Potential and Current Density Distributions at Electrodes Intended for

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Anal. Chem. 2009, 81, 453–459

Potential and Current Density Distributions at Electrodes Intended for Bipolar Patterning Christian Ulrich,† Olof Andersson,† Leif Nyholm,‡ and Fredrik Bjo ¨ refors†,* Division of Sensor Science and Molecular Physics, Department of Physics, Chemistry and Biology (IFM), Linko¨ping University, SE-581 83 Linko¨ping, Sweden, and Department of Materials Chemistry, Uppsala University, P.O. Box 538, SE-751 21 Uppsala, Sweden This paper deals with the use of reaction gradients on bipolar electrodes for the patterning of electrode surfaces. More specifically, the potential and current density distributions in two setups containing bipolar electrodes were investigated to optimize and design specific gradient geometries. Comparisons with simulations based on simple conductivity models showed a good qualitative agreement, demonstrating that these models could be used to predict bipolar behavior in more complex setups. In conjunction with imaging surface plasmon resonance (iSPR) experiments, the reaction gradients on bipolar electrodes could further be visualized. It was, for example, found that the gradient in potential difference was approximately linearly distributed in the center of the bipolar electrode and that these potential differences could be determined using an ordinary Ag/AgCl reference electrode. The present results thus provide a better understanding of the processes relevant for bipolar patterning. This approach was finally used to generate a circular gradient region in a self-assembled monolayer, thereby showing the possibilities to create interesting substrates for biosensors and microarray applications. When an isolated conducting substrate in a solution is subjected to a parallel electric field, it can become a bipolar electrode, i.e., an electrode acting as both anode and cathode simultaneously. The requirement is that the electric field exceeds a certain threshold value, thereby inducing redox reactions at both ends of the substrate. The floating electrode will then act as an additional, less resistive, path for a part of the current passing through the solution. It is thus the external electric field in the solution that is used to control the interfacial voltages at the electrode, as opposed to in a regular electrochemical setup. The length of the electrode and the conductivity of the solution are also important factors that can be used to control the bipolar reactions. Bipolar electrochemistry is quite a versatile field, and in recent years, several new and interesting applications have been reported. * Corresponding author. E-mail: [email protected]. Phone: +46 13 281374. Fax: +46 13 288969. † Linko ¨ping University. ‡ Uppsala University. 10.1021/ac801871c CCC: $40.75  2009 American Chemical Society Published on Web 11/26/2008

The phenomenon has been used in battery applications,1,2 in proton exchange membrane based fuel cells,3 for energy storage and load leveling,4,5 as well as to carry out electrochemical reactions in poorly conducting media.6 More recently, Bradley et al. have extensively studied the use of bipolar electrochemistry for electrodeposition of palladium catalysts onto micrometer-scale particles7 and carbon nanotubes and nanofibers.8 The directional growth of copper wires between micrometer-sized particles9 was further demonstrated. Warakulwit et al.10 also showed that dissymmetric metal-modified carbon nanotubes could be generated in a capillary electrophoresis setup. The use of bipolar electrochemistry has likewise been used as an external electric field driven in-channel detection technique in microfluidic PDMS channels.11 This type of electrochemistry also provides the possibility of studying chemical reactions without any physical contact to the electrode, for instance in electrochemiluminescence applications.12-14 Surface gradients are excellent tools in many biosensor and biomimetic applications.15,16 Numerous surface gradient-forming (1) Karami, H.; Mousavi, M.; Shamsipur, M. J. Power Sources 2003, 124, 303– 308. ¨ rmo (2) Wiesener, K.; Ohms, D.; Benczu´r-U ¨ssy, G.; Berthold, M.; Haschka, F. J. Power Sources 1999, 84, 248–258. (3) Mehta, V.; Cooper, J. J. Power Sources 2003, 114, 32–53. (4) Walsh, F. Pure Appl. Chem. 2001, 73, 1819–1837. (5) Price, A.; Bartley, S.; Male, S.; Cooley, G. Power Eng. J. 1999, 13, 122– 129. (6) Fleischmann, M.; Ghoroghchian, J.; Rolison, D.; Pons, S. J. Phys. Chem. 1986, 90, 6392–6400. (7) Bradley, J.; Ma, Z. Angew. Chem., Int. Ed. 1999, 38, 1663–1666. (8) Bradley, J.; Babu, S.; Ndungu, P. Fullerenes, Nanotubes, Carbon Nanostruct. 2005, 13, 227–237. (9) Bradley, J.; Chen, H.; Crawford, J.; Eckert, J.; Ernazarova, K.; Kurzeja, T.; Lin, M.; McGee, M.; Nadler, W.; Stephens, S. Nature 1997, 389, 268–271. (10) Warakulwit, C.; Nguyen, T.; Majimel, J.; Delville, M.; Lapeyre, V.; Garrigue, P.; Ravaine, V.; Limtrakul, J.; Kuhn, A. Nano Lett. 2008, 8, 500–504. (11) Ordeig, O.; Godino, N.; del Campo, J.; Munoz, F.; Nikolajeff, F.; Nyholm, L. Anal. Chem. 2008, 80, 3622–3632. (12) Arora, A.; Eijkel, J.; Morf, W.; Manz, A. Anal. Chem. 2001, 73, 3282–3288. (13) Zhan, W.; Alvarez, J.; Crooks, R. J. Am. Chem. Soc. 2002, 124, 13265– 13270. (14) Chow, K.; Mavre´, F.; Crooks, R. J. Am. Chem. Soc. 2008, 130, 7544–7545. (15) Morgenthaler, S.; Zink, C.; Spencer, N. Soft Matter 2008, 4, 419–434. (16) Genzer, J.; Bhat, R. Langmuir 2008, 24, 2294–2317. (17) Chaudhury, M.; Whitesides, G. Science 1992, 256, 1539–1541. (18) Liedberg, B.; Tengvall, P. Langmuir 1995, 11, 3821–3827. ¨ stblom, M.; Lundstro (19) Riepl, M.; O ¨m, I.; Svensson, S.; Deiner van der Gon, A.; Scha¨ferling, M.; Liedberg, B. Langmuir 2005, 21, 1042–1050. (20) Jeon, N.; Dertinger, S.; Chiu, D.; Choi, I.; Stroock, A.; Whitesides, G. Langmuir 2000, 16, 8311–8316. (21) Morgenthaler, S.; Lee, S.; Zucher, S.; Spencer, N. Langmuir 2003, 19, 10459–10462.

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Figure 1. Experimental setup showing the current paths in a bipolar setup where the electric field is parallel to the surface.

techniques have previously been reported, based on, e.g., diffusion,17-19 microfluidic systems,20 immersion procedures,21,22 and electrochemical methods.23-25 Recently,26 we demonstrated that bipolar electrochemistry readily can be used to form reaction gradients on gold surfaces (based on the setup shown in Figure 1). The electric field parallel to the gold substrate gives rise to a gradient in the potential difference between the (equipotential) conducting surface and the solution. If the field strength is sufficiently large, the interfacial potential differences at both ends of the electrode will induce redox reactions. The driving force for these reactions will vary laterally across the surface and therefore gives rise to reaction gradients on the bipolar electrode. To demonstrate the possibility to create molecular gradients, we patterned a self-assembled monolayer of poly(ethylene glycol)containing alkanethiols to create anchoring sites for a protein. The widths of the resulting molecular gradients were in the range between 0.5 and 1 mm. This width is sufficient for many applications, but also wider gradients and patterning with different spatial geometries are desired. It is therefore important to understand how the presence of bipolar reactions affects the local potential and current density in a solution to be able to predict the size and geometry of the reaction gradients. Without a floating electrode in a setup like that in Figure 1, the current density will be more or less constant and the solution potential will in practice vary linearly with respect to the position. When reactions take place at a bipolar electrode, this will no longer hold. This prompted us to investigate the potential and current density distributions in order to better understand critical parameters and to explore the possibilities further. Double layer charging currents will naturally also influence the current and potential distributions when the electric field in the solution is changed (in the present experiments, however, only static conditions were considered). Theoretical modeling of the influence of these parameters for a similar setup has previously been made by Duval et al.27,28 In this case, two parallel plate (22) Morgenthaler, S.; Lee, S.; Spencer, N. Langmuir 2006, 22, 2706–2711. (23) Terrill, R.; Balss, K.; Zhang, Y.; Bohn, P. J. Am. Chem. Soc. 2000, 122, 988–989. (24) Balss, K.; Coleman, B.; Lansford, C.; Haasch, R. T.; Bohn, P. J. Phys. Chem. B 2001, 105, 8970–8978. (25) Wang, X.; Bohn, P. J. Am. Chem. Soc. 2004, 126, 6825–6832. (26) Ulrich, C.; Andersson, O.; Nyholm, L.; Bjo ¨refors, F. Angew. Chem., Int. Ed. 2008, 47, 3034–3036. (27) Duval, J.; Kleijn, J.; van Leeuwen, H. J. Electroanal. Chem. 2001, 505, 1– 11. (28) Duval, J.; Buffle, J.; van Leeuwen, H. J. Phys. Chem. B 2006, 110, 6081– 6094.

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bipolar electrodes were used in a flow-cell setup, intended for electrokinetic measurements, and simulations were made for many different model conditions. Our goal in this work was to experimentally measure the potential and current density distributions, since such knowledge would facilitate optimizations of this type of gradient forming technique. In addition, it was desirable to evaluate the possibility of using a basic conductivity model of the bipolar setup in order to perform simulations, as successful modeling would make it possible to explore and investigate new and exciting patterning approaches (based for example on spherical electric fields). Imaging surface plasmon resonance (iSPR) enables the monitoring of electrochemical reactions on an electrode via local changes in the refractive index.26,29,30 By the combination of iSPR with bipolar electrochemistry, reaction gradients can hence be visualized and evaluated. Further, if a three-electrode setup is used in conjunction with iSPR, the response can be correlated with the potential difference across the electrode/solution interface using a reference electrode. As the probe depth of SPR is about 100 nm, at the wavelengths used in this study, it is a very surface sensitive technique. On the other hand, if the potential in the bulk of the solution is sought, another method has to be employed. Our approach involved measuring the potential difference between the bipolar electrode and an Ag/AgCl reference electrode in the solution. With the placement of this reference electrode at different positions, the potential distribution in the cell could be obtained. Further, the current density distribution could also be evaluated using a similar setup with two reference electrodes. Both the potential and current density distributions were also simulated, and the results were compared with the experimental data. The present investigation was thus performed to facilitate the understanding and optimization of the bipolar gradient forming technique recently developed in our laboratory. There are several interesting geometries and applications that need to be evaluated, and basic, yet effective, simulations can readily be used to assist in this process. This was also demonstrated by forming circular gradient regions in self-assembled monolayers. The results of this work clearly show that the gradient forming technique is quite versatile and that it can be used for several different applications. EXPERIMENTAL SECTION Chemicals and Materials. Deionized water (18.2 MΩ cm) from a Millipore Milli-Q system was used throughout this work. Potassium ferrocyanide (K4[Fe(CN)6] · 3H2O, 10 mM, Merck) potassium ferricyanide (K3[Fe(CN)6], and 10 mM, Merck) were used as a redox couple together with 500 mM potassium nitrate (Merck) as the supporting electrolyte. The gold substrates (10 mm × 15 mm) consisted of 200 nm evaporated gold on silicon (prepared with a 2.5 nm adhesion layer of titanium), using an ultrahigh vacuum equipment. Prior to all experiments, the gold substrates were cleaned in a 5:1:1 mixture of water, 30% hydrogen peroxide (Merck), and 25% ammonia (Merck), at 80 °C for 5 min. All electrochemical data were obtained either with an Autolab PGSTAT20 or PGSTAT30 (EcoChemie, The Netherlands). The (29) Fla¨tgen, G.; Krischer, K.; Pettinger, B.; Doblhofer, K.; Junkes, H.; Ertl, G. Science 1995, 269, 668–671. (30) Andersson, O.; Ulrich, C.; Bjo ¨refors, F.; Liedberg, B. Sens. Actuators, B 2008, 134, 545–550.

ADC164 module on the PGSTAT30 potentiostat was used to record a second voltage signal, using an isolation amplifier with a gain of 1 or 1000. Ag/AgCl reference electrodes (3 M KCl, Bioanalytical Systems Inc.) were used in all three-electrode experiments and for the evaluation of the potential and current density distributions. To reduce the dimension of the reference electrode, a glass pipet filled with electrolyte solution was placed on the tip. The diameter of the opening of the pipet tip was approximately 0.5 mm. iSPR Measurements. The iSPR experiments were performed with an in-house custom built setup based on the Kretschmann configuration.31 The setup consisted of two vertically oriented synchronously movable rotation stages, each carrying an optical rail, and an optically centered equilateral prism (BK7, Melles Griot Inc.). A discharge lamp (150 W xenon, Acton Research) was used as a fixed white light source, and the light was passed through a monochromator (SpectraPro 300i, Acton Research), collimated, and TM-polarized before being guided toward the prism using mirrors mounted on one of the movable arms. A refractive index matching oil (n ) 1.515, Cargille-Sacher Laboratories Inc.) was employed to achieve optical contact between the prism and the substrate. A CCD camera (1 MP, Retiga EXi, Qimaging Corp., Canada) and imaging optics, mounted on the second movable arm, were used to measure the intensity of the reflected light. The rotation stages enabled selection of the incidence and reflection angles, which in the present case were set to 70.65°. Each pixel in the images depicted an area of about 2 µm × 4 µm of the substrate. The wavelength of the incident light was chosen to maximize the sensitivity, which resulted in the use of 655 nm for the redox couple and 645 nm for the supporting electrolyte only. The SPR response was defined as the shift in the reflected intensity of TM-polarized light, normalized by the intensity of TEpolarized light, ∆R ) ∆(RTM/RTE). At positive surface charges, the SPR response can to some extent be influenced by changes in the optical properties of the gold, due to contributions from deshielded bound electrons.32 However, when faradaic reactions are induced at the surface, the SPR response is mainly caused by the difference in refractive index of the redox species. The SPR sensor surfaces (simultaneously used as bipolar electrodes) consisted of 12 mm × 12 mm glass slides coated with a 45 nm thick film of gold (obtained from GE-Healthcare (Biacore), Sweden). The electrochemical experiments were performed in a PTFE cell, tightly sealed to the gold surface using a nitrile rubber O-ring with a diameter of 8 mm. Two stainless steel feeder electrodes were immersed in the cell to facilitate the current control through the electrolyte. One feeder electrode was used as the working electrode while the other was employed as a combined counter and reference electrode, when connected to the potentiostat. For the threeelectrode experiments, one of the feeder electrodes was employed as the counter electrode. Each experiment was carried out with (1.5 mL) fresh electrolyte solution. Potential and Current Density Evaluation. In the potential and current density measurements, a rectangular polystyrene liquid cell (79 mm × 29 mm × 11.5 mm) filled with electrolyte (15 mL) was used. At both short ends, stainless steel feeder electrodes (31) Kretschmann, E.; Raether, H. Z. Naturforsch., A 1968, 23, 2135–2136. (32) Gordon, J. G., II; Ernst, S. Surf. Sci. 1980, 101, 499–506.

Figure 2. Illustrations of setups used for potential (A) and current density (B) measurements.

having the same width as the cell were immersed. The gold electrode was then placed in the middle, and pieces of an oxidized silicon wafer were used to cover the rest of the bottom in order to minimize edge effects on the electrode. To estimate the distribution of the solution potential, the voltage between a tip modified reference electrode and the surface was measured at different positions, 0.5 mm above the surface (see Figure 2A). The reference electrode was mounted on a movable stage, allowing exact positioning, and the gold surface was contacted using a thin isolated stainless steel wire. The potential differences were recorded using the ADC164 module with the amplifier set to a gain of 1. To induce the bipolar reactions, a current was passed between the feeder electrodes (0 mA for 5 s, 1.0 mA for 10 s, followed by 0 mA for 10 s). Between each measurement, the modified reference electrode was moved to a new position and the solution was stirred. To evaluate the current density distribution in the cell, the voltage between two modified reference electrodes was measured, see Figure 2B. The reference electrodes were placed about 0.5 mm apart and again 0.5 mm above the surface. This potential difference was also recorded using the ADC164 module but with the amplifier set to a gain of 1000. In addition, reference measurements were performed at different positions when the gold had been replaced with an inert nonconducting substrate with the same dimensions. Simulations. The simulations were carried out using COMSOL Multiphysics 3.3 (Comsol AB, Sweden), employing a conductive media dc model. The original system was modeled in 2-D and consisted of two centered rectangles in contact with each other, having only one boundary in common, representing the present experimental setup. The larger rectangle (79 mm × 7 mm) represented the electrolyte, with a conductivity of 1 S/m. The gold was modeled as a rectangle (15 mm × 0.5 mm) with a conductivity of 12 S/m. This value is fairly low but was used to provide results qualitatively comparable with those experimentally obtained. The left side of the electrolyte rectangle was given an inward current density of 1 A/m2, while the right side was ascribed an equal outward current density. This value was comparable to the actual value used in the experiments. The potential and current densities were then simulated for a distance of 0.5 mm above the gold rectangle. The system in which one feeder electrode consisted of a thin rod placed above the bipolar electrode was modeled in 3-D. The conductivities of the electrolyte (79 mm × 29 mm × 7 mm) and the gold (15 mm × 10 mm × 0.5 mm) were again 1 and 12 S/m, respectively. The rod electrode was modeled as a rectangular box (0.5 mm × 0.5 mm × 6 mm) positioned 1 mm above the center of the gold electrode. This rod was given a conductivity of 45.5 MS/ m. As in the 2-D model, the left side of the electrolyte rectangle was given an inward current density of 1 A/m2, but here the top of the rod was given an outward value of 812 A/m2, due to the Analytical Chemistry, Vol. 81, No. 1, January 1, 2009

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Figure 3. (A) The SPR response for different currents passed through the electrolyte, simultaneously showing the regions of the reduction (left side) and oxidation (right side) reactions. When only the supporting electrolyte was present, the surface did not become a bipolar electrode. (B) SPR response for different potentials when the sensor surface acted as a working electrode in a three-electrode setup. The solid line was calculated using the Nernst equation. In both parts A and B, 10 mM K4[Fe(CN)6] · 3H2O and 10 mM K3[Fe(CN)6] were used as a redox couple together with 500 mM KNO3 as supporting electrolyte, and the scan rate used to obtain the cyclic voltammogram was 50 mV/s.

area relation between the side of the electrolyte rectangle and the top of the rod. The current densities with and without the gold rectangle were simulated 1 µm above the bipolar electrode. Bipolar Patterning. A self-assembled monolayer of an inhouse synthesized33 oligo(ethylene glycol)-terminated alkanethiol amide, HS-C11H22-CONH-(C2H4-O)3-H, was employed to demonstrate bipolar patterning. The preparation involved incubation of a gold surface (10 mm × 15 mm) in a 100 µM solution (99.5% ethanol) for 24 h. The substrate was then rinsed and sonicated in ethanol and placed in the center of a rectangular polystyrene liquid cell (39 mm × 29 mm × 11.5 mm). The electrolyte (10 mL) consisted of 1 M KOH (Merck) in ethanol and was filtered (0.22 µm Filterunit, Millipore Corp.) prior to use. A stainless steel feeder electrode (having the same width as the cell) was immersed at one short end of the cell. The other feeder electrode consisted of a platinum rod (1 mm in diameter), which was pointed and placed about 0.5 mm above the center of the gold surface. A total of 10 mA was passed between the feeder electrodes for 30 s, after which the surface was thoroughly rinsed in water. Imaging null-ellipsometry was performed with an EP3 imaging null-ellipsometer (Nanofilm, Germany) equipped with a xenon lamp and a CCD camera detector. The angle of incidence was set to 70°, and the wavelength was 631.2 nm, selected from the spectrum of the xenon lamp by an interference filter. A ×2 magnification objective was employed, resulting in a spatial resolution of 6.5 µm per pixel. Reference measurements yielded the complex refractive index for the gold, and a refractive index of 1.5 was assumed for the thiol monolayer. The effective layer thickness was calculated using a three-layer optical model based on Fresnel’s formulas, together with the ellipsometric angle ∆, which was obtained for each pixel in the CCD camera. RESULTS AND DISCUSSION As mentioned in the introduction, we have recently shown that bipolar electrochemistry can be used to form molecular gradi(33) Svedhem, S.; Hollander, C.; Shi, J.; Konradsson, P.; Liedberg, B.; Svensson, S. J. Org. Chem. 2001, 66, 4494–4503.

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ents.26 In brief, this work involved the patterning of a selfassembled monolayer (SAM) of a methoxy terminated poly(ethylene glycol) thiol on a bipolar gold surface by selectively desorbing it from the cathodic side. After backfilling with a carboxyl terminated poly(ethylene glycol) thiol and activation of the carboxyl groups, the surface could then further be incubated in a lysozyme solution resulting in a protein gradient. This method was also tested on SAMs based on thiols of different lengths and functionalities, formed both by incubation and microcontact printing. Without the need for any electric connections to the substrate, the method is well-suited for patterning of electrode surfaces, particularly as no advanced laboratory equipment is needed, and the gradients can be formed within seconds to minutes. A better understanding of the parameters affecting the geometry of the reaction gradients is however needed. This is consequently the main objective of the present study. Potential Measurements Using iSPR. To visualize and evaluate the reaction gradients on bipolar electrodes, iSPR was used. In this setup, the SPR sensor surface was subjected to parallel electric fields and the resulting response was recorded. Because of the differing refractive indices of the ferro- and ferricyanide ions in the electrolyte, a change in the composition gives rise to a change in the SPR response. The presence of oxidation and reduction on the sensor surface could therefore readily be visualized. Figure 3A shows the SPR responses for a bipolar electrode for the case where increasing total currents were passed between the feeder electrodes in the electrolyte. For the chosen wavelength, reduction was found to give an increase in the SPR response while oxidation resulted in a decreased signal. Because of the potential gradient across the surface, the rates of these reactions will vary laterally, and in the middle of the electrode (at about 3.1 mm), no net reaction takes place. Since the latter corresponds to an unchanged electrolyte composition, the SPR response will consequently be zero, regardless of the current through the solution. The potential at this position will hence correspond to the formal potential of the ferro/ferricyanide redox couple. On either side of the midpoint, however, different total currents will induce different reaction rates. Also shown in

Figure 3A is an experiment in which a current of 5 mA was passed through the supporting electrolyte alone (i.e., in the absence of the redox couple). For this current, no reactions could be induced and no change in the SPR response was consequently seen in this experiment (solvent electrolysis would for example require much higher currents through the cell). The reaction gradients seen in Figure 3A were the result of the distribution of the potential difference between the surface and the electrolyte. To investigate the influence of the interfacial potential differences on the SPR response, a three-electrode setup was used, in which the sensor surface also acted as the working electrode. Again, the SPR response was a result of the shift in electrode potential from the open circuit value, which can be seen in Figure 3B (9) for different applied potentials. The result of this experiment can hence be used to correlate the potential difference across the bipolar electrode/solution interface to the electrode potential in a normal three-electrode setup. It is therefore clear that imaging SPR can give valuable information about the potential distribution and the resulting reactions on a bipolar electrode. The formal potential of the redox couple was found to be about 0.24 V (i.e., this is the potential where the SPR response was equal to zero). This value was in good agreement with the value obtained by cyclic voltammetry, as is also shown in Figure 3B. When the dependence of the SPR response on the potential is looked at, it appears to be Nernstian. To relate this response to the electrode potential, its dependence on the concentrations of the redox species has to be determined. The sensitivity of the SPR response (∂R/∂c) will, for the experimental conditions used, be approximately constant. This yields a linear relationship between the SPR response and c, which in this case is defined as c)

[Red] [Red] + [Ox]

(1)

This normalized concentration is hence the fraction of redox species in the reduced form, and its value will therefore vary between zero and unity. The latter definition is convenient when relating the concentrations of redox couples to the SPR response. For this system, the reaction quotient, Q, in the Nernst equation then becomes Q)

c 1-c

(2)

The formal potential was set to 0.24 V, and the derivative ∂R/∂c was set to 0.08, corresponding to the range in the measured SPR response in Figure 3B (i.e., where c varies between zero and unity). The dependence of the SPR response on the potential was then calculated via the Nernst equation and plotted in Figure 3B (solid line). The calculated values correlate quite well with the experimental data, which suggests the presence of an approximately linear potential distribution in the solution close to the surface. A limitation of this method is that the SPR response does not change very much when the potential difference becomes large enough to yield mass transport controlled reactions. The potential difference can then clearly still vary but the refractive index in the close vicinity of the surface will be practically constant, and the SPR response will hence also be constant.

An induced reaction gradient on a bipolar electrode can thus be visualized using iSPR. Compared to a situation without a bipolar electrode, the reaction gradient also gives rise to a different distribution of the current in the solution. It is thus desirable to find a way to measure the current density distribution in the electrolyte surrounding the bipolar electrode. Measurements of Potential and Current Density. A current passed in an electrolyte containing a gold bipolar electrode will distribute itself in the cell according to the resistances of the electrolyte, the charge transfer reactions, and the gold surface. This will give rise to a nonlinear potential distribution in a cell (such as the one in Figure 1), provided that redox reactions take place at both ends of the surface. To measure the current density in such a setup, a straightforward method was used. The voltage between two closely placed reference electrodes is proportional to the current density passing in the region of the tips. This was used to gain information about the current density distribution in the solution above, and surrounding, a bipolar electrode. Two reference electrodes modified with glass pipet tips (0.5 mm in diameter) were placed about 0.5 mm apart and 0.5 mm above the bipolar electrode, as described in Figure 2B. The potential difference between these electrodes was then recorded at different positions in the solution as a current was passed between the feeder electrodes. With division of the voltage with the corresponding one in the absence of a bipolar electrode, a relative current density was obtained, which more clearly showed the influence of the bipolar reactions. In these experiments, the current density was taken as the difference between a value recorded 0.2 s after the application of 1 mA and a mean of the values of the first 5 s (at 0 mA). A high relative current density for a position thus corresponds to a high current passing in this region, parallel to the surface. Not surprisingly, the relative current density peaks at the edges of the bipolar electrode because of the high reaction rates present there (see Figure 4A). The current passed through the gold will reach a maximum value in the center of the surface. This will coincide with a corresponding minimum of the current density in the solution. For a distance of 0.5 mm above the center of the electrode, the current density will be reduced by approximately 50%. The height difference for the current density peaks in Figure 4A was found to be reproducible. The explanation for this difference is presently not clear but probably involves local changes in the ionic strength very close to the surface, when redox species are oxidized and reduced. These changes will then influence the current passing the two reference electrodes. If the relative current density is measured at positions much further away from the electrode, the effects of the bipolar reactions are not seen, and the relative current density is constant and equal to unity. The corresponding potential distribution here will thus be linear. On the surface of the bipolar electrode the potential will, however, be constant due to the low resistivity of the gold. If the voltage between a reference electrode in the solution and the bipolar electrode is measured, the solution potential distribution can be evaluated. For positions close to the surface, this distribution will be neither linear nor constant. The results of measurements carried out 0.5 mm above the bipolar electrode can be seen in Figure 4A (right axis). The potential profile shows a slight deviation from a straight line, having a decreased slope over the electrode. The latter is due to the fact that when current was Analytical Chemistry, Vol. 81, No. 1, January 1, 2009

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Figure 4. Relative current densities and solution potentials (0.5 mm above the surface) for different positions with respect to the bipolar electrode. The shaded areas represent the position of the surface. (A) Experimental results and (B) simulated results obtained with the conductivity model.

Figure 5. Relative current density at different positions with respect to the bipolar electrode (1 µm above the surface). The shaded area represents the position of the surface. The inset shows the setup model used in the simulation.

Figure 6. Results from imaging null-ellipsometry measurements, showing the effective layer thickness, d, from a region where the thiols were selectively removed. The inset shows a larger image and the region from where the thickness map was taken.

passed through the bipolar electrode, the potential drop in the solution decreased. It was found that for a longer surface (which yields a larger potential drop in the solution across the surface) this slope was much lower, as can be expected (data not shown). Duval et al.28 have performed simulations of the potential and current density distributions in a solution containing a bipolar electrode, and have shown that the current density peaks at the edges and that the slope of the potential profile decreases in the middle region. Simulations of the Potential and Current Density. Simulations of the setup used to obtain the results in Figure 4A were carried out to investigate the validity of a simple model of the 458

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system, based only on conductivity differences (i.e., the goal was hence not to make a quantitative comparison between the simulated values to those obtained experimentally). For the simulations, the conductivity of the gold was set to 12 S/m, a value several orders of magnitude smaller than the true value. However, using the conductivity model, a good qualitative agreement was obtained between the measured and simulated values (see Figure 4B). The lower conductivity of the gold can in this case be seen as partly encompassing the influence of reaction resistances and mass transfer effects. As the conductivity of the whole system determines the total potential drop, the latter will be mostly determined by the electrolyte. If the conductivity of the gold is increased to a more realistic value, the current distribution will change somewhat. The relative current density at the edges of the surface will increase to about two, and in the middle it will decrease to near zero. More importantly, the general shape of the curves will, however, be maintained. These results clearly demonstrate that a simple conductivity model can be used to evaluate and predict the potential and current densities in bipolar setups. Bipolar Patterning. To test a more complex patterning geometry, a simulation using a 3-D model with a rod feeder electrode positioned above the center of the bipolar electrode was performed. Such a setup would result in a semispherical electric field around the end of the rod and could therefore be used to selectively induce redox reactions at different positions on the surface. The setup and resulting relative current density distribution can be seen in Figure 5. High relative current densities were present right below the rod feeder electrode and at the left side of the gold (the side closest to the other feeder electrode). These results show the possibility of using spherical electric fields for the formation of more complex and interesting patterns on bipolar electrodes. This was also verified by initial experiments using electrodeposition of copper and electropolymerization of pyrrole. To demonstrate the relevance of bipolar patterning with spherical electric fields, a self-assembled monolayer of an oligo(ethylene glycol)-terminated alkanethiol amide was used. A pointed platinum feeder electrode was placed above the monolayer (as in the inset in Figure 5) to enable the selective removal of thiols, via reductive desorption. About 40% of the thiols were removed under the tip when forcing 10 mA through the electrolyte (the resulting effective layer thickness map can be seen in Figure 6). This surface could now be used further, by for instance backfilling with a second thiol in order to create anchoring sites

for biorelevant molecules. Similar spots can of course be produced with several other patterning techniques, but with the use of the present approach, a well-defined circular gradient region is also obtained. Moreover, several such spots could be formed on a single substrate, resulting in an array of different gradient regions, possibly with several different biomolecules attached. Such a substrate would be very valuable in for instance biosensors and microarray applications. CONCLUSIONS It has been shown that it is possible to analyze and simulate the resulting potential and current density distributions when reaction gradients are induced on bipolar electrodes. This has provided important information regarding the possibility to optimize this gradient forming technique. It was also shown that iSPR can be used to image such reaction gradients, enabling, for example, determinations of the potential differences with respect

to an ordinary Ag/AgCl reference electrode. A simple conductivity model was employed to predict the magnitude and location of redox reactions in more complex bipolar setups. Finally, it was demonstrated that semispherical electric fields could be used to selectively desorb thiols in a self-assembled monolayer, leading to circular gradient spots. ACKNOWLEDGMENT This work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), VINNOVA, and the Carl Trygger Foundation (CTS). The authors would like to thank Lan Bui for providing the oligo(ethylene glycol)-terminated alkanethiol amide. Received for review September 4, 2008. Accepted October 31, 2008. AC801871C

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