Rapid Exploration of Phase Behavior in Surfactant Systems Using

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Langmuir 2006, 22, 11412-11419

Rapid Exploration of Phase Behavior in Surfactant Systems Using Flow in Microchannels Jinkee Lee,† Arijit Bose,*,‡ and Anubhav Tripathi*,† DiVision of Engineering, Brown UniVersity, ProVidence, Rhode Island 02912, and Department of Chemical Engineering, UniVersity of Rhode Island, Kingston, Rhode Island 02881 ReceiVed June 23, 2006. In Final Form: September 11, 2006 The paper describes a study for the determination of the phase behavior of a self-assembling dilute aqueous cetyl trimethylammonium bromide (CTAB) and dodecyl benzene sulfonic acid (HDBS) system using flow in microchannels. The diffusional length scales of ∼10-100 µm and volumes on the order of a few tens of nanoliters allow fast composition and temperature homogeneity compared to “bulk” experiments, where characteristic volumes and length scales are on the order of milliliters and centimeters, respectively. Fluorescence emission of a polarity-sensitive fluorophore was used with the surfactants for phase characterization. To demonstrate the validity of the new approach, the critical micelle concentrations (cmc) for CTAB and HDBS were first shown to agree with the cmc obtained in the literature under bulk conditions. Subsequently, the microstructures of dilute (less than 0.8 wt % total surfactant) aqueous mixtures of CTAB and HDBS were examined. The range of desired concentrations and accurate flow dilutions of the samples were achieved by imposing controlled pressure gradients across the channel network. Marked changes in slopes of fluorescence emission intensity versus composition were used to demarcate phase boundaries. A series of microstructures ranging from mixed micelles (M), vesicles (V), and giant vesicles (GV) was observed in the ternary CTAB/HDBS/water system. Experimental data from the microfluidic method was found to be consistent with the results obtained from bulk phase experiments using fluorescence, turbidity, dynamic light scattering, and cryogenic transmission electron microscopy.

1. Introduction Surfactants have the ability to self-assemble into a wide variety of supramolecular structures such as micelles, bilayers, vesicles, and liquid crystals and emulsions1 in bulk solution. The lyophobe chain length, nature of solvent, surfactant concentration, temperature, salt concentration, and the presence of one or more cosurfactants affect aggregate morphologies.2-4 Surfactant aggregates of different morphologies have a direct impact on their application, as well as their performance. Knowledge of the phase behavior of single surfactants as well as mixtures over a range of compositions is therefore critical toward defining their usefulness for applications. The most commonly used technique for quantitatively determining phase behavior in these systems is to monitor changes in turbidity as either composition or temperature is varied. These experiments are typically done in vials where uniformity in composition and temperature must be achieved over length scales on the order of a centimeter to produce reproducible results. For systems that are shear sensitive, this homogeneity must be achieved by diffusion. The time scale th for achieving this homogeneity can be estimated to be th ∼ l2/2D ) 1 cm2/(2 × 10-6 cm2/s) ) 5 × 105 s. For this reason, a typical phase diagram can take several weeks to develop. A judiciously designed microfluidic chip offers a unique opportunity to rapidly develop * To whom correspondence should be addressed. A.B.: tel, 401-8742804; e-mail, [email protected]. A.T.: tel, 401-863-3063; e-mail, [email protected]. † Brown University. ‡ University of Rhode Island. (1) Imae, T. Colloids Surf. A 1996, 109, 291-304. (2) Freeman, K. S.; Tan, N. C. B.; Trevino, S. F.; Kline, S.; McGown, L. B.; Kiserow, D. J. Langmuir 2001, 17 (13), 3912-3916. (3) Koehler, R. D.; Raghavan, S. R.; Kaler, E. W. J. Phy. Chem. B 2000, 104 (47), 11035-11044. (4) von Berlepsch, H.; Bottcher, C.; Ouart, A.; Regenbrecht, M.; Akari, S.; Keiderling, U.; Schnablegger, H.; Dahne, S.; Kirstein, S. Langmuir 2000, 16 (14), 5908-5916.

phase behavior in amphiphilic systems as a function of composition and temperature. Microfluidics5-9 lends itself naturally to a massively parallel setup to quickly map phase behavior over a range of concentrations using precise metering, which allows dilutions to be performed accurately. There are other factors that distinguish microfluidics: (i) The length scales over which composition and temperature uniformity have to be achieved are on the order of tens of micrometers. Even by diffusion of the relatively high molecular weight surfactant molecules, this can be achieved within tens of seconds (th ∼ l2/2D ) 50 s). This is 4 orders of magnitude faster than in bulk phase experiments, where characteristic lengths are on the order of 1 cm. (ii) Volumes are small, typically on the order of a few microliters. Thus, the system can equilibrate rapidly after any changes to temperature because it has low thermal mass. In addition, very small amounts of surfactant are consumed. (iii) Flow rates and thus compositions can be controlled very accurately and the resulting solutions can be probed over a continuous composition range using on-line detectors. (Discrete variations in composition have been used in the experiments reported here because fixed increments in pressure were applied to drive the fluids in the channels.) The high surface area-to-volume ratio in a microfluidic assembly can be a potential disadvantage, since adsorption on bounding surfaces can change concentration significantly within a channel. However, robust techniques where the surfaces of a microfluidic channel are treated to suppress adsorption are now available and have been exploited here. (5) Suzuki, H.; Tabata, K.; Kato-Yamada, Y.; Noji, H.; Takeuchi, S. Lab Chip 2004, 4 (5), 502-505. (6) Manz, A.; Eijkel, J. C. T. Pure Appl. Chem. 2001, 73 (10), 1555-1561. (7) Pfeifer, A.; Verma, I. M. Annu. ReV. Genom. Hum. Genet. 2001, 2, 177211. (8) Razzacki, S. Z.; Thwar, P. K.; Yang, M.; Ugaz, V. M.; Burns, M. A. AdV. Drug DeliVery ReV. 2004, 56 (2), 185-198. (9) Santini, J. T.; Richards, A. C.; Scheidt, R. A.; Cima, M. J.; Langer, R. S. Ann. Med. 2000, 32 (6), 377-379.

10.1021/la061818m CCC: $33.50 © 2006 American Chemical Society Published on Web 11/02/2006

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In this paper, we describe a new microfluidic-based method to construct the phase behavior of the two surfactants CTAB and HDBS, and their mixture over a range of compositions in water. The paper also describes delineation of the surfactant microstructures by developing a criterion based on fluorescence gradient versus composition. Because of the inherently high surface areato-volume ratio, the microchannel experiments also provide new insights into adsorption-desorption behavior of surfactants in microchannel flows. The experimental details are described in section 2, while the results are discussed in section 3. 2. Experimental Details 2.1. Materials. Aqueous stock solutions of Cetyltrimethylammonnium bromide (CTAB, >99% purity, Sigma-Aldrich (St. Louis, MO)) and dodecyl benzene sulfonic acid [HDBS, Stepan Co. (Northfield, IL)] were prepared. All solutions were prepared with 18.2 MΩ ultrapure water at room temperature and then stored at 25 °C until used. The CTAB and HDBS samples were kept above their Kraft points10 to avoid any precipitation. 2.2. Fluorescence Probe. An aqueous stock solution of 6-propionyl-2-(dimethylamino)naphthalene (Prodan; Invitrogen Co., Carlsbad, CA) was dissolved in dimethyl sulfoxide (DMSO; Aldrich, HPLC grade) to produce a 25 mM stock solution. The final concentration of Prodan in the surfactant solutions was 5 µM. The low concentration of the probe was selected to minimize the amount of “free” Prodan and to ensure a low probability of multiple probe molecules per micelle. Prodan exhibits measurable fluorescence emission in both polar and nonpolar solvents, undergoing a red shift in emission wavelength as the polarity of the environment increases. Thus, fluorescence emission at a fixed wavelength, or spectral shifts in the emission profiles are indicators of changes in the microenvironment around the probe. These features have been exploited extensively to map microstructures in other surfactant systems including CTAB/SOS (sodium octyl sulfate)/water,11 didecyldimethylammonium bromide/octyl-β-D-glucopyranoside/water,12 SDS (sodium dodecyl sulfate)/DTAB (dodecyltrimethylammonium bromide)/water,13 and N-alkyl-N-methylpyrolidinium bromide/water14 systems. 2.3. “Bulk” Phase Experimental Techniques. (a) Turbidity and Dynamic Light Scattering. Turbidity measurements for determining the phase boundaries and dynamic light scattering measurements for the estimation of particle hydrodynamic radii were performed on a Brookhaven model BI-200SM laser light scattering system (Brookhaven Instrument Corp.) at a scattering angle of 90° and wavelength 514 nm. The solution temperature was maintained at 25 °C. Samples were passed through a 0.22-µm filter to remove dust prior to all measurements. (b) Fluorescence Measurements. A Photon Technology spectrophotometer (PTI International) was used to obtain fluorescence emission spectra using an excitation wavelength of 360 nm. The emission wavelength was scanned from 380 to 620 nm. The sample was placed in a quartz cell of path length 0.5 cm in a stirred cuvette holder, whose temperature was kept constant at 25 °C. (c) Viscosity Measurements. The viscosities of all solutions were measured with a controlled-stress rheometer (TA Instruments) using a double gap cylindrical geometry (0.035 radius and 4 cm length). (The viscosities are necessary to determine required pressure drops for flow control.) Since the measured torques were small, long time averaging procedures were adopted for accurate shear rate measure(10) Van Os, N. M.; Haak, J. R.; Haak, L. A. M. Physicochemical Properties of Selected Anionic, Cationic, and Nonionic Surfactants; Elsevier: New York, 1993. (11) Karukstis, K. K.; McCormack, S. A.; McQueen, T. M.; Goto, K. F. Langmuir 2004, 20 (1), 64-72. (12) Junquera, E.; del Burgo, P.; Boskovic, J.; Aicart, E. Langmuir 2005, 21 (16), 7143-7152. (13) Karukstis, K. K.; Suljak, S. W.; Waller, P. J.; Whiles, J. A.; Thompson, E. H. Z. J. Phys. Chem. 1996, 100 (26), 11125-11132. (14) Karukstis, K. K.; McDonough, J. R. Langmuir 2005, 21 (13), 57165721.

Figure 1. (a) Photograph of a wet-etched microchannel. The insert shows the isotropic cross-section of the channel. (b) Design mask used for fabrication of the chip. The design shows the fluid reservoirs A, B, C, and D; the detector location (D2) for adsorption desorption experiments; and the detector location (D1) for cmc and phase diagram measurements. ments. The viscosity of the dilute solutions was measured at 25 °C and the rheometer was calibrated with the known water viscosity. (d) Cryogenic Transmission Electron Microscopy. A sample of the solution (2-3 µL) was withdrawn from a vial stored at 25 °C in a controlled environment vitrification system (CEVS, University of Minnesota; the temperature within the CEVS box was precisely controlled, and the relative humidity was kept at >90%). The sample was then deposited on a specially prepared holey carbon electron microscope grid and blotted to remove excess liquid. All of this processing took place within the CEVS unit, preventing water evaporation and temperature changes in the sample. The grid bearing the sample was then plunged into a liquid ethane reservoir, cooled by liquid nitrogen to a temperature close to its freezing point. The rapid heat transfer away from the grid vitrified the sample. The specimen was transferred under liquid nitrogen to the cooled tip of a cryotransfer stage (CT3500J; Oxford Instruments). The stage was then inserted under positive dry nitrogen pressure into the JEOL 1200TEM and imaged at slight underfocus (1-3 µm). The sample temperature was maintained at -165 °C at all times during imaging to prevent the amorphous-to-crystalline phase transformation in ice. 2.4. Experimental Technique. (a) Microchip Fabrication. The microfluidic chip was fabricated at the Brown University Microfabrication Facilities. Glass substrates were used to fabricate microchannels using a wet etching protocol based on standard microlithographic techniques but recently optimized in our laboratory. Figure 1a shows a photograph of an etched microchannel network on glass substrate. The figure also shows isotropic channel crosssection shape. The microchannel design used in this study is shown

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in Figure 1b. The design consisted of a network (cross) of four microchannels connecting to four fluid reservoirs. The width, depth, and length of the channels were 85 µm, 12.5 µm, and 60 mm, respectively. Unlike traditional poly(dimethyl siloxane) (PDMS) microfluidic chips, the glass chips are free from solvent absorption, swelling, and other detection related problems, making them ideally suited for surfactant phase exploration. (b) Microchip Control and Detection. The dilutions and flow of fluids were regulated with a programmable control system designed and developed in-house. This control system consisted of four independent pressure ports that were capable of imposing and measuring pressure profiles in any microchannel network. The pressure ports were connected using air lines to the fluid reservoirs on the microchip. Unlike conventional syringes and tubes, this system is contamination-free, since pressure is applied through air compression. This feature is important when dealing with surfactants. The liquid flow rate Qi in the microchannel was evaluated by solving the conservation of linear momentum equation Qi )

∆Pi R iη

(1)

where ∆Pi is the pressure difference across the microchannel, ηi is the viscosity of liquid i. The hydrodynamic resistance Ri of a isotropically etched (see Figure 1a) microchannel i (i ) 1-4) is given by

Ri ) RiRirect )

[

1-

12 Li Ri widi3 192di

∞

∑

]

1 1 - exp(-nπwi/di)

π5wi n)1,3,5...n5 1 + exp(-nπwi/di)

(2)

where wi, di, and Li are the width, depth, and length of the microchannel i, respectively. The correction factor Ri, which multiplies the hydrodynamic resistance of a rectangular channel, accounts for the isotropic shape of the channel.15 The correction factors Ri were evaluated numerically (Ri = 1.07) using the computational software CFDRC-ACE (ESI-CFD Group, Huntsville, AL).15 A Nikon TE 2000U inverted microscope (Nikon Inc., Japan) with epi-fluorescence, phase contrast, and dual channel photometer was used to measure the fluorescence intensity in the microchannels. The attached photomultiplier tube (PMT) system (Photon Technology International, Inc., Birmingham, NJ) allowed us to use a diachronic filter, splitting the 435- and 480-nm signals. Although data was collected at both wavelengths, the 480-nm signal was dominant. Hence, microstructure information was interpreted using the 480nm signal only. (c) Surface Coating. The glass microfluidics channel was coated with dodecylchlorosilane (obtained from Gelest Inc, Morrisville, PA) to suppress the adsorption of surfactant. A 2 wt % chlorosilane solution was made using ethanol and then incubated for about 1 h to produce alkoxysilane and HCl. The reaction of HCl with alcohol produces small quantities of alkyl halide and water. The water causes formation of silanol groups at the surface. After the coating step, the chip was cleaned thoroughly with ethanol. Finally, all the fluid was dried out by keeping the sample in an oven at 110 °C for 20 min.

3. Results and Discussion The optical path length across a microfluidic channel was too small to meaningfully detect changes in turbidity as microstructures changed. Thus, the phase diagram experiments reported here were performed using an alternative and attractive fluo(15) Lee, J.; Tripathi, A. Anal. Chem. 2005, 77 (22), 7137-7147.

Figure 2. Prodan fluorescence emission spectra at various CTAB sample concentrations. The insert shows a linear increase in the maximum intensity (480 nm) with CTAB concentration.

rescence technique, where the signal-to-noise ratio was excellent over all compositions. 3.1. Calibration of Prodan Fluorescence in CTAB Solution. The fluorescence emission from Prodan was observed in a spectrophotometer for various surfactant concentration samples higher than the critical micelle concentration of CTAB (0.87 mM). These experiments were performed using a fixed molar ratio of CTAB to Prodan. Figure 2 shows fluorescence emission spectra for increasing concentrations of CTAB. For all CTAB sample concentrations, the fluorescence intensity attained its maximum value at ∼480 nm with a high signal-to-noise ratio. Figure 2 (inset) shows a linear increase in fluorescence intensity with increasing surfactant concentration. If a fixed Prodan concentration (5 µM) was used, the emission intensity showed a nonlinear dependence with surfactant concentration. To avoid this nonlinear effect, all the experiments in this work were performed at a fixed molar ratio of surfactant to Prodan of 600. Fluorescence emission at 480 nm from HDBS solutions had approximately one-sixth of the intensity as the CTAB solutions but also varied linearly with concentration. 3.2. Critical Micelle Concentration (cmc) of CTAB and HDBS Solutions. The critical micelle concentrations of CTAB and HDBS were measured using the chip shown in Figure 1b. The microchannels, coated with dodecylchlorosilane, were initially primed with deionized (DI) water, the reservoir B was loaded with 30 µL of 2 mM CTAB premixed with 5 µM Prodan, and all other reservoirs were loaded with 30 µL of DI water. The CTAB solution flowing from reservoir B was diluted with water flowing from reservoirs A and C, to achieve the desired concentrations of CTAB solution in the detection (mixing) channel. The pressures at each reservoir required to produce a given flow rate were calculated using eqs 1 and 2 and the measured viscosity (1.04 cP) for the 2 mM CTAB solution. The average velocity in the mixing channel was kept at 1.03 mm/s to maintain laminar flow, and mixing across the channel was by diffusion only. The conditions for mixing15 were obtained by balancing the convective time (length of channel/flow velocity) with the diffusion time (square of the half-width of microchannel/twice the diffusivity of molecules) across the microchannel. With the diffusivity of CTAB assumed to be 9.47 × 10-7 cm2/s,16 the diffusion time was 9.5 s. Thus, the transit (convective) time of 50 s in the mixing channel allowed complete mixing of CTAB molecules before the fluorescence emission signal from the solution was detected (position D1, Figure 1b). (16) Balakrishnan, A.; Rege, B. D.; Amidon, G. L.; Polli, J. E. J. Phar. Sci. 2004, 93 (8), 2064-2075.

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Figure 3. Fluorescence intensity measurement from CTAB solutions at different concentrations. The results from on-chip and bulk (offchip) measurements show excellent agreement. The results also confirm the cmc value of 0.87 mM.

Figure 3 shows a plot of the normalized fluorescence intensity, measured at 480 nm, versus CTAB concentration. The fluorescence intensities are normalized using the minimum (pure water) and maximum (1.8 mM CTAB) signals in the microchannel. As the concentration of CTAB decreases, the fluorescence intensity also decreases linearly with a slope of 1. Since Prodan emission is proportional to the number of micelles, the signal decrease is indicative of the breakup of micelles and the consequential drop in micelle number density as the concentration of surfactant decreases. Once the CTAB concentration reaches 0.87 mM, the observed slope of the fluorescence intensity versus concentration undergoes a sudden decline to 0.1. The low fluorescence of the CTAB sample below 0.87 mM suggests complete absence of micelles. Hence, 0.87 mM represents the critical micelle concentration for CTAB in water at 25 °C. The results were repeated three times, and the corresponding errors bars are shown in Figure 3. The experiments were also performed with increasing concentrations of CTAB, and results overlap with those shown in Figure 3. Data from bulk experiments where fluorescence intensity was measured as a function of surfactant concentration on the spectrophotometer are also shown in Figure 3. Both onchip and off-chip data agree well. The measured cmc is also in close agreement with literature values,17,18 where a break in a plot of the surface tension with concentration marked the cmc. Similar experiments were also performed for HDBS, and the cmc value of 0.08 wt % is in agreement with that reported in the literature.19,20 These agreements with bulk phase cmc measurements validated the accuracy of microchip dilutions and the diffusional mixing in the microchannel. The reproducibility of the results also suggested that the coating procedures were effective. 3.3. Absorption and Desorption Measurements of CTAB and HDBS on Microchannel Walls. Microchannel measurements provide a huge surface-to-volume ratio (∼2 × 105 m-1) that is 2 orders of magnitude larger than surface-to-volume ratios (∼4 × 103 m-1) observed in vials used for conventional bulk scale measurements. Thus surfactant adsorption at these surfaces can produce unspecified changes in concentration when understanding the evolution of phase behavior in amphiphilic systems. (17) Furst, E. M.; Pagac, E. S.; Tilton, R. D. Ind. Eng. Chem. Res. 1996, 35 (5), 1566-1574. (18) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems NSRDS-NBS 36. U.S. Government Printing Office: Washington, DC, 1971. (19) Walker, S. A.; Zasadzinski, J. A. Langmuir 1997, 13 (19), 5076-5081. (20) Flaming, J. E.; Knox, R. C.; Sabatini, D. A.; Kibbey, T. C. Vadose Zone J. 2003, 2 (2), 168-176.

Figure 4. (a) Measured CTAB concentration at junction D2 as a function of time. The hatched areas (a, b, c) indicate the total number of molecules adsorbed onto surface. The figure also shows the model fits to the experiment data for CTAB adsorption on the microchannel walls. The right ordinate is the intensity of fluorescein. (b) Measured CTAB concentration as function of time when CTAB solutions were replaced by water in reservoir B.

Here, we describe a new approach to understand the time scale and concentration dependence of adsorption/desorption processes in a microfluidic channel, primarily meant to delineate any limits on concentrations for the subsequent experiments on phase behavior in the microchannels. Microfluidic chips were prepared by first priming channels with DI water and subsequently loading reservoir B (Figure 1b) with CTAB solution. The other reservoirs were loaded with DI water. A constant CTAB/Prodan molar concentration ratio, 600, was preserved in each CTAB solution. A negative pressure of -1 psi was then applied in reservoir D, resulting in flow of CTAB solution from reservoir B at 0.42 nL/s. The fluorescence detector was placed at the junction D2 to measure the timedependent fluorescence signal from the flowing solution. Under conditions of negligible adsorption on the microchannel surface, the signal was expected to rapidly jump at the instant corresponding to travel time between reservoir A and junction D2. A solid line (marked as fluorescein dye in Figure 4a) shows the signal jump at ta ) 172 s for a sample consisting only of fluorescein dye molecules. Here, the signal rapidly reaches a steady value corresponding to the concentration of fluorescein in the loaded sample. Figure 4a also shows the normalized signal (solid lines) versus time for experimental runs using 1, 2, and 3 mM CTAB solutions. Contrary to the characteristics of fluorescein sample, the measured signal from the CTAB samples was delayed and then increased gradually, indicating a loss of CTAB molecules due to adsorption on the channel walls. Figure 4a shows delay

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Table 1. Molar Concentration of CTAB Adsorbed and Desorbed on the Microchannel Surface concn of loaded sample, Cbulk (mM)

adsorbed molar concn ΓA (10-5 mol/m2)

total mol desorbed/ unit area in t < 400 s, ΓD (10-5 mol/m2)

1 2 3

6.15 6.58 6.59

1.16 2.19 2.78

times of 960, 570, and 380 s for detecting CTAB molecules at sample concentrations of 1, 2, and 3 mM, respectively. In each of these samples the signals were finally observed to reach the steady value corresponding to the CTAB concentration in the loaded sample. The surface concentration of adsorbed CTAB molecules, ΓA(t) (mol/m2), on the microchannel surface was easily calculated as

ΓA(t) )

∫t t (Cbulk - Cstream)dt

Q S

(3)

a

where Q (m3/s) is the volumetric flow rate, Cbulk (mol/m3) is the concentration of CTAB of loaded samples, Cstream (mol/m3) is the time-dependent CTAB concentration in the flowing solution, ta (s) is the travel time of molecules in the microchannel, and S (m2) is the total surface area of the microchannel prior to the detection point D2. The total adsorbed molecular concentration ΓAss (mol/m2) was estimated by evaluating the integral from ta to ts, the time to reach steady state. This is shown by the shaded area over the curve in Figure 4a. The computed values for ΓAss are tabulated in Table 1. ΓAss appears to be approximately the same for all three sample concentrations, suggesting strong surface adsorption of CTAB molecules. The results also suggest area coverage of 2.7, 2.52, and 2.52 A2/molecule for 1, 2, and 3 mM CTAB, respectively. These values are approximately 10 times larger than monolayer values21-23 evaluated using reflectometry. This suggests multilayer or micellar adsorption of CTAB. After achieving a steady state in the adsorption experiments, the flow was stopped and the CTAB solution in reservoir A was carefully replaced by pure DI water. Subsequently, the flow was established and the fluorescence signal was measured. Figure 4b shows the observed signal with time for the three samples. After an initial clearance (t e ta ) 172 s) of CTAB solution in the channel, a rapid decrease in signal was observed up to t ≈ 200s. For t > 200 s, the signal was observed to decrease at very slow rate. It is important to note that even after 15 min the signal failed to reach its expected value corresponding to negligible CTAB in the flowing solution. These observations suggest that the desorption of CTAB was slow from the “saturated” microchannel surfaces. The amount of CTAB molecules initially desorbed from the microchannel walls was estimated by integrating the measured concentration plots. The results are presented in Table 1. The data suggests that the microchannel surfaces remained ∼75% saturated for long times even when flowing pure DI water solution. Although adsorption-desorption kinetics of CTAB molecules is complex, some important experimental details were established using a Langmuir isotherm model.24 While this model is not applicable for multilayer adsorption, the purpose of this part of the exercise is to establish concentration conditions required for the experiments. The adsorption rate is proportional to the number (21) Atkin, R.; Craig, V. S. J.; Biggs, S. Langmuir 2001, 17 (20), 6155-6163. (22) Atkin, R.; Craig, V. S. J.; Biggs, S. Langmuir 2000, 16 (24), 9374-9380. (23) Velegol, S. B.; Fleming, B. D.; Biggs, S.; Wanless, E. J.; Tilton, R. D. Langmuir 2000, 16 (6), 2548-2556. (24) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John Wiley & Sons: New York, 1990.

Figure 5. Measured fluorescence spectrum for different surfactant aggregates.

of available sites (Γ∞ - ΓA) and the solute concentration in the flowing solution Cstream; the desorption rate can safely be assumed to be proportional to ΓA. Hence, the rate of surface accumulation of CTAB is written as

dΓA ) -kACstream(Γ∞ - ΓA) + k-AΓA ) dt -kA[Cstream(Γ∞ - ΓA) - KΓA] (4) Here kA (m3/s mol) and k-A (1/s) denote adsorption and desorption rate constants, and Γ∞ denotes the total number of sites available on the microchannel surface. At steady state, eq 4 results in

k-A (Γ∞ - ΓAss)Cbulk ) K) kA Γ ss

(5)

A

where K is the adsorption-desorption equilibrium constant. Equations 3-5 can be used to describe the observed adsorption/ desorption kinetics. As shown in Figure 4a, the best fit routines resulted in K ) 1 mM and kA ) 1.23, 2.51, and 3.95 m3/s mol for 1, 2, and 3 mM CTAB samples, respectively. The value of adsorption-desorption equilibrium constant K suggest that desorption of CTAB molecules was insignificant when CTAB concentrations were much larger than 1 mM. The above adsorption-desorption kinetic analysis not only offers a new approach for characterizing microchannel surfaces, but also provides a better understanding of the time scales needed to achieve steady-state conditions during microstructure evolution. The experiments establish the accuracy of dilution and in-channel concentrations. Similar experiments were performed using HDBS samples, and the adsorbed surface concentration was found to be 1.6 × 10-5 mol/m2, which is approximately 24% of the adsorbed surface concentration for CTAB. Hence, the microchannel concentrations of HDBS were essentially unaffected by loss or gain of surfactant molecules from the surface. 3.4. Microstructure Evolution in CTAB/HDBS/Water Solutions. Before examining the microstructures in a ternary system consisting of CTAB/HDBS/water, fluorescence emission spectra from different solutions of CTAB, HDBS, and mixtures were measured. Figure 5 shows the fluorescence spectra obtained for five solutions of 0.8 wt % (total concentration) surfactant mixtures. As the polarity of the microenvironment around Prodan increases, there is a well-known red shift in peak emission wavelength. The environment around the fluorophore is clearly becoming more polar as the HDBS ratio increases. This feature is extremely useful in tracking phase behavior in the mixed system.

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Table 2. Set of Reservoir Pressures for Various Compositions surfactant flow from reservoir B (%) 90 80 70 60 50 40 30 20 10

reservoir A -0.525 -0.438 -0.345 -0.252 -0.158 -0.064 0.029 0.122 0.217

pressure (psi) reservoir C -0.525 -0.438 -0.345 -0.252 -0.158 -0.064 0.029 0.122 0.217

reservoir D -1.18 -1.122 -1.06 -1.00 -0.939 -0.877 -0.81 -0.75 -0.69

In the experiments reported below, the emission at 480 nm has been monitored as an indication of the nature of the aggregates in the solution. Four overall (total) surfactant concentrations were examined in the microfluidic chip, 0.8 wt % (22 mM), 0.6 wt % (16.5 mM), 0.4 wt % (11 mM), and 0.2 wt % (5.5 mM). Note that these concentrations are much higher than the “saturation” concentration of 1 mM for minimum surfactant desorption from the microchannel surface. The concentrations of surfactants in the microchannel were unaffected by loss or gain of surfactant molecules from the surface. For each experiment, the microchannels were primed with CTAB and HDBS solutions of the targeted overall concentration for 500 s to achieve surface saturation. The phase diagram experiments were divided into two sets (S1 and S2) of experiments in order to achieve a large number of mixture dilutions. Set S1 was performed by loading a CTAB solution in reservoir B and a 50:50 mixture of CTAB: HDBS in reservoirs A and C. The liquid flow rates from B and A + C were then varied to achieve nine concentration ratios of CTAB:HDBS (in increments of 5 wt % in the mixing channel) in the CTAB-rich region. Similarly, set S2 was carried out by loading a HDBS solution in reservoir B and a 50:50 mixture of CTAB:HDBS in reservoirs A and C. The liquid flow rates were again varied to achieve nine concentration ratios of CTAB:HDBS in the HDBS-rich region. In all experiments, the liquid flow rates were adjusted by controlling the pressure difference between reservoirs B and D as well as between reservoirs A or C and D. The set of applied pressures are shown in Table 2. The residence time of the fluid in the detection channel was kept at 50 s or larger to ensure complete diffusional mixing of the surfactants by the time they reached the detector. To account for the viscosity effects, the samples were premixed with an inert dye (fluoroscein) and accurate compositions for the corresponding applied pressures were calibrated using fluorescein signals. Figure 6 is a sample fluorescence emission data obtained in set S2 with 0.8 wt % overall surfactant concentration. The ordinate represents the experimental timeline in which the HDBS solution was serially diluted with a 50:50 mixture of CTAB:HDBS. Nine ratios of HDBS are shown, with time steps of 100 s, each separated by a small fluorescence spike. The spikes were the result of slight pressure overshoots in the control pumps. The data shows a high signal-to-noise ratio, and the quantitative variation of fluorescence emission intensity with composition is a signature of a particular surfactant phase. The long time steps were chosen to achieve steady-state signals. Similar signatures were obtained in the CTAB-rich region of the phase diagram by loading CTAB in reservoir A. Once the reservoirs are loaded, all data for a set of experiments were collected within 1500 s. Figure 7 shows the normalized intensity versus surfactant composition for four overall surfactant concentrations of 0.2, 0.4, 0.6, and 0.8 wt %. The intensities are normalized with the intensity at 50:50 CTAB/HDBS for each experiment. The solid

Figure 6. Microchannel fluorescence signal for the S2 experiments.

Figure 7. Microchannel fluorescence intensity vs composition for 0.2, 0.4, 0.6, 0.8 wt % total surfactant in the CTAB/HDBS/water system The signal is normalized using the maximum (giant vesicles) and minimum signals (DI water).

line is a cubic spline fit through the data. The fluorescence emission from a surfactant mixture is not only a function of the local composition of surfactants but also a function of overall surfactant concentration. The characteristic behavior of the fluorescence signal is both quantitatively and qualitatively different for each composition and concentration. The effect of dilution on fluorescence emission depends on the microstructure that exists within a composition range. Therefore, the slope of fluorescence versus concentration was expected to change at phase boundaries. Figure 8 shows a plot of these slopes (obtained from cubic spline fits of the emission data to reduce noise). Phase boundaries are identified by locating concentrations at which the slope of the intensity versus concentration shows a distinct change. The observed phases can be split into mixed micelles (M), vesicles (V), giant vesicles (GV), and coexisting regions between phases, each marked by a difference in the emission intensity variation with composition. For compositions where one of the surfactants dominates, there is a tendency to form small vesicles because the differences in curvature between the inner and outer leaflets can be supported by differences in concentration in these layers. As the surfactant ratio approaches unity, it becomes more difficult to maintain different compositions in the inner and outer leaflets, thus creating structures of very small curvature, termed giant vesicles here. For the CTAB/HDBS system at 0.8 wt %, the microstructures change from micelles to small vesicles to large or giant vesicles. This general range of structures repeated at 0.6, 0.4, and 0.2 wt % total surfactant. These data can then be used to generate the

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Figure 9. Ternary phase diagram constructed using the microfluidic technique: red, micellar phase; blue, CTAB-rich vesicle phase; dark green, giant vesicle/vesicle phase; purple, giant vesicle phase; light green, HDBS-rich vesicle phase.

Figure 8. Gradient of measured fluorescence with composition for (a) 0.2 wt %, (b) 0.4 wt %, (c) 0.6 wt %, and (d) 0.8 wt % CTAB/ HDBS/water. The plots also show turbidity signals measured in the bulk for different composition samples (∆). The phase boundaries are selected by marked changes in the gradient: red, micellar phase; blue, CTAB-rich vesicle phase; dark green, giant vesicle/vesicle phase; purple, giant vesicle phase; light green, HDBS-rich vesicle phase.

phase diagram for the ternary system consisting of the two surfactants and water, as shown in Figure 9. To confirm that the microfluidic setup indeed provides information in agreement with more traditional measurements done in bulk systems, samples were examined using turbidity measurements, dynamic light scattering, and cryogenic transmission electron microscopy. Prior to each of these bulk phase measurements, samples in vials were equilibrated for 2 weeks. Turbidity was measured in a BI 200SM laser light scattering system, with the detector set at 90° to the incident laser beam. Changes in turbidity are a good indication of variations in microstructure, since the scattering intensity varies with the square of the mass of the scattering centers. Dynamic light scattering provides an indication of the hydrodynamic diameter of objects in solution and were also measured on the BI-200SM system. Since all solutions were filtered through a 0.2-µm filter to remove dust prior to dynamic light scattering measurements, the size distribution in the giant vesicle (GV) region was expected to be skewed toward the lower end. A similar result can be expected in cryo-TEM, where preparation of a thin film (∼200-500 nm thickness) of the sample on the holey carbon grid prior to vitrification tends to exclude large vesicles. However, each of these techniques allowed a powerful way to corroborate the results from the new method proposed in this paper. Table 3 summarizes results from bulk phase experimental measurements for 0.8 wt %. Each region in the phase diagram is accompanied by a characteristic turbidity, hydrodynamic size or microstructure visible using cryo-TEM. Note that all of these methods produced data that are consistent with that from the microfluidic setup, confirming that the microfluidic technique is indeed providing robust results. The clear advantage of microfluidics is the ease and speed with which such a phase diagram can be developed. One limitation to the microfluidic approach to determining phase behavior is that aggregate formation times must be fast compared to the residence time of the fluid in the microchannels. Thus slow self-assembling systems cannot be probed by this method.

4. Conclusions The phase behavior of a dilute CTAB/HDBS/water surfactant system was examined in a microchannel flow. Since the surfactant

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Table 3. “Bulk” Phase Experimental Techniques (a) Viscosity Measurement, (b) Dynamic Light Scattering, and (c) Cryo-TEM Pictures for Different Phases

evolution in microchannels undergoes diffusional transport at length scales between ∼10 and 100 µm, the determination of phase behavior in a microfluidic setup is rapid and accurate. A wide range of microstructures ranging from micelles (M) to vesicles (V) and to giant vesicles (GV) were observed in the ternary CTAB/HDBS/water system. Experimental data were independently compared and found to be consistent with the results obtained from “bulk” phase experiments using fluorescence, turbidity, light scattering, and cryogenic transmission electron microscopy. The determination of phase behavior in aqueous surfactant mixtures is an important problem for consumer product applications. The current methods that use bulk phase measurements are time-consuming and are serial in nature, that is, vials containing different concentrations of surfactants have to be

prepared and equilibrated separately prior to sampling. This process can take several weeks. The microfluidic setup proposed here allows fast sample equilibration and continuous dilution, so this process can be speeded up severalfold. This has important implications for the screening of surfactants for specific applications. Acknowledgment. This work was supported by the Petroleum Research Fund (PRF# 44637-G9) of the American Chemical Society (A.T.) and Ostrach Graduate Fellowship of Brown University (J.L.). We thank Jacinta Dos Santos (URI) and Kareem Reda (Brown) for help with fluorescence and turbidity measurements and Jayashri Sarkar (URI) for the cryo-TEM images. LA061818M