Anal. Chem. 1883, 65, 683-688
Ma
Application of Square Wave Voltammetry to Strongly Adsorbed Quasireversible Redox Molecules James H. Reeves* Department of Chemistry, University of North Carolina at Wilmington, 601 South College Road, Wilmington, North Carolina 28409
Shihua Song and Edmond F. Bowden' Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204
The thoory and appllcatlon of square wave voltammetry to wrface-confined quarkevenlble redox mdeculer (Ox ne= Red) k described. Thwretkal voltammograms were calculated b a s d on the followlng assufnptlons: (1) stable rodox rtateq (2) monolayer or -1 surface coverage; (3) equlvaient surfMea and adsa&ates; (4) no adsorbateadsorbate Interact(5) no dmurlonal contrlbutlonr to the currand (6) Butler-Vohner ekctrode klnetks. A working curve strategy baud on peak separation between podtlva scan and nogathraocan n d current voltammogram was d.vd0p.d to fadHlate the wmtquantltathre ddermlnatlon of ekchon-transfer rate conrtants. Major thaordlcal predictlor#, were exp.rlmentaliy confirmed through characterization of strongly adrorkd cytochrome con carboxylicadd-tetmlnated 8 e I f - m M . d monolayer electrodesof the alkanethlol/gokl
+
WP.. INTRODUCTION The electrochemistryof interfacially confined redox molecules is a subject of long-standing scientific Adsorption, covalent attachment, self-assembly, and Langmuir-Blodgett methods have been used to create a diverse family of electroactive (sub)monolayersthat exhibit a broad range of properties and potential uses. A full range of chemical redox species, including metal ions, organic molecules, organometallics, and proteins, have been employed in these studies. A major theme in the evolution of this field has been the rapid advancement of physical characterization in the areas of voltammetryl-3 and spectroelectrochemistry.4~5 The present contribution addresses the characterization of quasireversible electroactive (sub)monolayersusing square wave voltammetry(SWV). Numerous voltammetricmethods have previously been applied to this problem with varying degrees of success. The most successful methods have been h e a r sweep and cyclic voltammetry,1~3,~J impedance methods such as ac voltammetry and impedance spectroscopy,l#+l' differential pulselJ2 and normal pulse13J4 voltammetry, and
* To whom correspondence should be addressed.
(1)Laviron,E. InElectroanalytical Chemistry; Bard, A. J.,Ed.;Marcel Dekker: New York, 1982;Vol. 12,pp 53-157. (2)Murray, R. W. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1984;Vol. 13, pp 191-368. (3)Shannon,C.; Frank,D. G.; Hubbard, A. T. Anno. Reu. Phys. Chem. 1991,42,393-431. (4)Gale, R. J., Ed. Spectroelectrochemistry: Theory and Practice; Plenum Prese: New York, 1988. (5)A b m a , H. D.,Ed.ElectrochemicalInterfaces:Modern Techniques forIn-SituZnterface Characterization; VCH Publishers: New York, 1991. (6)Laviron, E.J.Electroanal. Chem. Interfacial Electrochem. 1979, 101,19-28. (7)Laviron, E. J.Electroanal. Chem. Interfacial Electrochem. 1980, 115,65-74. 0003-2700/93/0365-0683$04.00/0
chronocoulometry.1 Although S W V has emerged over the past decade as the most powerful and general pulsed voltammetric technique,16 it has yet to see widespread application in the characterization of electroactive (sub)monolayer systems. Lovric and Lovric compared the calculated square wave response of solution-resident electroactive substances to that obtained when ahrptioddesorption equilibria and surface electron-transfer reactions involving these substances are considered.16 They found a significant enhancementin the square wave signal due to the contribution of quasi-reversible surface reactions. More recently, Osteryoung and co-workers have reported the S W V of an electrochemically irreversible adsorbate, midazolam,17 which undergoes diffusion controlled adsorption under the conditions of the experiment. In both of these studies, the electrochemical response depends critically on processes associated with the solution-resident species. In this paper we present a theory for the S W V of quasireversible adsorbates that are chemically stable and strongly adsorbed in both redox states. The theory is patterned after the physical model previously elaborated by Laviron in his development of comparable linear potential sweep voltammetric theory.6 This model assumes that the molecules are strongly adsorbed and noninteracting in both redox states and that adsorption and electron-transfer processes involving solution-resident species have an insignificant effect on the measured currents. Experimental verification of our theory is provided using electroactivecytochrome c adsorbed on selfassembled monolayer e l e c t r o d e ~ . ~The ~ J ~well-known capability of SWV for minimizing the contribution of charging current provided motivation for undertaking this study. (8)Armstrong, R. D.; Bell, M. F.; Metcalfe, A. A. In Electrochemistry (A Specialist Periodical Report); Think, H. R., Ed.; Chemical Society: London, 1978; Vol. 6; pp 98-127. (9)Sluyters-Rehbach, M.; Sluyters, J. H. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1970;Vol. 4,pp 1-128. (10) Macdonald, J. R., E d . I m p e d a n c e S p e c t r o s c o p y ; Wiley-Interscience: New York, 1987. (11)Laviron, E. J.Electroanal. Chem. InterfacialElectrochem. 1979, 105,35-42. (12)Brown, A. P.; Anson, F. C. Anal. Chem. 1977,49,1589-1595. (13)Seralathan, M.;Rives, A.; O'Dea, J.;Osteryoung,J. J.Electroanal. Chem. Interfacial Electrochem. 1991,306,195-211. (14)Lovric, M. J. Electroanal. Chem. Interfacial Electrochem. 1984, 181,35-49. (15)Osteryoung,J.; ODea, J. J. InElectroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, Vol. 14,pp 209-308. (16)Lovric, M.; Lovric, S. K. J. Electroanal. Chem. Interfacial Electrochem. 1988,248,239-253. (17)Ribes, A. J.; Osteryoung, J. Anal. Chem. 1990, 62, 2632-2636. Ribes, A.; Osteryoung, J.; J.Electroanal. Chem.InterfacialElectrochem. 1990,287,125-147. (18)Tarlov, M.J.; Bowden, E. F. J.Am. Chem. SOC. 1991,113,18471849. (19)Song, S.; Bowden, E. F.; Tarlov, M. J., submitted. 0 1993 American Chemical Society
884
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993
A
'
E,, V
A&
9gSE-11
'
"
"
r131
0 01
0
'
'
'
to) +tF "
0 02
"
'
'
' ' 003
'\ '
'
"
"
7121
'
004
'
'
"
T ( 2 ) + 1P
005
'
'
006
Time (6)
Flgure 2. Illustratlon of computational technique. Decay curves for the condltlons ks = 1 s-', = 1X mol/cm2, tp = 10 ms. Step 1: potential stepped to 150 mV, ~ ( 1 = ) 0. Step 2: potential stepped to 190 mV, ~ ( 2= ) 41 ma. Step 3: potential stepped to 140 mV, ~ ( 3 ) = 9 ms.
rtot
Flgure 1. Wave form for square wave voltammetry.
EXPERIMENTAL SECTION Square wave voltammetry and cyclic voltammetry were performed using a Cypress Systems CYSY-2 PC-controlled potentiostat. All experimental voltammograms reported in this work were smoothed using a Savitsky-Golaysmoothingalgorithm. The small volume glass cell featured a Ag/AgCl (1.00 M KC1) reference electrode, a Pt wire auxiliary electrode, and bottommounted planar working electrodes. Solutions were sparged with argon. 16-Mercaptohexadecanoic acid (16-MHDA) and ll-mercaptoundecanoic acid (11-MUDA) were synthesized and purified according to published procedures.*O Horse heart cytochrome c (Sigma Type VI) was chromatographically purifiedz1and used within 1 week. Gold thin film electrodes were prepared as previously described.ls Water was purified with a Milli-Q/ Organex-Q system (Millipore). Other chemicals were reagent grade. Self-assembled monolayer (SAM) electrodes were prepared by immersing gold electrodes in 1 mM ethanolic solutions of 16-MHDA or 11-MUDA for 2-3 days followed by rinsing and drying. Cytochrome c was adsorbed by depositing 100 fiL of a 30 fiM buffered solution onto the SAM/Au substrate for 15 rnin.'sJ9 The solution was then removed, and the cell was thoroughly rinsed and filled with buffer. The buffer was pH 7.0, 4.4 mM potassium phosphate, which has an ionic strength of 10 mM. Experiments were performed at laboratory temperature, 23 2 OC. Under these conditions, the cell time constants were estimated from cyclic voltammetry charging currents and uncompensated solution resistance (-800 Q) to be 0.6 ms (16MHDA/Au) and 1 ms (ll-MUDA/Au). All potentials refer to the Ag/AgCl reference, which is +0.23 V vs NHE. Square wave voltammograms were calculated using a Quick Basic 4.5 (Microsoft) computer program developed in our laboratory. The program prompts the user to provide pertinent experimental parameters such as the pulse width (tp),step height (Us), and pulse amplitude (Esw)of the experimental wave form (cf. Figure l),as well as the formal potential, standard rate constant, transfer coefficient, surface coverage, electrode area, and number of electrons transferred. The calculation of theoretical voltammogram is then performed using eq 2 and 4 introduced below. The theoretical difference current voltammograms were visually fitted to the corresponding experimental results by estimating the formal potential as the average of the experimental peak potentials for the positive scan (oxidation) and the negative scan (reduction), adjusting k, to reproduce the experimental separation between oxidation and reduction peak potentials, and (20) Bain, C. D.; Troughton, E. B.; Tao, Y.-T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G. J. Am. Chern. SOC. 1989, 111, 321-335, see supplementary material. (21) Brautigan, D. L.; Ferguson-Miller, S.; Margoliash, E. Methods Enzymol. 1978,530, 128-164.
choosing a value of ro that reproduced the experimental peak current. The choice of a = 0.45 was made to maintain consistency with the value obtained from cyclic voltammetry experiments.
RESULTS AND DISCUSSION Square Wave Theoretical Model. The eyetem modeled in this work is derived from the following reaction scheme: kr
O(ads) + ne- + R(ads) kb
where kf and kb represent the rate constants for electron transfer between the electrode and the adsorbed reactant. This scheme is applied in the present work to strongly adsorbed electroactive reactants subject to the following assumptions: (1)lateral interactions among adsorbed species are negligible, (2) all surface sites are equivalent, and (3) processes involving solution-resident species can be ignored. The rate of the surface reaction can be represented by the equation
'2
--- - kJ'o - kbrR = ro(kf + kb) - rtotk,
(1)
where I'o and r R are the surface concentrations of oxidized and reduced reactant (mol/cm2)and rtot= ro + r R . With rtot= ro at t = 0, the solution to eq 1 is
This solution was obtained by assuming that kf and kb are constant over the interval of time to which eq 1applies. For linear scan voltammetry the solution to eq 1is considerably more difficult to obtain because kf and kb vary continuously with time. However, as illustrated in Figure 1,the potential in square wave voltammetry is held constant for a duration of time (tp) after each potential step. Equation 2 can therefore be used to compute ro at the end of any potential step if the proper set of initial conditions are specified for that step. If a potential step (pulse) resulting in the rate constants kf and kb is applied to an electrode in a solution satisfying the rR(0) = 0, the concentraboundary conditions I'O(0) = rtot, tion-time profile for rois given by eq 2. The decay of r o in this case is illustrated as curve 1in Figure 2. If the surface concentrations at the beginning of the step correspond to r R = O),r o at the end these boundary conditions (I'o = rtot,
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1909
of this step (t = tp) will be
3.5
2.5
while r R becomes r R ( t p ) = rtot - ro(t,). The current, which is sampled at the end of the step, can be computed using the equation
1.5
dr0 n3A= n3A{ro(t,)(kb+ kf) - r&,) dt
0.5
i
(3)
When a new potential step (pulse) is initiated, r o and r R will vary according to new concentration-time profiles (e.g., curve 2 of Figure 2) computed by substituting the rate constants ( k l and kb') appropriate to the new potentid into eq 2. The initial concentrations r o and r R for this step are identical to the surface concentrations at the end of the previous step. These initial concentrations can be located on the new concentration-time profiles at time
1
Y
-0.5
-1.5
-2.5
-3.5
t
200
as designated in Figure 2 for I'o. It should be emphasized that T is not a real experimental time, but rather a computational variable. Since rois now constrained to follow the new profie, its concentrationat the end of the step (tp seconds later) is
and the sampled current for this step is dr i = n3A2 = n3A{ro(7+ t,)(k{ + k ( ) - I',,k,'] dt This calculational scheme is repeated sequentially to provide the forward and reverse currents arising from each pulse. It should be emphasized that this scheme works because there is no diffusional component to the current. To confirm the validity of the voltammograms calculated using eqs 2,2a, and 3, voltammograms were also computed using the "finite difference" approach applied to eq 1. In this case, ro(t + At) was computed by assuming the reaction rate
to be constant over the interval At(= tp/lOO). Thus
ro(t + At) = - {ro(t)(kf + kb) - rtotkb]At Next ro(t)was replaced with ro(t + At) and the process repeated until the end of the pulse. Finally, the value of l?o determined at the end of the pulse was substituted into eq 3 to calculate the current. Voltammograms determined by this method were found to be indistinguishable from those computed using eqs 2, 2a, and 3 but required significantly greater computational times. The rate constants used in this work were assumed to obey the Butler-Volmer relations: k, = k , W
685
kb = k,8'-"
(4)
where
e = enF(E-hY/RT However, equations for kfand kb derived from more funda-
1 150
100
50
0 E
-50
-100 -150 -200
- EO' (mV)
Figure 8. Calculated square wave voltammograms for strongly adsorbed redox species when a = 0.5, n = 1, A (=k&): (a)0.005; (b) 0.007; (c) 0.015; (d) 0.050; (e) 0.200; (f) 0.500. represents the difference current function. Simple adsorption lnvohrlng equivalent surface sites and no lateral lnteractlons Is assumed.
*
mental theories of electron transfer, (e.g., see ref 22) could also be employed in eq 3. , In Figure 3, the difference (Le., forward - reverse) current function (9= i/nFAI'ok,) is plotted vs potential for a series of theoretical square wave voltammograms generated from this model. The wave form applied is depicted in Figure 1. A pulse height (Esw) of 50 mV was used in all calculations. The group of voltammograms for which > 0 represent oxidations of species R; the calculations begin at a potential 200 mV negative of the formal potential, and proceed in 2 mV steps (AI&) to a final potential 200 mV positive of EO'. The group of voltammograms for which \k < 0 begin at 200 mV, end at -200 mV, and represent the reduction of species 0. The different square wave voltammograms in Figure 3 were determined using different values for the product of the standard rate constant and the pulse width (A = k,t,) in the calculations. Separation of the peak potentials for oxidation and reduction ranges from 108 mV for A = 0.005 to 4 mV for A = 0.100. This behavior parallels that observed in cyclic voltammetry of strongly adsorbed reactants, where peak separation has been used as a diagnostic tool to determine the value of the standard rate constant k8.6J8J9 A working curve ( a = 0.5, n = 1) to facilitate the determination of the standard rate constant from square wave peak separations of 10 mV or more is shown in Figure 4. Peak separations below 10 mV were excluded from this working
*
(22) Chidsey, C. E. D. Science 1991,251, 919-922. (23) Chidsey, C. E. D.; Bertozzi, C. R.; Putvinski, T. M.; Mujsce, A. M. J.Am. Chem. SOC.1990,112,4301-4306. (24) Gomez, M.; Li, J.; Kaifer, A. E. Langmuir 1991, 7, 1797-1806. (25) De Long, H. D.; Buttry, D. A. Langmuir 1990,6, 1319-1322. (26) Collard, D. M.; Fox, M. A. Langmuir 1991, 7,1192-1197. (27) Acevedo, D.; Abruna, H. D. J.Phys. Chem. 1991,95,9590-9594. (28) Bae, I. T.; Huang, H.; Yeager, E. B.; Scherson, D. A. Langmuir 1991, 7, 1558-1562. (29) Creager, S. E.; Rowe, G. K. Langmuir 1991, 7, 2307-2312. (30) Finklea, H. 0.;Hanshew, D. D. J. Am. Chem. SOC.1992, 114, 3173-3181. (31) Uosaki, K.; Sato, Y.; Kita, H. Langmuir 1991, 7, 1510-1514. (32) Willit, J. L.; Bowden, E. F. J. Phys. Chem. 1990,94,8241-8246. (33) Collinson, M.; Bowden, E. F. Anal. Chem. 1992,64, 1470-1476.
006
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993
I 0.007
Oo6
0.0035
h 0.03
0.02
-0.0035
-0.007
0
IO
30
50
70
90
100
110
Peak Separation (mv)
-
curve due to the difficulty inherent in determining accurate peak separations for U p < 10mV. The data have been fitted using two quadratic equations. For peak separations (hEp) between 10and 40 mV, A (and thus k,) can be calculated from the relationship
-
A = (3.2 X 10")hEp2 0.00305hEp
+ 0.0808
(5a)
and for peak separations greater than 40 mV A
(1.99 X 1O")hE,2
-50
-100
-
E p'(rnw
~tguro4. Working curve for estimating A (=k,$) from square wave peak mparatbns of 2 10 mv: (.) pohrts from calculated voltammogams; (-) working curve from eq 5a; (- 4 working curve from eq
5b.
0
50
- O.OO0 44MP + 0.0294
(5b)
can be used to determine A. Our calculations indicate that peak potentials for voltamrnogramswithO.l3 1, however, the square wave peak is predicted to split into two peaks symmetrically positioned about E". The origin of the peak splitting in the difference current at high A is shown in Figure 5, where the difference current for an oxidation with A = 1.6 is displayed along with the forward and reverse current components (cf. Figure 1). When A is this large, current is typically sampled with the system very close to equilibrium, where the net current is zero. For a given tp, a measurable response will result only if the rate constant is small enough so that unreacted substrate remains when the current is sampled. For the forward step (oxidation), this condition is met when the potential is negative of E". The maximum forward current produced in this step shifta to more negative potentials as A increases. The reverse step (reduction),by analogy,produces measurable currents in the positive potential regionsthat shift to more positive potentials as A is increased. Ae these peaks separate, the overlap region at E" becomes progressively smaller, resulting in proportionately less difference current at E". Figure 5 indicates that experimental currents associated with the appearance of peak splitting will tend to be small. Thus for A = 1.5, a standard rate constant k, = 1.0 s-l, a surface coverage of 10 pmol/cmZ, and an electrode area of 0.1
Fll(ur. 5. Calculated square wave voltammogram for a = 0.5, n = 1, A = 1.5. The voltage is varled from -100 to +lo0 mV: (-1 dlfferenoe current;(- -)forward (oxldatlon), and (...)reverse (reductbn)
-
components of dlfference current.
cm2, a peak current of 5.5 nA is predicted. This may be compared with the 80-nA peak current predicted for A = 0.5 under the same conditions. Comparison with Experiment. The selection of a suitable experimental system to test the predictions of a diffusionlessvoltammetry model is a somewhat thorny issue. The simplest models require that all surfacesitesbe equivalent and that no interactions occur between adsorbed molecules. Under these circumstances, the physical properties of individual electroactiveadsorbates w i l l be independent of surface coverage. An ideal experimentalsystem for evaluating simple diffusionless models will be one with a molecularly uniform electrode surface (or one in which surface "defects" and polycrystallinity effeda are obviated in some manner) and a sufficiently low and homogeneously distributed density of adsorbates to insure negligible lateral interactions. Furthermore, the adsorbate molecules must be uniformly bound and oriented at the surface. Lavirons used organic redox adsorbates on mercury electrodesto evaluate his cyclic voltammetry model. Several groups have recently described the creation of electroactive monolayers on solid electrodes using selfassembly techniques.n The most ideal example is Chidsey'~?~ in which a diluted ferrocenylalkanethiolfilm was prepared on aAu(ll1) substrate. Ferrocene groups at defect sites were apparently removed via post-self-assembly exchange with a methyl-terminated alkanethiol. Thisis certainly an attractive candidate as a model experimental system. In our laboratory, we have been interested in the electrochemical behavior of biologically active molecules such as proteins1*J9and flavins%when these materials are strongly adsorbed to electrodesurfaces. Cytochromec stronglyadsorbs in a stable functional state at near-monolayer coverage on carboxylic acid-terminatedself-assembledmonolayers.18J9 In important respects, cytochrome c adsorbed on S A M electrodes is potentially an attractive experimental model system for evaluating dif€ueionleesvoltammetry theories. Cytochrome c is a reasonably well-behaved, stable, extensively charac(34)Reeves, J., manuscript in preparation.
ANALYTICAL CHEMISTRY, VOL. 85, NO. 8, MARCH 15, 1993
I
(PA)-0.5
687
1 0'5
a -0.5
150
100
50
0
-50
-100
-150
-200
100
E (mV vs Ag/AgCVI M KCI)
50
0
-50
-100
-150
-200
E (mV vs Ag/AgCVl M KCI)
FIgwo 6. Experknentai square wave vottammograms of cytochrome cadsorbed on l&MHDA/Au, tp = (a) 10 ms; (b) 17.5 ms; (c)25 ms; (d) 37.5 ms; (e) 250 ms.
Flgure 7. Experimental (-) and calculated (---) square wave vottammograms for cytochrome c adsorbed on 16MHDA/Au, 0.32-
terized,35 one-electron outer sphere redox molecule. When electrostatically oriented against a surf~ce,~SJ3 lateral electronic interactions between hemes are expected to be small, if not completely negligible, because of the natural insulation provided by the polypeptide chain. Thus, for a monolayer of adsorbed cytochrome c, heme-to-heme separation will be on the order of 30 A, the diameter of the protein. In this paper we have tested adsorbed cytochrome c on SAMIAu electrodes against the main predictions of our SW theory. Admittedly,cytochrome c/SAM/Au is not yet an ideal experimental model system for diffusionless voltammetry. In our previous work, however, it was shown to be areasonably good approximation. For cytochrome c/l6-MHDA/Au, we found that staqdard electron-transfer rate constants calculated from CV peak separations using Laviron's simplemodel6 exhibited very little dependence on scan rate.l8J9 Furthermore, we found excellent agreement among standard rate constantsdeterminedby three independenttechniques: cyclic voltammetry, chronoamperometry,and electrochemicalimpedance spectroscopy.'g The most obvious nonideality noted was a larger than theoretical full width at half maximum value of approximately 120 mV compared with 90 mV predicted by the model. We believe that cytochrome c adsorbed at film defect sites probably accounts for at least part of this peak broadening. Work is planned for the near future to address this issue. With these thoughts in mind, the experimental results and comparison to theory are now Considered. Figure 6 presents a series of square wave voltammograms for the oxidation and reduction of cytochrome c adsorbed on 16-MHDAIAu. As predicted by our model (see Figures 3 and 4), the peak separation for oxidation and reduction decreases as the pulse width (and therefore the product A) increases. At some pulse widths, variations of up to 10mV were observed in peak positions when experiments were repeated. For this reason, average peak positions were determined separately for oxidationsand reductions at pulse widths between 20 and
50 ms. Using the differences in these average peak potentials at each pulse width, values fork, were calculated from eq 5a or 5b. The average of these constants was found to be 1.1f 0.3 s-l. This value is in good agreement with k, = 0.4-0.9 8-1 obtained from cyclic voltammetry experiments performed on other 16-MHDA electrodes. In Figure 7,two experimental square wave voltammograms of cytochrome c adsorbed to a 16-MHDA monolayer are compared to theoretical voltammograms calculated using our model. The calculation of the 25-ms response (top) was performed using rtot= 6.4 pmollcmz, E" = -48 mV, and k, = 0.8 8-1, while that at 50 ma (bottom) used rtot= 5.3 pmol/ cm2, EO' = -48 mV, and k, = 0.8 s-1. The value of a! = 0.45 used in both calculations accounts for the higher peak current and narrower peak width of the oxidation wave compared with the corresponding reduction wave. A similar effect is observed in the cyclic voltammetry of these systems.19 The calculated voltammograme are good representations of the experimental curves, suggesting that the model adequately describes the major features of the voltammetric behavior of cytochrome c/lG-MHDA/Au. In an effort to compare the predictions of our model with results for systems exhibiting larger standard rate constants, the SWV of cytochrome c adsorbed to a thinner SAM electrode, Le., 11-mercaptoundecanoicacid (ll-MUDA/Au), was performed. The shorter electron-transfer distance associated with 11-MUDA results in an increase in k,.l9 Unfortunately, the S W V response of cytochrome c adsorbed on these thinner fiis proved to be less satisfactory due to an apparent instability of these films when subjected to a series of wave forms of the type shown in Figure 1. We do not have an explanation for this instability phenomenon at present. A further complication arose as a result of the shorter pulse widths that were required to satisfy the quasi-reversible SWV criterion of 0.005 < A < 0.1. This became a problem because of the slow charging current decay (about 5 ms) associated with the low ionic strength solution that is required to stabilize the adsorbed protein. Experiments performed in this laboratory,however, have demonstratedthat electroactive
(35)Moore, G. R.; Pettigrew, G. W. Cytochromes c; Springer-Verlag: Berlin, 1990.
cm2electrode.
888
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993
-0.05 0'0°
-O"O -0.15
5 i\ 150
100
50
0
-50
-100
-150
E (mV vs Ag/AgCUl M KCI)
Flguro 8. Experimental squere wave voltammogram for cytochrome c adsorbed on 11-MUDA. 0.32cm2 electrode: tp = 32.5 ms, A€SW = 100 mV.
cytochrome c can be covalently attached to ll-MUDA,%which should permit the future acquisition of voltammograms at higher ionic strength where charging currents decay much more rapidly. Figure 5 suggests an alternative approach for determining rate constants when residual charging currents compromise results obtained with the peak separation approach. Our SWV model predicts that peaks will exhibit characteristic splitting when A > 1, which can be achieved by using long pulse widths. Figure 8 displays the experimental voltammogram that was obtained for adsorbed cytochrome c on an 11-MUDAJAu electrode at a pulse width of 32.5 ma. An increased. pulse amplitude of 100 mV was used in these experiments to enhance the magnitude of the observed currents. The peak splitting predicted by our model is evident in the experimental response. This result suggests that the onset of square wave peak splitting withincreasedpulse width should be useful for at least semiquantitative determinations of electron-transfer rate constants. The tradeoff in using the slower experimental time frame is a marked reduction in the current. A more careful analysis of this result is planned for future work.
CONCLUSIONS The strategy used in this work to calculate the square wave voltammetric response of strongly adsorbed quasireversible reactants is both simple and versatile. It is based on ButlerVolmer charge-transfer kinetics for the adsorbed redox ~~
reactants and ignores any contributions from solution-resident species. The utility of the approach was demonstrated by the successful prediction of experimental square wave voltammograms of strongly adsorbed cytochrome c on 16mercaptohexadecanoicacid self-assembled monolayer electrodes. For evaluating standard electron-transfer rate constants, the dependence of anodic-cathodic peak separation on A (=tpks) < 0.06 proved to be a quite useful diagnostic, as did the characteristic peak splitting that occurred for A > 1.0. These results suggest that square wave voltammetry should be quite useful for analyzing surface-bound reactants that display a wide range of rate constants. Furthermore, a particularly attractive feature of this strategy is the anticipated ease by which Butler-Volmer theory can be replaced with any other formalism that assumes no significant interactions between adsorbates (i.e., no variation ink, during tp). Thus, the technique has the potential to be a powerful and versatile addition to the group of voltammetric methods currently used to elucidate the electrochemical properties of surface-bound species. The working curve approach outlined in this work for determining k , when A < 0.06 requires that both oxidation and reduction voltammograms be obtained for each value of t p investigated. The actual mechanics of extracting rate constants from the square wave voltammograms is similar to the method previously described by Laviron for linear potential sweep voltammetry.6 For many situations, this approach can provide important kinetic information in a simple and straightforward manner. Moreover, when both voltammograms are available, a determination of the surface formal potential can readily be made. For these reasons, a cyclic square wave procedure such as that described by Bottomley for solution-residentspecies38 could be quite useful to investigators of strong electroactive adsorbates, since it presents pertinent information in a convenient form. Statistically-based methods (e.g. the COOL algorithm) that have been developed for the characterization of single square wave voltammograms of solution-resident species are currently being extended to the analysis of strong adsorbates and will provide an alternative to our working curve approach.3' Our immediateconcern is to optimizethe cytochrome c/16MHDA/Au composite monolayer system to provide, if possible, a near-ideal voltammetric response. Presumably, attention to the role of defect sites will be crucial in this endeavor.
ACKNOWLEDGMENT We are very grateful to Mike Tarlov for supplyingthe gold electrodes; to Janet Osteryoung, John O'Dea, and Susan Morris for their critical reading of an earlier version of the manuscript;to William Kwochka and Tarakeshwar Anklekar for synthesis of 16-MHDA and 11-MUD& and to Holden Thorp and Larry Bottomley for valuable discussions. We would ala0 like to thank the National Science Foundation (CHE-8820832) for providing financial support including a Research Opportunity Award for J.H.R.
~~
(36)Collinson, M.; Bowden, E. F.; Tarlov, M. J. Langrnuir 1992, 8, 1247-1260.
(37) ODea, J. J.; Ribes, A.; Osteryoung, J. G., submitted. (38) Bottomley, L. A.; Helfrick, J. C., manuscript in preparation.
RECEIVED for review August 4, 1992. Accepted December 1, 1992.
