Electrochemistry in Deep Eutectic Solvents - American Chemical Society

Oct 31, 2007 - Department of Chemistry and Physics, Chicago State UniVersity, Chicago, ... difficulties in achieving steady-state conditions, SECM app...
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J. Phys. Chem. B 2007, 111, 13271-13277

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Electrochemistry in Deep Eutectic Solvents Chiemela A. Nkuku and Robert J. LeSuer* Department of Chemistry and Physics, Chicago State UniVersity, Chicago, Illinois 60628 ReceiVed: July 23, 2007; In Final Form: September 15, 2007

We report the cyclic voltammetry, chronoamperometry, and scanning electrochemical microscopy of ferrocene dissolved in deep eutectic solvents (DES), consisting of choline chloride (ChCl) and either trifluoroacetamide (TFA) or malonic acid as the hydrogen-bond donor. Despite the use of ultramicroelectrodes, which were required due to the modest conductivities of the DES employed, linear diffusion behavior was observed in cyclic voltammetric experiments. The high viscosity of 1:2 ChCl/TFA relative to non-aqueous electrochemical solvents leads to a low diffusion coefficient, 2.7 × 10-8 cm2 s-1 for ferrocene in this medium. Because of the difficulties in achieving steady-state conditions, SECM approach curves were tip velocity dependent. Under certain conditions, SECM approach curves to an insulating substrate displayed a positive-feedback response. Satisfactory simulation of this unexpected behavior was obtained by including convection terms into the mass transport equations typically used for SECM theory. The observance of positive-feedback behavior at an insulating substrate can be described in terms of a dimensionless parameter, the Peclet number, which is the ratio of the convective and diffusive timescales. Fitting insulator approach curves of ferrocene in 1:2 ChCl/TFA shows an apparent increase in the diffusion coefficient with increasing tip velocity, which can be explained by DES behaving as a shear thinning non-Newtonian fluid.

Introduction The development and utilization of environmentally friendly solvents is an active area of research, and room-temperature ionic liquids have been at the forefront of this work due in large part to their low or negligible vapor pressures.1 The possibility, indeed the reality, of alternate mechanistic pathways occurring in novel solvents necessitates the development or modification of techniques capable of investigating reaction mechanisms in these media, and electrochemistry has contributed significantly to this.2,3 One particular type of ionic liquid recently introduced4,5 consists of a salt, choline chloride, with a hydrogenbond donor (HBD) such as an organic acid or amide. Unlike ionic liquids, the liquid state is produced through freezing point depression, whereby hydrogen-bonding interactions between an anion and a HBD are more energetically favored relative to the lattice energies of the pure constituents. The term deep eutectic solvents (DES) has been used to differentiate these liquids from traditional molten salts. DES have properties similar to ionic liquids, in particular, their potential as tunable solvents that can be customized to a particular type of chemistry. DES have several advantages over traditional ionic liquids in that they are easy to prepare in high purity and are not sensitive to water. Furthermore, toxicological properties of the components used for DES have been determined and are available, with some DES being biodegradable. DES have opened up interesting avenues of chemistry, in particular, due to their ability to dissolve metal oxides.6 Solubility properties are dependent on the HBD of the DES; for example, CuO is preferentially soluble in 1:1 choline chloride/malonic acid versus 1:1 choline chloride/oxalic acid, whereas the solubility of Fe3O4 is higher in the oxalic acid DES.4 The utility of DES in industrially relevant electrochemical processes has been demonstrated in both the electropolishing * Corresponding author. E-mail: [email protected].

of stainless steel7 and the electrodeposition of zinc-tin alloys.8 Our interests lie in the employment of electrochemical methodologies for exploring electron-transfer reaction mechanisms in these novel solvents. Thus, we sought to investigate the electrochemistry of a Nernstian redox couple, ferrocene, in DES to set a benchmark for typical electrochemical behavior in these solvents. Owing to the high viscosities and modest conductivities of DES relative to non-aqueous electrolyte solutions, our studies focused primarily on the use of ultramicroelectrode (UME) techniques, including SECM. Because of the low currents observed using UMEs, solution resistance does not interfere significantly with these techniques. SECM in an ionic liquid9 has recently shown that approach curves obtained in this medium do not obey steady-state SECM theory. The high viscosity of the solvent leads to a low diffusion coefficient of the redox mediator. The diffusion time scale is decreased enough that electrode movement can become the major component of mass transport. Therefore, the steady-state theory typically used to describe SECM approach curves will not apply to data collected in DES. In this paper, we extend SECM theory to incorporate UME-induced convection into the mass transport equations and describe the approach curve behavior in terms of a dimensionless parameter, the Peclet number. In applying this theory to approach curves in DES, we observed a diffusion coefficient for ferrocene that is dependent on the tip velocity used in the approach curve and propose that this phenomenon is consistent with DES behaving as a non-Newtonian fluid. Experimental Procedures Chemicals. Choline chloride (ChCl), trifluoroacetamide (TFA), malonic acid (MA), and ferrocene (Fc) were all reagent grade. ChCl was recrystallized from ethanol and dried under vacuum. Malonic acid was dried under vacuum for 24 h prior to use, and all other chemicals were used as received. DES were

10.1021/jp075794j CCC: $37.00 © 2007 American Chemical Society Published on Web 10/31/2007

13272 J. Phys. Chem. B, Vol. 111, No. 46, 2007 formed by mixing ChCl with the HBD in the appropriate ratio (1:1 for the acid and 1:2 for the amide).4,10 The two solid components were mixed and heated under an argon atmosphere until a liquid formed. This procedure typically took about 2 h. The solution was then allowed to cool, with stirring and under argon, until it reached room temperature. In the case of ChCl/ TFA, residual solid was observed after the mixing/heating process. The solid was removed by filtration prior to use. To facilitate solution preparation, ferrocene was added to the solid components of the DES prior to forming the liquid. No color change was observed when the solution was heated and stored under argon. DES solutions of ferrocene slowly oxidized, as evidenced by a color change from yellow to blue, when left out in air for several days. When kept under a blanket of argon, however, these solutions were stable for several weeks. Electrochemistry. Electrochemical and SECM measurements were made using a CH900B bipotentiostat. With the exception of determining the solvent potential limits, no effort was made to maintain the DES under an inert atmosphere during the experiment. The UME was a 10 µm diameter platinum tip, purchased from CHInstruments, with a RG (ratio of insulating sheath to metal radius) of 5. The counter electrode was a Pt wire, and the reference electrode was aqueous Ag/AgCl. For approaches to a conductive substrate, a 2 mm diameter platinum disk was used as a substrate. For insulator approaches, either the Teflon cell or the Kel-F insulating sheath of an electrode were used as substrates. Unless otherwise noted, approach curves were obtained at a constant velocity of 1 µm/s with a potential applied to the UME at least 200 mV positive of the E1/2 of the redox mediator. This potential was held for 60 s prior to initiating the approach. Conductive substrates were held at a potential at least 200 mV negative of the E1/2 of ferrocene. Simulations. Theoretical simulations were performed using COMSOL multiphysics version 3.3 (COMSOL Inc.). Simulations were performed on a standard desktop computer (3 GHz dual-core CPU with 1 GB of RAM) and typically required approximately 10 min of processor time per approach curve. Unless otherwise noted, the distance in the SECM approach curves is normalized by the UME radius, L ) d/a, and the current is normalized by the current observed at the UME in the bulk solution after a 60 s quiet time, I ) it/i60s. Results and Discussion Cyclic Voltammetry (CV) in DES. Of the two deep eutectic solvents used in this work, the amide-containing solvent shows more promise as an electrochemical solvent. The potential limits of oxygen-free 1:2 ChCl/TFA DES are +0.95 and -0.85 V versus aqueous Ag/AgCl, with the potential limit defined here as the current due to solvent alone being equal to the peak current observed for the oxidation of 15 mM ferrocene at 0.1 V/s. The malonic acid DES has a slightly larger oxidative window (+1.1 V) but is of little use for reductive chemistry owing to the onset of the acid reduction at -0.35 V. Figure 1 shows the cyclic voltammograms of 15 mM ferrocene in ChCl/ TFA DES at a 5 µm radius Pt electrode at scan rates from 0.1 to 5 V/s. In traditional solvents, these conditions would result in sigmoidal-shaped voltammograms due to radial diffusion. Because of the very low diffusion coefficients observed in deep eutectic solvents, voltammetry at an ultramicroelectrode yields linear-diffusion behavior. Plotting the forward peak current versus the square root of the scan rate results in a linear relationship, indicating that the oxidation of ferrocene is a diffusion-controlled process and demonstrating that ferrocene behaves as a solute in ChCl/TFA DES rather than a suspension

Nkuku and LeSuer

Figure 1. Cyclic voltammograms of 15 mM ferrocene in 1:2 ChCl/ TFA DES. Scan rates are 0.1, 0.2, 0.5, 0.75, 1, 2, and 5 V/s. Inset is a plot of forward peak current vs (scan rate)1/2.

of particles. The Nicholson reversibility11,12 criterion was used to determine that the oxidation of ferrocene is chemically reversible at all scan rates investigated. The separation between forward and reverse peaks, ∆Ep, increases from 81 mV at 0.5 V/s to 118 mV at 5 V/s. Deviations from the ideal peak separation of 59 mV for a one-electron redox process can be attributed to either slow electron transfer or ohmic drop due to solution resistance. The conductivity of ChCl/TFA has been determined10 (κ ) 0.286 mS cm-1) and can be used to estimate the degree to which solution resistance contributes to the increase in ∆Ep. Noting that the ohmic drop for a microdisk occurs in solution near the electrode,13,14 the solution resistance can be determined using (4κa)-1, where a is the electrode radius. For the 5 µm radius UME used, this amounts to approximately 2 MΩ. Despite the large resistance, the ohmic drop accounts for only 4 mV of the ∆Ep at 5 V/s due to the small currents observed in the CV experiments. Making this minor correction to the peak separation, the electron-transfer rate for ferrocene in ChCl/TFA can be estimated15 as 4 × 10-3 cm s-1. The reported electron-transfer rate of ferrocene in acetonitrile using SECM techniques is 3.7 ( 0.6 cm s-1.16 Rate constants for the oxidation of ferrocene range from 0.1 to over 200 cm s-1 (ref 17) with the discrepancies attributed to ohmic drop and assumptions of ideal electrode geometry. Solute electron-transfer rates tend to increase with increasing solvent HBD or acceptor properties,17 so it is unclear at present why the electron-transfer rate of ferrocene in a DES would be so low. Chronoamperometry was used to determine the diffusion coefficient, D0, of ferrocene in the ChCl/TFA DES. The peakshaped cyclic voltammograms observed at an ultramicroelectrode are indicative of a very low D0 as was seen in a study of diffusion in polymeric electrolytes.18 Despite the shape of the cyclic voltammograms, chronoamperometric data did not obey the linear diffusion form of the Cottrell eq 1, which states that a plot of current versus t-1/2 should be linear with an intercept of zero

i)

nFa2 xπD0C

xt

(1)

In this equation, n is the number of electrons, F is Faraday’s constant, a is the electrode radius, t is time, and C is the bulk concentration. The chronoamperometric data (Figure S1) clearly show a non-zero intercept, suggesting a radial component to diffusional mass transport. The radial form of the Cottrell eq 2

Electrochemistry in Deep Eutectic Solvents

J. Phys. Chem. B, Vol. 111, No. 46, 2007 13273

fits the data nicely with an apparent diffusion coefficient of 2.9 × 10-8 cm2 s-1

i)

nFa2 xπD0C

xt

+ 4nFaD0C

(2)

There is likely some uncertainty in this measurement as well, owing to the presence of linear diffusion. Shoup and Szabo have developed an empirical expression (eq 3) that accurately describes the chronoamperometry i-t curve under mixed diffusion conditions:19

0.4431 i ) 0.7854 + + 0.2146exp[-0.3911/xτ] i∞ xτ τ ) tD0/a2

(3)

where i∞ is the steady-state current that in this work is taken as the intercept from eq 2. The diffusion coefficient obtained from a best fit using eq 3 is 2.7 × 10-8 cm2 s-1. The diffusion coefficient of a solute can be predicted using the StokesEinstein equation, which states that the product of the diffusion coefficient and viscosity should be constant for a given solute in the absence of solvent/solute interactions.20 The reported diffusion coefficient of ferrocene in acetonitrile is 2.0 × 10-5 cm2 s-1.21 Given the viscosities (at 25 °C) for acetonitrile, 0.37 cP,22 and ChCl/TFA, 120 cP,10 the Stokes-Einstein relationship predicts a diffusion coefficient of ferrocene in ChCl/TFA of ∼6 × 10-8 cm2 s-1. The Stokes-Einstein equation assumes a non-interacting solvent, so it is not surprising that the predicted value is higher than that determined using chronoamperometry measurements; however, it appears that the low diffusion coefficient of ferrocene in DES can be attributed primarily to solvent viscosity. Earlier work has quantified the shapes of cyclic voltammograms obtained under mixed diffusion conditions using the characteristic time of a CV experiment, p (eq 4)23

p)

x

nFa2ν RTD0

(4)

A large characteristic time results in peak-shaped voltammograms indicative of linear diffusion, which would be encountered with large electrodes, high scan rates, or low diffusion coefficients. Using the diffusion coefficient obtained from eq 3, p ranges from 6 to 42 for the cyclic voltammograms in Figure 1, with radial contributions to the current in excess of 15% at scan rates below 0.5 V/s. Typical operating conditions for CV experiments result in a mixed diffusion condition when investigating electrochemistry in viscous solvents such as DES, and a quantitative analysis of electron-transfer mechanisms in such media will require consideration of the diffusion mode. SECM Approach Curves in DES. Figure 2 shows typical approach curves to a conducting (panel A) or insulating (panel B) substrate ChCl/TFA DES using ferrocene as the redox mediator. Tip velocities were held constant at either 0.5, 1, or 2 µm/s. The dashed lines indicate the theoretical response using the established SECM approach curve theory.24 The y-axis, I, is normalized by the current observed after the tip has sat distant from any surface at an oxidizing potential for 60 s. The x-axis, L, is normalized by the tip radius, and zero is defined as the point at which the tip made contact with the surface. More appropriate distance normalization procedures follow a discussion of the theoretical model next.

Figure 2. Conductor (A) and insulator (B) approach curves in 1:2 ChCl/TFA DES with 15 mM ferrocene as the redox mediator. Note that the x-axis represents normalized distance only for theoretical curves (dashed lines). Experimental curves were normalized by assuming that tip/substrate contact occurred at L ) 0.

There are three important points to make regarding the shapes of the approach curves in Figure 2. First, it is clear that the approach curves do not obey the response predicted from steadystate theory. This behavior has been recently observed in ionic liquids9 and is attributed to the mixed transport conditions present during the electrode approach. In both the positive and the negative approach curves, the influence of the substrate on the UME current is attenuated relative to steady-state theory. This effect can be qualitatively explained in terms of the time required for electrogenerated material to diffuse from the UME to the substrate. For viscous media, a smaller tip/substrate gap will be necessary before the substrate can influence the tip current, regardless of whether the influence is positive feedback or blocking. The second important point demonstrated in Figure 2 is the dependence of the insulator approach curve shape on the tip velocity. With diffusion coefficients on the order of 10-8 cm2 s-1 and tip velocities around 1 µm/s, the diffusion length is the same order of magnitude as the distance the tip will travel during the time frame of a typical approach curve experiment. It is therefore possible to set up conditions where mass transport via tip movement will predominate over diffusional transport. A more subtle tip velocity dependency is observed under positive-feedback conditions. As the electrode approaches the conductive substrate, one can consider the regeneration of electroactive species at the substrate as an additional form of mass transport. Under these conditions, neither diffusion nor tip velocity plays a significant role in the transport of material to the UME. It was surprising to observe an increase in current above the steady-state value when a UME traveling at 2 µm/s was brought close to an insulating substrate, and this positive feedback at an insulator is the third important feature of the DES approach curves. This behavior was also observed in a malonic acid DES, which has a nearly 5-fold greater viscosity versus 1:2 ChCl/ TFA. The insulator approach curve shown in Figure 3 is that of ferrocene in ChCl/MA with a tip velocity of 1 µm/s. The current increases to nearly 4 times the steady-state current before insulator behavior begins to set in. The more viscous ChCl/ MA will result in even lower diffusion coefficients for redox mediators, and we believe that this combination of tip velocity and diffusion coefficient leads to mixed diffusive/convective transport conditions in the SECM approach curve. To further understand the tip velocity/D0 dependence of approach curves in low viscosity media, we incorporated fluid dynamics into the diffusion equations typically used for SECM theory.

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Nkuku and LeSuer

Pe )

νa D0

(9)

where C* is the bulk concentration of the analyte, ν is the tip velocity, and Pe is the Peclet number. Substitution of the normalization variables and rearrangement yields the following dimensionless convection/diffusion eq 10

∂C′ 1 + u′∇C′ ) ∇2C′ ∂t′ Pe

Figure 3. Insulator approach curve in 1:1 ChCl/MA with ferrocene as the redox mediator. The tip velocity is 1 µm/s. The distance axis is normalized according to the theoretical curves.

Theoretical Model. It is clear from the data shown that any mechanistic analysis of SECM data obtained in high viscosity media must consider convective transport, since tip velocity, and therefore fluid velocity, plays an important role in the shape of the approach curve. Several authors have presented theoretical models that incorporate fluid dynamics into SECM measurements; however, in all cases, electrode movement is restricted to lateral motion above a surface, focusing on the imaging aspects of this technique.25,26 In these cases, it is possible to simplify the model by adjusting the frame of reference, noting that an electrode moving laterally over an infinite plane is mathematically equivalent to a stationary electrode in a flowing fluid. This simplification is not feasible for simulating a nonsteady-state approach curve, and the actual movement of the electrode must be included in the theoretical model. The COMSOL multiphysics package, a finite element method solver, includes an application mode that allows one to address the dynamic geometry found in this problem. In the deformed mesh application mode, the software perturbs the mesh to conform to distortions in geometry. Geometry boundaries can be changed as a function of time, and we use this feature to simulate the movement of a UME tip as it approaches an infinite substrate (both insulating and conducting). The convection/ diffusion application mode is used to describe the spatial distribution of an electroactive substrate and, more importantly, the current observed at the UME. Fluid flow is modeled using the Navier-Stokes equations for incompressible fluid flow. We briefly describe the normalized equations used in this model,27 noting that the SECM theoretical methods have been described in greater detail elsewhere.24 Mass transfer with flow is governed by eq 5

∂C + u∇C ) D0∇2C ∂t

(5)

where C and D0 are the concentration and diffusion coefficient, respectively, of the redox mediator, t is time, and u is the fluid velocity. The terms in the convection/diffusion equation are normalized

C′ ) C/C*

(6)

u′ ) u/ν

(7)

t′ )

tν a

(8)

(10)

Pe is the ratio of convective and diffusive timescales and as shown next is the sole parameter that determines the shape of an insulator approach curve. For non-moving boundaries, the boundary conditions are typical of those used in steady-state theory. The normalized concentration was set to 0 at the electrode surface and 1 at the geometry boundaries representing the bulk solution and, when appropriate, the conducting substrate. At boundaries representing moving insulators (i.e., the electrode sheath), the normal of the concentration gradient was set to 0, nsC′ ) 0. At the insulating substrate, the flux is also set to 0, n(sC′ - C′u′) ) 0. The fluid velocity in the previous equation is given by the Navier-Stokes eq 11

∂u F + Fu∇u ) -∇p + η∇2u ∂t

(11)

where F and η are the fluid density and viscosity, respectively, and p is pressure. Eq 7 is normalized using the terms27

p′ )

pa ην

(12)

Re )

Fνa η

(13)

where Re is Reynolds number. Substitution and rearrangement gives the normalized Navier-Stokes eq 1427

Re

∂u′ + Reu′∇u′ ) -∇′p′ + ∇′2u′ ∂t′

(14)

A no-slip boundary condition was used for each non-moving surface, and an inflow velocity equal to Pe was used for all moving boundaries. A normal flow condition was applied to geometry boundaries representing the semi-infinite solution limits. The moving electrode was simulated by setting the mesh velocity equal to Pe along the electrode boundaries (including the electrode sheath). All other boundaries had either the mesh velocity fixed at zero or, as in the case of the axis, were allowed to shrink as the electrode approached the substrate. To facilitate convergence of the model, two internal boundaries were drawn starting from the edge of the electrode and running parallel to the axes. These boundaries eliminated severe distortions in the mesh that would prevent a solution from being found. Figure 4 shows a series of insulator approach curves for Pe changing from 0.01 to 5. Because the tip velocities used in SECM are typically slow, the Reynolds number is very small and has a negligible influence on the shape of the approach curves. In all simulations, Re was held constant at 10-4. The dashed line in Figure 4 is the insulator approach curve predicted by steady-state theory for an electrode with an RG of 5.24 For a Pe of 0.01, the non-steady-state approach curve agrees with the traditional theory to within 1%. Recall that Pe describes the magnitude of convective transport relative to diffusive

Electrochemistry in Deep Eutectic Solvents

Figure 4. Pe-dependent approach curves to an insulating substrate. The trace of open squares is the steady-state theory for an UME with RG ) 5. A non-steady-state approach curve with Pe ) 0.01 overlaps the steady-state data. Curves represent Pe values of 1-5 in 0.25 unit increments. The inset is a plot of maximum normalized current and normalized distance at which this maximum is observed as a function of Pe.

Figure 5. Pe-dependent conductor approach curves for Pe values from 1 to 5. The dashed line represents the steady-state theory for a UME with RG ) 5.

transport. For Pe values at or below 0.01, convection is not a significant component to mass transfer, and the steady-state assumption applies under these conditions. Eliminating convection from an approach curve obtained in a DES would be difficult. With a diffusion coefficient of 2.7 × 10-8 cm2 s-1 and a 5 µm radius electrode, a tip velocity of ∼5 nm/s is required to achieve Pe of 0.01. Unless the approach curve is being performed over a very short distance, the time required to conduct the experiment would be lengthy. It is clear from Figure 4 that convection cannot be ignored for Pe values greater than 1. Furthermore, the positive-feedbacklike behavior observed in the insulator approach curves in DES is predicted. The Pe-dependent conductor approach curves are given in Figure 5. As observed experimentally, changes in Pe have little influence on the shape of the approach curve, and the curve for Pe of 1 is very similar to the steady-state curve. This lack of tip velocity dependency in DES is analogous to the lack of significant RG dependence found under positive feedback conditions. At small (L ) ∼0.1) UME/substrate separations, the time required to traverse the gap decreases, and the positive feedback loop becomes the dominant source of electroactive material to the UME. Unlike steady-state conditions, the Pe-dependent insulator approach curves do not show an appreciable RG dependence. Figure S2 in the Supporting Information contains theoretical insulator approach curves with a Pe of 2 at RG values between 2 and 10. The differences in peak heights, an approximately 2% increase from RG of 2 to 10, is not experimentally useful. Under steady-state SECM

J. Phys. Chem. B, Vol. 111, No. 46, 2007 13275 conditions, decreasing the thickness of the insulating sheath surrounding a UME increases the amount of back-diffusion that contributes to the UME current. A lower diffusion coefficient, such as that observed in a DES, will decrease the effect of this phenomenon since the diffusion length during the approach curve experiment does not extend beyond the electrode sheath. An inherent problem with SECM is the difficulty in determining the tip/substrate gap. Assuming fast electron-transfer kinetics and the absence of coupled chemical reactions, the shape of the insulator approach curve, in particular, the observed peak, can be used to determine this distance. The inset in Figure 4 shows the relationships between Pe, normalized peak height (Imax), and normalized distance at which the peak is observed (Lmax). At Pe values greater than ∼1.75, Imax increases with Pe, whereas Lmax decreases until Pe ) ∼5, where no peak is observed within reasonable values for L. Imax in a non-steadystate approach curve should therefore allow one to determine Pe and the tip/substrate distance. Admittedly, the region in which this method is useful, 1.75 e Pe < ∼5 is somewhat limited. However, since Pe depends on the tip velocity and electrode radius, both of which are readily adjustable, peak-shaped approach curves in viscous media should be attainable with an appropriate selection of experimental conditions. The effect of Pe on the concentration profile can readily be observed in Figure 6, which shows a snapshot of insulator approach curves with a Pe of 0.01 (panel A) or 5 (panel B). In both cases, the approach was started at L ) 10 and stopped at L ) 0.5. The simulations predict normalized currents at these electrode positions of 0.38 and 1.92 for Figure 6A, B, respectively. Three factors contribute to the approximately 5-fold difference in normalized current. First, the low diffusion coefficient in Figure 6B results in no depletion of electroactive species near the insulating substrate, whereas the region surrounding the UME in Figure 6A has largely been depleted. Second, the relatively high tip velocity in Figure 6B is forcing an appreciable net flow of material away from the electrode. This can be observed as a distortion of the diffusion layer: compression along the z-axis and elongation along the r-axis. The resultant steeper concentration gradient yields a higher observed current at the UME. The arrows in Figure 6 show the differences in total flux between the two conditions. Under high Pe conditions, flow through the channel formed by the tip and substrate is fully developed and Poiseuille-like, with a radially dependent flux that has a velocity of zero at the walls. Contrarily, flow under low Pe conditions is inward, plug-like, and dominated by diffusion. Animations of insulator approach curves under Pe of 0.01 and 5 conditions are provided in the Supporting Information. Before applying the simulated approach curves to those experimentally obtained in a DES, it is fruitful to confirm that the moving mesh algorithm is in fact representing the movement of an electrode under SECM geometry. Lateral fluid flow induced by the compression of two parallel disks can be solved analytically, and details are provided in the Supporting Information. The radial velocity, u, of fully developed flow is described by eq 15 (see eq S.5 in the Supporting Information)

u)

3rν(d2 - 4z2) 4d3

(15)

where r and z are the radial and axial coordinates, respectively, d is the tip/substrate gap, and ν is the tip velocity. Note that in eq 15, z ) 0 is taken as d/2, such that the maximum radial velocity occurs midway between the tip and the substrate. The

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Nkuku and LeSuer

Figure 6. Effect of Pe on mediator concentrations during an insulator approach. Panel A is Pe ) 0.01, which behaves like steady-state conditions. Panel B is Pe ) 5. The arrows represent total flux (diffusion + convection). Under high Pe conditions, flow is outward and governed by convection, whereas for low Pe values, diffusional flux dominates.

parabolic flow observed between the moving electrode and the insulating substrate in the SECM model agrees very well with the analytical expression at radial distances away from the UME edge (Figures S3 and S4). Close to the electrode edge, the maximum velocity deviates from the analytical expression by 5%. In this region, the influence of flow in the axial direction cannot be ignored as it is in the 1-D solution. During an approach curve experiment, a UME will induce shear stress, τ, on the substrate (eq 16)

τ ) ηγ˘ ) -η

3rν d2

(16)

The inverse square relationship between shear and tip/ substrate gap suggests that even at modest tip velocities, an appreciable force may be applied to the substrate when the gap is small. This phenomenon should be taken into consideration when conducting SECM measurements over fragile substrates such as membranes or liquid/liquid interfaces, which may be susceptible to shearing damage. Consider a typical UME with a radius of 5 µm and RG of 5 approaching a surface at 1 µm/s. At a tip/substrate gap of 500 nm (L ) 0.1), the shear rate at the UME edge is on the order of 300 s-1. Shear rates as low as 1 s-1 have been shown to perturb the shape of giant unilamellar vesicles,28 so deformation of liposomes or cells during an approach curve is feasible. With a theoretical model in hand, insulator approach curves of ferrocene in ChCl/TFA with tip velocities ranging from 1 to 10 µm/s using a 5 µm radius electrode were simulated (Figure 7). Solid lines in Figure 7 represent the experimental data and the squares represent the best fit, where the value of Pe was used as an adjustable parameter. Because Pe is proportional to tip velocity, a plot of Pe versus ν should be linear with a slope of a/D and an intercept of zero. The TFA DES approach curves clearly do not obey this relationship (Figure 8, upper graph). Since the electrode radius is fixed and the tip velocity is welldefined by SECM instrumentation, the observed decrease in Pe with increasing tip velocity could be explained by an apparent increase in the diffusion coefficient. While further studies are necessary to support this argument, we propose that the changes in observed diffusion coefficient are suggestive of DES behaving as a non-Newtonian fluid.

Figure 7. Experimental (solid lines) and simulated (squares) approach curves of 15 mM ferrocene in ChCl/TFA DES.

Few studies on the rheological properties of ionic liquids are available in the literature, and none pertain directly to solvents that would qualify as deep eutectics; therefore, any discussion of DES rheology is at this point speculative. Deep eutectics likely possess long-range order as do ionic liquids,29 and recent reports have shown that transport properties in deep eutectics can be explained using hole theory,30,10 where ionic mobility is governed by the availability of voids within the solvent that are of suitable dimensions to allow motion. Pure ionic liquids appear to behave as Newtonian fluids; however, they take on both shear thinning and thickening properties in the presence of solutes.31,32 A shear thinning fluid would exhibit a decrease in viscosity with an increase in external force, which in the SECM experiment would be supplied by the UME and the substrate, with higher tip velocities resulting in lower viscosities at the UME/liquid interface. Because solute diffusivity and solvent viscosity are inversely proportional, it is reasonable to expect the diffusion coefficient to increase with increasing tip velocity for a non-Newtonian, shear thinning fluid. The simplest empirical model for describing the viscosity of a non-Newtonian fluid is the power law (eq 17)

η ) mγ˘ n-1

(17)

where m and n are parameters characteristic of the fluid. Given the analytical expression for shear rate (see eq 16) for this geometry, the definition of Pe, and the Stokes-Einstein

Electrochemistry in Deep Eutectic Solvents

J. Phys. Chem. B, Vol. 111, No. 46, 2007 13277 SECM theory can be used to simulate approach curves. In the regime 1.75 < Pe < 5, the peak observed in an insulating approach curve can be diagnostic of the tip/substrate gap. Simulations of insulator approach curves in ChCl/TFA DES with ferrocene as the mediator suggest that the diffusion coefficient of the solute increases with increasing tip velocity. These results suggest that SECM may provide some insight into the nonNewtonian behavior of viscous electrolytes. Acknowledgment. This research was supported by the ACS Petroleum Research Fund (44483-GB3) and the NIH (R25 GM059218). R.J.L. thanks Sam Bowen for many helpful discussions. Supporting Information Available: Derivation of the equations for compressed-disk-induced fluid flow and eq 18, COMSOL script, and chronoamperometric data. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 8. Pe vs tip velocity relationships. Upper graph: triangles are theoretical values for a diffusion coefficient of 2.7 × 10-8 cm2 s-1. Circles are taken from the best fits in Figure 7. Lower graph: log-log plot of Pe vs tip velocity is linear, which suggests that DES behaves as a non-Newtonian fluid.

equation, a relationship between Pe and tip velocity for a nonNewtonian fluid can be developed (eq 18)

log(Pe) ) n log(ν) + log

(

() )

4πR°man 3 kbT d2

n-1

(18)

where kb is Boltzmann’s constant, T is temperature, and R° is the solute effective radius. A log-log plot of the apparent Pe obtained from the fit of the approach curves in Figure 7 versus tip velocity is linear (R2 ) 0.999) with a slope of 0.495 and an intercept of 6.95 (Figure 8, lower graph). The value of n obtained from this analysis is in agreement with a shear thinning fluid, which should have n < 1. It is recognized that eq 18 should be used with caution since the tip/substrate gap, d, appears in the intercept term. Because the shear rate changes throughout an approach curve, the solvent viscosity and therefore solute diffusion coefficient should not be constant during the experiment. Extracting a steady-state diffusion coefficient from a Pedependent approach curve would require a means to accurately account for the changing solvent viscosity in the vicinity of the UME. Conclusion The modest viscosity of DES makes electrochemistry in this media challenging since electrochemical measurements at UMEs fall into a mixed-diffusion regime. Nevertheless, with the aid of a sophisticated mathematical package, it is possible to simulate experimental observations. Ferrocene is soluble in a 1:2 ChCl/TFA DES and with a diffusion coefficient of 2.7 × 10-8 cm2 s-1 displays peak-shaped voltammograms at a 5 µm radius UME at scan rates as low as 0.1 V/s. SECM approach curves to an insulating substrate in this medium show tip velocity dependency and positive-feedback-like behavior that can be explained in terms of Pe, the ratio of the convection and diffusion timescales. When diffusion dominates mass transport (Pe e 0.01), the steady-state assumption is valid, and traditional

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