10194
Langmuir 2004, 20, 10194-10199
Enhancement of Electrochemical Activity by Small-Sizing the Vinylferrocene-Immobilized Polystyrene Latex Particles Cuiling Xu and Koichi Aoki* Department of Applied Physics, University of Fukui, 3-9-1 Bunkyo, Fukui-shi 910-8507, Japan Received May 10, 2004. In Final Form: August 5, 2004 Voltammetry of vinylferrocene (VFc)-immobilized polystyrene(PS)-based latex particles was carried out in aqueous suspensions by changing the size of latex particles in order to investigate the dependence of the electroactivity of the particles on their size. The anodic peak current was controlled by diffusion of the latex. The voltammetric peak currents increased with an increase in the diameter of PS latex particles for a given analytical concentration of the particles, exhibiting the dependence on 1.5 powers of the diameter of the particles. The increase can be explained in terms of combination of the uniform distribution of VFc in the particle, the partial charge transfer, and the Stokes-Einstein equation for diffusion coefficients. The oxidation of VFc occurs in the restricted domain (0.07 µm) from a contact point of the particle with the electrode. The overall reaction mechanism is diffusion of the particle to the electrode, partial oxidation to VFc+, release of VFc+ from the particle to the solution, and reduction of the released VFc+.
1. Introduction Particle size often alters physical properties such as luminescence, conductivity,1 vacancy formation energy,2 melting point,3 and the evaporation temperatures of nanoparticles.4 Metal nanoparticles are an exemplification of exhibiting size-dependent optical and electronic properties. As their particle size decreases, the surface plasmon adsorption peak shifts to a higher energy region,5 as has been explained in terms of the Mie theory.6 Size-dependent chemical properties are well documented in the field of metal cluster chemistry7 and have been applied to catalysts.8 Organic nanoparticles also show the size dependence in the optical adsorption,9,10 which may result from the aggregate effect,11 surface effect,12 or variation of intermolecular interaction.9 With an increase in crystal size of perylene nanoparticles, for example, their excimer emis(1) (a) Alivisatos, A. P. Science 1996, 271, 933. (b) Lieber, C. M. Solid State Commun. 1998, 107, 607. (2) Qi, W. H.; Wang, M. P. Physica B 2003, 334, 432. (3) Zeng, H.; Sun, S.; Sandstrom, R. L.; Murray, C. B. J. Magn. Magn. Mater. 2003, 266, 227. (4) Nanda, K. K.; Kruis, F. E.; Fissan, H. Phys. Rev. Lett. 2002, 89, 256103/1. (5) (a) Wang, X.; Sudol, E. D.; El-Aasser, M. S. Langmuir 2001, 17, 6865. (b) Fujii, M.; Nagareda, T.; Hayashi, S.; Yamamoto, K. Phys. Rev. B 1991, 44, 6243. (c) Tsunekawa, S.; Kasuya, A.; Kawazoe, Y. IPAP Conf. Ser. 2001, 3, 88. (d) Ma, X.; Shi, W. Microelectron. Eng. 2003, 66, 153. (6) Mie, G. Contributions to the optics of turbid media, particularly of colloidal metal solutions; Royal Aircraft Establishment Library Translation 1873; Her majesty’s Stationery Office: London, 1976. (7) Moraga, G. G. Cluster Chemistry; Spring-Verlag: Berlin, 1993; Chapter 2. (8) Mu¨ller, B. R.; Majoni, S.; Meissner, D.; Memming, R. J. Photochem. Photobiol., A 2002, 151, 253. (9) (a) Kasai, H.; Kamatani, H.; Okada, S.; Oikawa, H.; Matsuda, H.; Nakanishi, H. Jpn. J. Appl. Phys. 1996, 35, L221. (b) Kasai, H.; Kamatani, H.; Yoshikawa, Y.; Okada, S.; Oikawa, H.; Watanabe, A.; Itoh, O.; Nakanishi, H. Chem. Lett. 1997, 26, 1181. (10) (a) Fu, H. B.; Yao, J. N. J. Am. Chem. Soc. 2001, 123, 1434. (b) Forrest, S. R. Chem. Rev. 1997, 97, 1793. (c) Fu, H. B.; Luo, B. H.; Xiao, D. B.; Xie, R. M.; Ji, X. H.; Yao, J. N.; Zhang, B. W.; Zhang, L. Q. Angew. Chem., Int. Ed. 2002, 41, 962. (11) Xie, R. M.; Xiao, D. B.; Yao, J. N. Wuli Huaxue Xuebao 2002, 18, 34. (12) Xie, R. M.; Fu, H. B.; Ji, X. H.; Chen, Z. H.; Yao, J. N. Appl. Phys. A 2002, 74, 239.
sion was weakened, prolonging the decay time.11 An increase in the size of 4,4′-dibromobiphenyl nanoparticles made the adsorption band shift in the red direction.12 The size dependence was found in bathochromic adsorption transition for nanoparticles of a series of pyrazoline derivates.13 It was caused by the variation of the intermolecular interaction with structural change in the derivatives. The emission of the pyrazoline chromophore was blue-shifted with an increase in the particle size.13 It is microspheres or latex particles that are sizecontrollable materials. Polystyrene (PS) latex particles have been widely used as models of molecular ordering because they provide well-stabilized suspensions in a broad range of sizes with a sharp size distribution. Size controllability of PS particles has often played a significant role in investigating adsorption properties,14,15 the stability of the suspension,16 aggregation,17 adhesion,18 microrheology,19 and the glass transition temperature.20 The nanometer-scaled PS particles have exhibited more rapid aggregation than micrometer-scaled ones at a common mass concentration. Li et al.14 observed that the layer thickness of PEO/PPO/PEO copolymers adsorbed on PS particles increased with an increase in particle size, although the inverse variation was also reported.15 Polyaniline-coated large PS particles caused electrochemically oscillating current at the oxidation potential.21 Aqueous (13) Xiao, D. B.; Xi, L.; Yang, W. S.; Fu, H. B.; Shuai, Z. G.; Fang, Y.; Yao, Y. N. J. Am. Chem. Soc. 2003, 125, 6740. (14) (a) Li, J. T.; Caldwell, K. D. Langmuir 1991, 7, 2034. (b) Li, J. T.; Caldwell, K. D.; Rapoport, N. Langmuir 1994, 10, 4475. (15) (a) Lee, J.; Martic, P. A.; Tan, J. S. J. Colloid Interface Sci. 1989, 131, 252. (b) Tan, J. S.; Martic, P. A. J. Colloid Interface Sci. 1990, 136, 415. (16) Kallay, N.; Zˇ alac, S. J. Colloid Interface Sci. 2002, 253, 70. (17) (a) Selomulya, C.; Bushell, G.; Amal, R.; Waite, T. D. Langmuir 2002, 18, 1974. (b) Boller, M.; Blaser, W. Water Sci. Technol. 1998, 37, 9. (18) (a) Rimai, D. S.; Quesnel, D. J.; Busnaina, A. A. Colloids Surf., A 2000, 165, 3. (b) Busnaina, A. A.; Kashkonsh, I. I.; Gale, G. W. J. Electrochem. Sci. 1995, 148, 2812. (19) Lu, Q.; Solomon, M. Phys. Rev. E 2002, 66, 61504. (20) (a) Ellison, C. J.; Torkelson, J. M. Nat. Mater. 2003, 2, 695. (b) Jiang, Q.; Shi, H. X.; Li, J. C. Thin Solid Films 1999, 354, 283. (21) (a) Lei, T.; Aoki, K.; Fujita, K. Electrochem. Commun. 2000, 2, 290. (b) Lei, T.; Aoki, K. J. Electroanal. Chem. 2000, 482, 149. (c) Mohammad, A. Y.; Aoki, K. J. Electroanal. Chem. 2004, 565, 219.
10.1021/la0488405 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/06/2004
VFc-Immobilized Polystyrene Latex Particles
suspensions of nanometer-scaled sulfonated PS particles showed a striking iridescence depending on the applied electrode potentials,22 whereas those of the micrometerscaled ones did not.23 In a series of our electrochemical study on PS-based latex suspensions, we have noticed empirically that the larger the size distribution of redox latex particles is, the broader are the current-voltage curves.24,25 This observation may belong indirectly to the size effect. In this report, we describe the effects of particle size on voltammetric electroactivity by the use of vinylferroceneimmobilized PS (VFc-PS) microspheres in aqueous suspension. VFc is adsorbed hydrophobically in nearly monodispersed PS particles, of which size is synthetically controlled. Points of interest are (i) whether VFc is distributed on the particle surface or within the particle, (ii) in which process VFc is controlled for the electrode reaction, (iii) the stability of the adsorbed VFc for the redox reaction, and (iv) the ratio of the amount of reacting VFc to the immobilized amount. Points i, iii, and iv are predicted to exhibit specific size dependence. To respond to these questions, voltammetry and UV spectroscopy experiments were conducted for various sizes of VFc-PS microspheres to give data for heterogeneous and homogeneous reactions of the VFc-PS latex particles, respectively. We expect that the study on the size dependence may answer the previous question30 why VFc-coated particles reacted under only restricted conditions. The voltammetric anodic current will be represented by the radii of the latex particles. 2. Experimental Section Chemicals. Styrene was purified as was previously mentioned26 and stored in a refrigerator before use. The steric stabilizer, poly(N-vinylpyrrolidone) (PVP), with a molar mass of ∼360 kg mol-1, and the initiator, R-azoisobutyronitrile (AIBN), were used as received. Commercially available VFc (TCI, Tokyo) had been stored at 3 °C before use. All solvents used were of analytical grade. Aqueous solutions were prepared using ionexchanged and doubly distilled water. Synthesis of Vinylferrocene-Adsorbed Polystyrene Latex. The core, made of PS, was synthesized in the mixed solvent of 2-propanol and water, as described previously.26 VFc was dissolved in 2-propanol and mixed with the PS aqueous suspension. The mixture was stirred for 24 h with the aim of adsorbing VFc on the PS latex, purified by centrifugation, and dispersed in water. This centrifugation/redispersion procedure was repeated five times. The resulting latex was dispersed in distilled water. The size of all PS particles was evaluated by a scanning electron microscope (SEM) (SEM&EDX type N, Hitachi) and an optical microscope (VMS-1900, Scalar). Electrochemical Measurements. A Pt disk electrode 0.8 mm in radius was used as a voltammetric working electrode. The electrode surface was polished with alumina paste on wet cotton and rinsed with distilled water in an ultrasonic bath before each experiment. The Pt wire and the Ag|AgCl|NaClsat electrode were used as a counter electrode and as a reference electrode, respectively. Voltammetric measurements were taken by the (22) (a) Aoki, K.; Wang, C. Langmuir 2001, 17, 7371. (b) Aoki, K.; Lei, T. Electrochem. Commun. 1999, 1, 101. (23) Aoki, K.; Wang, C.; Chen, J. J. Electroanal. Chem. 2003, 540, 135. (24) Aoki, K.; Chen, J.; Ke, Q.; Armes, S. P.; Randall, D. P. Langmuir 2003, 19, 5511. (25) Aoki, K.; Lei, T. Langmuir 2000, 16, 10069. (26) Chen, J.; Xu, C.; Aoki, K. J. Electroanal. Chem. 2003, 546, 79. (27) Tuncle, A.; Kahraman, R.; Piskin, E. J. Appl. Polym. Sci. 1994, 51, 1485. (28) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, U.K., 1998; p 749. (29) Saji, T.; Hoshino, K.; Ishii, M.; Goto, M. J. Am. Chem. Soc. 1985, 107, 6865. (30) Xu, C.; Chen, J.; Aoki, K. Electrochem. Commun. 2003, 5, 506.
Langmuir, Vol. 20, No. 23, 2004 10195
Figure 1. SEM photographs of dried VFc-PS latex particles at the (A) fourth and (B) second lines in Table 1. Table 1. Parameters of the VFc-PS Particles
1 2 3 4 5 6 7 8
2a/µm (optical microscope)
2a/µm (SEM)
nUV/ ×107
D0 × 108/ cm2 s-1
0.39 ( 0.13 0.51 ( 0.13 0.62 ( 0.13 0.87 ( 0.13 1.09 ( 0.13
0.16 ( 0.002 0.18 ( 0.01 0.36 ( 0.03 0.63 ( 0.07 0.74 ( 0.03 0.92 ( 0.02 1.11 ( 0.03 1.20 ( 0.06
0.013 0.032 0.104 0.567 1.26 1.83 1.98 4.30
3.2 2.7 1.36 0.78 0.66 0.53 0.44 0.41
n/nUV 0.63 0.58 0.36 0.24 0.21 0.18
use of a potentiostat (model 1112, HUSO, Kawasaki) under the control of a computer. Bulk electrolysis was performed at a Pt mesh 35 × 26 mm2 electrode (mesh 80, BAS, Tokyo) as the working electrode, a Pt coil counter electrode, and the Ag|AgCl|NaClsat reference electrode. The working and the counter electrodes were separated with a Spectra/Por dialysis cellulose tube (Funakoshi Co.). The VFc-PS suspension was stirred vigorously with a magnetic stirrer during the bulk electrolysis. The supporting electrolyte used in all the experiments was 0.1 M (M ) mol dm-3) KCl aqueous solution.
3. Results and Discussion Various sizes of polystyrene latex particles were obtained by changing the concentrations of the monomer, of the steric stabilizer (PVP), and of the initiator (AIBN) and the volume ratio of 2-propanol to water. An increase in concentration of the monomer and the initiator yielded larger particles. This is because the higher concentration can facilitate growth of the nucleation. The particle became bigger with an increase in the ratio of 2-propanol to water because a higher volume ratio of 2-propanol can stabilize larger particles. A lower concentration of the stabilizer gave larger particles because it generated fewer nuclei for the growth. All these effects on the particle size are consistent with those described by Tuncel.27 VFc-PS particles were obtained by mixing VFc-dissolved 2-propanol solution with the PS aqueous suspension. The mixture was yellow, the color of which was from VFc. The particles rinsed with water showed also a yellow color. Consequently, VFc should be immobilized on the particles. The immobilization may be due to the hydrophobic interaction of VFc with PS in the aqueous solution. Indeed, the particles which were rinsed sufficiently with 2-propanol became white, leaving yellow in the supernatant. Figure 1 showed SEM photographs of the dried VFc-PS particles dispersed on a glass plate. All the particles were spherical, were nearly monodispersed, and had a smooth surface morphology. Some of them were aggregated during the drying process (Figure 1A), although suspended particles were well dispersed from the view of an optical microscope. The average diameters, 2a (a ) radius), of the particles obtained with a SEM are given in Table 1. They were slightly larger than the values obtained with the optical microscope, probably because of large digital errors (0.13 µm). Diffusion coefficients for
10196
Langmuir, Vol. 20, No. 23, 2004
Figure 2. UV spectra of dried VFc-PS particles (a) 0.16 and (b) 1.11 µm in diameter and (c) a VFc molecule dissolved in CH2Cl2 solution.
the particles were estimated according to the StokesEinstein relation, D ) kT/6πηa,28 on the assumption of a hard sphere model, where the viscosity, η, was taken to be 0.891 × 10-3 kg m-1 s-1 in water at 25 °C. VFc-PS particles could dissolve in dichloromethane to get a transparent, yellow solution. Figure 2 shows the UV spectra of two kinds of VFc-PS particles (2a ) (a) 0.16 and (b) 1.11 µm) and a VFc molecule (c) dissolved in dichloromethane. The spectral band of the latex suspensions at 440 nm was identical to that of the VFc molecule in the dichloromethane solution. Consequently, VFc is immobilized on the PS particles in a state similar to the dissolved VFc molecule. Immobilized VFc is in the reduced state because the oxidized state of the dissolved VFc shows a band at 628 nm.29 The supernatant of the aqueous suspension showed no absorption band of VFc, implying that VFc was immobilized strongly on the PS particles. The absorbance at 440 nm was used for evaluating average concentrations of VFc in the suspension by the use of a calibration curve. The concentration of particles in the suspension was evaluated26 as follows: The weight per particle was calculated from the diameter and the density (d ) 1.05 g cm-3) on the assumption that the density is identical to that of the bulk polystyrene. A given volume of the suspension was dried and weighed. The ratio of two weights gave the number of particles in the given volume. The loading of the ferrocene units per particle, nUV, was estimated from the absorbance at 440 nm of the particledissolved dichloromethane solution and the concentration of the particles. For example, one particle 1 µm in diameter had nUV ) 3 × 107 VFc units. Since this particle is composed of 4 × 109 styrene units estimated from the weight of the styrene unit, it is not necessary to take into account the contribution of the density of VFc. The values of nUV increased with the increase in the particle size, as depicted in Table 1. Since the values of nUV were determined by the use of the values of a for the estimation of the concentration of particles in the suspension, it is not fair to examine the variation of nUV with a. It is necessary to represent the loaded amount of VFc in terms of experimentally accessible values without using values of the radii. We represent the amount as the ratio of the molar concentration of VFc, cVFc, to its weight of the dried PS particles, WPS, in a given volume. The ratio means the number of molecules of VFc per weight of the particle. We plotted the ratio against the radii on the logarithmic scale in Figure 3. We assumed that VFc was adsorbed uniformly on the surface of the particles with the surface density, σ. Then, cVFc is given by 4πa2σN/V for N VFc-PS particles in volume V of the suspension, whereas WPS is given by 4πa3dN/3V. Therefore, the ratio cVFc/WPS is expressed by 3σ/da, and then, the plot in Figure 3 might have fallen on the dotted line with a slope of -1. However, experimental values showed independence of the radii. This independence suggests
Xu and Aoki
Figure 3. Variation of cVFc/WPS with the radii, a, on the logarithmic scale.
Figure 4. Dependence of the loading of VFc per particle, nUV, on a3.
Figure 5. Cyclic voltammograms of the water-suspended VFcPS particles with 2a ) (a) 0.16, (b) 0.74, and (c) 1.11 µm at the Pt electrode for a scan rate of 100 mV s-1 in 0.1 M KCl aqueous suspension and a voltammogram of VFc-dissolved aqueous solution including surfactant PVP (dashed curve) at 100 mV s-1.
the proportionality of cVFc with a3 rather than a2, implying that VFc should be immobilized uniformly even inside the PS particles. The uniform distribution of VFc is supported by the proportionality of nUV with a3, as is shown in Figure 4. The slope of the line gives the concentration of VFc in PS particles, nUV/(NA4πa3/3) ) 68 mM, where NA is Avogadro’s constant. The immobilization was achieved by immersing the PS particles in 5 mM VFc solution, and thus, VFc was accumulated in the PS particles 14 times larger than in the solution. Figure 5 shows cyclic voltammograms of the aqueous suspensions of three sizes of the VFc-PS particles at the 1.6 mm Pt electrode. As a control experiment for the electrochemical behavior of VFc in the water phase, cyclic voltammetry was carried out in the VFc-dissolved aqueous solution including the surfactant PVP, which was used to facilitate the dissolution of VFc in water (dashed curve in Figure 5). A couple of redox peaks at ∼0.21 V versus Ag|AgCl (the middle of the anodic and cathodic peak potentials) were ascribed to VFc dissolved in water. Suspensions for particles 0.16 and 0.74 µm in diameter show redox waves at potentials (0.23 V vs Ag|AgCl) close to those of VFc in the PVP aqueous solution. Therefore, the particles are electroactive by the VFc moiety. The positive potential shift by 20 mV can be explained in terms of the prediction that the free energy of VFc in PS is lower than that of VFc in PVP because of the greater hydrophobicity of PS compared with PVP and water. When the
VFc-Immobilized Polystyrene Latex Particles
Langmuir, Vol. 20, No. 23, 2004 10197
Figure 6. Dependence of the anodic, Ip,A, and cathodic, Ip,C, peak currents on the square root of the scan rate, ν1/2, in the VFc-PS (2a ) 0.16 (O) and 0.92 µm (0)) aqueous suspensions. The upper abscissa is ν for the replot of Ip,A of the particles (2a ) 0.92 µm (9)).
particle size was increased, voltammetric peaks disappeared (Figure 5c), even though the adsorption of particles on the electrode surface was observed by the optical microscopy, as was found previously.26,30 The size effect will be addressed later. The kinetics of the voltammetric behavior of suspensions was investigated by varying the scan rate in 0.1 M KCl aqueous suspension. The increase in the scan rate enhanced the voltammetric currents without any peak potential shift. Figure 6 shows the dependence of the anodic, Ip,A, and cathodic, Ip,C, peak currents on the potential scan rate, ν. The anodic peak current of the small particle (2a ) 0.16 µm) was proportional to ν1/2, suggesting diffusion control of VFc within the particle or of the particle itself in the suspension. In contrast, the anodic peak currents for the large particle (2a ) 0.92 µm) deviated slightly up from the proportionality with ν1/2. We replotted the current against ν for the large particle. Proportionality was somewhat improved, and hence, adsorption participates in the current. The smaller the particle, the more the anodic peak current is controlled by diffusion. The previously synthesized VFc-coated particles did not exhibit diffusion behavior30 because of the big diameter (1.2 µm) of the particles. On the other hand, the cathodic peak currents were proportional to ν1/2, regardless of particle size, suggesting a sufficiently diffusion-controlled wave. A difference between the anodic reaction and the cathodic one in the dependence of Ip on ν1/2 implies contribution of irreversible processes such as chemical reactions. To find an implication of chemical reactions, bulk electrolysis was carried out by applying 0.8 V vs Ag|AgCl to the Pt mesh electrode in the stirred aqueous suspensions including 0.1 M KCl. The anodic current decreased with the electrolysis time. Voltammetry was performed in the supernatants obtained by centrifugation of bulk-electrolyzed suspensions. A couple of the redox waves were observed at ∼0.21 V vs Ag|AgCl. They ought to be caused by VFc and VFc+, and hence, VFc and/or VFc+ should be released from the polystyrene particles. Since the release occurred at the oxidation, VFc+ rather than VFc should be released. VFc+ is hydrophilic, and hence, it is more stable in water than on the polystyrene particles. Thus, the overall reaction can be expressed by
Oxidation: VFc-PS - ne- f VFcn+-PS f nVFc+ + PS (1) Reduction: VFc+ + e- f VFc
(2)
However, there is a possibility for VFc+ to be left behind in the particle by neutralizing the charge with an anion in solution.
Figure 7. Dependence of aqueous suspensions of |Ip,C/Ip,A| of VFc-PS particles on the scan rate for various sizes of particles and the VFc molecules (×) dissolved in the PVP aqueous solution. The particle size increases from filled circles to filled rectangles in order.
Most of the anodic peak currents of the VFc-PS suspensions were smaller than the cathodic ones, whereas the anodic currents of the VFc molecules in the PVP aqueous solution were slightly larger than the cathodic ones. The latter is a conventional case for a simple soluble redox species, and hence, the former has been rarely found, to our knowledge. Figure 7 shows the dependence of |Ip,C/ Ip,A| on the scan rate for various sizes of the particles. Values of |Ip,C/Ip,A| increased with a decrease in the scan rate and with an increase in the particle size. The observation that | Ip,C| > Ip,A can be explained quantitatively in terms of the smaller diffusion coefficients of the particles relative to the diffusion coefficient of the released VFc+. We assume that Ip,A and Ip,C are controlled by the diffusion of VFc-PS and VFc+, respectively, through reactions 1 and 2. When an n-charged particle is oxidized successively with a one-electron transfer reaction as if the bulk concentration were to be n times higher than the particle concentration, c, the diffusion-controlled peak current has been expressed24 by
Ip ) 0.446ncFA(DνF/RT)1/2
(3)
The concentration of VFc in the suspension is given by cF ) nUVcP, where cP is the bulk concentration of the particle in the suspension. Letting the diffusion coefficients of VFc+ and the particle be DF and DP, respectively, the anodic and cathodic peak currents are expressed by
Ip,A ) 0.446cFFA(DPνF/RT)1/2
(4)
Ip,C ) 0.446cF′FA(DFνF/RT)1/2
(5)
where cF′ is the concentration of VFc+ if VFc+ is distributed uniformly in the bulk. A value of cF′ should be less than cF for cyclic voltammetry and might be close to cF, if a conventional reaction were to occur. Taking the ratio of eqs 4 and 5 yields
|Ip,C/Ip,A| ) (cF′/cF)(DF/DP)1/2
(6)
From the diffusion coefficients of DF ) 10-5 cm2 s-1 and 4 × 10-9 cm2 s-1 < DP < 3 × 10-8 cm2 s-1 in Table 1, we obtain 20 < (DF/DP)1/2 < 50. The experimental data of |Ip,C/ Ip,A| were Ip,A should be caused by the much slower diffusion of the particle relative to the diffusion of VFc+. Slopes of the lines which were forced to be drawn through the origin
10198
Langmuir, Vol. 20, No. 23, 2004
Xu and Aoki
Figure 8. Variation of |Ip,C/Ip.A| with DP-1/2 at scan rates of 0.02 (open circles) and 0.06 V s-1 (fill circles).
Figure 9. Variation of n/nUV with a on the logarithmic scale. The slope of the solid line is -0.8, while that of the dashed line is -1.
increased with a decrease in the scan rate. In other words, values of cF′/cF increase at longer electrolysis times, because of the release period in reaction 1. On the other hand, the value of |Ip,C/Ip,A| for the smallest particle (2a ) 0.16 µm) became
