AC-Modulated Voltfluorometric Study of the Transient Adsorption of

Jul 25, 2001 - Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan. J. Phys. Chem...
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J. Phys. Chem. B 2001, 105, 8162-8169

AC-Modulated Voltfluorometric Study of the Transient Adsorption of Rose Bengal Dianions in the Transfer across the 1,2-Dichloroethane|Water Interface Naoya Nishi, Kazuo Izawa, Masahiro Yamamoto, and Takashi Kakiuchi* Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto UniVersity, Kyoto 606-8501, Japan ReceiVed: March 7, 2001; In Final Form: June 4, 2001

The transfer of Rose Bengal dianion (RB2-), a fluorescent ion with asymmetric charge distribution, across the 1,2-dichloroethane (DCE)|water (W) interface, has been studied using ac-modulated voltfluorometry, a method that combines ac voltammetry with fluorometry. The phase angle of the ac component of the fluorescence shifts to a value that cannot be explained by the theory based on the simple combination of the heterogeneous ion transfer and mass transfer. This anomaly strongly suggests that RB2- ions transiently adsorb at the interface in the course of the heterogeneous ion transfer. The rate-determining step seems to be the adsorption-desorption of RB2- ions between DCE and the interface. The apparent standard rate constant for ion transfer across the interface is estimated to be 1.4 × 10-2 cm s-1. The adsorption of RB2- appears to decelerate the rate of ion transfer across the interface.

1. Introduction The ion transfer across the interface between two immiscible electrolyte solutions (ITIES) is unique in that ions moving across the interface experience the heterogeneous environment with respect to the solvent composition, the orientation of molecules, the gradient of the electrostatic potential, and the inhomogeneously distributed ions across the interface. This uniqueness, aside from the potential implications in various applications such as solvent extraction and phase-transfer catalysis, has attracted many researchers to this intriguing subject.1-7 Several models have been proposed for the mechanism of the interfacial ion transfer.8-15 Experimentally, the rate of ion transfer across the ITIES has been measured using electrochemical methods mainly for tetraalkylammonium ions and other relatively symmetric ions.16-33 Recent studies using ac techniques34-36 suggest that the rates of the interfacial ion transfer of tetraalkylammonium ions and other relatively symmetric ions are not distinctively slower than those in the adjacent bulk phases. On the other hand, by using potential-step voltfluorometry, we reported that the apparent standard rate constant of ion transfer, k0,app, of Eosin Y dianion(EY2-), a xanthene-type dianion with asymmetrical charge distribution, is 1 order of magnitude smaller than the value predicted from its hydrodynamic radius.37 The dependence of the rate constant on the potential difference across the interface indicates that the transfer of EY2- across the interface is activationless. The slower transfer of EY2- has been ascribed to the enhanced dielectric friction exerted on the ions in the interfacial region, resulting in the transient adsorption of EY2- ions during the ion transfer across the interface. In fact, a recent ac voltammetric study has shown that the transfer of xanthene-type dianions across the nitrobenzene (NB)|W interface gives rise to anomalously small values of cot φ; the delay in the interfacial ion transfer leads to cot φ < 1, where φ is the phase angle of the * Corresponding Author. Tel: (81) 75-753-5528. FAX: (81) 75-7533360. E-mail: [email protected]

ac admittances.38 This anomaly seems to be a good indication that xanthene-type dianions transiently adsorb at the interface in the course of the interfacial ion transfer. However, the contribution of the double-layer charging to the measured admittances always makes the interpretation of ac admittances ambiguous. The ion transfer admittance was evaluated by subtracting the admittance in the absence of transferring ions from that in the presence of the ion transfer.38 If the transferring ions are surface-active, the procedure of subtracting the base component from the measured admittance may not be appropriate to obtain the charge-transfer admittance because the adsorption of transferring ions can alter the double-layer capacitance. Recently, it has been shown that spectroscopic techniques are useful in detecting the interfacial ion transfer across the liquid-liquid interface.37,39-49 If the fluorescence signal from fluorescent ions is detected instead of the current signal in ac voltammetry, we can directly measure the admittance from the fluorescence that reflects the ac component of the interfacial ion transfer. This ac-modulated voltfluorometry44,48 is one of voltfluorometric techniques for the transfer of fluorescent ions across the ITIES.37,39-41,43 The advantage of the ac-modulated voltfluorometry over the conventional ac voltammetry is that the ac component of the fluorescence is not affected by the charging current, making this technique suitable for analyzing the interfacial transfer of xanthene-type dianions, possibly involving the adsorption and desorption processes. A recent study of the ac-modulated voltfluorometry focused on the transfer of porphyrins across the ITIES and interpreted the complicated admittance response as the adsorption of porphirins on both sides of the interface.48 The present study deals with an ac-modulated voltfluorometry of the transfer of Rose Bengal dianions (RB2-) (Figure 1) across the 1,2-dichloroethane (DCE)|water (W) interface. We will show that the transient adsorption of RB2- at the interface in the course of the interfacial transfer is responsible for the slower rate of RB2- ion transfer compared with that expected from its hydrodynamic radius.

10.1021/jp010875f CCC: $20.00 © 2001 American Chemical Society Published on Web 07/25/2001

Transient Adsorption of Rose Bengal Dianions

J. Phys. Chem. B, Vol. 105, No. 34, 2001 8163

Figure 1. (a) Molecular structure of Rose Bengal dianion (RB2-). (b) Optimized structure of RB2- by the semiempirical AM1 method; closed and open circles denote the negative and positive charge on each atom, respectively, and the sizes of them the magnitude of the charge.

Figure 2. Two-electrode electrochemical cell for ac-modulated voltfluorometry. Greek letters correspond to the electrochemical cell in the text.

2. Experimental Section

glass vessel and an inner glass tube. It has a window at the bottom to measure the fluorescence from the DCE|W interface. The aqueous solution in the inner glass tube is phase V. The polarized interface between phases IV and V was located at the orifice of the inner glass tube, which was set at the center of the outer vessel (Figure 2). The area of the interface was 0.26 cm2. The lower and upper solutions of the outer glass vessel are phases IV and III, respectively. The dc potential was swept at 2 mV s-1 from a more positive potential where RB2- stayed in W phase, toward a more negative potential where RB2- was driven to DCE phase. In the present study, the ac voltage of 40 mVp-p was superimposed to the dc potential to obtain sufficiently large ac fluorescence signals for further analysis. The ac voltage smaller than RT/nF is usually employed in conventional ac voltammetry, where R is the gas constant, T is the temperature, n is the number of charge transferred, and F is the Faraday constant. A recent analysis of the ac voltammetry for the reversible process suggests that the phase angle is not appreciably affected even when the ac amplitude is as high as 3RT/nF.51 A positive feedback method was used to compensate for potential drop due to the solution resistance. An Ar+ laser at 488 nm (2 mW) was used for the excitation of RB2-. The incident Ar+ laser beam of 2 mm diameter was introduced to the polarized interface at an incident angle of about 75° so that the light was totally reflected at the interface. The fluorescence from the interface was collected using a planeconvex lens, passed through a filter for cutting off the excitation light, and led to a photomultiplier (Hamamatsu, Japan, R7400P01). The output voltage from the photomultiplier was fed to a lock-in amplifier (NF Corporation, Japan, LI574A P-51A) to measure the phase angle and the amplitude of the fluorescent signal.

The electrochemical cell is represented as 3. Results and Discussion I

II

III

IV

V

VI

VII

20 µM Na2RB 5 mM TPnACl 20 mM TPnATPB 10 mM LiCl 10 mM phosphate- AgCl Ag Ag AgCl 10 mM MgCl2 1 mM sorbitan monooleate borate buffer (pH 8) (W) (DCE) (W)

where TPnACl and TPnATPB denote tetrapentylammonium chloride and tetrapentylammonium tetraphenylborate, respectively. The potential applied to phase I with respect to phase VII is denoted as E. The current corresponding to the flow of a positive charge from phase V to phase IV is taken to be positive. The interface between phases IV and V is the polarized interface. The interface between phases III and IV is nonpolarized, and hence, phases I-III act as a reference electrode reversible to TPnA+ in phase IV. Water was purified by using a Milli-Q system (Millipore). DCE was saturated with water. A phosphate-borate buffer was used to maintain the pH of phase V at 8 so that Rose Bengal ions existed as dianions. The values of pKa1 and pKa2 of EY2-, which has a structure similar to that of RB2-, are reported to be 3.25 and 3.80, respectively.50 TPnATPB was prepared by mixing tetrapentylammonium iodide and sodium tetraphenylborate in a mixture of water and ethanol (1:1), followed by recrystallization in acetone 3 times. Sorbitan monooleate (Nacalai Tesque), a nonionic surfactant, was added to DCE phase to suppress the convective motion in the vicinity of the interface. Rose Bengal sodium salt (Aldrich) was used without further purification. All other chemicals used were of reagent grade. Figure 2 illustrates a two-electrode electrochemical cell for ac-modulated voltfluorometry, consisting of an outer cylindrical

3.1. Anomaly of Phase Angle in AC Voltfluorometry. Figure 3a shows cyclic voltammograms for the transfer of RB2recorded using a four-electrode electrochemical cell. The midpoint potential of RB2-, Em,RB2-, was 335 mV, or -2 mV with respect to Em of TEA+. The cyclic voltammograms show that the interfacial transfer of RB2- is dc reversible; the peak separation was 38 mV irrespective of the scan rate, V, between 20 and 500 mV s-1, and the peak current was proportional to V1/2. The peak separation also indicates that Rose Bengal is dianion at pH 8. The diffusion coefficient in water, DW, was determined to be 4.1 × 10-6 cm2 s-1 from the slope of the peak current versus V1/2 plot. We measured the phase angle and the absolute value of the admittance of the fluorescence to the ac voltage at several different frequencies. First, we examine the relationship between the phase and the admittance in ac voltfluorometry and those in ac voltammetry. When an ac voltage, Eac, is applied to the interface, the current due to the ion transfer across the interface has an ac component, Iac. The ac voltage and the ac current are expressed by

Eac ) E0 exp(jωt)

(1)

Iac ) EacYi ) E0|Yi| exp[j(ωt + φi)]

(2)

where E0 is the ac amplitude, ω ) 2πf is the angular frequency, f is the frequency, Yi ) |Yi| exp(jφi) is the admittance, φi is the phase angle of the current to the ac voltage, and j ) (-1)1/2. In ac-modulated voltfluorometry of the transfer of fluorescent ions,

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the ac component of the fluorescence may also be represented as

∆Fac ) E0|Yf| exp[j(ωt + φf)]

(3)

where Yf ) |Yf| exp(jφf) is the admittance of the fluorescence and φf is the phase angle of the fluorescence to the ac voltage. As the fluorescence is proportional to the integral of the current with respect to time,39 the ac component of the fluorescence, ∆Fac is

∆Fac∝

∫Iac dt )

E0|Yi| exp[j(ωt + φi)] ) jω E0|Yi| exp[j(ωt + φi - π/2)] (4) ω

Comparing eq 3 with eq 4, we obtain

|Yf| ∝ |Yi|/ω

(5)

φf ) φi - π/2

(6)

and

Figure 3b shows the potential dependence of |Yf| for the transfer of RB2- at 2, 5, 10, 30, and 50 Hz. These curves were bell-shaped. The peak potential did not depend on ω and agreed well with Em,RB2-. The peak height was inversely proportional to the square root of ω (Figure 3c), as is expected in reversible ion transfer or quasi-reversible ion transfer when k0/(Dω)1/2 is greater than 4.7 in the case of semi-infinite linear diffusion (see Appendix I). The results in Figure 3b,c show that the ac component of the fluorescence reflects the ac component of the transferred amount of RB2- ions on the DCE side of the interface. In addition, the plot in Figure 3c confirms that the fluorescence from the adsorbed ions does not appreciably contribute to the fluorescent signal. The phase angle, φf, for the transfer of RB2- at 10 Hz is plotted in Figure 4a as a function of the applied potential. The error bars in Figure 4a show the standard deviation estimated from four independent measurements. We compare the observed behavior in Figure 4a with that expected for the simple ion transfer, that is, the heterogeneous ion transfer combined with semi-infinite linear diffusions on both sides of the interface. The flux of the heterogeneous ion transfer, Ji, is written as

k icW k icOs,i Ji ) B s,i - A

(7)

where cRs,i is the concentration of the ion i at the surface in the R phase (R ) W or O) and B ki (k Ai) is the rate constant of heterogeneous ion transfer from W to O (from O to W). In the theory of ac voltfluorometry for a simple ion transfer (See Appendix I), -tan φf is given by

21/2 1/2 ω λ

(8)

A k B k + (DW)1/2 (DO)1/2

(9)

-tan φf ) 1 + where

λ)

and DR is the diffusion coefficient in R (R ) W or O). This predicts that φf is between -45° and -90° or -tan φf is 1 and ∞, corresponding to the diffusion-limited angle and the chargetransfer-limited angle, respectively. The observed -tan φf values

Figure 3. (a) Cyclic voltammograms for the transfer of RB2- across the DCE|W interface in the presence of 2.5 × 10-4 M RB2- in water phase. Sweep rates are 20 (1), 50 (2), 200 (3), and 500 (4) mV s-1. (b) Absolute value of admittance |Yf| for the transfer of RB2- measured by ac-modulated voltfluorometry at 2 (1), 5 (2), 10 (3), 30 (4), and 50 (5) Hz. (c) Dependence of the peak value of |Yf| on ω-1/2. Solid line indicates the dependence when the interfacial ion transfer is diffusionlimited.

between 360 and 400 mV agree with this prediction. However, at potentials more negative than Em,RB2-, the phase angle shifted to the positive direction beyond -45° or -tan φf ) 1. This shift cannot be explained by eq 8 for the quasi-reversible charge transfer. Figure 4b shows -tan φf versus E plots at other frequencies, 5, 15, 30, and 47 Hz. One can see that the anomaly, -tan φf < 1, exists at all frequencies. Recently, a similar anomaly has been reported in ac voltammetry of the transfer of xanthene-type dianions.38 It has been interpreted as an indication for the transient adsorption for xanthene-type dianions, although the subtraction of the base component from the ion transfer admittance made an unequivocal interpretation difficult. Plots of -tan φf as a function of ω at several potentials are shown in Figure 5. All curves are concave, and -tan φf is less than unity at negative potentials. These characteristic features are in marked contrast to the case of a simple ion transfer; for example, in ac

Transient Adsorption of Rose Bengal Dianions

Figure 4. Potential dependence of -tan φf for the transfer of RB2measured by ac-modulated voltfluorometry (a) at 10 Hz and (b) at 5 (1), 15 (2), 30 (3), and 47 (4) Hz. Dotted lines are -tan φf ) 1 when the interfacial ion transfer is diffusion-limited. Vertical bars in panel a indicate the standard deviation.

J. Phys. Chem. B, Vol. 105, No. 34, 2001 8165 (CnH2n+1)4N+. Therefore, RB2- ions are likely to adsorb at the interface, protruding its negatively charged part to the water side of the interface, while its noncharged part is in the DCE side. 3.2. Phenomenological Model of the Transfer of SurfaceActive Ions across ITIES. The transient adsorption accompanied by the ion transfer across the interface has been reported for the transfer of alkaline-earth metal ions facilitated by poly(ethylene glycol)-type nonionic surfactants54 and for the transfer of methyl orange anions (MO-) studied by surface second harmonic generation.55 In the former case, cyclic voltammograms were explained in terms of the potentialindependent adsorption coefficient. In the latter, the linear dependence of the Gibbs energy of adsorption on the phaseboundary potential has been used to calculate the potential dependence of the adsorbed amount of MO- ions. Piron et al.55 assumed the Boltzmann distribution for the MO- ions to introduce the potential-dependent adsorption. In the adsorption accompanied by the ion transfer across the interface in the presence of supporting electrolytes, however, the surface concentration which enters the adsorption process is primarily determined by the combination of the mass transfer and the heterogeneous ion transfer. We treat here the ac admittance in the presence of the potential-dependent adsorption from this viewpoint. We assume an adsorption plane (A) between the oil phase (O) and the water phase (W) and that the transfer process of ions across the interface is subdivided into two adsorptiondesorption processes, one from W to A and the other from O to A: kW a

kO d

kd

ka

ion (W) y\ z ion(A) y\ z ion(O) W O

Figure 5. Dependence of -tan φf on ω1/2 for the transfer of RB2measured by ac-modulated voltfluorometry at 370 (closed circle), 350 (closed diamond), 330 (closed square), 310 (open circle), 290 (open diamond), and 270 (open square) mV. Dotted lines are -tan φf ) 1 when the interfacial ion transfer is diffusion-limited.

TEA+

voltammetry, the transfer of ions across the NB|W interface gives a straight line for the dependence of cot φi on ω1/2, and cot φi is equivalent to -tan φf from eq 6.25 Senda and Delahay proposed a general theory of ac voltammetry for the electrode processes in the presence of adsorption of reactants and/or products at an electrode.52 They showed that cot φi versus ω1/2 plots deviate downward from a straight line and become concave; the value of cot φi can be less than unity at the lower frequency range. These characteristic features explain the curves in Figure 5 well, suggesting that RB2- ions adsorb at the DCE|W interface on the way of the transfer across the interface. Figure 1b shows the charge distribution in RB2- calculated with the semiempirical AM1 method.53 One part of the negative charges is localized at the carboxyl group, and the other is delocalized over the xanthene moiety, while the chlorinated benzene ring is electrically neutral. This asymmetric charge distribution in RB2- should give rise to the surface activity in the ion, in contrast to symmetric tetraalkylammonium ions,

W O O where kW a , kd , ka , and kd are the adsorption and desorption rate constants from W to A and those from O to A, respectively. Correspondingly, the potential difference across the ITIES, ∆W O φ, may be divided into two parts, the potential difference between O and A, ∆AΟφ, and that between W and A, ∆W A φ. The φ that exists in O and W may be written as ∆AΟφ fraction of ∆W O W W W ) βi∆O φ and ∆A φ ) (1 - βi)∆O φ, respectively, where βi is a constant between 0 and 1. The flux at each side of A is given by assuming the rate equation about the adsorption-desorption

W W W JW s,i ) kd θ(1 - θ) - ka cs,i

(10)

JOs,i ) kOd θ(1 - θ) - kOa cOs,i

(11)

where JRs,i is the flux at the surface to the bulk in R phase (R ) W or O), and θ is the surface coverage. In eqs 10 and 11, we have assumed that the adsorption-desorption is Langmuirian for simplicity. It is straightforward to take account of the intermolecular interaction using an appropriate adsorption isotherm, such as the Frumkin isotherm. On the other hand, the rate constants for the adsorption and desorption processes are generally related to the standard Gibbs energy of adsorption of i from R, ∆GR,0 ads,i, through

kRa kRd

) exp(-∆GR,0 ads,i/RT)

(12)

∆GR,0 ads,i of an ionic species is known to linearly depend on 56 Then we may write φ. ∆W O

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Q W W Q ∆GW,0 ads,i ) ∆Gads,i - ziF(1 - βi)(∆O φ - ∆O φi ) (13) 0 ∆GO, ads,i

)

∆GQads,i

+

ziFβi(∆W Oφ

-

Q ∆W O φi )

(14)

where ∆GQads,i is referred to ∆GR,0 ads,i at the standard ion-transfer Q potential of i, ∆W O φi , and zi is the charge number of the ion i. The adsorption coefficient, BRi () kRa /kRd ), is given by using eqs 12-14 Q W W Q BW i ) Bi exp[ziF(1 - βi)RT(∆O φ - ∆O φi )]

[

]

ziFβi W Q BOi ) BQi exp (∆ φ - ∆W O φi ) RT O

(15) (16)

where BQi ) exp(-∆GQads,i/RT) is the adsorption coefficient at Q ∆W O φi . From eqs 15 and 16, one can see that the four rate constants of the two adsorption-desorption processes depend on ∆W O φ. According to the Goldman-type model for describing the interfacial ion transfer,12 the potential-dependent rate constants are represented as W,Q kW a ) ka a exp(a)/sinh(a)

(17)

Q W,Q kW d Bi ) ka a exp(-a)/sinh(a)

(18)

kOa ) kO,Q a b exp(-b)/sinh(b)

(19)

kOd BQi ) kO,Q a b exp(b)/sinh(b)

(20)

where

a)

ziF(1 - βi) W Q (∆O φ - ∆W O φi ) 2RT

b)

ziFβi W Q (∆ φ - ∆W O φi ) 2RT O

and kR,Q is the standard rate constant for the adsorption from R a Q R Q at ∆W O φi . In eqs 18 and 20, kd is multiplied by Bi so that the left-hand sides of eqs 18 and 20 have the same dimension as that of kRa . The mass transfer of i in W and O is assumed to be described by the semi-infinite linear diffusion. The boundary condition for the mass transfer is written for the continuity of the flux of RB2- at both sides of A:

dΓi O ) -JW s,i - Js,i dt

θ)

(21)

where Γi ) Γm,iθ is the adsorbed amount of the ion and Γm,i is the maximum adsorbed amount. 3.3. Transient Adsorption of Ions Moving across the Interface. We consider three cases here: case I, where the ion i does not adsorb at the interface, case II, where the adsorptiondesorption process from O is fast compared with that from W, and case III, where the adsorption-desorption process from W is fast compared with that from O. In case I, to satisfy Γi ) 0 numerically, the steady-state assumption, dΓi/dt ) 0, was used for eqs 10, 11, and 21. In case II, the adsorption from O is reversible and is described by the Langmuir isotherm, instead of eq 11

BOi cOs,i 1 + BOi cOs,i

(22)

In case III, the adsorption from W is reversible and in place of eq 10

θ)

W BW i cs,i W 1 + BW i cs,i

(23)

The current, I, is expressed in each case as

I ) JOs,i ziFA I ) - JW s,i ziFA

for I, III for I, II

(24) (25)

In case I, eqs 24 and 25 are the same meaning because dΓi/dt ) 0. For cases II and III the adsorption-desorption from the solution side of the rate-determining step is defined as the current across the interface. We numerically calculated ac impedance for the three cases and compared theoretical curves with the experimental results W,Q Q by using parameters, Em,i, kO,Q a , ka , βi, Γm,i, and Bi . The numerical simulations of the ac impedance method have been reported for the system with adsorption57 or without adsorption.58 The former used the potential-dependent equivalent circuits for adsorption and numerically calculated the ω dependence of the nonlinear impedance. The latter used a model which contains the heterogeneous charge transfer and the mass transport in the bulk phase, similar to us except the adsorption. They superimposed the ac modulation to the dc sweep and decoupled the dc current to extract the ac current. We used the method given in Appendix II to separately evaluate the dc and the ac currents. Figure 6 shows the calculated curves for the potential dependence of cot φi for I-III described above at 5, 10, and 15 ) kW,Q ) 1.4 × 10-2 cm s-1 (case I), kW,Q ) 1.4 Hz when kO,Q a a a -2 -1 ) 1.4 × 10-2 cm s-1 (case III), × 10 cm s (case II), kO,Q a βi ) 0.5, Γm,i ) 1.7 × 10-10 mol cm-2, and BQi ) 1.1 × 106 M-1. The value of kO,Q or kW,Q was chosen so that the value of a a cot φi around Em,i becomes greater than unity, as found experimentally (Figure 4). The value of Γm,i was fixed to 100 Å2/molecule (1.7 × 10-10 mol cm-2), estimated from the size of RB2- ion. In case I, cot φi is always greater than unity and Q have a peak around ∆W O φi (Figure 6a). This feature reflects the ac response for the quasi-reversible ion transfer without the adsorption (see Appendix I). On the other hand, in case II (Figure 6b), cot φi decreases to less than unity at potentials more Q positive than ∆W O φi . In contrast, cot φi in case III becomes smaller than unity at potentials more negative than Em,i (Figure 6c). The decrease in cot φi below unity (Figure 6b,c) results from the temporal residence of the ion at the adsorption plane. Figure 6b,c clearly shows that the potential range where cot φi < 1 depends on the location of the rate-determining step. The observed decrease in -tan φf in Figure 4a,b agrees with the tendency of cot φi in Figure 6c, suggesting that the ratedetermining step for the transfer of RB2- ions across the interface is the adsorption-desorption process between O and A. The variation of θ with the applied potential is illustrated in Figure 7 for five different values of βi, 0.1, 0.3, 0.5, 0.7, and 0.9. The values of other parameters are the same as those in Figure 6c. The dependence of θ on E has a maximum when 0

Transient Adsorption of Rose Bengal Dianions

J. Phys. Chem. B, Vol. 105, No. 34, 2001 8167

Figure 8. Fitting the numerical cot φi vs E curves to the experimental -tan φf vs E curves at 5 (1, 1′), 10 (2, 2′), and 15 (3, 3′) Hz. The condition of the numerical calculation is the same as that in Figure 6c. Dotted lines are cot φi ) 1 when the interfacial ion transfer is diffusionlimited.

It would be interesting to compare the predictions of Goldman-type equation assuming the activationless ion transfer with the Butler-Volmer equation based on the activated charge transfer.8 In the case of Butler-Volmer model, the rate constants are represented as

Figure 6. Numerically calculated cot φi for three different cases at 5 (1), 10 (2), and 15 (3) Hz by using Goldman-type equation (solid line) and Butler-Volmer equation (Broken line) when kO,Q ) 1.4 × 10-2 a Q -1 -10 -2 cm s , βi ) 0.5, Γm,i ) 1.7 × 10 mol cm , and Bi ) 1.1 × 106 M-1. (a) There is no adsorption, (b) the O-A process is reversible, and (c) the W-A process is reversible. Dotted lines are cot φi ) 1 when the interfacial ion transfer is diffusion-limited.

Figure 7. Numerically calculated θ at several βi values. βi is 0.1 (1), 0.3 (2), 0.5 (3), 0.7 (4), 0.9 (5). The condition of the numerical calculation except that for βi is the same as that in Figure 6c.

< βi < 1, as is predicted by the thermodynamic reasoning of the potential-dependent adsorption of ion components between the two-immiscible phases.56

W,Q kW exp[2a(1 - ζ)] a ) ka

(26)

Q W,Q kW exp[-2aζ] d Bi ) ka

(27)

exp[-2bζ] kOa ) kO,Q a

(28)

exp[2b(1 - ζ)] kOd BQi ) kO,Q a

(29)

where ζ is the transfer coefficient. Broken lines in Figure 6a-c are the curves calculated using eqs 26-29 instead of eqs 1720, assuming that ζ is 0.5. The curves using the Butler-Volmer equations deviate downward from those using the Goldmantype equations at potentials away from Em,RB2-. In the case of the simple ion transfer, the downward deviation has been shown in the theoretical comparison of the Butler-Volmer model with the Goldman-type model.59 Figure 6b,c shows that this difference persists also in the presence of the adsorption. The discrepancy is associated with the difference in the Tafel characteristics between the Butler-Volmer model and the Goldman-type model; the former predicts the linear dependence, while the latter the convex. Experimentally, an unambiguous distinction between the two models is difficult, mainly because of the limited width of the experimentally accessible potential window. In Figure 8, the calculated curves based on the Goldmantype model were fitted to the experimental results (Figure 4a,b) Q at 5, 10, and 15 Hz. The values of kO,Q a , βi, Γm,i, and Bi are the 2same as those in Figure 6c. The value of Em,RB was set to be 350 mV, which is 15 mV more positive to the experimental value, 335 mV. In fact, the shape of the curves is not sensitive to the values of βi, Γm,i, and BQi . Attempts have been made to determine the value of βi, assuming that ions are soluble only in one phase.60,61 The insensitivity to the value of βi in the present case means that βi cannot easily be determined when ions are soluble in both oil and water phases. The relatively large scattering of the data at both ends of the applied potential renders the meaningful least-squares fitting of calculated curves to the experimental values difficult. However, it is seen that strongly affects the shape of the curves in the value of kO,Q a

8168 J. Phys. Chem. B, Vol. 105, No. 34, 2001 Figure 8; the height of the peak is primarily determined by kO,Q a , without appreciably affecting the slope of the curves. The applicability of the Langmuir isotherm to the adsorption of RB2- ions suggests that the van der Waals attractive interaction cancels out the electrostatic repulsion. The repulsion between charge groups of adsorbed RB2- ions might be screened by the electrical double layer in the aqueous side of the interface. The apparent standard ion-transfer rate constant, k0,app, defined in case III, as the in eq 7 may be identified with kO,Q a rate-determining step of the entire interfacial ion transfer is the adsorption-desorption of i in the O side of the interface. The -2 cm s-1, for the transfer of RB2- ions value of kO,Q a , 1.4 × 10 is close to the two experimental values of k0,app previously reported for other fluorescent anions, 9.5 × 10-3 cm s-1 for EY2- 37 and the order of 10-2 cm s-1 for methyl orange and ethyl orange.45 On the other hand, these k0,app values are at least one-tenth of recently reported k0,app values for symmetric tetraalkylammonium ions, >0.5 cm s-1 for TEA+ 34 and >32 cm s-1 for TMA+,35 whereas the diffusion coefficient of RB2ions is only one-third that of TEA+ ions.23,25,27 This fact highlights the anomalous slowness in the interfacial transfer of ions having asymmetric charge distributions. From molecular dynamics simulations62 and sum frequency measurements,63 solvent molecules at the interfacial region are ordered due to the interaction with solvent molecules on the other side of the interface. The rotational friction at the interfacial region is expected to be greater than that in the bulk environment.64 Further, in the case of ions with asymmetric charge distribution such as RB2-, the rotation is slower than that of ions with symmetric charge distribution because the inhomogeneous solvation of surrounding molecules around the ion enhances the dielectric friction for the rotation.65 Ions with asymmetric charge distribution at the interface are likely to have a certain stabilized orientational angle. The ions which come to the interface from the bulk solution then need to rotate to take a stable position. The slow rotational dynamics and the stabilized angle at the interface of this kind of ions are other aspects of the adsorption in the course of the interfacial transfer of RB2- and are probably related also to the slowness of the rate of the heterogeneous ion transfer. 4. Conclusions The ac-modulated voltfluorometry has demonstrated the transient adsorption of RB2- on the way of the ion transfer. The adsorption-desorption process between DCE phase and the adsorption plane is suggested to be the rate-determining step. The slowness of RB2- ion transfer is likely to be related to the slow rotational dynamics of RB2- ion at the interfacial region and its preferential orientation at the interface. A recently proposed model of ion transfer across the liquid-liquid interface by Marcus15 distinguishes three steps; the first step is the attachment of ions near the interface in W to the tip of the protrusion of the thermally fluctuated interface, the second is the diffusive process across the phase-boundary, and the third is the detachment of ions from the tip near the interface in O. The present results may be reinterpreted in terms of the Marcus’s model. Acknowledgment. This work was partially supported by a Grant-in-Aid for Scientific Research (No.10440220) and a Grant-in-Aid for Exploratory Research (No. 11875183) from the Ministry of Education, Science, Sports, and Culture, Japan, and CREST of JST (Japan Science and Technology).

Nishi et al. Appendix I: Theory of AC-Modulated Voltfluorometry for Quasi-Reversible Ion Transfer across the Planar ITIES From the theory of the ac impedance method,20 the dependence of the absolute value of admittance under the condition of the semi-infinite linear diffusion is given by59,66

|Yi| )

(

)

1

1/2

(2σ/λ + σ/ω ) + (σ/ω ) 1/2 2

1/2 2

(A-1)

and the dependence of cot φi on ω is

cot φi ) 1 +

21/2 1/2 ω λ

(A-2)

where

σ)

RT zF2

2 2 1/2

λ)

(

1

(DW)1/2cW b

B k (D )

W 1/2

+

+

1 (D°)1/2cOb

)

A k (D°)1/2

(A-3)

(A-4)

and cRb is the concentration in the bulk phase (R ) W or O) and B k (k A) is defined by eq 7. From eqs 5, 6, A-1, and A-2, |Yf| and φf are given by

|Yf| ∝

(

)

1 1 ω (2σ/λ+σ/ω1/2)2 + (σ/ω1/2)2 -tan φf ) 1 +

1/2

21/2 1/2 ω λ

(A-5)

(A-6)

Equation A-5 is simplified to the form, |Yf| ∝ ω-1/2, in reversible ion transfer, i.e., ω1/2/λ f 0. In quasi-reversible ion transfer, when the parameter k0/(Dω)1/2 is larger than 4.7, assuming that DW ) DO ) D, |Yf| is no less than 90% of that in reversible ion transfer. The linear relationship between |Yf| and ω-1/2 approximately holds in this range. As shown in eq A-6, in the case of ac-modulated voltfluorometry, -tan φf is the physical quantity which is equivalent to the cot φi in ac voltammetry. -tan φf has a linear relationship with respect to ω1/2, and at the limit of ω f 0, -tan φf is unity, corresponding to the entirely diffusion-limited condition. Appendix II: Method for the Numerical Calculation The dc potential was stepped at 1 mV intervals. The ac potential (8 mV) was modulated at every 10 dc steps. The concentration gradient due to the dc sweep was first stored for the next step of the dc potential and was taken as the initial concentration for the ac modulation at a constant dc potential. The ac potential was stepped such that an ac cycle was divided to 256 steps and the ac perturbation was made for 256 cycles (i.e., 65 536 steps). The first half of the ac current was discarded because of the distortion of ac response. The latter half was transformed into the phase angle and the amplitude by using the Fourier transform method. References and Notes (1) Kazarinov, V. E., Ed. In The interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids; SpringrerVerlag: Berlin, 1987. (2) Senda, M.; Kakiuchi, T.; Osakai, T. Electrochim. Acta 1991, 36, 253-262.

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