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Microelectrochemical Measurements at Expanding Droplets (MEMED): Mass-Transport Characterization and Assessment of Amperometric and Potentiometric Electrodes as Concentration Boundary Layer Probes of Liquid/Liquid Interfaces Christopher J. Slevin and Patrick R. Unwin* Department of Chemistry, University of Warwick, Coventry CV4 7AL, U.K. Received March 22, 1999. In Final Form: June 9, 1999 Microelectrochemical measurements at expanding droplets (MEMED) is a new technique for studying the kinetics of reactions that occur spontaneously at the interface between two immiscible liquids. The idea is to create the interface in a well-defined manner by forming a droplet of one (feeder) liquid, by slowly flowing that phase through a tiny (100-µm-diameter) nozzle submerged in the second (receptor) phase. The interfacial reaction is investigated using an ultramicroelectrode (UME) positioned directly opposite the orifice from which the droplet expands. The UME measures directly the concentration profiles that develop at the expanding droplet due to the interfacial process. Both amperometric and potentiometric electrodes are shown to be suitable boundary layer probes. In the case of amperometric detection, the optimal spatial and temporal response is obtained by deploying the smallest possible electrodes, with characteristic dimensions (radii) of 0.5 µm or less. Both modes of detection are proven in studies of bromine transfer across an aqueous/1,2-dichloroethane (DCE) interface. These studies, together with investigations of electron transfer between ferrocene in a DCE phase and hexachloroiridium(IV) in an aqueous phase, allow the nature of mass transport in the MEMED configuration to be determined unequivocally. Mass transport is very well-defined in terms of convective diffusion to a symmetrically expanding sphere, although a moving plane model also provides a good description. The well-defined and variable mass-transport regime, coupled with the renewable nature of the interface, makes MEMED a useful technique for investigating liquid/liquid interfacial kinetics. First-order rate constants up to 10-2 cm s-1 should be easily measurable.
Introduction Many processes of fundamental,1 industrial,2 and biological3 significance occur at the interface between two immiscible liquids. An important requirement for developing an understanding of this important range of processes is the ability to precisely determine the underlying kinetics and mechanisms. There has been spectacular recent progress in the study of charge-transfer processes at liquid/liquid interfaces through the introduction of polarized interfaces of micrometer dimensions4 and various scanning electrochemical microscopy (SECM) techniques.5-8 Some of the latter methods can also be used to study the interfacial transfer of neutral molecules.7,8 However, there is a whole class of liquid/liquid interfacial reactions, of widespread significance, that occur sponta* Corresponding author. (1) (a) Benjamin, I. Chem. Rev. 1996, 96, 1449. (b) Adamson, A. W. Physical Chemistry of Surfaces; Wiley: New York, 1997. (2) (a) Hanna, G. J.; Noble, R. D. Chem. Rev. 1985, 85, 583. (b) Danesi, P. R.; Chiarizia, R. CRC Crit. Rev. Anal. Chem. 1980, 10, 1. (c) Atherton, J. H. Res. Chem. Kinet. 1994, 2, 193. (3) (a) Volkov, A. G.; Deamer, D. W.; Tanelian, D. L.; Markin, V. S. Liquid Interfaces in Chemistry and Biology; Wiley: New York, 1998. (b) Gennis, R. B. Biomembranes: Molecular Structure and Function; Springer-Verlag: New York, 1989. (4) (a) Taylor, G.; Girault, H. H. J. J. Electroanal. Chem. 1986, 208, 179. (b) Stewart, A. A.; Taylor, G.; Girault, H. H.; McAleer, J. J. Electroanal. Chem. 1990, 296, 491. (c) Stewart, A. A.; Shao, Y.; Pereira, C. M.; Girault, H. H. J. Electroanal. Chem. 1991, 305, 135. (d) Shao, Y.; Osborne, M. D.; Girault, H. H. J. Electroanal. Chem. 1991, 318, 101. (e) Beattie, P. D.; Delay, A.; Girault, H. H. J. Electroanal. Chem. 1995, 380, 167. (f) Shao, Y.; Mirkin, M. J. Am. Chem. Soc. 1997, 119, 8103. (g) Beattie, P. D.; Delay, A.; Girault, H. H. Electrochim. Acta 1995, 40, 2961. (h) Murtoma¨ki, L.; Kontturi, K. J. Electroanal. Chem. 1998, 449, 225. (i) Osborne, M. C.; Shao, Y.; Pereira, C. M.; Girault, H. H. J. Electroanal. Chem. 1994, 364, 155. (j) Cunnane, V. J.; Schiffrin, D. J.; Williams, D. E. Electrochim. Acta 1995, 40, 2943.
neously on contact between the two liquid phases, which cannot be readily studied by these methods. Such processes have proved challenging to study, typically because welldefined mass-transport regimes are difficult to establish.9 In this paper, we describe a new technique for studying general chemical reactions at liquid/liquid interfaces that is applicable to both electrochemical and nonelectrochemical processes. A number of techniques have been proposed for measuring the kinetics of spontaneous reactions at liquid/ liquid interfaces. These approaches were discussed in a review,2a covering the literature up to 1984, which highlighted that “there are many methods presently in (5) For reviews, see, for example: (a) Bard, A. J.; Fan, F.-R. F.; Mirkin, M. V. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 18. (b) Bard, A. J.; Fan, F.-R. F.; Pierce, D. T.; Unwin, P. R.; Wipf, D. O.; Zhou, F. Science 1991, 254, 68. (c) Arca, M.; Bard, A. J.; Horrocks, B. R.; Richards, T. C.; Triechel, D. A. Analyst 1994, 119, 719. (d) Unwin, P. R.; Macpherson, J. V. Chem. Ind. 1995, 21, 874. (e) Mirkin, M. V. Anal. Chem. 1996, 68, 177A. (f) Barker, A. L.; Gonsalves, M.; Macpherson, J. V.; Slevin, C. J.; Unwin, P. R. Anal. Chim. Acta, in press. (6) (a) Wei, C.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1995, 99, 16033. (b) Solomon, T.; Bard, A. J. J. Phys. Chem. 1995, 99, 17487. (c) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1996, 100, 17881. (d) Selzer, Y.; Mandler, D. J. Electroanal. Chem. 1996, 409, 15. (e) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Am. Chem. Soc. 1997, 119, 10785. (f) Delville, M. H.; Tsionsky, M.; Bard, A. J. Langmuir 1998, 14, 2774. (g) Shao, Y. H.; Mirkin, M. V.; Rusling, J. F. J. Phys. Chem. B 1997, 101, 3202. (7) (a) Slevin, C. J.; Atherton, J. A.; Umbers, J.; Unwin, P. R. J. Chem. Soc., Faraday Trans. 1996, 96, 5177. (b) Barker, A. L.; Macpherson, J. V.; Slevin, C. J.; Unwin, P. R. J. Phys. Chem. B 1998, 102, 1586. (c) Yamada, H.; Akiyama, S.; Inoue, T.; Koike, T.; Matsue, T.; Uchida, I. Chem. Lett. 1998, 147. (8) Slevin, C. J.; Macpherson, J. V.; Unwin, P. R. J. Phys. Chem. B 1997, 101, 10851. (9) Unwin, P. R. J. Chem. Soc., Faraday Trans. 1998, 94, 3183.
10.1021/la990337i CCC: $18.00 © 1999 American Chemical Society Published on Web 08/14/1999
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use, but all...have various drawbacks”. In addition, a recent survey2c concluded that for many studies in this area “the experimental design and interpretation is unsatisfactory.” The general criteria for an experimental investigation of the kinetics of reactions at liquid/liquid interfaces may be summarized as follows: a known interfacial area and well-defined interfacial contact are essential; controlled, variable, and calculable mass-transport rates are required to allow the mass-transfer and interfacial kinetic contributions to the overall rate to be quantified; direct interfacial contact is preferred, since the use of a membrane to support the interface adds further resistances to the overall rate of the reaction;10 a renewable interface is useful, as the accumulation of products at the interface is possible; ideally, measurements must be made at the shortest times following contact; it is also clear that direct measurements of reactive fluxes at the interface of interest are desirable. This latter attribute is inherent in the electrochemical techniques discussed above (with the current flow giving a direct measure of interfacial flux) but is more difficult to achieve when reactions occur spontaneously. In fact, this is a widely encountered problem in most of the techniques that have been used to study spontaneous processes at liquid/liquid interfaces.2 We describe here the details of a new approach, which significantly expands on work reported in a recent preliminary communication,11 for measuring reaction rates at liquid/liquid interfaces using ultramicroelectrodes (UMEs). Termed microelectrochemical measurements at expanding droplets (MEMED), the technique meets all of the criteria listed above and overcomes many problems inherent in previous approaches. In MEMED, liquid/liquid contact is established by forming drops of one liquid from a capillary submerged in a second immiscible liquid. The feeder solution, typically comprising an organic solvent, flows into the aqueous receptor solution at a constant rate, such that drops form at the capillary tip, grow, and eventually detach, periodically in a well-defined manner. This approach is similar to the dropping mercury electrode (DME)12 and electrolyte dropping electrode13 and conveys the same advantage in terms of providing a constantly renewable, clean interface. In MEMED, the interfacial reaction is monitored with a stationary UME, positioned directly beneath or above (depending on the relative densities of the two liquids) the expanding drop. The electrode operates in either an amperometric or potentiometric mode, to measure local changes in concentration in the receptor phase, at the probe tip, as the drop approaches the electrode. The probe penetrates and measures directly the developing concentration profile at the drop surface in the receptor phase, due to the two-phase reaction. By solving the convectivediffusion equation appropriate to this particular configuration, with appropriate boundary conditions, theoretical concentration profiles can be generated for comparison with experiment. In this way, the nature of the mass (10) (a) Albery, W. J.; Burke, J. F.; Leffler, E. B.; Hadgraft, J. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1618. (b) Leahy, D. E.; Wait, A. R. J. Pharm. Sci. 1986, 75, 1157. (11) Slevin, C. J.; Unwin, P. R. Langmuir 1997, 13, 4799. (12) Heyrovsky, J. Chem. Listy 1922, 16, 256. (13) (a) Koryta, J.; Vany´sek, P.; Brezina, M. J. Electroanal. Chem. 1976, 67, 263. (b) Samec, Z.; Marecek, V.; Weber, J.; Homolka, D. J. Electroanal. Chem. 1979, 99, 385. (c) Wang, E.; Sun, Z. Trends Anal. Chem. 1988, 7, 99. (d) Kihara, S.; Suzuki, M.; Maeda, K.; Ogura, K.; Umetani, S.; Matsui, M.; Yoshida, Z. Anal. Chem. 1986, 58, 2954. (e) Marecek, V.; Samec, Z. Anal. Chim. Acta 1983, 151, 265. (f) Kihara, S.; Suzuki, M.; Maeda, K.; Ogura, K.; Matsui, M.; Yoshida, Z. J. Electroanal. Chem. 1989, 271, 107. (g) Allen, R. M.; Williams, D. E. Faraday Discuss. 1996, 104, 281. (h) Williams, D. E. Private communication (unpublished work).
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transport and the interfacial reaction can be investigated quantitatively. A key strength of the technique is that the electrode measures directly the concentration profile of a target species involved in the reaction at the interface, i.e., the distribution of a product or reactant, on the receptor phase side. The shape of this concentration profile is sensitive to the mass-transport characteristics for the growing drop and to the interfacial reaction kinetics. In a previous communication,11 we studied the hydrolysis of triphenylmethyl chloride, dissolved in 1,2dichloroethane (DCE), at the DCE drop/aqueous solution interface using MEMED with a relatively large (50-µmdiameter disk) potentiometric electrode. In that initial study, we assumed that mass transport to the drop was described by a convective-diffusion expression consistent with a symmetrically expanding spherical geometry. Here we characterize the mass-transport regime more thoroughly by carefully selecting reactions for study that are transport-controlled and using the data to assess several mass-transport models. Additionally in this study, we evaluate the probe response in modeling nonreacting systems and assess the conditions under which amperometric probes, as well as the potentiometric probes used previously, may be employed. The methods and simulations are examined through studies on two model systems. First, the transfer of bromine from aqueous solutions to DCE, driven by the enhanced solubility of bromine in the organic solvent, is measured by probing the bromine concentration profile using a 1-µm-diameter Pt UME probe operating in either an amperometric or potentiometric mode. This process is predicted to be mass-transport-controlled, under the MEMED conditions,8 and the ability to measure bromine concentrations both amperometrically and potentiometrically (with Br- present) enables both of these methods to be compared on the same system, as well as allowing the nature of mass transport to be identified. Second, the bimolecular redox reaction between ferrocene (Fc) in a DCE drop and hexachloroiridium(IV) (IrCl62-) in the aqueous receptor phase is studied. In this example, the reactants are confined in separate phases, and electron transfer occurs at the interface. The probe electrode is used to measure both the reactant (IrCl62-) and product (IrCl63-) distributions. The amperometric electrode probe used for these measurements was of nanometer dimensions, termed a “nanode”.14 The advantages of this type of probe for MEMED studies will be discussed. Theory Mass transfer to an expanding droplet has been considered previously for the DME15 arrangement and other growing liquid drop techniques.16 At a simple level, convective diffusion to a growing drop may be described by the following equation, which is based on a symmetrically expanding sphere geometry: (14) Penner, R. M.; Heben, M. J.; Longin, T. L., Lewis, N. S. Science 1990, 250, 1118. (15) (a) Levich, V. G. Physicochemical Hydrodynamics; PrenticeHall: Englewood Cliffs, NJ, 1962. (b) Britz, D. Digital Simulation in Electrochemistry, 2nd ed.; Springer-Verlag: New York, 1988. (c) Pons, S.; Speiser, B.; McAleer, J. F.; Schmidt, P. P. Electrochim. Acta 1982, 27, 1711. (16) (a) Popovich, A. T.; Jervis, R. E.; Trass, O. Chem. Eng. Sci. 1964, 19, 357. (b) Bauer, G. L. Solvent Extraction of Copper: Kinetic and Equilibrium Studies, Ph.D. Thesis, University of Wisconsin, Madison, 1975.
Microelectrochemical Measurements at Expanding Droplets
(
)
∂ci ∂2ci 2 ∂ci ∂ci + - νr ) Di 2 ∂t r ∂r ∂r ∂r
(1)
In eq 1, Di and ci are the diffusion coefficient and concentration of the species, i, of interest in the receptor phase, respectively, and r is the spherical coordinate starting at the center of the drop. The variable νr represents the convective velocity due to the moving surface of the expanding drop and is given by
(
)
q 1 1 νr ) 4π r2 r 2 0
(2)
where q is the volume flow rate and r0 is the (timedependent) drop radius. This equation assumes that the drop behaves as a symmetrically expanding sphere, i.e., that the drop expands from a fixed center. While this is not the case for a droplet growing from a capillary, since the center of the drop moves, it will be shown to be a reasonable approximation to the real system at the relatively slow flow rates employed. A second approach is to assume that the drop surface approaching the electrode is a moving plane. This is appropriate since the diffusion layer is almost always considerably smaller than the size of the drop under practical conditions (vide infra). To a good approximation, the convective effect close to the moving front is then calculated based on velocities that are twice those determined from eq 2, in order to account for the moving center of the drop. The center of the drop must move away from the capillary at a rate equal to the movement of the surface of the drop in the expanding sphere treatment, and therefore, at a point directly opposite the capillary, the rate of movement of the drop surface is 2νr. The convective-diffusion equation which describes this case is given by
∂2ci ∂ci ∂ci ) Di 2 - 2νr ∂t ∂r ∂r
(3)
A linear approximation for the velocity term, which was used to treat the DME problem,15b does not work for MEMED, because the concentration boundary layers tend to be much larger for MEMED due to the longer drop times employed. The diffusion-only case was also simulated by eliminating the second, convective, term on the right hand side of eq 3. The presence of the capillary is ignored in the simulation since, for most of its lifetime, the dimensions of the drop are much larger than the capillary diameter. Moreover, the capillary is not expected to influence measurements that are made (in a micrometer region) at the opposite side of the drop given the time scale of the measurements. Depletion or accumulation inside the drop was not treated for two reasons. First, the probe was generally positioned close to the portion of the drop where the surface was constantly renewed. Internal streamlines in a drop expanding from a capillary have been investigated experimentally,17 and from these observations, it is suggested that fresh material may be carried from the capillary to the front face of the drop, directly opposite the capillary. Second, for the systems studied, the concentrations of reactants were chosen such that neither depletion nor accumulation inside the droplet was important. (17) (a) Clift, R.; Grace, J. R.; Webber, M. E. Bubbles, Drops and Particles; Academic Press: New York, 1978. (b) Guha, D. K.; Vyarawalla, F.; De, F. Can. J. Chem. Eng. 1987, 65, 448.
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Equations 1 and 3 are readily cast into dimensionless form using the following terms:15b
R)
r
xDitd
(4)
τ)
t td
(5)
Ci )
ci ci*
(6)
Vr ) ν r
x
td Di
(7)
where ci*, used to calculate the normalized concentration for species i, is typically the initial or bulk concentration of the reactant in the receptor solution but may be the concentration at the surface of the drop (for processes involving transport-limited transfer from the drop to the receptor phase). The variable td is the total drop time from the beginning of growth to the point of contact with the electrode. The resulting normalized equations are, for the expanding sphere (eq 8) and the moving plane (eq 9) models,
∂Ci ∂Ci ∂2Ci 2 ∂Ci ) - Vr + 2 ∂τ R ∂R ∂R ∂R
(8)
∂Ci ∂Ci ∂2Ci ) - 2Vr 2 ∂τ ∂R ∂R
(9)
These were solved numerically, using the simple explicit method,15b in normalized time with suitable boundary conditions, appropriate to the problem of interest, at the drop surface and at a semiinfinite distance from the drop. We employed a uniform grid, with one boundary fixed at the drop surface, while the other was situated at a distance, rf, from the moving drop surface in the radial direction, where rf was the same magnitude as the final drop radius. Within the simulation, the number of points in the r direction, nr, was 1000, resulting in a step size, ∆r, of rf/1000. This corresponded to 0.5 µm for a typical drop radius of 0.5 mm. If normalized values are used, then for typical values of Di ) 5 × 10-6 cm2 s-1 and td ) 5 s, ∆R ) 0.01 for 0 e R e 10. These parameters were found to be sufficient to obtain converged concentration distributions, confirmed by the fact that employing either half the number of points or a domain twice as large gave identical solutions for the cases considered. The time step, ∆τ, was chosen such that the requirement for a stable simulation, ∆τ/∆R2 e 0.5,15b was obeyed. The time step was calculated from ∆τ ) 0.3∆R2 and was of the order of 3 × 10-5, which corresponds typically to a step size of 0.15 ms. This model enabled the simulation of the concentration vs radial distance profile as it developed with time, from which the time-dependent concentration vs distance profile, observed at the probe, could be extracted. Experimental Section Solutions. All aqueous solutions were prepared using MilliQ-reagent water (Millipore Corp., resistivity g 18 MΩ cm). The organic phase was DCE (99.8%, HPLC grade, Sigma-Aldrich, Gillingham). Aqueous ferrocyanide solutions contained 1 × 10-2 mol dm-3 potassium ferrocyanide trihydrate (A.R., Fisher), with 0.5 mol
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Slevin and Unwin U.K.). All connectors and three-way taps were of PTFE construction (Omnifit Ltd.). The syringe pump flow system was filled from a reservoir, and air bubbles were completely eliminated from the system to ensure constant flow rates. The video camera enabled the measurement of the electrode-capillary separation, as well as observation of the motion and shape of the droplet; typical values for the drop time and drop diameter at contact were 1-20 s and 1 mm, respectively. These values were commensurate with the spatial and temporal resolution of the microscopy system employed to visualize the drop growth process. Drops with smaller final size and shorter lifetimes would be examinable with enhanced microscopy capabilities. Continued reaction in the base of the cell, due to the collection of drops, was not a problem as the measurements are made directly at the drop surface. Any background buildup or depletion could be accounted for in the simulation, and if it became too great, it was simple and quick to replace the receptor phase. Probe Construction. Pt UMEs (1- and 2-µm Diameter). Glass-coated UMEs of radius a ) 0.5 or 1 µm were constructed according to a documented procedure.18 Electrodes were characterized by a particular RG value, where
RG ) Figure 1. Schematic illustration of the experimental arrangement for MEMED. dm-3 potassium chloride (A.R., Fisher) as supporting electrolyte. Aqueous bromine solutions had two different compositions. For amperometric detection, the aqueous solution contained 5 × 10-3 mol dm-3 Br2 (99.99%, Sigma-Aldrich), 5 × 10-4 mol dm-3 H2SO4 (A.R., 1.84 g cm-3, Sigma-Aldrich), and 0.1 mol dm-3 KNO3 (A.R., Fisher). For potentiometry, potassium bromide (A.R., Fisher) was also added at a concentration of 1 × 10-3 mol dm-3, as the other half of the Br2/Br- redox couple. Ferrocene solutions consisted of 5 × 10-2 mol dm-3 ferrocene (98%, Sigma-Aldrich) in DCE, with 0.02 mol dm-3 tetra-n-hexylammonium perchlorate (THAClO4) (Alfa, Royston, Hertfordshire, U.K.) added. The iridium(IV) aqueous phase contained 4 × 10-3 mol dm-3 sodium hexachloroiridate(IV) hexahydrate (99%, Strem), with 1 mol dm-3 sodium perchlorate hydrate (99.99%, Sigma-Aldrich) added. The solution for etching Pt wires was saturated sodium nitrite (97%, Sigma-Aldrich). MEMED Apparatus. A schematic diagram of the setup for measurements at an expanding drop comprising a liquid that is more dense than the receptor phase is given in Figure 1. When the drop is less dense than the receptor phase, the positions of the electrode and capillary are simply reversed. The cell used was fully detachable, comprising a PTFE base with a 2-mm-diameter hole drilled vertically through in the center to enable the electrode or capillary to be inserted into the cell. PTFE tape wound around the electrode or capillary prior to insertion ensured no leaks. The cell was fixed in position by inserting it into a metal mounting plate and then bolting the plate to a marble block. Mounting posts were used to raise the level of the mounting plate. The relative positions of the capillary and the probe were controlled using x, y, and z direction translators (Newport Corp., Fountain Valley, CA; 2 × M-421-M, 1 × M-431-M, and an M-360-90 L-piece mount were combined. The z axis actuator was an SM50 micrometer, and SM25 actuators were used for the x and y axes). The diameter of the cell was 40 mm, the depth was 50 mm, and an optically flat window (30-mm diameter) was incorporated in the side to facilitate video microscopy, which was described previously.11 The diameter of the drop at the contact point was controlled by initially setting the desired distance between electrode and capillary. The drop time, from the beginning of growth to the contact time, is dictated by this distance and the flow rate, which was controlled using a syringe pump (Model KD100, C-P Instruments, Bishop’s Stortford, U.K.) fitted with a 500-µL syringe (Hamilton Co., Gas Tight, Reno, NV), which allowed flow rates in the range 4-6360 µL h-1 to be employed. Connection of the syringe to the capillary was via PTFE tubing, 3.2-mm outer diameter, 1.5-mm inner diameter (Omnifit Ltd., Cambridge,
rglass a
(10)
In eq 10, rglass is the overall radius of the tip of the electrode including the insulating glass sheath. Final polishing of the electrode using 0.05-µm alumina (Buehler, Coventry, U.K.) on a wet polishing cloth (Kemet, Maidstone, U.K.) yielded smooth electrode surfaces. The RG value and smoothness were determined by optical microscopy using an Olympus BH2 light microscope, equipped with Nomarski differential contrast objectives (overall magnification ×50 to ×1000). Electrodes were polished with 0.05-µm alumina, before each use, to remove any contaminants. Nanodes. Nanodes were constructed using the following procedures. First, a 25-µm diameter platinum wire was attached by soldering it to a solid core tinned copper connecting wire. This assembly was then inserted into a glass capillary which had been pulled to a fine point, by a previously described procedure,11 such that approximately 3-5 mm of the microwire protruded from the tip of the capillary. The tip of the capillary was then heated in the center of a home-built heating coil to seal the glass around the wire, leaving only the tip of the wire exposed to the solution. The tip of this wire was then etched to a sharp point using the procedure advocated elsewhere.19 In order to achieve a tiny exposed electrode area, the etched wire was coated with an insulating material, which left only the very tip uncoated. The coating was deposited on the platinum surface electrochemically, using a cathodically depositing paint20 (PPG powercron 641 lead-free paint, paste P982201:resin T3992C8480 ratio 1:5, with 1% butyl glycol and 0.4% phenoxypropanol, kindly supplied by ANCA Electrocoat, Warwick, U.K.). The paint was deposited at -5 V for 150 s, the insulating procedure being completed by curing in an oven at 200 °C for 180 s. This procedure resulted in a coating that contracted from the tip of the electrode, consistently leaving a small exposed area of nanometer to micrometer dimensions. Capillaries. Capillaries were of pulled borosilicate glass construction, identical to those used to fabricate electrodes. In order to achieve a flat end, the pulled capillaries were initially cut by hand using a hand-held blade. This resulted in capillaries of approximately the required internal diameter, typically 100 µm. Final polishing was carried out using a home-built polishing wheel. A computer hard-drive unit was employed, providing a flat rotating surface to which diamond impregnated polishing pads (6-µm grade, Buehler) could be attached. The capillary was positioned normal to the polishing surface using x,y,z positioning stages (Newport Corp., Model M-461-xyz-M, with AJS screws on (18) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 15, p 267. (19) Lee, Y. H.; Tsao, G. T.; Wankat, P. C. Ind. Eng. Chem. Fundam. 1978, 17, 59. (20) (a) Pierce, P. J. Coatings Technol. 1981, 53, 52. (b) Boyd, D.; Zwack, R. Prog. Org. Coat. 1996, 27, 25.
Microelectrochemical Measurements at Expanding Droplets the x and y axes, and a DM13 differential micrometer controlling the z axis). The latter actuator allowed the capillary end to be lowered carefully onto the surface for polishing until flat. Electrochemical Measurements. Amperometric UME measurements generally employed a two-electrode setup, with a silver wire (Goodfellow) operating as a quasi-reference electrode (AgQRE). The potential was controlled using a purpose-built triangular wave/pulse generator (Colburn Instruments, Coventry). The current was measured using a home-built current follower (gains 10-5-10-9 A/V) or a Cypress Systems (Lawrence, KS) Model EI-400 bipotentiostat. Current-potential and current-time data were recorded directly by a PC, through a data acquisition card (NI-DAQ Lab PC+ card, National Instruments, Austin, TX). Software was written in QuickBasic 4.5 (Microsoft) in-house. Potentiometric responses were measured with the Pt UME serving as a redox indicator electrode and a saturated calomel electrode (SCE) as the reference. Data were acquired with the system described above, with a home-built high-input impedance voltage follower. Current-time or potential-time transients and video images were simultaneously recorded during drop growth.
Results and Discussion Characterization of the UME Probe Responses. Potentiometry was employed in preliminary MEMED studies, reported earlier, and its use as a passive concentration probe is relatively straightforward, with the potential governed by the concentrations of the potential determining species in solution (ideally dictated by the Nernst equation). The response of an amperometric electrode, in contrast, depends on the flux of the target species at the electrode as indicated by
i ) nFAji
(11)
where A is the electrode area and ji is the mean flux of species i at the electrode surface. Equation 12 relates the steady-state diffusion-limited current, i, at a microdiskshaped UME, of radius a, to the diffusion coefficient and concentration of the mediator, when the flux of material is by diffusion only.21
i ) 4nFDiaci*
(12)
In the MEMED configuration, the moving droplet may perturb the diffusive flux at the UME probe in two ways. First, the drop may be moving so rapidly that the diffusion layer of the UME cannot respond to those changes rapidly enough so that steady-state diffusion is not achieved. The diffusional relaxation time, tdiff, may be estimated from
tdiff )
(13)
where δ is the size of the diffusion layer. For a disk-shaped UME, the mean diffusion layer thickness, δ, is of similar dimension to the electrode radius:21
δ ) πa/4
(14)
Second, the moving drop surface may generate convective flow in the solution, adjacent to the electrode, which may add to the flux of material by diffusion, thus increasing the observed current. Additionally, amperometric measurements may cause depletion of the measured species, due to electrolysis at the electrode surface. The effect would be to distort the concentration boundary layer adjacent to the droplet, and indeed this may influence the interfacial reaction itself. (21) Saito, Y Rev. Polarogr. Jpn. 1968, 15, 177.
Figure 2. Hemispherical and hindered diffusion regimes expected at an amperometric probe UME for different dropelectrode separations, d.
For amperometric detection, it was first necessary to investigate the effect, on the current response, of the moving drop surface adjacent to the electrode. The simplest scenario is that transient perturbations to the diffusion field and convective effects due to the drop motion are negligible so that local mass transport to the UME is by steady-state diffusion only, in which case eq 12 would provide a route to local concentrations. In order to achieve this desired response, a small electrode, for which the diffusional relaxation time is fast compared to the rate of movement of the drop and for which diffusion would be rapid compared to convection, is mandatory. To test this premise, the transport-limited current for the oxidation of aqueous ferrocyanide (receptor phase) was measured as a function of drop-electrode separation for growing drops of DCE, with the UME positioned beneath the drop. The electrode was biased at a potential of 0.7 V vs AgQRE to effect the transport-limited oxidation of ferrocyanide to ferricyanide. This type of experiment is similar to SECM approach curve measurements;22 however, in this case, instead of scanning the electrode toward an interface, the interface is mobile while the electrode remains stationary. Figure 2 illustrates the two expected limiting mass-transport regimes, namely, hemispherical and hindered diffusion (at large and small dropelectrode separations, respectively), which the electrode should display in the case of true steady-state diffusion.22 The transport-limited current responses of 25- and 2-µm diameter Pt UMEs are shown in Figure 3. The current data have been normalized with respect to the steadystate current measured in the bulk of a quiescent solution, i(∞), while the electrode-interface separation, d, may be calculated as a function of time for a symmetrically expanding droplet from
( ())
d ) df 1 -
2
δ Di
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t td
1/3
(15)
where df is the final droplet diameter at the contact time t ) td. The validity of this equation was verified by examining video recordings of drop position vs time for a range of expanding droplets. The spherical geometry of the drop, the dimensions of which were determined with an accuracy equivalent to less than 1% of the final drop size, was confirmed by these measurements. The separation, d, calculated from the experimentally measured parameters should therefore be accurate to within 1%. In this experiment, the current depends only on the transport of ferrocyanide to the probe electrode. There is no chemical reaction at the drop surface so that any deviation in the current-distance response from that expected for approach to an inert interface under steadystate diffusion conditions22 must be due to perturbation of the mass transport, caused by the approaching drop. (22) Kwak, J.; Bard, A. J. Anal. Chem. 1989, 61, 1221.
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Figure 3. Normalized current vs electrode-drop distance plot for ferrocyanide oxidation at (a-c) a 2-µm-diameter and (d) a 25-µm-diameter UME mounted beneath a growing droplet of DCE. The drop times were (a) 14.0, (b) 10.5, (c) 3.8, and (d) 14 s. The solid line indicates the predicted distance dependence for conditions of steady-state diffusion of ferrocyanide with convection absent.22
The simplest theoretical treatment22 assumes that the interface is planar, which is reasonable given that the final diameter of the drop is ca. 1 mm, while the largest probe UMEs employed are characterized by micrometer dimensions. For a 2-µm-diameter disk electrode at long drop times (Figure 3a and b), the experimentally measured curves closely match the response for a UME approaching an inert (planar) interface with diffusion only controlling the current, indicating that a steady-state diffusion layer is maintained and that convection is negligible, even at close separations between the surfaces of the drop and the electrode. Even when higher flow rates and more rapidly moving drops are employed (Figure 3c), convective effects are minimal, and it is concluded that for all d > 5 µm, the current is close to i(∞) and thus directly proportional to the concentration, as described by eq 12. At closer distances, hindered diffusion plays a greater role, as evidenced by the smaller measured currents. In contrast, with a 25-µm-diameter electrode, the response is modified even with slow flow rates. This is attributable to a timeresponse effect, due to the relatively long relaxation times (eq 13) for diffusion as the electrode size increases. Additionally, in an SECM-type configuration where hindered diffusion is dominant (Figure 2), the diffusion lengths increase and so do the relaxation times. It should also be noted that convection at the electrode may contribute an increase to the current response, relative to that predicted. For distances up to 50 µm from the drop, the current is higher than predicted for steady-state diffusion. It is clear then that only very small, a e 1 µm, electrodes may be used for amperometric measurements. Another advantage of using particularly small electrodes is that depletion effects are minimized. There is expected to be very little perturbation to the concentration
profile adjacent to the drop, which will be demonstrated to extend over a distance approximately 2 orders of magnitude greater than the diffusion layer thickness at the probe (eq 14). Furthermore, with a tiny electrode, the effective volume of solution sampled is small, which results in an enhanced spatial resolution, in addition to the improved response times already discussed. Characterization of Mass Transport to an Expanding Drop. In order to determine the nature of convective diffusion at the drop, in the MEMED experimental arrangement, interfacial processes were chosen that were expected to proceed at a transport-controlled rate in this geometry. With no interfacial kinetic resistance, the response depends only on the transport step in the receptor phase (and feeder phase), and the masstransfer model proposed can therefore be tested. Transfer of Bromine at the Aqueous/DCE Interface. The transfer of bromine from aqueous sulfuric acid solutions to DCE was previously shown by SECM measurements to be a rapid process.8 An advantage of this system, for these MEMED experiments, was that the two electrochemical detection methods could be tested. For the bromine-transfer studies, the boundary condition reflecting mass-transport-controlled depletion of bromine at the DCE drop surface is as follows:
r ) r0:
cBr2 ) 0
(16)
The aqueous-phase concentration of Br2, cBr2, may be normalized by the initial concentration of bromine, cBr2*. The partition coefficient of Br2 in the aqueous/DCE system
Ke )
[Br2]aq [Br2]DCE
(17)
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is ca. 0.025, but since the solution close to the interface inside the drop is constantly replenished by convection and the transfer experiment is conducted with the DCE phase under sink conditions, an equilibrium distribution is never established, and the interfacial concentration of Br2 on the aqueous side will approach zero. At a semiinfinite distance from the drop surface, in the receptor phase, a no-flux boundary condition was used:
r ) r0 + rf:
DBr2
∂cBr2 ∂r
)0
(18)
The electrode used was a 1-µm-diameter Pt UME, coned such that the RG value (eq 10) was as small as possible (RG ≈ 5), to minimize possible physical perturbation to the developing concentration profile. For amperometric detection, the aqueous solution contained 5 × 10-3 mol dm-3 Br2, 5 × 10-4 mol dm-3 H2SO4, and 0.1 mol dm-3 KNO3. The electrode was biased to reduce bromine to bromide at a diffusion-controlled rate at the UME (0.7 V vs AgQRE). The current in the bulk of the solution gave a measure of the bulk phase concentration of Br2, cBr2*, and changes in the current with the probe in the diffusion layer of the drop were related to corresponding changes in concentration via eq 12. In the case of potentiometric detection, the bromine concentration was determined by measuring the potential at the indicator electrode, Eind/V, vs saturated calomel electrode (SCE). The Pt indicator UME was first calibrated to ensure a Nernstian response:
(19)
Figure 4. Current vs time behavior for bromine transfer to a DCE drop measured at a 1-µm-diameter Pt UME positioned beneath the drop. Images a-e indicate the relative positions of the capillary, drop, and UME and correspond to the points indicated on the transient.
where Eind is the measured potential of the indicator with respect to the reference electrode and E* is a constant. The electrode calibration demonstrated that the response was Nernstian (typical slope of 32 mV/log cBr2) for Br2 concentrations in the range 1 × 10-5 to 6 × 10-3 mol dm-3 with Br- at a fixed concentration of ca. 1 × 10-3 mol dm-3. The calibration procedure allowed E* to be determined. Raw experimental data for bromine transfer studied by amperometry are shown in Figure 4, for a typical example case. Also shown are video images, recorded at particular times during the transient, showing the positions of the capillary, drop, and electrode. The key stages in the transient are (a) detachment of the previous drop, (a-b) relaxation of the bulk concentration to the level of background (initial) concentrations as reflected by the diffusion-limited current, (b-c) bulk concentrations observed due to the drop-electrode distance being too great for the electrode to detect the interfacial concentration gradient adjacent to the drop, (c) interception of the concentration boundary layer at the drop by the UME, (c-d) decreasing current as the concentration of bromine decreases near the drop surface due to the interfacial transfer process, (d) the clearly defined contact point, and (e) the drop in contact with the electrode. Typical processed results, in the form of a plot of the concentration vs distance, d, from the drop surface (which is time-dependent), are displayed in Figure 5 for a range of drop times. The theoretical response is simulated for DBr2 ) 0.94 × 10-5 cm2 s-1 8,23 and with the boundary conditions defined above. For these particular cases, the concentration profile is seen to extend over a distance of
ca. 150 µm from the drop surface. Comparing the experimental data with the various theoretical responses indicates that both the moving plane and symmetrically expanding sphere models provide a good description of mass transfer, with the latter model perhaps yielding the best fits to the data. The wide discrepancy of the experimental from the diffusion-only simulation demonstrates the importance of including convective effects in the model. Good agreement between experiment and the two convective-diffusion models was found for drop times in the range 5-15 s. The nonperturbing nature of the 1-µm-diameter electrode used to study this system is also proven; high-resolution measurements of concentration profiles can be made with an amperometric electrode of this size. The experiments carried out using potentiometric detection yielded similar results to the amperometric method. The solution composition was similar to the amperometric case, except, as described above, 1 × 10-3 mol dm-3 KBr was added to the aqueous phase to ensure that the redox indicator electrode could function appropriately. The relatively low concentrations of Br2 and Br- employed ensured that the formation of Br3- could be neglected.23,24 A typical concentration transient obtained from potentiometric data is displayed in Figure 6. The key stages marked on this plot are as defined in Figure 4. When converted to the concentration profiles in Figure 7, the experimental results are seen to match the two convectivediffusion models well, for the greater part of the concentration profile, confirming that the 1-µm-diameter Pt
(23) Compton, R. G.; Stearn, G. M.; Unwin, P. R.; Barwise, A. J. J. Appl. Electrochem. 1988, 18, 657.
(24) Griffith, R. O.; McKeown, A; Winn, A. G. Trans. Faraday Soc. 1932, 28, 101.
Eind ) E* +
( )
cBr21/2 RT ln F cBr-
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Figure 5. Normalized concentration vs distance profile for bromine transfer to a DCE drop measured amperometrically at a 1-µm-diameter Pt UME (O). Drop times were (a) 4.07, (b) 7.03, (c) 10.54, and (d) 14.05 s. In each case, the solid lines indicate the theoretical response for, from upper to lower, the moving plane, expanding sphere, and diffusion-only models.
solution was employed in this study. The interest was not to study the kinetics but to characterize the technique with a process that would be effectively transportcontrolled under the experimental conditions. The interfacial redox reaction may be expressed by
Figure 6. Concentration-time behavior for bromine transfer measured potentiometrically. Positions a-e correspond to those described previously in Figure 4.
potentiometric electrode also responds well, with a sufficient resolution. Some deviation is observed close to the interface at all drop times. This deviation may be a problem associated with the electrode response time in the region ([Br2] f 0) where the [Br2]/[Br-] concentration ratio changes most significantly. Nonetheless, the potentiometric technique works well in reflecting the concentration profile up to ca. 10 µm from the interface. For finite kinetics, to which the technique will be applied in the future, the concentration changes close to the interface will, of course, be more gradual, and this mode of detection is expected to be better still. Bimolecular Interfacial Electron Transfer. Bimolecular interfacial electron transfer was investigated to expand the range of phase-transfer processes used to characterize mass transport. The oxidation of Fc (5 × 10-2 mol dm-3) in DCE by IrCl62- (4 × 10-3 mol dm-3) in aqueous
IrCl6(aq)2- + Fc(org) f IrCl6(aq)3- + Fc(org)+
(20)
Fc(org)+ h Fc(aq)+
(21)
The ferrocenium cation produced does partition into the aqueous phase6d,25,26 during this process (eq 21), but this is an unimportant detail for the purposes of this study. The suitability of nanometer-scale electrodes was investigated for these studies, due to the very high rates of diffusional mass transport (leading to rapid response times) and high spatial resolution that would result from such electrodes. For this system, it was possible to measure both the reactant, IrCl62-, and the product, IrCl63-, in the aqueous phase amperometrically, simply by changing the potential bias of the electrode. The UME potential was held at 0.4 V vs AgQRE to promote the reduction of IrCl62and at 0.9 V to oxidize IrCl63-. The former potential is insufficient to reduce any Fc+ that partitions into the aqueous phase. Concentration profiles for the two species were measured on subsequent drops. Typical linear sweep voltammograms for the oxidation of IrCl63- and the reduction of IrCl62- at nanodes are shown in Figure 8. The voltammetric signals are seen to be of a high quality, with well-defined steady-state limiting currents in each case. To ensure that the interfacial reaction would be driven, under the experimental conditions, voltammo(25) Nakatani, K.; Uchida, T.; Misawa, H.; Kitamura, N.; Masuhara, H. J. Phys. Chem. 1993, 97, 5197. (26) Barker, A. L.; Unwin, P. R. Manuscript in preparation.
Microelectrochemical Measurements at Expanding Droplets
Figure 7. Normalized concentration vs distance profile for bromine transfer to a DCE drop, measured potentiometrically, with a 1-µm-diameter Pt UME vs SCE reference (O). Drop times were (a) 7.06 and (b) 8.30 s. In each case, the upper solid lines indicate the theoretical response based on a moving plane, while the lower lines correspond to the expanding sphere model.
grams were recorded for the IrCl62-/IrCl63- couple in the aqueous phase and the Fc/Fc+ couple in the organic phase against a common aqueous reference electrode (AgQRE in 1.0 mol dm-3 NaClO4). The measured difference in the reversible half-wave potentials, ∆E1/2, is determined by the difference in the formal potentials of the two couples, ∆E°′, and the potential across the DCE/aqueous interface, ∆φ:
∆E1/2 ) ∆E°′ + ∆φ
(22)
The measured value of ∆E1/2 ) 570 mV indicated that the interfacial reaction should be driven. The appropriate boundary conditions at the interface were, for the transport-controlled depletion of IrCl62- and generation of IrCl63-,
r ) r0: (cIrCl62- ) 0) DIrCl62-
∂cIrCl62∂r
) -DIrCl63-
∂cIrCl63∂r
(23)
where cIrCl62- is the concentration of IrCl62-, and cIrCl63- is the concentration of IrCl63-. Normalized concentrations may be obtained by dividing each by the initial concentration of IrCl62-. A no-flux (semiinfinite) boundary condition at r ) r0 + rf, described for the bromine case, also applies here for each species. Typical experimental and simulated concentration profiles for both IrCl62- and IrCl63-, recorded using a nanode, characterized by r ) 300 nm, are shown in Figure 9. The simulation used the diffusion coefficients, DIrCl62-
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Figure 8. Linear sweep voltammetry for (a) the oxidation of IrCl63- and (b) the reduction of IrCl62- at cathodically deposited paint-coated nanodes. The bulk mediator concentrations and calculated sizes of the two electrodes (assuming a hemispherical geometry of radius, r) were (a) [IrCl63-]* ) 4 × 10-3 mol dm-3, r ) 27 nm, and (b) [IrCl62-]* ) 1 × 10-2 mol dm-3, r ) 121 nm. The scan rate was 20 mV s-1.
and DIrCl63-, determined by voltammetry at a 25-µmdiameter Pt UME in solutions of known concentration, 6.8 × 10-6 and 7.7 × 10-6 cm2 s-1, respectively, which were in good agreement with previously quoted values.27 Once again, an excellent agreement between the experimental data and the theoretical responses for the two convective-diffusion models confirms the applicability of the models for this case of a bimolecular interfacial reaction. As in the previous cases discussed above, the symmetrically expanding sphere model gives a slightly better fit to the experimental data. The interfacial reaction is confirmed to be transport-controlled with complete conversion of IrCl62- to IrCl63- at the interface. The versatility of the technique in measuring both reactants and products on subsequent drops is also proven, and verification that the simulation is accurate in this different arrangement has been established. The nanodes are shown to function successfully, giving an excellent response and offering the possibility of measuring concentration profiles with very high spatial resolution. Range of Measurable Rate Constants. The numerical model was used to determine the range of rate constants measurable. The simplest case to consider is a first-order irreversible process with kinetic limitations at the interface. The following reaction scheme represents this for species i, crossing the interface, from the aqueous receptor phase to the organic drop, with a first-order (27) Birkin, P.; Silva-Martinez, S. Anal. Chem. 1997, 69, 2055.
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Figure 9. Normalized concentration-distance profiles for (a) IrCl62- and (b) IrCl63-, recorded during reaction of IrCl62- in aqueous solution with Fc in a DCE drop (O). The drop time was 8.46 s. The solid lines indicate the theoretical response for a transport-controlled process, based on the diffusion coefficients measured. In a, the upper line represents the moving plane model and the lower line corresponds to the expanding sphere model, whereas in b, the lower line (at d > 25 µm) represents the moving plane model and the upper line corresponds to the expanding sphere model.
heterogeneous rate constant, k1/cm s-1, describing the interfacial resistance to transfer: k1
i(aq) 98 i(org)
(24)
The interfacial boundary condition required for this case is derived from the interfacial flux expression:
r ) r0:
-Di
∂ci ) k1ci ∂r
(25)
where ci is the concentration of the reacting species. In normalized form, this boundary condition becomes
r ) r0:
[x ]
td k C ) K1Ci Di 1 i
∂Ci )∂R
(26)
where K1 is a normalized rate constant given by
[x ]
K1 ) -
td k Di 1
(27)
The resulting simulated concentration profiles in Figure 10, produced assuming convective diffusion to a symmetrically expanding sphere (eqs 1 and 2), are for a range of typical drop times and show the effect of differing rate
Figure 10. Simulated normalized concentration vs distance profiles, using the expanding sphere model, for typical D ) 10-5 cm2 s-1, and drop times of (a) 1, (b) 5, and (c) 15 s. A range of rate constants, k1, is considered, from upper to lower 10-5, 10-4, 10-3, 10-2, 10-1, and 1 cm s-1.
constants, k1. The results clearly indicate that the maximum rate constant resolvable by this approach is ca. 10-2 cm s-1. The lower limit is controlled by the ability of the probe to detect small changes in concentrations; however, rate constants over several orders of magnitude should typically be resolvable by this approach. The effect of changing the drop time on the shape of the concentration profile is significant, and some effect on the ability to ascertain a particular rate constant is seen. Shorter drop times are more suitable for determining rate constants at the higher end of the scale, whereas when detection limits are a problem due to a slow reaction, longer drop times will improve the performance. While the upper rate constants do not compete with those accessible to microelectrochemical techniques such as SECM and measurements with polarized interfaces of micrometre dimensions, MEMED will be applicable to a wide range of spontaneous processes that may not be tractable to study by these techniques. Studies of important systems that fall into
Microelectrochemical Measurements at Expanding Droplets
this category are currently underway, and will be discussed in future publications. Conclusions MEMED has been developed as a new technique for probing reactions that occur spontaneously on contact between two immiscible liquids. The technique has been shown to operate under well-defined hydrodynamic conditions, which have been evaluated using simple models. Interfacial first-order rate constants up to 10-2 cm s-1 may be determined by MEMED. The range of conditions under which MEMED may be used and the kinds of probes that can be employed have been investigated thoroughly, demonstrating that both amperometric and potentiometric
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measurements may be employed. Consequently, a wide range of species may be detected, and there is considerable scope for using the technique in a huge range of areas. In addition to the probes employed here, we also expect mercury-plated UMEs to be used to measure heavy metals in studies of two-phase metal extraction processes. Acknowledgment. We thank the EPSRC (GR/ L15074) for support and Zeneca for an industrial CASE award for C.J.S. Helpful discussions with Dr. John Atherton and John Umbers (Zeneca Huddersfield Works, U.K.) are much appreciated. LA990337I
