Anal. Chem. 1995,67, 820-828
Diffusional Electrotitration: Generation of pH Gradients over Arrays of Ultramicroelectrodes Detected by Fluorescence Stefan Fiedler,t Rolf Hagedom,t Thomas Schnelle,t Ekkehard Richter,t Bemd Wagner,* and GUnter Fuhr*pt
lnstitut flsr Biologie, Humboldt-Universiklt zu Berlin, Lehrstuhl flsr Membranphysiologie, lnvalidenstrasse 43, 101 15 Berlin, Germany, and Fraunhofer lnstitut flsr Siliziumtechnologie, Dillenbuger Strasse 53, 14 199 Berlin, Germany
Electrode reactions near the surface of planar platinum and gold ultramicroelectrodes in aqueous electrolyte solutions were visualized by fluorescence microscopy. Millisecond pulses of direct current (0.5-5V dc) caused pH alterations in the vicinity of the electrodes and in the interelectrode gaps. These changes caused differences in the fluorescence intensity of fluorescein or of its dextran conjugate (MW 2 x lo6), allowing visualization. Redox reactions at the electrodes created pH gradient patterns on a micrometer and submicrometer scale. It is possible to delay the diffusional dissipation of the electrogenerated “protonation clouds” by adding up to 30% (w/v) poly(vinylpyrrolidone) (MW 7.5 x lo5). We used 50,20,10, and 3 pm wide electrode strips with either dc, pulsed dc, or dc-shifted ac (kHz-MHz) excitation. Steep pH gradients could be moved perpendicular to the electrode strip array. Traveling pH waves with speeds of about 1 “/s could be generated. We have developed a numerical procedure for modeling the time-dependentconcentration of electroadive species. The numerical pH patterns are in good agreementwith the experimentallyobtained ones. Electrotitration and its numerical modeling open new perspectives. Micro- and ultramicroelectrodes should find applications in analytical chemistry and biomedical research. Titration techniques within microcompartments may now be practicable. The visualization of cathodically driven electrodes is also useful for assessing the working state of microelectrode arrays. + -
Reactions occurring at electrodes are an important topic for research, especially with the development of electrodepositionand electrocoating technologies.’ The acidification of solutions at anodes and increasingpH at cathodes has been well-known since the early work of Davy.2 These processes can be used to establish concentration (including pH) gradients. Current-generated pH gradients have been visualized with colorimetric indicator dyes in solutions surrounding stainless steel microelectrode^.^ Recently, Engstrom and co-workers have used the pH indicator fluorescein with platinum disk and gold minigrid electrodes and
’ Humboldt-UniversitXt zu Berlin.
* Fraunhofer Institut fiir Siliziumtechnologie. (1) Bosso, J. F.; Zwack R R Electrodeposited organic coatings. In Encyclopedia of materials science and engineering; Bever, M. B., Ed.; Massachusetts Institute of Technology: Cambridge, MA,1986 pp 1427-1436. (2)Davy, H. Nicholsons J. Nut. Philos. 1800, 4, 275,326 1801, 7, 114. (3)Rand, R P.;Burton, A C.; Canham, P. Nature 1965, 4975,977-978. 820 Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
in an Al/Cu corrosion cell4 pH gradients are utilized in the isoelectric focusing of protein^,^ electrophoresis,G and isotachoph~resis.~ The growing interest in micrometer and s u b micrometer systems and electrode arrays8-” demands the scaling down of these techniques. Diffusion-limited currents become more important at the micrometer scale and have been put to practical Furthermore, the growing interest in small structures has led to a critical re-examination14J5 of some fundamental theoretical presumptions.’6J7 We are interested in microenvironments compatible with living cells and need to test procedures for the control and monitoring of pH in picoliter volumes. This paper focuses on methods for visualizing electrically produced pH shifts and modeling such shifts. For practical purposes in analytical chemistry, applied biology, and medicine,18-22such models have to be flexible enough to represent different experimental situations. Methods for adjusting the pH within microsystems include the electrogenerationof acids (EGA) and bases (EGB) in the vicinity of electrodes. The first examples of EGA and EGB usage in synthetic chemistry were described in the 1 9 8 0 ~ . 2However, ~~~~ (4)Engstrom, R C.; Ghaffar, S.; Qu, H. Anal. Chem. 1992, 64,2525-2529. (5) Righetti, P. G. Isoelectric focusing; Elsevier Science: Amsterdam, 1983. (6)Yarmush, M. L.;Olson, W. C. Electrophoresis 1988, 9, 111-120. (7) Gebauer, P.;Caslavska, J.; Thormann,W.J Biochm. Biophys. Methods 1991, 23, 97-105. (8)Manz,A;Graber, N.; Widmer, H. M. Sens. Actuators 1990, El,244-248. (9)Manz, A;Harrison, D. J.; Verpoorte, E. J. M.; Fettinger, J. C.; Liidi, H.; Widmer, H. M. Chimiu 1991, 45, 103-105. (10)Bissell, R A; Cordova, E.; Kaifer, A E.; Stoddart, J. F. Nature 1994, 369, 133-137. (11) Jacobson, S.C.; Hergenr6der, R; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994,66,1114-1118. (12)Heinze, J. Angew. Chem. Int. Ed. Engl. 1993, 32, 1268-1288. (13)Aoki, K Electroanalysis 1993, 5, 627-639. (14)Aoki, K;Morita, M.; Niwa, 0.;Tabei, H. J. Electroanal. Chem. 1988,256, 269-282. (15)Aoki, K Electroanalysis 1990,2, 229-233. (16)Bockris, J. O’M. Modern Electrochemistry; Plenum Press: New York, 1970. (17)Smith, C. P.; White, H. S. Anal. Chem. 1993, 65, 3343-3353. (18)Fromherz, P.;Offenhdusser, A;V e e r , T.; Weis, J. Science 1991,252,12901293. (19)W a s h , M. Micro Electro Mechanical Systems ’92 TravemPnde (Gemany) February 4-7,1992,IEEE Proceedings,IEEE Catalog No. 92CH3093-2,1992; 196-201. (20)Cooper, J. M.; Barker, J. R; Magill, J. V.; Monaghan, W.; Robertson, M.; Wilkinson, C. D. W. Biosens. Bioelectron. 1993, 8, xxii-xxx. (21)Schnelle, Th.;Hagedom, R; Fuhr, G.; Fiedler, S.; Miiller,T. Biochim. Biophys. Acta 1993, 1157,127-140. (22)Gavazzo, P.;Paddeu, S.; Sartore, M.; Nicolini, C. Sew. Acfuaton 1994,B1819,368-372. (23)Uneyama, K In Electrochemistry k Steckhan, E., Ed.; Topics in Current Chemistry 142;Springer Verlag: Berlin, 1987; pp 167-188. 0003-2700/95/0367-0820$9.00/0 @ 1995 American Chemical Society
these studies used organic solvents, which are incompatible with living cell systems. Accordingly, we used the classical redox reactions in aqueous solutions to generate pH gradients. The reactions responsible for the pH changes at the electrodes are the electrochemical reduction of water at the cathode (2Hz0 2e- = Hz 20H-) and oxidation at the anode according to @I20 2e- = ‘ / 2 0 2 2H+). The presence of a dissociating species like the disodium salt of fluorescein (denoted as FlNa2) will influence the concentrations of the ions.25 Our need to measure the pH near electrode surfaces was best met by fluorescent probes. These are usable at the micrometer size scale.4 The well-studied pH reporter fluorescein has high sensitivity in the pH range 5-9 (with excitation, 488 nm, and emission, 510 nm). This compound is a weak acid with pKs of 2.4, 4.6, and 6.7.26 In an electric field , the dissociated indicator ion migrates toward the anode, creating a concentration gradient and a pH gradient. Thus the fluorescence marker is both a cause and a reporter of pH shifts. Analytical solutions for electric-field-induced concentration gradients are only available for some special and, usually, quasitwo-dimensional experimental situations. For a soluble redox couple consisting of FeOD /Fe(IID in ferrocene, mathematical descriptions of cyclic voltammetric measurements were given by Aoki et They considered the steady state distribution of the soluble redox components within the field generated by interdigitated microelectrodes. Their analysis also assumes an infinite plane of electrodes so that edge effects can be neglected and that the equiconcentration profiles of reduced and oxidized species cross current lines. Equiconcentration profiles are analogous to the diffusion layers at electrodes’6 and with concentration 1aye1-s.~~ This study summarizes our experience with pH alterations at microelectrode surfaces caused by stationary and traveling electric waves. As a first application,we have used the results to visualize the working state of complex electrode arraysz8
+
+
+
a
feedback
n nr-scanning
Microscope
+
EXPERIMENTAL SECTION E-beam and photolithographically structured Pt and Au electrodes on silicon, SiO,N, , and Pyrex glass wafer surfaces were processed according to common procedure^.^^^^ Chips 8 x 8 mm carrying electrode arrays were bonded onto ceramic carriers (LCC-68, Kyocera Ceramic Co., Ltd., Kyoto, Japaqn) with 25 pm Au bond wire. Pads were covered with Epo-Tek 302-3 (Epoxy Technology Inc., Billerica, MA) to increase mechanical stability. Supply electrodes on the chip were, if necessary, isolated from electrode strip arrays by coating with colorless nail polish. Electrical contact was via a socket (Glyn GmbH, Iderstein, Germany). Disodium fluorescein and fluorescein isothiocyanate labeled dextran (FITC-Dx; molecular weight 2 000 000; Sigma) were used as 1.6 x M (equimolar to fluorescein) aqueous solutions. The (24) Utley, J. H. P. In Electrochemistry I; Steckhan, E., Ed.; Topics in Current Chemistry 142; Springer Verlag: Berlin, 1987; pp 133-165. (25) Diehl, H., Markuszewski, R Talanta 1 9 8 5 , 32, 159-165. (26) Slavik, J. In Fluorescence spectroscopu: new methods and applications. Wolfbeis, 0. S., Ed., Springer-Verlag: Berlin, 1993; pp 173-185. (27) Heinze, J.J Electroanal. Chem. 1 9 8 1 , 124, 73-86. (28) Fuhr, G.; Fiedler, S.; Miiller,T.; Schnelle, Th.; Glasser, H.; Lisec, T.; Wagner, B. Sens. Actuators 1 9 9 4 , A41, 230-239. (29) Reimer, IC;Kohler, C.; Lisec, T.; Schnakenberg, U.; Fuhr, G.; Hintsche, R; Wagner, B. Proceedings: Eurosensors VIII September 25-28, 1994. (30) Fuhr, G.; Arnold, W. M.; Hagedom, R; Muller, T.; Benecke, W.; Wagner, B.; Zmmermann, U. Eiochim. Eiophys. Acta 1 9 9 2 , 1108, 215-223. (31) Vasudevan, D.; Anantharaman, P. N . J Appl. Electrochem. 1 9 9 3 , 2 3 , 8 0 8 812.
BC
uOIcsCence microscope
generator
dc source I
b V max time
V cat
-
m ANODE for pulsed dc reglme
V cat
-
ANODE for chopped dc regime
J V cat
m
mW& -
offset interval
-
ANODE for pulsed and chopped dc regime, rasp. ac with offset
vcat
1
~
U
ANODE for asymmetric ac
tl
U 42-
Figure I. Scheme of the experimental setup and the used wave forms. (a) Schematic diagram of the experimental setup. (b) Electrode drive: The electrolytic concentration shifts at electrodes described in this paper depend solely on the dc part of the current. Possible wave forms that have been investigated are summarized.
instability of fluorescein under electrolysis conditions3* can be neglected when working with excess dye in solution. A stock solution of colorimetric pH indicator dyes was prepared32by dissolving phenolphthalein, methyl red, methyl orange, bromthymol blue, and thymol blue in ethanol at 0.2,0.4,0.6, 0.8, and 1.0% (w/v), respectively. This was adjusted to pH 6 (yellow) with 0.1 M NaOH. To increase the viscosity of the electrolyte/indicator system, poly(viny1pyrrolidone) (€‘I% MW 750 000; Serva) was added as 7.5,15, or 30% (w/v) aqueous solution. The ethanolic indicator mixture was diluted 1:l with 15%aqueous PVP. All solutions were made with HPLC-quality water. Indicator solutions were pipeted dropwise onto the electrode array and covered with a microscope cover slip. The general experimental setup was as depicted in Figure la. A confocal laser scanning microscope (CLSM; Aristoplan, Leica Lasertechnik GmbH) or an epifluorescence microscope (Axioplan, Zeiss; in conjunction with a video recording system) was used to observe fluorescence (488 nm excitation, 510 nm emission filter block). The applied current was pulsed to minimize gas evolution (to give time for electrogenerated oxygen and hydrogen to dissolve). Up to 16 individual electrodes were driven independently from a direct current (dc), pulsed dc, or dc-shifted ac source via a PC~
(32) M e , Y. Y. Spravocnik Po analiticeskoi khimii, 5th ed., Izdatel’stvo “Khimiya”, Moscow, 1979.
Analytical Chemistty, Vol. 67, No. 5, March 1, 1995
821
Fluorescence intensity units 3000 r
0’ 3
.
I
’
5
7
9
solution pH
Figure 2. Relative fluorescence intensity as function of the pH. The calibration curve was obtained by covering the microelectrodes with a thin layer of pH-calibrated fluorescein solution and measuring the intensity with the confocal laser scanning microscope at 510 nm wavelength (488 nm excitation).
driven multiplexer. The frequency (kHz-MHz) and amplitude (0.5-5 V,A.,A ) of pulses from a pulse generator TR-O332/D (EMG) or pulse/function generator 50 MHz-HP 8116A (Hewlett Packard) were monitored with an oscilloscope HP 54503A (Hewlett Packard) and manually regulated. Figure l b shows schematically some possible and actual electrode drives. In all cases, the time-average voltage is nonzero. Between measurements, electrode arrays were cleaned by rinsing with hot tap water, briefly covered with one drop of H,Oz/ HzS04 (1:4), and subsequently rinsed with HPLC-pure water. Nail polish was first removed with ethyl acetate, if necessary. RESULTS AND DISCUSSION
The pH vs intensity curve (Figure 2) was obtained for known pH of calibrating fluorescein solutions in.the experimental device. It was used to transform calculated pH values into intensities.The C U M proved to be valuable for obtaining vertically resolved intensity pictures at the electrodes. For the demonstration of traveling pH waves and the complex pattern generation discussed below, vertical resolution was not necessary: therefore, common epifluorescence equipment was used. We monitored the pH changes occumng when the microelectrodes were switched on (Figure 3). At first (Figure 3a), the horizontal electrodes were driven for 2 s as cathodes and the vertical ones as anodes. This time is sufficient to make a parabolic region near the cathodes alkaline. Then the field was reversed. After the transient stages shown in Figure 3b,c, the pattern in Figure 3d was obtained. Although the viscosity of the fluorescein solution was increased by additives, the transition between parts a and d of Figure 3 occurred within a period of only 5 s. To stabilize the observed “clouds”,we increased the molecular weight of the indicator by using the dextran conjugate. We also tried to introduce diffusion barriers by using agarose sols or polyacrylamide gels. We obtained the best intensity contrast and time stability with aqueous PVP. At 30% (w/v) PW, the viscosity of the solution is increased to 7.8 Pa s. The pattern of fluorescence intensity was shown to be due to pH by the use of the indicator dye mixture (no figure). The 822 Analytical Chemistty, Vol. 67,No. 5, March 7, 7995
indicator mixture surrounding the cathodes became blue (alkaline) and that near the anodes became red (acid). This pattern corresponds to the results obtained with fluorescence indicator dyes. Analogous acid~cation/alkalization depending on applied potential has been described for electrospraying droplets33and in the voltammetric analysis of weak acids in the absence of supporting ele~trolyte.~~ Figure 4a-c shows the fluorescence over an array of parallel electrodes. Every fourth electrode was driven as a cathode, and the remaining ones were driven as anodes. To demonstrate the possibility of moving pH patterns, the cathodic connections were stepped along the array. The situation in Figure 4d-f is similar, except that the polarity is inverted. The possibility of moving pH gradients seems to be promising for biomedical applications and can find applicationsin artiiicial signal transmission on living cell/ silicon junctions. We changed the field every 10 ms. The gradient “jumps”within this time interval by one electrode (10 pm). This gives a “speed of the whole pH gradient of 1 mm/s. The propagation speed of generated pH waves depends on the distance between the electrodes and on the drift velocity of the ions as well as kinetic parameters. A similar conclusion recently was made for electrochemiluminiscencegeneration at microelectrodes, however, caused by an other mechanism.35 To discover whether it would be possible to titrate solution over smaller electrodes, we tested arrays of 3 pm wide electrode strips spaced by 3 pm. Figure 5 shows that the extent of the pH gradient can be further reduced. It should be possible to generate defined gradients with submicrometer dimensions. This size range is of great importance for the applications mentioned above. At such dimensions, however, diffusion processes became more important (diffusion-limited current). pH clouds can also be generated over long interelectrode gaps. Figure 6 shows a structure where a central channel is bounded by two arrays of electrodes. The pH gradient spans the channel (50 pm width). There is great flexibility in pH gradient formation. We obtained quite different fluorescence patterns solely by changing the driving regime of the electrode array. Engstrom and colleagues, working on minigrid electrodes: observed a broadening of the fluorescence image. This suggested that pH changes could also be detected away from the electrode/ solution interface. To compare horizontal and vertical pH distribution over band microelectrodes, we have recorded intensity pictures using CLSM. Figure 7 shows the profiles. Whereas in Figure 7a the central electrode is driven as the anode, the same electrode is the cathode in the subsequent frames (b,c). The spatial distributions of the pH changes over the electrodes are clearly visible as cupola-like formations of changed fluorescence intensity. Their shape resembles that of the diffusion layers.l6bZ7The volume affected by the electrogenerated pH change for each of the 10 pm wide, 300 pm long cathodes is -120 pL (20 pm x 20 pm x 300 pm). As shown in Figure 5, even compartments in the femtoliter range could be electrotitrated. The analytical model best describing our experimental situation is that of A0ki.13-l~ However, it calculates only the steady state of an infinite electrode area and cannot be used to describe transient effects. Therefore, we used a numerical procedure (33) Gatlin, C. L.; Turecek, F. Anal. Chem. 1994, 66, 712-718. (34) Stojek, 2.; Ciszkowska, M.: Osteryoung,J. G . Anal. Chem. 1994, 66,15071512. (35) Collinson, M. M.; Wightman, R M. Anal. Chem. 1993, 65, 2576-2582.
I.
Figure 3. Video frames taken from an epifluorescence microscope (488 nm excitation, >510 n on wavelengths). pH indicator fluorescein isothiocyanate labeled dextran (MW 2 x 106),unbuffered in 7.5% (wh) aqueous poly(vinylpyrro1idone) in a thin layer over dc driven microelectrodes (3V) without current pulsing. The four planar gold microelectrodeswere 50 pm wide and perpendicularto each other: (a) Both vertical electrodes ns represent areas of high pH. (b-d) The are positively driven and the horizontal ones are negative. The parabolic-shaped fluorescence ormer dark anodic (acid) region becomes polarity is reversed. Progressively, the brightness around the vertical electrodes vanishes and bright. The time intervals between the single stages were a-b, 2 s; b-c, 1 s; and c-d, 2 s.
allowing us to calculate the time course of concentrations for an arbitrary electrode geometry. (See Figures 7 and 8 and details in the Appendix.) We have tested our numerical model with the help of the parallel electrodes (10 pm wide and 10 pm spaced) shown in Figure 4 . This allowed us to compare the calculations of Aoki (see Figure 8a) with our calculations (Figure 8 b,c). To verify our model, we have simulated the situation represented in Figure 7b,c. Aoki’s model (Figure 8a) gives a quantitative correspondence between the measured and the generated pH profile. The observed asymmetries between acidified and alkaline regions above the electrodes and the shape of the concentration profiles, however, are better modeled by our numerical procedure (Figure 8b-e). We have taken into account (i) the time course of gradient formation, (ii) the different (and pH-dependent) mobilities of the species, and (iii) the finite size of the device. Note that panels b and d of Figure 8 give the pH gradient over the electrodes; panels c and e show the appropriate fluorescence profiles corresponding to Figure 7b,c. We have found that the fluorescence just above the central cathode is less than expected although the most alkaline pH is predicted there (see Figure 8a,b,d). This is because the fluorescent species is an anion. Due to its negative charge, the indicator travels toward the anode where the pH is low and the indicator does not exhibit fluorescence. The experimental observed “float-
ing” of equiprotonationzones after prolonged electropulsing was well described by the numerical technique. As expected, we found, that the numerical calculations are very sensitive to the concentrations and the mobility parameters of the ions immediately after switching on the current. This could be used to deduce kinetic parameters and concentrations of analytes from their fluorescence data. Current-generated pH changes in microvolumesare candidates for applications in analytical chemistry and in living cell systems. The controllable dimensions of the “pH clouds” suggest exploitation as a quick diffusional microtitration method. Pico- and femtoliter samples can be titrated without pipet contact, in contrast cribed t e ~ h n i q u e . For ~ ~ applications spanning there are two main problems: (i) The fluoresepresent transient stages. That means the longer the field is switched on, the more fluorescein would be accumulated at the anodes. Finally, at steady state, most of the indicator would be near the anodes and fluorescence would no longer been observed. Under such circumstances, control of pH profiles by a feedback mechanism is necessary. (ii) Living systems are sensitive to dc fields. e use of the high molecular weight indicator FITC-Dx nded by a diffusion barrier can delay the electrophoretic depletion of the indicator at the electrodes. However, only with Analytical Chemistty, Vol. 67, No. 5, March 1, 1995
823
Figure 5. Video frame of an E-beam processed ultramicroelectrode array formed by platinum band electrodes on silicon. The electrode strips are 3 pm wide, the central gaps 3 pm, and the peripheral ones 9 pm. A thin layer of 4.1 mg/mL FITC-dextran (MW 2 x lo6 ) in 30% PVP (MW 7.5 x lo5)formed between chip surface and microscope slide was used as electrolyte. Electrodes were driven by repeated 200 ms sequences of pulsed dc (229 kHz, 5 Vpeak-to-peak) interrupted by 10 ms pauses of grounding the whole array. The actual polarities in the picture for the 16 left-hand electrodes from top to bottom wereas follows -, -, +, -, -, +, +, -, -, -, -. The 16 right-hand electrodes repeat the same pattern in the opposite direction.
+,
1-
I
Figure 4. Dependency of the fluorescence intensity pattern over an array of planar platinum band ultramicroelectrodeson the electrode polarities. The electrode widths and spacings are 10 pm. Electrolyte consists of 4.1 mg/mL FITC-labeled dextran (MW 2 x lo6) in unbuffered7.5% aqueous poly(vinylpyrro1idone)(MW 7.5 x 1 05).The fluorescence intensity images were generated with dc-shifted ac of 225 kHz (-5 V) and recorded with CLSM. Light regions correspond to alkaline, dark regions to acid pH. Every fourth electrode was connected together. In (a), every fourth electrode works as the cathode (bright); the intervening three dark ones worked as anodes. In (d), the polarity of the electrodes was inverted. (a-c) show respective sequential pattern of changed polarities, demonstrating traveling pH wave generation.
+, +,
+, +,
sign were held at a fixed potential while the others were switched on and off with that frequency. Our results show that there was no difference in generated pH pattern but a higher voltage was needed. Effective voltage (dc shift vs ground) was in the range of only 0.5-5 V. We found the best control of the effects in the case of dc-shiftedac. Another way to reduce possible cell damage is the shielding of electrodes by inert layers. For comparison, we used platinum microelectrode arrays covered with a thin ~ ~ 10 pm wide porous SiO,N, layer of -300 nm t h i ~ k n e s s .For electrode strips, no differences in the pH pattern could be detected. The fluorescence of the indicator dye mixture increases over cathodes and decreases over anodes; therefore, nonworking electrodes will not change the intensity of the solution covering them. Before use for chemical or biotechnological application, the working state of complex electrode arrays under static and dynamic conditions can so be visualized. We could observe disconnected or passivated electrodes28 and so check otherwise inaccessible electrode arrays in channel systems. The high fluorescence of alkaline fluorescein solutions means that cathodic driving is preferable for detecting the working state of electrodes.
immobilized indicator dye could a fluorescence intensity-pH feedback control be made. Additional salts would be necessary to generate the desired ion gradients. We stabilized these transient gradients by using chopped dc fields. Chopped fields have the advantage that by an appropriate choice of time intervals between different connection states it should be possible to design any continuous pH profile. This would be advantageous in analytical separation techniques such as isoelectric focusing. The second problem can be at least partly solved by chopping. As our experiences ~ h o ~ac ,fields ~ ~arel much ~ ~ better tolerated than dc ones. The loading of biological membranes can be minimized by applying high-frequencyac instead of direct current. On the other hand we have to take into account that the effects reported here depend on the dc part of the current only. Therefore, we have used dc fields, which were chopped with a frequency in the kilohertz to megahertz range. Electrodes of one
We have observed fluorescence changes of the pH indicator dye fluorescein and its dextran derivative over cathodically and anodically driven band microelectrodes of 50, 20, 10, and 3 pm width in arrays. The cause of such fluorescence modulation is the strong local pH pattern in the vicinity of electrodes during charge transfer. Colorimetric indicator dyes corroborated this finding. Current generated pH gradients can be obtained at electrodes and electrode interspaces. They can even be driven over unmet-
(36) Gratzl, M.; Yi, C . Anal. Chem. 1993,65, 2085-2088. (37) Fuhr, G.; Muller, T.; Hagedom, R Biochim. Bioflhys. Acta 1989,980,1-8.
(38) Fuhr, G.; Voigt, A; Muller, T.; Wagner, B.; Reimer, K.; Lisec, T. Proceedings: Eurosensors WZZ, September 25-28, 1994.
824 Analytical Chemistryl Vol. 67, No. 5, March 1, 1995
CONCLUSION
Figure 6. Different pH patterns, viewed as fluorescence intensity pattern over a double array of planar platinum microelectrodes (20 pm wide) recorded with CLSM. The electrodes were formed on silicon and coated, except at their tips, by an SiO& insulating layer. The whole was covered by a channel made from quartz glass. (a) shows the channel filled with electrolyte-indicator mixture in disconnected state. The dark corner on the lower side was caused by a hardened epoxy glue that entered the channel during construction. Smooth horizontal stripes are caused by channel fabrication in the quartz glass. In (b) and (c), the polarity of the two arrays is staggered (and shifted between (b) and (c)). In (d), opposite electrodes are of the same polarity. In (e) and (f), the array is connected as staggered pairs. In (g), the electrodes are connected in a staggered (2)-1-(3)-2 pattern. In (h), there is a staggered 1-(3)-1-(3) pattern, and in (i) this polarity is reversed. In (j), there is a staggered (4)-4 connection, and (k) shows the same at a later time. In (I), even as in previous pictures cathodic regions are light, anodic ones dark. The expansion of the pH clouds over the central gap region is clearly visible in (h), (i), and (k).
aliied and possibly transparent regions of a channel system, if the electrodes are suitably arranged. Our attempt to restrict diffusivity of reporter probes by conjugation with high molecular weight dextran and additional supplementation with inert polymer poly(vinylpyrro1idone) was effective. The generated fluorescence gradients reflect “true” surface pH values at ultramicroelectrodes
without surface modification in electrolyte systems consisting of only fluorescein or fluorescein coupled to dextran. The robust numerical modeling procedure was shown to be suitable for artificial concentration gradient design in electrode systems. The principles can be useful for microsystem develop ment, cell physiological research, or chemical analysis in minute Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
825
R. Ehwald and Dr. S. G. Shirley for stimulating discussions and critical reading of the manuscript. This work was supported by BMFT (Grants 0310260A and 13MV03032). APPENDIX
(a) General Information. pH gradients are generated by both electromigration and diffusion of the buffer constituents.The motion of ionic species produces current densitiesTi that are given by the Nemst-Planck equation: 39
where F is Faraday's constant, R and Tare the molar gas constant and absolute temperature, respectively, Y! is the electric potential, electrophoretic mobility, the total charge of the migrating species i, dissociation sequences of the form HMX
-
H+
+ X-
-
2H'
XOHN
Q
KH
I
color
I-
+ X2- ...
Q
M*H'
+ XM-
(2)
KAM
KA2
KA1
...
Q
N*OH-
KBN
+ XN+
the mean charge (aj) of a component j can be expressed via the dissociation constants ( K h for acids, KB=for bases, both for ampholytes): N
i
i=O
n
M
i
I n=O
1
c{n
1
i=o n=O
where N and M represent the possible dissociation steps (for simpler notations we used: KAO= KBO= 1). The general balance equation may be written as Figure 7. CLSM-observedfluorescence intensity profile of 4.1 mg/ mL fluorescein-dextran in 30% aqueous poly(vinylpyrro1idone)over planar platinum electrodes on SiO& recorded by CLSM using a relative intensity scale. (Electrode strip and interelectrodegap 10 pm wide). Electrodes were repeatedly driven with 400 ms dc, pulsed with 486 kHz (1.5 V amplitude), and 10 ms grounding interrupts: (a)The intensity pattern was recorded immediately after current connection; polarity from left to right, -_ (b) Polarity reversed, from left to right, (c) As (b), but the intensity pattern was recorded after longer equilibration. Note the "flying cloud' formation over cathodicdriven electrode as calculated in Figure 8c.
+ +.
+
qi is the rate at which a species is generated/consumed via chemical reactions. Fortunately, within the bulk solution this rate is zero for all components but water.40 (b) Numerical Information. Computational Flow Schema
samples. Their use as a remote checking procedure for ultramicroelectrode arrays was demonstrated.
(i) input: initial distribution of salt concentrations
ACKNOWLEDGMENT
(ii) calculationof the potential: eq 9 (with eq 8 )
We acknowledge contribution and practical support in all electronicwork by Mr. Stephan Schmidt. We are grateful to Prof. (39) Mosher, R A; Saville, D. h;Thormann,W. In The dynamics of electrophoresis; Radola, B. J., Ed.; ElectrophoresisLibrary; VCH Publishers Inc.: New York, 1992; pp 23-30. (40) Hagedorn, R.; Fuhr, G. Electrophoresis 1990, 11, 281-289. (41) Prentice, G. In Techniquesfor characterization of electrodesand electrochemical processes; Varma, R., Selman, J. R., Eds.; Wiley & Sons, Inc.: New York, 1991; pp 649-676.
826 Analytical Chemistry, Vol. 67, No. 5,March 1, 1995
+ +
(iii) calculationof the time-dependentchanges: eq 4 (with condition 11); increment of time; new H, OH (eqs 3 and 6)
Calculation of the Potential. For given concentration of the species (at fixed time) the potential expression \v (x,y,z) can be
Figure 8. Calculated profile over planar electrodes with interelectrodegaps of the electrode width dimension: (a) isoconcentrationplot calculated according to Aoki et aI.;l4 (b-e) gradients over band microelectrodes, modeled according to our numerical procedure (See Appendix), by assuming electrophoretic mobility of the dextran-conjugated fluorophore (FITC-Dx) to be 3 x 10-9 m2 s-l V-l, pKa= 2.4,23 U = 1.5 V, and T = 300 K; (b) pH gradients after 2 ms of unpulsed dc; (c) simulated fluorescence profile corresponding to (b); (d) pH gradients after 10 ms of unpulsed dc; (e) simulated fluorescence profile corresponding to (d).The gray scale values correspond to pH value (a, b, d) or to the fluorescence intensity (C, e) calculated from the corresponding pH values (b, d) using the fit function from Figure 2.
derived by integrating the law of charge conservation:
vxTi = 0;
species i = I, ..., n
(5)
1
To obtain eq 5, additionally electroneutrality
Cajq= o
(6)
i
was assumed. This is a good approximation in aqueous electrolyte
solution. Equation 6 and the dissociation constant of water (H*OH = can be used to substitute for the solvent parameters in the eqs 1, 3, and 4 and the following. To solve eq 5 we used a finite difference method; i.e., the integration space was divided into a sufficiently large number of volume elements. The electrolyte concentration inside each of them is assumed to be constant. Combining eqs 1 and 5 and approximating the resulting differential equation by the corresponding difference equation one gets for each volume element (AxAyAz) Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
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The resulting system of difference equations (6) is to be solved by the following iteration procedure (Gauss-Seidel): where the definitions of A, B and G are This procedure converges for 0 < w < 2 and has been found to be very robust if w = 1.75. If electrode kinetics are taken into account, then the potential in the thin layer immediately adjacent to the electrode surface (W,)is different from the electrode potential (Vel>:
y,= Ve, + 7 s
Lj&
+ ... +
- A x / ~ J J ~ , z ~ ) ] ...) (8)
with Lj = Fa$&tj and Dj = R M j a j . The index j represents the different electrolyte species and the notation Lj = (xi A d 2 , yi, zi) stands for the arithmetic mean between two adjacent volume elements; i.e. Lj(xi &/2yi,~i)= (Lj(Xi,yiJi)+ Lj(xi+lyi,~i))/2. TO complete eq 8 for the used dummy ... ..." two terms of the same form as that in the brackets in front of it, but with Dy and D, instead of D,, have to be introduced. Finally, the boundary conditions between neighboring volume elements have to be expressed in terms of Lj and D, : (1) If an electrode element is next to an electrolyte element other than the values of 4,Dj, and cj of that electrolyte element are continued into the electrode space. (2) If the element next to an electrolyte element is an edge element (e.g., in the x direction) then
+
+
Y (xi
+ h,yi,.zi) = Y (xi,yiti)
The overpotential rs,which modifies the boundary conditions, is of the order of 10 mV and depends on kinetic limitations. Although not considered here, it can easily be included by an equation of the Butler-Volmer type.41 Calculation of Time-Dependent Concentrations. After the potential is known, eq 4 can be evaluated for all volume elements. In order to make sure that the numerical algorithm does not "produce" molecules one has to adjust the time increment At such that for each element
(aCj(x;y)) At + ci(xi,yiyzi)t 0
"+ +
(no flow in this direction)
828 Analytical Chemistry, Vol. 67, No. 5,March 1, 1995
(10)
Vi,j
(11)
Furthermore, one has to take into account that both edge and electrode elements are not sources of electrolyte ions. Received for review July 26, 1994. Accepted November 30, 1994.@ AC9407476 @
Abstract published in Advance ACS Abstracts, January 15, 1995
