Alternating Current Impedance Imaging of Membrane Pores Using

Department of Chemistry, University of Utah, 315 South 1400 East Salt Lake City, Utah 84112 ... Lushan Zhou , Yi Zhou , Wenqing Shi , and Lane A. Bake...
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Anal. Chem. 2005, 77, 5564-5569

Alternating Current Impedance Imaging of Membrane Pores Using Scanning Electrochemical Microscopy Eric Nathan Ervin and Henry S. White*

Department of Chemistry, University of Utah, 315 South 1400 East Salt Lake City, Utah 84112 Lane A. Baker

Department of Chemistry, Center for Research at the Bio/Nano Interface, University of Florida, Gainesville, Florida 32611

Alternating current impedance imaging of a 6-µm thick membrane containing conical-shaped pores (60-nm and 2.5-µm diameter openings) using scanning electrochemical microscopy (SECM) is described. Impedance images of the pore openings were obtained by rastering a glasssealed conically shaped Pt tip (∼1-µm radius) above the membrane surface, while measuring the total impedance between the tip and a large area Pt electrode located on the opposite side of the membrane. Individual pore openings in the high pore density membrane (∼8 × 104 pores/cm2) are observed in the SECM impedance image. The image contrast is due to the decrease in tip and membrane resistance, in the vicinity of the pore opening. An equivalent circuit for the SECM cell and membrane is proposed and evaluated against the measured SECM imaging impedance. Criteria for employing SECM in impedance mode to image membranes are discussed. Scanning electrochemical microscopy (SECM) is frequently used to image and quantify molecular transport across synthetic and biological membranes,1-7 including transport across the membrane of individual cells.8-12 These experiments are based on measuring the flux of redox molecules, by electrochemical oxidation or reduction at the SECM tip, as they emerge from or enter13-15 into the membrane. For membranes with well-defined pore structures, it is frequently possible to visualize pores at the * Corresponding author. E-mail: [email protected]. (1) Scott, E. R.; White, H. S.; Phipps, J. B. Anal. Chem. 1993, 65, 1537-1545. (2) Macpherson, J. V.; Jones, C. E.; Barker, A. L.; Unwin, P. R. Anal. Chem. 2002, 74, 1841-1848. (3) Scott, E. R.; White, H. S.; Phipps, J. B. J. Membr. Sci. 1991, 58, 71-87. (4) Scott, E. R.; White, H. S.; Phipps, J. B. Anal. Chem. 2000, 17, 471-475. (5) Bath, B. D.; White, H. S.; Scott, E. R. Anal. Chem. 2000, 72, 433-442. (6) Bath, B. D.; White, H. S.; Scott, E. R. Pharm. Res. 2000, 17, 471-475. (7) Bath, B. D.; Lee, R. D.; White, H. S.; Scott, E. R. Anal. Chem. 1998, 70, 1047-1058. (8) Liu, B.; Rotenberg, S. A.; Mirkin, M. V. PNAS 2000, 97, 9855-9860. (9) Tsionsky, M.; Cardon, Z. G.; Bard, A. J.; Jackson, R. B. Plant Phys. 1997, 113, 895-901. (10) Cai, C.; Liu, B.; Mirkin, M. V. Anal. Chem. 2002, 74, 114-119. (11) Liu, B.; Rotenberg, S. A.; Mirkin, M. V. Anal. Chem. 2002, 74, 6340-6348. (12) Liu, B.; Cheng, W.; Rotenberg, S. A.; Mirkin, M. V. J. Electroanal. Chem. 2001, 500, 590-597. (13) Uitto, O. D.; White, H. S.; Aoki, K. Anal. Chem. 2002, 74, 4577-4582. (14) Uitto, O. D.; White, H. S. Pharm. Res. 2003, 20, 646-652. (15) Uitto, O. D.; White, H. S. Anal. Chem. 2001, 73, 533-539.

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membrane surface, a consequence of the variation in the redoxmolecule flux near the pore opening. In the present work, we have explored a new approach for imaging membrane pores and quantifying the resistance of single pores, based on measuring the ac impedance between the SECM tip and a larger electrode positioned in the solution on the opposite side of the membrane. The key advantage of imaging based on measuring the spatial variation in the impedance is that a redox active molecule is not required. A second advantage is that information about the pore transport dynamics can be transmitted much faster in the ac impedance signal than in the measurement of the flux of a redox active molecule. For example, we have recently reported the use of SECM to detect the capture of nanoparticles at the opening of a membrane pore.16 This detection method is based on measuring the decrease in flux of a redox molecule passing through the pore when the nanoparticle blocks the opening. Transmission of the time-varying flux signal, through the pore of length l, to the SECM tip is characterized by a delay time5 of t ∼ l2/6D (where D is the diffusion coefficient) that is determined by diffusive motion of the redox molecule within the pore. The transmission of the diffusion signal can be in the range of tenths of seconds for pores that are 10 µm in length. In contrast, the ac impedance signal can be transmitted to the tip at rates controlled by the electrical time constant of the cell and recording instruments, which can be several orders of magnitude faster. Measurement of the tip impedance in SECM experiments has been previously used primarily as a means of feedback to control the vertical position of the tip relative to a surface.17,18 Recently, Schuhmann and co-workers19,20 and Vivier et al.21 have developed ac impedance SECM to image the topography and electrical properties of various solid surfaces. While the basic theory and instrument requirements for imaging membranes, reported herein, are the same as in imaging solid surfaces and in tip positioning, (16) Lee, S.; Zhang, Y.; White, H. S.; Harrell, C. C.; Martin, C. R. Anal. Chem. 2004, 76, 6108-6115. (17) Alpuche-Aviles, M. A.; Wipf, D. O. Anal. Chem. 2001, 73, 4873-4881. (18) Horrocks, B. R.; Schmidtke, D.; Heller, A.; Bard, A. J. Anal. Chem. 1993, 65, 3605-3614. (19) Katemann, B. B.; Inchauspe, C. G.; Castro, P. A.; Schulte, A.; Calvo, E. J.; Schuhmann, W. Electrochim. Acta 2003, 48, 1115-1121. (20) Katemann, B. B.; Schulte, A.; Calvo, E. J.; Koudelka-Hep, M.; Schuhmann, W. Electrochem. Commun. 2002, 4, 134-138. (21) Gabrielli, C.; Huet, F.; Keddam, M.; Rousseau, P.; Vivier, V. J. Phys. Chem. B 2004, 108, 11620-11626. 10.1021/ac050453s CCC: $30.25

© 2005 American Chemical Society Published on Web 07/12/2005

Scheme 1. Schematic Drawing Depicting the Interaction of the SECM Tip and the Membrane during Impedance Imaging

Figure 1. Schematic of SECM cell and instrumentation for impedance imaging of nanopores.

the principles underlying the correlation of features in the impedance image and the membrane pore structure have some unusual nuances that have not been previously considered to our knowledge. Consider Scheme 1, which depicts a cone-shaped SECM tip and a flat membrane (with a single pore shown). The success of the impedance imaging experiment depends on whether the overall impedance between the SECM tip and a much larger electrode, located on the opposite side of the membrane (not shown), changes significantly as the tip passes over the pore. There are four resistances that need to be considered in this experiment: (i) the tip resistance, Rtip; (ii) the pore entrance resistance, Rentry; (iii) the resistance of the pore, Rpore; and (iv) the pore exit resistance, Rexit. Each of these resistances depends on geometrical factors (tip radius, pore length, pore diameter, etc.) and the conductivity of the solutionsprecise mathematical expressions will be presented later in the paper. Because of the divergent flux of ions between tip and solution, the resistance associated with the tip is localized to a small solution volume surrounding it that can be approximated as having a radius several times larger than the tip radius. This is depicted in Scheme 1 by the isopotential lines drawn around the tip, to indicate the localized Ohmic potential drop. Analogously, the divergent ion fluxes at the pore entrance and exit also give rise to resistances that are localized to the solution adjacent to these structures. For the purpose of introducing the imaging principles, we consider qualitatively how the overall resistance (i.e., (Rtip + Rentry + Rpore + Rexit)) changes when moving the tip from point A to B to C as depicted in Scheme 1. First, in moving the tip from the bulk solution (A) to a position close to the surface but far removed from a pore opening (B), the only resistance that changes is that associated with the SECM tip, Rtip. As noted by previous researchers, Rtip increases as the tip is moved toward an insulating surface because the surface reduces the volume of the ion-conducting solution surrounding the tip (so-called negative feedback).17,18,21 As the tip is scanned over a pore (C), two resistances are altered. First, Rtip will decrease, as the pore opening results in an increase in the volume of current-carrying solution around the tip. Second,

Rexit will also decrease, a consequence of the decrease in the distance that current is carried between the pore opening and the SECM tip. The remaining resistances, Rentry and Rpore, are independent of tip position and remain constant when an image is being acquired. An image of a pore can be successfully obtained if the combined change in Rtip and Rexit is significant in comparison to the total resistance (Rtip + Rentry + Rpore + Rexit) as the tip is rastered across the membrane (i.e., ∆(Rtip + Rexit) ∼ (Rtip + Rentry + Rpore + Rexit)). Whether this criterion is met depends on the tip and membrane geometry. In situations where ∆(Rtip + Rexit) is small in comparison to (Rtip + Rentry + Rpore + Rexit), imaging may still be possible if the membrane contains a large number (N) of pores. In this case, the overall cell resistance is equal to (Rtip + [Rentry + Rpore + Rexit]/N), and the criterion for successful imaging, ∆(Rtip + Rexit) ∼ (Rtip + [Rentry + Rpore + Rexit]/N), can be much less stringent (by roughly a factor of 1/N when the resistance of one pore is greater than that of the tip). Thus, the ability to resolve an individual pore opening by SECM impedance imaging increases as the pore density increases. EXPERIMENTAL PROCEDURES Chemicals and Materials. KCl (Mallinckrodt) was used as received. Ferroccenylmethyltrimethylammonium hexaflourophosphate (FcTMA+) was prepared by metathesis of the iodide salt (Strem 99%) with ammonium hexaflourophosphate (Strem 99%). The crystals were collected by vacuum filtration and recrystallized from water. All solutions were prepared using 18 MΩ cm H2O from a Barnstead E-pure water purification system. Track-etched polycarbonate membranes22 used in these studies were ∼6 µm thick and contained a nominal pore density of ∼8 × 104 pores/cm2. The conically shaped pores (Scheme 1) have a small and large opening diameter of ∼60 nm and ∼2.5 µm, respectively, as determined by scanning electron microscopy. Preparation and characterization of the membranes have been described elsewhere.23 Scanning Electrochemical Microscopy. A schematic diagram of the home-built SECM cell and instrumentation for imaging membranes is shown in Figure 1. The SECM cell is constructed from Teflon following a previous paper1 and allows the positioning of a membrane between two compartments containing aqueous solutions. The membrane is sandwiched between two glass slides each containing a 0.18-cm diameter hole (22) Fleischer, R. L.; Price, P. B.; Walker, R. M. Nuclear Tracks in Solids, Principles and Applications; University of California Press: Berkeley, CA, 1975. (23) Apel, P.; Korchev, Y. E.; Siwy, Z.; Spohr, R.; Yoshida, M. Nucl. Instrum. Methods, Sect. B 2001, 184, 337-346.

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to allow the solution contact to the membrane on both sides. Highvacuum grease (Dow Corning) was used to seal the membrane between the slides. The SECM tip is located in the upper compartment of the SECM cell. In the experiments reported here, the lower and upper compartments contained 10 and 1 mM KCl, respectively, to optimize the impedance image contrast, as discussed later. The position of the SECM tip is controlled with ∼10-nm precision using piezoelectric inchworm microtranslation stages with optical encoding (8200, EXFO) interfaced via a controller box to Lab View. The impedance between the SECM tip and a 2-mm radius Pt disk electrode was measured by applying a 10 mV rms ac signal from a lock-in amplifier (R810, Stanford Research Systems) between the electrodes, using a potentiostat, and measuring the ac current response by phase-sensitive detection. Two different potentiostats were used based on the required sensitivity. A Pine AFRDE5 bipotentiostat was used for high current measurements (>100 nA), while a Dagan Chem-Clamp voltammeter/amperometer was used for lower current measurements. The linearity and accuracy of the phase-sensitive measurement were initially tested by measuring the ac current across known real resistors substituted for the SECM cell. The value the of resistors was calculated from the magnitude of the ac current, iac, using Ohm’s law

iac ) Vin/R

(1)

where Vin is the 10 mV rms input signal. Linear plots of iac versus R-1 with zero intercept were obtained at frequencies below 1 kHz for 104 < R < 106 Ω. At higher frequencies, the combination of the potentiostat, the resistor, and the lock-in amplifier act as a low pass filter. Lab View was programmed to scan the SECM tip across the membrane in the XY directions. Briefly, the tip is manually positioned approximately 15 µm away from the pore in the -X and the -Y direction. Two thousand data points are acquired at 10 000 points/s and averaged to obtain one data point of the image. Data acquisition is paused for 0.5 s, and the SECM tip moved 2 µm at 10 µm/s in the +X direction before stopping and collecting another data point. This process is repeated 15 times, thus moving the tip 30 µm in the +X direction. The tip is moved back to the original starting position and then moved 2 µm in the +Y direction. The program proceeds to take data in the +X direction as before, and the whole process is repeated 15 times. A 30 µm × 30 µm area of the membrane takes ∼20 min to image. The data are plotted using DeltaGraph to produce SECM images. SECM Tip Preparation. Conical-shaped glass-sealed Pt SECM tips (Figure 2) were prepared following a method reported for sealing Pt-Ir electrodes in glass.24,25 A 25-µm diameter Pt wire was attached to a 0.01-in. diameter W rod (FHC) using Ag paint (Dupont). The Pt wire was then electrochemically etched,26 in a 2:1 (v/v) H2O/acetone solution containing 1.2 M CaCl, by applying a 60 Hz, 10 mV peak-to-peak signal to the wire until a sharp point (24) Penner, R. M.; Heben, M. J.; Lewis, N. S. Anal. Chem. 1989, 61, 16301636. (25) Heben, M. J.; Dovek, M. M.; Lewis, N. S.; Penner, R. M.; Quate, C. F. J. Microsc. (Oxford) 1988, 152, 651-661. (26) Libioulle, L.; Houbion, Y.; Gilles, J. M. Rev. Sci. Instrum. 1995, 66, 97100.

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Figure 2. SEM images of (a) 25 µm Pt wire etched to a sharp tip and (b) the end of the glass-sealed conical SECM tip. The radius of the exposed Pt at the end of the tip is ∼1 µm.

was obtained, as observed by optical microscopy. The Pt wire was then inserted in a 5-µL glass capillary (Drummond), such that the sharp point was ∼1 mm from the end. A butane flame was used to seal the Pt wire into the glass. The capillary was continuously flamed until the Pt tip extruded from the glass as determined by electrochemical measurements and scanning electron microscopy (SEM). The opposite end of the wire was sealed in the capillary with epoxy. SECM tip radii, rt, were estimated by measuring the steadystate limiting current for the reduction of FcTMA+ in an aqueous solution containing 2 mM FcTMA+ and 0.1 M KCl. The diffusion limiting current at a conical electrode is related to rt by the expression reported by Mirkin and Zoski, ilim ) 4nFDCrt(1 + qHp),27 where n is the number of electrons transferred, F is Faraday’s constant, D and C are the diffusivity and the solution concentrations of the redox molecule, respectively, and q and p are the numerical constants 0.30661 and 1.14466, respectively. H is the ratio between the height (h) and base radius (rt) of the cone, which was found to be ∼5.7 from SEM images of bare etched Pt wires. Electrodes with tip radii ranging from ∼0.2 to ∼1 µm were prepared and characterized by this method. The larger (∼1 µm) electrodes were used in the experiments reported herein. RESULTS AND DISCUSSION In addition to visualization of membrane pores, a goal of impedance imaging is to measure the resistance of a single pore in a membrane containing many pores. In contrast to conventional SECM measurements of molecular redox fluxes in pores, in which the faradaic current at the tip can be shown to be directly proportional to pore transport rate,5,28 the ac current is a complex function of tip and membrane resistances, the electrolyte concentration, and the impedances of the measurement electronics. In presenting the results, we first demonstrate in section a that the magnitude of the ac current between the glass-coated SECM tip (27) Zoski, C. G.; Mirkin, M. V. Anal. Chem. 2002, 74, 1986-1992. (28) Bath, B. D.; Scott, E. R.; Phipps, J. B.; White, H. S. J. Pharm. Sci. 2000, 18, 1537-1549.

Figure 3. (a) Alternating current response (iac) for the SECM imaging cell as a function of frequency. The solid line is obtained when a 10 mV rms signal is applied between a 1-µm radius SECM tip in the upper solution (1 mM KCl) and a 1.5-mm radius Pt disk electrode in the lower solution (10 mM KCl). The two solutions are separated by a porous polycarbonate membrane. The dotted line is the simulated response function of the equivalent electrical circuit shown in panel b using R3 ) 8 MΩ, C3 ) 40 pF, and C2 ) 5 pF (stray capacitance) for the SECM cell and R1 ) 10 MΩ, R2 )1.7 MΩ, R4 ) 1.2 MΩ, C1 ) 25 pF, and C4 ) 15 pF for components of the measurement instrumentation. The dashed curve corresponds to the frequency response when a real resistor (R3 ) 8 MΩ) and a real capacitor (C3 ) 40 pF) are connected in series between auxiliary and working electrode connections of the potentiostat. Inset of panel a: ac current response at low frequencies. Between 500 < f < 1500 Hz, iac is nearly independent of f and is inversely proportional to R3, as demonstrated in Figure 4.

and the larger auxiliary electrode can be directly related to the cell resistance, which is dominated by the tip and membrane resistances. In section b, the dependence of the ac response on electrolyte concentration is presented. The dependence of the ac current on electrolyte concentration is important in selecting the solution compositions that yields the highest image contrast in impedance SECM. Expressions for the tip and membrane resistances are then presented in section c and used to predict the measured cell resistance in response to tip-to-membrane separation distance and to variations in lateral tip position relative to a pore opening. In section d, these numerical predictions are compared to the experimentally observed dependence of the cell resistance on tip position during approach curve measurements and in impedance imaging of an individual pore. (a) SECM Cell Impedance. The solid line in Figure 3a shows a plot of iac versus excitation frequency, f, in response to a 10 mV rms ac signal applied between the SECM tip and a 1.5-mm radius Pt disk electrode. The two electrodes are separated by a porous membrane, with a nominal pore density of 8 × 104 pores/cm2 and a solution contact area of ∼2.5 mm2. This iac response function in Figure 3a contains a relatively flat region between 25 and 1000 Hz, in which iac is observed to be nearly independent of frequency (see inset of Figure 3). In this flat region, iac is directly proportional to the inverse of the resistance of the SECM cell, as demonstrated later. The width of the frequency-independent region is significant only when the capacitive reactance of the SECM cell is small

relative to the resistance of the cell. When the capacitive reactance of the SECM cell makes up a significant portion of the total impedance, the frequency independent region is not observed, and iac extrapolates directly to zero at low frequencies. An equivalent circuit of the SECM cell and measurement system that is consistent with the ac response function is presented in Figure 3b. Starting with the left side of the circuit, an ac potential is applied to a potentiostat, which is represented by a parallel resistor and capacitor in series with a finite system resistance. The SECM cell, which consists of everything between the SECM tip and auxiliary electrode connections, contains the resistance of the bulk solution (which is insignificant relative to the total resistance of the SECM cell), the resistance of the porous membrane, and the capacitance and resistance of the tip electrode.29-31 These latter two components can be modeled by a resistor and a capacitor in series. The SECM cell is in parallel with a stray capacitance that is associated with the wires and electrical connections. The resulting ac current response is measured using the lock-in amplifier, also modeled by a resistor and capacitor in parallel. The accuracy of the equivalent circuit in Figure 3b in modeling the SECM cell was tested by two methods. First, the frequency response of the equivalent circuit was computed using an electrical circuit simulator, SwCADIII. Fixed values for R1, R2, R4, C1, C2, and C4 were determined (listed in the caption of Figure 3) so that when variable values of R3 and C3 where chosen, the iac frequency response would closely match that of the real circuit. Second, the SECM cell was replaced by a real series RC circuit, using C3 ) 40 pF and R3 ) 8 MΩ, which were chosen in the electrical circuit simulator to match the iac frequency response of the SECM cell with the membrane in place. The value of 40 pF for a 1-µm radius hemispherical electrode corresponds to a double layer capacitance of 650 µF/cm2. This value is over an order of magnitude larger than the expected double layer capacitance of this electrode based on the exposed Pt area and typical values of capacitance per area for Pt/aqueous electrolyte interfaces (50-100 µF/cm2). The large value of C3 indicates a contribution of the Pt/ glass/electrolyte interfacial capacitance to C3. This conclusion was demonstrated by observing that C3 was a function of how deep the SECM tip was immersed in the solution. The dashed line in Figure 3b shows the frequency response of this dummy cell, which matches very well that of the SECM cell with membrane in place. With the dummy R3C3 series circuit inserted between working and auxiliary leads of the potentiostat, the ac current is inversely proportional to the value of the resistor, R3, at frequencies between ∼25 and ∼1500 Hz. A linear plot of iac as a function of 1/R3 at f ) 1.0 kHz is presented in Figure 4 for R3 ranging from 2 to 20 MΩ and C3 ) 40 pF. As predicted, the slope of the linear plot of iac versus 1/R3 is equal to the input ac signal voltage (2 mV rms). A similar linear plot of iac versus 1/R3 was obtained using a 10 mV rms signal. All further experiments were therefore performed at f ) 1.0 kHz, so that the total resistance of the SECM cell could be directly computed from iac. (29) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley & Sons: New York, 1980. (30) Wang, J.; Feldberg, S. W.; Bard, A. J. J. Phys. Chem. B 2002, 106, 1044010446. (31) LeSuer, R. J.; Fan, F.-R. F.; Bard, A. J. Anal. Chem. 2004, 76, 6894-6901.

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Figure 4. iac as a function of 1/R3 for a simple R3C3 circuit mimic of the SECM cell (2 MΩ < R3 < 20 MΩ and C3 ) 40 pF, at 1 kHz). The slope of the plot is equal to Vin (2 mV rms).

(c) Overall Cell Resistance. The resistance of the SECM cell encompasses the resistance at the SECM tip (Rtip) and the resistance of the membrane. As indicated in Scheme 1, the resistance of a membrane containing a single pore comprises the resistances of the large pore opening (Rexit), the pore (Rpore), and the small pore opening (Rentry). In this section, we compute approximate values of each based on their geometry and the solution conductivity. Numerical estimates of these resistances help guide the interpretation of the impedance SECM approach curves and imaging experiments. The SECM tips used in this experiment are conical shaped. However, for the purpose of these approximate calculations, we assume a simpler hemispherical geometry. The resistance at a hemispherical tip is given by

Rtip ) 1/2πκrt

(2)

where κ is the solution conductivity. Thus, in a 1 mM KCl solution, the resistance of a 1-µm radius tip is ∼10.6 MΩ. The resistances at the pore entrance and exit are calculated assuming disk-shaped openings (eq 3).

Rexit ) 1/4κrexit and Rentry ) 1/4κrentry

Figure 5. SECM cell resistance measured between a ∼1-µm radius SECM tip and a Pt disk electrode as a function of [KCl] (f ) 1.0 kHz and Vin ) 10 mV rms).

(b) Dependence of Response Linearity on Electrolyte Concentration. To determine the optimal electrolyte concentration for imaging a pore, KCl solutions ranging from 1 to 100 mM where prepared, and their resistances were measured by applying a 1 kHz, 10 mV rms signal between the SECM tip and the Pt disk, in the absence of the membrane. The measured resistance, which thus corresponds to Rtip, was directly calculated from iac using eq 1. The data are presented in Figure 5. At low electrolyte concentrations, less than ∼5 mM, the resistance roughly decreases in inverse proportion to the salt concentration. At high electrolyte concentrations, the computed resistance approaches a constant value, indicating that the capacitive reactance of the tip is contributing significantly to the overall impedance. Thus, in SECM experiments described later, a 1 mM KCl solution was used in the upper compartment of the imaging cell, which contains the SECM tip. As discussed in the introductory paragraphs, a significant image contrast in SECM impedance microscopy of membranes requires that the variation in (Rtip + Rexit) is comparable in magnitude to the overall cell resistance (Rtip + Rentry + Rpore + Rexit). Thus, the contrast can be improved significantly by minimizing the two resistances whose values do not depend on tip position, Rentry and Rpore. One method of reducing Rentry and Rpore is to simply increase the electrolyte concentration on the donor (lower) side of the membrane, while maintaining a low electrolyte concentration on the receptor (upper) side to minimize the capacitive reactance of the SECM tip. This strategy is employed in the imaging experiments described later. 5568

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(3)

Thus, Rexit in the upper solution (1 mM KCl) has a value of ∼16.7 MΩ, while Rentry in the lower solution (10 mM KCl) is ∼56 MΩ. The larger value of Rentry is due to the much smaller radius of the entry pore. If the lower solution contained 1 mM KCl, then Rentry would be ∼560 MΩ, which would dominate the total resistance of the impedance cell and hinder successful impedance imaging based on measuring ∆(Rtip + Rexit). Thus, a higher electrolyte concentration was used in the lower solution. While this approach is not rigorously necessary for imaging pores, it does allow a pore to be more easily found and imaged. The resistance of the conical-shaped pore is given by

Rpore ) lp/(πκrentryrexit)

(4)

where lp is the length of the pore (i.e., the thickness of the membrane). This resistance is a bit more difficult to estimate, as the solution composition is not well-defined due to the pore being contacted by solutions of different electrolyte concentrations (1 and 10 mM, respectively, on the exit and entrance side). If the pore was completely filled with 10 mM KCl, it would have a resistance of ∼430 MΩ. If the pore was filled entirely with 1 mM KCl, it would have a resistance of ∼4.3 GΩ. We assume an average resistance of ∼2.6 GΩ. The total SECM cell resistance, Rtot, then consists of Rtip in series with the resistance of N pores in parallel (Rentry + Rpore + Rexit)/N (eq 5).

Rtot ) Rtip + (Rentry + Rpore + Rexit)/N

(5)

where N ∼ 2000 for the polycarbonate membrane with a pore density of 8 × 104 cm-2 and an exposed membrane opening of ∼2.5 mm2. Substituting the previous values yields (Rentry + Rpore + Rexit)/N ) 1.3 MΩ and Rtot ) 11.9 MΩ. Thus, the SECM tip

Figure 6. SECM cell resistance vs SECM tip-membrane separation distance, d, for a ∼1-µm radius Pt SECM tip over a porous polycarbonate membrane in a 1 mM KCl solution. The auxiliary electrode is positioned on the opposite side of the membrane in a 10 mM KCl solution (f ) 1.0 kHz and Vin ) 10 mV rms).

resistance (∼10.6 MΩ) represents ∼90% of the overall cell resistance, the remainder associated with the membrane. (d) Approach Curve and Imaging. As the SECM tip approaches an insulating surface, Rtip is expected to increase due to the surface impeding ion transport (Scheme 1). Figure 6 shows a representative approach curve above the porous polycarbonate membrane obtained by applying a 10 mV rms, 1.0 kHz signal between the tip and the auxiliary electrode. We measured Rtot ranging from 1 to 30 MΩ in experiments using different SECM tips and different membranes, in reasonable agreement with the estimated value of 11.9 MΩ (section c). The scatter in Rtot is primarily due to differences in the sizes of SECM tips used in this measurement. As the tip approaches the membrane, there is no a priori means of knowing the relative position of the tip relative to pore openings on the membrane surface, although the likelihood of approaching the surface directly above a pore opening is quite small (∼0.2% based on the fraction of the membrane surface area occupied by the pore openings). Thus, no attempt was made in this study to quantitatively interpret approach curves. Nevertheless, as shown in Figure 6, we typically observed a ∼5% increase in Rtot as the tip approaches the surface within a distance of a few micrometers, a consequence of the membrane blocking the ionic current. Figure 7 presents representative impedance images of the pore exits of (a) a single conical pore and (b) two adjacent pores, obtained by rastering the SECM tip across the polycarbonate membrane surface at a tip-to-surface separation of ∼2 µm. The small difference in image contrast in these images is due to differences in tip-to-membrane separation distance, as well as the use of different SECM tips. Changes in the cell impedance as the tip passes over a pore ranged from 0.1 to 30%. In principle, the size of the SECM tip, the tip-to-membrane separation distance, the resistance of the pore opening, and the number of pores in the membrane each influence the change in impedance as the tip is rastered across the pore. As discussed in the introductory paragraphs, the relative change in Rtot as the tip passes over the pore is anticipated to be larger for membranes containing a larger number of pores. Several attempts were made to obtain impedance images of the pore in a membrane that contained only a single pore (N ) 1). We were unable to observe the single pore by SECM impedance imaging,

Figure 7. SECM image of the variation in resistance above (a) the large opening (2.5 µm) of an individual conical-shaped pore and (b) the large openings (2.5 µm) of two conical-shaped pores in close proximity to each other. The images were measured with ∼1-µm radius Pt SECM tips, with 1 and 10 mM KCl, in the upper and lower solutions, respectively (f ) 1.0 kHz and Vin ) 10 mV rms).

presumably due to the fact that when one pore separates the SECM tip and auxiliary electrode, the change in (Rtip + Rexit), as the tip is rastered over the pore, is negligible relative to (Rtip + Rentry + Rpore + Rexit). A systematic study on the influence of N on image resolution of impedance imaging is being pursued. CONCLUSION The results reported previously demonstrate that the pore structure in a membrane can be imaged by ac impedance mode SECM. This capability greatly extends the potential applications of SECM in imaging membranes to situations where redox mediators cannot be employed. With appropriate choices of frequency and electrolyte concentration, the SECM cell impedance can also be directly related to the resistance of an individual membrane pore, even in the presence of a large number of neighboring pores. Thus, it appears possible to measure changes in the ac conductivity of a single pore in response to processes that physically or chemically alter the pore structure. We are especially interested in monitoring the changes in pore conductivity in response to the transport of small particles through the pore (e.g., polymeric particles, viruses, and spores). These investigations are currently underway and will be reported in the future. ACKNOWLEDGMENT This research was supported by the Defense Advanced Research Project Agency. The assistance of Mr. R. Jones in analysis of the cell impedance is gratefully acknowledged. Received for review March 16, 2005. Accepted June 7, 2005. AC050453S Analytical Chemistry, Vol. 77, No. 17, September 1, 2005

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