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J. Phys. Chem. B 2007, 111, 12478-12484
Use of Microdevices To Determine the Diffusion Coefficient of Electrochemically Generated Species: Application to Binary Solvent Mixtures and Micellar Solutions Tiago L. Ferreira,† Thiago R. L. C. Paixa˜ o,† Eduardo M. Richter,‡ Omar A. El Seoud,† and Mauro Bertotti*,† Instituto de Quı´mica, UniVersidade de Sa˜ o Paulo, Sa˜ o Paulo, SP, Brazil 05508-900, and Instituto de Quı´mica, UniVersidade Federal de Uberlaˆ ndia, Uberlaˆ ndia, MG, Brazil ReceiVed: July 25, 2007
A new approach for the determination of diffusion coefficient, D, of redox species is presented. It is based on the use of a home-constructed twin electrode within a thin-layered cell (TETLC) filled with a solution of electroactive species. Values of D are readily calculated, provided that the time required for the electrochemically generated species (produced at the generator electrode) to reach the collector electrode and the distance between both electrodes are known. Other parameters typically required to calculate D, e.g., concentration of the redox species, area of the electrode, and number of electrons transferred, are not needed. Diffusion coefficients of Fe(CN)63-, Ru(NH3)62+, and quinone were determined in water and, for Fe(CN)64-, in binary mixtures with glycerol. The results obtained were in good agreement with literature values. Aqueous glycerol solutions are microheterogeneous, as shown by the dependence on medium composition of the empirical solvent polarity scale, ET(30), determined by the solvatochromic probe RB. The responses of RB and the electrochemically generated species (Fe(CN)64-) to the composition of aqueous glycerol mixtures were found to be remarkably similar. Measurements of D of ferrocene in micellar solutions of the cationic surfactant CTABr were also performed. Values of D for ferrocene and the ferrocenium cation are very different, in agreement with the chemical affinity of both species for the cationic micelle.
Introduction Diffusion studies are used to investigate the structure and dynamics of chemical systems, in particular, the transport properties of species. Several methods are employed to study diffusion, including Taylor dispersion, NMR, dynamic light scattering, and interferometry.1 This information can also be obtained by using electrochemical techniques.2,3 Accurate measurement of the diffusion coefficient (D) and investigations on diffusional processes are important for the determination of the transport rate of the substrate to the electrode surface.4 Additionally, D values can be used to determine hydrodynamic radii of dissolved species, and to gain information on the behavior of solutes in viscous polymer solutions.5 Most electrochemical methods for the determination of D depend on the experimental conditions that allow mass-transport control. In general, information on the experimental setup is required, e.g., the concentration of the species investigated, the dimensions of the electrode, and the number of electrons transferred during the electrochemical step.2 There are procedures, however, where some of these additional data are dispensable.6 Thin-layered devices with electrodes in parallel configuration have been successfully employed to increase mass transport7 in order to follow coupled reactions with very fast kinetics using hydrodynamic voltammetry,8 as well as in the development of analytical methods.9 The use of electrochemical cells fabricated with generator-collector electrodes also constitutes a useful * To whom correspondence should be addressed. Fax: 5511-3815-5579. E-mail:
[email protected]. † Universidade de Sa ˜ o Paulo. ‡ Universidade Federal de Uberla ˆ ndia.
approach to investigate the diffusion of products generated electrochemically. A methodology for direct measurement of D, by using an array of individually addressable parallel microelectrodes, has been reported.10,11 In this device, the diffusion of species can be tracked as a function of the response time of the collector electrode once the distance between the generator and collector electrodes is known. Other devices based on a similar approach (measurement of the transit time needed by the species to diffuse from the location of its generation12-14 or dispensing spot15 to the collector electrode) were also reported in the literature. Finally, it is worth mentioning that scanning electrochemical microscopy measurements in the feedback mode also constitute a reliable approach for determining diffusion coefficients based on the generatorcollector principle.16-22 The miniaturization of analytical systems has been largely developed and applied in a wide range of applications to offer more sensitive and faster analyses, using smaller sample volumes, with lower reagent consumption.23-25 This trend includes electrochemical sensors and assays to meet new requirements involving high-throughput testing and parallel processing. To this end, electrochemical devices with closely spaced twin electrodes (in micrometer scale) have been employed to collect the electrochemically generated species with 100% efficiency.26,27 The use of these devices to measure the rate of homogeneous reactions following electrode processes and to completely remove the influence of interfering species in analytical applications has also been reported.28 More recently, generator-collector electrochemical devices have been used to amplify the current from redox molecules by a factor of approximately 400 through cycling.27 Because the potential is kept constant, there is no capacitive charging current at the
10.1021/jp075878s CCC: $37.00 © 2007 American Chemical Society Published on Web 10/09/2007
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Figure 1. Schematic representation of the diffusion of electrochemically generated species (A and B) in the twin-electrode thin-layered cell (TETLC) device between the generator and collector electrodes (separated by a distance d).
collector electrode; this leads to a remarkable increase in the signal-to-noise ratio. Consequently, these devices are of special interest in terms of lowering the limit of detection in analytical determinations. In the present paper, we describe the use of a homeconstructed twin-electrode thin-layered cell (TETLC) operating in quiescent solutions to determine the diffusion coefficient of electrochemically generated species. Values of D were calculated based on the time taken for the species produced at the generator to reach the collector (transit time), and the distance between both electrodes. Details of the calculation of interelectrode distance and measurement of the transit time are discussed below. In order to probe the potential of TETLC in the determination of D, we have tested the Stokes-Einstein equation for binary mixtures of glycerol and water. An excellent linear correlation was obtained between D and the inverse of solution viscosity. Binary mixtures of water and glycerol are microheterogeneous; this is evidenced from the nonlinear plot between the empirical solvent polarity, ET(30) (in kilocalories per mole), or D versus the mole fraction of water, χW. The similar response of both properties to medium composition is remarkable, and indicates that ferrocyanide is preferentially solvated by glycerol. Electrochemical techniques give information on long-time self-diffusion coefficients in surfactant solutions, as a gradient of micelles does not build up upon the application of an electrical field. As the probe resides predominantly inside the micelle, information on the micelle diffusion rather than probe diffusion is obtained. Furthermore, in such systems diffusion occurs over macroscopic distances near the surface electrode (diffusion layer) which are significantly larger than the mean intermicellar spacing; i.e., the time scale of the experiment is dependent on the transport of the micelle-solubilized probe instead of the dynamics of micelle formation/dissociation. By using the device proposed, we show that relevant information on the diffusion of ferrocene and ferrocenium cation in cetyltrimethylammonium bromide solutions can also be obtained. Experimental Section Chemicals. All solid reagents were of analytical grade and were used without further purification. Potassium ferricyanide, potassium ferrocyanide, hydroquinone, potassium chloride, and potassium nitrate were obtained from Merck (Darmstadt,
Figure 2. Waveform potential applied in the chronoamperometric experiment at W1 (A). Chronoamperometric curves recorded at W1 and W2 in 1 mmol L-1 Fe(CN)63- + 0.1 mol L-1 KCl solution at two different conditions: W2 at open circuit (B) and W2 at 0.5 V (C). Distance between the generator and collector electrodes ) 37 ( 2 µm.
Germany). Hexaammineruthenium(III) chloride was obtained from Alfa Aesar (Ward Hill, MA). The solvatochromic probe RB, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate, was from Merck. Ferrocene was obtained from Eastman-Kodak (Rochester, NY). Cetyltrimethylammonium bromide, CTABr, was obtained from Sigma-Aldrich (Steinheim, Germany). Glycerol (Acros) was distilled from CaH2, and kept over activated molecular sieves. Solutions were prepared by dissolving the reagents in deionized water processed through a water purification system (Nanopure Infinity, Barnstead). Electrodes and Instrumentation. An Autolab PGSTAT 30 (Eco Chemie) bipotentiostat with data acquisition software made available by the manufacturer (GPES 4.8 version) was used for
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TABLE 1: Simulated K Values as a Function of tD and the Interelectrode Gap d/µm
tD/ms
K
12 24 30 33 36 48
9.70 42.7 64.7 77.3 95.0 169
4.85 4.63 4.70 4.73 4.65 4.65
electrochemical measurements. Experiments were done in the proposed electrolytic cell, where a Ag/AgCl (saturated KCl) electrode and a platinum wire were used as reference and counter electrodes, respectively. Toner masks were printed using an HP LaserJet 1160 series printer. The heat transference of the toner masks was accomplished with a thermal press (HT 2020, Ferragini, Sa˜o Carlos, SP, Brazil). Details on the construction of the TETLC can be found elsewhere.26,28 Briefly, the basic steps for construction of the TETLC are as follows: (1) Twin gold electrodes are constructed from a gold recordable CD.29 (2) Two orifices (solution inlet and outlet) are made in the CD polycarbonate slice where the top gold electrode is situated. (3) Two toner masks are heat transferred (100 °C/1.5 min) to the polycarbonate slice containing the orifices and the top gold electrode. (4) A second piece of polycarbonate containing the other gold electrode is heat sealed (120 °C for 2.5 min) on the first CD slice to produce the microstructure. Each toner mask generates a microchannel, and as two toner masks were used to prepare the electrochemical cell, the unprinted areas generated microchannels with a depth (d) of approximately 12 µm. (5) Finally, a microtip and a reservoir (500 µL) are glued (epoxy glue) in the inlet and outlet sides, respectively. The same glue is used to reinforce the structure of the microdevice. Reference and auxiliary electrodes are positioned in the reservoir of the outlet side. A device with six toner masks was used in the majority of experiments; devices with other interelectrode gaps were also fabricated. Spectrophotometric Determination of ET(30). Binary mixtures of water and glycerol were prepared by weight at 25 °C. Solution of RB in acetone was pipetted into 1 mL volumetric tubes, followed by solvent evaporation under reduced pressure, over P4O10. Pure glycerol or binary solvent mixtures were added, and the probe, final concentration (2-5) × 10-4 mol L-1, was dissolved. A Shimadzu UV-2550 UV-vis spectrophotometer was used. Each spectrum was recorded twice, at 25 °C, at a rate of 120 nm/min; values of λmax were determined from the first derivative of the absorption spectra. Values of ET(30) were calculated from the equation30
ET (kcal/mol) ) 28591.5/λmax (nm)
(1)
where λmax is the longest wavelength of absorption, i.e., that due to the intramolecular charge transfer within RB. Results and Discussion Figure 1 shows a schematic representation of the device proposed for measuring the diffusion coefficient of an electro-
chemically generated species. The generator electrode is maintained at a potential where the electroactive species (A) does not react at its surface. Subsequently, the potential of the generator electrode is stepped to a new value, producing the electrochemically generated species (B). The time required for (B) to reach the W2 electrode (polarized at a suitable potential) can be used to determine the diffusion coefficient (D) of the species B. Results obtained from chronoamperometric experiments performed with ferricyanide in the TETLC are shown in Figure 2. Initially, W1 was polarized at 0.5 V; under this condition no faradaic current flows through the electrochemical cell. After 5 s the potential of W1 was stepped to 0 V (Figure 2A), a potential where the electrodic reaction presented in eq 2 takes place:
Fe(CN)63- + e- h Fe(CN)64-
at W1 (generator)
Figure 2B shows that, at W1, current starts to flow and drops to zero because of the extensive consumption of the electroactive species in the device. The latter operates as a thin-layered cell as the dimension of the solution layer is comparatively smaller than the thickness of the diffusion layer.26,28 No current is observed at W2, because the latter was maintained at opencircuit conditions. When W2 is turned on at a potential where the material produced at W1 (ferrocyanide) is electroactive (i.e., at 0.5 V), current flows according to eq 3 (Figure 2C):
Fe(CN)64- h Fe(CN)63- + e-
at W2 (collector)
D × 106/cm2 s-1 3-
[Fe(CN)6] [Ru(NH3)6]2+ quinone
electrolyte L-1
0.1 mol KCl 0.1 mol L-1 KCl 1 mol L-1 KNO3
(3)
The subsequent diffusion of ferricyanide back to the generator electrode enhances the flux of this species. Because of this forced redox cycling (positive feedback effect),21,26,28 a large current enhancement is observed and a steady-state condition is rapidly attained at both electrodes. Note that the collection efficiency (ratio between steady-state current at both collector and generator electrodes) is close to 100% (Ia/Ic ) 1), in agreement with results reported in the literature on the use of twin electrodes in thin-layered cells.26,28,31 Figure 3 shows in more detail the current versus time curve at W2 during the chronoamperometric experiment where both electrodes are polarized at conditions that allow the forced redox cycling to occur. As shown, after 5 s W1 is turned on and the electrodic reaction depicted in eq 2 takes place. Note that some time is required for the current signal to appear at the collector electrode (W2) after the potential step at W1. This delay was arbitrarily defined as the time (transit time, tD) that is necessary for the electrochemically generated species to diffuse and reach the collector electrode. It should be pointed out, however, that other procedures have been proposed in the literature to define tD, e.g., the time required for the current at the collector to reach some arbitrary fraction of its plateau value.10,14 Transit time values were measured in triplicate from chronoamperometric curves by extrapolation of the straight line fitting the rising current curve to the time axis. Note that tD is dependent on both the distance (d) between W1 and W2, and the diffusion coefficient (D) of the species generated at W1. The relationship between these parameters is given by the
TABLE 2: Diffusion Coefficient Values electroactive species
(2)
tD/ms
proposed method
literature2,10
84 ( 5 80 ( 9 42 ( 9
7.3 ( 0.5 7.7 ( 0.9 15 ( 3
7.6 7.8 12.7
Diffusion Coefficients of Redox Species
J. Phys. Chem. B, Vol. 111, No. 43, 2007 12481
Figure 3. Time dependence of collector (W2) current following generation of Fe(CN)64-. Diffusion time, tD, represents the time needed for the current starting to increase at the collector. Distance between the generator and collector electrodes ) 37 ( 2 µm. Other experimental conditions as in Figure 2C.
Einstein-Smoluchowsky equation,15 which can be generally represented as
d ) KxDtD
(4)
where K is a constant that depends on the geometry of the space through which the species diffuses.13 Values of K can be (i) calculated from digital simulation of current vs time plots for different values of (d) or (ii) determined empirically by calibrating the system with a species of known D and using d values measured by an independent technique (e.g., scanning electron microscopy). In the present work the value of K was determined by using the previously reported digital simulation data.28 Table 1 shows K values calculated for several TETLCs, with interelectrode spacing in the range 12-48 µm; the average K value was found to be 4.70 ( 0.08. The diffusion coefficient was obtained by measuring defined transit time values and relating them to those obtained in calibration experiments, carried out with a chemical species with known electrochemical behavior. Hence, the distance between the electrodes, d, was determined by operating the cell with ferricyanide as the standard. Using the diffusion coefficient value for ferrocyanide (the electrochemically generated species at W1) in a 0.1 mol L-1 KCl solution (D ) 6.3 × 10-6 cm2 s-1),2 the time for the current to appear at W2 during the chronoamperometric experiment (tD ) 97 ( 5 ms), and the K value 4.70 ( 0.08, d was found to be 37 ( 2 µm for a structure fabricated with six toner layers. A similar procedure was used to determine the distance, or gap, in the remaining TETLCs, constructed by employing different numbers of toner layers. For example, Figure 4 shows a comparison between the current responses measured at the collector electrode for two TETLCs having different gaps between the electrodes. Several points are worth mentioning: (i) in both cases, steady-state currents were reached after a few seconds as a consequence of the fast turnover associated with both anodic and cathodic processes (feedback); (ii) as expected, the steady-state current is inversely dependent on the distance between the electrodes; (iii) both tD and the time required to reach the steady-state current are inversely proportional to the distance between the electrodes. Further experiments were carried out in order to demonstrate the usefulness of the TETLC device in the determination of the diffusion coefficients of electroactive species where Fe(CN)64-, Ru(NH3)63+, and hydroquinone were used as precursors of Fe(CN)63-, Ru(NH3)62+, and quinone. Table 2 presents the
Figure 4. Time dependence of collector current following stepped generation of Fe(CN)64- for two structures with different gaps (36 ( 2 (a) and 65 ( 3 (b) µm). Other experimental conditions as in Figure 2C.
results obtained by using the methodology proposed, as well as D data reported in the literature. The good agreement between the sets demonstrates the potentiality of TETLC to extract information on the dynamics of electrodic processes. For noninteracting spheres undergoing Brownian motion in an ideal solution, the self-diffusion coefficient is given by the Stokes-Einstein equation
D0 )
kBT 6πηa
(5)
where kB is the Boltzmann constant, T is temperature, η is the viscosity of the solution, and a is the radius of the diffusing species. According to eq 5, diffusion coefficients are inversely proportional to solution viscosity in an ideal solution. On the other hand, increases in solution viscosity for some systems are not associated with a corresponding decrease in D values, as reported in nonideal solutions consisting of polystyrene in cyclohexane/benzene.32 In order to vary systematically the diffusion coefficient of ferrocyanide, experiments were performed by changing the viscosity of the supporting electrolyte by addition of glycerol. Figure 5 shows the chronoamperometric curves at W2. The effect of increasing the viscosity is observed, as both the steady-state current and tD are clearly dependent on the binary mixture composition. Accordingly, tD is inversely proportional to D; the latter decreases as a function of the increasing viscosity of the medium. A plot of D vs η-1 is shown
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Figure 5. Time dependence of collector current following stepped generation of Fe(CN)64- carried out in a 1 mmol L-1 Fe(CN)63- + 0.1 mol L-1 KCl solution before (a) and after addition of glycerol (10 (b), 30 (c) 60 (d), and 70% (e), m/v). Distance between the generator and collector electrodes ) 55 ( 3 µm. Other experimental conditions as in Figure 3. Inset shows D versus 1/η.
in the inset of Figure 5, and the excellent agreement between experimental results and the theoretical predictions confirms that the Stokes-Einstein equation applies to the ferrocyanide/water/ glycerol system. The inset in Figure 5 is interesting because Kirkwood-Buff integral functions, which describe water-water, solventsolvent, and solvent-water interactions, indicate that binary mixtures of water with many organic protic solvents are microheterogeneous. There exist microdomains composed of solvent surrounded by water, and of water solvated by organic solvent.33 Indeed, a plot of the empirical solvent polarity parameter, ET(30), for aqueous glycerol mixtures shows a nonlinear dependence on χW; see Figure 6A. ET(30) values of the mixtures lie below the straight line that connects the polarities of both pure solvents; i.e., RB is preferentially solvated by glycerol, the solvent of lower polarity. A similar plot (not shown) was observed for D versus χW. Figure 6B shows the perfect linear correlation between D and ET(30), at comparable values of χW. This plot is remarkable because the phenomena involved have distinct origins, diffusion of an electrochemically generated species and excitation of the zwitterionic ground state of RB, shown in Figure 6C. Figure 6B means that ferrocyanide is preferentially solvated by glycerol; its interaction with the medium is sensitive to the same solute-solvent interactions that affect solvation of RB, namely hydrogen-bonding and dipolar interactions.33 Note that preferential solvation of “probes” occurs in ideal binary mixtures, via the so-called “dielectric enrichment”, whereby the solvation shell of the probe is enriched (relative to the bulk mixture) in the component of higher relative permittivity, due to nonspecific solute-solvent interactions.34 If the diffusion of electrochemically generated species proves to be sensitive to the changes of structure of binary mixtures, at the microscopic leVel, as shown in Figure 6B, then TETLC represents a simple, independent, and welcomed method for probing both solute-solvent and solvent-solvent interactions. The incorporation of electroactive hydrophobic probes in micelles has been recognized as a useful strategy to obtain information on the transport of the micelles. An important assumption in this approach is that probe solubilization does not perturb the micelle. We have recently shown the advantages associated with the use of microelectrodes, as they allow steadystate measurements to be obtained in quiescent solutions, in the presence or absence of supporting electrolytes.35 The diffusion coefficients of CTABr aggregates have been measured by using ferrocene as an electrochemical probe, and the influence of KBr concentration on the morphology of the micelles has been investigated.36
Figure 6. (A) Dependence of the empirical solvent polarity parameter ET(30) on the mole fraction of water, χW, for water-glycerol binary mixtures. (B) Correlation between ET(30) and D, at the same values of χW, at 25 °C. (C) Zwitterionic ground state and diradical excited state of RB.30
The reversible electrochemistry of ferrocene in CTABr solutions has already been reported;35 it consists of a welldefined voltammetric curve with E1/2 ) 0.243 V. A typical voltammogram obtained with the TETLC filled with a solution
Diffusion Coefficients of Redox Species
J. Phys. Chem. B, Vol. 111, No. 43, 2007 12483 ferrocenium in the TETLC in a preliminary step (both W1 and W2 polarized at 0.5 V, first 30 s in panel B, Figure 7). Consequently, W1 is stepped to 0 V to produce ferrocene, which diffuses to W2. By comparing results in panels A and B, a much longer time for the current to appear in W2 is required when micelle-solubilized ferrocene is the diffusing species. The calculated value of D was (6.4 ( 0.4) × 10-7 cm2 s-1, in agreement with results reported in the literature35 by using a platinum microelectrode: D ) 6.7 × 10-7 cm2 s-1. The value is significantly lower than the one reported37 in the absence of surfactant (D ) 6.9 × 10-6 cm2 s-1 in 0.1 mol L-1 Li2SO4) because it reflects the mobility of a slower moving entity: the micelle-incorporated probe. Note that outside the micellar domain, 0.1 mol L-1 Li2SO4, the diffusion coefficients for ferrocene and ferrocenium are comparable.17 Conclusions
Figure 7. (A) Time dependence of collector current (polarized at 0.0 V) following potential step generation of ferrocenium at W1 at t ) 10.0 s (from 0.0 to 0.5 V) in a solution containing 1.5 mmol L-1 ferrocene + 0.15 mol L-1 CTABr. (B) Time dependence of collector current (polarized at 0.5 V) following potential step generation of ferrocene at W1 at t ) 30.0 s (from 0.0 to 0.5 V) in a solution containing 1.5 mmol L-1 ferrocene + 0.15 mol L-1 CTABr. Schematic drawings show the electrochemical and diffusional processes, and gray and white circles represent, respectively, ferrocene and ferrocenium species. Distance between the generator and collector electrodes ) 55 ( 3 µm.
SCHEME 1
containing CTABr-bound ferrocene and operating in the feedback mode (i.e., oxidation of ferrocene occurs at W1 (polarized at 0.5 V) simultaneously with the reduction of ferrocenium at W2 (polarized at 0 V)) yields a sigmoidal curve because of the enhanced flux of material. Ferrocene regenerated at the collector (W2) diffuses back to W1, and a steady-state diffusional crosstalk between both electrodes is noticed. Further experiments were performed to investigate in more detail the transit time of the species in this surfactant system. Accordingly, Figure 7A presents the dependence of current at W2 when both electrodes (generator and collector) are maintained at 0 V for 10 s. Subsequently, the potential of the generator was stepped to 0.5 V, so that anodic oxidation of ferrocene occurred. As the electrogenerated ferrocenium is positively charged, Scheme 1, its diffusional transport to W2 occurred without interference from the cationic micelle, because of electrostatic repulsion. The diffusion coefficient calculated for ferrocenium in CTABr solution was found to be D ) (4.9 ( 0.3) × 10-6 cm2 s-1, in agreement with the value determined for the same species in 0.1 mol L-1 Li2SO4 solution, D ) (5.5 ( 0.4) × 10-6 cm2 s-1. CTABr-solubilized ferrocene, however, behaved differently. This study was carried out by coulometric electrogeneration of
The TETLC serves as a reliable and cost-effective device for measuring diffusion coefficients of redox species in solutions of interest. Compared to other time-of-flight approaches, the present one offers additional simplicity. The reason is that once the system has been previously calibrated against a species of known diffusion coefficient, and the interelectrode spacing is calculated or measured from scanning electron micrographs, no further information is required for the calculation of D, e.g., the characteristics of the diffusing species. A 100% collection efficiency can be easily achieved without mechanically perturbing the system (e.g., by stirring or rotation of the electrodes). Compared to commercially available ring-disk electrodes, TETLCs have shorter, easily controlled tD’s, because these times depend on the number of toner masks employed. The remarkable difference between tD’s for CTABr-bound ferrocene and ferrocenium cation is due to the electrostatic repulsion between the latter and the positively charged micellar interface. By using the generator-collector approach with the TETLC, we can envisage new relevant chemical and biological applications. For example, information on solute-solvent and solventsolvent interactions in binary solvent mixtures can be obtained from the dependence of D of the electrochemically generated species on the medium composition. Moreover, the areaaveraged transport rates through Langmuir monolayer films or lipidic membranes can be extracted by using specifically designed redox-active probe molecules. These films/membranes display size-selective porosity with respect to molecules smaller than the intrasquare cavity and blocking behavior with respect to larger molecules. Selective molecular transport can be then engineered for applications such as chemical sensing, energy conversion, and chemical catalysis; these are subjects of our ongoing investigations. Acknowledgment. We are thankful to FAPESP (Fundac¸ a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo) and CNPq (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico) for financial support. We thank Clarissa T. Martins for carrying out the measurements of polarity of aqueous glycerol. References and Notes (1) Cussler, E. Diffusion: Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, U.K., 1985. (2) Adams, R. Electrochemistry at Solid Electrodes; Marcel Dekker: New York, 1969. (3) Baur, J. E.; Wightman, R. M. J. Electroanal. Chem. 1991, 305, 73. (4) Nernst, W. Z. Phys. Chem. 1904, 47, 52. (5) Bockris, J. O. Q. ReV. 1949, 3, 173.
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