Investigation of Potential Distribution and the Influence of Ion

Sep 21, 2009 - measurement of the effects of aqueous ion complexation on diffusion ... dimensional Nernst-Planck equation employing the elec- troneutr...
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Anal. Chem. 2009, 81, 8373–8379

Investigation of Potential Distribution and the Influence of Ion Complexation on Diffusion Potentials at Aqueous-Aqueous Boundaries within a Dual-Stream Microfluidic Structure Jo¨rg Strutwolf, Mary Manning, and Damien W. M. Arrigan* Tyndall National Institute, Lee Maltings, University College, Cork, Ireland The occurrence of reactions at boundaries between adjacent miscible but unmixed aqueous streams coflowing in a microfluidic channel structure has been studied by simulation of the diffusion potentials that develop between the two coflowing aqueous electrolyte streams and by measurement of the effects of aqueous ion complexation on diffusion potentials. The microfluidic structure consisted of a Y-shaped microchannel with off-chip electrodes immersed in electrolyte reservoirs connected by capillaries to the Y-microchannel. The time-dependent, onedimensional Nernst-Planck equation employing the electroneutrality condition was solved numerically to calculate the diffusion potentials established at the boundary between the two coflowing aqueous streams. Under the experimental conditions (channel length and width, flow rate) employed, it was shown that the use of the Henderson equation was appropriate. It was also shown that the cross-channel diffusion potential remained constant from the entrance of the channel to the exit. The influence of cation complexation by a neutral ionophore was investigated by experimentally measured diffusion potentials. It was found that potassium complexation by the cyclic polyether 18-crown-6 altered the experimental diffusion potential, whereas the interaction of sodium or lithium cations with the ionophore did not perturb the diffusion potential. The results are consistent with the literature data for aqueous-phase complexation of these cations by this ionophore. The results of these investigations demonstrate that relatively simple diffusion potential measurements between coflowing streams in microchannels may be used as a basis for study of ion complexation reactions occurring at boundaries between miscible fluids. Electrochemical measurements in microfluidic structures have been investigated for a number of applications, including on-chip capillary electrophoretic detection1,2 and interfacial ion electroextractions.3 The combination of electrochemistry with microflu* To whom correspondence should be addressed. E-mail: damien.arrigan@ tyndall.ie. Fax: +353-21-4270271. (1) Nyholm, L. Analyst 2005, 130, 599–605. (2) Vandaveer, W. R.; Pasas-Farmer, S. A.; Fischer, D. J.; Frankenfeld, C. N.; Lunte, S. M. Electrophoresis 2004, 25, 3528–3549. (3) Berduque, A.; O’Brien, J.; Alderman, J.; Arrigan, D. W. M. Electrochem. Commun. 2008, 10, 20–24. 10.1021/ac901061r CCC: $40.75  2009 American Chemical Society Published on Web 09/21/2009

idics is highly attractive because of the simplicity of the detection device and associated instrumentation and their ease of miniaturization. Electrochemical experiments may also be employed to study processes occurring within microfluidic structures that are difficult to achieve without microfluidics. In Y-shaped microfluidic channels, two inlet channels enable the introduction of two different flowing solutions into the main channel. Under the laminar flow regime which is easily attained in microfluidics, no convective mixing of the two coflowing streams occurs. This type of behavior has been exploited in several areas, e.g., for optimizing hydrodynamic fuel cells, where the side-by-side laminar flow of the fuel and oxidant removes the need for physical separation of the two aqueous streams by membranes4-8 and for diffusion-based analysisofmolecularinteractionsofbiologicallyrelevantmolecules.9-12 Recently, we reported a microfluidic device based on a variation of the Y-shaped channel design, in which off-chip electrodes connected via microcapillary channels to the main microfluidic channel were used.13 A plan view of the microfluidic chip is shown in Figure 1, together with the dimensions of the device. The offchip electrodes were used to monitor changes in the open-circuit potentials in order to determine the diffusion (or liquid junction) potential φd developing at the boundary between the two coflowing aqueous solutions containing different ion concentrations and/or different ion species. The measured open-circuit potentials for various concentrations and different ionic species were predicted by calculations based on the Henderson equation14,15 combined with the Falkenhagen-Pitts equation16-19 (4) Chen, F. L.; Chang, M. H.; Hsu, C. W. Electrochim. Acta 2007, 52, 7270– 7277. (5) Choban, E. R.; Markoski, L. J.; Wieckowski, A.; Kenis, P. J. A. J. Power Sources 2004, 128, 54–60. (6) Ferrigno, R.; Stroock, A. D.; Clark, T. D.; Mayer, M.; Whitesides, G. M. J. Am. Chem. Soc. 2002, 124, 12930–12931. (7) Lee, J.; Lim, K. G.; Palmore, G. T. R.; Tripathi, A. Anal. Chem. 2007, 79, 7301–7307. (8) Lim, K. G.; Palmore, G. T. R. Biosens. Bioelectron. 2007, 22, 941–947. (9) Hatch, A.; Garcia, E.; Yager, P. Proc. IEEE 2004, 92, 126–139. (10) Hatch, A.; Kamholz, A. E.; Hawkins, K. R.; Munson, M. S.; Schilling, E. A.; Weigl, B. H.; Yager, P. Nat. Biotechnol. 2001, 19, 461–465. (11) Kamholz, A. E.; Weigl, B. H.; Finlayson, B. A.; Yager, P. Anal. Chem. 1999, 71, 5340–5347. (12) Munson, M. S.; Cabrera, C. R.; Yager, P. Electrophoresis 2002, 23, 2642– 2652. (13) Strutwolf, J.; Herzog, G.; Homsy, A.; Berduque, A.; Collins, C. J.; Arrigan, D. W. M. Microfluid. Nanofluid. 2009, 6, 231–240. (14) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001.

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Figure 1. Plan view of the microfluidic chip. The dimensions are given in millimeters. The height of the gray colored area is 0.05 mm.

(to take into account the ion mobility at finite ionic strength) and also considering the potential difference introduced by the electrode system. The theoretical predictions for the open-circuit potentials were in agreement with experimental measurements for a variety of chloride salt solutions.13 This article presents further investigations into the electrochemical behavior of two coflowing aqueous electrolyte streams under laminar flow conditions in Y-shaped microchannel devices. There were two aims of the study. First, the validity of the theoretical approach employed previously to compute the opencircle potentials established in the microfluidic device was examined in more detail. The Henderson equation was used to evaluate diffusion potentials as a function of the ionic mobilities, the charges of the ions, and their (bulk) concentrations, assuming linear concentration profiles within a “mixed” zone where the two streams are in contact. At the boundary of this zone, the ion concentration is fixed to the bulk concentration of the ion under consideration. The diffusion potential calculated by the Henderson equation is in agreement with numerical steady-state solutions of the Nernst-Planck (NP) equation20,21 for this system. This is not a surprise, since the Henderson equation can be derived from the NP equation under the assumptions mentioned previously.22 In this report, the time dependent one-dimensional NP equation is solved to calculate diffusion potentials and concentration profiles. The extension of the mixed layer of ions depends on the contact time of the two coflowing streams. The broadening of the initially narrow mixed layer is allowed using the channel side walls as boundaries, where no-flux conditions prevail. The second aim of this study was to investigate whether the microfluidic structure can be useful as a simple device to examine ion complexation. As an example, the well-known complexation Henderson, P. Z. Phys. Chem. 1907, 59, 118–127. Falkenhagen, H.; Leist, M.; Kelbg, G. Ann. Phys. 1952, 11, 51–59. Jouyban, A.; Kenndler, E. Electrophoresis 2006, 27, 992–1005. Pitts, E. Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 1953, 217, 43–70. Porras, S. P.; Riekkola, M. L.; Kenndler, E. Electrophoresis 2003, 24, 1485– 1498. (20) Morf, W. E.; Pretsch, E.; De Rooij, N. F. J. Electroanal. Chem. 2007, 602, 43–54. (21) Sokalski, T.; Lingenfelter, P.; Lewenstam, A. J. Phys. Chem. B 2003, 107, 2443–2452. (22) Morf, W. E. Anal. Chem. 1977, 49, 810–813.

(15) (16) (17) (18) (19)

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of alkali metal cations by cyclic polyethers was used. The selectivity shown by cyclic polyethers, or crown ethers, toward cations is well documented23-25 and has been exploited in many areas such as in chemical analysis,26 in phase-transfer catalysis,27 and in solvent extraction.28 In the present study, if the mobility of the complex of the (uncharged) crown ether with the cation is different from that of the solvated cation, the diffusion potential developed at the boundary of the two coflowing streams should change. In such cases, the easily measured diffusion potential can be used to monitor complexation reactions. If the complexation is ion specific, the microfluidic device presented here might thus be developed into an analytical tool similar to ion selective electrodes but without the need for membranes. EXPERIMENTAL SECTION The fabrication of the microfluidic chip was based on molding of poly(dimethylsiloxane) (PDMS), as described previously.13 A plan view of the microfluidic device is shown in Figure 1 to illustrate the dimensions. The height of all channels, capillaries, and reservoirs was 50 µm. AgCl-coated silver wires were used as reference electrodes and fabricated by immersing Ag wire (Advent, U.K.) into a concentrated FeCl3 solution for 1 h. The electrodes were inserted through holes into the electrolyte reservoirs of the device, and the holes where then sealed by small amounts of PDMS. Open circuit potentials were measured using a CHI620 potentiostat (CH Instruments, IJ Cambria, Burry Port, U.K.). The aqueous solutions were propelled into the microfluidic channels using a KDS 200 series syringe pump. A six-port injection valve (C22-3186 valve, Carl Stuart Ltd., Ireland) with a 100 µL injection loop was connected between one of the syringes and (23) Izatt, R. M.; Pawlak, K.; Bradshaw, J. S.; Bruening, R. L. Chem. Rev. 1991, 91, 1721–2085. (24) Bradshaw, J. S.; Izatt, R. M. Acc. Chem. Res. 1997, 30, 338–345. (25) Izatt, R. M.; Pawlak, K.; Bradshaw, J. S.; Bruening, R. L. Chem. Rev. 1995, 95, 2529–2586. (26) Kolthoff, I. M. Anal. Chem. 1979, 51, R1–R22. (27) Dehmlow, E. V.; Dehmlow, S. S. Phase Transfer Catalysis; Wiley-VCH: Weinheim, Germany, 1993. (28) Bond, A. H.; Dietz, M. L.; Chiarizia, R. Ind. Eng. Chem. Res. 2000, 39, 3442–3464.

the microfluidic cell, enabling injection of 100 µL of a sample solution through one of the inlets instead of the reference solution. The reference solution of 10 mM KCl was pumped through each arm of the Y-channel and run under laminar flow conditions through the main channel. The volumetric flow rate was 1.67 × 10-9 m3 s-1 in all experiments. Temporary injection of a sample solution into one side of the main channel was achieved with the injection loop. The potential difference between the two silver/silver chloride electrodes was measured continuously during these experiments, i.e., during coflow of the 10 mM KCl reference solutions in each side and coflow of the KCl solution with the injected sample solution. Sample injections were performed in triplicate, and the reproducibility of the measured potentials was such that the standard deviation was smaller than the symbol size used in the figures to plot the experimental data. Potassium chloride, sodium chloride, lithium chloride, and 1,4,7,10,13,16-hexaoxacyclooctadecane, also called 18-crown-6 (18C6), were purchased from Sigma Aldrich Ireland and used as received. All solutions were prepared in deionized water (which had a resistivity of 18 MΩ cm and was obtained from an Elga water purification unit). The solutions containing mixtures of alkali chloride and 18C6 were prepared 12 h before use. Computation of the Nernst-Planck equation was performed using the finite element method program package COMSOL Multiphysics, version 3.5, equipped with the chemical engineering module (COMSOL Ltd., Hertfortshire, U.K.). THEORY Previously,13 we applied the Falkenhagen and Pitts model16-19 to take into account the deviation of the ion mobility from the absolute mobility with increasing concentration. For a 1:1 electrolyte, the actual mobility of the ith ion, ui (in units of 10-9 m2 V-1 s-1), can be expressed by ui ) u0,i -

(

8.20 × 105u0,i (εT)3/2

+

4.275 η(εT)1/2

(

)

I1/2 1 + 50.29a(εT)-1/2I1/2

)

I ) 1/2

∑z

i

ci

Ni(x, t) ) -Di∇ci(x, t) - ziuiFci(x, t)∇φ(x, t)

(3)

where Di (units m2 s-1), zi, and ui (m2 V-1 s-1) are the diffusion coefficient, the charge, and the mobility (calculated from eq 1) of each species involved. The relationship between the diffusion coefficient and the mobility of a species is given by Di ) uiRT/F. The electrical potential (in volts) is denoted by φ. For the one(space)-dimensional problem, the differential operator is defined as ∇ ) ∂/∂x, where x is the space direction across the width of the microchannel (see Figure 1). The evolution of concentration and potential with time is given by ∂ci(x, t) ) -∇Ni(x, t) ∂t

(4)

In order to solve eqs 3 and 4, an additional equation is required. For the present case we apply the electroneutrality assumption

∑ z c (x, t) ) 0

(5)

i i

Insteadofthesimpleelectroneutralityassumption,theNernst-Planck equation is often solved together with the Poisson equation, which links the spatial variation of the electric potential to the charge distribution. The later approach is more general and has wider applications.21,33 However, it has been shown that the electroneutrality assumption is justified for a direct liquid junction where the steady state develops rapidly,34-36 as may be the case in the two-stream microchannel flow cell used here. The system of equations was solved using the following boundary conditions. There was no flux across the channel wall at the left-hand and right-hand sides of the microchannel, i.e., for t > 0, x ) 0, and x ) w, the flux eq 1 is zero nNi(x, t) ) -n(Di∇ci(x, t)) + ziuiFci(x, t)∇φ(x, t)) ) 0

(1)

(6)

where 2

The flux Ni of each ion i under the influence of both an ionic concentration gradient and electric field gradient is described by the Nernst-Planck equation

(2)

where n is the normal vector to the boundary at x ) 0 and x ) w. For the potential, the boundary condition at t > 0 and x ) 0 was

i

is the ionic strength (mol dm-3). The absolute mobility, i.e., the limiting mobility at zero ionic strength, is denoted by u0,i, T is the absolute temperature, ε is the relative permittivity (78.36 for water), and η is the dynamic viscosity (1.002 × 10-3 Pa s for pure water at 298.15 K).29 The last term in eq 1 contains the ionic size parameter, a, which allows for the finite size of the ions. As previously discussed,13,30-32 a value of a ) 5 × 10-10 m was used. (29) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press LLC: Boca Raton, FL, 2004. (30) Bockris, J. O. M.; Reddy, A. K. N. Modern Electrochemistry 1. Ionics, 2nd ed.; Plenum Press: New York, 1998. (31) Geiser, L.; Mirgaldi, M.; Veuthey, J. L. J. Chromatogr., A 2005, 1068, 75– 81. (32) Li, D. M.; Fu, S. L.; Lucy, C. A. Anal. Chem. 1999, 71, 687–699.

φ(0, t) ) 0

(7)

while at x ) w we have n

-n(F

∑ z (-D ∇c i

i

i

- ziuiFci∇φ)) ) 0

(8)

i

The potential at the boundary at x ) 0 was set to zero for t > 0 in order to define a reference value for the potential. During an opencircuit potential measurement, there is no net current, which (33) (34) (35) (36)

Sokalski, T.; Lewenstam, A. Electrochem. Commun. 2001, 3, 107–112. Hafemann, D. R. J. Phys. Chem. 1965, 69, 4226. Mafe, S.; Pellicer, J.; Aguilella, V. M. J. Phys. Chem. 1986, 90, 6045–6050. Aguilella, V. M.; Mafe, S.; Pellicer, J. Electrochim. Acta 1987, 32, 483– 488.

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means that the boundary condition for potential at x ) w, eq 8, is equivalent to electrical isolation. To start the simulation, initial values for ci(x,t) and φ(x,t) were defined. The initial concentration profile (at time t ) 0 for 0 e x e w) of ion i was given by ci(x, 0) ) cib,l + (cib,r - cib,l)Ξ(w/2, δ)

(9)

where cib,l and cib,r are bulk concentrations of the ith ion in the left and right streams, respectively. Ξ(x,δ) denotes a smoothed version of the Heaviside function (unit step function) centered at x with a continuous second derivative implemented in COMSOL Multiphysics. Unlike the unit step function, which has a discontinuity at the step, the Ξ function is continuous over the whole range of definition. The function Ξ(w/2, δ) attains a value of zero for x < (w/2 - δ) and one for x > (w/2 + δ). By choosing a small value for δ, Equation 9 describes the concentration profile in the x-direction with a sudden jump over an interval of 2δ between the bulk concentrations of both streams at x ) w/2, the center line of the channel. A value of δ ) 10-9 m was chosen. Finally, the diffusion potential was calculated from the boundary potentials according to φd ) φ(w, t) - φ(0, t)

(10)

The description of ion transfer by eqs 3 and 4 incorporates the following assumptions: (i) transport by diffusion in the direction of the liquid flow (y-direction, see definition of coordinates in Figure 1) is neglected. The time scale for convection, using the channel length as a characteristic length and a flow speed of 0.033 m s-1 (corresponding to a volumetric flow rate of 1.67 × 10-9 m3s-1) is 0.45 s, compared to 22.5 × 106 s for the time scale of diffusion, taking a typical diffusion coefficient of 1 × 10-9 m2 s-1 into account. The much shorter time scale for transport by convection justifies the disregard of diffusional mass transport in the y-direction. (ii) The system is assumed to be homogeneous in the z-direction. The same assumption was used by Munson et al.12 together with a detailed discussion about the validity of the assumption for a microfluidic cell of similar geometry to the one used. (iii) Laminar flow is fully developed upon entry into the main channel and entry and exit effects on the flow are neglected.12 Kamholz et al.37 studied this entry effect by experiment and simulations for a very similar microfluidic device (“T-sensor”) to that used here and found that laminar flow was fully developed immediately upon entering the main channel. The COMSOL report containing the computation model is given in the Supporting Information. RESULTS AND DISCUSSION Potential Distribution in the Microchannel. Previously we have employed the Henderson equation15 to calculate the opencircuit potentials for the dual aqueous-stream microfluidic device, using the ion mobilities at finite concentrations calculated from eq 1 and taking into account the half-cell potentials of the silver-silver chloride electrode system in cases where chloride concentrations in both streams were different. In Henderson’s (37) Kamholz, A. E.; Schilling, E. A.; Yager, P. Biophys. J. 2001, 80, 1967–1972.

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Figure 2. Concentration profiles for coflowing streams of 10 mM KCl and 10 mM NaCl. K+, Na+, and Cl- concentrations are presented by solid, dashed, and pointed lines, respectively. The contact time of the streams are 0.001 s (A) and 0.45 s (B).

approach, a mixed zone between the two electrolyte solutions is assumed, with a linear change of ion concentration and timeinvariant concentration profiles within this zone. In publications on numerical solution of the NP equation using either the electroneutrality assumption20 or the Poisson equation,21 agreement has been found between the Henderson equation and the numerical calculations. This agreement was also found in our simulations. However, we are interested in the time-dependent development of the concentration profiles and potential across the contact zone between the two fluid streams as the liquids flow through the microchannel. Instead of a linear concentration profile between the spatial boundaries at x ) 0 and x ) w, which has been used as an initial condition recently,20 eq 8 mimics the situation at a short time, i.e., at the beginning of the channel, where a sharp concentration jump is expected at x ) w/2. From the volumetric flow rate and the dimensions of the main channel, the transit time for a cross-sectional volume element (in the x-z plane) in the channel can be calculated. Neglecting the outflow and inflow via the capillaries connecting the main channel with the electrode electrolyte reservoirs, which will be slow due to the high flow resistivity caused by the small diameter of the capillaries, a residence time of 0.45 s is calculated for a volume element to advance from the entrance to the exit of the main channel, employing a volumetric flow rate of 1.67 × 10-9 m3 s-1, as used in experiments. Calculated concentration profiles for the system 10 mM KCl in contact with 10 mM NaCl at times 0.001 and 0.45 s are shown in Figure 2. The concentrations of K+, Na+, and Cl- are presented by solid, dashed, and dotted lines,

Table 1. Absolute Ion Mobilites µ0,i14 and Mobilities µi in Aqueous Solution at an Ionic Strength of 10 mM, Calculated from Equation 1 ion species +

K Na+ Li+ Cl18C6-K+

µ0,i/10-9 m2 s-1 V-1

µi/10-9 m2 s-1 V-1

76.19 51.93 40.10 79.12 26.00a

71.99 49.23 37.40 74.86 25.30

a The absolute mobility for the 18C6-K+ complex was estimated by comparison to experiments.

Figure 3. Potential profiles for coflowing streams of 10 mM KCl and 10 mM NaCl at contact times of 0.001, 0.2, and 0.45 s (in order of decreasing slopes).

respectively. With increasing time, a broadening of the mixed zone at the channel center is observed. However, even at the longest time, when the streams exit the microchannel, the width of the mixed zone is smaller than the width of the channel (Figure 2B). The broadening of the mixed zone is unconstrained by the channel walls at x ) 0 and x ) w. The chloride concentration within the mixed zone has a maximum (greater than the Cl- bulk concentration) on the side of the stream carrying NaCl and a minimum (lower than the bulk concentration) on the KCl side. This distortion of the chloride concentration profile is due the higher mobility of K+ compared to the Na+ mobility (see Table 1). Figure 3 presents the potential profiles across the channel width at different times, which correspond to different locations along the length (y coordinate) of the channel. As found for the concentration profiles, the potential change is not affected by the width of the channel and therefore the Henderson equation may be used to describe the diffusion potential. Note also that the potential differences shown in Figure 3 do not depend on time (or location along the channel length). For the shortest time shown in Figure 3, 0.001 s, the calculated value of φd is in agreement with the potential at t ) 0.45 s. This is because the diffusion potential has a risetime of the order of 10-9 s.21,34,35 If absolute values for ion mobilities (as given in Table 1) are used, the diffusion potential for the system 10 mM KCl/10 mM NaCl is computed to be 4.4 mV, in agreement with the Henderson equation and numerical simulations from the literature.20,33 Because of ion-ion interaction, the actual mobilities calculated from eq 1 for 10 mM concentrations are 5-7% smaller than the

mobilities at zero ionic strength (Table 1). The effect on the diffusion potential in this case is minor, resulting in a slight decrease to φd ) 4.3 mV. The agreement between the numerical solution of the NP equation at all contact times while the two streams flow through the channel with the Henderson equation shows that the approach used in a previous report13 to analyze measured open circuit potentials for different ion concentrations and/or different ionic species is valid within the model assumptions. Influence of Ion Complexation by 18C6 on the Diffusion Potential. Next, attention is turned to investigate the effect on the experimental open-circuit potentials when the crown ether 18C6 is added to one alkali ion-containing aqueous stream of the dual-streamflow. These measurements are compared to calculated diffusion potentials made using the Henderson equation. Since the 18C6 is a neutral ionophore, a change of the diffusion potential for a 18C6-cation complex may be attributed to the complex having a different mobility from the uncomplexed cation. However, if the equilibrium constant for the 18C6-cation complex is low and/or if the complex has a mobility in solution similar to the solvated cation, the presence of the ionophore should have no noticeable influence on the diffusion potential. Figure 4 shows diffusion potential transient measurements (φd-t) between 10 mM KCl as a reference stream and costreaming injections of 10 mM KCl (Figure 4A), 10 mM NaCl (Figure 4B), and 10 mM LiCl (Figure 4C) solutions premixed with increasing concentrations of 18C6. The presence of 18C6 in the 10 mM KCl solution has a clear effect on the measured diffusion potential. It can be seen that with increasing 18C6 concentration, the diffusion potential increases (Figure 4A). In contrast, the diffusion potential between the reference stream and 10 mM NaCl (Figure 4B) or 10 mM LiCl (Figure 4C) remains unaffected upon addition of various concentrations of 18C6. It is well established that 18C6 is selective toward K+ since the diameter of the potassium ion and the diameter of the cavity of the polyether ring are similar, while the diameters of the sodium and, especially, of the lithium cations are smaller.24,38-40 The positive change of the diffusion potential in the potassium experiment is in line with a decrease in the mobility of the cation after complexation. The increase of the diffusion potential with increasing crown ether concentration (Figure 4A) is a consequence of the increasing fraction of 18C6-K+ complexes relative to uncomplexed (but solvated) K+ ions. The complexation reaction between the alkali ion M+ and the crown ether 18C6 is expressed by 18C6 + M+ S 18C6M+

(11)

In the following, the activities of all dissolved species are assumed to be unity, which does not introduce any appreciable error.41 Therefore the equilibrium constant Keq is Keq ) (38) (39) (40) (41)

[18C6M+] [18C6][M+]

(12)

Frensdorff, H. K. J. Am. Chem. Soc. 1971, 93, 600. Pedersen, C. J. J. Am. Chem. Soc. 1970, 92, 386. Christen, J. J.; Eatough, D. J.; Izatt, R. M. Chem. Rev. 1974, 74, 351–384. Dagade, D. H.; Kumbhar, R. R.; Patil, K. J. J. Solution Chem. 2008, 37, 265–282.

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Figure 5. Calculated (s) and measured (9) diffusion potentials between aqueous 10 mM KCl carrier solution and aqueous 10 mM KCl containing different 18C6 concentrations. The dashed and dotted lines are calculated diffusion potentials between aqueous 10 mM KCl carrier solution and 10 mM NaCl containing different 18C6 concentrations, using log10 Keq values of 0.3 and 0.8, respectively. The 2 are the measured diffusion potentials between aqueous 10 mM KCl carrier solution and aqueous 10 mM NaCl with different concentrations of 18C6.

[M+]0, respectively, eq 12 can be written as Keq )

Figure 4. Measurements of diffusion potentials between aqueous 10 mM KCl carrier solution and aqueous sample solution of (A) 10 mM KCl with 18C6 concentrations of 2.16, 3.52, 7.23, and 12.60 mM (from left to right); (B) 10 mM NaCl and 18C6 concentrations of 0.00, 4.92, 7.19, and 13.9 mM; (C) 10 mM LiCl and 18C6 concentrations of 0.00, 2.35, 5.75, and 10.00 mM.

where the brackets denote the concentrations of the species. In order to calculate the diffusion potentials, the concentrations of all ions in solution have to be known. With the employment of the initial concentrations of 18C6 and the cation, [18C6]0 and 8378

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R ([18C6]0 - R)([M+]0 - R)

(13)

where R is the concentration of the ligand-ion complex, [18C6M+]. Since the equilibrium constant is known from the literature, eq 13 can be solved for R and the concentrations of species in solution can be estimated. The diffusion potentials between the reference stream containing 0.01 M KCl and the sample stream containing three charged species M+, 18C6M+, and Cl- can then be calculated. While the absolute mobilities of alkali cations and Cl- are taken from the literature,14 the absolute mobility for the 18C6M+ complex is unknown and was used as a free parameter to fit the calculations to the diffusion potentials measured at different concentrations of 18C6 in 0.01 M KCl. For the equilibrium constant of the reaction between K+ and 18C6, log10 Keq values of 2.03, 2.06, and 2.19 were found in the literature.38,42,43 The log10 Keq value of 2.06 was used to calculate the ion concentration from eq 13. Figure 5 presents the experimental values of φd (9) together with calculated values (s) using an absolute mobility of 26.00 × 10-9 m2 s-1 V-1 s for the 18C6-K+ complex as an input parameter for eq 1. The initial concentration of K+, [K+]0, was 10 mM and the initial concentration of the crown ether, [18C6]0, was between 2.26 and 12.60 mM. Upon complexation with 18C6, the absolute mobility of the complex 18C6-K+ was ∼2.7-times smaller than that of K+ (Table 1). It should be noted that the calculation of diffusion potentials using either the Henderson equation or the NP approach (eqs 3-5) does not take into account chemical reactions occurring at the contact zone between the liquids. In the present case, the influence of complexation reactions between 18C6 from the sample (42) Izatt, R. M.; Terry, R. E.; Haymore, B. L.; Hansen, L. D.; Dalley, N. K.; Avondet, A. G.; Christensen, J. J. J. Am. Chem. Soc. 1976, 98, 7620–7626. (43) Patil, K.; Dagade, D. J. Solution Chem. 2003, 32, 951–966.

stream and K+ from the reference stream is expected to be minor because (i) the concentration of 18C6 in the sample stream is low, (ii) the contact time of 0.45 s between the two streams is relatively short, and (iii) one of the reactants (18C6) is neutral and its presence within the mixed zone has no influence on the diffusion potential. The equilibrium constant for the 18C6-Na+ complex is smaller than for the 18C6-K+ complex and values of 0.3, 0.8, and 0.82 for log10 Keq have been reported.38,42,43 With the use of log10 Keq ) 0.3 and log10 Keq ) 0.8, the diffusion potentials between the reference stream and a solution of 10 mM NaCl in the presence of different 18C6 concentrations (including zero concentration) were calculated. The results are given in Figure 5 by the dashed lines. Note that a diffusion potential is also now established in the absence of 18C6, due to the difference in mobilities of Na+ ions in the sample stream and K+ ions in the reference stream. Compared to the 18C6-K+ system, the influence of the 18C6 concentration is much smaller, as indicated by the low slope (Figure 5). Even at the highest concentration of 18C6 (12.6 mM), the diffusion potential increases by only 0.4 mV (log10 Keq ) 0.8) and 0.1 mV (log10 Keq ) 0.3) compared to the case where no crown ether is present in solution. This is because of the small fraction of the 18C6-Na+ complex in solution. For comparison, with initial concentrations of 10 mM 18C6 and 10 mM alkali ions, 45.7% of the K+ ions present will be complexed by the crown ether, but only 5.3% (log10 Keq ) 0.8) and 1.9% (log10 Keq ) 0.3) of the Na+ ions will be complexed. Furthermore, if we assume identical mobilities for the 18C6-K+ and 18C6-Na+ complexes, the differences in mobilities between the uncomplexed and complexed ions is 64% in the case of K+ and 50% for Na+. This difference in mobilities of complexed/uncomplexed ions also contributes to the small change in diffusion potential for the Na+ case. The measured values for the 18C6/Na+ system are represented by the 2 in Figure 5. These experimental values are ∼0.5 mV lower than the calculated potentials, in the presence as well as in absence of 18C6. This difference is attributed to the measurement instrumentation used. The diameter of the lithium ion (1.52 Å) is considerably smaller than the diameter of the cavity in the 18C6 ring (2.6-3.2 Å), and it is well established that 18C6 does not form host-guest complexes with lithium ions in water: no equilibrium constant data were found in the literature. Consequently, the diffusion potential is not influenced by the presence of 18C6, as shown in Figure

4C. CONCLUSIONS The distribution of potentials based on mobility differences and the influence of ion complexation on measured diffusion potentials at the boundaries between coflowing (but unmixed) aqueous streams have been investigated. The results of the studies show that under the prevailing conditions, i.e., of channel geometry and flow rate employed, open-circuit potential measurements can be analyzed in terms of the Henderson equation. The simulation study showed that the potential difference generated due to different ion mobilities across the channel did not vary with time or distance along the channel. A maximum and minimum of Clion concentration was found to occur, due to differences in the counterion mobilities. The microchannel device incorporating laminar flow and off-chip electrodes enabled continuous monitoring of open-circuit potentials. The influence of a complexation reaction on the diffusion potential was investigated using this microfluidic device. It was shown that complexation of alkali cations by crown ether ionophores could be detected using this simple electrochemical microfluidic structure. The agreement between calculated and measured diffusion potentials for different ions and concentrations was reasonable, with a deviation of ∼10% between calculated and measured diffusion potentials. Nevertheless, it is clear that ion complexation reactions influence the diffusion potentials measured. These simple electrochemical microfluidic measurements may provide a basis for ion detection devices in due course. ACKNOWLEDGMENT This work was supported by Science Foundation Ireland (Grant No. 07/IN1/B967) and the European Commission (Marie Curie Transfer of Knowledge Programme, Grant No. MTKD-CT-2005029568). M.M. was the recipient of a Science Foundation Ireland Science Teacher Assistant Researcher (STAR) award during summer 2007 (Grant No. 07/IN.1/B967STAR08). SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review May 15, 2009. Accepted August 29, 2009. AC901061R

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