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The Effect of Surface Polarity on the Electrochemical Double Layer and Its Influence on the Measurement of the Standard Rate Constant of Electron Transfer Paul K. Eggers, D. Brynn Hibbert, Michael N. Paddon-Row,* and J. Justin Gooding* School of Chemistry, The UniVersity of New South Wales, Sydney, New South Wales 2052, Australia ReceiVed: December 17, 2008; ReVised Manuscript ReceiVed: March 30, 2009
The influence of surface polarity and, hence, the electrical double layer on long-range electron transfer was investigated using 35 different electrode constructs. These constructs were prepared using five different lengths of ferrocene-modified alkanethiols (of general formula HS(CH2)nCONHCH2Fc where n was 7, 10, 11, 14, and 17 and Fc refers to ferrocene) mixed with an appropriate ratio of hydroxyl-terminated to methyl-terminated alkanethiols as diluents. The mixtures of diluents in different ratios served not only to separate and dilute the redox-active species but also to control the surface polarity of the self-assembled monolayer (SAM). The ratios of the three components in each SAM were 1:20:0, 1:16.6:3.4, 1:13.4:6.6, 1:10:10, 1:6.6:13.4, 1:16.6: 3.4, and 1:0:20 of the ferrocene-, hydroxyl-, and methyl-terminated species, respectively. The formal redox potential and electron transfer rate constant were measured for each construct. It was found, first, that formal potentials changed according to the theory of interfacial potential distribution and, second, that rate constants measured using cyclic voltammetry are strongly influenced by the Stern layer of the electrical double layer, which forms at the SAM-solution interface. Introduction The potential close to a surface in an electrolyte is influenced by the presence of the electrochemical double layer that is formed between the solution-side surface of the electrode and the bulk solution. A redox-active species located within the electrical double layer will not feel the potential difference between the working electrode and the reference electrode but, rather, something in between, as determined by the nature of the double layer.1,2 It is necessary to understand how kinetic measurements are influenced by the double layer to understand basic surface electrochemistry and how to design functional sensors that have redox moieties that are located in this region. This is an area which we are very interested in, and we are currently preparing and testing a series of molecules to further probe the influence of the electrical double layer on surface electrochemical measurements.3-5 The interactions between the surface of a self-assembled monolayer (SAM) and the solution will depend on the components that are used to make up the SAM.6,7 The effects of the electrochemical double layer on the potential become apparent when the equilibrium potential difference between a reference electrode and a working electrode with a redox-active SAM is calculated by equating electrochemical potentials (µ j ) of the reactants and products of the overall reaction. This is an inherent aspect in the theory of interfacial potential distribution first proposed by Smith and White.1 By this theory, the potential difference between the plane of the redox-active groups and the bulk solution (i.e., across the double layer) are included in the expression.
E ) Eo + (φPET - φSOL) +
( )
Γο RT ln nF ΓR
(1)
* To whom correspondence should be addressed. E-mails: (M.N.P.-R.)
[email protected], (J.J.G.)
[email protected].
Here, R is the ideal gas constant, T is the thermodynamic temperature, n is the number of electrons, F is the Faraday constant, E is the equilibrium potential difference between modified electrode and reference electrode, Eo is the standard reduction potential of the cell (including the activity of ions in the reference electrode half-cell), ΓO and ΓR are the equilibrium surface activities (taken as the amount coverage (in mol m-2) of surface-bound, redox-active species when Eo strictly becomes the formal potential Eo′) of oxidized and reduced species, and (φPET - φSOL) is the potential difference between the plane of electron transfer (PET) and the bulk solution (SOL). The term E0′ + (φPET - φSOL) will be called the “apparent formal potential” (E′app) henceforth, as this quantity is what is actually measured in a typical electrochemical experiment. It can be seen that to recover the usual Nernst equation from eq 1, the (φPET - φSOL) must be zero. This will be the case only at the potential of zero charge (pzc) of the electrode.8 The pzc is the potential at which the charge on the surface of the working electrode is zero, (φSAM - φSOL) ) 0. A simplistic physical description of (φPET - φSOL) can be derived at the minima of the potential energy curves for the electron transfer reaction when the applied potential has caused the Gibbs free energy barrier for the forward reaction (∆G‡r ) to equal that of the reverse reaction (∆Gp‡) and
Γο ) ΓR
( ) ( )
exp
∆G‡r kBT
∆G‡p exp kBT
)1
(2)
At this point, the Gibbs energy for the same reaction occurring in the environment of either the bulk solvent or at the plane of electron transfer can be written by adding the contributing energies,9
10.1021/jp811127f CCC: $40.75 2009 American Chemical Society Published on Web 04/23/2009
Effect of Surface Polarity on the Double Layer
( (
PET ∆GREF ) GREF + Gε -
N(ze)2 1 18πr εPΕΤ
SOL ∆GREF ) GREF + Gε -
1 N(ze)2 18πr εSOL
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8965
) )
(3) (4)
Here, z is the charge number, e is the charge of an electron, r is the radius of the redox group, εPET is the permittivity at the plane of electron transfer, εSOL is the permittivity for the bulk solution, Gε is the Gibbs energy of the reactants electronic energies, and GREF has a value that normalizes the Gibbs energies to the reference electrode. Subtracting eq 3 from eq 4 and dividing by nF yields
φPET - φSOL )
PET SOL ∆GREF - ∆GREF
nF
(
N(ze)2 1 1 8πr εPET εSOL ) nF
) (5)
Thus, using the continuum model, which Marcus used for his initial model for electron transfer,9 (φPET - φSOL) can be attributed to a decrease in the permittivity with increase in the electric field close to an electrode with a hydrophilic surface. How the potential drops depends on the structure of the double layer, which in turn will depend on the surface of the SAM it forms on and the component ions of the electrolyte. Figure 1 shows a sketch of an electrochemical double layer on a bare electrode, as described by Bard and Faulkner,8 with the modification of an alkanethiol SAM. In Figure 1, the potential drop from metal to solution is split across three layers. The left-most layer, the SAM, has been typically modeled as a constant dielectric;1 hence, the potential drop across it is linear. It is noted though, that it has been suggested that the permittivity of the SAM varies linearly across its thickness due to a dipole created by the thiol-gold interface.10 The middle layer depicted in Figure 1 is the Stern layer. At a bare metal electrode, the Stern layer is composed of a monolayer of specifically adsorbed dehydrated ions.8 It is this layer that will likely create a difference between SAM-modified and bare metal electrodes.1,2 With a SAM-modified electrode, the polarity of this interface depends on the groups at the distal end of the SAM, which can be, to some extent, chosen to produce a desired polarity. For instance, polar distal groups such as hydroxyls may have a strength of interaction with dehydrated ions similar to a bare metal electrode. This is in contrast to the unfavorable interaction that is expected to occur between nonpolar distal groups, such as methyl groups. It has been suggested that there is a significantly smaller water density close to an aqueous-alkane interface than close to an aqueous-polar interface.11-17 This smaller water density will decrease the permittivity and, thus, change the structure of the double layer significantly from that at a bare metal electrode. Further from the electrode, after the Stern layer, is the diffuse-double (Gouy-Chapman) layer.18 This can be modeled using the Poisson-Boltzmann equation and leads to an approximately exponential drop of the electrostatic field at a planar electrode. It has been generally assumed that the majority of the potential drop between the working electrode and the bulk solution occurs across the alkanethiol SAM.1 As a consequence, the drop in the potential between the surface of the SAM and the bulk electrolyte has been assumed to be minimal. Thus, the potential difference measured by the potentiostat, where eq 2 is true, has been assumed to be the formal potential (which ignores the potential difference φPET - φSOL) instead of the apparent formal potential. However, this ignores literature on
Figure 1. Illustration showing a possible construct of the electrochemical double layer formed on an alkanethiol SAM with perchloric acid as the electrolyte.
the polarization10,19-21 and the pzc of alkanethiols.22 SondagHuethorst et al.,19-21 using tensiometry, reported that the surface tension on alkanethiol SAMs varies significantly with both chain length of the alkanethiol and the potential applied to the working electrode. They showed the surface of an electrode became significantly more hydrophilic with a positive potential applied to the working electrode. Increasing hydrophilicity of a nonpolar surface implies that the polarization of the distal groups also increases. Hence, the potential does not drop completely across the SAM and continues to change in solution close to the SAM surface. This is supported by measurements of surface potentials of alkanethiols, which varied with length by 9.3 mV per methylene group,10 and a negative shift in the pzc of alkanethiol SAMs with an increase in length.22 If the redox group is attached at the distal surface of the SAM, it is positioned within the Stern layer, where there is a change in potential. Hence the measured potential difference will include (φPET - φSOL), which we note is a function of applied potential. As described above, the change in this potential difference will be determined by how the permittivity of the plane (more exactly a “slab”) in which the redox moiety is located changes with potential. Furthermore, the permittivity may not vary linearly with potential. For instance, it is unlikely that a SAM with distal methyl groups has an adsorbed monolayer of ions at its surface, and the degree to which the methyl groups interact with the solution will change with the potential applied to the working electrode. Hence, the structure of the Stern layer, as well as the applied potential difference, will influence the value of the permittivity. We will show in this paper that voltammetric techniques give more information about the structure of the double layer than
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Figure 2. The structures of the five ferrocene-derivatized alkanethiols used in this study.
has previously been realized. The hypothesis of this paper is that the structure of the Stern layer changes with the polarity of the SAM surface and influences the measured potential of the redox group. This will be investigated by cyclic voltammetry of a ferrocene/ferricinium redox couple incorporated at the surface of a three component SAM composed of the ferroceneterminated species, a hydroxyl-terminated species, and a methylterminated species. These constructs were prepared using five different lengths of ferrocene-modified alkanethiols (of general formulism HS(CH2)nCONHCH2Fc where n was 7, 10, 11, 14, and 17 and Fc refers to ferrocene) mixed with the appropriate ratios of hydroxyl-terminated to methyl-terminated alkanethiols as diluents. The polarity is systematically changed, keeping the amount of ferrocene approximately constant and varying the ratio of polar to nonpolar groups such that the SAMs investigated were in the ratios, 1:20:0, 1:16.6:3.4, 1:13.4:6.6, 1:10: 10, 1:6.6:13.4, 1:16.6:3.4, and 1:0:20 of the ferrocene-, hydroxyl-, and methyl-terminated species, respectively. Hence, 35 different electrode constructs in all were used.
Eggers et al. cell containing the modified gold mirror working electrode, a platinum foil counter electrode and a Ag|AgCl| 3 M NaCl reference electrode. The area of the working electrode exposed to the surface was less than 0.78 cm2. The solution resistance and double layer capacitance were less than 3 Ω and 1 × 10-6 F, respectively, as measured by impedance spectroscopy. This gave a maximum time constant of 100 nm across) was ruled out by Whitesides et al.31 Evidence that any possible small clusters were not influencing the electrochemistry of the ferrocene species arises from the near ideal cyclic voltammetry of the surface-bound ferrocene. Nonideality in surface electrochemistrysin particular, the full width at half-maximum of the Faradaic peakshas been attributed to the redox species’ being in a range of environments30 due to the proximity of neighboring ferrocene moieties. Ideal Efwhm of surface-bound ferrocene has been shown to occur when the ferrocene is diluted with a diluent at ratios greater than 1:10. The fact that the Efwhm’s in the current study were typically in the range of 95-105 mV and, hence, close to ideal indicates that the ferrocene-containing molecules do not form aggregates and that the environments around all ferrocene moieties are similar. This can be used as an indication that the diluent alkanethiol species do not phaseseparate but, rather, are reasonably homogeneously distributed throughout the SAM. The influence of interfacial potential distribution on surface electrochemistry is shown by changes in the apparent formal potentials. Figure 4 shows the apparent formal potential as a function of diluent ratio and the alkane chain length of the ferrocene redox moieties, depicted in Figure 2. Evident from Figure 4 is a positive (anodic) shift in apparent formal potential with both an increase in the proportion of nonpolar head groups and chain length. This shift with chain length becomes significant only when the diluent is predominantly methylterminated. Hence, because ferrocene has been reported to adsorb onto methyl-terminated SAMs, and even to nestle into the SAM at gauche defects,6 it has been hypothesized that the
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Figure 4. Variation of apparent formal potential with decreasing polarity of the surface for the 11- (+), 14- (4), 18- (9), and 19-bond (×) systems.
Eggers et al.
Figure 6. The standard rate constant for the couple ferrocene/ ferrocenium divided by the standard rate constant for the surface with 1:20:0 (hydroxyl to methyl) diluent ratio for surfaces of different polarities and different lengths of alkanethiol.
Figure 7. The natural logarithm of the standard rate constant for the oxidation (Ox) and the reduction (Red) of the 14- (+ Ox, × Red) and 19-bond (4 Ox, 9 Red) ferrocene-derivatized alkanethiols for different diluent ratios.
Figure 5. Semipeak potential difference against scan rate (diamonds) with associated Marcus fits (lines) for (a) the 18-bond ferrocene redox moiety with the normal 16-bond methyl-terminated diluent and (b) the 18-bond ferrocene redox moiety with the normal 19-bond methylterminated diluent.
variation in formal potential with chain length may be related to the interaction of ferrocene with the diluent layer.6 To provide evidence to test this hypothesis, a construct was prepared in which the diluent partially overlaps with the redox moiety (the 18-bond diluent with 18-bond ferrocene molecules shown in Figure 5b). This construct serves as a model for ferrocene nestling into the SAM. The electrochemistry of this construct (Figure 5 b) was then compared to that of a construct with a shorter 15-bond diluent, which was used throughout this study where nestling of the ferrocene into the SAM may or may not have been occurring (Figure 5a). Figure 5 a and b shows the variation in peak potentials versus scan rate and the fit to the predictions made by Marcus theory. It is clear that the changes in peak potentials of the “forced nestling” SAM (Figure
5b) cannot be fit to Marcus theory, in contrast to the excellent fits (Figure 5a) obtained with the shorter diluent. It was also observed that the CV peaks in the “forced nestling” SAM were broader than those of the standard constructs. This is in agreement with the literature for ferrocene redox moieties buried within a monolayer.6,7 From these experiments, we infer that the faradic processes observed in the electrochemistry of the 35 constructs being evaluated are not due to the ferrocene species “nestling” in the SAM. Hence, the trends in Figure 4 cannot be attributed to “nestling’s” becoming more prevalent as the polarity of the SAM reduces. The influence of the surface polarity on ks is shown in Figure 6 for all five SAM lengths (where the rate constants are normalized relative to the 1:20:0 surface for that length). From Figure 6, it can be seen that the rate constant of the shortest redox moiety increases as the diluent type changes from pure hydroxyl-terminated (1:20:0) to pure methyl-terminated (1:0: 20). However, as the alkyl chains become longer, the relative increase in rate constant becomes less significant. The constructs with the longest alkyl chains have a distinct reduction in the rate constant as the surface polarity decreases. The rate constant passes through a maximum with decreasing polarity, which indicates more than one process is influencing the data. Figure 7 shows the effect of diluent ratios and lengths of redox moieties on the oxidation and reduction standard rate constants. Three trends are demonstrated in Figure 7: (1) the
Effect of Surface Polarity on the Double Layer value of the reduction rate constant is always less than that of the oxidation rate constant, (2) the difference between the values of the oxidation and reduction rate constants for a given construct are greater with increasing chain length, and (3) the changes in ks presented in Figure 6 appear to be due to changes in the value of the reduction rate constant. Discussion The results above show the polarity of the diluent layer has a profound effect on both the apparent formal potential and the rate of electron transfer, both determined from cyclic voltammetry measurements. Here, these two observations will be discussed in turn, starting with the influence of the polarity and the length of the diluent on the apparent formal potential. The emphasis on apparent formal potential used here arises from the work of Smith and White1 and Fawcett2 who showed that measured potential difference (E in eq 1) for surface-bound redox species contains a term that is the potential difference between the plane of electron transfer and the bulk solution. That is, the apparent formal potential is equal to Eo′ + (φPET - φSOL). Importantly, at the pzc, when the entire potential drop occurs across the SAM and φPET ) φSOL, the apparent formal potential becomes the formal potential. φPET ) φSOL is the implicit assumption made when using cyclic voltammetry to measure kinetic parameters of surface-bound redox species.1 However, as discussed below, the variation in formal potential with polarity of the SAM observed here shows that with nonpolar SAMs, this is not the case. Figure 4 shows two trends within the apparent formal potential. They are (1) the apparent formal potential increases as the polarity of the surface decreases, and (2) once the diluent ratio has a greater proportion of methyl-terminated diluent than hydroxyl-terminated diluent, the apparent formal potential increases with chain length. This is consistent with observations made by Creager and co-workers,6 who suggested that the change in the apparent formal potential could be attributed to the ferrocene “nestling” in the surface of the monolayer. In their work,6 the Born equation is invoked, in which a change in the Gibbs energy of solvation results in a different formal potential for two environments having different permittivities. The data presented in Figure 5 provides evidence that in the present study, nestling of the ferrocene into the SAM is not responsible for the change in apparent formal potential. The evidence is based on the ability to fit the potential-versus-scan rate data to the Marcus model. In all 35 surface constructs used in this study to derive apparent formal potentials and rate data, the potentialversus-scan rate data provided an excellent fit to the Marcus model for electron transfer. However, when a surface construct was prepared in which the ferrocene is forced to partially “nestle” into the SAM, the data did not fit the Marcus model and reliable values for rate constants were not obtainable. The nestling hypothesis by Creager and co-workers6 places the ferrocene in a region of lower permittivity and, hence, causes an increase in the formal potential. Here, it is proposed that this lower permittivity environment is not due to nestling but, rather, is due to the lower permittivity created by the polarization of the electrolyte and the interaction between the electrolyte and the surface in the Stern layer surrounding the ferrocene. The Stern layer is the interface between the Gouy-Chapman region and the distal surface of the monolayer; hence, its properties would be expected to be highly dependent on the properties of the distal surface of the monolayer. For instance, it is highly unlikely that the deformable, nonpolar distal surface of the methyl-terminated diluent would form the “textbook”
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8969 Stern layer with a monolayer of ions adsorbed at its surface.11-17 It would be expected that the poor interaction between the distal surface of the monolayer and electrolyte ions would increase the disorder in the Stern layer and, hence, increase its thickness. Neutron reflectivity measurements have implied this disorder by demonstrating a lesser water density above the distal surface of the SAM than there is in the bulk solution.17 This is supported by vibrational sum frequency spectroscopy measurements16 and impedance measurements,12 and it has been treated theoretically.11,15 The lesser water density would mean the Stern layer has a lesser permittivity than bulk water. How this relates to apparent formal potential can be seen from eqs 1 and 5. As shown by eq 1, an increase in potential difference between the surface of the monolayer and the bulk solution (φPET - φSOL) will result in an increase in the apparent formal potential. Since φSOL will remain constant, eq 5 shows that φPET increases as the permittivity at the PET decreases. Thus, a lower permittivity at the PET means that φPET - φSOL must increase, which, in turn, means the apparent formal potential must also increase. Thus, the lesser permittivity caused by the lower water density at a nonpolar surface will increase the apparent formal potential over that of a polar surface. On the basis of the above discussion, the obvious question is, because it is only the distal moiety of the SAM that alters the polarity of the SAM, then why is the apparent formal potential influenced by the length of the SAM with the nonpolar interfaces? The answer to this question relates to the relative polarizability of the terminal methyl groups as the alkane chain becomes longer. As mentioned in the Introduction, both Evans et al.10 and Sondag-Huethorst et al.19-21 have shown that the distal methyl groups of alkanethiol SAMs become polarized as the potential on the underlying gold surface is changed. This polarization is sensitive to the length of the SAM. The greater the polarization of the distal methyl surface, the greater the interaction of the SAM with the polar electrolyte ions and the closer the Stern layer will be to its “textbook” structure on a hydrophilic electrode.32 Sondag-Huethorst et al.19,20 show that at a potential away from the pzc, the shortest methyl-terminated diluent has a stronger interaction with the aqueous electrolyte and, hence, a higher polarized surface than a longer diluent. It then follows that the permittivity of the Stern layer close to the terminal surface of the shorter methyl-terminated diluent will be greater than the longer methyl-terminated diluent. The greater permittivity of the shorter methyl-terminated diluent, as shown in eqs 1 and 5, will result in a smaller (φPET - φSOL) and, hence, a less positive apparent formal potential than the longer methylterminated diluent. This explains the variation with length of the apparent formal potentials for the nonpolar surfaces shown in Figure 4. In contrast, the apparent formal potentials of the pure, distal hydroxyl surfaces are essentially the same. With respect to the Stern layer, this can be explained by the distal hydroxyl surfaces’ providing sufficient polarity to have a strong interaction with the electrolyte ions, irrespective of chain length. Sondag-Huethorst et al.21 have shown that hydroxyl-terminated SAMs over the potential range in which the oxidation and reduction of ferrocene occurs have a very small difference in Helmholtz energy of their double layers. In other words, the interaction between the electrolyte and the distal hydroxyl groups does not change. This lack of variation of (φPET - φSOL) also suggests that the hydroxyl-terminated monolayers form a “textbook” Stern layer where the majority of the electrostatic field drops across a monolayer of adsorbed perchlorate ions. This is in agreement with the lack of variation in the apparent formal potentials for the 1:20:0 surfaces shown in Figure 4.
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Attention is now turned to the second discussion point regarding the change in electron transfer kinetics with SAM polarity. Cyclic voltammetry is used to obtain the kinetic data reported here. In cyclic voltammetry, the standard rate constant is calculated from peak potential data gathered by sweeping the potential at various scan rates. As the scan rate is increased to values greater than the electron transfer rate can accommodate, the oxidation peak shifts in a positive direction, and the reduction peak shifts in a negative direction. The overpotential, corresponding to the peak current, is then calculated by subtracting the peak potentials from the apparent formal potential, which was determined from a very slow scan rate with respect to the rate constant. The overpotential as a function of scan rate is then used to calculate the rate constant. As described above, the apparent formal potential as calculated from a CV will have a contribution from (φPET - φSOL), as will the peak potential. However, as discussed above, (φPET - φSOL) must change with the potential. Hence, the overpotential used to calculate the rate is, in fact, an apparent overpotential given by
ηapparent ) [Epeak + (φPET - φSOL)peak potential] [Eo′ + (φPET - φSOL)formal potential] (12) The implication of eq 12 is that in situations that (φPET - φSOL) changes significantly with potential and that the peak separation is large, the rate constant calculated using changes in peak potential will underestimate the rate. This is because when sweeping the potential anodic of the apparent formal potential, the value of (φPET - φSOL) will increase, and when sweeping the potential cathodic of the apparent formal potential, (φPET - φSOL) will decrease. Hence, in both instances, the calculated rate constant is less than the true rate constant. As observed from Figure 6, such a situation is faced with longchain SAMs with a nonpolar diluent. The entire body of data in Figure 6 indicates two processes are influencing the apparent rate constant. In all cases, as the polarity of the SAM decreases from the 1:20:0 surface, the apparent rate constant increases. However, with the exception of the shortest series SAM, as the polarity of the SAM decreases further, the rate constant reaches a maximum and thereafter decreases. We attribute the increasing rate constant with decreasing polarity to inductive destructive interference first described and shown by Napper et al.33 Napper et al.33 used an electrode construct containing an alkanethiol diluent possessing an ether within the alkyl chain and a ferrocene-terminated alkanethiol. It was found that the SAM with the ether diluent had a slower rate constant as compared with a diluent with no ether.33 A hydroxyl group at the distal end of the diluent would have similar interaction with the ferrocene bearing alkanethiol as a diluent containing an ether and, hence, is expected to influence the rate constant in a similar fashion. The decrease in rate constant for the longer SAMs, as opposed to the general rate increase exhibited by the shortest SAMs, is then attributed to the change in the apparent overpotential. As eq 12 shows, the apparent overpotential is different from the true overpotential due to (φPET - φSOL)formal potential and (φPET - φSOL)peak potential. There are two main factors that influence the difference between (φPET - φSOL)formal potential and (φPET - φSOL)peak potential. They are the change in applied potential and the change in the permittivity at the PET due to the change in applied potential. In terms of a change in applied potential, in the systems measured here, the difference between the apparent peak potential and the apparent formal potential was up to 300 mV. An applied potential of 300 mV will change φPET but not φSOL. Thus, the effect of (φPET - φSOL)peak potential on the apparent over-
Eggers et al. potential will be noticeable. We have already shown (Figure 4) that a change in permittivity at the PET changes (φPET - φSOL)formal potential by up to 80 mV between the longest, most nonpolar SAM measured and the most polar SAM measured. The effects that were attributed to influencing (φPET - φSOL)formal potential in the previous discussion of Figure 4 will also affect (φPET - φSOL)peak potential. As described previously, the lowest permittivity is inherent to the longest, most nonpolar SAM. As discussed above, Sondag-Huethorst et al.19,20 have shown that in the potential window in which ferrocene undergoes oxidation and reduction, there is a significant polarization of distal methyl surfaces of alkanethiol SAMs and that the degree of polarization decreases with increasing length of the alkanethiol that makes up the SAM.20 Their plots of the interaction of water with the surface of various lengths of alkanethiol SAMs against potential agree with the trends that we observe in both Figures 4 and 6. The data also agrees with a conclusion reached from the data of Iwami et al.,22 in which the contact angle and, hence, surface dielectric constant of a methyl-terminated SAM decreases at a given potential with increasing length of the SAM. This decreased as the overpotential approaches the pzc. In cyclic voltammetry, the rate constants are typically calculated from half of the difference between the oxidation and reduction peak potentials. This procedure provides a rate constant that is the average of the oxidation and the reduction rate constants. However, in cyclic voltammetry, the reduction and oxidation rate constants can be calculated separately, which here serves to provide information on whether the apparent overpotential effects discussed above are influencing only one or both of the electron transfer processes. As seen from Figure 7, for the 14-bond SAM, there is little difference between the oxidation and reduction rate constants. However, for the 19bond system, there is a dramatic slowing of the reduction rate constant as the SAM becomes more nonpolar for the reduction process than the oxidation process (in which only with the most nonpolar 1:0:20 surface is there any decrease in rate constant). The reason why the reduction process is more dramatically influenced than the oxidation process relates to the polarity of the Stern layer. With these long-chain SAMs, the peak separation can be up to 570 mV at scan rates of 10 240 mV/s with oxidation peaks around 462 mV and reduction peaks around -103 mV. The further away from the pzc, the greater the polarization of the SAM becomes.22 Because the pzc for octadecanethiol SAMs is around -0.5 V versus Ag/AgCl,22 the SAM at the potential of the oxidation peak and the apparent overpotential will be more polarized than the potential for the cathodic peak. In fact, the contact angle data of Iwami et al.22 indicates that around the pzc, there is a several hundred millivolt region where the SAM is reasonably nonpolar. Hence, due to the significant decrease in the permittivity at the PET, as the apparent peak potential approaches the pzc during the reduction process of the longest, most nonpolar SAMs, (φPET - φSOL)peak potential will be significantly greater than (φPET - φSOL)formal potential. Thus, there will be a significant difference between the apparent overpotential and the true overpotential. This will result in an underestimate of the electron transfer rate constant, whereas during the oxidation process, the permittivity at the PET will increase with increasing overpotential and, hence, decreasing (φPET - φSOL)peak potential. Thus, the apparent overpotential will be closer to the true overpotential for the oxidation than for the reduction process. Experimental evidence from AC voltammetry supports the above statements.34 In AC voltammetry, the standard rate constant is
Effect of Surface Polarity on the Double Layer calculated from the ratio of the peak current to the background current at the apparent formal potential using various frequencies and small amplitudes. Thus, the effects from varying the potential are not likely to be as great as in cyclic voltammetry. Differences between AC voltammetry and cyclic voltammetry have been described in the literature. In an early paper describing an AC voltammetry technique, the rate constant measured via AC voltammetry on N-(mercaptopentadecyl)-ferocenecarboxamide with a 16-mercaptohexadecanol diluent was 13 s-1, whereas the rate constant measured from cyclic voltammetry data was 6 s-1.34 This difference is consistent with the results described in this paper. Although the polarity of the hydroxyl-terminated diluents means that the apparent formal potentials are independent of length, the potential drop across the Stern layer should still increase with increasing potential. Hence, the actual rate will be faster than that measured via cyclic voltammetry. Conclusion We have demonstrated that the apparent electron transfer rate constant and the apparent formal potential are strongly influenced by the polarity of the surface. We have shown that this influence is exactly what would be expected according to the theory of interfacial potential distribution. This has consequences with regard to voltammetric measurements of the potential. We have shown that, in particular, the electron transfer rate constant as calculated from cyclic voltammetry data depends on the double layer structure. This observation does not imply that voltammetric measurements are useless. It means that they can be used to extract hitherto unknown information about the structure of the electrochemical double layer. Such experiments will be reported in a future paper using rigid norbornylogous bridges3,5 to place a redox-active group at known distances above the distal surface of the monolayer. Acknowledgment. This research was supported under the Australian Research Council’s Discovery Projects funding scheme (Project no. DP0556397). Supporting Information Available: Synthetic experimental, β values for all diluent polarities, an example fit Marcus fit for both oxidation and reduction curves, all of the oxidation and reduction rate constant data and contact angle measurements for all polarities. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Smith, C. P.; White, H. S. Anal. Chem. 1992, 64, 2398. (2) Fawcett, W. R. J. Electroanal. Chem. 1994, 378, 117.
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