Langmuir 2001, 17, 821-827
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Microelectrochemical Measurements at Expanding Droplets: Effect of Surfactant Adsorption on Electron Transfer Kinetics at Liquid/Liquid Interfaces Jie Zhang,† Christopher J. Slevin,† Lasse Murtoma¨ki,‡ Kyo¨sti Kontturi,‡ David E. Williams,§ and Patrick R. Unwin*,† Department of Chemistry, University of Warwick, Coventry CV4 7AL, U.K., Laboratory of Physical Chemistry and Electrochemistry, Helsinki University of Technology, PO Box 6100, FIN-02015 HUT, Finland, and Department of Chemistry, Christopher Ingold Laboratories, University College London, 20 Gordon Street, London WC1H 0AJ, U.K. Received August 3, 2000. In Final Form: November 6, 2000 Adsorption of the nonionic surfactant Triton X-100 at the interface between two immiscible electrolyte solutions (ITIES) and its effect on the electron transfer (ET) reaction between tetracyanoquinodimethane in 1,2-dichloethane and aqueous Fe(CN)64- was studied using microelectrochemical measurements at expanding droplets (MEMED). A numerical model was developed for this process by assuming that adsorption of the surfactant at the ITIES was Langmuirian and that the ET reaction only occurred at the uncovered portion of the ITIES. Theoretical results show that, for typical MEMED conditions, the surfactant adsorption process attains the diffusion-controlled limit if the rate constant is greater than 1 cm s-1. The inhibitory effect of surfactant adsorption on the ET process produces changes in the reactant concentration profile adjacent to the droplet, which depend on the bulk surfactant concentration, equilibrium constant (K), the maximum surface coverage (Γmax), and the ET kinetics. Methods for determining these parameters are suggested. The effect of Triton X-100 on the ET reaction was measured over a wide range of conditions, with bulk aqueous Triton X-100 concentrations in the range 2.5 × 10-5 to 2.5 × 10-4 M, over various time scales. Experimental results were found to be in excellent agreement with theoretical predictions and yielded an ET rate constant of 0.0020 ( 0.0001 cm s-1 for the clean interface, with the potential across the ITIES established with 0.1 M ClO4- in each phase. The diminution in the ET rate with surfactant present was consistent with diffusion-controlled surfactant adsorption, characterized by K ) 2.7 × 104 M-1 and a value of Γmax ) 3 × 10-10 mol cm-2.
Introduction Microelectrochemical measurements at expanding droplets (MEMED) is a powerful new approach for studying the kinetics of reactions that occur at liquid/liquid interfaces.1-7 In MEMED, the interfacial reaction is monitored with a stationary ultramicroelectrode (UME), positioned directly opposite an expanding droplet of one phase that is grown into a second immiscible (receptor) phase. The probe penetrates and measures directly the developing (time-dependent) concentration profile adjacent to the drop surface in the receptor phase, due to the two-phase reaction. By solution of the convective-diffusion equation for this particular configuration, with appropriate boundary conditions, theoretical concentration profiles can be generated for comparison with experiment. In this way, the nature of mass transport and the interfacial reaction can be investigated quantitatively. MEMED belongs to a growing family of techniques in which an UME probe is used to directly measure concentration * Corresponding author. E-mail address: warwick.ac.uk. † University of Warwick. ‡ Helsinki University of Technology. § University College London.
P.R.Unwin@
(1) Slevin, C. J.; Unwin, P. R. Langmuir 1997, 13, 4799. (2) Slevin, C. J.; Unwin, P. R. Langmuir 1999, 15, 7361. (3) Zhang, J.; Slevin, C. J.; Unwin, P. R. Chem. Commun. 1999, 1501. (4) Zhang, J.; Unwin, P. R. Phys. Chem. Chem. Phys. 2000, 2, 1267. (5) Zhang, J.; Unwin, P. R. J. Phys. Chem. B 2000, 104, 2341. (6) Zhang, J.; Barker, A. L.; Unwin, P. R. J. Electroanal. Chem. 2000, 483, 95. (7) Slevin, C. J.; Unwin, P. R.; Zhang, J. In Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications; Volkov, A. G., Ed.; Marcel Dekker: New York, 2001; Chapter 13, pp 325-354.
boundary layers near reactive interfaces.8 In contrast to MEMED, many of these techniques use a mobile UME to probe the concentration boundary layer at a fixed interface, whereas in MEMED the interface moves and the timedependent concentration profile is sensed by a fixed electrode as the droplet advances toward the probe. Mass transport for MEMED has been well characterized1,2 and the methodology tested on some model systems, including interfacial hydrolysis of an acid chloride,1 neutral molecule (Br2) transfer,2 coupled electron-ion transfer,3 and cupric ion stripping4 processes. MEMED was recently applied to study electron transfer (ET) reactions at the interface between two immiscible electrolyte solutions (ITIES) and shown to complement scanning electrochemical microscopy (SECM),5,6 allowing the measurement of slow processes that could barely be detected by SECM, yet providing consistent data in the kinetic region where the two techniques overlapped. A key attribute of MEMED is that the drop lifetime can be used as a variable in the study of interfacial kinetics. For processes involving the adsorption of reactants, (8) See for examples: (a) Engstrom, R. C.; Weber, M.; Wunder, D. J.; Burgess, R.; Winguist, S. Anal. Chem. 1986, 58, 844. (b) Engstrom, R. C.; Meany, T.; Tople, R.; Wightman, R. M. Anal. Chem. 1987, 59, 2005. (c) Pohl, E. E.; Rokitskaya T. I.; Antonenko, Y. N.; Phol, P. Biophys. J. 1996, 70, SU364. (d) Pohl, P.; Rokitskaya, T. I.; Pohl, E. E.; Saparov, S. M. Biochim. Biophys. Acta 1997, 1323, 163. (e) Bath, B. D.; Lee, R. D.; White H. S.; Scott, E. R. Anal. Chem. 1998, 70, 1047. (f) Ragsdale, S. R.; White, H. S. Anal. Chem. 1999, 71, 1923. (g) Tsionsky, M.; Zhou, J. F.; Amemiya, S.; Fan, F. R.-F.; Bard, A. J.; Dryfe, R. A. W. Anal. Chem. 1999, 71, 4300. (h) Slevin, C. J.; Gray, N. J.; Macpherson, J. V.; Webb, M. A.; Unwin, P. R. Electrochem. Commun. 1999, 1, 282. (i) Gray, N. J.; Unwin, P. R. Analyst 2000, 125, 889. (j) Amatore, C.; Szunerits, S.; Thouin, L. Electrochem. Commun. 2000, 2, 248. (k) Amatore, C.; Szunerits, S.; Thouin, L.; Warkocz, J. S. Electrochem. Commun. 2000, 2, 353.
10.1021/la001113z CCC: $20.00 © 2001 American Chemical Society Published on Web 01/06/2001
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products, or intermediates, the ability to vary the drop lifetime is particularly important, since it could allow unwanted adsorption processes to be minimized or provide a way of elucidating adsorption kinetics. To expand the application of MEMED, this paper considers the situation where surfactant adsorbs from the receptor phase at the drop surface at which an ET process occurs spontaneously between reactants confined to the two phases. This situation is examined theoretically, through the development of a numerical model, and experimentally with studies of the effect of Triton X-100 on the ET kinetics for the reduction of 7,7,8,8-tetracyanoquinodimethane (TCNQ) in 1,2-dichloroethane (DCE) by aqueous Fe(CN)64-. Understanding the effect of surfactants on ET processes at ITIES is of considerable intrinsic interest,9-11 although there have been relatively few studies in this direction. Initial investigations by Cheng and Schiffrin9 demonstrated that the presence of a lipid monolayer at an ITIES inhibited the redox reaction of TCNQ, lutetium bis(phthalocyanine) [Lu(PC)2], and bis(pyridine)(meso-tetraphenylporphyrinato)ruthenium(II) complex [Ru(TPP)(py)2] in DCE by aqueous Fe(CN)64-/3-. Increasing inhibition of the ET rate, when the organic phase reactant was changed from TCNQ to Ru(TPP)(py)2 and Lu(PC)2, was attributed to a “size effect”, in which the approach of the redox centers present in the ITIES was increasingly inhibited. The rate constant measured for the ET reaction between TCNQ and Fe(CN)64- in the presence of a lipid monolayer was found to be lower than that measured under the same conditions at a native liquid/liquid interface, while the reactions between either Ru(TTP)(py)2 or Lu(PC)2 and Fe(CN)64- were completely inhibited by the monolayer. Bard and co-workers10 investigated the effect of a lipid monolayer on the reduction of (5,10,15,20-tetraphenyl21H,23H-porphine)zinc cation in benzene, by aqueous reductants using SECM. In these experiments, a chloroform solution of a symmetric saturated synthetic lipid, 1,2-diacyl-sn-glycero-3-phosphocholine, was injected into the organic phase, resulting in adsorption at the ITIES. A strong blocking effect of the lipid monolayer on the interfacial ET reaction was observed when the driving force was small (ca. 100 mV) because, under these conditions, the reaction was considered to occur only at the uncovered portion of ITIES. When the driving force was high (ca. 0.6 V), the ET reaction occurred at a measurable rate via tunneling through the monolayer. In this study, the equilibrium adsorption of lipid at the ITIES was found to follow a Langmuir isotherm. In a more recent investigation, Bard and co-workers10b showed that the addition of a phospholipid with a conjugated hydrocarbon chain increased the ET rate by at least a factor of 2 compared to a monolayer with only a saturated hydrocarbon chain. We have recently applied SECM to study the equilibrium adsorption of Triton X-100 at the water/DCE interface and its effect on the oxidation of decamethylferrocene in DCE by aqueous Ru(CN)63-.11 The diminution in apparent rate constant with increasing Triton X-100 concentration in the aqueous phase was successfully analyzed in terms of Langmuirian adsorption of the surfactant, with an equilibrium constant of (2.72 ( 0.06) × 104 M-1. Under the experimental conditions, complete (9) Cheng, Y.; Schiffrin, D. J. J Chem. Soc., Faraday Trans. 1994, 90, 2517. (10) (a) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Am. Chem. Soc. 1997, 119, 10785. (b) Delville, M. H.; Tsionsky, M.; Bard, A. J. Langmuir 1998, 14, 2774. (11) Zhang, J.; Unwin, P. R. J. Electroanal. Chem., in press.
Zhang et al.
monolayer coverage was not achieved, and the behavior observed suggested that the ET reaction occurred primarily at the uncovered portion of the ITIES. The reduction of TCNQ by Fe(CN)64-, of interest in this paper, has been studied previously and shown to be a useful system for the investigation of heterogeneous ET at a native ITIES.5,9,12 Under the conditions of the experiments reported herein, the driving force is very low, and thus the ET reaction is expected to occur predominantly at the uncovered portion of the ITIES in the presence of surfactant.10a In contrast to previous studies of ET across molecular monolayers at ITIES,10,11 which were carried out under equilibrium adsorption conditions, the MEMED measurements in this study consider a dynamic situation, where the initial condition is far from equilibrium. Theory We have previously analyzed mass transfer to an expanding droplet,1,2 based on established models for the dropping mercury electrode (DME)13 and other growing liquid drop techniques.14 The conditions for MEMED are usually arranged so that mass transport need only be considered within the receptor phase. Convective diffusion to the expanding droplet, within this phase, may be described by the following equation, assuming that the droplet is a complete sphere, which is reasonable under MEMED conditions where the droplet size is relatively small, with a radius typically up to a maximum of about 0.5 mm:
(
)
∂ci ∂2ci 2 ∂ci ∂ci ) Di 2 + - vr ∂t r ∂r ∂r ∂r
(1)
Here Di and ci are the diffusion coefficient and concentration of the reactant of interest in the receptor phase, i.e., Fe(CN)64- in this study; r is the spherical coordinate starting at the center of the drop, and t is time. The convective velocity due to the moving surface of the expanding droplet is given by
vr )
(
)
q 1 1 4π r2 r 2 0
(2)
where r0 is the time-dependent drop radius and q is the volume flow rate. If the initial drop volume is zero, the drop radius is given by
r0 )
(3qt 4π )
1/3
(3)
Following earlier work for the DME, we introduce a new variable,13a
x ) r - r0
(4)
(12) (a) Cheng, Y.; Schiffrin, D. J. J Chem. Soc., Faraday Trans. 1993, 89, 199. (b) Ding, Z.; Fermin, D. J.; Brevet, P. F.; Girault, H. H. J. Electroanal. Chem. 1998, 458, 139. (c) Webster, R. D.; Dryfe, R. A. W.; Coles, B. A.; Compton, R. G. Anal. Chem. 1998, 70, 792. (13) (a) Markowitz, J. M.; Elving, P. J. Chem. Rev. 1959, 59, 1047. (b) Levich, V. G. Physicochemical Hydrodynamics; Prentice Hall: Englewood Cliffs, NJ, 1962. (c) Britz, D. Digital Simulation in Electrochemistry, 2nd ed.; Springer-Verlag: New York, 1988. (d) Pons, S.; Speiser, B.; McAleer, J. F.; Schmidt, P. P. Electrochim. Acta 1982, 27, 1711. (14) (a) Popovich, A. T.; Jervis, R. E.; Trass, O. Chem. Eng. Sci. 1964, 19, 357. (b) Bauer, G. L. Solvent Extraction of Copper: Kinetics and Equilibrium Studies. Ph.D. Thesis, University of Wisconsin, Madison, WI, 1975.
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from which eqs 1 and 2 can be transformed to
(
)
∂ci ∂2ci ∂ci 2 ∂ci ) Di 2 + - vr ∂t r0 + x ∂x ∂x ∂x vr )
(
)
q 1 1 4π (r + x)2 r 2 0 0
(5) (6)
For the surfactant, the mass balance at the drop surface can be written as
( )
∂cs d(ΓA) dΓ dA )A +Γ ) DsA dt dt dt ∂x
x)0
(7)
where Γ is the surface excess concentration (mol cm-2), A is the surface area (cm2), and Ds and cs, respectively, are the diffusion coefficient and concentration of the surfactant which is also contained entirely within the receptor phase. It readily follows from eq 7 that
( )
1 dΓ 1 dA Ds ∂cs + ) Γ dt A dt Γ ∂x
x)0
electrodes indicate that any heterogeneities in interfacial reactivity must occur on a length scale significantly smaller than the UMEs used (25 µm diameter or less). This is much less than the concentration boundary layer probed in MEMED studies (vide infra). For a blocked interface that results in an array of active sites that are small-sized compared to the diffusion layer, eq 13 is expected to provide a good description of the reduction of the interfacial flux due to the adsorption processes, provided that θ is not too close to unity.15 The experimental data presented later confirm the validity of this assumption. Equation 14 is the boundary condition for the surfactant adsorption process, where ka and K are the adsorption rate constant and equilibrium constant, respectively. For diffusioncontrolled adsorption, eq 14 can be simplified to
(cs)x)0 )
(8)
Since the droplet is spherical
R0 )
(9)
From eq 3
2 2 dr0 ) r0 dt 3t
(10)
x
( )
r0
so that
( )
Ds ∂cs dθ 2θ + ) dt 3t Γmax ∂x
(12)
x)0
where θ ) Γ/Γmax is the surface coverage and Γmax is the maximum surface excess concentration. On the basis of previous studies at low driving force,10a,11 it is reasonable to assume that, in the presence of an incomplete surfactant layer, the ET reaction occurs predominantly at the uncovered portion of the ITIES and also to consider Langmuirian adsorption as a first approximation. The boundary conditions for the droplet surface (x ) 0) can then be written as
( )
kci(1 - θ) ) Di
( ) [
∂ci ∂x
(13)
]
∂cs θ ) ka cs(1 - θ) Ds ∂x K
τ)
t td
(18)
Ci )
ci ci*
(19)
Cs )
cs cs*
(20)
x x x x
V r ) vr
td Di
(21)
Ki ) k
td Di
(22)
td Di
(23)
K a ) ka Kd )
ka Kcs*
td Di
(24)
where ci* and cs* are the bulk concentrations of Fe(CN)64and Triton X-100 in this particular study. The resulting normalized equations are
∂Ci ∂Ci ∂Ci ∂2Ci 2 ) - Vr + 2 ∂τ R + X ∂X ∂X ∂X 0
(14)
Equation 13 is the boundary condition for the ET reaction, where k (cm s-1) is heterogeneous ET rate constant. This equation is valid provided that adsorption does not result in patches of the interface covered with a continuous adsorbed phase and uncovered patches which are comparable to the size of diffusion layer, which would otherwise invalidate the assumption of a spherical diffusion field. Our earlier SECM studies11 with small-scale
(17)
xDitd
(11)
x)0
(16)
xDitd
Combining eqs 8-10 gives
Ds ∂cs 2 1 dΓ + ) Γ dt 3t Γ ∂x
(15)
Equations 5 and 12-15 can be cast into dimensionless form using the following terms:
X)
1 dA 2 dr0 ) A dt r0 dt
θ K(1 - θ)
(25)
X ) 0:
dθ 2θ DsCs* + ) dτ 3τ Γmax
x
(26)
X ) 0:
KiCi(1 - θ) )
∂Ci ∂X
(27)
td ∂CS Di ∂X
(15) Amatore, C.; Save´ant, J. M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39.
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X ) 0:
x
Ds ∂Cs ) Ka xD t ∂X i d
X ) 0:
Cs )
x
Di C (1 - θ) - Kd td s
Di θ (28) td
Kd θ ka 1 - θ
(29)
Far from the drop surface, the following boundary conditions hold:
X f ∞:
Ci ) 1
(30)
Cs ) 1
(31)
The problem was solved numerically, using the simple explicit method13c as described in our previous study.2 The modeling produced surface coverage-time behavior, along with concentration vs radial distance profiles, as a function of time, for both the surfactant and the reactant in the receptor phase. The time-dependent concentration vs distance, d, profile for the reactant, observed at the probe electrode, could readily be evaluated from these data. Theoretical Results and Discussion The model highlighted above allows several physicochemical characteristics of the system be explored. There are clearly a large number of variables that could be considered (e.g. drop size, drop lifetime, surfactant concentration, adsorption rate constant, equilibrium constant, and the rate constant for the ET process), but we restrict our analysis here to some of the most important aspects that arise from the model. Effect of Adsorption Rate Constant on Surfactant Adsorption at the ITIES. Although it is established that nonionic surfactants undergo diffusion-controlled adsorption at fluid/fluid interfaces,16-18 it is first necessary to use eq 13 (eq 27 in normalized form) as the boundary condition to find the conditions where the diffusioncontrolled limit is reached in MEMED. To investigate the effect of ka on the adsorption process, the following parameter values were used: K ) 2.7 × 104 M-1, which was obtained from our previous study;11 Ds ) 1 × 10-6 cm2 s-1, which is the mean value from the literature;16,19,20 Γmax ) 3 × 10-10 mol cm-2, which was based on both literature values16,19,21 and our experimental observations (vide infra). Typical results are given in Figure 1, showing the variation of surfactant surface coverage, θ, with normalized time. In these simulations, two bulk concentrations of surfactant in the receptor phase have been considered, 2.5 × 10-5 and 2.5 × 10-4 M, with a range of adsorption rate constants. A typical real drop time of 6.3 s and a final drop radius of 0.5 mm were employed. It is evident that the bulk surfactant concentration and the adsorption rate constant have a significant influence on the θ-τ characteristics. For a particular ka value considered, the lower the bulk surfactant concentration, (16) Wu, N.; Dai, J. L.; Micale, F. L. J. Colloid Interface Sci. 1999, 215, 258. (17) Diamant, H.; Andelman, D. J. Phys. Chem. 1996, 100, 13732. (18) (a) Borwankar, R. P.; Wasan, D. T. Chem. Eng. Sci. 1988, 43, 1323. (b) Miller, R.; Kretzschmar, G. Adv. Colloid Interface Sci. 1991, 37, 97. (19) Go¨bel, J. G.; Joppien, G. R. J. Colloid Interface Sci. 1997, 191, 30. (20) Campanelli, J. R.; Wang, X. J. Colloid Interface Sci. 1999, 213, 340. (21) Myers, D. Surfactant Science and Technology; VCH Publishers: Weinheim, Germany, 1988.
Figure 1. Effect of ka on θ-τ characteristics. For this simulation td ) 6.3 s and the final drop radius was 0.50 mm. From top to bottom, the curves are for ka ) 10 and 1 (which virtually coincide), 0.1, 0.01, 0.001, and 0.0001 cm s-1. The simulations consider two surfactant concentrations: (a) cs* ) 2.5 × 10-5 M; (b) cs* ) 2.5 × 10-4 M.
the longer is the time required to achieve equilibrium surface coverage and, of course, the lower the final surface coverage (eq 15 in rearranged form with (cs)x)0 ) cs*). The value of ka is seen to have a major influence on the characteristics, until a value is reached, beyond which the adsorption process becomes diffusion-controlled. In general, it can be seen that the adsorption process attains the diffusion-controlled limit when the ka value is higher than ca. 1 cm s-1. Effect of Surface Coverage on the ET Process. The effect of cs* on θ and, in turn, on the rate of the ET process is clearly illustrated by the data in Figures 2 and 3. The results in Figure 2 build on those in Figure 1, showing a more complete set of θ-τ profiles for diffusion-controlled surfactant adsorption, for the K and Γmax values cited above, with the rate constant for the redox reaction, k ) 2.0 × 10-3 cm s-1. The data clearly show the effect of increasing cs* on the final θ value. Surfactant adsorption blocks the ET process, according to eq 13, and this can be probed by measuring the reactant concentration profile, in the receptor phase, adjacent to the drop surface. Figure 3 shows that as the surfactant concentration increases (promoting surface coverage), the reactant profiles become less steep near the droplet, reflecting the diminished flux due to the ET reaction being impeded. The data in Figure 3, presented as normalized (time-dependent) reactant concentration at distance, d, from the droplet surface, ci(d)/ci*, clearly demonstrate that the redox process could be used as a sensitive probe of surfactant coverage. Effect of Γmax on the ET-Reactant Profiles. Both K and Γmax are important parameters in surfactant science, and it is interesting to elucidate the extent to which values
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) 2.7 × 104 M-1; final drop radius of 0.50 mm, with Γmax taking various values. The data show that Γmax is measurable, by studying the blocking effect of surfactant on the ET kinetics, provided that cs* is sufficiently high. At low cs*, the surface excess does not reach sufficiently high values to allow the different reactant profiles resulting from the various contributions of Γmax to be resolved, whereas at higher cs*, resolution of Γmax values becomes possible, over the ranges considered. A similar effect was observed when Γmax was kept constant at a typical value of 3 × 10-10 mol cm-2 and K varied through a range of values 2 × 104 to 4 × 104 M-1. This discussion highlights the potential of the technique to determine either Γmax or K for surfactant adsorption, if one of them is known. Figure 2. Effect of cs* on θ-τ characteristics. For this simulation td ) 6.3 s and the final radius was 0.50 mm. From bottom to top, cs* ) 2.5 × 10-5, 5 × 10-5, 1 × 10-4, 1.5 × 10-4, 2 × 10-4, and 2.5 × 10-4 M.
Figure 3. Effect of diffusion-limited surfactant adsorption on an ET reaction (k ) 2.0 × 10-3 cm s-1), illustrated via the timedependent reactant profiles that would be seen by a static probe electrode with an advancing droplet. The drop time was 6.3 s, and the final radius was 0.50 mm. From bottom to top, cs* ) 0, 2.5 × 10-5, 5 × 10-5, 1 × 10-4, 1.5 × 10-4, 2 × 10-4, and 2.5 × 10-4 M.
Figure 4. Reactant concentration profiles showing the effect of Γmax on an ET process (k ) 2.0 × 10-3 cm s-1) with different cs* for diffusion-controlled adsorption. K ) 2.7 × 104 M-1 was used together with Γmax ) 2 × 10-10 mol cm-2 (dotted lines), Γmax ) 3 × 10-10 mol cm-2 (solid lines), and Γmax ) 4 × 10-10 mol cm-2 (dashed lines). Surfactant concentrations cs* ) 2.5 × 10-4 M (top group of curves) and 2.5 × 10-5 M (bottom group of curves) have been considered.
for these could be determined via MEMED. The results in Figure 4 are for a diffusion-controlled adsorption process with the following parameters: Di ) 6.7 × 10-6 cm2 s-1; Ds ) 1 × 10-6 cm2 s-1; k ) 2 × 10-3 cm s-1; td ) 6.3 s, K
Experimental Section Chemicals. All chemicals were used as received. These were Triton X-100 (AR), TCNQ (98%), NaClO4‚xH2O (AR), and DCE (HPLC grade) (all from Sigma-Aldrich), NaCl (AR, Fisons), Na4Fe(CN)6‚10H2O (AR, Strem), and tetra-n-hexylammonium perchlorate ((THA)ClO4, crystalline, Alfa). All aqueous solutions were prepared from Milli-Q reagent water (Millipore Corp.). Apparatus and Procedures. All electrochemical measurements were made using a two-electrode arrangement. A saturated calomel electrode (SCE) served as the reference electrode, and a glass-coated Pt ultramicroelectrode (UME, 2 µm diameter) functioned as the working electrode tip. The UME had a defined RG value of 4. RG ) rs/a, where rs is the overall radius of the tip end (electrode plus insulating sheath) and a is the electrode radius. The electrodes were fabricated and polished as described previously.22 The basic apparatus developed for MEMED experiments was described earlier.1-7 To investigate the effect of Triton X-100 on the heterogeneous ET rate constants for the reduction of TCNQ in DCE by aqueous Fe(CN)64-, DCE droplets containing 10 mM TCNQ and 0.1 M (THA)ClO4 were grown from a capillary with an internal diameter of 200 µm. The aqueous receptor phase contained 1 mM Fe(CN)64-, 0.1 M NaCl, 0.1 M NaClO4, and 2.5 × 10-5 to 2.5 × 10-4 M Triton X-100. With the reactant concentration in the feeder phase 10 times that of the reactant in the receptor phase, depletion and mass transport within the droplet could be neglected. As ClO4was the only ion common to both phases in all experiments, electroneutrality of the two phases was maintained by the transfer of this common ion when the ET reaction occurred at the ITIES. The interfacial reaction was monitored by employing an amperometric Pt UME to measure the local changes in the Fe(CN)64- concentration near to the drop surface in the aqueous phase during the reaction. The tip current for the oxidation of Fe(CN)64- was recorded as a function of time as the drop grew toward the tip (see Figure 5). In contrast to SECM,5,6,10,11,22,23 the small size of the tip used for these measurements ensured that the electrode was a noninvasive probe of the concentration boundary layer that developed adjacent to the droplet. A method for obtaining the time-dependent droplet concentration profile from the UME response has been outlined fully elsewhere.2 The distance at which the tip contacted the ITIES was taken as the point where the tip current changed suddenly on reaching the interface. (22) Macpherson, J. V.; Unwin, P. R. J. Phys. Chem. 1994, 98, 1704. (23) (a) Bard, A. J.; Fan, F.-R. F.; Pierce, D. T.; Unwin, P. R.; Wipf, D. O.; Zhou, F. M. Science 1991, 254, 68. (b) Bard, A. J.; Fan, F.-R. F.; Mirkin, M. V. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1993; Vol. 18. (c) Bard, A. J.; Fan, F.-R. F.; Mirkin, M. V. In Physical Electrochemistry: Principles, Methods and Applications; Rubinstein, I., Ed.; Marcel Dekker: New York, 1995. (d) Unwin, P. R. J. Chem. Soc., Faraday Trans. 1998, 94, 3183. (e) Barker, A. L.; Gonsalves, M.; Macpherson, M. V.; Slevin, C. J.; Unwin, P. R. Anal. Chim. Acta 1999, 385, 223. (f) Amemiya, S.; Ding, Z.; Zhou, J.; Bard, A. J. J. Electroanal. Chem. 2000, 483, 7. (g) Barker, A. L.; Slevin, C. J.; Unwin, P. R.; Zhang, J. In Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications; Volkov, A. G., Ed.; Marcel Dekker: New York, 2001; Chapter 12, pp 283-324.
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Figure 5. Schematic of the MEMED arrangement for investigating the ET reaction between aqueous Fe(CN)64- and TCNQ in DCE, with parallel adsorption of surfactant from the aqueous receptor phase at the ITIES.
Figure 6. Effect of Triton X-100 on aqueous Fe(CN)64concentration profiles for the ET reaction. The solid lines are the experimental results for the system without Triton X-100 (bottom) and with [Triton X-100]w ) 2.5 × 10-4 M (top). The dashed curves are the theoretical profiles for k ) 0.0020 cm s-1 (bottom) and the effect of surfactant with Γmax ) 3 × 10-10 mol cm-2 and the other parameters as cited in the text. The drop time was 6.3 s, and the final drop radius was 0.55 mm.
Experimental Results and Discussion Measurement of Γmax. As described above, it should be possible to measure Γmax when the surfactant concentration is sufficiently high. The determination of Γmax involves fitting experimental reactant profiles to the best theoretical prediction, by varying Γmax with the other parameters known. On the basis of earlier work,16-18 and the results that follow, diffusion-limited surfactant adsorption was considered, with K ) 2.7 × 104 M-1 derived from a recent SECM study.11 These experiments were carried out without Triton X-100 and then with Triton
Figure 7. Effect of [Triton X-100]w on aqueous Fe(CN)64profiles for the ET reaction. In each case, the final drop radius was 0.55 mm and, from bottom to top, the solid experimental curves are for [Triton X-100]w ) 0, 2.5 × 10-5, 5.0 × 10-5, 1.0 × 10-4, 1.5 × 10-4, 2.0 × 10-4, and 2.5 × 10-4 M. (a) The drop time was 12.5 s, and the dashed theoretical curves (bottom to top) are for k ) 0.0020, 0.0019, 0.0020, 0.0019, 0.0021, 0.0019, and 0.0020 cm s-1. (b) The drop time was 8.3 s, and the dashed theoretical curves (bottom to top) are for k ) 0.0020, 0.0019, 0.0019, 0.0020, 0.0019, 0.0021, and 0.0020 cm s-1. (c) The drop time was 6.3 s, and the dashed theoretical curves (bottom to top) are for k ) 0.0020, 0.0018, 0.0018, 0.0020, 0.0019, 0.0020, and 0.0020 cm s-1. For all theoretical analyses, the other adsorption parameters were as cited in the text.
X-100 present in the aqueous phase at a concentration of 2.5 × 10-4 M. The dramatic effect of surfactant in inhibiting the ET reaction rate is clearly evident from the change in the Fe(CN)64- profiles in Figure 6. The data obtained at a clean ITIES were found to analyze well with k ) 0.0020 cm s-1 for the ET rate constant under the experimental
Measurements at Expanding Droplets
conditions. With surfactant present, the same rate constant could be used to analyze the data in conjunction with the K value cited and a Γmax value of 3 × 10-10 mol cm-2. The Γmax value deduced is comparable to previous values for oil/water interfaces (Γmax ) 2.38 × 10-10 mol cm-2)24 and the water/air interface (Γmax ) 2.2 × 10-10 mol cm-2 21 and Γmax ) 3.09 × 10-10 mol cm-2).16 Experimental results obtained at different time scales (6.3-12.5 s) were found to fit well to the theoretical model, with typical data shown in Figure 6. This is particularly satisfying since the model used is quite simple and assumes that the ET rate is diminished due to surfactant adsorption blocking the area available for the reaction. Although Triton X-100 has found use as an ionophore for assisted alkali metal ion transfer voltammetry,25 the interfacial potential drop in the present studies is insufficient to promote the transfer process. Our earlier SECM studies also suggested negligible specific adsorption of any ions complexed by Triton X-100 at the ITIES,11 which might have compromised the model in the present application. Effect of [Triton X-100]w on the ET Reaction Rate. As shown in Figures 2 and 3, as the surfactant concentration in the receptor phase increases, the ET rate should decrease due to the increasing blocking of the ITIES by surfactant. Experimentally, this effect can be determined from the reactant profiles in the receptor phase in the presence of different [Triton X-100]w. The experimental results presented in Figure 7 were obtained at three drop times with various Triton X-100 concentrations. The behavior was analyzed theoretically by fixing Ds ) 1 × 10-6 cm2 s-1, Γmax ) 3 × 10-10 mol cm-2, K ) 2.7 × 104 M-1, and changing k (the rate constant that prevails at a clean ITIES), until the best fit between the experimental and theoretical curves was obtained. As shown in Figure 7, the Fe(CN)64- concentration profiles adjacent to the droplet in the receptor phase are less steep as [Triton X-100]w increases. This is consistent with an increasing blocking effect of the surfactant on the ET kinetics at the ITIES, in agreement with the theoretical predictions (see Figure 3). All of the measured data were found to fit well to the theoretical curves with k ) 0.0020 ( 0.0001 cm s-1, which is the value measured at a clean ITIES. The fact that experiment agrees well with theory for a wide range of [Triton X-100]w and drop times indicates that the various assumptions in the model, i.e. Lang(24) Campanelli, J. R.; Wang, X. Can. J. Chem. Eng. 1998, 76, 51. (25) Yoshida, Z.; Kihara, S. J. Electroanal. Chem. 1987, 227, 171.
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muirian, diffusion-limited surfactant adsorption, with ET only occurring at the uncovered portion of the ITIES, are reasonable for this system. Conclusions A numerical model has been developed for the adsorption of a surfactant at a symmetrically growing sphere of one fluid which forms an interface with a second fluid where a spontaneous ET process occurs. The model has assumed that adsorption of the surfactant at the ITIES is Langmuirian and that the parallel ET reaction only occurs at the portion of ITIES that is free from surfactant. The surfactant adsorption process attains diffusion-control when the adsorption rate constant is higher than 1 cm s-1, for typical conditions encountered in MEMED. The theory has been examined experimentally through studies of the effect of Triton X-100 on the reduction of TCNQ in growing DCE droplets by aqueous Fe(CN)64-. The experiments cover different time scales and Triton X-100 concentrations in the aqueous phase. The experimental results have been found to be in excellent agreement with theory with an ET rate constant of 0.0020 ( 0.0001 cm s-1 for a clean interface, together with diffusion-controlled adsorption of Triton X-100, with a Γmax value of 3 × 10-10 mol cm-2, assuming K ) 2.7 × 104 M-1.11 In addition to understanding generally how surfactant adsorption affects reaction kinetics within MEMED, this study also suggests the possibility of measuring the adsorption of a nonelectroactive species (e.g. surfactant) indirectly. With the assumptions outlined herein, the effect of surfactant on a known reaction (e.g. the ET reaction between two redox species) depends critically on the maximum surface coverage of adsorbed surfactant and the equilibrium constant for adsorption. The possibility of deriving these parameters from the analysis of reactant profiles may further expand the application of MEMED in kinetic measurements beyond those already envisaged.1-7,11 Acknowledgment. C.J.S., P.R.U., and J.Z. thank the EPSRC and Avecia for support and Dr. John Atherton (Avecia, Huddersfield, U.K.) for informative discussions. J.Z. also acknowledges scholarships from the ORS scheme and the University of Warwick. L.M. acknowledges the Academy of Finland for a research position. K.K. and D.E.W. acknowledge support via the TMR Project No. FMRX-CT96-0078. LA001113Z
