charge state, may be used to analyze apparent electron hopping rates in different types of MPC films. The main factors revealed in the study are issues related to the nanoparticle film itself, which was a central motivation for exploring the rotated disk method. These preliminary results raise a number of questions with respect to film structure and electrontransfer controlling factors in solvent-swollen films that require further study. ACKNOWLEDGMENT This research was supported by grants from the National Science Foundation and the Office of Naval Research. SUPPORTING INFORMATION AVAILABLE A table of the calculated apparent diffusion coefficients for Cp*Fe in each experiment, Koutecky-Levich plots of the effect of solvent and temperature on the RDE experiment (as summarized in Table 2), and the cyclic voltammograms and KouteckyLevich plot for the film thickness study (as summarized in Table 3). This material is available free of charge via the Internet at http://pubs.acs.org. Received for review May 14, 2004. Accepted July 14, 2004. AC049289J

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