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Application of Electromodulated Fluorescence to the Study of the Dynamics of Alexa 488 Fluorochrome Immobilized on a Gold Electrode Li Li, C. Meuse, V. Silin, and A. K. Gaigalas* Biotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Yu-zhong Zhang Molecular Probes Inc., Eugene, Oregon Received September 9, 1999. In Final Form: February 8, 2000
Alexa 488 fluorochrome was immobilized on a gold electrode. The formation of the layer of fluorochrome was followed in real time using surface plasmon resonance (SPR). Both SPR and spectroscopic ellipsometry (SE) gave a thickness of ∼0.7 nm for the fluorochrome layer. SE showed a strong optical absorption peak at 512 nm which is red-shifted relative to the absorption peak at 490 nm for fluorochrome in solution. The electromodulated fluorescence (EmF) intensity was measured and found to be predominantly out-of-phase with the modulating potential. The amplitude of the EmF depended inversely on the modulating frequency and was large only for frequencies less than 5 Hz. The EmF amplitude had a large dependence on solution ionic strength. Measurements of the electromodulated reflectance (EmR) indicated minimal changes in absorbency so that the EmF was most likely due to quantum yield modulation. We assumed that the underlying cause of the fluorescence modulation was local surface reorganization, which led to changes in the separation between the surface and the fluorochrome. The EmF response was described by a model which assumed that the fluorochrome had two locations relative to the surface, and a potential-dependent rate constant described the transition between the two locations. The rate constant was found to be less than 0.002 s-1. We also considered a second model which assumed fluorochrome electrophoretic transport. The transport model did not reproduce the measured EmF response. Electron transfer from the excited state was also considered.
Introduction Fluorochrome can be used to study the interaction of molecules with surfaces. At metal surfaces, the quenching of fluorescence depends on the third power of the distance between the fluorochrome and the metal surface, providing a sensitive indicator of the relative distance of the fluorochrome from the electrode surface. The fluorescence from 12-(9-anthroyloxy)stearic acid was used to study the formation of a self-assembled monolayer on a gold surface.1 Similar investigations were carried out with the fluorochrome 10-decyl-9-[2-(4-pyridyl)ethyl]anthracene to study the spreading of 4-pentadecylpyridine onto an Au(111) electrode.2 The exponential decay of the evanescent wave from internally reflected light has served as a tool for the study of fluorochrome at glass surfaces.3 Recently suggestions were made for a wider applicability of surfaceconfined fluorochrome to the study of surface processes.4 In recent measurements, we found that the fluorescence from Alexa 488 fluorochrome immobilized on gold electrodes exhibited quasi-reversible behavior over a limited range of applied electrode potentials.5 In the present work, * Corresponding author. E-mail:
[email protected]. Fax: (301) 975-5449. Phone: (301) 975-2873. (1) Bizzotto, D.; Lipkowski, J. J. Electroanal. Chem. Interfacial Electrochem. 1996, 409, 33-43. (2) Sagara, T.; Zamlynny, V.; Bizzotto, D.; McAlees, A.; McCrindle, R.; Lipkowski, J. Isr. J. Chem. 1997, 37, 197-211. (3) Hlady, V.; Reinecke, D. R.; Andrade, J. D. J. Colloid Interface Sci. 1986, 111, 555-569. (4) Fox, M. A.; Li, W.; Wooten, M.; McKerrow, A.; Whitesell, J. K. Thin Solid Films 1998, 327-329, 477-480.
10.1021/la991192i
we extended the measurements to electromodulated fluorescence (EmF) and determined the frequency response at two applied potentials. The measurements of the EmF were supplemented by electromodulated reflectance (EmR) and electrochemical (EC) measurements. The EmR measurements suggested that the potential-induced change in absorbency was not sufficient to explain the large EmF signal. EC measurements were used to estimate the actual potential that the fluorochrome experiences. The EmF response was interpreted in terms of a modulation of the distance between the immobilized fluorochrome and the metal surface. The change in separation was assumed to originate from a potential-induced local reorganization of the surface. For potentials more negative than -0.7 V, the fluorochrome desorbed (reduction of the S-Au bond) completely from the surface, resulting in a loss of the EmF signal. The measurement of electromodulated fluorescence from immobilized fluorochrome may be a useful technique for the study of some aspects of the dynamics of molecules confined on electrodes. Analysis The analysis of the EmF signal follows the formalism originally developed by Kofman6 for describing electromodulated reflectance. It is assumed that there exists a functional relation, F(V), between the fluorescence intensity from the fluorochrome im(5) Li. L.; Ruzgas, T.; Gaigalas, A. K. Langmiur 1999, 15, 63586363. (6) Kofman, R. Contribution a l’etude optique des interfaces chargees metal-electrolyte aqueux. Ph.D. Thesis, University of Nice, 1980; p 88.
This article not subject to U.S. Copyright. Published 2000 by the American Chemical Society Published on Web 03/28/2000
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mobilized on the surface of the gold electrode and the potential, V, applied to the electrode. For small variations of the potential, ∆V, the fluorescence intensity is given by
F(V + ∆V) ) F(V) +
( )
∂F(V) ∆V ∂V V
(1)
We let ∆V be an oscillatory function of time, and to allow for a phase shift between the applied potential and the measured fluorescence intensity, we assume that F(V) is a complex function of V. The average fluorescence intensity, S1, is given by S1 ) GI0F(V0) where G represents detection efficiency and photomultiplier gain, I0 is the intensity of the incident light beam, and V0 is the constant bias potential. The time-varying part of the fluorescence intensity is detected by a lock-in amplifier which is driven by the same oscillatory potential that is applied to the potentiostat. The output of the lock-in amplifier, S2, is given by GI0(∂F(V)/∂V)∆/2 where ∆ is the amplitude of the applied modulating potential. The ratio of the two measured quantities, S2/S1, is related to the derivative of the fluorescence intensity with respect to the applied potential:
S2 ∆ 1 ∂F(V) ) S1 2 F(V) ∂V
(2)
The change of fluorescence intensity due to the applied potential must be associated with the change in the properties of the fluorescing molecules. A property which is known to exert a strong influence on the fluorescence intensity is the separation of the fluorochrome from the electrode surface. The fluorescence is quenched by resonant energy transfer between the fluorochrome and the metal states, and the quenching depends on the third power of the distance.7 In accordance with observations in a previous work,5 we will assume that the local reorganization of the electrode surface with the immobilized fluorochrome changes the distance of the xanthene moiety relative to the metal surface. The three-ring xanthene moiety is responsible for the fluorescence of the Alexa 488 fluorochrome. We will let Γ(z) represent the moles of fluorochrome per unit area per increment dz, where z is the distance from the immobilized fluorochrome to the surface. The total fluorescence intensity, F(V), per unit area of the surface will be given by F(V) ) ∫ FM(z) Γ(z) dz,3 where FM(z) is the fluorescence intensity of a mole of fluorochrome located at a distance z from the electrode surface (z ) 0). The electromodulated fluorescence signal is given by
S2 ∆ 1 ) S1 2 F(V)
∫
[
FM(z)
]
∂FM(z) ∂UFl ∂Γ(z) dz + Γ(z) ∂UFl ∂UFl ∂V
(3)
In eq 3, we made the assumption that the potential can change the relative population of the fluorochrome at different distances from the electrode and possibly change the inherent optical property of the fluorochrome such as absorptivity. The symbol UFl represents the potential experienced by the fluorochrome. The potential UFl is a function of the distance from the electrode surface and is different from the potential V applied to the external electrode connections. Since the measured quantity, S2/S1, is a ratio of fluorescence intensities, all instrumental factors drop out in eq 3. The integration over z is carried out over a distance of the order of Debye length (∼10 Å for an ionic strength of 0.1 M), where there is significant variation of the interface potential, UFl, experienced by the fluorochrome. The term ∂Γ(z)/∂UFl in eq 3 can be written as Γω/∆Fl, where Γω is the complex amplitude of the time-dependent solution of the kinetic equations driven by a time-dependent potential ∆Flejωt. The amplitude Γω may be a function of the distance z. The last term, ∂UFl/∂V, describes the dependence of the potential UFl on the applied potential V. It can be represented as ZFl/ZT, where ZFl is the part of the cell impedance between the site of the fluorochrome and the electrode interface and ZT is the total cell impedance. We will use the classical model of the cell impedance consisting of a solution resistance in series with a double-layer capacitance, ZDL, which models the charging (7) Chance, R. R.; Prock, A.; Silbey, R. Adv. Chem. Phys. 1978, 37, 1-65.
Figure 1. A model of the Alex 488 fluorochrome immobilized on a gold surface. On the basis of the bond lengths, the nominal distance between the xanthene moiety (three ring structure) and the gold surface is about 10 Å. of the double layer. The fluorescence-modifying process is assumed to be in series with RS + ZDL. This impedance model gives for the ratio of impedances
ZFl ZT - (RS + ZDL) ∆ - i(RS + (1/jωCDL)) ) ) ZT ZT ∆
(4)
Here the total cell impedance, ZT, is given by ∆/i, where i is the complex amplitude of the measured electrochemical current. The above impedance model is very attractive since all quantities in eq 4 can be either measured or estimated. Equation 4 shows that if the fluorescence response, S2/S1, is multiplied by ∆/(∆ - i(RS + 1/jωCDL)), the result will be directly related to the changes in the distribution of fluorochrome (eq 3).
Experimental Procedures The electrodes were prepared and modified by Alexa 488 fluorochrome as described in ref 5. Figure 1 shows a schematic of the proposed fluorochrome configuration at the surface. In accordance with spectroscopic observations on similar systems,8 we show the dissociated form of cystamine with a S attached to a gold atom. Fluorescence Measurements. The apparatus used to measure electromodulated fluorescence from fluorochrome immobilized on gold electrodes was reported previously.5 In summary, the electrode surface of area 0.07 cm2 was illuminated by the 488 nm light from a laser with s polarization. Two SR 580 lock-in amplifiers detected the modulated current from the electrode and the modulated fluorescence intensity from the fluorochrome on the electrode. A low-pass filter was used to channel the d.c. component of the fluorescence signal to a digital voltmeter (DVM). The ratio of the lock-in amplifier output, ∆F, and the DMV output, F, constituted the measured electromodulated fluorescence. An EG&G model 263A potentiostat provided the potential control, with the external modulation provided by the output of the SR 580 amplifier that also detected the modulated fluorescence intensity. The constant potential was kept more positive than -0.7 V since the reduction of the S-Au bond becomes significant at -0.7 V. Electroreflectance measurements9 were carried out with a larger electrode, which had a diameter of 1 cm. The electrochemical cell was illuminated by the output of a monochromator which was in turn illuminated by a 75 W Oriel xenon lamp. The reflected light was detected by a diode detector and the other SR 580 lock-in amplifier. (8) Szafranski, C. A.; Tanner, W.; Laibinis, P. E.; Garrell, R. L. Langmuir 1998, 14, 3570-3579. (9) Ruzgas, T.; Wong, L.; Gaigalas, A. K.; Vilker, V. L. Langmuir 1998, 14, 7298-7305.
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Spectroscopic Ellipsometry. Multiple-wavelength ellipsometric measurements were performed on a J. A. Woollam (Lincoln, NE) M-44 spectroscopic ellipsometer aligned at an incidence angle 70.33° from the surface normal. Modeling and thickness calculations were done using the WVASE32 software from Woollam. A bare gold surface was used first to obtain the optical constant of the gold. Thickness for the cystamine layer on gold was calculated using a two-layer model where the first layer had the optical constants taken from a clean Au sample and the second layer (cystamine) had a refractive index of 1.45. For the samples with immobilized fluorochrome, a three-layer model was used for the analysis. The properties of the first two layers were set to those of the cystamine sample, and the program was allowed to determine the refractive index and thickness of the third layer (immobilized fluorochrome). Three independent measurements at different points on the surface were performed, and the results were consistent with each other. Surface Plasmon Resonance (SPR). The SPR minimum was detected by using a CCD linear array with 1024 pixels and a laser diode operating at λ ) 790 nm.10,11 The face of the prism with the thin gold film and the immobilized fluorochrome was part of a flow cell. The flow rate was 0.05 mL/min. Calibration of the SPR device was done using a water-ethylene glycol solution.10
Results Figure 2a shows the SPR response taken while Alexa 488 fluorochrome was being immobilized on the gold film evaporated on a glass slide. The value of surface mass concentration, M, was calculated from the data in Figure 2a by the following formula:12
M)
df(nf - nb) dn/dc
(5)
where df is the film thickness and nf, nb are the refractive indices of the film and the buffer, respectively. dn/dc is a refractive index increment. The fluorochrome layer thickness, df, was measured by SPR and spectroscopic ellipsometry, which gave the same value of ∼7.0 Å. The refractive index of the film at 790 nm was measured by spectroscopic ellipsometry, giving nf ) 1.3960. The refractive index of the buffer was calculated using the refractive index of water (1.3284) at 790 nm,13 and the difference of refractive index of water and buffer (0.002 375) measured using the SPR (data not shown). The final result is nb ) 1.330 78. The refractive index increment was estimated from the fast change in the kinetic curve (Figure 2a, between arrows) when fluorochrome solution was exchanged with buffer. The difference in the refractive indices of the solution of fluorochrome plus buffer and buffer only is 0.000 145. Using this number and the known fluorochrome concentration of 643.4 µg/mL, the refractive index increment was estimated as dn/dc ) 1.780 × 10-7 mL/µg. The estimated surface concentration of the fluorochrome was 25.6 ng/cm2 or 48 × 10-8 mol/m2 (MW ∼ 532). The estimate neglects interactions between adsorbed molecules. Figure 2b shows the results of spectroscopic ellipsometry measurements for a layer of fluorochrome immobilized on a gold electrode (in air). There is a strong absorption peak at 512 nm, and the thickness of the fluorochrome layer was 7.0 ( 0.1 Å. (10) Silin, V.; Weetall, H.; Vanderah, D. J. Colloid Interface Sci. 1997, 185, 94-103. (11) Silin, V.; Plant, A. TIBTECH 1997, 15, 353-359. (12) Go¨lander, C.-G; Kiss, E. J. Colloid Interface Sci. 1988, 121, 240253. (13) Dorsey, N. E. Properties of ordinary water substance; Reinhold Publishing Corp.: New York, 1940; pp 279-295.
Figure 2. (a) Surface plasmon resonance taken during the immobilization of Alexa 488 on the gold electrode. (b) Optical constants of a thin film on a gold surface obtained from spectroscopic ellipsometry measurements on a dried electrode with immobilized Alexa 488. The index of refraction and the loss constant both indicate an absorption peak at ∼512 nm.
Figure 3. Out-of-phase components of consecutive EmF measurements. The various symbols represent EmF frequency responses taken at different times for a potential of -0.4 V in 0.1 M phosphate buffer, pH 7.4. The solid curves represent the result of a fit to an exponential function parametrized as amplitude × exp(-decay × frequency). The inset shows the variation of the fit parameters with time. The “decay” parameter, which characterizes the frequency dependence, is the same for all curves. The amplitude decreases with time.
Figure 3 shows the out-of-phase components of four consecutive electromodulated fluorescence measurements taken at -0.4 V. There is a clear decrease in the amplitudes of the signals; however, the dependence on the frequency remains the same as seen by the constancy of the “decay” parameter in the fit to an exponential function shown in the inset of Figure 3. The “decay” parameter describes the dependence on frequency and has no physical meaning at this point. The constancy of the “decay” parameter suggests
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Figure 4. A typical reflectance signal from an electrode with immobilized fluorochrome after subtraction of electroreflectance from a bare gold electrode. The solid circles show the in-phase electroreflectance response from a gold electrode with immobilized Alexa 488 taken at -0.5 V and 47 Hz. The open circles show the out-of-phase response (shifted by 90° relative to the in-phase response). The solid line represents a fit to a sum of a Gaussian function and its derivative. The center of the Gaussian function is at ∼512 nm.
that the dynamic processes remain the same for the sequential scans. Figure 4 shows a typical electroreflectance signal from an electrode with immobilized fluorochrome after subtraction of electroreflectance from a bare gold electrode. The in-phase component is dominant, and the response is seen at a relatively high frequency (47 Hz). Measurements (data not shown) were made only down to 7 Hz because of increased noise at lower frequencies. This indicates that, in the case of the EmR, there is no increase in signal at low frequency as observed in the EmF case. The EmR signal did increase as the potential was decreased to more negative values. Figure 5 shows the EmF response after correction for cell impedance taken at different electrode potentials, -0.4 V (a) and -0.5 V (b). At these potentials, the S-Au bond remains intact5 and the changes in fluorescence intensity are most likely due to potential-induced reorganization of the surface. The out-of-phase component dominates although, at -0.5 V, a small in-phase component appears. This in-phase component increases at -0.6 V; however, due to the relative instability of the signal at -0.6 V, we did not include it in the analysis. The reduction of the S-Au bond becomes significant at -0.7 V, resulting in the appearance of fluorochrome in the solution surrounding the electrode. In this case, the fluorescence signals associated with the modulated component and the “d.c.” component arise from fluorochromes in two different environments. The responses shown in Figures 4 and 5 were reproducible. Figure 6 shows the EmF response taken at -0.4 V in phosphate buffers of different concentrations (different ionic strengths). There is a marked decrease in the response taken in the buffer with low ionic strength relative to the response in the buffer with high ionic strength. Discussion The EmF response was interpreted by assuming that the average distance of the Alexa 488 fluorochrome relative to the interface depends on the potential. Single-crystal gold electrodes are known to possess reconstructed surfaces in reponse to the asymmetry of the environment
Figure 5. Frequency dependence of the EmF responses at -0.4 V (a) and -0.5 V (b). The open circles show the out-ofphase response, and the solid circles show the in-phase response. Both responses are shown after correction for double-layercharging potential drop. The amplitude of the response at -0.5 V is approximately 2 times larger than that at -0.4 V. The solid lines in (a) and (b) are model calculations as explained in the text.
Figure 6. Frequency dependence of the EmF response taken at -0.4 V in buffers with two different ionic strengths. The open symbols show the out-of-phase response, and the solid symbols show the in-phase response The response in the 0.1 M buffer is much greater than the response in the 0.005 M buffer. The solid lines are model calculations as explained in the text.
at the interface.14 As the potential (and hence the charge) of the electrode changes, the density of atoms redistributes, leading to transitions between reconstructed and unreconstructed single-crystal surfaces.15 A polycrystalline gold surface is relatively disorganized; however, the surface is likely to undergo local reconstruction which may be different at different points on the surface. The im(14) Kolb, D. M. Prog. Surf. Sci. 1996, 51, 109-173. (15) Ibach, H.; Bach, C. E.; Giesen, M.; Grossmann, A. Surf. Sci. 1997, 375, 107-119.
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mobilized Alexa 488 (charge of -2e) will contribute a significant amount of electrostatic energy to driving the local reconstruction process at the electrode surface. The increase in electrostatic energy of a -2e charge in going from solution to a negatively charged electrode biased at -0.5 V relative to the solution is about 23 kcal/mol. Under our experimental conditions, this potential drop occurs in about ∼10 Å (Debye length). Thus, even small changes in the relative separation of Alexa 488 and the electrode can lead to significant changes in the electrostatic energy. We hypothesize that the local reconstruction of the electrode surface is responsible for the observed EmF response. The complexity of the local reconstruction process will be simplified by assuming that the surface-confined fluorochrome can be located at two discrete distances relative to some average electrode surface. In the first model, we assume that the transition between the two locations has an activation energy and the rate of transition depends on the potential. In the second model, we assume that the distribution of fluorochrome between the two locations is governed by a transport equation with the flux dominated by an electrophoretic contribution which represents the average effects of local surface reconstruction. Both models assume that the fluorescence intensity change is due to a change in the relative distance of the fluorochrome and the electrode surface. While both models yielded a large potential-dependent increase in the magnitude of the fluorescence intensity, the relative amounts of in-phase and out-of-phase components are different. The activation model gives a better fit to the EmF data. Since the fluorescence intensity depends on the product of quantum yield and molecular absorbency, we first estimate the dependence of absorbency on potential using electromodulated reflectance measurements. Electromodulated Reflectance (EmR). The EmR response was largely in-phase and was observed at large modulation frequencies. This suggests a relatively fast process such as a direct interaction with the electric field resulting in a Stark shift or a reorientation of transition moments leading to change in the maximum absorbency.16,17 The EmR signal can be written in analogy to eq 3 as
S2 ∆ 1 ∂R ∂A ∂λ ∂A ∂amp ∂UFl + ) S1 2 R(V) ∂A ∂λ ∂U ∂amp ∂U ∂V
[
]
(6)
where amp ) amplitude, R(V) is the potential-dependent reflectivity from a gold surface with a layer of absorbing molecules, and (1/R(V))∂R/∂A is an optical constant describing the change in reflectance from a gold surface due to the presence of a layer with absorbency A m2/mol. Its approximate value is -2.3Γ.18 The solid line in Figure 4 shows the results of a fit to the data by a sum of a Gaussian function and its derivative to represent the change of absorbency due to the realignment of transition dipole moments and the Stark shift, respectively. The absorption line is located at 512 nm, in agreement with ellipsometry measurements. Using values of A ∼ 9000 m2/mol and Γ ∼ 40 × 10-8 mol/m2, the EmR data give an estimate of ∼400 for dA/dU due to the transition dipole realignment (the second term in the brackets in eq 6; ∆R/R ≈ ∆Γ∂A/∂U). Using eq 3, we estimate the part in fluorescence modulation due to absorption modulation to (16) Umeuchi, S.; Nishimura, Y.; Yamazaki, I.; Murakami, H.; Yamashita, M.; Ohta, N. Thin Solid Films 1997, 311, 239-245. (17) Pope, J. M.; Tan, Z.; Kimbrell, S.; Buttry, D. A. J. Am. Chem. Soc. 1992, 114, 10085-10086. (18) Gaigalas, A. K.; Reipa, V.; Niaura, G. J Colloid Interface Sci. 1998, 203, 299-310.
be of the order of 10-4 (∆F/F ≈ (∆/A)∂A/∂U). This is about 40 times smaller than the observed fluorescence modulation in Figure 5, justifying the modeling of the EmF as a change in the quantum yield. (The location of the absorption line at 512 nm relative to 490 nm in solution is most likely a result of the strong optical image dipole interaction between the fluorochrome and the gold.19 The static interface electric field can lead to an additional Stark shift in the absorption peak. Setting the surface electric field to 0.5 × 109 V/m, the difference in the static dipole moments of the ground and excited states to 10-29 C m, and assuming complete alignment of the dipole moments with the electric field, we estimate a Stark shift of about 5 nm. The true Stark shift will be significantly less than 5 nm.) The Model Using Activation Energy. We will employ a simplified model in which the immobilized fluorochrome can be located at only two distances relative to the surface. The location with the smaller fluorochrome distance from the surface is occupied by Γ1 mol/unit area, and the location with the larger distance from the surface is occupied by Γ2 moles/unit area. The potential changes the relative population at the two locations. In this case, the electromodulated fluorescence described by eq 3 is given by
[ ]
S2 ∆ F2 ∂f2 ∂UFl ) -1 S1 2 F1 ∂UFl ∂U
(7)
where F2 and F1 are the fluorescence intensities per unit surface area from fluorochromes far away from and close to the surface, respectively, and f2 ) Γ2/Γ, where Γ is the total surface density of immobilized fluorochrome, which is assumed to be constant. In eq 7, the quantity (F2/F1 1) is a constant which describes the relative differential change in the fluorescence of fluorochrome at the two locations. The term ∂f2/∂UFl describes the change in the fraction of fluorochrome Γ2 caused by a change in the potential experienced by the fluorochrome. This term can be written as fω/∆Fl where fω is the complex amplitude of the time-dependent solution of the kinetic equations driven by a time-dependent potential ∆Flejωt. The kinetic equation describing the time evolution of the population of fluorochrome at the “far” location can be written as
∂f2 ) kde(U) (1 - f2) - kad(U) f2 ∂t
(8)
Here kad and kde are the potential-dependent rates for the transition between the two locations. The explicit form of the rates will be taken as
(
kde(U) ) k0 exp -
(
kad(U) ) k0 exp
)
zeffF(U(t) - E0) RT
)
zeffF(U(t) - E0) RT
(9a) (9b)
where k0 is the frequency factor, E0 is the potential at which the fluorochrome molecules are distributed equally among the two locations, R is the gas constant, F is the Faraday constant, T is the temperature, and zeff is the effective charge of the fluorochrome. The potential that drives the relocation process can be written as U(t) ) EDC + ∆Fl sin(ωt), where EDC is the constant part of the applied potential and ∆Fl is the modulation amplitude. Figure 5 (19) Chance, R. R.; Prock, A.; Silbey, R. Phys. Rev. A 1975, 12, 14481452.
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shows the response calculated by solving eq 8 and substituting the result into eq 7. The in-phase component was small only if the frequency factor k0 was small; the solid lines in Figure 5 show the results for k0 ) 0.0015 s-1, F2/F1 ) 5, E0 ) -0.6 V, and zeff ) 0.26. The shapes of the frequency dependence and the dependence on the constant potential, EDC, are reproduced. The solid line in Figure 6 shows the calculated response with the same parameters as used for Figure 5 except that E0 ) -0.7 V was used for the data at low ionic strength (0.005 M). Thus it appears that the activation energy (∼E0) for the transition between the two locations increases in low ionic strength buffers. This suggests that the direct electrostatic interaction between the negatively charged fluorophore and the negatively charged interface is not the dominant factor in the transition, since at low ionic strength this direct repulsive interaction would not be screened, resulting in a decrease in activation energy. For all of the potential corrections, we used RS ) 150 Ω and CDL ) 20 µF. The value of RS was obtained from the high-frequency limit of the measured impedance, while the value of the capacitance was estimated from frequencies >5 Hz. The measured impedance did not follow a simple RC series combination at low frequencies (
