Langmuir 1994,10,2800-2806
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Electron Transfer Rates in Electroactive Films from Normal Pulse Voltammetry. Myoglobin-Surfactant Films James F. Rusling* and Alaa-Eldin F. Nassar Department of Chemistry, Box U-60, University of Connecticut, Storrs, Connecticut 06269-3060 Received March 28, 1994. In Final Form: May 18, 1994@ A diffusion-kinetic model for normal pulse voltammetry was evaluated for the estimation of standard for films on electrodes heterogeneous rate constants (k"')and charge transport diffusion coefficients (D') featuring small signal to background ratios. Individual voltammograms are easily tested for adherence to the model. Analysis of errors by using nonlinear regression of theoretical data indicated that reliable determination of electron transfer rate constants requires use of an optimum pulse width range, depending mainly on K = k"'/D1/2. The method was applied to ao-pm-thick, liquid crystal films of didodecyldimethylammonium bromide containing the heme protein myoglobin. Values of k"' and D' were in good agreement with those obtained by cyclic voltammetry. Pulse widths of 5 10 ms were required for reliable k"' values, while longer pulse widths gave reliable D' values.
Introduction Designing electrode coatings for specific tasks has evolved into a major area of chemical research.l Kinetics of electron transfer involving electroactive films are important for their characterization and performance. Several voltammetric methods are available to estimate heterogeneous electron transfer rate constants in ultrathin or monomolecular films on electrodes. These methods involve experiments where mass transport is unimportant, employing thin-layer condition^.^-^ Some films cannot be made thinner than experimentally attainable diffusion layers a t the electrode surface, and diffusion within the film will influence the data. In such cases, it should be possible to estimate heterogeneous electron transfer rate constants from voltammetric data obtained under diffusion-kinetic control. The key requirement is that the diffusion layer developed at the electrode during electrolysis should be a small fraction of the film thickness. Under these conditions semi-infinite linear diffusion theory5 should apply. This paper discusses the application of normal pulse voltammetry (NPV) under diffusion-kinetic control to estimating rate and thermodynamic parameters in relatively thick, fluid films on electrodes. The genesis of our work was our development of multilayer films of waterinsoluble surfactants containing redox catalysts.6-10 These surfactant films in the liquid crystal state exhibit good mass and charge transport. In typical applications, such films containing metal macrocycliccatalysts were used to reduce organohalide ~~
@Abstractpublished in Advance ACS Abstracts, July 1, 1994. (1) Murray, R. W., Ed., Molecular Design of Electrode Surfaces, Techniuues in Chemistry: Saunders, W. H., Series Ed.; Wiley: New York, i922; Vol. 22. (2) Laviron, E. InElectroanalytical Chemistry;Bard, A. J., Ed.;Marcel Dekker: New York, 1982: Vol. 12. DD 53-157. (3) Seralathan, M.; Ribes, A.; ODea, J. J.; Osteryoung, J. J. Electroanal. Chem. 1991,306, 195. (4) O'Dea, J.J.; Osteryoung, J. Anal. Chem. 1993,65, 3090. ( 5 ) Bard, A. J.;Faulkner, L.R. Electrochemical Methods; Wiley: New York, 1980. (6)Rusling, J. F.; Zhang, H. Langmuir 1991,7 , 1791. (7)Rusling, J. F.; Hu, N.;Zhang, H.;Howe, D.;Miaw, C.-L.;Couture, E. InElectrochemistry in Colloids and Dispersions; Mackay, R. A.,Texter, J., Eds.; VCH Publishers: New York, 1992; pp 303-318. (8)Miaw, C.-L.;Hu, N.;Bobbitt, J.M.;Ma, Z.; Ahmadi, M. F.;Rusling, J. F. Langmuir 1993,9 , 315. (9) Zhang, H.; Rusling, J. F. Talanta 1993,40,741. (10) Hu, N.; Howe, D.; Ahmadi, M. F.; Rusling, J. F. Anal. Chem. 1992,64,3180.
Recently, we incorporated the Fe(II1) heme protein myoglobin (Mb) into ordered surfactant films. We found that electron transfer rates between pyrolytic graphite electrodes and myoglobin increased more than 1000-fold in surfactant films compared to aqueous so1utions.l' These films were stable in thicknesses of 1-40 pm. It was difficult to achieve stable ultrathin films to obtain electron transfer rate constants under thin-layer conditions.l' Also, background currents were large relative to the faradaic signals obtained in cyclic voltammetry, and needed to be accounted for in the data analysis. Analysis of cyclic voltammetric data by conventional methods12J3indicated that the system fit the diffusion-kinetic model. This analysis also provided the standard heterogeneous rate constant (k"') for the Fe(III)/Fe(II) couple of Mb in the films. We confirmed these results by using a method which provides tests of the model for each individual NPV experiment. This was difficult with cyclic voltammetry because of the problem of modeling or subtracting the large and variable background current on both forward and reverse scans. In normal pulse voltammetry (NPV),a series of periodic pulses of linearly increasing or decreasing potential which are applied to the electrochemical cell.6 All pulses begin at a base potential a t which there is no electrolysis a t the working electrode. At the end of each pulse, the applied potential returns to the base value, and a time lag precedes the next pulse in the series. Current measurements are made a t the end of each pulse, at which time the charging component of the current has decayed appreciably relative to the faradaic component. This increases the faradaic to charging current ratio in the output current vs potential curve, relative to methods such as cyclic voltammetry which measure current continuously. NPV is well suited to the determination of electron transfer rate constants, and a closed form diffusion-kinetic model is available for analyzing data.14 Use of this model with nonlinear regression analysis affords rapid estimation of k"', D, E"', and the electrochemical transfer coefficient a. NPV was recently extended into the microsecond regime, and applied to estimation of large (11) Rusling, J. F.;Nassar, A.-E. F. J.Am. Chem. Soc. 1993,115, 11891. (12) Nicholson, R. S.A n d . Chem. 1966,37, 1351. (13) Amatore, C.; Saveant, J.-M.;Tessier, D. J.Electroanal. Chem. 1983,146, 37. (14) Go, W. S.;O'Dea, J. J.; Osteryoung, J. J. EZectroanal. Chem. 1988,255,21.
0743-746319412410-2800$04.50/0 0 1994 American Chemical Society
Electron Transfer Rates in Electroactive Films
Langmuir, Vol. 10, No. 8, 1994 2801
heterogeneous rate constants. Values of k"' of 0.2-1.23 cm s-l were estimated15 with an average precision of f25%. In this paper, we first examine the predicted errors in k"' as they relate to pulse width, k"', and a. Appropriate experimental conditions thus predicted are used to estimate electrochemical parameters for Mb-didodecyldimethylammonium bromide (DDAB) films.
Diffusion-Kinetic Model for NPV With only 0 present initially in the medium, the electrode reaction under 'consideration is O+ne-tR For linear diffusion-kinetic-controlledcharge transfer, the current-potential data obtained in normal pulse voltammetry are described by14 i(t) = idn'/'x exp(x') erfc(x)/(l
+ e)
(1)
where
and i d is the limiting current, COis the concentration of electroactive species in the bulk medium, a is the electrochemical transfer coefficient, t, is the pulse width, D is the diffusion coefficient of the electroactive species assumed to be equal for oxidized and reduced forms, A is the electrode area, F is Faraday's constant, R is the gas constant, E"' is the formal potential, and Tis temperature in kelvin. The apparent standard heterogeneous electron transfer rate constant k"' is derived from the kinetic parameter K (eq 5). The diffusion coefficient is obtained from the limiting current (eq 3). The term x exp(x2)erfc(x) in eq 1 was computed by Oldham's approximation16to an accuracy of better than f0.2%. The background currents on the carbon electrodes used in this work were rather large and had to be taken into account in the data analysis. Preliminary studies with noisy theoretical data and data from a soluble, quasireversible redox couple indicated that inclusion of a linear background term in the model gave better convergence in the regression analyses than subtraction of individuallymeasured background currents. Thus, the following model was used for the nonlinear regression analysis:
with E"', i d , K, a (eqs 1-51, background slope m , and intercept b as regression parameters. Equation 6 is a general model for electron transfer in NPV. In the special case of a fast, reversible electron transfer following the Nernst equation, we have
i = id/(1 + 8 ) + m E + b
(7)
(15)Karpinski, Z.J.; Osteryoung,R. A. J . Electroanal. Chem. 1993, 349,285. (16)Oldham, K.B. Math. Comput. 1968,22,454.
The limiting current is given by eq 3 independent of electrode kinetics.
Experimental Section Chemicals. Lyophilized horse muscle myoglobin (Sigma,MW 17 000) was dissolved in buffers of acetate, pH 5.45, or tris[(hydroxymethyl)aminolmethane,pH 7.5. Buffers were 0.01 M in conjugate base, and contained 50 mM NaBr. Myoglobin solutions were filtered through a YM30 filter (Amicon, 30 000 MW cutoff)to remove higher molecularweight species.17Js Purity was confirmed by gel permeation chromatography. Didodecyldimethylammonium bromide (DDAB, 99+%) was from Eastman Kodak. Water was purified with a Barnstead Nanopure system to a specific resistance of '15 MQ cm. All other chemicals were reagent grade. Apparatus and Procedures. A PARC Model 273 electrochemical analyzer was used for normal pulse (NPV) and cyclic (CV) voltammetries. The three-electrode cell employed a saturated calomel reference electrode (SCE), a Pt wire counter electrode, and a pyrolyticgraphite disk (HPG-99,Union Carbide, geometric A = 0.2 cm2)or glassy carbon disk (A = 0.07 cm2)as a working electrode,as describedp r e v i o u ~ l y . ~ ~Glassy J ~ J ~carbon electrodeswere polished with 0.2- and 0.05-pm alumina on billiard cloth before each scan. Surfactant coatings were cast onto electrodes as described previously.lOJ1PG disks were coated with 10 p L of 0.1 M DDAB (1pmol total,5 x mol cm-2)in chloroform. The film thickness estimated6 from the amount of DDAB used is ca. 20 pm. Chloroform was evaporated overnight. Mb-DDAB films were prepared by placing DDAB-PG electrodes into 0.5 mM Mb solutions, with potential scanning until steady-state CVs were observed. NPV on Mb-DDAB films was done after transferring electrodes to buffers containing no Mb. Fully loaded films contained on average 0.45 mM Mb a t pH 5.5, and 0.35 mM a t pH 7.5, as estimated by slow scan cyclic vo1tammetry.l' Experiments were thermostated a t 25 "C. Solutions were purged with purified nitrogen for at least 20 min prior to the beginning of a series of experiments to remove oxygen. Nitrogen atmosphere was maintained over the solutions during experiments. Complete removal of oxygen is very important in these systems, since Mb catalyzes the reduction of oxygen. Absence of oxygen in the films was confirmed by observation of a characteristic quasireversible CV a t 0.1 V s-l for the Fe(III)/ Fe(I1) heme redox couple of Mb with equal cathodic and anodic peak heights. The ohmic drop of the cells was compensated by external feedback to '90% for CV and NPV. The actual area of the working electrodes was 0.37 cm2,estimated from the slope of the linear scan rate dependence of the CV peak current of 1 mM cm2s - ~ ) . ~ O potassium hexacyanoferrate in 1M KCl(7.63 x Analysis of Data. Nonlinear regression analysis was done on an IBM type 486 personal computerby using a general program employing the Marquardt-Levenberg algorithm.21 Data to be analyzed were spaced evenly 5 mV apart on the potential axis and chosen to includecurrents between 2% and 98% of the limiting current. A similar data analysis schedule was shown to provide reliable electrochemical parameters from steady-state voltammograms.22 For experimental NPV data, the slope of the background current for several hundred millivolts prior to the initial rise of the reduction current was computed by linear regression, and the current resulting from the extension of this background current line was subtracted from the raw data before regression analyses. The linear background term in the model then accounts for any error in this background subtraction procedure, and may partly compensate for small amounts of nonlinearity in the background. Errors in currents were assumed to be independent of the size of the current. Potentials were assumed to be free of (17)Taniguchi, I.; Watanabe, K.; Tominaga, M.; Hawkridge, F. M. J . Electroanal. Chem. 1992,333, 331. (18)Walker, J.M., Ed.Methods in Molecular Biology, Vol.I , Proteins; Humana Press: Clifton Heights, New Jersey, 1984. (19)Kamau, G. N.; Willis, W. S.; Rusling, J. F. Anal. Chem. 1985, 57,545. (20)Adams, R. N. Electrochemistry ut Solid Electrodes; Marcel Dekker: New York, 1969. (21) Rusling, J. F. CRC Crit. Rev. Anal. Chem. 1989,21,49. (22)Rusling, J. F.Anal. Chem. 1983,55, 1713;1719.
Rusling and Nassar
2802 Langmuir, Vol. 10, No. 8, 1994
0.00
'
0.00
0.0 1
I
0.40
0.20
0.60
-E, V 2.00
0.1
10
1
pulse width, ms Figure 2. Influence of pulse width on errors in the kinetic parameter for K = 12 and three different values of a: (a)a = 0.5, (A)a = 0.65, (0)a = 0.35. Other parameters are as in Figure 1.
Y
.-E
40
t
L
0.00 L 0.00
I
0.20
0.40
0.60
2 b ae
0
i
0.1
-E, V Figure 1. Theoretical NPV data computed from eq 6 with random noise of 0.5%of i d for K = 12, i d = 1.0pA, E" = -0.3 V, a = 0.35, m = 0.8 p A V-l, and b = 0.1 pA. Pulse widths: (a) 2 ms; (b) 30 ms. Dashed lines are for background only. errors. Normally distributednoise was added to theoretical data as described previously.21
Results Electroactive films are sometimes characterized by small voltammetric signals superimposed on large backgrounds. We first studied the influence of the pulse width on the error in the rate constant k"' by analyzing noisy theoretical data by nonlinear regression. A relatively large background slope of 0.8 pA V-' was used with a limiting current of 1.00 pA. For most of this work, normally distributed noise of f0.5% of the limiting current was added to data generated from eq 6 . This represents a n attainable signal to noise level for NPV in aqueous solutions.22 Theoretical data for K = 12, a = 0.35, and E"' = -0.3 V illustrate how the pulse width influences the voltammetric curve shape (Figure 1).With a 2-ms pulse width, the sigmoid NPV curve is relatively broad and centered somewhat negative of E"', reflecting mixed diffusionkinetic control of the current-potential curve. At a 30ms pulse width the sigmoid curve increases more sharply and is symmetric aroundEO', characteristic of a reversible, diffusion-controlled electrochemical r e a ~ t i o n . ~ When similar data for 1-2-ms pulse widths were analyzed by nonlinear regession onto eq 6 , errors on the order of f l %in K resulted. In contrast, analysis of the 30-ms data gave a 20% error in K . Thus, for K = 12, data obtained with pulse widths in the shorter time range retain kinetic information and provide more accurate values of K.
Fits of K = 12 data for t, 2 30 ms to the reversible model in eq 7 were excellent, and will be discussed below. As the pulse width is increased, the shape of the currentpotential curve eventually becomes reversible and the kinetic information in it decreases.
J
1
pulse width,
10
ms
Figure 3. Influence of pulse width on errors in the kinetic parameter for K = 5 (a= 0.35) (a),1 (a= 0.35), (A), and 0.1 ( a = 0.5) (0). Other parameters are as in Figure 1.
Results of similar error analyses for K = 12 and three values of a show a n optimum range of pulse widths for obtaining K with minimum errors (Figure 2). At the shortest pulse widths for a = 0.35, large errors in id and E"' were also found. This optimum range did not seem to depend critically on a, but the a = 0.65 data showed a n extended optimum range in the small pulse width region. Errors in K over this range were larger than those for a 5 0.5. Convergence of regression analyses in the optimum time range typically was achieved in < 15iterative cycles. Optimum pulse width ranges shifted to longer times as K decreased (Figure 3). For K = 5, small errors in K were found in the 0.5-20-ms range. Data for 30-50-ms pulses gave very slow convergence, and the computations usually did not converge even after 120 iterative cycles. Data for K = 1and 0.1 a t pulse widths of
