Quantification of the Interaction between Charged Guest Molecules

Anal. Chem. 1999, 71, 2528-2533

Quantification of the Interaction between Charged Guest Molecules and Chemisorbed Monothiolated β-Cyclodextrins Axel Michalke, Andreas Janshoff, Claudia Steinem, Christian Henke, Manfred Sieber, and Hans-Joachim Galla*

Institut fu¨r Biochemie, Westfa¨lische Wilhelms-Universita¨t, Wilhelm-Klemm-Strasse 2, D-48149 Mu¨nster, Germany

The quantification of small molecules in aqueous solution by surface bound supramolecular host molecules is an important goal in the research field of chemo- and biosensor development. In this paper we present an attempt to quantify the interaction of different charged guest molecules with chemisorbed monothiolated β-cyclodextrin monolayers by means of impedance spectroscopy in the presence of the redox couple [Fe(CN)6]3-/[Fe(CN)6]4-. Self-assembled monolayers of mercaptopropane-N-mono6-deoxy-β-cyclodextrin amide (MPA-CD) on gold surfaces were formed with coverage of 99-100%. The inclusion of charged guest molecules was detected by monitoring the changes in the charge-transfer resistance, which is sensitive to the surface charge density in terms of repulsion or attraction of the redox active ions. Adsorption of positively charged 1-adamantanamino hydrochloride (1ADHC) led to a considerable increase in the chargetransfer resistance, whereas the inclusion of both negatively charged 1-adamantanecarboxylic acid (1-ADC) and 2-(p-toluidinyl)naphthalene-6-sulfonate (2,6-TNS) caused a decrease. Applying the Frumkin correction to obtain the surface charge density and the Gouy-Chapman-Stern theory to account for the electrochemical double layer, we were able to quantify the binding of the charged guest molecules in terms of binding isotherms. The isotherms display a distinct two step adsorption process probably owing to the presence of two energetically different binding sites on the surface. Complete reversibility of the binding process of the guest molecules could be demonstrated by the addition of β-cyclodextrin in solution, which allowed the reuse of the functionalized surfaces. One of the major goals in the development of chemosensors, biosensors, and applied supramolecular chemistry is the design of surface bound host molecules with high specificity for small molecules (M < 2000 g/mol). Besides the design of new molecules, it is of enormous interest to find sensitive transducers, which are capable of detecting and quantifying small molecules on surfaces. State of the art transducers such as surface plasmon resonance setups and quartz crystal microbalance are operating at their detection limit if molecules are smaller than 2000 g/mol * Corresponding author: (e-mail) [email protected]; (fax) + 49 251 833 3206.

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and cover the surface in a monomolecular fashion. Here we present a sensitive electrochemical approach based on detecting shifts of the charge-transfer resistance due to changes in the surface charge density by binding of charged guest molecules to a cyclodextrin-functionalized surface. Cyclodextrins are cyclic oligosaccharides consisting of at least six R-D-glucose units. The oligosaccharide forms a truncated cone in which the primary hydroxyl groups are directed to the narrow side and the secondary hydroxyl groups are on the wide side of the torus. Because of the arrangement of the functional groups, the interior of the torus is hydrophobic whereas the outer surface is hydrophilic. Because of their hydrophobic cavity, cyclodextrins are capable of forming inclusion complexes with small hydrophobic molecules that fit into the cavity. This host-guest interaction is applied in drug delivery, chromatography, solubility enhancement, and selective removal of undesired substances1 partially demanding for an immobilization of either the host or the guest molecule on a solid support. Besides the Langmuir-Blodgett technique,2 attempts have been made to form oriented solid supported monolayers of cyclodextrins by means of selfassembly.3-7 Rojas et al.3 synthesized a 7-fold thiolated β-cyclodextrin derivative, which chemisorbs on gold surfaces achieving a coverage of about 64%. Nelles et al.4 and Weisser et al.8 investigated the influence of the length of the spacer as well as the number of thiol groups per cyclodextrin molecule on the kinetics and the film structure on gold. In conclusion, a longer spacer allows the extended formation of hydrogen bonds due to the higher flexibility of the cyclodextrins and results in a high surface coverage. However, the multithiolated molecules showed only weak hydrogen bonding and a low surface coverage due to (1) Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803-822. (2) Odashima, K.; Kotato, M.; Sugaware, M.; Umezawa, Y. Anal. Chem. 1993, 65, 927-936. (3) Rojas, M. T.; Ko¨niger, R.; Stoddart, J. F.; Kaifer, A. E. J. Am. Chem. Soc. 1995, 117, 336-343. (4) Nelles, G.; Weisser, M.; Back, R.; Wohlfart, P.; Wenz, G.; Mittler-Neher, S. J. Am. Chem. Soc. 1996, 118, 5039-5046. (5) Kaifer, A. E. Isr. J. Chem. 1996, 36, 389-397. (6) Henke, C.; Steinem, C.; Janshoff, A.; Steffan, G.; Luftmann, H.; Sieber, M.; Galla, H.-J. Anal. Chem. 1996, 68, 3158-3165. (7) Maeda, Y.; Fukuda, T.; Yamamoto, H.; Kitano, H. Langmuir 1997, 13, 41874189. (8) Weisser, M.; Nelles, G.; Wohlfart, P.; Wenz, G.; Mittler-Neher, S. Phys. Chem. 1996, 100, 17893-17900. 10.1021/ac980932+ CCC: $18.00

© 1999 American Chemical Society Published on Web 05/19/1999

Scheme 1

the restriction of the orientation of the torus axis. Weisser et al.9 investigated the host-guest interaction of different guest molecules with cyclodextrin derivatives immobilized on gold surfaces. One major problem in their study was the nonspecific adsorption of guest molecules on the bare gold surface, which was dependent on the chemical structure of the guest and the cyclodextrin derivative. While the close packing of the cyclodextrin molecules achieved by a highly flexible spacer resulted in a small nonspecific adsorption, a very densely packed cyclodextrin monolayer did not allow the inclusion of guest molecules because of steric restrictions. In this study, we used a monofunctionalized cyclodextrin derivative, mercaptopropane-N-mono-6-deoxy-cyclodextrin amide (MPA-CD), with a five atom long spacer between the cyclodextrin ring and a thiol group, enabling the molecule to chemisorb on gold surfaces (Scheme 1). In a preceding paper, we demonstrated that this compound forms a densely packed monolayer.6 Impedance spectroscopy was employed to quantify the binding of different charged guest molecules by monitoring changes in the charge-transfer resistance of the redox couple [Fe(CN)6]3-/ [Fe(CN)6]4-. Submonolayer coverage was easily detectable by this method. Binding constants of the guest molecules were determined by applying an electrostatic repulsion model, which accounts for the electrostatic interaction between the guest molecules in solution and on the surface.

Figure 1. Impedance spectra of an 11-MUD (0) and an MPA-CD monolayer (4) on gold in 100 mM NaOAc, pH 5.5, 1.6 mM K3[Fe(CN)6]/K4[Fe(CN)6]. For comparison a gold electrode (O) after 24 h in the same solution is shown. The continuous lines represent the results of fitting the parameters of the equivalent circuit to the corresponding spectra. In the case of the MPA-CD monolayer the Warburg impedance element σ was neglected. The results of the fitting procedure are summarized in Table 1.

EXPERIMENTAL SECTION Materials. 1-Adamantanamine hydrochloride (1-ADHC) and 1-adamantanecarboxylic acid (1-ADC) were purchased from Fluka (Buchs, Switzerland). 1-Anilinonaphthalene-2-sulfonate (1,2-ANS), 2-(p-toluidinyl)naphthalene-6-sulfonate (2,6-TNS), potassium ferricyanide ([Fe(CN)6]3-), potassium ferrocyanide ([Fe(CN)6]4-), and sodium acetate (NaOAc) were from Sigma (St. Louis, MO). Water was first purified by a Millipore water purification system Milli Q RO 10 Plus and then by Millipore ultrapure water system Milli Q Plus 185 (specific resistance: 18 MΩ/cm). Gold used for the working electrodes was a generous gift from DEGUSSA (Hanau, Germany). Chromium was obtained from Bal Tec (Balzers, Liechtenstein). Immobilization of Cyclodextrins on Gold Surfaces. The self-assembled cyclodextrin monolayers were formed on two equally designed gold electrodes each with an area of 0.13 cm2 deposited on a glass slide.6 The gold coating was performed in an evaporation unit (E 605, Edwards, Great Britain). After a thin layer of chromium (10-20 nm) was evaporated, the gold layer was deposited subsequently with a final thickness of about 100

nm. Before being exposed to a 1 mM solution of (MPA-CD)2 in ultrapure water, the gold electrodes were first cleaned in a plasma cleaner (Harrick, NY) for 5 min. After being incubated for 24 h, the electrodes were rinsed several times with ultrapure water to remove nonchemisorbed disulfides. The functionalized gold electrodes were used immediately for the impedance measurements. Impedance Analysis. Ac impedance analysis was performed using an impedance gain/phase analyzer from Solartron Instruments (SI 1260, Great Britain). All data were recorded without offset potentials at an ac amplitude of 30 mV to avoid nonlinear responses. The magnitude of the impedance |Z(f)| and the phase angle Φ(f) between voltage and current were recorded in the frequency range from 10-1 to 106 Hz. Data analysis was performed by a nonlinear least-squares fit based on the LevenbergMarquardt algorithm.10 Impedance spectra of the MPA-CD monolayers were taken in a solution composed of 1.6 mM K4[Fe(CN)6], 1.6 mM K3[Fe(CN)6], and 100 mM NaOAc, pH 5.5 in the case of 1-ADHC and pH 8.0 in the case of 1-ADC to ensure fully charged guest species. To follow the time course of the charge-transfer resistance while adding guest molecules, the impedance of the system was recorded at a fixed frequency, which was individually determined before each experiment, by taking complete impedance spectra. In all experiments, the charge-transfer resistance of an MPA-CD monolayer was most well defined in a frequency range of 0.1-1 Hz indicated by a constant magnitude of the impedance (|Z(f0)| ) Rct + Re). The accuracy of this value could be confirmed by comparing the Rct obtained by fitting the parameter to the spectrum and the value measured at the fixed frequency. In all experiments, the chosen frequency was between 0.2 and 0.3 Hz.

(9) Weisser, M.; Nelles, G.; Wenz, G.; Mittler-Neher, S. Sens. Actuators B 1997, 38-39, 58-67.

(10) Bevington, P. R. Data reduction and error analysis for the physical sciences; McGraw-Hill: New York, 1969.

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RESULTS AND DISCUSSION Electrical Properties of Chemisorbed MPA-CD Monolayers. To garner information about the dielectric properties of MPA-CD monolayers in the presence of [Fe(CN)6]3-/[Fe(CN)6]4ions, impedance spectra were taken and the electrical parameters of an appropriate circuit were fitted to the data (see Figure 1). The spectra of MPA-CD monolayers are mainly characterized by three distinct frequency regions (Figure 1). At low frequencies (0.1-1 Hz) the charge-transfer resistance Rct representing the oneelectron reaction of [Fe(CN)6]3-/[Fe(CN)6]4- ions at the gold surface dominates the impedance spectrum indicated by a constant magnitude of impedance |Z(f)|. The capacitance of the interface/ monolayer Cd is determined in the frequency range of 10-1000 Hz. At frequencies above 1000 Hz the electrolyte resistance Re of the solution can be read. The Warburg impedance σ that accounts for the mass transfer of the redox ions is not determined in the case of the MPA-CD monolayer because of the high chargetransfer resistance and was therefore neglected in the fitting procedure. From the charge-transfer resistance the electrode coverage can be calculated using the following equation introduced first by Sabatini and Rubinstein:11

RctAu Θ)1Rct

system

Cd/µF/cm2

Rct/Ωcm2

θ (%)

clean gold contaminated goldb 11-MUD (MPA-CD)2

30 ( 10 7(2 2.6 ( 0.2 10 ( 1

6(2 ndc 300 ( 70 8300 ( 3300

0 0 98.0 ( 0.5 99.92 ( 0.02

a θ is the surface coverage calculated using eq 1. The values are mean values obtained from three independent measurements. b The expression “contaminated gold” refers to an electrode incubated for 24 h in 100 mM NaOAc, pH 5.5. c Not determined.

(1)

RctAu denotes the charge-transfer resistance of the uncovered gold electrode, Rct the resistance of the functionalized surface. As mentioned previously, an incubation time of about 10 h led to a high surface coverage of about 99-100%.6 To evaluate the dielectric parameters of MPA-CD monolayers to those of monolayers also exposing hydroxyl groups we investigated 11-mercaptoundecanol (11-MUD) monolayers on gold (Figure 1). As expected, MPA-CD monolayers display greater capacitances due to a greater dielectric constant of the molecule. However, remarkably, MPA-CD monolayers exhibit much higher charge-transfer resistances than 11-MUD monolayers. The more efficient blocking of the electron transfer is probably due to a higher coverage and/or intermolecular hydrogen bonds between the glucose subunits. Because of the lower charge-transfer resistance of the 11-MUD monolayers in this case the mass transfer of the redox couple is apparent at low frequencies indicated by the slight increase in the magnitude of the impedance. The electrical parameters obtained by fitting the parameters of the equivalent circuit depicted in Figure 1 are summarized in Table 1. Adsorption Isotherms of Charged Adamantane Derivatives on CD Monolayers. We investigated the influence of the positively charged guest molecule 1-adamantanamine (1-ADHC)12 and the negatively charged 1-adamantenecarboxylic acid (1-ADC) on the charge transfer across CD monolayers. It is reasonable to assume that the adamantane derivatives are both fully charged at the respective pH values, even when they are bound to the surface.13 After each addition of the negatively charged carboxylic (11) Sabatani, E.; Rubinstein, I. J. Electroanal. Chem. 1987, 219, 365-371. (12) We investigated the free adamantanamine as well as the hydrochloride salt. In both cases we obtained the same binding constants indicating that the chloride ions do not influence the charge-transfer resistances.

2530 Analytical Chemistry, Vol. 71, No. 13, July 1, 1999

Table 1. Capacitances and Charge-Transfer Resistances of Different Monolayers Compared to Neat Gold Surfacesa

Figure 2. Charge-transfer resistance of the electron transfer of the redox couple [Fe(CN)6]3-/[Fe(CN)6]4- of an MPA-CD monolayer chemisorbed on gold at different concentrations of guest molecules in solution. (A) Addition of the negatively charged guest molecule 1-adamantanecarboxylic acid (1-ADC); (B) addition of the positively charged 1-adamantanamine (1-ADHC). Because of the specific inclusion of the adamantane derivatives into the hydrophobic cavity of the immobilized cyclodextrin molecules, the surface charge density changes lead to a decreased (attraction of the negative charges of the ferri/ferrocyanides by positive charges) or increased (repulsion of the negative charges of the ferri/ferrocyanides by negative charges) charge-transfer resistance Rct, respectively.

acid adamantane derivative a significant increase in Rct could be detected (Figure 2A). In contrast, adding the positively charged amine derivative to a cyclodextrin monolayer led to a considerable decrease of the charge-transfer resistance (Figure 2B). To obtain binding constants of the host-guest interaction on the surface, the surface charge density at any given adamantane concentration in solution was calculated from the measured charge-transfer resistance (see Appendix). As depicted in Figure (13) (a) Zhang, H.; He, H.-X.; Wang, J.; Mu, T.; Liu, Z.-F. Appl. Phys. A 1998, 66, 269-271. (b) Wang, J.; Frostman, L. M.; Ward, M. D. J. Phys. Chem. 1992, 96, 5224-5228.

Table 2. Parameters of the Adsorption Isotherms Obtained by Fitting Eq 4 to the First Part of the Corresponding Isotherma Ka/M-1 guest molecule

on surface

in solution14

σmax/mC m-2

1-ADHC 1-ADC 2,6-TNS 1,2-ANS

1.3 × 104 0.24 × 104 1.9 × 104 n.b.

0.22 × 104 (pH 6.5) 3.30 × 104 (pH 8.3) 0.25 × 104 (pH 6.0) n.b.

11.0 2.7 2.3

a

Figure 3. Adsorption isotherms of 1-ADC (A) and 1-ADHC (B) on an MPA-CD monolayer as the surface charge density vs concentration of the corresponding adamantane derivative. A two-step adsorption is observed. The continuous lines are the results of fitting the parameters of eq 4 to the first part of the isotherms (separated by the dotted line).

3A and B, the resulting isotherms exhibit a two-stage adsorption process. We assume that the first adsorption is due to specific interaction of the guest molecules with the cyclodextrin cavities. We were able to confirm this hypothesis by investigating the binding of the negatively charged guest molecule 6-(4-toluidino)2-naphthalene sulfonate (2,6-TNS) which is known to interact with the hydrophobic CD cavity and 1-anilino-naphatalene-2 sulfonate (1,2-ANS) which does not bind to cyclodextrins but is similar in its chemical structure. Whereas the addition of 2,6-TNS showed the expected increase in the charge-transfer resistance, no significant change could be detected in the case of 1,2-ANS. The curve shape of the 1,2-TNS binding exhibits a similar two-stage process as observed for 1-ADC but less pronounced. The second part of the isotherm may be due to nonspecific adsorption of the guest molecules to the cyclodextrin/guest-modified surface. It might be possible that already bound hydrophobic guest molecules enhance the amount of nonspecific binding since even in the case of 1,2-ANS, where no binding was observed, the nonspecific binding was suppressed as well. On the basis of this assumption only the first part of the isotherms was fitted according to eq 4. The binding constants obtained for the four different guest molecules are shown in Table 2. Compared to binding constants in solution, those obtained on the surface differ by a factor of six to eight.14 It is well established that binding constants of immobilized host molecules or receptors are in some cases significantly different from those of dissolved species. For instance, the binding constant of histidin-tagged proteins to surface-confined (14) Palepu, R.; Reinsborough, V. C. Aust. J. Chem. 1990, 43, 2119-2123.

The theoretical maximum surface charge density is 68 mC/m2.

receptors is reported to be larger than that obtained from experiments with receptor-doped vesicles in solution.15 Another well-known example is the streptavidin binding to biotin which exhibits a binding constant of about 1015 M-1 in solution while immobilized biotin derivatives on surfaces led to considerably smaller binding constants of 108 - 1011 M-1.16,17 It remains to be elucidated why the observed binding constants differ from those in solution. Crucial parameters might be the orientation and packing of the receptor molecules on the surface. Notably, the maximum surface charge densities σmax (Table 2) are much lower than the theoretical calculated maximum surface charge density of 0.068 C/m2, assuming a square arrangement of the cyclodextrin molecules on the surface and that each cyclodextrin molecule has bound one guest molecule. Responsible for this deviation might be the lack of accessibility of the immobilized cyclodextrin cavities due to close packing of the headgroups in a stacked manner. The assumption that ferri- and ferrocyanide ions are presented as the simple 3- and 4- species might not be entirely true. As shown by Beriet and Pletcher,18 different counterions can have a significant influence on the ion parity of these ions. It could be demonstrated that particularly [Fe(CN)6]4- ions tend to form complexes such as Mez+[Fe(CN)6]4- in solution. Assuming an average charge of the redox couple of 3 instead of 3.5, the binding constant would decrease 3.4% and the maximum charge density increase 11%. Reversibility of Adsorption by Competition with CD Molecules in Solution. Adsorbed 1-ADC and 1-ADHC were removed from the surface by adding β-cyclodextrin in solution to the loaded monolayer (Figure 4). The inclusion of 1-ADHC obtained by adding 1 mM of 1-ADHC to a cyclodextrin monolayer decreased the charge-transfer resistance by 80%. Addition of β-cyclodextrin in a concentration of 16 mM resulted in an almost complete regain of the charge-transfer resistance within a few minutes. The same result was obtained by adding 16 mM β-cyclodextrin to a CD monolayer loaded with 1-ADC. The concentration of 1-ADC was 1 mM. Because of the negative charge of 1-ADC, the blocking of the electron transfer process was increased by 100%. The addition of β-cyclodextrin decreases R/R0 almost to the initial value. The complete desorption of the guest molecules bound to the immobilized CD molecules by adding (15) Dorn, I. T.; Neumaier, K. R.; Tampe´, R. J. Am. Chem. Soc. 1998, 120, 27532763. (16) Zhao, S.; Walker, D. S.; Reichert, W. M. Langmuir 1993, 9, 3166-3173. (17) Zhao, S.; Reichert, W. M. Langmuir 1992, 8, 2785-2791. (18) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1993, 361, 93-101.

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not shown). We assume, as mentioned above, that nonspecific adsorption of guest molecules is enhanced by the guest molecules already bound to the surface due to an increase in the surface hydrophobicity. This would imply that nonspecific adsorption at low guest concentrations without presaturated cyclodextrins is lower than with loaded CD molecules.

Figure 4. Desorption of the bound adamantane derivatives 1-ADHC and 1-ADC by addition of β-CD in solution. The first bar shows the Rct before addition of any guest molecule. This value was set to R0. The ratio Rct/R0 decreases upon addition of the positively charged 1-ADHC while increasing using the negatively charged 1-ADC as guest compound. Addition of β-CD reverses this effect in both cases almost completely.

Figure 5. Nonspecific adsorption of 1-ADHC demonstrated by using a presaturated MPA-CD monolayer with the uncharged p-nitrophenol as a guest molecule. Change of Rct/R0 upon addition of different concentrations of 1-ADHC in solution in the presence of 85 mM p-nitrophenol (O), change of Rct/R0 upon addition of 1-ADHC to a cyclodextrin monolayer in the absence of p-nitrophenol (b).

unmodified β-cylcodextrin in solution can provide a fresh sensor surface for further binding studies, which is a crucial step toward sensor applications. Nonspecific Adsorption. To address the important question of the role and amount of nonspecific adsorption occurring at the monolayer/solution interface we presaturated the cavities of the immobilized CDs with the uncharged guest molecule p-nitrophenol which does not alter the charge-transfer resistance of the system prior to the addition of charged guest molecules (Figure 5). The decrease in the charge-transfer resistance, which occurs in the absence of p-nitrophenol, is almost two times larger than in the presence of it. The decrease in the resistance even in the presence of the uncharged guest molecule is attributed to nonspecific adsorption of 1-ADHC on the preloaded MPA-CD monolayer. The same effect was observed for the adsorption of 1-ADC to a surface preincubated with 85 mM p-nitrophenol (data 2532 Analytical Chemistry, Vol. 71, No. 13, July 1, 1999

CONCLUSIONS The increasing interest in artificial receptor surfaces for chemical sensors has led to the establishment of several different immobilized supramolecular host molecules on different kinds of surfaces.5 We were able to use immobilized cyclodextrins on gold surfaces to detect small charged guest molecules in solution. The extraordinary blocking properties of the immobilized cyclodextrin molecules due to the hydrogen bond network enabled us to quantify the electrostatic repulsion of the redox active marker ions with high signal-to-noise ratio. The obtained adsorption isotherms displayed a two-step appearance as if there were two binding sites with different affinities to the guest molecules. We attributed the first part of the isotherm to specific interaction of the guest molecules while the second part might be of nonspecific nature. Usually the desorption process in pure aqueous solution is very slow which makes unloading of the sensing surface difficult on a reasonable time scale. We accomplished fast removal of the bound guest molecules by adding water-soluble β-CD to the functionalized surface which makes the surface reusable after each binding experiment, an important issue for analytical applications. ACKNOWLEDGMENT This work has been financially supported by the Deutsche Forschungsgemeinschaft as a contribution from the SFB 424 project B2. A.J. received a predoctoral fellowship from the Fonds der Chemischen Industrie, and C.S. was a recipient of a predoctoral fellowship of the Graduiertenfo¨rderung des Landes Nordrhein Westfalen. The experienced help in electronics from Dr. F. Ho¨hn and Dipl.-Ing. W. Willenbrink is gratefully acknowledged. APPENDIX Determination of the Surface Charge Density. The surface charge density at any given concentration of a charged guest molecule in solution was calculated from the measured chargetransfer resistances. Whereas adsorption of negatively charged molecules decreases the surface potential Φ2, positively charged guests increases Φ2. The specific adsorption of ions alters the surface potential by ∆Φ2 affecting the exchange current of the redox system [Fe(CN)6]3-/[Fe(CN)6]4-:

I0 ) FAk0 exp

(

)

(

)

3.5FΦ2 3.5F∆Φ2 cFe exp ) RT RT

(

FAk˜ 0cFe exp

)

3.5F∆Φ2 (2) RT

F denotes the Faraday constant, T the temperature, R the ideal gas constant.19 A is the electrode area, cFe the equilibrium concentration of the [Fe(CN)6]3-/[Fe(CN)6]4- ions which are (19) Bard, A. J.; Faulkner, L. R. Electrochemical methods; Wiley-Interscience: New York, 1980.

assumed to be equal for the oxidized and reduced species and k˜ 0 the corrected rate constant. By using the definition of Rct the corrected rate constant was first determined from the chargetransfer resistance of the uncharged CD monolayer (Φ2) so that the change of the surface potential ∆Φ2 could be calculated by eq 2. The actual surface charge density σG-CD can be estimated by applying the Gouy-Chapman-Stern theory for electrochemical double layers considering each ion concentration ci. The concentration of each ion ci at the outer Helmholtz layer x2 results from the Boltzmann distribution assuming a neutral surface before adsorption takes place (Φ2 , ∆Φ2):20

ci(x2, t) ) c0,i exp

(

)

-ziF∆Φ2 RT

length of a 0.1 M 1:1 electrolyte amounts to 0.9 nm19 justifies the assumption that Φ2 , ∆Φ2. Adsorption Isotherm of Charged Molecules. Upon binding of charged guest molecules at the electrolyte/electrode interface, electrostatic interaction between the adsorbed species and those in solution occurs. To take this into account, we used an electrostatic repulsion model given by Schwarz et al.20,21 and applied by Zhao and Reichert22 and Pe´rez-Paya´ et al.23 Since the surface charge density is proportional to the surface concentration of the adsorbed guest molecules the adsorption isotherm can then be written as

σG-CD ) σmax

(3)

zi denotes the charge of each ion. Considering the distance between the cyclodextrin headgroups which include the charged guest molecules and the actual electrode/electrolyte interface where the charge transfer takes place and the fact that the Debye (20) Stankowski, S.; Schwarz, G. Biochim. Biophys. Acta 1990, 1025, 164-172. (21) Schwarz, G.; Beschiaschvili, G. Biochim. Biophys. Acta 1989, 979, 82-90. (22) Zhao, S.; Reichert, W. M. Biophys. J. 1994, 66, 305-309. (23) Pe´rez-Paya´, E.; Porcar, I.; Go´mez, C. M.; Pedro´s, J.; Campos, A.; Abad, C. Biopol. 1997, 42, 169-181.

KacG γG-CD + KacG

(4)

σmax is the maximum charge of a monolayer on the surface, Ka the equilibrium binding constant of the host-guest complex formation, cG the equilibrium concentration of the guest molecule in solution and γG-CD the activity constant containing the repulsion of the adsorbing guest molecules. Received for review August 19, 1998. Accepted March 25, 1999. AC980932+

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