Soap Bubbles in Analytical Chemistry. Conductometric Determination

Soap bubbles provide a fascinating tool that is little used analytically. With a very low liquid volume to surface area ratio, a soap bubble can poten...
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Anal. Chem. 2006, 78, 2786-2793

Soap Bubbles in Analytical Chemistry. Conductometric Determination of Sub-Parts Per Million Levels of Sulfur Dioxide with a Soap Bubble Tinakorn Kanyanee,†,‡ Walter L. Borst,§ Jaroon Jakmunee,| Kate Grudpan,| Jianzhong Li,† and Purnendu K. Dasgupta*,†

Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Lubbock, Texas 79409-1051, and Department of Chemistry, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Soap bubbles provide a fascinating tool that is little used analytically. With a very low liquid volume to surface area ratio, a soap bubble can potentially provide a very useful interface for preconcentration where mass transfer to an interfacial surface is important. Here we use an automated system to create bubbles of uniform size and film thickness. We utilize purified Triton-X 100, a nonionic surfactant, to make soap bubbles. We use such bubbles as a gas-sampling interface. Incorporating hydrogen peroxide into the bubble provides a system where electrical conductance increases as the bubble is exposed to low concentrations of sulfur dioxide gas. We theoretically derive the conductance of a hollow conducting spherical thin film with spherical cap electrodes. We measure the film thickness by incorporating a dye in the bubble making solution and laser transmission photometry and find that it agrees well with the geometrically computed thickness. With the conductance of the bubble-making soap solution being measured by conventional methods, we show that the measured values of the bubble conductance with known bubble and electrode dimensions closely correspond to the theoretically computed value. Finally, we demonstrate that sub-ppm levels of SO2 can readily be detected by the conductivity change of a hydrogen peroxidedoped soap bubble, measured in situ, when the gas flows around the bubble.

Bubbles are part of our everyday experience. Soap bubbles are easy to create; children, and perhaps more than a few adults, enjoy the evanescent iridescence of a soap bubble.1 Soap bubble walls consist of a layer of water sandwiched between two layers of surfactant molecules where the hydrophilic ends point to the water layer and the hydrophobic ends face the gas side.2 * Corresponding author. E-mail: [email protected]. ‡ Permanent address: Department of Chemistry, Chiang Mai University, Chiang Mai 50200, Thailand. † Department of Chemistry and Biochemistry, Texas Tech University. § Department of Physics, Texas Tech University. | Chiangmai University. (1) Cassidy, J.; Stein, D. The Unbelievable Bubble; Klutz Press: Palo Alto, CA, 1987.

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In chemical education, soap bubbles have long served as elegant demonstration tools.3 Conglomerations of soap bubbles placed on a transparency are readily projected overhead to serve as molecular models.4 The force required to move soap bubbles on the surface of water is particularly small; this property has been used for sensing minuscule amounts of force. The literature describes experiments that demonstrate the paramagnetism of O2 and the diamagnetism of N2 in which the respective gas-filled soap bubbles move toward and away from a magnet.5 The nearly frictionless movement of bubbles is also the basis of measuring gas flow with “soap bubble meters”.6 Soap bubbles have been used as highly sensitive pressure transducers and to study gas flow.7 In a more exotic vein, both the flame speed and unburned gas velocity ahead of a methane-burning flame were measured simultaneously using soap bubbles and a hot-wire anemometer.8 The movement of bubbles has been used in many engineering studies for flow visualization.9-11 Soap bubbles have other alluring properties that make them attractive for exploration by an analytical chemist. They represent easily created thin membranes in which other polar or nonpolar substances can be readily dissolved and thus impart other properties to the film. Such bubbles should provide, for example, an interesting means of investigating selective transport of vaporphase compounds through the bubble wall. Optically, a gas-filled soap bubble represents a higher refractive index (RI) medium bounded by lower RI gas. The optical transmission characteristics along the film of a large-diameter soap bubble should therefore be particularly interesting. Soap bubbles also provide uniquely large surface area-to-volume ratio. It is this last aspect that we wish to exploit in the present paper. (2) Isenberg, C. The Science of Soap Films and Soap Bubbles; Advanced Education Toys Ltd.: England, 1978; pp 17-23. (3) Williams, K. R. J. J. Chem. Educ. 2002, 79, 1168-9. (4) Raemme, G. Educ. Chem. 1992, 29, 159-60. (5) Matsuyama, Y.; Yasuoka, T.; Shimada, H.; Mitsuzawa, S.; Sasaki, T. Kagaku to Kyoiku 1995, 43, 716-7. (6) Guo, J.; Heslop, M. J. Flow Measure. Instrum. 2004, 15, 331-4. (7) Cummins, K. J. Chem. Educ. 1991, 68, 617-8. (8) Sakai, Y., Nippon Kikai Gakkai Ronbunshu B-hen 1987, 53, 3785-91. (9) Kessler, M.; Leith, D. Aerosol Sci. Technol. 1991, 15, 8-18. (10) Qiu, S.; Simon, T. W. Proc. Intersoc. Energy Conv. Eng. Conf. 1992, 27, 5517-21. (11) Kakuta, Y.; Adachi, H.; Tanaka, N.; Matsuto, T.; Haikibutsu, G. R. Haikibutsu Gakkai Ronbunshi 1997, 8, 22-30. 10.1021/ac052198h CCC: $33.50

© 2006 American Chemical Society Published on Web 02/23/2006

first and then compare the predictions with experimental conductance values measured for soap bubbles prepared with a nonionic soap solution containing various concentrations of H2SO4. We then prepare bubbles containing H2O2 and flow air containing various concentrations of SO2 around the bubble for periods up to 10 min and show that sub-ppm concentrations of the gas are readily sensed by the bubble extraction conductivity cell. PRINCIPLES Conductivity of a Hollow Sphere with Spherical Cap Electrodes. Referring to Figure 1, consider the cross sectional view of a hollow bubble of uniform wall thickness δ and radius rb. The electrodes at the polar caps each have an arc length 2re such that the arc re subtends an angle θo radians at the center of the bubble. It should be noted that rb . re . δ. A voltage V is applied between the two electrodes. Ohm’s law in differential form states that the current density BJ is related to the specific conductance σ and the electric field strength E B by

BJ ) σ‚E B

(1)

Equation 1 can be rewritten in the following form by noting that the current density BJ and field E B point along the meridians of the bubble between the polar caps:

dI/dA ) σ‚(dV/ds) Figure 1. Model of a soap bubble of radius rb and wall thickness δ with spherical cap electrodes of half arc length re subtending an angle of θ0 radians at the center of the bubble.

(2)

where dI is the current that flows along a meridian through an area dA given by

dA ) δrb sin θ dφ In this laboratory, we have used small liquid drops or a wiresupported film repeatedly for situations where an analyte is extracted into a liquid drop/film from another fluid stream.12-21 The surface area to contained liquid volume ratio for a soap bubble is in fact far more attractive than such drops or films. One extant patent utilizes soap bubbles to remove pollutants from an air stream.22 Other than this, we are unaware of any applications, especially analytical applications, involving the extraction of an analyte. The illustrative example that we have chosen for the present exposition is to monitor the bubble conductometrically. Two small electrodes of circular cross section touch the bubble on opposite sides and the conductivity is measured. As a first approximation, we assume the system to represent a hollow sphere of uniform thickness made of a material of finite specific conductance, with oppositely placed spherical metallic cap electrodes. To our knowledge, the overall conductance of such a system has never been theoretically described. We derive this (12) Liu, S.; Dasgupta, P. K. Anal. Chem. 1995, 67, 2042-9. (13) Cardoso, A.; Dasgupta, P. K. Anal. Chem. 1995, 67, 2562-6. (14) Dasgupta, P. K.; Kar, S. Anal. Chem. 1995, 67, 3853-60. (15) Liu, H.; Dasgupta, P. K. Anal. Chem. 1995, 67, 4221-8. (16) Liu, H.; Dasgupta, P. K. Anal. Chem. 1996, 68, 1817-21. (17) Kar, S.; Dasgupta, P. K. J. Chromatogr. 1996, 739, 379-87. (18) Huang, H.; Dasgupta, P. K. Talanta 1997, 44, 605-15. (19) Cardoso, A. A.; Liu, H.; Dasgupta, P. K. Talanta 1997, 44, 1099-106. (20) Pereira, E. A.; Dasgupta, P. K. Int. J. Environ. Anal. Chem. 1997, 66, 20113. (21) Genfa, Z.; Dasgupta, P. K. Anal. Chem. 2000, 72, 3165-70. (22) Wuest, R. Eur. Pat. Appl EP 1308197 A1 20030507, 2003.

(3)

Note that we have azimuthal uniformity of the current in this spherical coordinate system (r, θ, π). Thus, the area A through which the total current I flows is

A ) 2πδrb sin θ

(4)

dI I I ) ) dA A 2πδrb sin θ

(5)

and thus

The infinitesimal arc length ds along a median is given by

ds ) rb dθ

(6)

Substituting eqs 5 and 6 in 2 and integrating, we have

V)

I 2πδσ

∫

dθ sin θ

π-θ0

θ0

(7)

The solution to this integral is

∫

θ0

[ ( )]

dθ θ ) ln tan sin θ 2

π-θ0

π-θ0 θ0

( ) θ0 2

) 2 ln cot

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Hence, the desired voltage-current relationship is given by

V)

( )

θ0 1 ln cot ‚I πδσ 2

(9)

Comparing eq 9 with Ohm’s law in integral form

V ) I/G

(10)

one obtains the experimentally measured conductance G as

G)

πδσ ln(cot(θ0/2))

(11)

The angle θ0 (in radian) is given by (see Figure 1)

θ0 ) re/rb

(12)

πδσ ln(cot(re/2rb))

(13)

Thus, one finally obtains

G)

It is interesting to note that the observed conductance is governed by the ratio of re and rb and not by their individual values. EXPERIMENTAL SECTION Soap Bubble Setup. To be analytically useful, the test bubbles must be of (a) reproducible size, (b) reproducible film thickness, and (c) exhibit significant longevity (g10 min). Additionally, bubbles should not have adherent smaller “satellite” bubbles. We found that it is possible to meet these goals if a constant amount of bubble-making liquid is used to form the bubble, and the amount of gas to “inflate” the bubble is also held constant. To perform efficiently, the bubble-forming liquid should not be in significant excess of what is required to minimally form the bubble; otherwise it will run down and accumulate at the bottom of the bubble (some of this is unavoidable but needs to be minimized), which will compromise both shape uniformity and longevity of the bubble. As a bubble-forming device, or bubble head, we use an annular tube system where a polymer inner tube (0.57-mm i.d., 0.95-mm o.d.) supplies the soap solution and the glass outer tube (1.8-mm i.d.) brings in gas. The inner tube is recessed ∼1 mm from the tip. At the other end, the two are separated through a T-fitting. The overall arrangement is shown in Figure 2. The soap solution SS was delivered to the bubblehead BH by an early version of a solenoid valve pump (SVP) from Biochem Valve Corp., NJ. A short capillary tube SC (8.5 cm × 125 µm i.d.) is placed on the SVP delivery side to dampen the sudden impulse these types of pumps produce. The nominal pump output was 5 µL/stroke; a single actuation was used in the present experiments to deliver the soap solution. After ∼2 s to allow the soap solution to fill the tip of the annular tube system, solenoid valve SV was turned on to admit gas (except as stated, 180 standard cubic centimeters per minute (sccm) for 5 s). The gas flows through a coiled 50-cm length of polyurethane tubing CT (1.5-mm i.d., 3-mm 2788

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Figure 2. Experimental setup for bubble. Bubble head BH produces bubble in box B with retractable stainless steel electrodes E touching bubble; water W is maintained at the bottom to humidify bubble chamber; it also collects waste that is periodically emptied through a bottom port, not shown. To produce bubble, soap solution SS is aspirated through Teflon filter TF and delivered by solenoid valve pump SVP through capillary SC. Compressed air is then metered through mass flow controller MFC, through solenoid valve SV, and coiled elastomeric tubing CT. The dashed arrow indicates where auxiliary flow components (AUX) are connected to the system (e.g., a syringe pump and a 6-port injector, cf. Figure 3; or a gravity flow soap solution bottle and a solenoid valve).

o.d.) that serves as a restrictor and dampener for the gas pressure. When inflated with the aforementioned amount of air, the bubble just touched the opposite electrodes E spaced, except as stated, 30 mm apart. (The inflation volume is varied based on the electrode spacing chosen and thus changes the bubble size.) The soap solution was 2% v/v Triton X-100 dissolved in water; this was then purified by passage through a short column of a nuclear grade mixed-bed ion-exchange resin column (Dowex MR3). There was a significant decrease in the specific conductance of the solution upon deionization. To increase the bubble film thickness and thus promote bubble longevity, 10% v/v glycerol was added to the bubble-making solution. Various concentrations of sulfuric acid (5 × 10-4-0.01 M in final solution) were made in this basic matrix (2% TX-100, 10% glycerol). The specific conductance values of the solutions were measured using a calibrated commercial cell, and the conductance values of the resulting bubbles were also measured. When measuring SO2, the TX-100glycerol reagent was augmented with 0.9% w/v H2O2. As indicated in Figure 2, the bubbles were formed in chamber B, a clear polystyrene box (10 × 10 × 12 cm, W × L × H). Water W in the bottom of the chamber provided humidity. A humid environment is essential to prolong bubble life. The conductivity measurement electrodes E were made from 6-mm-diameter stainless steel rods (type 316) and were housed in a snug-fit 0.75mm-wall thickness polyether ether ketone (PEEK) insulating cylinder (which could be laterally moved in and out to accommodate different size bubbles). The electrodes were directly connected to a commercial conductivity monitor (model CDM III, Dionex Corp.), calibrated to display absolute conductance (in µS). For experiments with SO2 as test gas, the gas was introduced at a flow rate of 350 sccm at the top of chamber B adjacent to BH. The gas exited through a port in one of the faces near the bottom as indicated in Figure 2, through a soda lime packed tube. Since we wanted to avoid complications from evaporation, a moist

gas source that relies on Henry’s law equilibrium through the walls of a porous membrane was used. The general arrangement was similar to that described by Liu and Dasgupta for the generation of ammonia.23 In the present case, two streams of purified air are individually controlled by mass flow controllers (model UFC 1000, Unit Instruments Inc., Orange, CA). The first stream flows at 200 mL/min through a copper thermal equilibration coil maintained in a 20 °C bath and then through a porous polypropylene tube (60 cm × 5.5 mm i.d., Accurel, V8/2, mean pore size 0.2 µm, Membrana, Wuppertal, Germany) that is wholly contained in a glass bottle filled with 600 µM NaHSO3 + 50 mM potassium hydrogen phthalate (pH 4) maintained in the same bath. The SO2 concentration at the exit of the membrane-based source was measured to be 1.9 parts per million by volume (ppmv) by absorption into 0.3% w/v H2O2 contained in a glass midget bubbler (type 7532, Ace Glass Inc., Vineland, NJ) over 20-60-min periods. The resulting sulfate formed was then measured by ion chromatography. This concentration is in good agreement with prior measurements.24 The source solution was changed every 3 days and was generally used within 18 h of preparation to avoid effects of oxidative decay of S(IV). This primary SO2 concentration was diluted by a second stream with a flow rate between 200 and 2000 sccm, humidified by two serial bubblers filled with water. With the help of two polypropylene flow control valves, the desired amount of the diluted flow was directed to bubble chamber B and the rest was vented. Bubble formation and all attendant measurements were controlled with a 16-bit A/D-D/A PCMCIA card (PC-Card-DAS16/ 16AO) by a laptop computer with instructions written in-house in SoftWire (Measurement Computing, Middleboro, MA). The codes are available from the authors on request. Measurement of Bubble Film Thickness. The bubble film thickness was measured optically under conditions identical to those described for conductivity measurements, i.e., with conductance probes touching the bubble. In this case, the bubblemaking solution incorporated various concentrations of a yellow dye (Food Yellow No. 6). The beam from a blue laser (3 mW at 409 nm, model LDCU, Power Technology Inc., Little Rock, AR) was passed through the bubble perpendicular to the axis connecting the electrodes, at the same vertical plane. The transmitted beam was incident on a photodiode (Siemens BPW34), and the resulting current was displayed, converted to voltage (model 480 Picoammeter, Keithley Instruments), and acquired on a PC, where the transmittance signal was log-transformed to compute the absorbance. The film thickness was then estimated from absorbance values for the same concentration of Food Yellow solutions made in the same matrix and measured with a 100-µm-path length cuvette (Hellma Cells, calibrated to actually provide a path length of 103 ( 1.8 µm) in a commercial spectrophotometer (Agilent model 8451).

Figure 3. Bubble as a flow cell. The bubble-making solution was 2% TX-100, 10% glycerol. After forming the bubble, further soap solution was continuously pumped at the indicated flow rate and 5 µL of 10-3 M H2SO4 in the same soap solution matrix was injected.

RESULTS AND DISCUSSION Bubble Reproducibility. Although except as stated the bubbles were created with a fixed volume of gas, it was of interest to determine the exact bubble diameter and its reproducibility, especially in the absence of the electrodes to confine the bubble.

The electrodes were retracted to the wall, and a transparent measurement grid was put on the face adjacent to the faces holding the electrodes. The grid was backed up by a mirror to avoid parallactic reading errors. A high-resolution digital photograph was taken immediately after making the bubble (with 210 sccm gas flow for 5 s), avoiding parallax as best as possible. The bubble diameter, calculated from the difference of the left and right edge readings, averaged 41.7 ( 0.8 mm (n ) 74, RSD 1.9%). Temporal Variation in Bubble Film Thickness. The first item of note is that the confinement of the bubble by the two oppositely placed electrodes endows dimensional stability to the bubble. We found it readily possible to locate a drain tube at the bottom of the bubble and use the bubble as a flow-through cell. In this experiment, the output of a syringe pump was tied in common with the output of the solenoid pump. After forming the bubble with the solenoid pump, further bubble-making solution was continuously pumped with the syringe pump at the indicated flow rate and 5 µL of a test electrolyte was periodically injected through a loop injector. The results are shown in Figure 3. Referring to confinement by the electrodes, it was observed that the light transmission through a dye-containing bubble, as measured by the photocurrent, was substantially more stable with the electrodes in place than without them. We conducted, therefore, all further optical measurements with electrodes in place, generally carrying out optical and conductivity measurements simultaneously. The visible absorption band of Food Yellow in the TX-100-glycerol medium is broadly centered at 425 nm. This made the measurements with a 409-nm laser and by a conventional spectrometer with a 2-nm bandwidth, centered at 409 nm, very comparable. By spectroscopic techniques, others have previously documented that bubble film thickness often changes with time after initial formation.25,26 In our experiments, we also observed changes in absorbance with time; the film thickness of the bubble must

(23) Liu, S.; Dasgupta, P. K. Anal. Chem. 1995, 67, 2042-9. (24) Dong, S.; Dasgupta, P. K. Atmos. Environ. 1986, 20, 1635-7.

(25) Kravarik, J.; Kubes, P. Physica B 1994, 193, 232-8. (26) Chattopadhyay, A. J. Chem Educ. 2000, 77, 1339-42.

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therefore be measured with specific reference to the age (τ) of the bubble. (The bubbles remained attached to the bubblehead for a period that generally ranged from 15 to 18 min. After selfdetachment from the bubblehead, they still remained attached to the conductivity electrodes for an extended period of time.) Relatively large concentrations (percent level) of the dye have to be incorporated into the bubble-making solution to achieve reliable absorbance measurements, when the path length is few micrometers. Consequently, one must make the admittedly tenuous assumption that the large amount of dye put in the bubblemaking solution does not change the film thickness in a dramatic fashion. When the laser beam traverses the bubble, it traverses a solution path length equal to twice the bubble film thickness. However, a comparison of the absorbance of the bubble versus that of the same solution in the ∼100-µm cell at any one concentration is inappropriate. This is because different interfaces are involved in the two cases and a different degree of Fresnel loss at the interfaces will be expected to take place. We reasoned that the ratio of Beer’s law slopes in the two cases will be more appropriate. In the range of 2-6% dye concentration, both systems obeyed Beer’s law with the following equations:

Figure 4. Temporal conductance profile of bubbles blown from 2% Triton X-100 and 10% glycerol containing various amounts of H2SO4.

A103 µm cell ) 0.0341((0.0675) + 0.1696((0.0156) [Food Yellow, w/v%],

r2 ) 0.9916 (14)

and

Abubble,τ)5min ) 0.0106((0.0025) + 5.35((0.58) × 10-3 [Food Yellow, w/v%],

r2 ) 0.9885 (15)

In the range of the dye concentration used, the observed absorbance is dominated by the second term in each of eqs 14 and 15. As a first approximation, we have therefore calculated the bubble film thickness δ at 5 min (δτ)5min) simply from the ratio of the slopes of eqs 15 and 14 and the path length of the conventional cell:

δτ)5min ) 1.62 ( 0.23 µm

(16)

remain constant in the absence of evaporative concentration. Since G is directly proportional to δ, the change in conductance directly reflects a change in the bubble wall thickness. Similar to discharging a capacitor or draining a water-filled tank, this excess bubble liquid runoff should also be an exponential process as a first approximation. Figure 4 shows log G versus τ plots, for the highest to the lowest concentration traces, the linear r2 values of 0.9697, 0.9262, 0.9752, and 0.9708, respectively. Further, at any specific points in time, the conductance values are linearly correlated with the H2SO4 concentration in the bubblemaking solution

Gτ)0min, nS ) (11.2 ( 21.9) + (88.1 ( 3.9) [H2SO4, M], r2 ) 0.9961 ... (17) Gτ)1min, nS ) (11.3 ( 14.8) + (80.5 ( 2.6) [H2SO4, M], r2 ) 0.9979 ... (18)

Values of film thickness were also measured at other times and are discussed later. It is useful to note here that if 5 µL of liquid is made into a hollow bubble 3 cm in diameter, the computed wall thickness will be 1.8 µm. The exact amount of liquid delivered can vary, however, by the restriction placed on the pump and the solution viscosity. Bubble Conductance and Its Temporal Profile. The conductance of a bubble containing various concentrations of H2SO4 decreases with time. The behavior is reproducible. Figure 4 shows the mean (n ) 5-7) temporal conductance profiles of bubbles containing different amount of H2SO4 with (1 standard deviation indicated as an error bar. We propose that this occurs because the bubble wall thins out over time; that is, the excess liquid in the bubble gradually runs to the bottom (this process can actually readily be seen). It can be observed in eq 13 that, among the parameters that control the experimental conductance G, all terms other than the thickness of the bubble wall δ are expected to 2790

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Gτ)5min, nS ) (17.7 ( 27.5) + (54.3 ( 4.9) [H2SO4, M], r2 ) 0.9840 ... (19) Gτ)9min, nS ) (18.8 ( 33.4) + (44.4 ( 5.9) [H2SO4, M], r2 ) 0.9654 ... (20)

The slope of the concentration-dependent conductivity curve also decreased exponentially with time; the logarithm of the slope values in eqs 17-20 was linearly related to τ with an r2 value of 0.9770. The specific conductance σ of the soap-making solution is also predictably linearly related to its H2SO4 content:

σ (µS/cm) ) (192.2 ( 123.5) + (6.503 ( 0.246) × 105 [H2SO4, M],

r2 ) 0.9957 ... (21)

Figure 5. Temporal thickness profile of bubbles of various compositions calculated from eq 22 based on conductance. The points with error bars are optically measured thicknesses from bubbles containing 2-6% dye.

Film Thickness. Conductance versus Optical Measurements. Equation 13 is readily recast as

δ)

G ln(cot(re/2rb)) πσ

(22)

The bubble conductance G, the solution-specific conductance σ, and the bubble radius rb are measured as described; from these, the film thickness δ is calculated from eq 22. This calculated thickness is shown in Figure 5 for solutions of 10 mM H2SO4 in 2% TX-100, 10% glycerol, with and without 2-6% dye. The data are shown also for a solution of 5 mM H2SO4 in 2% TX-100, 10% glycerol. The solutions without dye appear to start out with a greater film thickness but decrease in thickness more rapidly with time such that over most of the bubble lifetime there is relatively little dependence of the film thickness on either the dye content or the H2SO4 concentration. In Figure 5, the optically measured film thicknesses at four different points in time are shown as individual points with error bars; these were determined from the absorbance slope of bubbles containing 2-6% dye, in much the same way the film thickness was determined in eq 16 for τ ) 5 min. It will be observed that, within experimental uncertainty (which admittedly is not insubstantial), the conductometrically and photometrically determined values of the film thickness are the same. This is reassuring toward validating the model of the conductance of a hollow sphere as well as its applicability in the present situation. Solution-Specific Conductance versus Bubble Conductance. Other factors remaining the same, the observed conductance of a bubble is solely governed by the conductance of the bubble-making solution. For a larger bubble (8.3 cm) with proportionately larger electrodes, we studied the conductance

Figure 6. Temporal conductance profile of bubbles made from 10 mM H2SO4 in 2% Triton X-100. Different volumes of liquid and gas were used to blow the different size bubbles. The error bars represent (1 standard deviation, four separate bubbles for each diameter.

properties where the conductance of a 10 mM H2SO4 solution was changed by adding different concentrations of TX-100 into it (0.2, 0.5, 0.75, 1, 2, and 6% v/v; no glycerol was used in these experiments), the observed bubble conductance was linearly related to the conductance of the bubble-making solution with a linear r2 of 0.9942. The conductance of the solution decreases with increasing TX-100 content primarily because of increased viscosity. In the case of the bubble, there are also significant changes in surface tension. However, it is not possible to separately determine the contribution of a parallel, concomitant effect of the surface tension change. Electrode Distance. Conductance as a Function of Electrode Separation (and Bubble Size). These experiments were conducted with a bubble-making solution containing 10 mM H2SO4 in 2% TX-100 that flowed under gravity to the bubble head for a fixed period of time governed by a computer-controlled solenoid valve. The flow rate was gravimetrically calibrated and the volume of solution delivered (Vs) could be adjusted with the period the valve was switched on. Bubbles were formed by different amounts of air, by varying the time over which air flow was on. The separation of the 2.7-mm-diameter electrodes used in this experiment ranged from 28.7 to 39.0 mm, and the measured bubble size was within (0.2 mm of this. Optical measurements of bubble film thickness were not made since the uncertainty in these measurements was significant. As previously discussed, at least early during the life of the bubble, the measured film thickness tends to be quite close to δgeom, that calculated from geometrical considerations:

δgeom ) Vs/4πrb2

(23)

The results are shown in Figure 6. Figure 7 shows the computed values (the uncertainties here depict primarily the uncertainties Analytical Chemistry, Vol. 78, No. 8, April 15, 2006

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Figure 7. Bubble conductance at τ ) 1 min calculated according to eq 13 for the data in Figure 6 based on geometrically computed thickness (eq 23) vs those actually measured.

in Vs and the measured value of σ) as well as the measured bubble conductance values at τ ) 1 min (the uncertainties here reflect the standard deviation of measurement (n g 3 bubbles)). For all but the smallest bubble, there is excellent agreement between the computed and the measured values. The same amount of liquid was used for the smallest and the 33.6-mm-diameter bubble (next larger size), the excess liquid in the smaller bubble may have rapidly flowed to the bottom of the bubble rather than be distributed into a film of even thickness as implicitly assumed in eq 23. Conductometric Measurement of Sulfur Dioxide with a Soap Bubble. The significant concentration of a soluble gas that can be attained by a soap bubble is demonstrated by the use of a soap bubble as an interface for sampling SO2. The oxidation of sulfur dioxide by solution-phase hydrogen peroxide has often been used for the measurement of SO2, typically by measuring the sulfate. Recent examples of this by ion chromatographic27 or nephelometric28 sulfate determination are available. Direct conductometric determination is possible if the sample gas is pretreated through, for example, a solution of sulfamic acid29 or if the peroxide absorber is itself acidified.30 It constitutes a simple, easy to practice test system.31 The uptake of SO2 by a bubble containing H2O2 has certain similarities with uptake by a cloud droplet containing H2O2; the latter was studied extensively by Schwartz and Freiberg.32 The following steps are involved: (i) transport of the gas to the gasliquid interface; (ii) Henry’s law dissolution at the interface; (iii) ionization of dissolved SO2 to HSO3- and SO32-; (iv) oxidation of the S(IV) anions by H2O2; and (v) mass transport of the H2SO4 to (27) Velasquez, H.; Ramirez, H.; Diaz, J.; deNava, M. G.; deBorrego, B. S.; Morales, J. J. Chromatogr., A 1996, 739, 295-9. (28) Milani, M. R.; Cardoso, A. A. Microchem. J. 2003, 74, 75-82. (29) Gacs, I.; Ferraroli, R. Anal. Chim. Acta 1992, 269, 177-85. (30) Ohira, S.-I.; Toda, K.; Ikebe, S.-I.; Dasgupta, P. K. Anal. Chem. 2002, 74, 5890-6. (31) Dasgupta, P. K.; McDowell, W. L.; Rhee, J.-S. Analyst 1986, 111, 87-90.

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Figure 8. Temporal profile of the bubble conductance at two different concentrations of SO2, electrodes washed between runs.

the interior liquid.32 Steps ii and iii are expected to not be rate limiting, and with large amounts of H2O2 as used here, step iv is also going to be rapid. In the present experimental setup, the test gas is introduced from the top. As a result, the top half of the bubble captures the analyte efficiently as the gas is first introduced. Gas-phase diffusion becomes the limiting factor for the bottom half of the bubble. (This limitation can be overcome by introducing the gas at multiple points around the bubble; however, this was not presently attempted.) On the other hand, when one measures the conductivity of the bubble as a whole, the distribution of the H2SO4 formed in the bubble becomes the rate-limiting process because in a series circuit the highest resistive element controls the overall passage of current. This is quite similar to the case of a cloud droplet where typically the slowest step is diffusion of H2SO4 within the bulk liquid.33 Accordingly, the temporal profile of the conductance signal is dependent both on the gas flow rate and on the gas concentration. Figure 8 shows that the observed signal monotonically increases with time. However, even here, at the higher concentration, a step increase around 6 min is observable. The time for this step increase is both concentration and flow rate dependent. These two traces were obtained with fresh electrodes. The present setup contains no mechanism for washing the electrodes (although it would be readily possible to have electrodes with a pinhole through which wash liquid can be introduced). As such, if one conducts experiments with one bubble after the other, although most of the liquid does drop off the electrodes each time, some residual liquid, containing the H2SO4 formed, remains. This not only causes the initial conductance of the bubble to be higher but the exact values become dependent on previous sampling history. Figure 9 shows averaged traces at several different concentrations obtained after the system was randomly used for SO2 sampling with concentrations up to 1200 ppbv, and then an ascending calibration series was executed. It is apparent that the (32) Schwartz, S. E.; Freiberg, J. E. Atmos. Environ. 1981, 15, 1129-44. (33) Schwartz, S. E.; Freiberg, J. E. Atmos. Environ. 1981, 15, 1145-54.

Figure 9. Temporal conductance traces of bubbles exposed to different concentrations of SO2 for 10 min. Electrodes were not washed between runs. Note increased starting conductance relative to Figure 8.

starting conductance is g0.45 µS, much higher than the nearzero initial conductance shown in Figure 8. Also, there is a rapid initial rise of conductance from the distribution of the H2SO4, and then there is plateau (even possibly a minor dip) until ∼120 s following which the signal increases monotonically. Nevertheless, we found that accurate quantitation is possible if the conductance value at 120 s is considered the baseline. This value is thus subtracted from the data between 120 and 600 s before integrating the signal over that period. The resulting calibration plot exhibited a linear r2 value of 0.9778 and the standard deviation of the blank corresponded to an S/N ) 3 limit of detection of 37 ppbv. With a minute of zero air flow between samples to flush out the chamber, the reproducibility was 3.9% in relative standard deviation (n ) 5). (34) www.nanodrop.com.

CONCLUSIONS Although generally considered intrinsically variable and evanescent, soap bubbles can be produced reproducibly, maintained for tens of minutes, and provide an unusual interface for the concentration of soluble and reactive gases. We have derived and experimentally validated the model for the electrical conductivity of a bubble. While we have demonstrated here that parts per billion levels of a soluble trace gas can be measured by concentration in a soap bubble within minutes with admittedly crude arrangements that had not been optimized, it is felt that the basic lesson here is that soap bubbles represent a largely unexplored territory that can be attractive for analytical applications. This need not involve in situ measurements as carried out in the present case. Whether bubbles are blown with the sample gas or the sample gas flows around a bubble, the bubble can be deliberately collapsed to collect the liquid postsampling. UV-visible spectrometric measurements, where the bubble-making solution already incorporates the necessary chromogenic reagents, should be straightforward. Inexpensive fiber-optic spectrometers that require only 1 µL of sample are now commercially available.34 ACKNOWLEDGMENT T.K. acknowledges support from The Institute for the Promotion of Teaching Science and Technology (IPST), Government of Thailand, and the Postgraduate Education and Research Program in Chemistry, Government of Thailand for his research stay at Texas Tech University. This research was supported in part by Paul Whitfield Horn Professorship funds at Texas Tech University. NOTE ADDED AFTER ASAP PUBLICATION This article was released ASAP on February 23, 2006, with a minor error in eq 8. The correct version was posted on February 28, 2006.

Received for review December 12, 2005. Accepted January 31, 2006. AC052198H

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