AC Research
Anal. Chem. 1998, 70, 1047-1058
Accelerated Articles
Imaging Molecular Transport in Porous Membranes. Observation and Analysis of Electroosmotic Flow in Individual Pores Using the Scanning Electrochemical Microscope Bradley D. Bath, Rachel D. Lee, and Henry S. White*
Department of Chemistry, Henry Eyring Building, University of Utah, Salt Lake City, Utah 84112 Erik R. Scott
ALZA Corporation, 8295 Central Avenue N.E., Spring Lake Park, Minnesota 55432
A method of determining absolute rates of diffusion and electroosmotic convective flow through individual pores in porous ion-selective membranes is described. The method is based on positioning a scanning electrochemical microscope (SECM) tip directly above a membrane pore and detecting electroactive molecules as they emerge from the pore. Absolute diffusive and electroosmotic fluxes, electroosmotic drag coefficient, convective velocity, and pore radius can be evaluated in a single experiment by measuring the faradaic current at the SECM tip as a function of the iontophoretic current passed across the membrane. Electroosmotic transport of hydroquinone through a permselective polymer (Nafion), contained within ∼50-µm-radius pores of a 200-µm-thick mica membrane, is used as a model system to demonstrate the analytical method. Analysis of electroosmotic transport parameters obtained by SECM suggests that the average electroosmotic velocities of solvent (H2O) and solute (hydroquinone) in the Nafion are significantly different, a consequence of the differences in their chemical interactions with the current-carrying mobile cations (Na+).
Iontophoresis is the transport of molecular species under the influence of an electrical potential gradient.1 The pharmaceutical and medical communities are actively researching the iontophoretic transport of ions and molecules through skin as an (1) (a) Ledger, W. Adv. Drug Deliv. Rev. 1992, 9, 289-307. (b) Singh, J.; Maibach, H. I. Dermatology 1993, 187, 235-238. S0003-2700(97)01213-4 CCC: $15.00 Published on Web 02/07/1998
© 1998 American Chemical Society
alternative method of drug administration for humans.2 In this application, a small electrical current is driven between two electrodes that are placed in contact with the outer surface of the skin. The molecular species of interestsi.e., the drugsis dissolved in a thin layer of solution between one electrode and the skin and is transported across the skin at a continuously controlled rate that is determined by the applied current. The drug molecules traverse the skin and are transported throughout the body by the circulatory system. In comparison with transport within synthetic membranes, molecular transport in skin is not as well understood. This situation is primarily due to the very complex and heterogeneous nature of skin tissue. It is generally accepted that the stratum corneum (outermost ∼20 µm of skin) acts as the largest single transport barrier to either passive diffusion or electrically enhanced transport.3 The stratum corneum is composed of partially dehydrated keratin-filled cells separated by lipid bilayers. In addition to transport across the stratum corneum, appendages (e.g., hair follicles, sweat glands) may act as low-resistance shunts for ion transport across skin. For instance, in previous investigations of iontophoresis across mouse skin, we demonstrated that ∼75% of the applied current passes through ∼20-µm-radius hair (2) (a) Srinivasan, V.; Higuchi, W. I.; Sims, S. M.; Ghanem, A. H.; Behl, C. R. J. Pharm. Sci. 1989, 78, 370-375. (b) Sing, P.; Roberts, M. S. J. Pharm. Sci. 1993, 82, 127-131. (c) Chien, Y. W.; Siddiqui, O.; Shi, W. M.; Lelawings, P.; Liu, J. C. J. Pharm. Sci. 1989, 78, 376-383. (3) (a) Scheulepin, R. J. J. Invest. Dermatol. 1976, 67, 672-676. (b) Chizmadzhev, Y. A.; Zarnitsin, V. G.; Weaver, J. C.; Potts, R. O. Biophys. J. 1995, 68, 749-765.
Analytical Chemistry, Vol. 70, No. 6, March 15, 1998 1047
follicles.4 The relative importance of shunt paths may vary between animal skin models and has not been quantitatively evaluated for human skin. A key issue of iontophoresis concerns the mechanism(s) by which ions and molecules are transported in the skin tissues. Of particular interest in the current investigation are previously reported observations that transport of neutral molecules across skin may be facilitated by an electrical current.5 This result suggests that, in addition to diffusion and migration, electric fieldfacilitated transport in skin tissues also occurs by electroosmotic convective flow, similar to that observed in natural clays and synthetic ion-exchange membranes.6 It has been shown that transport rates through skin are also dependent on the size, charge, and hydrophobic character of the molecular permeant.7 This specificity suggests that molecular transport in skin occurs, in part, within pores of nanometer dimensions. The location and structure of these nanometer-sized domains in skin is unknown, but a reasonable assumption is that they are located within the larger physiological structures previously identified as major iontophoretic pathsse.g., hair follicles.4 Pikal has suggested existence of pores having radii ranging from 7 to 27 Å in hairless mouse skin (HMS).5b In the present report, we describe the use of scanning electrochemical microscopy (SECM)8 to evaluate quantitatively the individual contributions of diffusion and electroosmosis to the iontophoretic transport of a molecule through individual pores of a porous membrane. SECM has been used in the past to monitor molecular transport through synthetic and biological porous membranes,4a,b,9,10 including osmotic pressure-driven convective transport through laryngeal cartilage.9c Briefly, the methodology is based on positioning the SECM tip above a pore during iontophoresis to measure the flux of a redox species as it emerges from the pore opening. To test the feasibility of applying this method to studies of skin, we have constructed an artificial membrane, Figure 1A, whose structure has functional properties that closely mimic those of skin. The membrane consists of a ∼200-µm-thick layer of mica in which one large (40-75-µm radius) pore has been introduced. This large pore is intended to mimic (4) (a) Scott, E. R.; Laplaza, A. I.; White, H. S.; Phipps, B. Pharm Res. 1993, 10, 1699-1709. (b) Scott, E. R.; Phipps, J. B.; White, H. S. J. Invest. Dermatol. 1995, 104, 142-145. (c) Lee, R. D.; White, H. S.; Scott, E. R. J. Pharm. Sci. 1996, 85, 1186-1190. (5) (a) Sims, S. M.; Higuchi, W. I.; Srinivasan, V. Int. J. Pharm. 1991, 69, 109-121. (b) Pikal, M. Pharm Res. 1990, 7, 118-126. (c) Delgado-Charro, M. B.; Guy, R. H. Pharm. Res. 1994, 11, 929-935. (d) Kim, A.; Green, P. G.; Rao, G.; Guy, R. H. Pharm. Res. 1993, 10, 1315-1320. (6) Probstein, R. F. Physicochemical Hydrodynamics; Butterworth: New York, 1989. (7) (a) Peck, K. D.; Ghanem, A. H.; Higuchi, W. I. Pharm. Res. 1994, 11, 13061314. (b) Peck, K. D., Srinivasan, V.; Li, S. K., Higuchi, W. I., Ghanem, A. H. J. Pharm. Sci. 1996, 85, 781-788. (c) Peck, K. D. Ph.D. Thesis, University of Utah, 1995. (8) (a) Fan, F. R.; Bard, A. J. Science 1995, 267, 871. (b) Bard, A. J.; Fan, F. R.; Mirkin, M. V. In Electroanalytical Chemistry; Bard A. J., Ed.; Marcel Dekker: New York, 1994; Vol. 18, pp 243- 373, and references therein. (9) (a) Macpherson, J. V.; Beeston, M. A.; Unwin, P. R. Langmuir 1995, 11, 3959-3963. (b) Nugues, N.; Denuault, D. J. Electroanal. Chem. 1996, 408, 125-140. (c) Macpherson, J. V.; O’Hare, D.; Unwin, P. R.; Winlove, C. P. Biophys. J. 1997, 73, 2771. (d) Macpherson, J. V.; Beeston, M. A.; Unwin, P. R.; Huges, N. P.; Littlewood, D. J. Chem. Soc., Faraday Trans., 1995, 91, 1407. (10) (a) Scott, E. R.; White, H. S.; Phipps, J. B. Anal. Chem. 1993, 65, 15371545. (b) Scott, E. R.; White, H. S.; Phipps, J. B. Solid State Ionics 1992, 53-56, 176-183. (c) Scott, E. R.; White, H. S.; Phipps, J. B. J. Membr. Sci. 1991, 58, 71-87.
1048 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
Figure 1. (A) Schematic diagram of a Nafion-filled pore in mica. Transport of hydroquinone through the pore occurs by diffusion and electroosmotic flow. The membrane separates donor (lower) and receptor (upper) compartments containing equal concentrations of NaCl (0.1, 0.2, or 2.0 M). The donor solution contains 0.2 M HQ. (B) Coordinate system.
the macroscopic structure of skin appendages, e.g., hair follicles, which carry the majority of current in the mouse skin model. The pores in mica are then filled with the cation-exchange polymer Nafion to impart charge and size selectivity to the pore and to induce electroosmotic flow through the pore during iontophoretic measurements. Cation transport numbers in Nafion approach unity, and electroosmotic transport of water and organic solvents (e.g., methanol) occur readily in this polymeric material.11 The transport properties of the Nafion-filled pore interior are intended to mimic those of the nanometer-sized pores in skin that are believed to be responsible for the observed size and charge selectivity, as well as electroosmotic behavior. To demonstrate the feasibility of quantifying electroosmosis in an individual pore, we have investigated the iontophoretic transport of a neutral molecular species, hydroquinone (HQ), through the artificial pores in mica. The mica membrane is mounted in a diffusion cell, separating a donor solution containing HQ and an electrolyte (NaCl) and a receptor solution containing only the electrolyte (Figure 1A). Depending on the direction of the iontophoretic current across the pore, electroosmotic flow enhances or opposes the diffusive flux of HQ, allowing a wide range of net molecular fluxes to be measured. We show that relatively straightforward analyses of the data from a single SECM experiment allow determination of the following: (i) the absolute values of diffusive and iontophoretic fluxes of a dilute solute species, (ii) the convective velocity through a single pore, (iii) the electroosmotic drag coefficient, and (iv) the pore radius. Although the methodology is developed for investigations of (11) (a) Pintauro, P. N.; Bennion, D. N. Ind. Eng. Chem. Fundam. 1984, 23, 234-243. (b) Verbrugge, M. W. J. Electrochem. Soc. 1989, 136, 417-423. (c) Verbrugge, M. W.; Hill, R. F. J. Electrochem. Soc. 1990, 137, 886-893. (d) Lakshminarayanaiah, N. Chem. Rev. (Washington, D.C.) 1965, 65, 492565.
Figure 2. Schematic diagram of the scanning electrochemical microscope and cell used for analysis of diffusive and electroosmotic transport through porous membranes. The two Ag/AgCl electrodes drive current (iapp) across the membrane. The flux of a redox species (e.g., HQ) through an individual pore is determined by measurement of the faradaic current at the SECM tip (it).
transport in skin, it is generally applicable to determining the transport parameters of any porous biological or synthetic membrane. EXPERIMENTAL SECTION Scanning Electrochemical Microscopy. The SECM instrumentation and diffusion cell (Figure 2) used in these studies have been previously described.10 Briefly, a porous membrane is mounted in a custom-built Teflon vertical diffusion cell, separating the donor (lower) and receptor (upper) compartments. The receptor compartment has an open top to allow the tip to access the sample. The donor compartment contains an electroactive molecule (0.2 M HQ) and supporting electrolyte (0.1, 0.2, or 2.0 M NaCl). The receptor compartment contains only supporting electrolyte, at a concentration equal to that in the donor compartment in order to prevent osmotic flow across the membrane. In the absence of an applied current, the electroactive molecule may diffuse freely through the pore in the membrane. During iontophoresis, a constant current is applied across the porous membrane, resulting in an increase or decrease in the transport of the electroactive molecule through the pore. The SECM tip is an electrochemically etched Pt microelectrode, prepared as described below. A custom-built low-current, potentiostat controls the tip potential, Et, with respect to a Ag/ AgCl electrode.10 Tip current is measured with a precision of (20 pA. Positioning of the electrode along the x, y, z axes, with a repeatability of 0.1 µm, is accomplished with piezoelectric inch-
worm microtranslation stages (model TSE-75, Burleigh Instruments, Fisher, New York). Using videomicroscopy, the z axis origin is defined by lowering the tip until it visibly makes contact with the sample. Data acquisition and x-y positioning are controlled by a PC, using a program written in BASIC. The SECM tip is rastered at a fixed height over the sample during imaging and is poised at a potential such that the species to be detected is reduced or oxidized at the mass-transfer-limited rate. In the experiments described in this paper, the tip is used to detect HQ as it exits a Nafion-filled pore in the membrane. HQ is oxidized to benzoquinone by a 2e-, 2H+ mechanism (E°′ ) 0.477 V vs Ag/AgCl).12 The first proton dissociation constant of HQ is ∼10-10.4.13 All measurements described in this report are performed in unbuffered solutions at pH ∼6, conditions in which HQ exists as a fully protonated and electrically neutral molecule. In unbuffered solutions, the oxidation of HQ results in a lowering of the pH near the SECM tip. However, voltammetric limiting currents for the oxidation of HQ at a SECM tip are independent of pH over the range 2-6; thus, the local variation of pH at the tip is not expected to interfere with the SECM measurement. The iontophoretic current, iapp, across the membrane (Figure 2) is delivered using two Ag/AgCl electrodes and a galvanostat (model RDE-4, Pine Instruments, Grove City, PA). The sign (12) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley and Sons: New York, 1980. (13) Weast, R. C., Astle, M. J., Eds. Handbook of Chemistry and Physics; CRC Press: Inc.: Boca Raton, FL, 1981-1982.
Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
1049
convention for iapp is as follows: a positive iapp refers to the cathode of the galvanic circuit being in the receptor compartment. Thus, a positive iapp corresponds to transport of the electrolyte cation (Na+) from the donor to the receptor compartment. Conversely, a negative iapp corresponds to transport of Na+ from the receptor to the donor compartment. SECM Tip Fabrication. SECM tips were constructed by etching 1.5-cm lengths of 0.127-mm-diameter Pt wire at ∼32 V (ac) in a solution containing 3 M NaCN in 1 M NaOH. The wires were placed inside 5-mL glass capillaries, attached to 6-cm lengths of W wire using conductive epoxy (Dupont), and cured at 125 °C for 30 min. The wires were then coated with melted polyethylene powder (850-µm particle size, Goodfellow, Cambridge, England) using a procedure similar to that described by Nagahara, to expose the very end of the wire.14 Tip radii, rt, were determined by measuring the steady-state limiting voltammetric current in a 0.01 M hydroquinone solution containing 0.1 M NaCl. Assuming a hemispherical tip geometry, rt is related to the limiting current by the expression it ) 2πnFDsC*srt, where C* s and Ds are the solution concentration and diffusivity ((9.2 ( 0.2) × 10-6 cm2/ s)15 of hydroquinone, respectively. Tip radii ranged from 0.5 to 5.0 µm. Membrane Preparation. The membranes (Figure 1) were constructed from 2-cm × 2-cm samples of mica, cleaved using Scotch tape (3M) to a thickness of ∼150 µm. The cleaved samples were taped to a Teflon block and a single pore (radius 40-75 µm) was created in each sample by pushing an etched W tip, heated white hot with an H2/O2 flame, through the sample. (Tungsten tips were etched in 1 M KOH at ∼31 V (ac).) Two ∼40-µL drops of a 5 wt % solution of Nafion 117 in alcohol/water (Aldrich) were placed over the pore, on both sides, allowing for evaporation of the solution between applications. The Nafion/ mica membranes were allowed to air-dry at room temperature for 8-16 h before use. The Nafion polymer protrudes slightly above the pore openings, yielding membrane thickness of ∼200 µm. Pore dimensions were characterized by optical microscopy and micrometer measurement. After preparation, the membranes were mounted in the diffusion cell between the donor and receptor compartments. For increased mechanical stability, the membrane was sandwiched between two glass slides, each containing a 0.5-cm2 hole that exposed the membrane pore to the donor and receptor solutions. Silicone vacuum grease was used to seal the mica/glass interface. The glass Teflon interfaces were sealed using built-in 1-in. diameter gaskets. Diffusivity and Partition Coefficient of Hydroquinone in Nafion. The analysis presented below requires knowledge of the diffusivity (Dp) of HQ in Nafion and the equilibrium distribution coefficient (κ) of HQ between the Nafion and aqueous phases. Ignoring activity effects, the distribution coefficient is defined as the ratio of the bulk concentrations of HQ in the Nafion (C* p) and aqueous (C* s) phases: (14) Nagahara, L. A.; Thundat, T.; Lindsay, S. M. Rev. Sci. Instrum. 1989, 60, 3128-3130. (15) The diffusivity of hydroquinone was determined by determining the limiting current of a calibrated disk microelectrode in a 0.100 M hydroquinone solution. The measurement was repeated five times and it ) 4nFDsC*sa was used to calculate the diffusivity. The uncertainty is based on one standard deviation.
1050 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
κ ) C*p/C*s Zook and Leddy have measured κDp ) (2.9 ( 0.4) × 10-7 cm2/s from steady-state voltammetric currents for HQ oxidation at a rotating disk electrode that was coated with a thin layer of Nafion and immersed in a solution containing HQ.16 Similarly, these researchers determined κ(Dp)1/2 ) (4.76 ( 0.95) 10-4 cm/ s1/2 from analysis of the cyclic voltammetric response of a stationary electrode. These values yield κ ) 0.78 and Dp ) 3.7 × 10-7 cm2/s. RESULTS AND DISCUSSION Iontophoretic transport of HQ through Nafion-filled pores was analyzed by recording the SECM tip current, it, above a single pore opening during iontophoresis. For example, Figure 3 shows the voltammetric response of a 4.6-µm-radius SECM tip positioned directly above a pore (z ∼ 0; see coordinate system in Figure 1B), measured as a function of the iontophoretic current, iapp, delivered by the Ag/AgCl electrodes. In this set of experiments, the donor compartment contained 0.2 M HQ and 0.2 M NaCl; the receptor compartment contained only 0.2 M NaCl. It is clear from inspection of Figure 3 that HQ is transported from the donor compartment to the receptor compartment at a rate that is controlled by iapp. Quantitative evaluation of the flux of HQ through a pore is made by measuring the SECM tip current corresponding to the faradaic reaction,
HQ f BQ + 2H+ + 2ewhere BQ is benzoquinone. The magnitude of the voltammetric limiting current measured at the tip, it(z), is proportional to the concentration of HQ in the local vicinity of the tip. For a hemispherical-shaped tip, it(z) is given by eq 1,12 where Ds is the
it(z) ) 2πnFDsCRs (z)rt
(1)
diffusivity of HQ in the aqueous phase ((9.2 ( 0.2) × 10-6 cm2/ s) and CRS (z) is the concentration of HQ in the receptor compartment at a tip-to-pore separation of z. In our experiments, CRS (z) is obtained using eq 1 by measurement of it(z). When the tip is positioned directly above the pore (z ) 0), the measured current is proportional to the concentration of HQ in the aqueous phase at the hypothetical surface separating the pore and receptor compartment, CRs (z)0).
it(z)0) ) 2πnFDsCRs (z)0)rt
(2)
For instance, for iapp ) 0 (corresponding to pure diffusion of HQ in the pore, Figure 3), the tip current measured at z ) 0 is ∼3 nA. This value corresponds to CRs (z)0) ∼ 0.6 mM. It is straightforward to show that the current measured at the SECM tip is proportional to the rate of transport of HQ through the pore. Consider the pore opening as a disk-shaped source from which HQ is emitted. Transport of HQ from the pore opening (16) Zook, L.; Leddy, J., unpublished results, University of Iowa, 1996.
placed directly at the pore opening.18 Thus, eq 5 is useful in our analysis only as an approximate relationship between it and Ω. Furthermore, the radius of the pore in real samples may not be known a priori. A quantitative method of analysis that circumvents both of these problems is presented in a later section. The key point here is that the magnitude of it(z)0) provides a qualitative measure of the flux of HQ in the pore. It is instructive to write the rate of diffusional mass transfer through a pore in terms of a series of mass-transfer resistances: R* Ω ) (CD* s - Cs )/(Rentry + Rpore + Rexit)
Figure 3. Cyclic voltammetric response at the SECM tip (it(z)0)) as a function of the applied current (iapp). The voltammetric response corresponds to the 2e-, 2H+ oxidation of HQ at a 4.6-µm-radius Pt SECM tip positioned directly above a pore. The donor compartment contained 0.2 M HQ and 0.2 M NaCl. The receptor compartment contained 0.2 M NaCl.
into the bulk solution occurs by diffusion. The rate of diffusional transport of HQ away from a disk-shaped pore (Ω, mol/s) is given by eq 3, where a is the pore radius.17 Dividing by the cross-
Ω ) 4aDsCRs (z)0)
(3)
sectional area of the pore (πa2), we obtain the flux (N, mol/cm2s) of HQ across the pore opening.
N ) 4DsCRs (z)0)/πa
(4)
Combining eqs 2 and 3 yields the relationship between the SECM tip current and the transport rate within the pore:
it(z)0) ) (πnFrt/2a)Ω
(5)
Equation 5 indicates that the current measured at the SECM tip is directly proportional to Ω. At steady state, mass continuity requires that the rate of transport of HQ away from the pore in the receptor compartment is equal to the rate of transport of HQ within the Nafion-filled pore. Thus, it(z)0) is also proportional to the rate of transport of HQ at any point within the pore. Note that, in deriving eq 5, no restrictions have been placed on the mechanism of transport within the pore. Thus, it(z)0) is proportional to the total flux in the pore, independent of whether the flux is due to diffusion, migration, or convection. In principle, eq 5 can be used to compute Ω for HQ in a single pore if the pore radius, a, is known. Implicit in eq 5 is the assumption that the tip does not interfere with the transfer of HQ from the pore. This is a reasonable approximation when the tip radius is very small compared with the pore radius, i.e., rt , a. However, in the present experiments, rt ∼ 4 µm and a ∼ 60 µm, and the tip cannot be treated as a noninterfering probe when it is (17) Saito, Y. Rev. Polarogr. 1968, 15, 177-187.
(6)
R* In eq 6, CD* s and Cs are the concentrations of HQ in the bulk solutions of the donor and receptor compartments. The quantity R* (CD* s - Cs ) represents the driving force for the diffusional flux of HQ through the pore. For all experiments reported herein, R* CD* s ) 0.2 M and Cs ) 0. Rentry and Rexit are the mass-transfer 3 resistances (s/cm ) at the pore entrance and exit, respectively, and Rpore is the transport resistance within the Nafion-filled pore. Rentry and Rexit have the same value because of the symmetric pore geometry. For a cylindrical-shape pore of radius a and length l, the diffusion-controlled resistances are17
Rentry ) Rexit ) (4aDs)-1 and
Rpore ) l/πa2κDp where Dp is the diffusivity of HQ in the Nafion-filled pore and κ is the equilibrium value for partitioning of HQ between the aqueous phase and Nafion (κ ∼ C* p/C* s). For the artificial pores considered here, a ∼ 60 µm and l ∼ 200 µm, yielding Rentry ) Rexit ) 4.5 × 106 s/cm3 and Rpore ) 6.1 × 108 s/cm3. Thus, the mass-transfer resistance of the Nafion-filled pore interior, Rpore, limits the overall flux of HQ across the membrane. Figure 3 shows that the magnitude of the SECM tip current increases when iapp is increased to 50 µA. Because it(z)0) is proportional to Ω (eq 5), this result indicates that the transport of HQ through the pore is enhanced when a positive current is driven through the pore. Recall that a positive iapp corresponds to flow of positive charge from the donor compartment to the receptor compartment (see Experimental Section), which can occur by cation (Na+) transport from the donor to the receptor compartment or by anion (Cl-) transport in the opposite direction. However, because of the fixed negative charge (SO3-) on the polymer chains of Nafion,19 the current in the pore is due only to cation transport (i.e., cation transference values are near unity in Nafion). Thus, for iapp ) 50 µA, the iontophoretic current is carried solely by Na+ moving from the donor to the receptor compartment. Because HQ is a neutral species in the pH ∼6 solution employed here, the electrically enhanced transport of this mol(18) The criterion for the SECM tip being a noninterfering probe is given by z/(rta)1/2 . 1, where z is the separation distance between the tip and the pore, a is the pore radius and rt is the tip radius (see eqs 9-11 in ref 10a). (19) Rubenstein, I.; Bard, A. J. J. Am. Chem. Soc. 1980, 102, 6641-6642.
Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
1051
ecule through the pore must occur by electroosmotic flow. Electroosmotic convective flow is due to the large difference in the cation/anion transference numbers within the Nafion-filled pores (t+ ∼ 1 and t- ∼ 0), with the solvent flow in the same direction as the migration of the mobile charge carriers (Na+). Solvent flow increases the net rate of HQ transport through the pore, giving rise to a larger faradaic current at the SECM tip. Figure 3 shows that the tip signal (it(z)0)) increases by a factor of ∼3 when iapp is increased from 0 to 50 µA. Thus, electroosmotic flow at iapp ) 50 µA results in a 3-fold increase in the flux of HQ across the membrane. Reversal of the direction of the iontophoretic current, i.e., iapp ) -50 µA, results in a decrease in it(z)0) to near zero levels (Figure 3). A negative iapp corresponds to a flux of Na+ from the receptor compartment to the donor compartment. As before, electroosmotic flow occurs in the same direction as the Na+ flux, which, in this case, is in the opposite direction of the diffusional flux of HQ. The fact that it(z)0) is negligibly small indicates that very little, if any, HQ is transported through the pore. We conclude that electroosmotic flow from the receptor compartment is sufficiently large at iapp ) -50 µA to prevent significant diffusional transport of HQ in the opposite direction. A side issue of the SECM measurement of iontophoretic transport concerns the electrostatic potential distribution across the pore. Although not readily apparent in the data reproduced in Figure 3, the voltammetric half-wave potential (E1/2) for HQ oxidation is slightly dependent upon iapp. This dependence reflects the nonzero potential difference between the SECM tip and the reference electrode (see Figure 2) caused by current flow through the narrow pore. A part of this potential drop apparently occurs in the aqueous phase near the pore opening and is sensed by the SECM tip. From Ohm’s law, it is readily deduced that the potential drop across any one pore is proportional to the applied current and inversely proportional to the number of pores in the membrane. For one pore per sample and iapp ) ( 50 µA, we observe that the ohmic shift in E1/2 is a few tens of millivolts, which introduces no serious difficulties in the analyses described below. Figure 4A shows an SECM image of the HQ distribution above the pore opening during iontophoresis at iapp ) 50 µA. To acquire this image, the tip was moved to a height of 50 µm above the membrane surface and scanned in the x-y plane at 10 µm/s. Tip current, it(z), was recorded at Et ) 0.9 V vs Ag/AgCl. This potential is sufficiently positive of E1/2 for HQ oxidation that it(z) always corresponds to a value on the limiting current plateau (see Figure 3). The bottom portion of Figure 4 displays a gray scale contour image of the SECM tip current and is shown to convey qualitatively the degree to which HQ is transported away from the pore in a radial pattern. The lighter colors correspond to larger tip currents and, thus, regions where the concentration of HQ is highest. Ideally, for transport away from a disk-shaped pore opening, the isocurrent contours should be exactly circular and concentric with the pore. We typically observed some skewing of the concentration contours because of tip-induced convection as the tip moves though the solution above the pore. However, this artifact does not have any significant effect on the analyses of electroosmotic flow in the pore. 1052 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
Figure 4. (a) SECM image of a Nafion-filled pore in mica during iontophoretic transport of HQ (iapp ) 50 µA). The SECM tip was scanned at a rate of 10 µm/s at a height of 50 µm above the membrane surface. Et ) 0.9 V vs Ag/AgCl. (b) Contour image of the same data. The donor compartment contained 0.2 M HQ and 0.2 M NaCl. The receptor compartment contained 0.2 M NaCl.
Figure 5. SECM tip current measured across a Nafion-filled pore in mica as a function of the applied iontophoretic current (iapp). The 5.0-µm-radius Pt SECM tip was scanned at a height of 45 µm above the membrane surface. Et ) 0.9 V vs Ag/AgCl. The donor compartment contained 0.2 M HQ and 0.2 M NaCl. The receptor compartment contained 0.2 M NaCl.
Figures 5 and 6 show the dependence of it(z) on iapp. In Figure 5, values of it(z) measured in x direction across the center of the pore are shown as a function of iapp. These curves represent center slices through an SECM image, such as that shown in
Figure 6. SECM tip current measured directly above a pore opening (it(z)0)) as a function of the applied iontophoretic current (iapp). The donor compartment contained 0.2 M HQ and 0.2 M NaCl. The receptor compartment contained 0.2 M NaCl. Tip radius 0.5 µm.
Figure 4. We have previously analyzed the quasi-Gaussian shape of these profiles10c and have shown that this shape results from radial diffusive transport of the redox molecule away from the pore opening. The new results shown in Figure 5 indicate that radial dispersion of the molecules in the receptor compartment occurs even though electroosmotic transport is significant within the Nafion-filled pore. This finding indicates that diffusion of HQ is the predominant mode of transport after HQ enters the aqueous phase of the receptor compartment, justifying the use of eqs 1-4 in our analyses, as well as the use of equations to be presented below. Values of it(z)0) measured above the center of a pore are plotted as a function of iapp in Figure 6. These data were recorded at a stationary tip positioned at the center of the pore opening. it(z)0) was obtained from the limiting voltammetric current plateaus. The dependence of it(z)0) on iapp is in qualitative agreement with theoretical considerations of combined diffusion and electroosmotic transport in a pore.20 For positive iapp, diffusion and electroosmosis occur in the same direction, and thus, electroosmosis facilitates HQ transport. Assuming that the convective flow rate is proportional to iapp, we anticipate that the flux of HQ should increase in direct proportion to iapp (vide infra). Thus, a plot of it(z)0) vs iapp should be linear at positive iapp. This expectation is borne out in the experimental data. For negative iapp, diffusion and electroosmosis occur in opposite directions, with electroosmotic flow acting to reduce the flux of HQ through the pore. In this case, it(z)0) should asymptotically approach zero as iapp is made increasingly more negative. This limiting behavior is also observed in Figure 6. The dependence of HQ transport on iapp is quantified in detail in the following sections. Before proceeding, it is worthwhile to consider the transient behavior of flow and iontophoretic transport within an individual pore. Figure 7 shows the transient response of the SECM tip current following changes in the applied iontophoretic current. As before, the SECM tip is positioned directly above a pore to measure the flux HQ from the donor compartment to the receptor compartment. it(z)0) was measured as the iontophoretic current iapp was varied among 50, 0, and -50 (20) Sims, S. M.; Higuchi, W. I.; Srinivasan, V.; Peck, K. J. Colloid Interface Sci. 1993, 155, 210-220. (b) Pikal, M. J. Adv. Drug. Deliv. Rev. 1992, 9, 201237. (c) Srinivasan, V.; Higuchi, W. I. Int. J. Pharm. Sci. 1990, 60, 133138.
Figure 7. Transient SECM-tip current (it(z)0)) measured while switching the iontophoretic current, iapp, among -50, 0, and 50 µA. Et ) 1.0 V vs Ag/AgCl. The donor and receptor compartments contained 0.1 M NaCl. The donor compartment contained 0.1 M HQ.
µA. We observe that the time necessary to obtain a new apparent steady state is on the order of 10 min. Because iapp is controlled by the galvanostatic circuitry, the iontophoretic current in the pore, and thus, the electroosmotic solvent flow must be established very rapidly following any change in iapp. It follows that the slow transient response of the HQ flux reflects the establishment of new steady-state concentration profiles within the Nafion-filled pore following the change in current. The time necessary to establish the HQ concentration profiles in a pore of length l can be estimated from the root-mean-square diffusional displacement of HQ, which is given by 〈z2〉1/2 ) (2Dpt)1/2. Replacing 〈z2〉1/2 with l, and using Dp ) 3.7 × 10-7 cm2/s and l ∼ 200 µm (see Experimental Section) yields a value of t ∼ 9.0 min, in good agreement with the experimental observations. Quantitative SECM Analysis of Electroosmotic Transport. Absolute values of the flux of HQ transport (N, eq 4) through individual pores were determined by measurement of the concentration profile of the molecule near the pore opening in the receptor-side solution. As shown in the following paragraphs, SECM measurements also provide sufficient information to determine the convective velocity in the pore, pore diameter, and dilute species electroosmotic drag coefficient. These key parameters characterize electroosmotic transport in ion-selective porous media. Diffusive transport of HQ from the disk-shaped pore into the receptor solution yields a concentration profile around the pore opening that, in cylindrical coordinates (r, radial coordinate; z, axial), is given by17
CRs (r,z) )
2CRs (z)0) × π
a21/2 tan-1 2 (7) 2 2 2 ((r + z - a ) + ((r + z2 - a2)2 + 4z2a2)1/2)1/2 The distribution profile is uniquely determined by two parameters: the surface concentration, CRs (z)0), and the pore radius, a. These parameters are also the two unknowns in eq 4 that are required to compute the flux of HQ through the pore. To evaluate CRs (z)0) and a, the SECM tip current may be measured as a function of r and z and used to establish the Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
1053
Figure 8. Theoretical normalized concentration profiles (eq 8) for HQ above a disk-shaped pore opening. Curves are computed for different pore radii (a).
concentration profile CRs (r,z) near the pore opening. Equation 7 is then fitted to the experimental CRs (r,z) profile to obtain values of CRs (z)0) and a. Once CRs (z)0) and a are determined, they are substituted back into eq 4 to obtain N. We simplify the above analysis by measuring only the concentration profile of HQ along the hypothetical center line axis of the pore that extends away from the pore surface into the receptor compartment. In the cylindrical coordinate system, this axis corresponds to r ) 0. From eq 7, the concentration profile along this axis is given by
CRs (z) )
2CRs (z)0) a tan-1 π z
()
(8)
As before, CRs (z) is also uniquely determined by CRs (z)0) and a. Values of these parameters, obtained by fitting eq 8 to the experimental CRs (z) profile, are used to determine N. Figure 8 shows theoretical profiles of normalized HQ concentration, CRs (z)/CRs (z)0), computed from eq 8 for pore radii (a) ranging from 10 to 200 µm. This plot is instructive in considering the sensitivity of experimental data to the value of a, one of the two unknown parameters used in the curve-fitting analyses. The curves in Figure 8 demonstrate that CRs (z) is most sensitive to a for smaller pore openings. As a increases above ∼200 µm, the concentration profiles approach the expected profile for diffusion from a large planar surface. In this limiting case, CRs (z) is independent of a. For the experimental measurements reported below, a is known, a priori, to be between 40 and 75 µm, and the tip current is measured in the range 0 < z < 70 µm. Inspection of Figure 8 shows that CRs (z) should be strongly dependent on a within this range of experimental parameters. Thus, fitting eq 8 to the data should allow a relatively precise evaluation of the pore radius. The following experimental protocol was used to measure the HQ concentration profiles. The center of the pore opening (r ) 0, z ) 0) was determined by positioning the tip as close as possible to the pore opening using the x, y, and z piezoelectric stages to maximize the tip current. The tip was then retracted in the z direction in 7-µm increments and the SECM-tip current was measured for 12 s (200 data points) at each z position. The average tip current at each value of z was converted to CRs (z) using eq 1, and the data plotted as CRs (z) vs z. 1054 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
Figure 9. Concentration profiles of HQ above Nafion-filled pores in mica membranes. The data correspond to passive diffusion (iapp ) 0 µA, squares) and iontophoretic transport (iapp ) 50 µA, triangles). The solid lines represent best fits of eq 8 to the data, obtained by varying the parameters CRs (z)0) and a. The concentrations of NaCl in the donor/receptor compartments are indicated on the figure. The concentration of HQ in the donor compartment was 0.2 M in all experiments. The data in each of the three panels were obtained using different membranes.
Figure 9 shows representative examples of experimental HQ concentration profiles, corresponding to diffusive (iapp ) 0 µA, squares) and iontophoretic transport of HQ (iapp ) 50 µA, triangles) in solutions containing 0.1, 0.2, and 2.0 M NaCl. The solid lines correspond to theoretical profiles (eq 8), and are based on best fits of the data obtained by varying CRs (z)0) and a. A curve-fitting program was written using a simplex algorithm to minimize the residuals. The data presented in Figure 9 at each individual NaCl concentration correspond to diffusive and iontophoretic transport through the same pore. However, the results for differing electrolyte concentrations were obtained using different membranes. The excellent fits of eq 8 to the data indicate that diffusion is the predominant mode of transport away from the pore opening, that the pore opening can be approximated as being disk shaped, and that the SECM tip does not significantly alter the concentration profiles. Results of the curve-fitting analysis (CRs (z)0) and a) are summarized in Table 1 for diffusive and iontophoretic transport though individual pores. In addition, values of the pore radii estimated by optical microscopy are also included. The latter values were obtained with significant difficulty because of low optical contrast between the Nafion-filled pores and surrounding regions of mica. Two conclusions concerning SECM measure-
Table 1. Diffusional and Iontophoretic Transport Parameters for Hydroquinone in Nafion diffusion, iapp ) 0 µA [NaCl] (M) 0.1
pore
radiusa
(µm)
CRs (z)0)
(mM)
a (µm)
Ndiff ×
iontophoresis, iapp ) 50 µA
1010
(mol/cm2s)
CRs (z)0)
(mM)
a (µm)
Niont × 1010 (mol/cm2s)
0.50 0.22 0.11 0.26
58.4 51.8 60.0 67.4
10.0 5.0 2.1 4.4
2.9 1.73 0.62 1.59
56.8 42.3 55.1 56.8
59.8 48.0 13.2 32.7
5.8 7.9 5.6 6.1
55 53 40 65
0.23 0.59 0.11 0.60
63.1 43.9 43.5 68.0
4.3 15.8 3.0 10.4
1.01 1.94 0.88 4.14
59.4 65.7 38.0 68.0
20.0 34.6 27.0 71.4
4.4 3.3 8.0 6.9
45 53 51 60
0.40 0.12 0.45 0.35
44.2 53.0 53.4 59.0
10.6 2.7 9.9 6.9
1.30 0.56 1.70 0.98
40.8 52.7 53.7 61.9
37.3 12.4 37.1 18.5
3.3 4.7 3.8 2.8
6.4 ( 1.1
av 0.2
5.7 ( 2.2
av 2.0
3.7 ( 0.8
av a
E
58 53 59 62
Determined by optical microscopy.
ments of pore radii can be immediately drawn from the data in Table 1. First, values of a that are determined during diffusive and iontophoretic transport agree, on average, to within 10%. This consistency demonstrates the reproducibility of the measurement, the soundness of the assumption of pure diffusional transport outside the pore, and the sensitivity of the experimental data to the pore dimension. Second, SECM-determined pore radii are in reasonable agreement (within 20%) with the corresponding values determined by optical microscopy, suggesting that the SECM analysis provides a relatively accurate estimation of the pore dimensions. Because of the difficulty in measuring pore radii by optical microscopy, we believe that it is likely that the SECMdetermined values are more reliable. A more rigorous test using better defined pores is necessary to address the issue of measurement accuracy. Table 1 also summarizes values of N for diffusion (iapp ) 0 µA) and iontophoretic transport (iapp ) 50 µA), using the symbols Ndiff and Niont, to indicate these values, respectively. As previously described, values of N were computed from eq 4 using a and CRs (z)0) obtained by analyses of the HQ concentration profiles. We find that Ndiff is ∼7 × 10-10 mol/(cm2 s) for pure diffusion (iapp ) 0 µA) and increases by a factor of ∼5 under the applied iontophoretic conditions, iapp ) 50 µA. The final column in Table 1 is the flux enhancement factor, E, defined as the ratio of diffusive and iontophoretic fluxes, Niont/Ndiff. Within error, E is independent of the concentration of NaCl in the solutions contacting the pore. Electroosmotic Flow Velocity and Drag Coefficient. Fundamental parameters that describe iontophoretic transport (convective flow velocities, solute drag coefficient) may be evaluated from the measured dependence of Niont on iapp. The diffusiveconvective flux of HQ through the Nafion-filled pore during iontophoresis is given by20c
the average solution velocity (vs), a consequence of differences in chemical interactions between the charge-carrying species (Na+) with the solute (HQ) and the solvent (H2O). Experimental values of vHQ and vs are presented and discussed below. Substitution of the flux Niont (eq 9) into the mass conservation law (∇‚Niont ) 0), and integration over the length of the pore (see pore geometry and coordinate system in Figure 1B), yields the steady-state flux between the donor and receptor compartments,20c
Niont ) -Dp∇Cp(z) + Cp(z)vHQ
In this limit, the flux of HQ from the donor compartment to the receptor compartment is due entirely to convection. Niont is proportional to the convective velocity, vHQ.
(9)
where vHQ is the velocity associated with electroosmotic convective transport of HQ. This velocity may be significantly different from
Niont )
vHQκCD* s (1 - exp(-vHQl/Dp))
(10)
and the concentration profile of HQ within the pore,
Cp(z) κCD* s
)
1 - exp(vHQz/Dp) 1 - exp(-vHQl/Dp)
(11)
The mass transport resistances at the pore entrance and exit are ignored in deriving eqs 10 and 11. This is equivalent to approximating the concentrations of HQ at the pore entrance (z ) -l) and exit (z ) 0) as being equal to the bulk concentration of HQ in the donor and receptor solutions, respectively. In a previous section, we demonstrated that this assumption is reasonable for the experimental system under study; i.e., Rpore . Rexit ) Rentry. It is useful to examine the behavior of Niont (eq 10) in the limits of large (I) positive and (II) negative flow velocities.
Niont ) vHQκCD* s in the limit vHQ f +∞
Niont ) 0 in the limit vHQ f -∞ Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
(I)
(II) 1055
In this limit, convective flow from the receptor to the donor compartment opposes diffusion, driving the net flux of HQ to zero. These limiting behaviors are to be compared with the results presented in Figure 6, which shows the SECM tip current, it, plotted against the applied iontophoretic current, iapp. As previously discussed, the flux of HQ in the pore, Niont, is proportional to it. Similarly, the electroosmotic flow velocity, vHQ, is generally assumed to be proportional to iapp. Thus, Figure 6 is qualitatively equivalent to a plot of Niont versus vHQ. The anticipated limiting behaviors are immediately apparent in this plot: it increases in proportion to iapp for large positive values of iapp and asymptotically approaches zero as iapp is made increasingly more negative. For passive diffusional transport, vHQ ) 0 and eqs 10 and 11 reduce to
Ndiff ) κCD* s Dp/l
(12)
Cp(z)/κCD* s ) -(z/l)
(13)
Figure 10. Iontophoretic flux, Niont, as a function of the convective velocity of HQ in the Nafion-filled pore, vHQ. Positive velocities correspond to flow from the donor to receptor compartments. vHQ is calculated from experimental values of Niont using eq 14 in the text with Dp ) 3.7 × 10-7 cm2/s and l ) 200 µm. The dashed lined corresponds to iapp ) 0; the flux at iapp ) 0 is due solely to diffusion.
The flux enhancement factor, E, defined above, is obtained from eqs 10 and 12:
E)
Niont Pe ) Ndiff 1-(exp(-Pe))
(14)
where the Peclet number (Pe) corresponds to the dimensionless group vHQl/Dp. Because the SECM tip current is proportional to the flux of HQ through the pore (i.e., it(z)0) ∝ Niont), it is clear that E is also equal to the ratio of tip current measured during iontophoresis (iapp * 0) and during passive diffusion (iapp ) 0), i.e.,
E)
Niont it(z)0) (iontophoresis) ) Ndiff it(z)0) (diffusion)
(15)
Values of it(z)0) from Figure 6 were normalized to the value at iapp ) 0, and the resulting values of E were used to compute Pe and, thus, vHQ from eq 14. The results of this analysis are shown in Figure 10 as a plot of Niont versus vHQ. Values of vHQ range from +10-4 to -10-4 cm/s for iapp between 100 and -100 µA. In agreement with theoretical expectations discussed above, Niont asymptotically goes to zero as vHQ f -∞ due to the opposition of the convective and diffusional fluxes. Conversely, Niont is proportional to vHQ as vHQ f ∞. The electroosmotic drag coefficient for HQ is defined as the ratio of the number of moles of HQ transported by convection per mole equivalent of charge passing through the pore, i.e.,
tHQ )
vHQCav p Ap (t+iapp)/z+F
(16)
Cav p is an average value of the concentration of HQ in the Nafionfilled pore, Ap is the cross-sectional pore area, and z+ is the charge of Na+. Cav p is difficult to evaluate, because the concentration of HQ varies along the length of the pore if both diffusion and convective transports are operative. Using eq 11, we compute 1056 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
Figure 11. Steady-state concentration profiles of HQ inside a 200µm-long Nafion-filled pore as a function of the iontophoretic current, iapp. Concentration profiles are computed from eq 11 using experimentally determined values of the convective flow velocity, vHQ (Figure 10). The nonlinearity of the profiles indicates that the relative contributions of diffusive and convective transport is a function of spatial position (z) inside the pore.
the steady-state concentration profile of HQ in the Nafion-filled pore, Figure 11, as a function of iapp and the experimentally determined values of κ, Dp, l, and vHQ . For any nonzero iapp, the concentration of Cp varies in a nonlinear fashion along the length of the pore. The nonlinearity of the steady-state profiles clearly indicates that the relative contributions of convection and diffusion to the total flux must vary along the length of the pore. For instance, for positive iapp, the profile of HQ is relatively flat near the pore entrance, indicating that convective transport at the pore opening dominates the flux. Conversely, the concentration profile at the pore exit is steep, indicating that diffusion contributes more to the flux in this region. We define the average concentration in the pore as
Cav p )
∫ C (z) dz/∫ 0 -l p
0
-l
dz
(17)
where Cp(z) is given by eq 11. From eq 17, Cav p is computed to be equal to 0.128 M at iapp ) 50 µA. Values for tHQ were computed from eq 16 using Cav p ) 0.128 M and are listed in Table 2 as a function of the NaCl concentration in the solutions contacting the pore. The cation transference
Table 2. Velocity and Electroosmotic Drag Coefficient for Hydroquinone in Nafion at iapp ) 50 µA [NaCl] (M)
vHQ × 104 (cm/s)
0.1
0.83 1.32 1.02 1.12
tHQ × 103 2.2 2.5 2.7 3.3
av
1.1 ( 0.2
2.7 ( 0.5
0.2
0.79 0.62 1.28 1.36
2.1 1.4 1.7 4.7
av
1.0 ( 0.4
2.5 ( 1.5
2.0
0.78 0.85 0.96 0.66
1.3 2.1 2.4 2.1
av
0.81 ( 0.13
2.0 ( 0.5
Table 3. Convective Flow Parameters for H2O in Nafion [NaCl] (M)
CNafion (M)a w
tH2Oa
vs (103 cm/s)b
0.1 0.2 2.0
16.3 16.2 14.3
12.6 12.6 7.8
3.6 3.6 2.9
a
Values taken from ref 11a. b Applied current 50 µA.
number (t+) in Nafion is assumed to be unity for experiments involving 0.1 and 0.2 M NaCl; however, Pintauro and Bennion found t+ ) 0.87 for Nafion in contact with 2 M NaCl solutions.11a These values are employed in evaluating tHQ. The data in Table 2 suggest that tHQ is independent of NaCl concentration and equal to ∼2.4 × 10-3. This value corresponds to one molecule of HQ being transported through the Nafion membrane per ∼400 Na+. Analysis of the Solvent Flow Velocity. The electroosmotic drag coefficient for H2O is defined as the rate of solvent transport per equivalent of ion flux,21
tH2O )
Ap vsCNafion w (t+iapp)/z+F
(18)
In eq 18, CNafion is the concentration of H2O in the membrane w (which is a function of the concentration of NaCl in the solutions in contact with the membrane11a) and vs is the velocity of H2O in the pore. Because the concentration of H2O is the same on both sides of the pore, no concentration gradient of H2O exists across the pore, and the diffusional contribution to the net flux of H2O is zero. Thus, no need exists to define an average concentration, as was the case above for HQ. Values for CNafion and tH2O for our w experimental conditions have been previously determined by Pintauro and Bennion and are listed in Table 3. Values of vs computed from eq 18 are also listed in Table 3. We compute vs to be ∼3.5 × 10-3 cm/s at iapp ) 50 µA, which is ∼35 times larger than the convective velocity of HQ (∼10-4 cm/s) at the same (21) Breslau, B. R.; Miller, I. F. Ind. Eng. Fundam. 1971, 10, 554-565.
Figure 12. Schematic drawing depicting the migration of solvated Na+ at velocity vp (under the influence of an electric field) and the convective flow of a dilute solute (e.g., HQ) at velocity vHQ. In the absence of specific association between solute and Na+, convective flow of solute (as well as nonassociated solvent molecules) results from momentum transfer between migrating Na+ and the solution. Net solution flow at an average velocity vs results from the transport of solvent (H2O) that is strongly associated with the cation (vp), in addition to momentum transfer to nonassociated solvent and solute molecules (vHQ).
current. The difference in these velocities indicates a significant difference in the degree of interaction of the charge-carrying ions with the solvent and solute. For an ideal incompressible fluid containing noninteracting species, the electroosmotic velocities of ions, solvent, and solute are expected to be identical. However, in the present experiments, Na+ will be preferentially solvated by H2O relative to the less polar organic molecule HQ. Thus, as depicted in Figure 12, H2O molecules within the first solvation sphere of Na+ will be transported through the pore at a velocity (vp) that is determined by the mobility of Na+. Solvent molecules removed from the cation, as well as the weakly interacting solute (HQ), will move at a lower velocity (vHQ) that is determined by the rate at which momentum is transferred from the solvated Na+ to the free solution. The observed velocity of the solvent, vs, results from convective transport of bound water molecules (at velocity vp) and free water molecules (at velocity vHQ). Admittedly, although the physical separation of velocities for chemical species comprising the solution is an oversimplification, it is clear that H2O must be transported by convection at a net higher rate than HQ, because of the stronger interaction of H2O with Na+. The ∼35-fold difference in the velocities of H2O and HQ suggests that solvent and solute molecules removed from the charge-carrying ions are relatively immobile. CONCLUSION The SECM-based analytical method presented in this report provides a means of fully characterizing transport phenomena in individual pores of a membrane. This capability is likely to be very useful in investigations of heterogeneous porous membranes, especially biological membranes, where pores of different sizes or pores displaying different molecular transport specificities, may contribute to the overall flux. The porous mica/Nafion membrane employed in the current investigation as a model system is characterized by pores of relatively large radius (40-70 µm). However, using smaller tips, the demonstrated resolution of SECM measurements in imaging surfaces is of the order of 10-20 nm.8a Thus, we believe that Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
1057
our method can be extended to investigations of pores of much smaller dimensions than investigated here. The methodology described in this paper is also useful for quantifying transport parameters of homogeneous ion-selective membranes that have pore dimensions that are too small to probe individually (e.g., Nafion). Traditionally, electroosmotic (and osmotic) flow rates have been determined by measurement of macroscopic volume changes that occur in the two solutions that are separated by a membrane. SECM analysis provides an alternative method for evaluating absolute electroosmotic and diffusive fluxes for solutes in real time. For instance, the transient flux measurements for HQ transport reported here (Figure 7) represents, to our knowledge, the first real-time measurement of electroosmotic transport dynamics of a dilute solute species through Nafion. ACKNOWLEDGMENT We thank Ms. Lois Zook and Prof. Johna Leddy (University of Iowa) for sharing unpublished transport data for hydroquinone in Nafion films, Dr. Shimshon Gottesfeld (Los Alamos National Laboratory) for discussions concerning electroosmotic drag coefficients, Dr. Stephen Feldberg (Brookhaven National Laboratory) for mathematical insight, and David Chamberlin and Rory Uibel (University of Utah) for developing data analysis computer programs used in this work. This research was supported by ALZA, Corp. (Palo Alto, CA) and the Office of Naval Research. ABBREVIATIONS AND SYMBOLS
CD* s
concentration of HQ in the donor compartment
C* p
equilibrium concentration of HQ in Nafion
Cav p CNafion w
average concentration of HQ in Nafion
Ds
diffusivity of HQ in the aqueous phase
Dp
diffusivity of HQ in the Nafion-filled pore
concentration of H2O in the Nafion-filled pore
E
flux enhancement factor
Eo′
formal redox potential
Et
SECM tip potential
HQ
hydroquinone
iapp
applied iontophoretic current
it(z)
tip current measured at a distance z from pore
l
pore length
Ndiff
diffusive flux measured at iapp ) 0
Niont
iontophoretic flux measured at iapp * 0
rt
SECM tip radius
tHQ
electroosmotic drag coefficient of HQ
tH2O
electroosmotic drag coefficient of H2O
t+, t-
cation, anion transference numbers in the pore
vHQ
convective velocity of HQ in pore
vp
velocity of charge-carrying ions in pore
vs
average convective solvent velocity in pore
κ
equilibrium distribution coefficient
Ω
rate of mass transport
a
pore radius
Ap
cross-sectional area of the pore
CRs (z)
concentration of HQ in the receptor solution at distance z from the surface of the pore
CRs (z)0)
concentration of HQ at the receptor side pore opening
Received for review November 3, 1997. Accepted January 8, 1998.
C* s
concentration of HQ in the bulk aqueous phase
AC971213I
1058 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
