Complexometric Determination of Metal Ions by Microscopic

Anal. Chem. 1996, 68, 1580-1584

Complexometric Determination of Metal Ions by Microscopic Diffusional Titration Chen Yi,† Dongjie Huang,‡ and Miklo´s Gratzl*,†

Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106, and Electrical Engineering Department, The University of Texas at Dallas, Richardson, Texas 75083

Acid/base titrations of pico- and femtoliter microsamples have been performed previously using a diffusional microburet (DMB) for reagent delivery in a simple dropletheptane system (Gratzl, M.; Yi, C. Anal. Chem. 1993, 65, 2085-2088). The lowest delivery rate achieved with a DMB was about 6 fmol/s, which would correspond to about a 1 µL/year volumetric flow rate with a hypothetical equivalent mechanical delivery scheme (Yi, C.; Gratzl, M. Anal. Chem. 1994, 66, 1976-1982). In this work, the feasibility of complexometric titrations in microscopic samples is explored. Stability of pH in the microdroplets required for different determinations and the effects of DMB shank geometry on titration characteristics are also studied. Diffusional microtitrations of Fe(III), Zn(II), and Cu(II) have been performed with EDTA. Xylenol orange and Eriochrome Black T provide clear color changes at the end point of the respective titrations, despite the microscopic size of the samples (between 16 and 1570 pL, corresponding to diameters between 30 and 144 µm). Random errors of the determinations relative to full scale were 6.6% for Fe(III), 5.8% for Cu(II), and 7.9% for Zn(II). The pH required for EDTA titrations of the individual metal ions stays stable in the acidic range. This makes the microscopic titration of a number of metal ions, such as Fe(III), Fe(II), Cu(II), and Pb(II), feasible in a simple droplet-heptane system without any modification. With a higher density of strongly alkaline buffer droplets (about 100 droplets/mm2) sprayed on the bottom of the Petri dish, or by flushing N2 above the heptane, the microscopic samples can also be kept alkaline despite ambient CO2 present. In this way, Zn(II) can also be titrated in microdroplets, requiring a pH around 10. This work renders it possible to perform a variety of complexometric titrations and other chemical manipulations in microdroplets even if they need to be kept alkaline. Similar titrations in single biological cells to assess intracellular buffer capacities of different metal ions, such as Ca(II) and Mg(II), are underway. Diffusional microtitration has been used for precise acid/base, complexometric and precipitate titrations in the microliter sample range using a planar diffusion membrane for reagent delivery.1,2 A microscopic version of this technique has been developed for acid/base titrations in droplets of pico- and femtoliter volumes

using a diffusional microburet (DMB) for reagent delivery.3 A DMB is a glass micropipet with a gel plug in its tip which prevents convective flow but allows diffusional delivery. The microscopic samples were kept under heptane as shown in Figure 1 of ref 3. The reagent delivery rate of a DMB is typically equivalent to a hypothetical volumetric delivery rate of about 1 µL/year.4 Characteristics of this technique include (1) continuous delivery of the reagent into very small samples by diffusion (a spontaneous natural process), (2) precise delivery of very small amounts on the order of femtomoles, and (3) no induced change in sample volume (i.e., no dilution) during titration. In this work, the application of the DMB to perform complexometric titrations in microscopic samples is explored on the examples of Fe(III), Cu(II), and Zn(II) determinations in the picoliter sample volume range. The smallest amount titrated was 16 pmol of Fe(III) in a 16 pL microdroplet. The special challenge in microscopic complexometric titrations is the need to keep the pH stable in the microdroplets near the required value for the titration reaction to proceed properly. These values vary over a wide range depending on the metal ions: they are about 2.5, 5, and 10 for Fe(III), Cu(II), and Zn(II), respectively.5 The main interference to pH is caused by air CO2 that spontaneously dissolves into heptane and diffuses into the microdroplets through the droplet-heptane interface. This may rapidly change the pH of the sample because of the high surface/ volume ratio of a microscopic droplet. The pH, of course, will not be affected by air CO2 when the required pH is acidic, such as in Fe(III) and Cu(II) titrations (this was also the case in the microscopic acid/base titrations published earlier3). This work proves that it is also possible to determine metal ions (e.g., Ca(II), Mg(II), and Zn(II)) in microscopic samples whose titration reactions need buffering in the alkaline range. This can be realized by increasing the density of alkaline buffer droplets on the bottom of the Petri dish or by flushing N2 above the heptane. The results of this work render it possible to perform a variety of complexometric titrations and other chemical manipulations in microscopic samples, even if their pH needs to be kept alkaline. Similar titrations to determine intracellular buffer capacities of different metal ions, such as Ca(II) and Mg(II), in single biological cells are underway. EXPERIMENTAL SECTION Apparatus. The DMB for Fe(III) microtitrations (Figure 1A) was fabricated according to our earlier procedure.3 Fabrication of the DMB to titrate the other studied ions was similar, with a

†

Case Western Reserve University. The University of Texas at Dallas. (1) Gratzl, M. Anal. Chem. 1988, 60, 484-488. (2) Gratzl, M. Anal. Chem. 1988, 60, 2147-2152. ‡

1580 Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

(3) Gratzl, M.; Yi, C. Anal. Chem. 1993, 65, 2085-2088. (4) Yi, C.; Gratzl, M. Anal. Chem. 1994, 66, 1976-1982. (5) Reilley, C. N.; Schmid, R. W. Anal. Chem. 1958, 30, 947-953. 0003-2700/96/0368-1580$12.00/0

© 1996 American Chemical Society

Figure 1. Diffusional microburet with different tip geometries. (A) DMB with a conical tip. (B) DMB with a cylindrical tip.

slight modification that produced a cylindrical tip (Figure 1B) instead of a conical one. The modified procedure was as follows: (1) a long carbon fiber (Zoltek, Co., 7.5 µm in diameter, about 12 cm long) was suctioned into a borosilicate glass capillary (A-M System, Catalog No. 6010) by low vacuum; (2) the capillary was single pulled with a PB7 Narishige microelectrode puller; (3) the extending part of the fiber was cut to about 1 cm in length from the capillary tip with a pair of scissors; (4) the tip of this pipet was kept inside an agarose solution (Sigma, Agarose Type VII, gelling temperature, 26-31 °C) at about 40 °C while the carbon fiber was pulled out from the capillary’s back end; and (5) after the tip of the pipet was taken out of the gel solution and cooled down to gelling temperature, the pipet was back-filled with the reagent solution by a Microfill (nonmetallic thin syringe needle for filling micropipets, World Precision Instruments, Inc.). To eliminate the air bubble usually present at the gel-reagent solution interface inside the DMB after back-filling, high pressure (2-3 atm) was applied to the internal solution by a syringe through a plastic tube connected to the capillary’s back end until the bubble dissolved into the reagent (about 10 min). All titrations were recorded in gray scale by a VCR (NEC PVS98A) through a TV camera (LTC-48, Ikegami Tsushinki) attached to the microscope (Nikon, Diaphot) with a ×10 objective lens. A band pass optical filter (center, 520 nm; bandwidth, 28 nm) was used for Cu(II) microtitrations, and a long pass filter (cut-on wavelength, 600 nm; LL-600-A-B860, Corion) was used for Zn(II) microtitrations, to increase the sensitivity of the system to the color changes of the respective indicator dyes. The other apparatus was similar to that described earlier.3,4 Reagents. Analytical grade reagents were purchased from Sigma, Aldrich, and Fisher. All solutions were prepared with virtually carbon dioxide-free distilled water (16-17 MΩ cm). Methods of pH Stability Tests. To test pH stability in microdroplets under heptane, first the bottom of a Petri dish was covered with a thin layer of heptane (about 2 mm). A simple water nebulizer was then used to spray droplets (20-200 µm in diameter) with a desired pH value (adjusted by NaOH or HCl) containing 0.001 M EDTA, 0.1 M KNO3, and a suitable pH dye (specified in Table 1) onto the bottom of the Petri dish. The solution contained no additional pH buffers beside EDTA, to render the pH change and its observation faster. The Petri dish was then placed on the stage of an inverted microscope, and the color of the droplets was monitored. If the pH of a droplet crossed

the color transient range of the pH dye, a color change was observed. To prove that the observed acidification was induced by air CO2, N2 was used to flush the surface of the heptane for 20 min after the acidification, and the pH status of the acidified microdroplets was monitored. Methods of Microscopic Complexometric Titrations. To stabilize the size of droplets in heptane, a large number (about 100/mm2) of pH-buffered droplets similar to the sample droplet were made to cover the bottom of the Petri dish, to keep the heptane saturated with water, and also to maintain the pH value of the sample droplet when higher than 7. The actual sample droplet was pressed out from a pulled micropipet under the heptane. The titration starts when the DMB is moved into this droplet by a micromanipulator. The gray scale image of the droplet is recorded by a VCR during the titration and digitized by a computer later. The color change due to the indicator dye is determined by image processing of digitally stored frames. The other experimental details were described earlier.3 RESULTS AND DISCUSSION pH Stability of Microscopic Droplets in Heptane. The minimum pH for effective titration of various metal ions by EDTA varies with the metal. For Mg(II), Ca(II), Cu(II), and Fe(III), these values are about 10, 8, 3, and 1, respectively.5 It is easy to keep the pH constant by using a suitable pH buffer in a conventional titration, or even in a diffusional microtitration performed in the microliter sample range. Therefore, complexometric titrations can be performed in a proper pH buffered sample solution in samples with volumes down to about 1 µL without any difficulties.1 A simple pH buffer, however, may not be strong enough to maintain the necessary pH in microscopic droplets, due to their large surface/volume ratio and fast spherical diffusion of CO2 toward a microdroplet in heptane. Stability of pH in microdroplets under heptane has been tested, and the results are reported in Table 1. We found that the pH will stay stable if it is lower than about 7, and it will gradually change to lower pH when it is initially higher than about 8. (The resolutions of the measured pH values are determined by the transient range of the pH dye used, listed in Table 1.) In the third experiment in Table 1, N2 was flushed above the heptane surface for about 20 min after the color had changed from blue to yellow (from pH ) 11 to pH < 8). As a result, the color of the droplets changed back to blue again. This proved that CO2 is responsible for the acidification of the microdroplets and that the diffusion of CO2 into the droplets through the heptane layer from air is reversible. The pKa1 value of H2CO3 is 6.37.6 When the pH of the sample is lower than this value, it will not be affected by absorbed CO2, since dissociation of H2CO3 in the microdroplets will then be negligible. Therefore, very little CO2 will be absorbed at all. For EDTA titration of some of the metal ions, such as Zn(II), Ca(II), and Mg(II), a pH higher than 6.37 is needed. We tried to pretreat heptane with dispersed Ca(OH)2 solution to absorb CO2 for 24 h and then use this Ca(OH)2-saturated heptane to cover the microdroplets just before the beginning of the experiments. The density of microdroplets on the bottom of the Petri dish was about 10/mm2. However, this pretreatment did not work very well: the color of a droplet containing Eriochrome Black T and Mg(II) (6) Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1993-1994; pp 8-47.

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Table 1. pH Stability in Microdropletsa expt no.

pH in µ-droplets

1b 2c

1.8 7.0

3b

11.0

pH indicator

pH transition range

initial color

final color

bromophenol blue (5 × 10-4 M) bromocresol purple (5 × 10-4 M) + bromothymol blue (5 × 10-4 M) thymol blue (5 × 10-4 M)

3.0-4.6 (yellow to blue) 5.2-6.8 (yellow to purple) 6.0-7.6 (yellow to blue) 8.0-9.6 (yellow to blue)

yellow blue

yellow blue

blue

yellow

a The pH in the microdroplets was monitored by a pH dye to see the effects of air CO absorption. The pH was adjusted to the required initial 2 value by HCl or NaOH. The time needed for color change was about 7 min in experiment 3. The density of the microdroplets on the bottom of the Petri dish was about 20 droplets/mm2, with diameters of 20-200 µm. b The droplets contained 0.01 M EDTA. c The droplets contained 0.1 M KNO3.

buffered at pH ) 10 would still change from red to blue in a few minutes without addition of EDTA. The only reason for this color change can be that the pH changes from 10 to a lower value.7 It seems that the relatively thin heptane layer with a large surface area above the microdroplets inside the Petri dish cannot prevent CO2 from acidifying the microdroplets in the expected time frame of a titration. Therefore, ambient CO2 plays an important role in pH stability of the microdroplets when this pH should be higher than 7. The difficulty of maintaining the pH in microscopic droplets in the alkaline range lies in the nature of diffusion-limited mass transport of CO2 toward a spherical microdroplet, which becomes more efficient with smaller droplet radius. This is similar to mass transport around a spherical microelectrode when a potential step is applied to oxidize or reduce electroactive species around the electrode. The equation8 to describe this process is

J ) DC [1/(πDt)1/2 + 1/r]

(1)

where D is the diffusion coefficient of CO2 in heptane, r is the radius of the microdroplet, C is the bulk concentration of CO2 in heptane, J is the flux of CO2, and t is time. This equation is valid as long as free CO2 concentration is negligible in the droplet, i.e., as long as it is alkaline. A droplet on the bottom of a Petri dish is schematically shown in Figure 2. In order to qualitatively describe CO2 transport from heptane to such a droplet, CO2 transport can be thought of as consisting of two parts, one being semispherical diffusion and the other approximately cylindrical, as shown in Figure 2. Because semispherical diffusion is much more effective than cylindrical diffusion when the diameter is very small, the cylindrical component can be neglected. Therefore, the ratio (R) of the total mass flux to the microdroplet and its volume (V) is

R ) JA/V ≈ [3DC/(2r)] [1/(πDt)1/2 + 1/r]

(2)

where the surface area, A, is approximated by that of the semispherical part of the droplet. When t is large enough,

R ≈ 1.5DC/r2

(3)

This ratio, R, for a picoliter microdroplet is about 104 times larger than that for a microliter droplet. This explains why CO2 plays (7) Ringbom, A. Chemical Analysis: Complexation in Analytical Chemistry; Interscience Publishers: New York/London, 1963; p 85. (8) Bard, J. A.; Faulkner, L. R. Electrochemical methods: fundamentals and applications; Wiley: New York, 1980; p 145.

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Figure 2. Schematic diagram of CO2 diffusion patterns around a truncated spherical microdroplet in heptane on the bottom of a Petri dish. The droplet contains an alkaline solution.

such an important role in the pH stability of microscopic samples in the alkaline range. Based on this approximate diffusion model, to minimize the interference by CO2, we can either decrease the concentration of CO2 in heptane by flushing N2 above its surface or increase the density of microdroplets on the bottom of the Petri dish to change the semispherical diffusion pattern around each microdroplet to planar diffusion toward a monolayer of microdroplets. Planar diffusion follows Cottrell’s equation and is much less efficient. Complexometric Microtitrations. Xylenol orange was used as the indicator for Fe(III) and Cu(II) microtitrations and Eriochrome Black T for Zn(II) determinations. In general, a sharp, clear end point can be obtained with the respective dye for microdroplets with diameters above 30 µm when the dye concentration is around 10-3 M. Because of the short optical path length (30-150 µm), it would be difficult to monitor the color change if lower dye concentrations were used. When Fe(III) was titrated with EDTA at pH 2.5, we could not observe the expected color change of xylenol orange from blue to orange in a reasonable time period. This can be explained by the fact that the reaction used for end point indication (eq 4) is so sluggish that even in boiling solution, the indicator must be regarded as being blocked.9

Fe(III)-XO (blue) + Y S Fe(III)Y + XO (yellow)

(4)

(Here Y stands for EDTA and XO for xylenol orange.) Due to this circumstance, back titration was tried with Fe(III) as the

reagent in the DMB and EDTA as the sample in the microdroplets. Figure 3A shows a typical back titration curve reconstructed from digitized gray scale images of a microdroplet taken during a titration. Each point corresponds to the average gray level at the same area in the droplet at different times. The droplet contained 241 fmol of EDTA in a volume of 241 pL, corresponding to a diameter of 77.2 µm (the compositions of the sample droplet and the reagent in the DMB are given in the caption of Figure 3). The concentration of EDTA is similar to that of xylenol orange in the sample droplet. Therefore, the amount of Fe(III) required to induce the color change of xylenol orange itself needs to be determined and excluded from the end point determination. The

absolute stability constants of the Fe(III)-EDTA9 and Fe(III)xylenol orange complexes10 are 1025.1 and 105.7, respectively. Even at pH ) 1, the effective stability constant for the Fe(III)-EDTA complex9 would then still be 107.9. This means that the Fe(III) ions delivered by the DMB will first react with EDTA, and the Fe(III)-xylenol orange complex will form only after almost all the EDTA in the microdroplet is consumed. Therefore, the chemical equivalence point of the titration curve, where the amount of delivered Fe(III) equals the initial amount of EDTA, is around intercept R of the titration curve in Figure 3A. Then, a transient period follows where the dye changes from one form to the other by combining with additional Fe(III) ions. The higher the concentration of the dye, the longer this transient period is. Because the concentration of xylenol orange in our sample is comparable to the concentration of EDTA, it is obvious that intercept R is the best choice for the end point of the titration. Intercept β of the curve is the end point of the titration of xylenol orange, and the time at that point equals the total time needed for titrating both the EDTA and xylenol orange. Experiments with conventional macrotitration using the same solutions and the same optical detection scheme have also been performed and gave similar results. This proved that the above interpretation of the R and β intercepts is correct. A titration curve of Zn(II) is presented in Figure 3B. EDTA was used as reagent in the DMB, since in this case the direct microtitration of the metal ion was not blocked by the indicator. The composition of reagent and sample are described in the figure caption. Many droplets containing the same pH buffer as the one in the sample were sprayed on the bottom of the Petri dish first to prevent pH in the sample from falling, as discussed above. The density of these buffer microdroplets was about 100/mm2, corresponding to an average distance on the order of 50-100 µm between neighboring drops (depending on their randomly distributed size and location). With an approximate diffusion coefficient of 10-5 cm2/s for CO2 in heptane, the individual semispherical diffusion domains will then fully overlap after a few seconds, resulting in a planar pattern of overall diffusion. This is why, when 0.1 M ammonium chloride was used as pH buffer, we found that the required pH will stay stable in the sample droplets for over 1 h. The end point for direct microtitrations of Zn(II) is at intercept β. Because the Zn(II)-EDTA complex is more stable than the Zn(II)-Eriochrome Black T complex, the delivered EDTA will combine with the free metal ions while inducing the ion-dye complex to disassociate accordingly. The equivalence point will be at the time when almost all the metal ions are combined with EDTA and almost all the dye molecules are free. This is at intercept β in Figure 3B, where all the dye changes to the free form. To analyze the indication scheme, identical titrations have been performed in macrosamples using the same sample/dye composition and the same optical setup coupled with conventional volumetric reagent delivery. This resulted in an absolute determination of the end point, proving that the above interpretation of intercept β is also correct. Direct microtitrations of Cu(II) have also been performed, with the end point determination similar to that of Zn(II) microtitrations. The solution compositions are given in Table 2. The pH

(9) Schwarzenbach, G.; Flaschka, H. Complexometric titrations; Methuen & Coltd: London, 1969; pp 236-238.

(10) Dean, J. A. Lange’s handbook of chemistry; McGraw-Hill Book Co.: New York, 1985; pp 5-91.

Figure 3. Typical reconstructed titration curves for back and direct complexometric microtitrations. (A) Microscopic back titration. Sample droplets: 0.001 M EDTA + 10-3 M xylenol orange + 0.1 M KNO3, acidified by HCl addition to pH ) 2.5. Reagent: 0.01 M FeCl3 + 0.1 M KNO3, acidified by HCl addition to pH ) 2.5. The sample diameter was 77.2 µm. A DMB with a tip i.d. of 7.5 µm and a membrane thickness of about 80 µm was used. 2, The delivered Fe(III) reacts with EDTA in the sample; 0, the delivered Fe(III) combines with xylenol orange; +, EDTA and xylenol orange are unavailable. The end point is the intercept of the linear section of regions symbolized with triangles and squares. (B) Microscopic direct titration. Sample: 10-3 M ZnCl2 + 0.1 M KNO3 + 0.1 M NH4Cl + 5 × 10-4 M Eriochrome Black T, pH ) 10. Reagent: 5 × 10-2 M EDTA + 0.1 M KNO3 + 0.1 M NH4Cl, pH ) 10. 2, The delivered EDTA reacts with free Zn(II) in the sample; 0, the delivered EDTA combines with Zn(II) disassociating from the Zn(II)-xylenol orange complex; +, no more Zn(II) is available. The end point is the intercept of the linear sections symbolized with squares and crosses.

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Table 2. Calibration Characteristics of Different Complexometric Microtitrations calibration graph

ions

sample pH

shank geometry

titration type

vol (pL)

Fe(III)a Cu(II)b Zn(II)a

2.5 5.0 10.0

cone cylinder cylinder

back direct direct

16-446 457-1570 131-943

sample range concn amt (M) (fmol)

teq range (s)

slope (s/fmol)

bias ( 95% confidence interval (s)

regression coefficient (r2)

full-scale relative error (%)

0.001 0.001 0.001

32-281 191-1091 185-799

0.62 0.73 0.72

19.5 ( 28.3 -100 ( 144 131 ( 77

0.95 0.94 0.90

6.6 5.8 7.9

16-446 457-1570 131-943

a The respective solution compositions in Fe(III) and Zn(II) microtitrations are given in Figure 2. b The compositions for Cu(II) microtitrations are (1) reagent, 5 × 10-2 M EDTA + 0.1 M KNO3 + 0.05 M sodium acetate; (2) sample, 10-3 M CuSO4 + 0.1 M KNO3 + 0.05 M sodium acetate + 5 × 10-4 M xylenol orange.

inside the reagent and the sample were adjusted to 5 by HCl or NaOH. Sodium acetate was used as pH buffer. All the calibration data are presented in Table 2. Linearity of the fitted curves was very good in all cases in the picoliter range, similar to the results reported earlier for microscopic acid/base titrations.3,4 For Fe(III), Cu(II), and Zn(II) titrations, we used a VCR to record the entire titration and then digitized the first frame at exactly the beginning of each titration. The uncertainty of starting time formerly encountered due to low image acquisition rate3 has been, therefore, overcome in these experiments. The tip diameter (i.d.) of the DMB used here is 7.5 µm, much larger than the ones reported earlier,3 and the geometry of the DMB tip is also different due to the new pulling procedure. The performance of this DMB, however, is similar to earlier results.3,4 This proved that tip geometry and diameter can be widely changed to fit the needs of different sample amounts. This also implies that no blocking of the tip by heptane occurs, even when the tip diameter of the DMB is around 7.5 µm, i.e., about 7 times larger than those reported earlier.3 Different DMB Shank Geometries and Their Effects on Reagent Delivery. Earlier, a standard silanization procedure was used to decrease the number of hydrophilic surface groups on the outer surface of the tip and shank of the DMB.3 This prevented the sample droplets from getting “pulled up” by adhesion forces to the outer DMB surface during titration. In some cases, however, even silanization was not sufficient to prevent this from occurring. In this work, DMBs with cylindrical tips were used in some of the experiments (Cu(II) and Zn(II) microtitrations) to decrease the pulling force due to adhesion. We found that these DMBs, even without silanization, did not pull up droplets with diameters reported in Table 2. Other reasons to use the procedure to make the DMB with a cylindrical tip are that (1) this way it is easy to fabricate DMBs with a tip opening larger than 5 µm, (2) it is easy to reproduce DMBs with identical tip size and geometry, controlled during fabrication by the inserted carbon fiber, and (3) the region in the DMB that limits mass transport is well defined: it is the small cylindrical tip alone. For a cylindrical diffusion membrane, the linear calibration curve intersects the vertical time axis at t° (t° ) lm2/3Dr, where lm is the thickness of the membrane, and Dr is the diffusion coefficient in the membrane2). The lower limit of the linear section

of the calibration graph for a cylindrical diffusion membrane can be considered to be at t° if it is expressed in end point time.2 The diffusion-limiting part of the modified DMB is the cylindrical tip, about 50 µm long in this work. The corresponding t° is around 0.8 s (the diffusion coefficient used is 1 × 10-5 cm2/s) according to eq 6 in ref 2. Then, the expected nonlinear transient (on the order of a few times t°) is still insignificant compared to the duration of a typical microscopic titration.

(11) Yi, C.; Bright, G. R.; Gratzl, M. Proceedings of the 15th Annual International Conference of IEEE/EMBS, San Diego, September 1993; IEEE: Piscataway, NJ, 1993; pp 1572-1573.

AC950636M

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CONCLUSIONS The work presented here proves that complexometric diffusional microtitrations can be performed in a wide pH range for many different metal ions. It is feasible to carry out back and direct complexometric microtitrations with relatively high dye concentration, still providing accurate and precise end point determination. DMBs can be fabricated with a cylindrical tip, providing another way to define the diffusion-limited region in the DMB. Another important conclusion is that microscopic droplets under heptane can be kept alkaline despite ambient carbon dioxide present. This makes, among others, acid/base titration of alkaline microsamples and also other chemical manipulations by a DMB requiring higher pH feasible. Because of the microscopic size of a DMB tip and the adjustable delivery rate, this technique can also be used for studying physiological processes on the single cell level. Such applications are clamping intracellular ion concentrations, determining intracellular buffer capacities, titrating the total amount of certain ions inside a single cell, and enforcing a constant influx of ions or drug molecules into a single cell.11 ACKNOWLEDGMENT The authors gratefully acknowledge D. L. Wilson for providing access to the imaging equipment and software in his laboratory, where a part of data evaluation has been performed. X. F. Fang also assisted in some experiments. This work was supported from the funds of the Elmer Lincoln Lindseth Chair of Biomedical Engineering at Case Western Reserve University and from Grant CA-61860 of the National Institutes of Health. Received for review June 26, 1995. Accepted February 14, 1996.X

X

Abstract published in Advance ACS Abstracts, April 1, 1996.