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Scanning electrochemical microscopy of a porous membrane
Science, 58 (1991) 71-87 Elsevier Science Publishers B.V.. Amsterdam
71
Journal of Membrane
Scanning electrochemical membrane
microscopy of a porous
Erik R. Scott and Henry S. White* Department of Chemical Engineering Minneapolis, MN 55455 (USA)
and Materials
Science,
University
of Minnesota,
and J. Bradley Phipps Medtronic,
Inc., 8299 Central Avenue,
NE, Spring Lake Park, MN 55432 (USA)
(Received August 13,199O; accepted in revised form December 12,199O)
Abstract Measurement of the local flux of electroactive ions across a porous membrane using scanning electrochemical microscopy (SECM) is described. SECM consists of rastering a hemispherical microelectrode ( u 3.0 pm diameter), held at constant electrochemical potential, across the membrane surface and oxidizing (or reducing) electrochemically active species that emerge from membrane pores. The resulting faradaic current is plotted to construct images of ion pathways in the membrane. SECM images resulting from the passive and electrophoretic flux of potassium ferrocyanide through 1.3 pm radius pores in mica are reported. microporous and porous membrane; electrochemistry; electrophoresis; facilitated transport; scanning electrochemical microscopy; porous mica membrane; ion pathways
Keywords:
Introduction Models of mass-transfer in porous materials are generally based on macroscopic measurements of average fluxes, coupled with structural and chemical properties derived from independent experimentation and theory. While such empirical, and often highly parameterized, models are extremely successful in predicting overall fluxes in porous materials the microscopic features incorporated within the models are often left untested by direct measurements. In this preliminary report, we describe spatially-resolved measurements of the flux of a molecular species across a porous membrane using scanning electrochemical microscopy (SECM). We demonstrate that the flux through individual pores can be directly measured and that “images” of the molecular flux *To whom correspondence should be addressed.
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0 1991-
Elsevier Science Publishers B.V.
across a porous membrane can be obtained using SECM with a resolution of several micrometers. The apparatus employed in our work for imaging porous materials is adapted from instrument designs reported by Engstrom [l-3], Bard [ 4-71 and coworkers. The SECM imaging system (Fig. 1) consists of a diffusion cell separated by the flat porous membrane to be imaged. The donor compartment contains an electroactive species, e.g. R-, at known concentration while the receptor compartment maintains an effectively zero bulk concentration of R-. The local flux of R- across the membrane resulting from the concentration gradient is detected through an electrochemical reaction, e.g. R- -+O + ee, occurring at a microelectrode probe that is rastered across the membrane surface in the receptor compartment. Spatial variations in the flux of R- that result from the porous membrane structure are reflected by an increase or decrease in the faradaic current measured at the microelectrode probe. The variations in the current are used to construct a 2-D surface image of the permeable regions of the membrane. SECM can also be used to image the electrophoretic flux of electroactive ions when a steady d.c. current is passed across the membrane. If R- carries a
electrode
Fig. 1. Schematic
of the scanning electrochemical
1
microscope
/electrode
(SECM).
significant fraction of the current, its flux will vary as a function of the applied current and will be detected as described above. In this mode, SECM images reflect the local distribution of ionic current carried by an electroactive species. Imaging techniques based on measurement of the total solution conductivity have been previously reported by Burnette [ 81, Hansma [ 91, and coworkers. However, in SECM, the contribution of individual types of ions to the total conductivity can be determined by varying the electrochemical potential of the microelectrode probe to an appropriate value where that ion is oxidized or reduced. Since different ions have different electrochemical reduction potentials, it is possible to analyze for the individual fluxes of several electroactive species in a multicomponent solution. In addition, it is noteworthy that the passive flux of an uncharged species (i.e. R instead of R- ) can also be imaged by SECM since detection at the scanning microelectrode requires only electrochemical activity of the diffusing species. SECM imaging of both diffusional and migrational fluxes are described in this report. Experimental Porous mica The membranes used in this study were 1.75 x 10M2cm2 diameter circular disks of porous muscovite mica provided by Prof. C.R. Martin of Texas A&M University. Pores were produced in the 10 ,um thick membrane by the tracketch process [lo]. Defect tracks produced in the mica by exposure to a collimated beam of 238Ufission fragments were etched in 48% HF for 25 min to produce pores with uniform cross section through the membrane. The mica membrane was characterized by scanning electron microscopy (SEM) . The pores have rhomboidal cross sections with 60 and 120 degree included angles, and with edge lengths ranging from 1.0-3.0 pm (Fig. 2). In the analysis of the transport data, the pore openings are approximated as circular disks of area nrg equal to the true rhomboidal cross-sectional area. An average value for rp of 1.3 -t 0.3 ,um was obtained from SEM measurements of 20 pores. The width of this size distribution ( + 25% ) is in agreement with that measured by Anderson and coworkers [lo]. The pores are randomly distributed through the membrane with an average density of 4.5 x 103/cm2. Microelectrode fabrication Microelectrodes for SECM imaging were fabricated by immersing the end of a 4 cm length of 250 pm diameter Pt-BO%Ir wire (Wilkinson, West Lake Village, CA) to a depth of 3 mm in an aqueous solution of 6M NaCN and 2M KOH and applying 25 V r.m.s. at 60 Hz until the end of the wire had etched itself out of solution ( N 2 min) . This procedure yields an approximately hemispherical tip at the etched end of the wire. Etched wires were sonicated in H20 for 10 min, soaked overnight in purified H20, and dried in a laminar flow hood.
Fig. 2. Scanning
electron micrographs
of porous mica membrane.
In order to reduce background capacitance and faradaic cur1‘ents, a polyi ner insulation was applied to the wires except at the very tip [ll 1. Th’is was ac:thcomplished by dipping the wires into a stirred solution of polo7(methyl rnE
75
Fig. 3. Scanning electron microscopy of poly (methylmethacrylate)-coated 80/20% Pt/Rh microelectrode after electrodeposition of Cu onto the exposed tip. (a) Secondary electron image; (b) Energy dispersive X-ray specroscopy map of Cu.
acrylate) (PMMA) dissolved in 1,2-dichloroethane (10% w/v). After removing the wire from the PMMA solution and drying in air, a stable PMMA coating insulates the shank of the wire leaving the metal exposed only at the tip. To verify that the end of the microelectrode is exposed and that the polymer coating is adherent elsewhere, copper was deposited onto one microelectrode from a O.lM CuClJO.1 M HCl solution. The electrode was then examined by SEM (Fig. 3). Comparison of the secondary electron image (Fig. 3a) and energy dispersive X-ray spectroscopy (EDXS) map for Cu (Fig. 3b) shows that the rough textured area at the tip of the wire is Cu. A subsequent EDXS map for Cl (not shown) revealed no excess Cl. Hence, we conclude that the metallic Cu was deposited only at the exposed tip of the Pt-Ir wire. The active areas of the electrodes were estimated from the transport-limited current for oxidation of Fe ( CN)G~ in a 0.1 M K,Fe ( CN)G/O.l M KC1 solution. For the electrode used in obtaining the images presented in this paper, a limiting current, ilim,of 120 nA was recorded. Assuming a hemispherical tip geometry and radial diffusion, the tip radius can be estimated from [ 12,131: r, = ilim/2xnFDC* where ilimis the limiting current, r, is the electrode radius, n is the number equivalents of electrons per mole, F is Faraday’s constant, D is the diffusivity ofFe(CN)g4 (6.5X10W’cm2/sec) [14] andC*isthebulkFe(CN)c4 concentration. From this formula, we estimate the tip radius to be 3.0 pm, in good agreement with SEM images. Scanning electrochemical microscopy SECM images of the porous mica membrane were made in a vertical diffusion cell. High-vacuum grease (Dow Corning, Midland, MI) was used to seal the mica between the diffusion cell compartments. A Pine Instruments Model RDE-4 bi-potentiostat/galvanostat was used to control the four electrodes in the cell (Fig. 1). A hemispherical microelectrode (working electrode 1) under potentiostatic control served as the scanning probe in the receptor compartment. The receptor compartment also contained a saturated calomel reference electrode (SCE) and a Pt wire auxiliary electrode. All potentials quoted in this paper are with respect to the SCE. The donor compartment contained a large Pt wire (working electrode 2). A cathodic current applied to this electrode caused migration of electroactive anions from the donor to the receptor compartment. The microelectrode (working electrode 1) was oriented at an angle of - 20 degrees from the membrane surface normal and was actuated by motorized microtranslator stages. Two Inchworm stages (Burleigh Instruments, Fischers, New York, NY), controlled by a Burleigh 6200 controller interfaced to an IBM PC, were used for X and Y movement. Z-axis positioning of the microelectrode was made by a d.c. actuator and controller (Newport Corp., Fountain
Valley, CA, models 850-A and 850 CD-l). All axes were positionable to a precision of 0.1 pm. A carpenter’s bull’s_eye level and a sample tilt stage were used to align the diffusion cell so that the mica membrane was parellel to the XY scanning plane to within + 2 degrees. An optical telescope (25 x magnification) was used to observe the microelectrode over the mica membrane. The microelectrode was lowered onto the membrane in increments of 10 pm. At each increment, the tip was moved laterally across the surface. If the microelectrode appeared to move freely, the process was repeated. Contact with the membrane was indicated when the lateral motion of the microelectrode was noticeably inhibited. The microelectrode was then raised in 2 pm increments until it was observed that lateral motion was no longer inhibited. When done carefully, this procedure was found not to damage the insulation of the microelectrode, as indicated by the ability to produce identical cyclic voltammetric responses for the oxidation of 0.1 M K,Fe(CN)6 before and after contact with the membrane. Faradaic currents were recorded as the electrode was scanned in the X direction. The electrode was incremented along the Y axis after each scan in the X direction. Analog current data from the potentiostat were converted to digital format by a HP 7090A measurement plotter (Hewlett Packard, Palo Alto, CA), and transferred to an IBM PC via an IEEE-488 bus. One thousand data points were recorded during each line scan. Data collection for each image required 1~35 min. All chemicals were used as received without further purification. Water was purified with a Water Prodigy (Labconco, Kansas City, MI) system to a resistivity of 14 MQ-cm. Results
SECM images of porous mica separating a 0.1 M K,Fe (CN ),/O.l M KC1 (donor) solution and 0.1 M KC1 (receptor) solution are shown in Fig. 4. The image in Fig. 4 (a) is a 250 x 250 pm region of the membrane. The image in Fig. 4 (b) is of a larger area (700 x 700 pm) over the same region shown in Fig. 4 (a). During imaging, a cathodic current, iapp,of 20 PA is applied to the large Pt electrode in the donor compartment (working electrode 2)) giving an average current density, based on the membrane area, of 1.1 mA/cm’. To detect Fe ( CN)c4 exiting from the pores, the potential of the scanning microelectrode is held at 0.5 V vs. SCE, which is sufficiently positive of the standard electrode potential of the Fe(CN);4’-3 redox couple (E”‘z0.185 V vs. SCE) to cause the mass-transfer limited oxidation of Fe (CN )t4, eqn. (1). Fe(CN);4-+Fe(CN);3
+e-
(1)
The grey scale contrast in the image indicates the magnitude of the current (lighter regions indicate higher currents) measured by the scanning microe-
79
lectrode, it, as a function of the lateral position of the electrode. Because Fe( CN);* is present in the receptor compartment at negligible concentrations, the current measured by the scanning microelectrode is due to an increased concentration of Fe (CN);* near the pore openings (uide infru). The regions of high current in these images are thus associated with the flux of Fe (CN&* through the membrane pores. The width of the SECM peaks at half their maximum height is typically about 15 ,um. This dimension is N 10x greater than the pore radii, a result of the microelectrode intercepting the quasi-radial flux of Fe(CN);* from the pores at a nonzero distance from the membrane surface. Individual peaks separated by -50 pm are clearly resolved. All peaks have nearly circular cross sections, leading us to believe that each peak is due to a single pore. Fourteen pores are resolved in the image shown in Fig. 4 (b) , corresponding to a density of “active” pores of 3 x lo3 cme2, in reasonable agreement with the density of pores measured by SEM (4.5 x lo3 cmP2). The heights of the lowest and highest peaks resolved in Fig. 4 vary by a factor of six. Some variation is expected since the pore cross-sectional areas vary by nearly an order of magnitude (Fig. 2 ) . However, partial plugging of pores may also be responsible for the observed differences in peak heights. We have observed on numerous occasions that some pores become inactive during imaging over timescales of N 1 hr. An example of this phenomenon is seen in a comparison of the image of Fig. 4(a) with the image of the same region shown within the box outlined in Fig. 4 (b). In Fig. 4 (a), there are three small pores in the vicinity of the large pore near the center. Only two of the smaller pores appear in Fig. 4 (b). During the intervening 50 min between obtaining images shown in Fig. 4 (a) and (b), the flux through the third pore became sufficiently small that it is no longer resolved. This effect, which is not fully understood, is possibly due to plugging of the pores by small particles, or by precipitation of the electrolyte or redox species within the pore. It should be noted that the electrolyte solutions were not filtered before being placed in the diffusion cell. The dependence of the tip current it on the migrational flux of Fe(CN),* was investigated by measuring i, as a function of iapp.Figure 5 shows a sequence of SECM images made over an 80 pm x 80 pm region of the membrane, as a function of iapp.Two pores are resolved within the scanned area. Observe that i.e. when there is only a passive Fe (CN);* flux, the pores are even at iapp-0, faintly resolved. As i,, is increased in 20 PA increments, the magnitude of it Fig. 4. SECM images of porous mica membrane while applying a 20 PA current across the membrane. The donor compartment contained 0.1 M K,Fe(CN), and 0.1 M KCl. The receptor compartment contained 0.1 M KCl. (a) 250 x 250 ,um image, electrode scanned across the membrane at 15 pm/set; (b) 700 x 700 ,nm image, scan rate of 40 pm/set. The box drawn on the image in (b) indicates the area scanned in (a). Note that only two of the three small peaks surrounding the large peak in (a) appear in (b). The microelectrode was poised at a potential of 0.5 V vs. SCE.
80
‘,PP
-l0.5nA I-
Fig. 5. SECM images (80 X 80 pm) of porous mica membrane as a function of the applied current. cBpp. Same solution conditions as in Fig. 4.
increased. Figure 6 is a plot of it, made over the centers of the two pores imaged in Fig. 5, as a function of iapp.For each pore, i, varies approximately linearly with iapp.The extrapolated non-zero intercepts of - 0.2 nA are slightly larger than the measured current resulting from the passive Fe(CN)c4 flux ( - O.l0.15 nA). The voltage required to yield the electrophotetic current at working
81
electrode 2 increased in magnitude from -0.4 V (ia,,= +A) to - 1.3 V vs. SCE (i,,,=80,~A). The current measured by the scanning microelectrode corresponds to a small fraction of the total flux of Fe(CN)g4 through a pore. The majority of Fe(CN)G4 that exits the pore diffuses and/or migrates quasi-radially away from the pore and is undetected by the microelectrode (Fig. 1). The fraction of electroactive species that is measured at the microelectrode can be defined as a collection efficiency e = it/i,
(2)
where i, is the theoretical maximum current at the microelectrode if every molecule of Fe ( CN)F~ exiting from the pore were electro-oxidized. This maximum current corresponds to the molar flux of Fe ( CN)g4 within a single pore, NF,+cN),~, after conversion to electrochemical units, i,= (~FA,)NF~(CN),~ (A, is the cross-sectional area of the pore). Approximating the passive flux of Fe ( CN)r4 as a purely diffusional flux, i,, can be estimated as
FzF(CT -CZ)
i, =
R entry + &ore + Rexit
(3)
In eqn. (3), CT and Cz denote the bulk concentrations of Fe(CN)r4 in the donor and receptor solutions, respectively. Rentw and Rexit are the mass-transfer resistances ( sec/cm3) due to diffusion at the pore entrance and exit [ 1.51, respectively, and Rpore is the resistance within the pore. For a cylindrical pore of radius rp and length 2 whose openings are circular-shaped, Rexit = Rentw = ( 4r,D ) - ’ and Rpore= (Z/m-ED). Substitution of these values into eqn. (3) yields 2nnFDr~(CT
a=
-Cz)
7vp + 21 2.0
I.5
2 1.0 .*0.5
Fig. 6. Microelectrode current, i,, as a function the applied current, i,,. Data (circles) correspond to the two current peaks in Fig. 5. The lines are the linear least squares fits to the data for each peak.
82
From the pore geometry, Rent,.JRpore~0.10. Thus, the flux of Fe (CN)g4 is limited primarily by the pore resistance, and not by entrance or exit effects. Using II = 6.5 x lo-” cm’, rP= 1.3 x 10e4 cm, Cy = 10 -’ mol/cm3, CZ = 0, and I= 10 -3 cm, the maximum passive current, ip, is calculated to be 3.0 nA. Using the measured values of it from Fig. 6 (0.1 and 0.15 nA), the collection efficiency (eqn. 2 ) is calculated to be 0.033-0.050. The low collection efficiency indicates that only a small fraction of the Fe(CN)c4 transported through the pore is detected by the microelectrode. To compare the collection efficiency for the passive flux to that obtained when iappis nonzero and Fe ( CN)c4 is driven through the pores by the applied current, the following calculations were performed. The theoretical maximum current that could be measured at the microelectrode is approximated by $ = i, + i,
(5)
where i, is current resulting from the diffusional flux of Fe(CN)F4 (eqn. 4) and i, represents the contribution resulting from the electrophoretic flux. The electromigrational component of the current is calculated from eqn. (6) n(i,,,)t &= ]zi [A&
(6)
where zi is the charge of the electroactive ion ( -4), A is the membrane area, N, is the density of pores (4.5 x 103/cm2 ), and t is the transference number for Fe ( CN)c4. The transference number was assumed to be the mean of the transference numbers in the bulk solutions of the donor (0.20) and receptor (0.0) compartments [ 161. From Fig. 6, we observe that for ia,,= PA, the corresponding measured current at the microelectrode is 0.65 nA. From eqn. (6)) i, is calculated to be 6.1 nA yielding a maximum theoretical current, $, (eqn. 5)) of 9.1 nA. The collection efficiency e from eqn. (2) (with $ replacing i,,) for this case is 0.071, slightly larger than the value obtained from passive transport measurements (0.033-0.050). The value based on the passive flux of Fe ( CN)c4 is probably more accurate, since it does not require knowledge of the solution transference numbers or the pore density of the membrane. The foregoing analysis does not require an estimate of the distance between the membrane and scanning probe. However, in regard to the resolution achievable in SECM measurements of local flux, it is clearly advantageous to position the scanning probe as close to the membrane as possible. This can be readily demonstrated by considering an approximate treatment, schematically diagrammed in Fig. 7, of the interaction between the pore opening and the scanning microelectrode. Approximations are made concerning the geometry of the pore opening and microelectrode in order to simplify the resulting equations. The pore is assumed to have a hemispherical opening of radius rl, producing a radial flux of electroactive ions away from the pore. The microelectrode is assumed to be a sphere (instead of a hemisphere ), located at a distance
83
Fig. 7. Schematic
of the pore-microelectrode
flux of electroactive
interaction.
The dashed arrows indicate the radial
species between the pore opening and the microelectrode
probe.
r from the center of the pore. The reason for making this approximation will become apparent below. The vertical (z) and lateral (3~)position of the probe are related to r by r2=z2+x2. The third assumption made is that the faradaic reaction occurring at the tip does not significantly alter the radial flux of electroactive ions from the pore. This assumption is valid when r >> r; , where r; is the radius of the pore opening. Solving the continuity equation, V‘%=O, for the concentration profile of electroactive ions surrounding the pore opening, yields the differential flux of electroactive species (dNi) through an area dA centered at a position r from the pore opening
where a is an integration constant to be evaluated. Replacing the differential area dA by the projected area of the spherical scanning microelectrode, nr$, yields the current measured at this electrode: i, = 7
(m-z)
(8)
The assumption of a spherical electrode geometry made earlier allows the projected area to be treated as a constant, independent of the pore-microelectrode probe separation, r. The integration constant, a, can be obtained by evaluating the flux at the pore opening. This is most easily accomplished by replacing dA in eqn. (7) by the surface area of the hemispherical pore (2n (r;) 2 ) and correspondingly substituting di by i,,, the total current through the pore. i, = 2nnFDa
(9)
84
Combining
eqns. (8) and (9) yields, after substitution
i,rE
of r2 = z2 + x2:
(10)
It = 2(22+x2)
The advantages of placing the microelectrode close to the membrane (i.e. decreasing z) are apparent from eqn. (10). First, the measured current is proportional to ( z2 +x2 ) - ‘. Thus, the lower limit of detection of species emerging from the pore decreases as z decreases. Second, eqn. (10) indicates that the width of the SECM current peak about a pore decreases with decreasing z. The peak width measured at half of the maximum current (at x = 0 ) is equal to 22. Therefore, the image resolution is proportional to z-l. From eqn. (10) it is possible to estimate the vertical position of the scanning microelectrode above the membrane surface. For example, the passive flux of Fe ( CN)c4 yields a current at the center of the right-hand SECM peak in Fig. 5 of 0.126 nA. The average value of i, from eqn. (4) was previously computed to be 3.0 nA. Substituting these values into eqn. (lo), along with X= 0, yields z = 9.0 ,um. This value is expected to be somewhat larger than the actual height of the probe over the pore, because of the assumption of a symmetrical radial flux of species from a hemispherical pore opening. For the flat pore opening of the mica membranes, the flux will be non-uniform, with higher values near the pore edges. The current measured above the pore will thus be expected to be lower at the center of a flat pore opening, resulting in an overestimation of z based upon the model shown in Fig. 7. Figure 8 shows a comparison of the experimental it profile for the right hand peak in Fig. 5 (points) with the profile (solid line ) calculated from eqn. (lo), using z = 9.0 pm. The two curves closely coincide within t 10 pm of the center of the pore. At greater lateral distances, the model underestimates the current. This is likely due to a combination of two factors: the pore opening is flush with the membrane rather than hemi0.16
I
I
0.12 2 6
0.08
._
I
I
I
I
*_ t%-A ‘.
0.04
,
0 -40
-30
I
-20
I
I
-10
L
I
I
I
I
0
10
20
30
40
X (Pm)
Fig. 8. Plot of tip current, i,, as a function of position x: from the center of the righthand pore in Fig. 4. Experimental data are shown as individual points. Solid line corresponds to eqn. (10) in text.
85
spherical as the model assumes, and there is a small positive background CUFrent away from the pores due to slight overlap of diffusion fields from neighboring pores. Given the crudeness of the model, however, the agreement with experiment is very good. Conclusion
A scanning electrochemical microscope has been constructed and used to measure the local permeability of a porous mica membrane by probing the concentration of electroactive species emerging from pore openings. The ability to detect - 1 pm radius pores separated by 50-100 pm has been demonstrated. SECM images show that the flux through individual pores in mica varies by an order of magnitude. Preliminary results indicated that pores suddenly become inactive in the KCl/K,Fe(CN), solution, a phenomenon that warrants further study. Increases in the SECM resolution can likely be achieved by decreasing the height at which the probe is rastered above the surface and by decreasing the probe dimension. Microelectrode probes with submicron dimensions [ 11,171 have been recently applied in SECM and scanning tunneling microscopy investigations and should be useful for studying porous materials. The ultimate resolution in resolving the flux from two closely spaced pores is a complex function of instrument design limitations, as well as the membrane and pore geometry. For instance, the concentration profile extending from smaller pore openings will be correspondingly shorter, thereby increasing the ability to resolve two pores. However, the total flux of electroactive species will eventually fall below the limit of electrochemical detection as the pore size decreases. A full analysis of this problem is in progress. Acknowledgment
This work was supported by Medtronic, Inc. (Minneapolis) and by the Center for Interfacial Engineering with funding from NSF Engineering Research Centers Program (CDR 8721551) and industrial sponsors. The generous gift of porous mica membranes from C.R. Martin is gratefully acknowledged. List of symbols
i
4 c
C* CT
integration constant ( mol/cm2 ) total cross-sectional area of membrane ( cm2 ) pore cross-sectional area ( cm2 ) concentration ( mol/cm3 ) bulk concentration ( mol/cm3 ) bulk concentration in donor solution ( mol/cm3)
bulk concentration in receptor solution ( mol/cm3) diffusion coefficient ( cm2/sec) collection efficiency (dimensionless ) formal potential (V) Faraday’s constant (Coul/eq) current (A) current applied across membrane (A ) diffusion limited current (A) current resulting from electrophoretic flux (A) current resulting from diffusional flux (A) current resulting from combined diffusional and electrophoretic flux (A) tip current (A) pore length (cm) equivalents of charge transferred per mol of reacted species (eq/mol) molar flux ( mol/cm2-set) flux of species i ( mol/cm2-set) density of pores (cmm2) oxidized species distance form tip to center of pore opening (cm) reduced species carrying negative charge electrode radius (cm) effective pore radius (cm) hemispherical pore radius (cm) transference number (dimensionless) lateral distance from tip to center of pore opening (cm) tip height above pore (cm) charge of ion References 1 R.C. Engstrom, Spatial resolution of electrode heterogeneityusing iontophoresis, Anal. Chem., 2 3 4 5 6 7
56 (1984) 890. R.C. Engstrom, T. Meaney, R. Tople and R.M. Wightman, Spatiotemporal description of the diffusion layer with a microelectrode probe, Anal. Chem., 59 (1987) 2005. R.C. Engstrom, M. Weber, D.J. Wunder, R. Burgess and S. Winquist, Measurements within the diffusion layer using a microelectrode probe, Anal. Chem., 58 (1988) 844. A.J. Bard, F.-R.F. Fan, J. Kwak and 0. Lev, Scanning electrochemical microscopy. Introduction and principles, Anal. Chem., 61 (1989) 132. J. Kwak and A.J. Bard, Scanning electrochemical microscopy. Theory of the feedback mode, Anal. Chem., 61 (1989) 1221. J. Kwak and A.J. Bard, Scanning electrochemical microscopy. Apparatus and two-dimensional scans of conductive and insulating substrates, Anal. Chem., 61 (1989) 1794. C. Lee, J. Kwak and A.J. Bard, Application of scanning electrochemical microscopy to biological samples, Proc. Natl. Acad. Sci. USA, 87 (1990) 1740.
87 8
9
10 11 12 13 14
15 16
17
R.R. Burnette and B. Ongipipattanakul, Characterization of the pore transport properties and tissue alteration of excised human skin during iontophoresis, J. Pharm. Sci., 77 (1988) 132. P.K. Hansma, B. Drake, 0. Marti, S.A.C. Gould and C.B. Prater, The scanning ion conductance microscope, Science, 243 (1989) 641. J.A. Quinn, J.L. Anderson, W.S. Ho and W.J. Petzny, Model pores of molecular dimensions. Preparation and characterization of track-etched membranes, Biophys. J., 12 (1972) 990. M.J. Heben, M.M. Dovek, M.S. Lewis, R.M. Penner and C.F. Quate, Preparation of STM tips for in-situ characterization of electrode surfaces, J. Microscopy, 152 (1988) 651. R.A. Alberty and G.G. Hammes, Application of the theory of diffusion-controlled reactions to enzyme kinetics, J. Phys. Chem., 62 (1958) 154. M.A. Dayton, J.C. Brown, K.J. Stutts and R.M. Wightman, Faradaic electrochemistry at microvoltammetric electrodes, Anal. Chem., 52 (1980) 946. M. von Stackelberg, M. Pilgram and V. Toome, Determination of diffusion coefficients of ions in aqueous solutions in the presence of foreign electrolytes (I), Z. Elektrochem., 57 (1953) 342. Y. Saito, Theoretical study on the diffusion current at stationary electrodes of circular and narrow band types, Rev. Polarogr., 15 (1968) 177. T.W. Chapman and J.A. Newman, Compilation of selected thermodynamic and transport properties of binary electrolytes in aqueous solution, Ernest 0. Lawrence Radiation Laboratory Document, University of California, Berkely, CA, 1968. C. Lee, C.J. Miller and A.J. Bard, Scanning electrochemical microscopy: preparation of submicrometer electrodes, Anal. Chem., 63 (1991) 78.
71
Journal of Membrane
Scanning electrochemical membrane
microscopy of a porous
Erik R. Scott and Henry S. White* Department of Chemical Engineering Minneapolis, MN 55455 (USA)
and Materials
Science,
University
of Minnesota,
and J. Bradley Phipps Medtronic,
Inc., 8299 Central Avenue,
NE, Spring Lake Park, MN 55432 (USA)
(Received August 13,199O; accepted in revised form December 12,199O)
Abstract Measurement of the local flux of electroactive ions across a porous membrane using scanning electrochemical microscopy (SECM) is described. SECM consists of rastering a hemispherical microelectrode ( u 3.0 pm diameter), held at constant electrochemical potential, across the membrane surface and oxidizing (or reducing) electrochemically active species that emerge from membrane pores. The resulting faradaic current is plotted to construct images of ion pathways in the membrane. SECM images resulting from the passive and electrophoretic flux of potassium ferrocyanide through 1.3 pm radius pores in mica are reported. microporous and porous membrane; electrochemistry; electrophoresis; facilitated transport; scanning electrochemical microscopy; porous mica membrane; ion pathways
Keywords:
Introduction Models of mass-transfer in porous materials are generally based on macroscopic measurements of average fluxes, coupled with structural and chemical properties derived from independent experimentation and theory. While such empirical, and often highly parameterized, models are extremely successful in predicting overall fluxes in porous materials the microscopic features incorporated within the models are often left untested by direct measurements. In this preliminary report, we describe spatially-resolved measurements of the flux of a molecular species across a porous membrane using scanning electrochemical microscopy (SECM). We demonstrate that the flux through individual pores can be directly measured and that “images” of the molecular flux *To whom correspondence should be addressed.
0376-7388/91/$03.50
0 1991-
Elsevier Science Publishers B.V.
across a porous membrane can be obtained using SECM with a resolution of several micrometers. The apparatus employed in our work for imaging porous materials is adapted from instrument designs reported by Engstrom [l-3], Bard [ 4-71 and coworkers. The SECM imaging system (Fig. 1) consists of a diffusion cell separated by the flat porous membrane to be imaged. The donor compartment contains an electroactive species, e.g. R-, at known concentration while the receptor compartment maintains an effectively zero bulk concentration of R-. The local flux of R- across the membrane resulting from the concentration gradient is detected through an electrochemical reaction, e.g. R- -+O + ee, occurring at a microelectrode probe that is rastered across the membrane surface in the receptor compartment. Spatial variations in the flux of R- that result from the porous membrane structure are reflected by an increase or decrease in the faradaic current measured at the microelectrode probe. The variations in the current are used to construct a 2-D surface image of the permeable regions of the membrane. SECM can also be used to image the electrophoretic flux of electroactive ions when a steady d.c. current is passed across the membrane. If R- carries a
electrode
Fig. 1. Schematic
of the scanning electrochemical
1
microscope
/electrode
(SECM).
significant fraction of the current, its flux will vary as a function of the applied current and will be detected as described above. In this mode, SECM images reflect the local distribution of ionic current carried by an electroactive species. Imaging techniques based on measurement of the total solution conductivity have been previously reported by Burnette [ 81, Hansma [ 91, and coworkers. However, in SECM, the contribution of individual types of ions to the total conductivity can be determined by varying the electrochemical potential of the microelectrode probe to an appropriate value where that ion is oxidized or reduced. Since different ions have different electrochemical reduction potentials, it is possible to analyze for the individual fluxes of several electroactive species in a multicomponent solution. In addition, it is noteworthy that the passive flux of an uncharged species (i.e. R instead of R- ) can also be imaged by SECM since detection at the scanning microelectrode requires only electrochemical activity of the diffusing species. SECM imaging of both diffusional and migrational fluxes are described in this report. Experimental Porous mica The membranes used in this study were 1.75 x 10M2cm2 diameter circular disks of porous muscovite mica provided by Prof. C.R. Martin of Texas A&M University. Pores were produced in the 10 ,um thick membrane by the tracketch process [lo]. Defect tracks produced in the mica by exposure to a collimated beam of 238Ufission fragments were etched in 48% HF for 25 min to produce pores with uniform cross section through the membrane. The mica membrane was characterized by scanning electron microscopy (SEM) . The pores have rhomboidal cross sections with 60 and 120 degree included angles, and with edge lengths ranging from 1.0-3.0 pm (Fig. 2). In the analysis of the transport data, the pore openings are approximated as circular disks of area nrg equal to the true rhomboidal cross-sectional area. An average value for rp of 1.3 -t 0.3 ,um was obtained from SEM measurements of 20 pores. The width of this size distribution ( + 25% ) is in agreement with that measured by Anderson and coworkers [lo]. The pores are randomly distributed through the membrane with an average density of 4.5 x 103/cm2. Microelectrode fabrication Microelectrodes for SECM imaging were fabricated by immersing the end of a 4 cm length of 250 pm diameter Pt-BO%Ir wire (Wilkinson, West Lake Village, CA) to a depth of 3 mm in an aqueous solution of 6M NaCN and 2M KOH and applying 25 V r.m.s. at 60 Hz until the end of the wire had etched itself out of solution ( N 2 min) . This procedure yields an approximately hemispherical tip at the etched end of the wire. Etched wires were sonicated in H20 for 10 min, soaked overnight in purified H20, and dried in a laminar flow hood.
Fig. 2. Scanning
electron micrographs
of porous mica membrane.
In order to reduce background capacitance and faradaic cur1‘ents, a polyi ner insulation was applied to the wires except at the very tip [ll 1. Th’is was ac:thcomplished by dipping the wires into a stirred solution of polo7(methyl rnE
75
Fig. 3. Scanning electron microscopy of poly (methylmethacrylate)-coated 80/20% Pt/Rh microelectrode after electrodeposition of Cu onto the exposed tip. (a) Secondary electron image; (b) Energy dispersive X-ray specroscopy map of Cu.
acrylate) (PMMA) dissolved in 1,2-dichloroethane (10% w/v). After removing the wire from the PMMA solution and drying in air, a stable PMMA coating insulates the shank of the wire leaving the metal exposed only at the tip. To verify that the end of the microelectrode is exposed and that the polymer coating is adherent elsewhere, copper was deposited onto one microelectrode from a O.lM CuClJO.1 M HCl solution. The electrode was then examined by SEM (Fig. 3). Comparison of the secondary electron image (Fig. 3a) and energy dispersive X-ray spectroscopy (EDXS) map for Cu (Fig. 3b) shows that the rough textured area at the tip of the wire is Cu. A subsequent EDXS map for Cl (not shown) revealed no excess Cl. Hence, we conclude that the metallic Cu was deposited only at the exposed tip of the Pt-Ir wire. The active areas of the electrodes were estimated from the transport-limited current for oxidation of Fe ( CN)G~ in a 0.1 M K,Fe ( CN)G/O.l M KC1 solution. For the electrode used in obtaining the images presented in this paper, a limiting current, ilim,of 120 nA was recorded. Assuming a hemispherical tip geometry and radial diffusion, the tip radius can be estimated from [ 12,131: r, = ilim/2xnFDC* where ilimis the limiting current, r, is the electrode radius, n is the number equivalents of electrons per mole, F is Faraday’s constant, D is the diffusivity ofFe(CN)g4 (6.5X10W’cm2/sec) [14] andC*isthebulkFe(CN)c4 concentration. From this formula, we estimate the tip radius to be 3.0 pm, in good agreement with SEM images. Scanning electrochemical microscopy SECM images of the porous mica membrane were made in a vertical diffusion cell. High-vacuum grease (Dow Corning, Midland, MI) was used to seal the mica between the diffusion cell compartments. A Pine Instruments Model RDE-4 bi-potentiostat/galvanostat was used to control the four electrodes in the cell (Fig. 1). A hemispherical microelectrode (working electrode 1) under potentiostatic control served as the scanning probe in the receptor compartment. The receptor compartment also contained a saturated calomel reference electrode (SCE) and a Pt wire auxiliary electrode. All potentials quoted in this paper are with respect to the SCE. The donor compartment contained a large Pt wire (working electrode 2). A cathodic current applied to this electrode caused migration of electroactive anions from the donor to the receptor compartment. The microelectrode (working electrode 1) was oriented at an angle of - 20 degrees from the membrane surface normal and was actuated by motorized microtranslator stages. Two Inchworm stages (Burleigh Instruments, Fischers, New York, NY), controlled by a Burleigh 6200 controller interfaced to an IBM PC, were used for X and Y movement. Z-axis positioning of the microelectrode was made by a d.c. actuator and controller (Newport Corp., Fountain
Valley, CA, models 850-A and 850 CD-l). All axes were positionable to a precision of 0.1 pm. A carpenter’s bull’s_eye level and a sample tilt stage were used to align the diffusion cell so that the mica membrane was parellel to the XY scanning plane to within + 2 degrees. An optical telescope (25 x magnification) was used to observe the microelectrode over the mica membrane. The microelectrode was lowered onto the membrane in increments of 10 pm. At each increment, the tip was moved laterally across the surface. If the microelectrode appeared to move freely, the process was repeated. Contact with the membrane was indicated when the lateral motion of the microelectrode was noticeably inhibited. The microelectrode was then raised in 2 pm increments until it was observed that lateral motion was no longer inhibited. When done carefully, this procedure was found not to damage the insulation of the microelectrode, as indicated by the ability to produce identical cyclic voltammetric responses for the oxidation of 0.1 M K,Fe(CN)6 before and after contact with the membrane. Faradaic currents were recorded as the electrode was scanned in the X direction. The electrode was incremented along the Y axis after each scan in the X direction. Analog current data from the potentiostat were converted to digital format by a HP 7090A measurement plotter (Hewlett Packard, Palo Alto, CA), and transferred to an IBM PC via an IEEE-488 bus. One thousand data points were recorded during each line scan. Data collection for each image required 1~35 min. All chemicals were used as received without further purification. Water was purified with a Water Prodigy (Labconco, Kansas City, MI) system to a resistivity of 14 MQ-cm. Results
SECM images of porous mica separating a 0.1 M K,Fe (CN ),/O.l M KC1 (donor) solution and 0.1 M KC1 (receptor) solution are shown in Fig. 4. The image in Fig. 4 (a) is a 250 x 250 pm region of the membrane. The image in Fig. 4 (b) is of a larger area (700 x 700 pm) over the same region shown in Fig. 4 (a). During imaging, a cathodic current, iapp,of 20 PA is applied to the large Pt electrode in the donor compartment (working electrode 2)) giving an average current density, based on the membrane area, of 1.1 mA/cm’. To detect Fe ( CN)c4 exiting from the pores, the potential of the scanning microelectrode is held at 0.5 V vs. SCE, which is sufficiently positive of the standard electrode potential of the Fe(CN);4’-3 redox couple (E”‘z0.185 V vs. SCE) to cause the mass-transfer limited oxidation of Fe (CN )t4, eqn. (1). Fe(CN);4-+Fe(CN);3
+e-
(1)
The grey scale contrast in the image indicates the magnitude of the current (lighter regions indicate higher currents) measured by the scanning microe-
79
lectrode, it, as a function of the lateral position of the electrode. Because Fe( CN);* is present in the receptor compartment at negligible concentrations, the current measured by the scanning microelectrode is due to an increased concentration of Fe (CN);* near the pore openings (uide infru). The regions of high current in these images are thus associated with the flux of Fe (CN&* through the membrane pores. The width of the SECM peaks at half their maximum height is typically about 15 ,um. This dimension is N 10x greater than the pore radii, a result of the microelectrode intercepting the quasi-radial flux of Fe(CN);* from the pores at a nonzero distance from the membrane surface. Individual peaks separated by -50 pm are clearly resolved. All peaks have nearly circular cross sections, leading us to believe that each peak is due to a single pore. Fourteen pores are resolved in the image shown in Fig. 4 (b) , corresponding to a density of “active” pores of 3 x lo3 cme2, in reasonable agreement with the density of pores measured by SEM (4.5 x lo3 cmP2). The heights of the lowest and highest peaks resolved in Fig. 4 vary by a factor of six. Some variation is expected since the pore cross-sectional areas vary by nearly an order of magnitude (Fig. 2 ) . However, partial plugging of pores may also be responsible for the observed differences in peak heights. We have observed on numerous occasions that some pores become inactive during imaging over timescales of N 1 hr. An example of this phenomenon is seen in a comparison of the image of Fig. 4(a) with the image of the same region shown within the box outlined in Fig. 4 (b). In Fig. 4 (a), there are three small pores in the vicinity of the large pore near the center. Only two of the smaller pores appear in Fig. 4 (b). During the intervening 50 min between obtaining images shown in Fig. 4 (a) and (b), the flux through the third pore became sufficiently small that it is no longer resolved. This effect, which is not fully understood, is possibly due to plugging of the pores by small particles, or by precipitation of the electrolyte or redox species within the pore. It should be noted that the electrolyte solutions were not filtered before being placed in the diffusion cell. The dependence of the tip current it on the migrational flux of Fe(CN),* was investigated by measuring i, as a function of iapp.Figure 5 shows a sequence of SECM images made over an 80 pm x 80 pm region of the membrane, as a function of iapp.Two pores are resolved within the scanned area. Observe that i.e. when there is only a passive Fe (CN);* flux, the pores are even at iapp-0, faintly resolved. As i,, is increased in 20 PA increments, the magnitude of it Fig. 4. SECM images of porous mica membrane while applying a 20 PA current across the membrane. The donor compartment contained 0.1 M K,Fe(CN), and 0.1 M KCl. The receptor compartment contained 0.1 M KCl. (a) 250 x 250 ,um image, electrode scanned across the membrane at 15 pm/set; (b) 700 x 700 ,nm image, scan rate of 40 pm/set. The box drawn on the image in (b) indicates the area scanned in (a). Note that only two of the three small peaks surrounding the large peak in (a) appear in (b). The microelectrode was poised at a potential of 0.5 V vs. SCE.
80
‘,PP
-l0.5nA I-
Fig. 5. SECM images (80 X 80 pm) of porous mica membrane as a function of the applied current. cBpp. Same solution conditions as in Fig. 4.
increased. Figure 6 is a plot of it, made over the centers of the two pores imaged in Fig. 5, as a function of iapp.For each pore, i, varies approximately linearly with iapp.The extrapolated non-zero intercepts of - 0.2 nA are slightly larger than the measured current resulting from the passive Fe(CN)c4 flux ( - O.l0.15 nA). The voltage required to yield the electrophotetic current at working
81
electrode 2 increased in magnitude from -0.4 V (ia,,= +A) to - 1.3 V vs. SCE (i,,,=80,~A). The current measured by the scanning microelectrode corresponds to a small fraction of the total flux of Fe(CN)g4 through a pore. The majority of Fe(CN)G4 that exits the pore diffuses and/or migrates quasi-radially away from the pore and is undetected by the microelectrode (Fig. 1). The fraction of electroactive species that is measured at the microelectrode can be defined as a collection efficiency e = it/i,
(2)
where i, is the theoretical maximum current at the microelectrode if every molecule of Fe ( CN)F~ exiting from the pore were electro-oxidized. This maximum current corresponds to the molar flux of Fe ( CN)g4 within a single pore, NF,+cN),~, after conversion to electrochemical units, i,= (~FA,)NF~(CN),~ (A, is the cross-sectional area of the pore). Approximating the passive flux of Fe ( CN)r4 as a purely diffusional flux, i,, can be estimated as
FzF(CT -CZ)
i, =
R entry + &ore + Rexit
(3)
In eqn. (3), CT and Cz denote the bulk concentrations of Fe(CN)r4 in the donor and receptor solutions, respectively. Rentw and Rexit are the mass-transfer resistances ( sec/cm3) due to diffusion at the pore entrance and exit [ 1.51, respectively, and Rpore is the resistance within the pore. For a cylindrical pore of radius rp and length 2 whose openings are circular-shaped, Rexit = Rentw = ( 4r,D ) - ’ and Rpore= (Z/m-ED). Substitution of these values into eqn. (3) yields 2nnFDr~(CT
a=
-Cz)
7vp + 21 2.0
I.5
2 1.0 .*0.5
Fig. 6. Microelectrode current, i,, as a function the applied current, i,,. Data (circles) correspond to the two current peaks in Fig. 5. The lines are the linear least squares fits to the data for each peak.
82
From the pore geometry, Rent,.JRpore~0.10. Thus, the flux of Fe (CN)g4 is limited primarily by the pore resistance, and not by entrance or exit effects. Using II = 6.5 x lo-” cm’, rP= 1.3 x 10e4 cm, Cy = 10 -’ mol/cm3, CZ = 0, and I= 10 -3 cm, the maximum passive current, ip, is calculated to be 3.0 nA. Using the measured values of it from Fig. 6 (0.1 and 0.15 nA), the collection efficiency (eqn. 2 ) is calculated to be 0.033-0.050. The low collection efficiency indicates that only a small fraction of the Fe(CN)c4 transported through the pore is detected by the microelectrode. To compare the collection efficiency for the passive flux to that obtained when iappis nonzero and Fe ( CN)c4 is driven through the pores by the applied current, the following calculations were performed. The theoretical maximum current that could be measured at the microelectrode is approximated by $ = i, + i,
(5)
where i, is current resulting from the diffusional flux of Fe(CN)F4 (eqn. 4) and i, represents the contribution resulting from the electrophoretic flux. The electromigrational component of the current is calculated from eqn. (6) n(i,,,)t &= ]zi [A&
(6)
where zi is the charge of the electroactive ion ( -4), A is the membrane area, N, is the density of pores (4.5 x 103/cm2 ), and t is the transference number for Fe ( CN)c4. The transference number was assumed to be the mean of the transference numbers in the bulk solutions of the donor (0.20) and receptor (0.0) compartments [ 161. From Fig. 6, we observe that for ia,,= PA, the corresponding measured current at the microelectrode is 0.65 nA. From eqn. (6)) i, is calculated to be 6.1 nA yielding a maximum theoretical current, $, (eqn. 5)) of 9.1 nA. The collection efficiency e from eqn. (2) (with $ replacing i,,) for this case is 0.071, slightly larger than the value obtained from passive transport measurements (0.033-0.050). The value based on the passive flux of Fe ( CN)c4 is probably more accurate, since it does not require knowledge of the solution transference numbers or the pore density of the membrane. The foregoing analysis does not require an estimate of the distance between the membrane and scanning probe. However, in regard to the resolution achievable in SECM measurements of local flux, it is clearly advantageous to position the scanning probe as close to the membrane as possible. This can be readily demonstrated by considering an approximate treatment, schematically diagrammed in Fig. 7, of the interaction between the pore opening and the scanning microelectrode. Approximations are made concerning the geometry of the pore opening and microelectrode in order to simplify the resulting equations. The pore is assumed to have a hemispherical opening of radius rl, producing a radial flux of electroactive ions away from the pore. The microelectrode is assumed to be a sphere (instead of a hemisphere ), located at a distance
83
Fig. 7. Schematic
of the pore-microelectrode
flux of electroactive
interaction.
The dashed arrows indicate the radial
species between the pore opening and the microelectrode
probe.
r from the center of the pore. The reason for making this approximation will become apparent below. The vertical (z) and lateral (3~)position of the probe are related to r by r2=z2+x2. The third assumption made is that the faradaic reaction occurring at the tip does not significantly alter the radial flux of electroactive ions from the pore. This assumption is valid when r >> r; , where r; is the radius of the pore opening. Solving the continuity equation, V‘%=O, for the concentration profile of electroactive ions surrounding the pore opening, yields the differential flux of electroactive species (dNi) through an area dA centered at a position r from the pore opening
where a is an integration constant to be evaluated. Replacing the differential area dA by the projected area of the spherical scanning microelectrode, nr$, yields the current measured at this electrode: i, = 7
(m-z)
(8)
The assumption of a spherical electrode geometry made earlier allows the projected area to be treated as a constant, independent of the pore-microelectrode probe separation, r. The integration constant, a, can be obtained by evaluating the flux at the pore opening. This is most easily accomplished by replacing dA in eqn. (7) by the surface area of the hemispherical pore (2n (r;) 2 ) and correspondingly substituting di by i,,, the total current through the pore. i, = 2nnFDa
(9)
84
Combining
eqns. (8) and (9) yields, after substitution
i,rE
of r2 = z2 + x2:
(10)
It = 2(22+x2)
The advantages of placing the microelectrode close to the membrane (i.e. decreasing z) are apparent from eqn. (10). First, the measured current is proportional to ( z2 +x2 ) - ‘. Thus, the lower limit of detection of species emerging from the pore decreases as z decreases. Second, eqn. (10) indicates that the width of the SECM current peak about a pore decreases with decreasing z. The peak width measured at half of the maximum current (at x = 0 ) is equal to 22. Therefore, the image resolution is proportional to z-l. From eqn. (10) it is possible to estimate the vertical position of the scanning microelectrode above the membrane surface. For example, the passive flux of Fe ( CN)c4 yields a current at the center of the right-hand SECM peak in Fig. 5 of 0.126 nA. The average value of i, from eqn. (4) was previously computed to be 3.0 nA. Substituting these values into eqn. (lo), along with X= 0, yields z = 9.0 ,um. This value is expected to be somewhat larger than the actual height of the probe over the pore, because of the assumption of a symmetrical radial flux of species from a hemispherical pore opening. For the flat pore opening of the mica membranes, the flux will be non-uniform, with higher values near the pore edges. The current measured above the pore will thus be expected to be lower at the center of a flat pore opening, resulting in an overestimation of z based upon the model shown in Fig. 7. Figure 8 shows a comparison of the experimental it profile for the right hand peak in Fig. 5 (points) with the profile (solid line ) calculated from eqn. (lo), using z = 9.0 pm. The two curves closely coincide within t 10 pm of the center of the pore. At greater lateral distances, the model underestimates the current. This is likely due to a combination of two factors: the pore opening is flush with the membrane rather than hemi0.16
I
I
0.12 2 6
0.08
._
I
I
I
I
*_ t%-A ‘.
0.04
,
0 -40
-30
I
-20
I
I
-10
L
I
I
I
I
0
10
20
30
40
X (Pm)
Fig. 8. Plot of tip current, i,, as a function of position x: from the center of the righthand pore in Fig. 4. Experimental data are shown as individual points. Solid line corresponds to eqn. (10) in text.
85
spherical as the model assumes, and there is a small positive background CUFrent away from the pores due to slight overlap of diffusion fields from neighboring pores. Given the crudeness of the model, however, the agreement with experiment is very good. Conclusion
A scanning electrochemical microscope has been constructed and used to measure the local permeability of a porous mica membrane by probing the concentration of electroactive species emerging from pore openings. The ability to detect - 1 pm radius pores separated by 50-100 pm has been demonstrated. SECM images show that the flux through individual pores in mica varies by an order of magnitude. Preliminary results indicated that pores suddenly become inactive in the KCl/K,Fe(CN), solution, a phenomenon that warrants further study. Increases in the SECM resolution can likely be achieved by decreasing the height at which the probe is rastered above the surface and by decreasing the probe dimension. Microelectrode probes with submicron dimensions [ 11,171 have been recently applied in SECM and scanning tunneling microscopy investigations and should be useful for studying porous materials. The ultimate resolution in resolving the flux from two closely spaced pores is a complex function of instrument design limitations, as well as the membrane and pore geometry. For instance, the concentration profile extending from smaller pore openings will be correspondingly shorter, thereby increasing the ability to resolve two pores. However, the total flux of electroactive species will eventually fall below the limit of electrochemical detection as the pore size decreases. A full analysis of this problem is in progress. Acknowledgment
This work was supported by Medtronic, Inc. (Minneapolis) and by the Center for Interfacial Engineering with funding from NSF Engineering Research Centers Program (CDR 8721551) and industrial sponsors. The generous gift of porous mica membranes from C.R. Martin is gratefully acknowledged. List of symbols
i
4 c
C* CT
integration constant ( mol/cm2 ) total cross-sectional area of membrane ( cm2 ) pore cross-sectional area ( cm2 ) concentration ( mol/cm3 ) bulk concentration ( mol/cm3 ) bulk concentration in donor solution ( mol/cm3)
bulk concentration in receptor solution ( mol/cm3) diffusion coefficient ( cm2/sec) collection efficiency (dimensionless ) formal potential (V) Faraday’s constant (Coul/eq) current (A) current applied across membrane (A ) diffusion limited current (A) current resulting from electrophoretic flux (A) current resulting from diffusional flux (A) current resulting from combined diffusional and electrophoretic flux (A) tip current (A) pore length (cm) equivalents of charge transferred per mol of reacted species (eq/mol) molar flux ( mol/cm2-set) flux of species i ( mol/cm2-set) density of pores (cmm2) oxidized species distance form tip to center of pore opening (cm) reduced species carrying negative charge electrode radius (cm) effective pore radius (cm) hemispherical pore radius (cm) transference number (dimensionless) lateral distance from tip to center of pore opening (cm) tip height above pore (cm) charge of ion References 1 R.C. Engstrom, Spatial resolution of electrode heterogeneityusing iontophoresis, Anal. Chem., 2 3 4 5 6 7
56 (1984) 890. R.C. Engstrom, T. Meaney, R. Tople and R.M. Wightman, Spatiotemporal description of the diffusion layer with a microelectrode probe, Anal. Chem., 59 (1987) 2005. R.C. Engstrom, M. Weber, D.J. Wunder, R. Burgess and S. Winquist, Measurements within the diffusion layer using a microelectrode probe, Anal. Chem., 58 (1988) 844. A.J. Bard, F.-R.F. Fan, J. Kwak and 0. Lev, Scanning electrochemical microscopy. Introduction and principles, Anal. Chem., 61 (1989) 132. J. Kwak and A.J. Bard, Scanning electrochemical microscopy. Theory of the feedback mode, Anal. Chem., 61 (1989) 1221. J. Kwak and A.J. Bard, Scanning electrochemical microscopy. Apparatus and two-dimensional scans of conductive and insulating substrates, Anal. Chem., 61 (1989) 1794. C. Lee, J. Kwak and A.J. Bard, Application of scanning electrochemical microscopy to biological samples, Proc. Natl. Acad. Sci. USA, 87 (1990) 1740.
87 8
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10 11 12 13 14
15 16
17
R.R. Burnette and B. Ongipipattanakul, Characterization of the pore transport properties and tissue alteration of excised human skin during iontophoresis, J. Pharm. Sci., 77 (1988) 132. P.K. Hansma, B. Drake, 0. Marti, S.A.C. Gould and C.B. Prater, The scanning ion conductance microscope, Science, 243 (1989) 641. J.A. Quinn, J.L. Anderson, W.S. Ho and W.J. Petzny, Model pores of molecular dimensions. Preparation and characterization of track-etched membranes, Biophys. J., 12 (1972) 990. M.J. Heben, M.M. Dovek, M.S. Lewis, R.M. Penner and C.F. Quate, Preparation of STM tips for in-situ characterization of electrode surfaces, J. Microscopy, 152 (1988) 651. R.A. Alberty and G.G. Hammes, Application of the theory of diffusion-controlled reactions to enzyme kinetics, J. Phys. Chem., 62 (1958) 154. M.A. Dayton, J.C. Brown, K.J. Stutts and R.M. Wightman, Faradaic electrochemistry at microvoltammetric electrodes, Anal. Chem., 52 (1980) 946. M. von Stackelberg, M. Pilgram and V. Toome, Determination of diffusion coefficients of ions in aqueous solutions in the presence of foreign electrolytes (I), Z. Elektrochem., 57 (1953) 342. Y. Saito, Theoretical study on the diffusion current at stationary electrodes of circular and narrow band types, Rev. Polarogr., 15 (1968) 177. T.W. Chapman and J.A. Newman, Compilation of selected thermodynamic and transport properties of binary electrolytes in aqueous solution, Ernest 0. Lawrence Radiation Laboratory Document, University of California, Berkely, CA, 1968. C. Lee, C.J. Miller and A.J. Bard, Scanning electrochemical microscopy: preparation of submicrometer electrodes, Anal. Chem., 63 (1991) 78.