Langmuir 1993,9, 223-227
223
Electrolyte and Temperature Effects on Long Range Electron Transfer across Self-AssembledMonolayers Harry 0. Finklea,’ Melissa S. Ravenscroft, and Daniel A. Snider Department of Chemistry, West Virginia University, Morgantown, West Virginia 26606 Received June 11, 1992. In Final Form: September 8,1992
The thermodynamicsand kinetics of electron transfer are examined as a function of aqueouselectrolyte and temperature on self-assembled monolayers containing attached redox centers. The monolayere are formed by coadaorbing an alkanethiolwith a pendant pyRu(NH& redox center with an alkanethiolwith a terminal carboxylic acid onto clean gold surfaces. The formal potential of the attached redox centers tracks the formal potential of a solution analog in all electrolytes (1M Na2S04,NaC1, NdOs, or NaClO4) and at all temperaturea (5-55 “C). No change in the monolayer structureis discerniblein chronoamperometry or Tafel plots over the same range of conditions. The electron transfer kinetics are independent of the identityof the anion in the electrolyte. The temperaturedependenceof theTafelplots conforms qualitatively withthe predictionsof the Marcus model. A comparison of three voltammetricmethods (cyclicvoltammetry, chronoamperometry,and ac impedance epectroscopy) confirms that one standard rate constant and one reorganization energy coneistently describes the electron transfer kinetics of the majority of the redox centers.
Introduction The incorporation of redox centers into self-assembled thiolate monolayers on electrodes provides a useful probe for the behavior of the monolayer.l-12 The coverage of the redox centers, which is easily measured by cyclic voltammetry, yields a direct measure of the concentration of the electroactivethiol in the monolayer. The concentration of the electroactive thiol is especially useful for studying the formation of mixed monolayers or the exchange of thiols in the monolayer with thiols in solution. Ion motion through the monolayeP4 and ion pairings can be studied with respect to the position of the redox center in the monolayer. Similarly, the monolayer provides a useful means of controlling spacing between the electrode and the redox center. Electron transfer kinetics can be measured as a function of potential and temperature without the complications of maw transfer. In order for the kinetic measurementa to be meaningful, several criteria which reveal monolayer order and uniformity should be met. The cyclic voltammogram under reversible conditions ~~~~~~
~
should exhibit ideal peak splitting (AE, = 0 mV) and peak half-width ( A E h b = 3.53RT/nF).’3 Electron transfer kinetics should be first order; i.e. the current should decay according to a single exponential after a potential step. The concentrationof the redox centersmust be sufficiently low that electron exchange between redox centers is not rate determining. These criteria have been met for two redox centers. Chidsey2J4examined self-assembled monolayers of ferrocenethiol (FcCOO(CHz)&H) and hexadecanethiol in perchloricacid. The reversiblecyclicvoltammogramswere ideal in shape and the chronoamperometry plota (log ( i ) vs t ) were linear over at least 1order of magnitude. Tafel plota were examined at 1,26, and 47 OC and for overpotentials (7 = E - E O ’ , where Eo’ is the formal potential) up to 1V. Recently,weI6reported that mixed monolayers containing the thiol HS(CHZ),CONHCHZ~~RU(NH&~+/~+ ( n = 10,11,15; py = pyridine) and nonelectroactivethiols HS(CHz),X ( n = 10, 11, 15; X = CH3 or COOH) also exhibited the same ideal behavior. The electron transfer kinetia were studied primarily as a function of chain length of the eledroactive thiol and the composition of the mixed monolayera; solution conditione were confiied to one electrolyte (aqueousNa804, pH 4) and room temperature. In both systems, Tafel plota are readily fitted with a simple version of the Marcus theory of electron transfer. The cathodic rate constant for any overpotential and temperature is given by the energy integral of the Fermi function for the metal (n(c))with the Gaussian distribution of donor levels in the solution (Dox(c))
(1)(e) Lee, K. A. B.; Mowry, R.; McLennan, G.; Finklea, H. 0. J. Electroonal. Chem. 1988,246, 217-24. (b) Finklea, H. 0.;Fedyk, J.; &web, J. Ekctrochemical Surface Science;ACS Symp. Ser. 378;Soriage, M,, Ed.;American Chemical Society: Washington, DC, 1988,pp 431-7. (2)Chideey, C. E. D.; Bertozzi, C. R.; Putvinski, T. M.; Mujsce, A. M. J . Am. Chem. SOC.1990,112,4301-6. (3)Lee, K. A. B. Langmuir 1990,6,70-12. (4) (e) De Long, H. C.; Buttry, D. A. Langmuir 1990,6,1319-22.(b) Nordyke, L L.; Buttry, D. A. Langmuir 1991,7,38&8. (c)De Long, H. C.; Donohue, J. J.; Buttry, D. A. Langmuir 1991,7,2196-2202. (5)(e) Creager, S.E.; Collard, D. M.; Fox, M. A. Langmuir 1990,6, 1617-20. (b) Collard, D. M.; Fox, M. A. Langmuir 1991, 7,1192-7. (6)(a) Creager,5.EL;Rowe, G. K. AM^. Chim. Acta 1991,246,233-9. (b) Rowe,G. K.;Creager,S. E.Langmuir 1991,7,2307-2312.(c)Creager, n(t) = (1 exp(e/kBT))-’ (2) S. E.; Itowe, G. K. A n d . Chim. Acta 1991,246,233-9. (7)(e) U d ,K.; Seto, Y.; Kite, H. Longmuir 1991,7,1510-4. (b) U d . K.; %to, Y.; Kite, H. Ekctrochim. Acta 1991,36, 1799. (c) ~ , , ( c ) = r0x(47rxkBT)-”2exp{-(t x eq1~/(4*,T)) Shirmrzu, K.; Yagi, I.; &to, Y.; U d ,K. Langmuir 1992,8,1385-7. (8) Obng, Y. S.; Bard, A. J. tangmuir 1991,7,195-201. (3) (9)Kwaa, W.5.V.; Atanasoeka, L.; Miller, L. L. Langmuir 1991,7, 1419-!& is the coverageof the oxidized form of the redox centers (10)(a)Hickman, J. J.; Ofer, D.; Laibinie, P. E.; Whitegides, G. M.; in mol/cm2. The corresponding anodic rate constant is Wrighton, M. S.Science 1991,252,688-91. (b) Hickman, J.J.; Laibinie, P.E;~r~~D.I.;Zou,C.;Gardner,T.J.;Whiteeid~,G.M.;Wrighton, (13)Bard, A. J.; Feulkner, L. R. Electrochemical Methoob: f i n d o M. 5.Lana& 1992,8,357-9. mentala and Applicationa; John Wdey & Sone: New York, lgS0,p 622. (11) (e) Tarbv, M.J.; Bowden, E. F. J . Am. Chem. SOC.1991,113, (14) Chidwy, C. E. D. Science 1991,261,919-22. 1847-9. (b) Collinson, M.; Bowden, E. F.; Tarlov, M. J. Langmuir 1992, Hanshew, D. D. J. Am. Ckem. SOC.1992,114, (15)(a) Finklea, H. 0.; 8,1247-50. 3173-81. (b)Finklee, H. 0.;Hemhew, D. D. J. Electroanol. Chem., in (12)W d d , M.M.; Popenoe, D. D.; Deinhammer, R. 5.;Lamp, B. press. D.; Chung, C.; Porter, M. D. Langmuir 1991,7,2687-93.
+
-
rOx
0743-7463/93/2409-0223$04.00/0Q 1993 American Chemical Society
-
Finklea et 41.
224 Langmuir, Vol. 9, No. 1, 1993
obtained by substituting n(a) with (1 - n(t)) and D0A4 with Dm(r) (-A in eq 3 is replaced with +A). The equations contain two adjustable parameters, the reorganization energy X and the preintegral factor K. The reorganization energy is intrinsic to the redox center and to ita local environment, while the preintegral factor includes the electroniccoupling of the redox center to the electrode. It is convenient when fitting Tafel plota with eq 1to normalize kapp at any overpotential q with respect to koapp,the rate constant at q = 0 V. The effects of temperature and electrolyte composition on electron transfer kinetics are examined for one type of monolayer: HS(CH2)tsCONHCHzpyRu(NHa)s2+/ HS(CHz)&OOH on gold electrodes.16 This mixed monolayer exhibits the slowest rate constanta and the highest kinetic uniformity of the five mixed monolayerspreviously studied.16 The electrolyte study is primarily intended to determine whether ion motion is controllingthe apparent kinetics to any extent. The temperature dependence provides a useful test for eq 1. Also of interest is the presence or absence of any phase transitions in the monolayer. For example, the disordering effects of a 'melting" transition should be readily apparent in the reversible voltammetry (increase in A E h b ) , the kinetic uniformity (larger spread of rate constants), and the rate constants (increase in k'app). In order to check the consistency of kinetic measurementa by different methods,we comparethe measurement of koappby cyclic voltammetry (CV),chronoamperometry (CA), and ac impedance spectroscopy (ACIS). The combination of these three methods also provides a clearer description of the presence of "fast" redox centers in the monolayer. Experimental Section Electrodes were predominately commercial gold mirrors (Evaporated Metal Films, Ithaca, NY). The 1 X 3cm gold mirrors were sonicated in chloroform for several minutes, immersed for 30 s in a hot (ca. 100 OC) mixture of concentrated sulfuric acid and 30% hydrogen peroxide (3:l volume ratio), and then thoroughly rinsed with deionized water. Hydrophilicity of the gold surfacewas the criterion for aclean electrode. Polycrystalline gold flags were also used; they were cleaned by heating to incandescence in a gas-air flame. The electrochemical cell was nonisothermal in design, with the temperature of the working and counter electrodes regulated with a circulating temperature bath and the reference electrode held at constant (ca. 20 "C) temperature. CV and CA experiments were performed as previously described.15 CV's yielded the formal potential Eo' and the coverage 8,the charge associated with conversion of the redox centers from one oxidation state to another. ACIS experiments used the EG&G Princeton Applied Research Model 378 Impedance System. The modified electrode was biased at the formal potential and the impedance was measured for frequenciesbetween 0.01 and l(r Hz (fivefrequenciesper decade). HS(CH2)l&ONHCHzpyRu(NH3)aZ+ and HS(CHz)&OOH were synthesized as previously described.16 The following protocol was determined to generate a monolayer with the smallest and most uniform rata constants (see Discussion): (a) immersion in the clean gold electrode in an acetonitrile deposition solution containing ca. 10-4M total thiol (typically 1:2 or 1:4 molar ratio of electroactive to diluent thiol) for ca. 30 min; (b) acquisition of a CV in 1 M NazSO4 electrolyts at room temperature; (c) a second immersion of the electrode in the deposition solution for 30 min; (d) acquisition of a second CV at room temperature (e) immersion of the electrode in 1 M NazSO4 at 55 OC for 2 miq (0acquisition of a final CV at room temperature. The electrode was rinsed with water and acetonitrile before each (16) Ravenacroft, Melissa S.Master's Thesis,West Virginia Univereity, 1992.
-2' 0.00
'
'
0.02
'
'
0.04
'
'
0.06
'
'
0.08
'
'
1
0.10
0.12
Time@)
Figure 1. CA plots at n = -0.20 V in four electrolytes. The In
(i)lines (where i is the current in rcA) are displaced vertically for clarity (anion (displacement): S04* (0); C1- (-1); C10!- (-2);NOs(-3)). The linear regression lines are obtained by fitting the data between 0.02 and 0.08 s.
Table I. Formal Potential6 in Different Electrolytes* anion redox centers solution analog difference s04'-0.029 -0.004 -0.026 +0.026 NOS+0.067 -0.031 c1+0.033 +0.061 -0.028 +om1 c104+OS03 -0,042 a All potentials are V vs SCE. Uncertainties in Eo' are ca. h0.004 V.
immersion in the deposition solution and with acetonitrile and water after each immersion in the deposition solution. All electrolytes (aqueous NazSO4, NaC1, NaNOs, and NaC104) were 1 M in concentration and adjusted to pH 4 with the appropriate acid. All temperature studies were done in 1M NazSO4. Higher pH values caused accelerated loes of theredox center while lower pH values limited the negative overpotential range due to water reduction. A solution analog, CHSCONHCH@YRU(NHdS2+(PFe-salt),was examined by CV in the same electrolytee and a t the same temperatures as the modifed electrodes. One SCE reference electrode was used for all measurements.
Results and Discussion Electrolyte Studies. The formal potentiale of the redox centers and of the solutionanalogsare given in Table I. The formal potentiale are not corrected for liquid junction potentiale, 80 the shifte in Eo' with anion cannot be unambiguously assigned to ion-pairing effecte. However, the formal potentiale of the redox centers track the formal potential of the solution analog. We concludethat the bound redox centers are subject to a similar degree of ion-pairing as the fully solvated redox centers. CA plota (In (i) vs t ) exhibit reasonable and constant linearity for all four electrolytes; a comparison at one overpotential is shown in Figure 1. We observe no change in the degree of curvature, indicating that the monolayer structure is unperturbed by the identity of the anion in the electrolyte. As noted previ~uely,~~ there is a noticeable deviation above the linear regression line at short times and for all overpotentiale. This deviation is attributed to a population of 'fast" redox centera. We attribute the "fast" redox centers to electroactive thiols which occupy defect sites in the monolayer; chain motion is sufficient in the looselypacked defect s i bto bring the redox centers much closer to the electrodeso that the kinetics of electron transfer are enhanced. The "fast" redox centera constitute a minority of the total population of the redox centers.
Lagmuir, Vol. 9, No. 1, 1933 226
Electron nansfer across Self-Assembled Monolayers
2 1 0 " -0.5
"
"
-0.3
"
' " -0.1 0.1
0.3
Overpotential Figure 2. Tafel plot for one monolayer in four electrolytes. The data were collected in the order SO4*-,C1-, Clod-, and NOS-.The solid line ie the predicted Tafel plot for X = 0.7 eV.
The majority of the redox centers have a rate constant given by the slope of the linear regression line. Proof of this aseertionis obtained by extending the linear regreasion to zero time. For a single exponential decay, the intercept is In (kappQ). Values of Q calculated from the intercept of the linear regression line are always within 20 % of the values of Q obtained by CV. A more quantitative estimate of the fraction of "fast" redox centers can be obtained from ac impedance spectroscopy (see below). A typical Tafel plot with data for one modified electrode in all four electrolytes is shown in Figure 2. The data are fitted with the theoretical Tafel line obtained with X = 0.7 eV. The anodicand cathodic branches are separatelyfitted with the theoretical lines. The slightly higher intercept (7 0 V) for the anodic branch is Erequently observed for these monolayers;we attribute the difference in intercepts to small changes in the monolayer conformation with oxidationstate of the redox centers.l6 There is a tendency for rate constants to decrease with use of the modified electrode. Consequently, data points for the last electrolyte are lower than for the firat electrolyte. This trend persists when the order of the electrolytes is altered. The KO, values (1.3-1.6 s-1) obtained by the intercepts are in gdagreement with values obtained by CV (1.0-1.6 s-9. Clearly, the identity of the anion has no effect on the measured rates of electron transfer. The Tafel plots represent true electron transfer kinetics. Temperature Studier. The accessible temperature range is set by the freezing point of the electrolyteand the stability of the redox centers in the monolayer. Rapid loee of redox centers occure above 60 OC (Figure 3). All further experiments are conducted with a maximum temperature of 56 "C. Losses of the redox center over the 8 h required to obtain CV's and CA data at four temperatures are less than 30% of the initial value. We find that there is an irreversible decrease in koa,, (measured by CV) when the modified electrode is fmt UBBd in high-temperature electrolytes. For example, in one experiment k'app at 25 "C dropped from 16 s-l before exposureto 56 "C to 3.6 8-l after exposure. We hypothesize that the drop is associated with a decrease in disorder in the monolayer. Since the mechanism of electron transfer is believed to be through-bond tunneling,'s a necessary corollary to the hypothesis is that the extended alkane chain with an all-trans conformation yields the slowest rata of electrontransfer. Alternately,the high temperature could promote the faster loss of the "fast" redox centers relative to the normal redox centers. Further evidence
-
0' 20
0.5
30
40
50
~ C I 70
Temperature (OC)
en
Figure 3. Coverage of the redox centers va temperature. Table 11. Interfacial Capacitancee ne a Function of TemperatCdl(lrflCm2)
temperature/°C
at -0.4 V
at +0.4 V
25 55 40 25 5
3.2 6.0 3.3 2.5 2.3
3.9 5.5 3.4 2.9 2.6
a All capacitancesare measuredfor a single electrode baaed on the charging current in a 0.1 V/s CV at potentials well separated from the redox wave. The measurements are sequential as listed.
Table 111. Formal Potentiale at Different Temmrntuma temperature/OC redox centers solution analog diffe%we 8 -0.043 -0.013 -0.030 16 26 35 45 55
-0.041 -0.035 -0.031 -0.025 -0.023
-0.013 -0.006 -0,003 +0.003 +0.011
-0.028 -0.029
-0.028 -0.028
-0.034
Potentials are V w SCE and have an uncertainty of hO.004 V. All measurementsof Eo' for the bound redox centers were made on a single modified electrode.
for the uannealing" of the monolayer is found in the interfacial capacitances (Table 11). Capacitances at 25 "C after exposure to 55 "C are consistently lower than capacitances before exposure. The mechanism for "annealing" is ale0 suggested by Table II. The increase of interfacial capacitances with temperature indicates that the monolayer becomes more permeable to ions in the aqueousphase. Increased permeability implies either the presence of greater molecular motion in the monolayer or the greater tendency of ions to lose their solvation sheath and enter the monolayer. The former condition would allow the spontaneous rearrangement of the alkane chains into a more ordered array. Consequently,e x p u r e to 56 OC electrolyte is included in the protocol for producing the self-assembled monolayer. The formal potentials of both the bound redox anters and the solution analog shift in the positive direction with increasingtemperature (TableIII). Plotsof AG (=nFEo') vs T yield slopes (as)of +44 (118)J/K for the bound redox centers and +50 (h18)J/K for the solution d o g . These values compare reasonably well with AS values tabulated for a variety of similar complexes.17 The similarity of AS for bound and solvated redox centers (17)Lee,E. L.; Cave, R. J.; Guyer, K. L.; +, J. Am. Chem. SOC.1979,101, 1131-7.
P.D.;Waver, M.J.
Finklea et 01.
226 Langmuir, Vol. 9, No. 1, 1993 8 r
I
1
-1L -0.5
'
'
-0.3
'
'
-0.1
'
'
'
0.1
'
0.3
'
-3' -0.4
' 0.5
Overpotential
Figure 4. Tafel plot for one monolayer at four temperatures. The data were collected in the order of decreasing temperature. The solid lines are predicted Tafel plota for A = 0.7 eV at the four temperatures;the lines are positioned by fitting the 25 "C data with the predicted l i e at that temperature.
indicates that the bound redox centers are fully solvated by the aqueous phase despite the proximity of the hydrocarbon layer. We observe no significant changes in the chronoamperometry plots at all temperatures and overpotentials; the plots exhibit the same degree of linearity with deviations from linearity occurring at short times.16 There is no evidence of any phase transition that alters the degree of order of the monolayer. The Tafel plots for a single modified electrode exhibit the qualitative features predicted by eq 1(Figure 4). The In (k)values for different temperatures converge as the absolute overpotential increases. T h e quantitative fit is lees satisfactory;when the data at 25 OC are used to defiie koa,! for the theoretical Tafel lines, the data at 55 OC conslstentlylie above the theoretical Tafel line. Sincethe temperatures are always decreased in each experiment, thh observation may be in part due to the tendency of koapptobecomesmallerwith use of themonolayer. Despite the slightdiscrepancy,we note that a reorganizationenergy of 0.7 eV adequately describee the slope of the Tafel plots at all temperatures. Chidsey also found that one reorganization energy X and one standard rate constant k'app wm sufficient to fit the Tafel plots at all temperatures.14 Compariron of Voltammetria Methods. T h e standard rate constantsobtained by CV and by extrapolation of Tafel plots are generally in good agreement for any madifiielectrode. Thereare twoconditionswhichmight alter the validity of koWpvalues obtained by CV the potential dependence of the transfer coefficient a and the proeenceof multiple rate constmtafor the redox centers. The published working curves18 which allow en estimation of k'app from Upassume that the transfer coefficient a is independent of potential. The Tafel plots for the attached redox centers clearly show that a changes w k e d l y with potential. Evidence for the potential dependenceof a hae also been found for organic molecules in aprotic media.l8V2O In order to simulate Cv's of the (18) hvkon, E. J. ElectrwMl. Chem. 1979,101, 19-28. (19) (a) S n v h t , J. M.; Teasier, D.J. Electroanul. Chem. 1976, 65, 57-68. (b) Sadant, J. M.; Teasier,D.J. Phys. Chem. 1977,81,2192-7. (c)Amatore, C.; S n v h t , J. M.; Twier, D.J. Electroonal. Chem. 1983, 146,87-4b. (20) (a) Petamen,R. A.; Evans, D. H. J. Electroanul. Chem. 1987,222, 129-50. (b)(hrrigau, D. A.; Evans, D. H. J. Ekctrwnul. Chem. 1980, 106,287. (c) E v m , D. H.; Gilichki, A. G. J. Phys. Chem. 1992,96, 2628-83.
I
'
'
'
-0.2
'
'
0.0
'
0.2
'
I
0.4
V V B SCE Figure 5. CV data and CV simulation. The CV data (solid line) is recorded for a monolayer at 5 OC at 0.1 V/s in 1 M NafiOd. The charging current has been subtracted from the original CV. CV data parameters: Bo' = -0.040 V w SCE,AE, = 140 mV, A E h b = 131 mV, & = 3.52 pC, electrode area 1.0 cm2. The CV simulation (circles) is calculated for ko = 0.53 s-l, @ = 3.52 pC, and duldv = 0.61 V-l. CV simulation parameters: AEp = 141 mV, A E h b = 127 mV.
bound redox centers, it is necessary to predict how a changes with potential. In previous papers, a is obtained from the Marcus modeP a($ = 0.5 + (F/2A)q (4) With eq 1,one can show that CY is linear with q provided that q is not large compared to A. However, the slope d d d q is emaller than F/2A as predicted by eq 4. For X = 0.7 eV, eq 1yields a slope of 0.61 V-l while eq 4 yields 0.71 V-l. To simulate a linear scan voltammogram (LSV) for the reduction of the redox centers, the followingequations can be solved by numerical methods:
dXdd.5 = exp((1- a(q))nFV/RT)(exp(-a(q)nFdRT) + exp((1- a(v))nFq/RT))X, (5) IC, = -(RT/nFu)(dXJdt) = i(RT/nF)/(nFAvr,)
(6)
x, = rdrT
(7)
dr = koappdt (8) rois the coverage of the oxidized redox centers, r T is the total coverage of redox centers, u is the scan rate, and $ is the dimensionless current. LSV simulations which combine eq 4 with eqs 6 8 demonstrate that the peak position (qp = Ep- E O ' ) shifts less than 4 mV for values of daldq between 0 and 0.8 V-l as long as the peak position does not exceed ca.150mV. Consequently,aEpfrom Cv's can be converted to koappusing Laviron's working curves without concern for the effects of a potential-dependent a.
In Figure 5, the faradaic current of a CV is overlayed with points for a simulated CV calculated as described abovewithda/dq=0.61V-l (A~0.7eV).Thepeakheight, peak splitting, and peak half-widths are well-matched, indicatingthat a singlerate constant adequately deecribee the behavior of this monolayer. Deviations of the experimental CV from the simulationstend to be in the direction of smaller peak currents and broader peak half-widths. T h e deviations are attributed to the small population of "fast" redox centers; it is easy to show that kinetic heterogeneityleads to a broadeningof CV peake when the currents are kinetically controlled. ac impedance spectroscopy is well-suited to meaeuring koa,, of the redox centers at low overpotentials. The
Langmuir, Vol. 9, No.1, 1993 227
Electron Transfer across Self-Assembled Monolayers
Table IV. Charger and Standard Rate Conatants from
4r
ACIS (Figure 6).
3 -
%2 -
v
QI/&
k1h-l
QdpC
kds-1
55 40 25 5
4.35 3.75 3.50 3.40
1.8 1.3 0.93 0.53
0.20 0.15 0.15 0.10
9 7.5 4.5 3.3
"All meaeurementa were made on a single monolayer-coated electrodein 1M NazSO4. Totalimpedancewae convertedtofaradaic impedance by removing an uncompensated resistanceof 6 D and an interfacial capacitanceof1.4& thew parameterewere obtained from the totalimpedance at the highest frequencies(1-10 -2). cot $ was calculated from the faradaic impedance. The plots are fitted a bimodal population of redox centers (two parallel RC circuits). See the text for details.
3 1-
0 10
temperature/OC
5
15
10
20
2.5
-
2.0
-
omega
Figure6. cot t$ vs o plots for one monolayerat four temperatures. The d i d symbols are the experimental data and the hollow
equivalent circuit for the faradaic current of the redox centers is a series RC circuit parallel to the interfacial capacitance. Laviron21has derived the expressions which relate Rldx and C,hto koa* and QT. When the dc potential is the formal potential, tien 2(RT/F)/(Q&'app)
(9)
1/(=&*app) = Q T / ( ~ T / F ) (10) A convenient method for measuring k'app by ACIS is to plot the cotangent of the phase angle 4 of the faradaic impedance with respect to the angular frequency w. The slope of the plot is 1/(2k0app). Actual cot c#ru plots of modified electrodes show a distinct curvature (Figure 6). Since the CA plots indicate the presence of "fast" redox centers in ahnost every monolayer, we hypothesize that the curved cot +w plots reflect the kinetic heterogeneity in the monolayer. The preeence of multiple rate constants is equivalent to parallel RC circuits in the impedancemodel. We aasume a bimodal population of redox centers with charges Q1 and Q2 (QT = QI + Q2) and standard rate constants of kO1and k02. It is poesible to fit the cot c#ru plots quite well with this BBBumption (Figure 6). Typically, the fitted parameters (Table n3 indicate that the majority of the redox centers (more than 95%) have the slower rate constant. Figure 7 summarizes the temperature dependence of ko,pp for a single monolayer subjected to all three voltammetric methods. The agreementbetween methods at each temperature supporta our hypothesis that the majority of the redox centers have a single rate constant and single reorganization energy. The increase in k'ap with temperature coincides with the predictions afforded: by eq 1 with h = 0.7 eV.
,C
Conclusions Mixed monolayers of HS(CH&&ONHCH2pyRu(m3)S2 and + HS(CH2)lsCOOH on gold are stable and _ _ _ _ _ ~
0.5
theory
cv
A Tafel D
symbols are the simulation based on two populations of redox centers. See Table IV for the simulation parameters.
Rrdx
0 0
ACIS
w
0.0 0
10
20
30
40
50
60
Temperature
Figure 7. Comparison of standard rate constants for one monolayer. T h e theory is calculated using eq 1 with X = 0.7 eV at 25 "C equal to 1 e-'. The Tafel rate constanta are and ,k the averege of the rate constante obtained at the anodic and cathodic intercepts.
well-behaved in aqueous electrolytes at pH 4 up to 60 OC. TheformalpotentialsfortheRu(II/III)redoxcenterstrack the formal potential of a fully activated analog in the presence of different anions and over the temperature range investigated; the bound and solution redox centers appear to be solvated and ion-paired to the same degree. Electron transfer kinetics are not affected by the identity of the anion in the electrolyte. Tafel plots agree qualitatively with the predictions of the Marcus model; the quantitative fit is l e a satisfactory but may be an artifact of slow changes in the monolayer structure. There is no indication that a exhibits a temperature dependence other than that predictsd by eq 1.22The internal consistency of the standard rate constant as determined by cyclic voltammetry, chronoamperometry (Tafel plots), and ac impedance spectroscopy is excellent. ACIS c o n f i i the presence of a small population of "fast" redox centers and provides a means of quantifying the population. The temperature dependence of the standard rate constant and the slope of the Tafel plots are both consistent with a reorganization parameter of 0.7 eV for the bound pyRu(NH3)~~+/~+ redox center.
~
(21) Laviron, E.J. Electroanol. Chem. 1979, 7,135-149. (22) Naey, Z.; H w ,N. C.; Yonco, R.M.J . Electrochem. Soc. 1989, 136,896-6.
Acknowledgment. The support of National Science Foundation (CHE-9114246) is gratefully acknowledged.
