2085
Anal. Chem. lQQ3,65, 2085-2088
Diffusional Microtitration: Acid/Base Titrations in Pico- and Femtoliter Samples Miklds Gratzl. and Chen Yi Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106
Diffusional microtitrationemploys controlled diffusion to deliver reagents into ultramicrosamples. Precise acid/base, complexometric, and precipitate titrations in the microliter sample range have been performed with this technique earlier. In this work, a further decrease in titratable sample size by 7 orders of magnitude has been achieved. A diffusional microburet is made from a glass capillary pipet by placing a miniature agar gel plug in its tip (1-2-pm outer diameter) and backfilling the pipet with the reagent. With this device, acid/base titrations of femtomole amounts in femto-and picoliter samples have been performed. Sharp end point detection was achieved with a color indicator mixture. Reagent delivery by the microburet as a function of time was linear (regression coefficient, P 2 0.99) over a broad sample range. An amount as small as 29 fmol of nitric acid could be precisely determined in a 1.9pL droplet. The smallest sample volume successfully titrated was 700 fL containing 42 fmol of the acid. Typical precision of the technique is about 2% full-scale error. Mechanical titration becomes inaccurate when samples smaller than about 100 p L are to be determined. This is due in part to parasitic diffusive reagent delivery from the immersed tip of the microburet into the sample solution. The significance of this uncontrollable process with respect to convective delivery increases when sample size is reduced to the microliter range. Much effort has been spent to avoid, or to implement different corrections for, this parasitic diffusion.3 Droplet-by-droplet reagent delivery that would completely eliminate the problem is difficult to realize on an ultramicroscale.4 One of the problems in this case is that extremely small droplets tend to repel each other because of enhanced surface tension, which would lead to an irreproducible reagent loss. Instead of eliminating spontaneous diffusion, it is easier and more straightfward to block convection and use diffusion itself for delivery. This fact is recognized in diffusional microtitrationlvz,which employs controlled reagent diffusion for continuous titration of extremely small samples. This is achieved by placing a diffusion membrane between a reagent reservoir and the ultramicrosample, thereby blocking convection but enabling diffusivereagent deliveryintothe sample. Precise acid/ base, complexometric, and precipitate titrations have been performed with this technique in the microliter sample range.112 This 2-3 orders of magnitude (1) Gratzl, M. Anal. Chem. 1988, 60,484-488. (2) Gratzl, M. Anal. Chem. 1988,60,2147-2152. ( 3 ) Treatise on Analytical Chemistry; Kolthoff, I. M., Elving, Ph. J., Eds.; Wiley-Interscience: New York, 1975; Part I, Vol. 11; Part 11, Vol. 11. (4) Steele, A. W.; Hieftje, G. M. Anal. Chem. 1984,56, 2884-2888. 0003-2700/93/0365-2085$04.00/0
decrease in accessible sample size with respect to existing techniques was accomplished with extremely simple equipment and the proper use of spontaneous phenomena like diffusion and capillary forces. In this work a further 7 orders of magnitude decrease in titratable sample size has been achieved with the principles of diffusional microtitration: continuous titration of femtomole amounts has been accomplished in femto- and picoliter droplets. This technique can find applications in the chemical analysis of extremely small samples such as substances available in minute quantities (products of microsyntheses, expensive materials), parta of precious objects (archaeologic artifacts), or samples gathered in space exploration (Moon and Mars rocks) or to titrate even single biological cells.
EXPERIMENTALSECTION The essentialpart of the apparatus used for diffusional titration of droplets in the microliter range consists of a planar diffusion membrane cast into a hole in a planar sheet of inert substrate that holds the sample droplet centered above the membrane. The bottom of the membrane and holder is in contact with the reagent solution (see Figure 1 in ref 2). To implement diffusional microtitration for the analysis of picoliter droplets with diameters in the micrometer range, both the apparatus and sample handling had to be modified. For reagent delivery, a glass capillary micropipet is used whose tip is filled with a miniature diffusion membrane. This device is called a diffusional microburet. To prevent quick evaporation, sampledropletsare kept under a hydrophobictransparent liquid. Titration begins when the tip of the microburet is moved into the droplet to be analyzed (Figure 1). Apparatus. The fabrication of a diffusional microburet consists of the following steps: (1)double pulling a borosilicate glaea capillary (A-M Systems, Catalog No. 6010)with a micropipet puller (Narishige, PB-7) to obtain a pipet shape shown in Figure 1B; (2) heating a 1%agarose solution (made of purified agarose Type VII, Sigma) to transparency (70 O C ) in an isotemperature oven (Fisher,Isotemp 500 Series);(3)cooling the agarosesolution to about 34O C by keeping it in the slowly cooling oven; (4)touching the surface of the agar solution with the pipet tip, still in the oven, by using a simple coarse micromanipulator (Narishige);(5) when gelling begins, the pipet is taken out and backfilled with the reagent solution. This must be done quickly to prevent the thin (10-100 pm) agar membrane inside the pipet tip from drying. The tip diameter can be adjusted from 0.1 to 10 pm by choosing appropriate parameters for the double pull. In this work, 1-2pm-0.d. tips were used. After step 1,it is advisable to implement a standard silanization procedureSs6to decrease the number of hydrophilic surface groups on the inside and outsideof the pulled glass capillary. This prevents agar from sticking to the outer surfaceof the microburet tip and the sampledropletsfrom getting “pulled up” by adhesion forces onto the outer buret surface at the beginning of titration. For this latter reason, the transfer micropipets were also silanized. An individual ready diffusional microburet can be used for subsequent titrations until it accidentally breaks. Because of (5) Deyhimi, F., Coles, J. A. Helu. Chim. Acta 1982, 65,1752-1759. (6) Ammann, D. Ion-Selective Microelectrodes: Principles, Design
and Applications; Springer-Berlin, 1986; p 112. 0 l9g3 American Chemlcal Soclety
2088
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
A. from light
heptane
-
sample
t
plastic Petri dish
B. agar gel membrane I , 1-2 pm I
t
I
100-200 pm reagent in aqueous solution about 80 pm Flgure 1. Experimental arrangement for diffusional microtitration of femto- and picoliter size sample droplets. (A) Basic arrangement. The transparent Petri dish is placed on the stage of a microscope. The diffusional microburet is held and moved with a three-axis fine micromanipulator. The aqueoussample droplet to betitratedis attached to the bottom of the dish and kept under a hydrophobic transparent liquid (heptane was used in this work). (B) Diffusional microburet (displayed with its approximate dimensions). 28 is the taper angle of the pulled tip.
the enormous difference between the volume of the analyzed femto- and picoliter droplets and that of the diffusional microburet and since the reagent is always more concentratedthan the samples, the titrations themselves do not induce any noticeable reagent depletion even if repeated many times. With carefulhandling, hundreds of droplets can be analyzedover many days with the same buret. If not in use, its tip may be kept immersed in its own filling reagent solution while the other end of the glass pipet is plugged with an inert wax or silicon grease so that evaporation or carbon dioxide absorption is minimized. This way the reagent may remain undepleted for the entire lifetime of the buret. Another way to keep the buret operation unchanged is daily renewal of its reagent filling. In the experiments reported here this latter method was used throughout. Before analyses, the ready diffusionalmicroburet is attached to a three-axishydraulicmicromanipulator(Narishige,MO-203) mounted on an inverted microscope (Nikon, Diaphot). The sample droplets are made, kept, and titrated under heptane (Aldrich,99 % ,spectrophotometricgrade)in a transparent plastic (polystyrene)Petri dish (Fisher, 100 X 15 mm) placed on the stage of the microscope. For instrumentalend point detection, digital image processing was used to monitor color change of an indicatordye in the titrated droplet. ATV camera (LTC-48,Ikegami Tsushinki)was attached to the microscope, and PixelGrabberand Pixelstore (Preceptics) were used for transferring and storing the digitized images (frames)in a computer (Macintosh IIfx). Commercialsoftware (DIP station made by Hayden Image Processing Group and PixelTools from Perceptics) was used for image processing. Reagents. Analytical grade reagents used were from Sigma (bromocresolblue), Aldrich (bromocresol purple), Fisher, and Mallinkrodt (basicchemicals). The solutionswere prepared with virtually carbon dioxide free distilled water (16-17 MQ cm). Procedure. The bottom of the Petri dish is covered with a large number of smallwater droplets (20-200-pmdiameter, about 20 droplets/mm2)using a simple water nebulizer. The tip of the diffusional microburet is then moved into one of the larger dropletswith the hydraulicmicromanipulator,to keep the surface
of the diffusion membrane hydrophilic while the dish is filled with heptane (presaturated with distilled water) up to a height of about 2 mm. The water droplets in the dish will keep the heptane saturated with water during the experiments. Another micropipet with an open tip (about 1-pm 0.d.) is inserted into the heptane with a mechanical micromanipulator (Narishige)close to the bottom of the dish, and a sample droplet is made by pressing a microdroplet of sample solution out of this pipet with a connected syringe. While still attached to the pipet tip, the droplet is perfectly spherical, and hence, its volume can be determined by measuring its diameter with a microruler under the microscope. To obtain more precise data, in this work diameters were measured on the large screen of an attached video monitor that has been previously calibrated for magnification. Then, the microdropletis moved to touch the bottom of the dish where the adhesion forces “trap” it, and the micropipet can be withdrawn. The apparent sample diameter on the bottom may become slightlygreater than the diameter found previously, due to a larger than 0”contact angle between aqueous solutions and the plastic bottom of the Petri dish under heptane. To perform a titration, the diffusional microburet is moved from the water drop through heptane into the freshly prepared sample droplet. Titration begins in the instant when the microburet tip enters the sample. End point detection is performed by visual observation of the appearance of transition color of the absorption dye in the sample or by image processing of digitally stored frames acquired during each titration at a fixed frequency (1frame/4 5). After a determinationis done, the tip of the diffusionalmicroburet is moved into the next sample. For calibration, the sample-making micropipet is filled with a known solution and used to prepare “samples” of different volumes. For calibrating with solutions of different concentrations, separatemicropipetsare used for each solution. To analyze a real microsample,it must be transported into the heptane with a clean micropipet and titrated with a previously calibrated diffusional microburet. After the entire sample is pressed out of this transfer pipet, it is attached to the bottom of the dish, as shown in Figure 1.
RESULTS AND DISCUSSION In this work the feasibility of diffusional microtitration of femto- and picoliter samples has been tested, using the experimental arrangement in Figure 1. Acid/base titrations were performed with a base (KOH) as reagent and an acid (HN03) as sample. To monitor the titrations and detect their end point, a color indicator dye was added to the samples in a final concentration low enough so that titration of the pH dye itself could not interfere with the main titration reaction. Thus, changes in optical absorbance had to be monitored at a low dye concentration and in extremely small droplets, with diameters of a few tens of micrometers. This means that optical path lengths in the order of 10-100 pm were to be encountered. For these reasons, very little absorbance (and even smaller changes in absorbance) could be expected to occur. Therefore, a sensitive dye with sharp end point indication had to be chosen. Such is the mixture of bromothymol blue and bromocresol purple, with a yellow to purple color change at pH 6.7. Nitric acid was in at least 60-fold excess with respect to this dye mixture in the samples in all experiments. Despite the unfavorablecircumstancesfor optical detection, the color change at the end point could be clearly seen under the microscope in each titration. This means that titrating picoliter sampleswith a diffusional microburet, and indicating these titrations with an absorbance dye, are both feasible. The time elapsed from the beginning of reagent delivery to the end point (“end point time”) could now be visually determined. Since a calibration graph with reasonable linearity with respect to sample amount was obtained with this simple visual indication method, the implementation of an instrumental end point detection scheme seemed worthwhile.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
2087
diameter, d (pm) 10
801 ! h W
0-
60 :
30
20
, /
-regression line .............95% confidence interval
4-99
$
.+ Y
5
6
0 a
a
5
h
3
~,
,
,
. .
,
,
,
, . . . . , . .
. .
,
. .I
30 40 50 time (s) Figure 2. Diffusional microtitration of 520 fmol of HN03 in a 8.7-pL droplet. Sample: 0.06 M HNO3 5 X lo4 M bromothymol blue and bromocresol purple 0.1 M KNOB. Reagent: 0.2 M KOH 0.1 M KN03. Sample diameter before touching the bottom of the Petri dish was 25.5 pm. A diffusional microburet with a tip outer diameter of 1.5 pm and a membrane thickness of about 80 pm was used. (A, top) Digitized grey-scale images of the sample at different time instants: t = 0 at the beginning of titration. The diffusional microburet is seen penetratingthe droplet from the right side. (B, bottom)Reconstructed titration curve. Numbers indicate corresponding images in (A). The average grey level of the same 4 X 4 pixel2( ~ 1 . pm2) 7 area near the center of the droplet was computed for each image, to obtain the experimental points in (B).
+
20
+
volume, V (pL)
+
240
1601.. . . . 0 10
20 :
sample amount, S (fmol) Figure 3. Calibration curve of the diffusional microburetused in Figure 2. Sample droplets: 0.06 M HNO3 4- 5 X lo4 M bromothymol blue and bromocresolpurple 0.1 M KN03. Reagent: 0.2 M KOH 4- 0.1 M KN03. The upper horizontal axis is calibrated for drop diameter.
2
1
.E
40 :
.+
+
Figure 2A displays a succession of digital grey-scale images of a 8.7-pL sample droplet containing 520 fmol of HN03while being titrated with KOH. The reagent is delivered from a microburet by diffusion. The visible movement of the buret tip within the sample droplet in the course of the recorded titration is spontaneous, induced by a change in adhesion force between the outer glass surface and the sample, and between the sample and the bottom of the Petri dish, respectively. These two simultaneous effects make the droplet ultimately adhere to the buret tip more strongly upon alkalinization. This is evidentfrom the significant difference between an acid versus an alkaline aqueous solution in the respective contact angles observed under heptane. Figure 2B shows the titration curve reconstructed from these images: each point represents an average grey level computed for a smallarea inside the droplet at different times. No change in color (and, consequently,in digitized grey level) was observed from image 1to 2. Thus, the instrumentally detected titration curve begins with a flat section and then exhibits a sharp end point that can be determined accurately with standard procedures. Such is the technique of fitting a polynomial spline to the data points and determining the minimum of the (smoothed) first derivative. With this procedure, a diffusional microburet has been calibrated by using it to titrate droplets of different volumes, all made of the same nitric acid solution (Figure 3). This
calibration curve exhibits an excellent linearity (with a regression coefficient, r2 = 0.99) in the picoliter/femtomole sample range. This fact proves that diffusional reagent delivery from the microburet occurs not only in a reproducible way but also in a steady state. The initial transient period (in terms of both concentration profile within the buret tip and net reagent flux) must be leading very quickly to steady transport conditions, because otherwise no linearity could have been achieved. From this conclusion it also followsthat the sampledroplets must be effectively homogenized during the entire titration process. The mechanism of this homogenization could be diffusion itself, since diffusion distances within the sample are extremely small, in the order of 10 pm. As a worst case estimate, the diffusion coefficient of KN03, D = 1.85 X lo" cm2/s can be used with the approximate formula, r = (Dt)1/2 where r is the radius of the droplet. Then, for a 20-pmdiameter sample, t = 0.05 s is obtained for the time necessary for completediffusive mixing. This is better than satisfactory for the time scale of our titrations. In this calculation, the buret tip was assumed to be in the center of the titrated droplet. This arrangement induces spherical diffusion of the sample in the direction of a point sink in the center. Thus, real diffusive mixing must be even much faster than the above estimate, which was obtained with a formula valid only for a much less efficient planar diffusion. In addition, diffusion of HN03 can only be faster than that of KN03. Hence, purely diffusive mixing itself must have been instantaneous in each titration performed in this work. Based on visual observations, however, a convective mechanism is likely to contribute to mixing; stirring inside the ultramicrodroplets visibly occurs. This is possibly due to local density gradients close to the buret tip. Spontaneous microvibrations may contribute to this effect, induced by building and air vibrations present in any laboratory. Besides excellent linearity, the precision of the determinations is also remarkable: standard deviation of the experimental data points from the fitted regression line is 2.4 s, which corresponds to only a 4 % full-scale error. Since the start of the individual titrations was not synchronized with the 0.25-Hz image acquisition frequency, a significant part of this already small random error is simply due to the limited temporal resolution of digital data processing. The standard deviation of 4-s-wide uniform statistical distribution is 2/3lI2 (7)Hundbook of Chemistry and Physics; Weast, R. C.,Ed.;CRC Press: Boca Raton, FL, 1985-1986, p F-47.
2088
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
= 1.2 s. After subtracting this from the apparent standard deviation, we obtain 1.2 s, or only 2% full-scale error. This is the experimentally observed true precision of diffusional microtitration of femtomole acid samples, over a very broad (from about 30 to loo0 fmol) range. The 5.48-s bias found (t, = 5.48 s when S = 0) may be due to a brief initial period needed for the removal of a thin hydrophobiclayer of heptane from the surface ofthe diffusion membrane and for establishment of a hydrophilic connection between the buret tip and the aqueous sample droplet. Taking, however, into account the 4 sf frame image acquistion rate used in this work, the true bias may be rather 7.48 s. Initial blocking of titration would thus last for about 7-8 s. After this period reagent delivery would begin, with a transient in mass transport leading quickly to steady-state operation. The width of the 95% confidence interval at S = 0 is about 6 s (or f 3 8). This is similar to the calculated bias itself. Thus, the very significance of a positive bias in end point time, as well as the tentative interpretation of this bias as outlined above, will have to be further investigated. Given the at least 60-fold excess in sample over indicator concentration, the indicator error in each titration was about 1.5 % This systematic error does not affect either precision or accuracy,since it is cancelledby the calibration procedure.
.
CONCLUSIONS The unique design of the diffusional microburet as introduced in this work expands the range of titratable samples down to the femtoliter and femtomolar range. The delivery rate of reagent from this device is constant, apart from a short initial period needed probably for establishing a hydrophilicconnection between microburet and sample. This period (lasting, at most, for a few seconds) is followed by an even shorter mass transport transient that quickly leads to steady-state reagent delivery. The femto- and picoliter samples are effectively homogenized during titration by spontaneous processes (diffusion within the droplets, convective stirring induced by concentration gradients, and microvibrations). These circumstancestogether lead to linear calibration characteristics. It is interesting that such small aqueous droplets are easy to prepare, maintain, and keep physically and chemically stable under a hydrophobicliquid if it is saturated with water. Despite the droplets’ huge specific surface area (e.g., 6,000 cm2fcm3for a 10-pm droplet), no interference was observed by either carbon dioxide or any acidlbase functionalities of the plastic surface of the Petri dish used in this work. The lack of any observable carbon dioxide interference can be explainedby the following considerations: (1)Samples of a strong acid were titrated that can absorb carbon dioxide up to only trace concentrations. (2) The titration end point in such solutions is virtually unaffected by the weak acid present. (3) The extremely small surface area of the agar gel plug exposed to heptane between titrations can only extract a negligible amount of carbon dioxide, which gets immediately neutralized by the highly concentrated reagent base within the buret tip. It is also surprising that the outer surface of the miniature diffusion membrane within the buret tip stays hydrophilic
when it is being moved from one aqueous droplet to the other through heptane. Any hydrophobic covering layer quickly clears off when the buret is inserted into the next aqueous sample. It is advisable to adjust the ionic strength of the reagent so that it approximately matches that of the samples. This avoids large differences in osmotic pressure between sample and reagent that could otherwise displace the diffusion membrane. Capillary forces and surface tension are also extremely strong on the micrometer scale. Since surface tension tends to minimize the surface of any aqueous droplet in a hydrophobic medium, a significant pressure, in our experiments 2-3 atm, had to be applied in order to press a droplet out of an open tip micropipet used for sample preparation or transfer. A sample droplet of similar size must be exerting at least the same amount of pressure (in the reverse direction) on the diffusion membrane during titration, provided that differences in osmotic pressurecan be neglected. Thus, the mechanical integrity of agar gel and the strength of its adhesion to the interior wall of the glass pipet tip are extraordinary on the micrometer scale. On the other hand these forces render our samplesperfectly spherical while attached to the transfer pipet. Without this effect, it would be difficut to determine precise sample volumes. Another unexpected conclusion of this work is that optical absorption dyes can be employed to detect end points in droplets of the size of biological cells. This is helped by the fact that since reagent delivery occurs solely by diffusion, the volume of the sample and, hence, its optically important dimensions do not vary during an analysis. The smallest amount titrated in this work was 29 fmol of nitric acid; the smallest sample volume analyzed was 700 fL. In this work mostly picoliter samples have been determined. According to preliminary studies, titration of nanoliter samples is also feasible with a diffusional microburet with a larger tip diameter. Thus, diffusional microtitration can be used to precisely (and with prior calibration, accurately)titrate samples from a few hundred femtoliters to tens of microliters. The dynamic range of the technique encompasses at least 8 orders of magnitude, which is a remarkable performance for a linear technique. Purely diffusive reagent delivery, if properly controlled, is a powerful tool for analyzing extremely small samples. As the sample volumes used in this work may suggest, future applications will possibly include, among others, titration of single biological cells.
ACKNOWLEDGMENT The authors gratefully acknowledgeD. L. Wilson for access to the imaging equipment and software in his laboratory, where a part of the data evaluation has been performed. This work was partly supported from the funds of the Elmer Lincoln Lindseth Chair of Biomedical Engineering at Case Western Reserve University. RECEIVED for review January 13, 1993. Accepted April 19, 1993.
