New Approach for Measuring Lateral Diffusion in Langmuir

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J. Phys. Chem. B 2001, 105, 11120-11130

New Approach for Measuring Lateral Diffusion in Langmuir Monolayers by Scanning Electrochemical Microscopy (SECM): Theory and Application Jie Zhang,† Christopher J. Slevin,† Colin Morton,† Peter Scott,† David J. Walton,‡ and Patrick R. Unwin*,† Department of Chemistry, UniVersity of Warwick, CoVentry CV4 7AL, UK and Centre for Molecular and Biomolecular Electronics, School of Natural and EnVironmental Sciences, CoVentry UniVersity, Priory Street, CoVentry CV1 5FB, UK ReceiVed: December 31, 2000; In Final Form: June 15, 2001

A new SECM approach for studying the lateral diffusion of redox-active amphiphiles in Langmuir monolayers at an air/water (A/W) interface is described. To apply this technique practically, a triple potential step transient measurement is utilized at a submarine ultramicroelectrode (UME) placed in the water phase close (1-2 µm) to the monolayer. In the first potential step, an electroactive species is generated at the UME by diffusioncontrolled electrolysis of a precursor. This species diffuses to, and reacts with, the redox-active amphiphile at the A/W interface resulting in the formation of the initial solution precursor, which undergoes diffusional feedback to the UME. In this first step, the rate constant for electron transfer between the solution mediator and the surface-confined species can be measured from the UME current-time transient. In the second period, the potential step is reversed to convert the electrogenerated species to its initial form. Lateral diffusion of electroactive amphiphile into the interfacial zone probed by the UME occurs simultaneously in this recovery period. In the third step, the potential is jumped in the same direction as for the first step and the corresponding UME current-time transient can be used to determine either the distance between the UME tip and the monolayer at the water surface, or the lateral diffusion coefficient of the amphiphile. A theoretical treatment for this technique is developed and discussed in detail. The method is demonstrated experimentally with measurements of the lateral diffusion of N-octadecylferrocenecarboxamide in a 1:1 Langmuir monolayer with 1-octadecanol.

Introduction Measuring and understanding lateral diffusion processes is currently of considerable interest.1-8 A variety of methods have been developed for investigating lateral diffusion in condensed phases, including electron spin resonance and nuclear magnetic resonance,2 along with the popular fluorescence recovery after photobleaching (FRAP) technique.3,4,5 FRAP allows lateral diffusion processes of fluorescent-labeled molecules to be investigated in a small region of a target interface (2-5 µm across), and involves three steps. In the first step, the emission produced by laser excitation of the fluorescent-labeled molecules is measured from a target area of the interface of interest. Next, an intense, short pulse of laser light is directed to the same space region, irreversibly destroying a significant fraction of fluorescent moieties. After this photobleaching process, the recovery of fluorescence within the photobleached regionsdue to lateral diffusionsis measured as a function of time. The lateral diffusion coefficient can be obtained by analyzing experimental data with diffusion theory.6 Electrochemical methods represent an alternative for studying lateral diffusion in monolayers. In particular, Majda and coworkers,1a,7,8,9 pioneered an innovative technique, in which a gold microband (or microline) electrode was positioned in the * To whom correspondence should be addressed. E-mail: P. R.Unwin@ warwick.ac.uk † Department of Chemistry, University of Warwick. ‡ Centre for Molecular and Biomolecular Electronics, School of Natural and Environmental Sciences, Coventry University.

plane of an air/water (A/W) interface and contacted directly with an electroactive monolayer. By deploying the monolayer in a Langmuir trough, it was possible to measure the lateral diffusion coefficient of an electroactive amphiphile, as a function of surface pressure, using cyclic voltammetry. This method has been used to study the lateral diffusion of alkylferrocenecarboxamides and octadecyl viologen.1a,7 The technique has also found application for the measurement of lateral electron hopping in osmium-tris-4,7-diphenylphenanthroline perchlorate (OTDPP) monolayers at the A/W interface8 and lateral diffusion processes in supported bilayers.9 Recently, Forster et al.10 developed this approach and measured lateral electron hopping in OTDPP monolayers at the A/W interface using horizontal touch voltammetry performed with a microdisk electrode. They discovered that the local microenvironment, e.g., packing density and molecule orientation, influenced the rate of electron transfer (ET) in the Langmuir monolayer. Scanning electrochemical microscopy (SECM)11 has proven powerful for the measurement of kinetics at a wide range of interfaces, including solid/liquid,12 liquid/liquid13 and A/W interfaces.1b,14,15 In the latter area, SECM was recently applied to study lateral proton diffusion along a stearic acid monolayer1b and the effect of a 1-octadecanol monolayer on oxygen transfer across the A/W interface.15 In these studies, the response of a probe ultramicroelectrode (UME) either translated toward, or held close to, a spot at a target interface was used to obtain quantitative kinetic data on a local scale.16,17 Although such measurements are not strictly microscopy, SECM has developed

10.1021/jp004592j CCC: $20.00 © 2001 American Chemical Society Published on Web 10/20/2001

Measuring Lateral Diffusion in Langmuir Monolayers

J. Phys. Chem. B, Vol. 105, No. 45, 2001 11121

Figure 1. Schematic (not to scale) of the potential step profile and corresponding processes for SECM triple potential step measurements of lateral diffusion at the air/water interface.

as a field to include fixed spot experiments, as well as scanned probe imaging. We therefore use the designation SECM for the UME studies described herein. In this paper, we demonstrate how SECM can be used to measure ET kinetics and lateral amphiphile diffusion via feedback mode transient measurements. The studies build on SECM induced desorption (SECMID),1b,18 part of a family of equilibrium perturbation-based approaches,19 introduced for studying lateral diffusion. A theoretical treatment for the proposed technique is developed numerically and discussed in detail, covering both a single potential step method and a triple potential step approach, described in the following section. Experiments of the lateral diffusion of N-octadecylferrocenecarboxamide (C18Fc) in a Langmuir monolayer are reported to demonstrate the basic technique. Principles The principles of the proposed technique will be introduced briefly, based on the system of interest in this paper. In the new application, a submarine tip UME19c is positioned in the water phase at a typical distance of 1 µm from the A/W interface. A triple potential step is applied to this working electrode, with respect to a reference electrode, resulting in the processes highlighted in Figure 1. Information on ET kinetics and lateral diffusion rates is obtained from the current-time transients recorded during steps 1 and 3. In step 1, the tip UME potential is jumped to a value such that the oxidation of the solution mediator, Ru(bipy)32+ in the studies herein, is diffusion-controlled. Electrogenerated Ru(bipy)33+ (Ox in Figure 1) diffuses to the A/W interface where it oxidizes C18Fc

Ru(bipy)33+ + C18Fc f Ru(bipy)32+ + C18Fc+

(1)

In this step, C18Fc is effectively “bleached” locally by the redox reaction, with the resulting tip (feedback) current response depending strongly on the ET kinetics for the reaction between Ru(bipy)33+ and C18Fc. Lateral diffusion is also possible during this step, as highlighted later. In step 2, the potential is switched to a value to reduce Ru(bipy)33+ to Ru(bipy)32+. The duration of this “recovery” step determines the information from step 3, when the potential is again jumped to a value to promote the diffusion-limited oxidation of Ru(bipy)32+. When surfaceconfined C18Fc is significantly “bleached” during step 1 and the period of step 2 is relatively short, lateral diffusion does not occur significantly, and the tip current-time response for the third step will be similar to that for an inert surface. The tip-interface separation can then be measured accurately in the third step.1b,14,19d,20 In contrast, if the duration of the second

period is longer, the bleached spot at the interface may recover via lateral diffusion, and the current-time response in the third step is then partly governed by the lateral diffusion coefficient of C18Fc, the ET kinetics and the surface coverage. This three step approach is clearly analogous to FRAP, although the recovery step involves the solution mediator, as well as the amphiphile. Theory To calculate the tip current-time response for the method outlined above, we solve the diffusion equation for the solution redox species in the axisymmetric cylindrical geometry of SECM

[

]

∂c ∂2c 1 ∂c ∂2c ) Dsol 2 + + ∂t r ∂r ∂z2 ∂r

(2)

where r and z are, respectively, the coordinates in the radial and normal directions relative to the electrode surface starting at its center, c and Dsol are the concentration and diffusion coefficient of Ru(bipy)32+ in solution, and t is time. Initially, the concentration of Ru(bipy)32+ is at the bulk concentration, c*

t ) 0, all r, 0 e z e d: c ) c*

(3)

where d is the tip/interface separation. The boundary conditions for Ru(bipy)32+ at the tip surface in the first potential step (0 0, z ) d: ) Dsurf 2 + ∂t r ∂r Γ ∂r r > 0, z ) d: Dsol

∂c ∂c′ ) -D′sol ) - kc′θ ∂z ∂z

The resulting key normalized equations are

(8) (9)

∂θ )0 ∂r

(10)

r > rs, z ) d: θ ) 1

(11)

r ) 0, z ) d:

where Dsurf is the lateral diffusion coefficient of the amphiphile, Γ is the surface density of C18Fc, θ is the fraction of amphiphile in the reduced state, k (cm s-1) is the rate constant for the ET process, and c′ is the concentration of Ru(bipy)33+, which has a diffusion coefficient, D′sol. In treating lateral diffusion using eq 8, we consider that for a given surface density of amphiphile, the surface diffusion coefficient is uniform over the region of interest and is the same for the reduced and oxdised form, which is a good assumption for the system of interest here.1a Moreover, both Dsurf and k are assumed to be independent of θ, which appears to be reasonable based on the experimental results presented later. Equation 11 implies that θ will recover its initial value outside the tip/interface domain, which is again reasonable given the condition on rs/a taking large values (stated above) and the rather short time scale employed when implementing this experiment in practice. To simplify the modeling calculation, we write c′ in terms of c by invoking local mass conversion

c′(r,z) + c(r,z) ) c*

∂C ∂2C 1 ∂C ∂2C ) + + ∂τ ∂R2 R ∂R ∂Z2

(12)

Strictly, this equation is valid only when Dsol ) D′sol. It is important to note that although the ratio Dsol/D′sol has no effect on steady-state positive feedback current characteristics, the potential step chronoamperometric transient response depends on the Dsol/D′sol ratio.22 For the system of interest in this paper, Dsol/D′sol is close to unity (vide infra) and we therefore develop a model based on this assumption. The conditions at all boundaries, except the electrode surface are the same for all three potential steps. For the probe electrode, the boundary conditions for the second and third steps, which occur at t1 and t2, are

t1 e t < t2, z ) 0, 0 e r e a: c ) c*

(13)

t2 e t, z ) 0, 0 e r e a: c ) 0

(14)

The problem can be cast into dimensionless form using the following terms

τ ) tDsol/a2

(15)

C ) c/c*

(16)

R ) r/a

(17)

Z ) z/a

(18)

K ) ka/Dsol

(19)

γ ) Γ/(ac*)

(20)

Dr ) Dsurf/Dsol

(21)

L ) d/a

(22)

R > 0:

[

(23)

( )]

K(1 - CZ ) L)θ ∂2θ 1 ∂θ ∂θ ) Dr 2 + (24) ∂τ R ∂R γ ∂R ∂C ) - K(1 - C)θ ∂Z

R > 0, Z ) L:

(25)

The problem was solved numerically, using the alternating direction implicit (ADI) finite difference method.23 The SECM current-time response in the first and third steps was calculated from18,23

RdR ∫01 (∂C ∂Z )Z)0

π i ) i(∞) 2

(26)

where i(∞) is the steady-state tip current, with the probe at an infinite distance from the target interface24

i(∞) ) 4nFDsolac*

(27)

where n is the number of electrons transferred and F is Faraday’s constant. Theoretical Results and Discussion The model highlighted above involves several key parameters, including K, γ, L and Dr. The purpose of this section is to analyze the effect of these parameters on the transient measurement, and so identify the characteristics that might be encountered practically. Effects of K and L. We first consider the initial potential step in isolation, both to illustrate the factors affecting the current-time response and to demonstrate why the triple potential step method, described above, is needed. The influence of K and L on the current transient response for the first potential step is illustrated by the data in Figure 2, which shows normalized current-time characteristics, plotted as i/i(∞) vs τ-1/2 to emphasize the short time characteristics, for a range of K at two values of L. The data clearly show that the chronoamperometric behavior depends strongly on the normalized rate constant (eq 19). After an initial period (τ-1/2 > 25 in Figure 2a and τ-1/2 > 8 in Figure 2b) where the current response is essentially Cottrellian and independent of K and L, the current displays temporal characteristics which depend on the value of K and L. In essence, the higher the K value, the higher the feedback current (up to a distance-dependent diffusion-limit), due to the ET reaction between the tip-generated mediator and the surfaceconfined amphiphile. However, the faster the ET kinetics, the sooner is the electroactive surfactant depleted, resulting in an earlier diminution in the current. As with other SECM transient techniques,1b,18,19 the results show that the current response at intermediate times is most sensitive to surface processes when the tip/interface distance is minimized (compare Figure 2a with (b)). Effect of γ. The data in Figure 3 show the effect of γ (eq 20) on the initial potential step current-time transient signal. It is clear that the current initially attained, once the positive feedback cycle due to the ET process is established, is similar for different γ. However, the higher the γ value, the longer the time taken to deplete the concentration of redox-active amphiphile at the interface and consequently the greater the period over which the enhanced feedback current flows. The transient



Figure 2. Effect of K on the chronoamperometric behavior for the first potential step for (a) log L ) -1.0 and (b) log L ) -0.5. From top to bottom, the theoretical curves are for K ) 1000, 100, 10, 1, 0.1, and 0.01 (effectively co-incident with 0) obtained with Dr ) 0.2 and γ ) 1.

Figure 4. Effect of Dr on the current-τ-1/2 characteristics for the first potential step (log L ) -1.0). In each of the cases (a) - (c), the solid lines show the theoretical characteristics for Dr ) 1, 0.5, 0.25, 0.1, 0.05, and 0 (top to bottom). The lowest dotted curve is the theoretical behavior for an inert interface. (a) K ) 50 and γ ) 1.0. (b) K ) 50 and γ ) 0.1. (c) K ) 5 and γ ) 0.1. Figure 3. Effect of γ on the chronoamperometric behavior for the first potential step. From left to right the curves show the theoretical charateristics for γ ) 10, 5, 1, 0.5, 0.1, 0.01 and 0, with K ) 50, log L ) -1.0 and Dr ) 0.2 in all cases.

for the system with the highest γ value differs most significantly from the curve for an inert interface (γ ) 0). The γ value can be optimized by using low c*, small a and high Γ (eq 20), although there are clearly limits to the range of values of these parameters that can be employed practically. In particular, the Γ value is governed by the pressure-area characteristics and composition of the monolayer. Moreover, from a practical viewpoint, background capacitative charging could compromise the electroanalytical transient signal were the bulk concentration of electroactive mediator species too low. Effect of Dr. Following earlier studies by SECM induced desorption,1b,18 lateral diffusion has most effect at longer times, sufficient to establish a concentration gradient of surface-

confined species. At relatively short times after the diffusion field of the UME has intercepted the interface, the currenttime characteristic depends on the local reactivity, with minimal influence from lateral diffusion. To illustrate this point, the effect of Dr is highlighted, for some typical example cases, in the plots of normalized current against both τ-1/2 (Figure 4) and τ (Figure 5). Values of Dr in the range 0-1 are considered, for several K and γ combinations. The results show that the shape of the normalized current - τ-1/2 curve is only affected by the value of Dr at the smallest τ-1/2 values (long times) over the wide range of conditions examined (Figure 4). This long-time effect is most evident in the corresponding normalized current - τ characteristics in Figure 5. Actually, Figure 5a shows that if both K and γ are relatively high, it should be possible to distinguish different Dr from current-time behavior, provided that transients are run for sufficiently long times. However, for other cases that could be encountered practically (Figure 5b and

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Figure 6. Theoretical transients demonstrating the measurement of d. The case considers k ) 1 cm s-1, Dr ) 1, and log L ) -1.0 with other parameters cited in the text. The top curve (a) is the theoretical behavior for the first step transient. The bottom solid curve (b) shows the theoretical behavior for the third step. The second and third potential steps occurred at normalized times τ1 ) 5.0 and τ2 ) 5.1. The dotted line (co-incident with b) shows the simulated behavior for simple hindered diffusion at this tip/interface distance.

Figure 5. Effect of Dr on the current-τ transients for the first potential step (log L ) -1.0). In each of the cases (a) - (c), the solid lines show the theoretical characteristics for Dr ) 1, 0.5, 0.25, 0.1, 0.05, and 0 (top to bottom). The lowest dotted curve is the theoretical transient for an inert interface. (a) K ) 50 and γ ) 1.0. (b) K ) 50 and γ ) 0.1. (c) K ) 5 and γ ) 0.1.

(c)), it would be more difficult to measure Dr from a single transient measurement. Interestingly, in all of these cases, the feedback current attained at normalized times up to τ ∼ 0.05 (τ-1/2 ∼ 5) is relatively insensitive to Dr. Coupled with the results above that showed an insensitivity of the initially attained feedback current to γ (over a wide range of values), this indicates that ET kinetics should be measurable from the first potential step transient, with little influence from the (unknown) lateral diffusion coefficient. Triple Potential Step Method. Because the single potential step method may not be generally applicable to the measurement of lateral diffusion processes, we consider the characteristics for the triple potential step method described above. The functions of the three steps are: “electrochemical bleaching” (with the measurement of k), “diffusional recovery” and “analysis” (for the measurement of both d and Dsurf). To provide a clear picture of how the method would operate practically, the following discussion considers typical values of the follow-

ing key parameters: log L ) -1.0, Γ ) 3.0 × 10-10 mol cm-2, a ) 12.5 µm, Dsol ) 4.8 × 10-6 cm2 s-1, c* ) 1 mM, with values for the other parameters stated as they arise. Tip-Interface Separation Measurements. As demonstrated by Figure 2, the shape of the current-time behavior for the first potential step is strongly dependent on the separation between the tip and the surface. From a practical viewpoint, it is thus of key importance that d can be measured precisely. If the period of the second “recovery” step is relatively short, and the surface is extensively “bleached” in the first step, then it should be possible to obtain d with high accuracy from the third step current-time transient because this will depend mainly on diffusion of the electroactive solution mediator to the tip by hindered diffusion (with negligible reaction at the interface). The chronoamperometric characteristic for this situation is a strong indicator of the tip/interface separation.14,20 This idea is illustrated by Figure 6, for a case of fast kinetics (k ) 1 cm s-1) and a relatively high lateral diffusion coefficient (Dr ) 1). The results are for second and third steps which occur at normalized times, τ1 ) 5.0 and τ2 ) 5.1. These data demonstrate that the third step transient, with a short “recovery” time and extensive “bleaching” in the first step, is essentially identical to the theoretical behavior for a single potential step at an inert surface,14 which depends only on the tip/interface separation (in the normalized form of Figure 6). Obviously, for fast ET kinetics and a relatively low lateral diffusion coefficient, a shorter time could be applied in the first potential step than needed for the case in Figure 6. For slow kinetics and a relatively high lateral diffusion coefficient, it would be necessary to “tune” the diameter of the electrode (larger a value to enhance K). However, approach curve measurements should also be possible for this case,1b which is rarely expected to be encountered practically. Lateral Diffusion Coefficient Measurements. Figure 7 considers how the lateral diffusion coefficient, in the range which is normally encountered in practice,1a could be measured precisely for a case with a medium ET rate constant, k ) 0.1 cm s-1. The current-time characteristic of the third step is seen to depend strongly on the lateral diffusion coefficient of the amphiphile and the period of the second step. In essence, for a fixed recovery time, the higher the relative lateral diffusion coefficient, the greater the flux of amphiphile diffusing into the interfacial zone of interest, and the stronger positive feedback


Figure 7. Theoretical characteristics illustrating the measurement of the lateral diffusion coefficient for k ) 0.1 cm s-1 and log L ) -1.0, with the other parameters cited in the text. For (a) the top dotted curve is the theoretical behavior for the first potential step, and the bottom dashed curve shows the theoretical behavior for an inert interface. From top to bottom, the middle five solid lines are for the third step with Dr ) 1, 0.5, 0.25, 0.1, and 0.05. The second and third potential steps occurred at normalized times τ1 ) 1.0 and τ2 ) 3.0. For (b) the top dotted curve is the theoretical behavior for the first potential step, duration τ1 ) 1.0, with Dr ) 1.0. The bottom dashed curve shows the theoretical behavior for an inert interface. From top to bottom, the middle eight solid lines are for the third step occurring at τ2 ) 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.25, and 1.1.

current obtained in the third “analysis” potential step. This is clear from Figure 7a which shows data for τ1 ) 1.0, τ2 ) 3.0 and Dr in the range 0.05-1.0. Likewise, for fixed Dr, the longer the recovery time in the second step, the greater the extent of amphiphile diffusion, and the higher the positive feedback current obtained in the third step transient. This is evident from Figure 7b which shows current-time transients for τ1 ) 1.0 and τ2 in the range 1.1-4.0 for Dr ) 1. These illustrative results demonstrate that it should be possible to “tune” the recovery time in the second step to optimize the measurement of the lateral diffusion coefficient of the amphiphile, with longer recovery times favoring the measurement of small Dsurf. However, for studies of monolayers at A/W interfaces as in this paper, one has to consider possible environmental perturbations to recovery (eg. vibrations, air flow, etc.), which might prohibit the use of excessive measurement times. Indeed, our model highlighted earlier specifically considered relatively short perturbations, to simplify the calculations. For a duration of a few seconds as the maximum recovery period, and a mediator with the Dsol value highlighted above, the smallest Dsurf accessible by the triple potential step method is ca. 10-7 cm2 s-1. The upper limit is at least Dr ) 1, although surface diffusion coefficients of this magnitude, compared to the solution mediator diffusion coefficient, are unlikely to be


Figure 8. Effect of Dr on the θ - R profile at the end of the first (a) and second (b) potential steps, for a typical case with τ1 ) 0.5 and τ2 ) 2.5. The curves are for Dr ) 0 (i), 0.1 (ii), 0.5 (iii), and 1.0 (iv). The following parameters were used: k ) 0.1 cm s-1, log L ) -1.0, a ) 12.5 µm, Dsol ) 4.8 × 10-6 cm2 s-1, c* ) 1 mM and Γ ) 3 × 10-10 mol cm-2.

encountered practically. It should be possible to apply longer recovery times for adsorbates at solid/liquid interfaces, greatly enhancing the range of Dsurf accessible to study. Time Dependence of the θ - R Distribution in the “Recovery” Step. To understand the effect of the redox process on the local composition of the surfactant monolayer during the “electrochemical bleaching” and “recovery” steps, it is informative to examine θ-R distribution profiles. This is particularly important with regard to identifying the spatial resolution of the technique, allowing comparison to FRAP. The θ-R distributions in Figure 8, parts a and b, are for this purpose, considering times at the end of the first and second steps, respectively, for a case defined by the following parameters: τ1 ) 0.5, τ2 ) 2.5, k ) 0.1 cm s-1, log L ) -1.0, a ) 12.5 µm, Dsol ) 4.8 × 10-6 cm2 s-1, c* ) 1 mM, Γ ) 3 × 10-10 mol cm-2 and Dr in the range 0-1. Figure 8 (a) shows that the “bleaching” process, which causes θ to tend to zero, is confined to an area that approaches the size of the UME probe (R e 1). Outside this domain (R > 1), θ rises rather sharply toward unity, although the profiles show some dependence on Dr, with the targeted zone becoming more diffuse, due to lateral diffusion, as Dr increases. Lateral diffusion is most significant during the recovery step, and Figure 8b demonstrates that the extent to which the target zone is replenished during this period depends critically on the value of Dr, with a higher value clearly promoting the most extensive recovery. It is the sensitivity of the recovery process to Dr which makes the current-time behavior during the third “analysis” step powerful as an


Zhang et al.

approach for measuring lateral diffusion coefficients, as illustrated earlier in this section. Experimental Section Chemicals. C18Fc was synthesized and purified according to the procedure of Majda and co-workers.1a Other chemicals were used as received. They were KNO3 (AnalaR, BDH), tris(2,2′-bipyridyl)dichlororuthenium (II) hexahydrate (Sigma-Aldrich) and chloroform (HPLC grade, BDH). All aqueous solutions were prepared from Milli-Q reagent water (Millipore Corp.). Apparatus. The Langmuir trough (model 611, Nima Technology, Coventry, UK) was housed inside a glovebox (Glovebox Technology, Huntingdon, UK). Monolayers were observed using a Brewster angle microscope (MiniBAM, Nanofilm Technologie GmbH, Go¨ttingen, Germany). The electrode was positioned using a set of x,y,z stages (M-462, Newport Corp., CA) and a piezoelectric positioner and controller (models P843.30 and E662, Physik Instrumente, Waldbronn, Germany). The procedure for the fabrication of submarine UMEs has been described previously.19c The platinum UME used was a 25 µm-diameter disk electrode with a glass insulating sheath, characterized by an RG value21 (overall probe radius to the electrode radius) of 10. Procedures. C18Fc and 1-octadecanol mixed monolayers were formed by spreading a known volume of a chloroform solution containing 1 mM C18Fc and 1 mM 1-octadecanol to the aqueous subphase at 28 °C, using a microliter syringe (100 µL volume, Hamilton, Reno, NV). The solvent was allowed to evaporate for 15 min before any measurements were made. Pressurearea isotherms were recorded with a barrier speed of 25 cm2 min-1, from an initial surface area of 500 cm2. Electrochemical measurements were made using a twoelectrode arrangement, with the UME as the working electrode and a silver wire as a quasi-reference electrode (AgQRE). The potential waveform for the triple step measurements was applied from a PC via the analogue output channel of a National Instruments’ (Austin, TX) Lab-PC-1200 card. The current-time transients were recorded using a digital storage oscilloscope (NIC 310, Nicolet, Coventry, UK) and also by the PC data acquisition card. Diffusion coefficients of (4.8 ( 0.2) × 10-6 cm2 s-1 and (4.7 ( 0.2) × 10-6 cm2 s-1 for Ru(bipy)32+ and Ru(bipy)33+, respectively, were measured using double potential step chronoamperometry (DPSC)14,20a,25 in aqueous bulk solution with 10 mM Ru(bipy)32+ together with 0.2 M KNO3 as the supporting electrolyte. The diffusion coefficient of Ru(bipy)32+ measured by DPSC was comparable to that deduced from steady-state linear sweep voltammetric measurements, calculated using eq 27. These results indicate that the model outlined in this paper, which considered equal diffusion coefficients for the reduced and oxidized forms of the redox mediator, is applicable. Experimental Results and Discussion The triple potential step method described above was examined and verified by studying the lateral diffusion of C18Fc amphiphile in a Langmuir monolayer because considerable prior information on this system is available from the work of Majda and co-workers.1a,7a-e Monolayer Characteristics. The pressure (π) - area (A) isotherm for C18Fc and 1-octadecanol (1:1) mixed monolayer obtained on an aqueous subphase containing 1 mM Ru(bipy)32+ and 0.1 M KNO3 at 28 °C is given in Figure 9. The A value is the mean area per molecule, and it can be seen that the surface

Figure 9. Pressure (π)-area (A) isotherm for C18Fc and 1-octadecanol (1:1) on an aqueous subphase containing 1 mM Ru(bipy)32+ and 0.1 M KNO3. A is the mean area per molecule in this binary system.

pressure begins to increase significantly when A is ca. 50 Å2 or less. The monolayer showed an abrupt collapse when the mean area per molecule was ca. 25 Å2. No clear phase transition was observed in the pressure region of interest, consistent with previous studies with 0.05 M HClO4 as the subphase.1a However, BAM measurements made while recording the isotherm showed evidence for heterogeneities in the monolayer for surface pressures lower than 0.1 mN/m (A > 55 Å2). When the surface pressure was higher than 25 mN/m, the formation of bright islands which increased in size, surface density and brightness was observed. This behavior, which was pressure and time-dependent, was tentatively attributed to the formation of bilayer and multilayer structures, suggesting that the mixed 1:1 monolayer formed by C18Fc and 1-octadecanol was not an ideal two-component system under these conditions.8b To minimize possible complications from this behavior, SECM measurements were restricted to surface pressures in the range 0.1-17 mN/m and were made quickly after the establishment of the monolayer at the surface pressure of interest. The surface pressure (with the area fixed) was monitored during all SECM measurements and found to be stable. Because a thorough systematic line-electrode study, over a wide range of surface pressure, has been reported by Majda and co-workers,1a,7 we limited our study to three distinct cases where surface diffusion effects would be expected to be quite different on the SECM time scale (vide infra). It should be noted that similar BAM results to those described above were obtained when 0.1 M HNO3, rather than 0.1 M KNO3, was the electrolyte in the subphase. However, when the conditions were analogous to those of Majda’s studies,1a,7 with aqueous 0.05 M HClO4 as the subphase, a uniform monolayer was observed over the entire pressure range of interest. Unfortunately, HClO4 could not be used in our studies, due to precipitation of Ru(bipy)32+ with ClO4- at the concentration required. HClO4 was used as the supporting electrolyte in earlier studies1a,7 partly so that the oxidized amphiphile, C18Fc+, would be stabilized by forming a water insoluble ion-pair with ClO4-. To test whether changing the supporting electrolyte would affect the stability of the oxidized form of the monolayer, a thin layer cell-type experiment was carried out in which an inverted 125 µm diameter Pt disk electrode was positioned in the aqueous subphase containing 1 mM Ru(bipy)32+ and 0.1 M KNO3. The tip-monolayer separation was ca. 10 µm, whereas the surface pressure of the monolayer was fixed at various values in the range 0.1-20 mN/m. A potential of 1.05 V vs AgQRE was applied to the probe electrode for 5 s to promote the diffusion-



Figure 10. Example transients illustrating the background subtraction method used for the subsequent analysis of SECM transient data. The top dashed line is the first step transient for the oxidation of 1 mM Ru(bipy)32+ in 0.1 M aqueous KNO3 with a tip positioned ca. 1.25 µm from the monolayer at the A/W interface (A ) 40 Å2); see later. The bottom dashed line is for the same conditions, but with only 0.1 M KNO3 present in the aqueous subphase. The solid line is the difference between the two data sets.

controlled oxidation of Ru(bipy)32+ to Ru(bipy)33+, which would serve to oxidize C18Fc moieties in the region of the monolayer directly opposite the electrode. The potential of the UME was then scanned in the cathodic direction and several cyclic voltammograms were recorded between 0.2 and 1.05 V vs AgQRE at a rate of 1 V/s. Neither the reduction of C18Fc+ nor any blocking of the probe electrode was observed, only the oxidation-reduction of the Ru(bipy)33+/2+ couple in this thin layer cell. As expected, this indicated that C18Fc+ did not dissolve in the aqueous subphase on the time scale of these measurements. Were C18Fc+ soluble in the aqueous phase and capable of reduction to C18Fc, the UME surface would almost certainly be expected to be blocked, affecting the response for the Ru(bipy)33+/2+ couple. Further consideration was given to whether C18Fc+ was likely to form an ion-pair with NO3-. A systematic investigation by Ju and Leech26 showed that ion-pair formation occurs between aqueous NO3- and the Fc+ headgroup on a self-assembled monolayer of 11-(ferrocenylcarbonyloxy)undecanethiol with an effective formation constant of 77 M-1. For the types of system of interest in the present study, there is evidence that the ionpair formation constant will increase significantly with increasing alkyl chain length.27 Consequently, we anticipate that ionpair formation between C18Fc+ and NO3- is likely. This process would certainly impede C18Fc+ dissolution in the aqueous subphase in the present study. Moreover, ion-pair formation means that surface potential effects-considered in our earlier related work on monolayers1b- can be ignored in the present case. Method for the Analysis of Transients. Considering the possible contribution of capacitative charging currents on the tip current response, a background subtraction method was used in the analysis of SECM transient data. The measured tip transient response for the oxidation of Ru(bipy)32+ was corrected by subtraction of the current-time data when the potential was stepped over the same range, with only 0.1 M KNO3 present in solution. Figure 10 shows typical transient responses for the first potential step in 0.1 M KNO3 solution in the presence and absence of 1 mM Ru(bipy)32+, with the tip ca. 1.25 µm from the interface (vide infra). It can be seen that the background current contribution is small and can readily be accounted for. Results obtained after background subtraction are used for the analysis presented below.

Figure 11. Transients for the C18Fc-Ru(bipy)32+ system, with A ) 50 Å2. (a) Measurement of d. The solid curve is the experimental characteristic during the third potential step, with t1 ) 0.4 s and t2 ) 0.44 s which is effectively co-incident with theory for an inert interface with log L ) -1.0 (dashed curve). The outlying upper and lower dashed theoretical curves are for log L ) -0.97 and -1.04. (b) Measurement of k. The solid curve is a typical experimental transient for the first potential step, which fits well to k ) 0.035 cm s-1 (d ) 1.25 µm), shown as a coincident dashed line. The outlying upper and lower dashed theoretical curves are for k ) 0.040 and 0.030 cm s-1, respectively. (c) Measurement of Dr. The solid curve is the experimental result which fits well to Dr ) 0.2, with the other parameters now defined. The outlying upper and lower dashed theoretical curves are for Dr ) 0.24 and 0.16, respectively.

Measurements of ET Kinetics and Lateral Diffusion. The results in Figures 11-13 are typical responses for the three-step method, obtained with the monolayer held at surface pressures where the mean area per molecule, A, was 50 Å2 (Figure 11), 40 Å2 (Figure 12) and 30 Å2 (Figure 13). To clearly demonstrate the procedures involved in these measurements and also to highlight the precision with which the measurements of k, d, and Dr can be made using the triple potential step method, the transient responses obtained in the different steps are considered separately in Figure 11. These


Figure 12. Lateral diffusion coefficient and ET kinetic measurements for A ) 40 Å2. The solid lines are the experimental results for the first step transient (top), the third step transient obtained with t1 ) 0.4 s and t2 ) 2.4 s (middle), and the third step transient obtained with t1 ) 0.4 s and t2 ) 0.44 s (bottom). The dashed lines are the best fits to the theoretical model for an inert interface with log L ) -1.0 and Dsol ) 4.8 × 10-6 cm2 s-1 (bottom). The top and middle dashed lines fit to k ) 0.045 cm s-1 and Dr ) 0.1.

Figure 13. Lateral diffusion coefficient and ET kinetic measurements for A ) 30 Å2. The three solid curves are experimental results for the first step transient (top), with t1 ) 0.4 s, and the third step transients for either t2 ) 0.44 or 3.4 s (two lines coincident at the bottom). The third step transient with t2 ) 0.44 s fits an inert interface model with log L ) -1.0 (lower dashed line). The upper dashed line is for the first step with k ) 0.06 cm s-1, whereas the remaining dashed line is for the third step with Dr ) 0.02 with t2 ) 3.4 s and the other parameters already cited.

data are for the case where the mean area per molecule was 50 Å2. First, d was measured from the current-time transient recorded during the period of the third potential step, with time scales for the potential steps defined by the switching times, t1 ) 0.4 s and t2 ) 0.44 s. The long “bleaching” time and short “recovery” time permitted a d value of 1.25 µm to be obtained for the case depicted in Figure 11a, by fitting the final step data to theory for an inert interface.20 The outlying theoretical curves in Figure 11a correspond to ca. (0.1 µm, indicating the very high precision of distance measurements with this approach. With a knowledge of d, the k value was obtained by fitting the transient result obtained in the first potential step to theoretical curves using k as the only unknown. We are able to do this, having already shown in the theory section that surface diffusion only makes a contribution to the current-time behavior in the first step under quite limited conditions, and even then only at the longest times. It can be seen in Figure 11b that there is a vast enhancement in the current flowing during the first step, compared to that found for an inert interface, due to the redox reaction between electrogenerated Ru(bipy)33+ and C18Fc (eq 1) resulting in positive feedback. Analysis of the data

Zhang et al. shown resulted in k ) 0.035 cm s-1 as the best fit, with Γ ) 1.66 × 10-10 mol cm-2 (defined by the A value). The outlying theoretical curves are for k ( 0.005 cm s-1, which suggests that the precision of the k measurements is within ( 10%. The lateral diffusion coefficient was finally obtained by analyzing experimental current-time curves obtained in the third potential step, with time scales for the three potential steps defined by switching times of t1 ) 0.4 s and t2 ) 2.4 s (Figure 11 (c)). With k ) 0.035 cm s-1 and d ) 1.25 µm already measured for the two cases, the surface diffusion coefficient was the only unknown. A lateral diffusion coefficient of (1.0 ( 0.2) × 10-6 cm2 s-1 provided the best fit for this case, with A ) 50 Å2. Experimental results obtained when A was either 40 Å2 or 30 Å2, were analyzed using the procedure described above. The results for these two cases are summarized in Figures 12 and 13. The ET rate constant and lateral diffusion coefficient measured for A ) 40 Å2 were 0.045 ( 0.006 cm s-1 and (5 ( 1) × 10-7 cm2 s-1, respectively. The ET rate constant measured for A ) 30 Å2 was 0.06 ( 0.01 cm s-1, while lateral diffusion was undetectable, suggesting a lateral diffusion coefficient less than 1 × 10-7 cm2 s-1. These initial data are consistent with Majda’s earlier work using the microline electrode technique which found surface diffusion coefficients of 8 × 10-7 and 4 × 10-7 cm2 s-1 in a (1:1) monolayer when A was 50 Å2 and 40 Å2, respectively.1b This favorable comparison serves to validate the new SECM method introduced in this paper. Analysis of ET Rate Constants. It is interesting to compare the ET rate constants measured in this study to theoretical predictions. We are unaware of relevant theory directly applicable to the problem of interest here, where one redox (monolayer) species is confined to two dimensions, and the second reactant is free to move in three dimensions (aqueous phase). To obtain an order of magnitude estimation, we therefore first apply Marcus theory for bimolecular reactions in solution,28 which has previously been used to analyze ET between a redoxactive monolayer on an electrode and a solution species.29 When the work term can be neglected, the bimolecular cross-electrontransfer rate in solution, k12, can be written as

k12 ) (k11k22K12f12)1/2

(28)

where k11 and k22 are the self-exchange rate constants for the reactants. K12 ) exp(nF∆E°′/RT) is the equilibrium constant for the cross-reaction, where ∆E°′ is difference in the formal potentials of the two redox couples. K12 is 1011 by approximating ∆E°′ from the measured half-wave potential of C18Fc+/0 (ca. 0.6 V)1a and the standard potential of Ru(bipy)33+/2+ (1.27 V),11c both values vs NHE. The coefficient f12 is a function of k11, k22, and K12 and in practice is often close to unity. A k12 value at the diffusion-controlled limit results from eq 28 using selfexchange rate constants of 9.1 × 106 M-1 s-1 for Fc+/0 (measured in acetonitrile)30 and 4 × 108 M-1 s-1 for Ru(bipy)33+/2+ (measured in water),28 which is orders of magnitude higher than the measured value, k/Γ ) 2 × 105 M-1 s-1. The second analysis is based on the Marcus sharp boundary model31 for ET at a liquid/liquid interface, which appears to be the closest analogy to the present situation. According to this theory,31 the ET rate constant can be calculated using

k12 ) 2πN(a1 + a2)(∆F)3κV exp(-∆Gq/RT)

(29)

where N is Avogadro’s constant, a1 and a2 are the radii of the Fc headgroup (3.8 Å)30 and Ru(bipy)32+ (6.8 Å),28 ∆F is



typically 1 Å, κV is ca. 1013 s-1 and ∆G q is the free energy for the ET reaction, which can be written as

∆G* )

λ ∆G°′ 2 1+ 4 λ

(

)

(30)

where λ ) (λ1 + λ2)/2 is the reorganization energy for the bimolecular interfacial reaction; λ1 and λ2 are the reorganization energies for the self-exchange ET reactions of the two redox couples. A value of 92 kJ/mol has been measured for the reorgnisation energy of Fc+/0 in a 1:1 propanol/water mixed solvent,32 the reorganization energy of Ru(bipy)33+/2+ can be calculated as 55 kJ/mol based on the self-exchange rate constant,28 yielding λ ≈ 74 kJ/mol. Thus, according to eq 29, a k12 value of 3.5 × 103 cm s-1 M-1 results, which is 5 orders of magnitude higher than the measured value, k/(Γ/2a1) ) 0.016 cm s-1 M-1. Although the theoretical analysis outlined here is not strictly applicable, it provides a guide, and suggests that the ET kinetics at the Langmuir monolayer interface are significantly slower than predicted by Marcus theory. This is most likely due to the highly constrained local environment in which the ET reaction occurs. These observations are qualitatively consistent with the results of Forster et al.10 who found slower ET kinetics from direct electrode contact measurements in Langmuir monolayers at the A/W interface. Conclusions A novel SECM triple step transient approach has been developed for the measurement of lateral diffusion processes of electroactive amphiphiles in Langmuir monolayers. This method complements the FRAP technique4 and the electrochemical microelectrode contact method introduced by Majda and co-workers1a,7 and extended by Forster et al.10 The SECM method involves “electrochemical bleaching” of the redox-active amphiphile at a portion of the target interface in an initial potential step. This occurs through ET between an electrogenerated redox species in the solution and the redox-active amphiphile. The theoretical results show that it is possible to measure the ET kinetics in this step from the corresponding chronoamperometric response, because lateral diffusion of the electroactive amphiphile is only important at longer times. The second step involves converting the solution mediator to its initial form for a defined period, in which lateral diffusion may occur. Both the tip/interface separation and the lateral diffusion coefficient can be measured from the current-time response of the third “analysis” potential step by judiciously selecting the time scale of the second “recovery” period. Having demonstrated the practical application of the technique, there is now considerable scope for applying it to other redox systems, particularly involving biologically important amphiphiles. Acknowledgment. We thank BBSRC for support for C.J.S. and the ORS scheme, Avecia and University of Warwick for scholarships for J.Z. Helpful discussion with Dr. Anna Barker (University of Warwick), Prof. Ian Peterson (Coventry University) and Dr. John Atherton (Avecia, Huddersfield) are much appreciated. References and Notes (1) (a) Charych, D. H.; Landau, E. M.; Majda, M. J. Am. Chem. Soc. 1991, 113, 3340 and references therein. (b) Slevin, C. J.; Unwin, P. R. J. Am. Chem. Soc. 2000, 122, 2597 and references therein. (2) (a) Saurel, O.; Cezanne, L.; Milton, A.; Tocanne, J. F.; Demange, P. Biochemistry 1998, 37, 1403. (b) Kochy, T.; Bayerl, T. M. Phys. ReV.

E. 1993, 47, 2109. (c) Trauble, H.; Sackmann, E. J. Am. Chem. Soc. 1972, 94, 289. (d) Kornberg, R. D.; McConnell, H. M. Proc. Natl. Acad. Sci. 1971, 68, 2564. (3) For detailed descriptions of this technique, see for example: (a) Wolf, D. E. In Fluorescence Microscopy of LiVing Cells in Culture, Part B. Taylor, D. L., Wang, Y. L., Eds.; Academic Press: San Diego, 1989, Chapter 10, p 271. (b) Elson, E. L.; Qian, H. In Fluorescence Microscopy of LiVing Cells in Culture, Part, B.; Taylor, D. L., Wang, Y. L., Eds.; Academic Press: San Diego, 1989, Chapter 11, p 307. (4) For reviews, see for example: (a) Peters, R. Cell Biol. Int. Rep. 1981, 5, 733. (b) Edidin, M. In Membrane Structure; Finean, J. B., Michell, R. H. Eds.; Elsevier: New York, 1981; p 37. (c) Vaz, W. L. C.; Derzko, Z. I.; Jacobson, K. A. Cell Surf. ReV. 1982, 8, 83. (d) Wade, C. G. In Structure and Properties of Cell Membranes; Benga, G., Ed.; CRC Press: Boca Raton, Vol. 1, 1985; p51. (e) Elson, E. L. Annu. ReV. Phys. Chem. 1985, 36, 379. (f) Elson, E. L. In Optical Methods in Cell Physiology; Weer, P. D., Salzberg, B. M., Eds.; Wiley: New York, 1986; p 367. (5) For recent applications, see for example: (a) Kruhlak, M. J.; Lever, M. A.; Fischle, W.; Verdin, E.; Bazett-Jones, D. P.; Hendzel, M. J. J. Cell Biol. 2000, 150, 41. (b) Auch, M.; Ficher, B.; Mo¨hwald, H. Colloid Surface A 2000, 164, 39. (c) Lalchev Z. I.; Mackie, A. R. Colloid Surface B 1999, 15, 147. (d) Mullineaux, C. W,; Tobin, M. J.; Jones, G. R. Nature 1997, 390, 421. (e) Johnson, M. E.; Berk, D. A.; Blankschtein, D.; Golan, D. E.; Jain, R. K.; Langer, R. S. Biophys. J. 1996, 71, 2656. (6) Axelrod, D.; Koppel, D. E.; Schlessinger, J.; Elson, E.; Webb, W. W. Biophys. J. 1976, 16, 1055. (7) (a) Charych, D. H.; Goss, C. A.; Majda, M. J. Electroanal. Chem. 1992, 323, 339. (b) Lindholmsethson, B.; Orr, J. J.; Majda, M. Langmuir 1993, 9, 2161. (c) Majda, M. Thin Solid Films 1995, 20, 331. (d) Kim, J. S.; Lee, S. B.; Kang, Y. S.; Park, S. M.; Majda, M.; Park, J. J. Phys. Chem. B 1998, 102, 5794. (e) Kang, Y. S.; Majda, M. J. Phys. Chem. B 2000, 104, 2082. (f) Torchut, E.; Laval, J. M.; Bourdillon, C.; Majda, M. Biophys. J. 1994, 66, 753. (8) (a) Lee, W. Y.; Majda, M.; Brezesinki, G.; Wittek, M.; Mobius, D. J. Phys. Chem. B 1999, 103, 6950. (b) Charych, D. H.; Anvar, D. J.; Majda, M. Thin Solid Films 1994, 242, 1. (c) Charych, D. H.; Majda, M. Thin Solid Films 1992, 210, 348. (d) Fujihira, M.; Araki, T. Chem. Lett. 1986, 921. (9) See for example: (a) Bourdillon, C.; Majda, M. J. Am. Chem. Soc. 1990, 112, 1795. (b) Miller, C. J.; Widrig, C. A.; Charych, D. H. Majda, M. J. Phys. Chem. 1988, 92, 1928. (c) Goss, C. A.; Miller, C. J.; Majda, M. J. Phys. Chem. 1988, 92, 1937. (10) Forster, R. J.; Keyes, T. E.; Majda, M. J. Phys. Chem. B 2000, 104, 4425. (11) For reviews of SECM, see for example: (a) Bard, A. J.; Fan, F.R. F.; Pierce, D. T.; Unwin, P. R.; Wipf, D. O. Science 1991, 254, 68. (b) Bard, A. J.; Fan, F.-R. F.; Mirkin, M. V. In Electroanalytical Chemistry; Bard, A. J., Ed.; New York: Marcel Dekker: 1993; p 243. (c) Bard, A. J.; Fan, F.-R. F.; Mirkin, M. V. In Physical Electrochemistry: Principles, Methods and Applications; Rubinstein, I., Ed.; New York: Marcel Dekker: 1995; p 209. (d) Unwin, P. R. J. Chem. Soc., Faraday Trans. 1998, 94, 3183. (e) Barker, A. L.; Gonsalves, M.; Macpherson, J. V.; Slevin, C. J.; Unwin, P. R. Anal. Chim. Acta 1999, 385, 223. (f) Amemiya, S.; Ding, Z.; Zhou, J. Bard, A. J. J. Electroanal. Chem. 2000, 483, 7. (g) Barker, A. L.; Slevin, C. J. Unwin, P. R.; Zhang, J. In Liquid Interfaces in Chemical, Biological and Pharmaceutical Applications; Volkov, A. G., Ed.; New York: Marcel Dekker: 2001, p 283. (12) See for example: (a) Bard A. J.; Mirkin, M. V.; Unwin P. R.; Wipf, D. O. J. Phys. Chem. 1992, 96, 1861. (b) Horrocks, B. R.; Mirkin, M. V.; Bard, A. J. J. Phys. Chem. 1994, 98, 9106. (c) Macpherson, J. V.; Unwin, P. R. J. Phys. Chem. 1995, 99, 3338. 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New Approach for Measuring Lateral Diffusion in Langmuir

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