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J. Phys. Chem. C 2007, 111, 10818-10823
Probing Zeta Potential in Flat Nanochannels Shaorong Liu,*† Qiaosheng Pu,† Chang Kyu Byun,† Shili Wang,† Juan Lu,† and Ya Xiong‡ Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409, and School of Chemistry and Chemical Engineering, Zhongshan UniVersity, Guangzhou, P.R. China ReceiVed: February 13, 2007; In Final Form: May 18, 2007
Measuring zeta potentials in nanometer-deep channels (nanochannels) is challenging but critical in modeling mass transport through these channels. To our knowledge, there are no reliable methods available to determine these potentials, presumably due to the fact that zeta potential changes with channel depth in nanochannels. In this work, we describe a novel approach to address this issue. The approach includes four steps: (1) a series of potential curves is calculated at various zeta potentials using an established model; (2) a set of corresponding concentration profiles of a selected ion is obtained according to the Boltzmann equation, and an average concentration is calculated from each of the profiles; (3) the average concentration of the selected ion in a nanochannel is experimentally measured; and (4) the actual concentration profile is identified by matching the measured concentration with the calculated results. Once the concentration profile is unveiled, the zeta potential is determined. To demonstrate the application of this method, we have measured the zeta potential in a 60-nm-deep channel under different electrolyte concentrations. When the ratio of channel depth to Debye length is greater than 20, the zeta potential in the nanochannel is comparable to that in a large (50-µm-deep) channel within the experimental uncertainties ((10%). As the ratio decreases, the absolute value of the zeta potential in the nanochannel becomes significantly lower than that in the large channel, that is, the zeta potential decreased from -124 mV in the 50-µm-deep channel to 90 mV in the 60-nm-deep channel at a ratio of ∼6.
Introduction Mass transport through nanometer-deep channels (nanochannels) is an interesting and important research area, and has attracted increasing attention recently.1-13 To quantify this transport, one needs to know the ion distributions in these narrow channels. Models have been developed to calculate concentration profiles,14-20 but the calculated results are functions of zeta potential (ζ). Therefore, finding ζ values is critical in assessing mass transport though nanochannels. (Note: The channel depths we are interested in this work are greater than 10 nm. At these depths, the macroscopic physical laws remain valid and unaltered. Also, the width and length of the nanochannel are practically infinite compared to its depth.) Electroosmotic mobility (µeo) is frequently utilized to evaluate ζ, since ζ and µeo have the following relationship:
ζ ) 4πηµeo/
(1)
where η is the viscosity and is the dielectric constant of the solution. This method has been successfully used to measure ζ in micrometer-scale capillaries/channels, but it has two major limitations: (i) eq 1 requires the thickness of an electrical double layer (EDL) to be small compared to the channel depths (2λ/h < 0.01,21,22 where λ is the Debye-length and h is the channel height or capillary diameter), and (ii) the ion-enrichment and ion-depletion effect23 in nanochannels may interfere with the measurements. Significant errors are created when this method is used to determine ζ in nanochannels. Corrections of some of * Corresponding author. E-mail address:
[email protected]. † Texas Tech University. ‡ Zhongshan University.
the errors can be done,13,22 but it is challenging to circumvent all of these problems simultaneously. Zeta potential can also be acquired by measuring the streaming current or potential. Streaming current and potential are functions of ζ but the relationships are complex, compared to that between µeo and ζ. Usually one has to know both the ion distribution and the flow velocity profile and overcome the effects of electrode polarization and surface conduction to achieve correct ζ values. Because of these requirements, this method is rarely used to measure ζ in nanochannels, although it has been used for micrometer-scale channels/capillaries.21,24 To our knowledge, no reliable methods are available to determine ζ in nanochannels. In this report, we introduce a novel approach to address this issue. The following outlines the working principle of this method. First, a series of potential (φ) curves are calculated at different ζ using models developed in the literature.14,15 In the second step, a set of corresponding concentration profiles of a selected ion are calculated using Boltzmann equation:
[Az] ) [Az]0‚exp[-z‚e‚φ/(k‚T)]
(2)
where [Az] is the concentration profiles of the selected ion, [Az]0 is the concentration of Az in its bulk solution, z is the charge on the ion, e is the charge on the electron, k is the Boltzmann constant, and T is the absolute temperature. In the third step, the concentration of Az in a nanochannel is measured. The detected concentration is referred to as [Az]dtctd. Owing to the fact that Az is ununiformly distributed across the depth of the nanochannel, [Az]dtctd is actually an average concentration of Az. Since the average concentration of Az can also be calculated from its concentration profile,
10.1021/jp071252q CCC: $37.00 © 2007 American Chemical Society Published on Web 06/29/2007
Probing Zeta Potential in Flat Nanochannels
[Az] ) {
h/2 [Az]dy}/h ∫-h/2
J. Phys. Chem. C, Vol. 111, No. 29, 2007 10819
(3)
where y is the distance to the nanochannel middle plane (defined as a plane in the middle of the channel and perpendicular to the channel depth), and h is the depth of the nanochannel. The true [Az] profile in the nanochannel is identified by (the fourth step) matching [Az]dtctd with [Az]. There will be only one [Az] profile that satisfies [Az]dtctd ) [Az]. From this [Az] profile, the actual φ curve and ζ are determined. Experimental Methods Materials and Chemicals. Borofloat wafers were obtained from Precision Glass & Optics (Santa Ana, CA). Fluorescein (disodium salt), sodium chloride, and other chemicals were all purchased from Fisher Scientific. All solutions were prepared with ultrapure water purified by a NANO pure infinity ultrapure water system (Barnstead, Newton, WA). Fabrication of Nanochannel Device. Figure 1a presents a schematic diagram of the nanochannel device used in this experiment. A nanogroove was made on one wafer, and large grooves were made on another wafer. The two wafers were then aligned face-to-face and bonded to produce the nanochannel device. A standard photolithographic process and two Cr photomasks were used for the fabrication. For production of the nanogroove, the process was similar to that described previously.23,25 Briefly, a borofloat glass wafer (Precision Glass & Optics, Santa Ana, CA) was cleaned, dried, and then coated with a thin layer of photoresist (Shipley1818, Shipley, Santa Clara, CA) using an EC101D spinner (Headway, Garland, TX). The photoresist was then soft-baked at 90 °C for 15 min. The nanochannel was then transferred from a photomask to the photoresist film using an ABM aligner (ABM, San Jose, CA). After the exposed photoresist was dissolved in a developer solution and the wafer was rinsed, the remaining photoresist on the wafer was hard-baked at 150 °C for 2 h. After the wafer was cooled down, it was immersed in a 12% hydrofluoric acid solution at ambient temperature for ∼10 s. After the residual photoresist was removed using a piranha solution (four portions of 96% sulfuric acid and one portion of 33% hydrogen peroxide), the wafer was rinsed with water and dried with nitrogen, and the groove depth was measured on an Alpha Step 200 profilometer (Tencor Instruments, Mountain View, CA). Figure 1b presents a typical profile of a nanogroove (Note: this nanogroove had a depth of ∼50 nm). The depth variation seems to be within ( 3 nm. However, the channel surface is microscopically rough, as indicated by the scanning electron microscope (SEM) image (see Figure 1c) of the etched channel surface. For fabrication of the large channels, a separate wafer was used. A sacrificial layer of Cr/Au was utilized to facilitate the groove etching. The procedure was pretty routine, and it has been described in the literature.26,27 After four through-holes were drilled at the ends of the grooves for the large channels, the two structured wafers were aligned as shown in Figure 1a and thermally bonded together at 600 °C for 3 h. The resulting chip device had a 60-nm-deep, 100-µm-wide, and 10-mm-long nanochannel and four 30-µm-deep, 1-mm-wide, and 50-mmlong large channels. The groove depths measured on the profilometer were taken as the channel depths after bonding. To examine whether the channel depth will change before and after bonding, a bonded chip was diced across the channels, and the channel depths were measured under an SEM.23 No significant differences were observed between the original profilometric groove depths and
the post-bonding microscopically measured groove depth, within the measurement uncertainties.23 Laser-Induced Fluorescence (LIF) Detection System. Figure 1d presents a schematic diagram of the LIF detector. A 488-nm laser beam from an argon ion laser (Laser Physics, Salt Lake City, UT) was reflected by a dichroic mirror (Q505LP, Chroma Technology, Rockingham, VT) and focused onto a microchannel or a nanochannel in the nanochannel device through an objective lens (20× and 0.5 NA, Rolyn Optics, Covina, CA). The positioning and focusing was achieved by an x-y-z translation stage to which the nanochannel device was affixed. Fluorescence from the microchannel/nanochannel was collimated by the same objective lens, and collected by a photosensor module (H5784-01, Hamamatsu, Japan) after passing through the dichroic mirror, an interference band-pass filter (532 nm, Carlsbad, CA), and a 200-µm pinhole. The output of the photosensor module was measured using an NI multifunctional card DAQCard-6062E (National Instruments, Austin, TX). The data were acquired and treated with a program written in-laboratory with Labview (National Instruments, Austin, TX). Measurement of the Fluorescein Concentration inside a Nanochannel. To determine the fluorescein concentration in a nanochannel, we first checked whether the concentrations of sodium chloride would affect the fluorescence intensity of fluorescein. The test was done in a large (30-µm-deep) channel by introducing solutions containing the same concentration of fluorescein but different concentrations (from 100 µM to 100 mM) of sodium chloride and measuring the fluorescence intensities of these solutions. No significant changes (less than ( 3%) in fluorescence intensities were observed. We then established a calibration curve of fluorescein in 1.0 mM NaCl and 30 µM NH4Cl/NH4OH (pH ) 9.4) in the large channel. The linear coefficient was r2 ) 0.999 for fluorescein solutions with concentrations ranging from 0.3 to 30 µM. After that, a blank solution (the same as the test solution but without fluorescein) was filled in all channels, and the background signals in both the large channel and the nanochannel were measured. An increased but fixed photosensor voltage was used to detect the fluorescence signals from the nanochannel. Then, the first test solution was filled in all the channels, and the fluorescence signals were measured in both the large channel and the nanochannel. After subtraction of the background signals, the fluorescence signal from the nanochannel was divided by that from the large channel to obtain a ratio. The same tests were performed for all other test solutions, and distinct ratios were obtained. Since the signal in the large channel was virtually constant, the ratio variations reflected the fluorescein concentration changes in the nanochannel. In this paper, we assumed the fluorescein concentration in the nanochannel to be the same (3 µM) as it was in the bulk solution when 100 mM NaCl was used as the dominant electrolyte, because the Debye length of the EDL was less than 1 nm16 under this condition, and EDL overlap should be insignificant in a 60nm-deep channel. The concentrations of fluorescein under other conditions were calculated using the following equation:
[Fl2-]dtctd,in x mM NaCl ) 3 × Ratioin x mM NaCl ÷ Ratioin 100 mM NaCl mM (4) Since the detector collected all fluorescence signals from all fluorescein molecules across entire depth, the measured concentration was actually an average concentration of fluorescein in the nanochannel. Figure 2 presents [Fl2-]dtctd as a function of [NaCl].
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Figure 1. Schematic arrangement of the experimental system. (a) Channel layout of the nanochannel device. The nanochannel had a channel depth of h ) 60 nm, a width of 100 µm, and a length of 10 mm. The four large channels had a depth of 30 µm, a width of 1 mm, and a length of 50 mm. (b) Channel profile measured on an alpha-Stepper 200 profilometer (KLA-Tencor, San Jose, CA). (c) SEM image of an etched channel surface from a Hitachi S-4300 high-resolution field emission SEM. (d) Configuration of the confocal LIF detector.
Results and Discussion One potential problem with the procedure outlined in the Introduction is the unavailability of suitable methods to measure the concentration of any of the electrolytes in the nanochannel. To address this issue, we can add a small amount of a probing electrolyte (e.g., 3.0 µM fluoresceindisodium salt in this experiment) that can be accurately detected in the nanochannel. The concentration of the probing electrolyte should be at a concentration considerably lower than those of the dominant ions in the nanochannel so that its presence will not affect the potential distribution, φ. Because eq 2 also applies to fluorescein (Fl2-), a series of concentration profiles ([Fl2-]) can be obtained corresponding the φ curves at different ζ values. By matching [Fl2-]dtctd with the calculated average concentration [Fl2-], the true [Fl2-] profile is identified, and hence the actual φ curve and zeta potential (ζ ) φ|y)(h/2). The following presents a concrete example demonstrating in detail how this new method is employed to determine the ζ in a 60-nm-deep silica channel filled with 1.0 mM NaCl + 30 µM NH4Cl/NH4OH (pH ) 9.4). Because none of the ions in this solution can be accurately measured in the nanochannel, 3.0 µM Na2Fl was introduced into the test solution as a probing
electrolyte. The model used in this work was similar to that described by Burgreen and Nakache,14
-
∫uu
m
du
xsinh u - sinh um 2
2
)
|y| λ
(5)
where u ) zeφ/2kT, um ) zeφm/2kT (φm is the midplane potential or the potential at y ) 0), and λ is the Debye length (at 25 °C, λ ≈ 0.3/xI nm,16 where I ) 1/2∑ Ci zi2). In 1.0 mM NaCl + 30 µM NH4Cl/NH4OH + 3.0 µM Na2Fl, λ ≈ 9.5 nm. Figure 3a presents three φ curves obtained by numerically solving eq 5 under the conditions given in the caption with ζ ) -1.76, -1.38, and -0.12 (2kT/e) [or -90, -71, and -6.2 mV, respectively]. Theoretically, an infinite number of φ curves can be obtained at all ζ values. For the sake of simplicity, only three are presented in Figure 3a. Figure 3b presents the three corresponding [Fl2-] profiles calculated using eq 2. On the basis of the data presented in Figure 2, the measured average fluorescein [Fl2-]dtctd was 1.4 µM. The concentration profile at ζ ) -1.76 (2kT/e) (see Figure 3b) was identified to be the true [Fl2-] profile in the nanochannel because its calculated [Fl2-] equals 1.4 µM. The φ curve at ζ ) -1.76 (2kT/e) (see Figure
Probing Zeta Potential in Flat Nanochannels
J. Phys. Chem. C, Vol. 111, No. 29, 2007 10821
Figure 2. Average fluorescein concentration in a nanochannel as a function of dominant electrolyte concentration. The four test solutions respectively contained 1, 3, 10, and 30 mM NaCl, and all these test solutions contained 30 µM NH4Cl/NH4OH (pH ) 9.4) and 3 µM fluorescein-disodium.
Figure 4. Concentration profiles of [Na+], [Cl-], and [H+] in a 60nm-deep silica channel. These profiles were calculated using eq 2 after the actual potential curve, φ, was identified. The channel was filled with an electrolyte solution containing 1 mM NaCl, 30 µM NH4Cl/ NH4OH (pH ) 9.4), and 3 µM fluorescein-disodium. (a) Concentration profile of Na+, (b) concentration profile of Cl-, and (c) concentration profile of H+.
Figure 3. Theoretically calculated potential curves and corresponding ion distribution profiles: (a) potential curves calculated using eq 5 and (b) [Fl2-] profiles calculated using eq 2 based on the potential curves in panel a. T ) 298 K, λ ) 9.5 nm, h ) 60 nm, and ζ ) -1.76, -1.38, and -0.12 (2kT/e), respectively.
3a) was subsequently recognized as the actual potential distribution function. In practice, when only a limited number of φ curves and [Fl2-] profiles are available, one should first determine where (between two ζ values) the true [Fl2-] profile is by comparing [Fl2-]dtctd with the calculated [Fl2-] data. Then, more φ curves and [Fl2-] profiles are generated between these two ζ values to narrow down the position of the true [Fl2-] profile. This process
is repeated until the difference between the calculated [Fl2-] and [Fl2-]dtctd is acceptable. With the φ curve obtained, concentration profiles of Na+ (Figures 4a), Cl- (Figure 4b), and H+ (Figure 4c) were calculated using eq 2. As can be seen from these figures, the cation concentrations near the surface were ∼5 times higher, while the anion concentration close to the surface was ∼5 times lower than that in the middle of the channel under the given conditions. It is worth mentioning that the fluorescein concentration close to the surface was ∼24 times lower than that in the middle of the channel. This is because fluorescein carries a -2 charge, and [Fl2-] changes proportionally with [Cl-]2 (this relationship can be derived from eq 2). Following the same procedure and using the [Fl2-]dtctd data presented in Figure 2, three additional [Fl2-] profiles were identified (see Figure 5) for [NaCl] ) 3.0 mM, 10 mM, and 30
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Figure 7. Fluorescence intensity of fluorescein as a function of pH.
Figure 5. Fluorescein concentration profiles under different [NaCl]. For all these curves, the areas underneath these curves divided by the channel depth (the average concentrations) match the data points presented in Figure 2.
Figure 6. Effect of [NaCl] on ζ and midplane potential: (a) effect on ζ and (b) effect on midplane potential. The circular and square symbols in panel a respectively represent the ζ in 60-nm-deep and 50-µm-deep channels. The ζ in the 50-µm-deep channel was calculated based on eq 1 from the electroosmotic mobility data (µeo) measured under various electrolyte concentrations.
mM. Under these concentrations, the Debye lengths are 5.5, 3.0, and 1.73 nm, respectively. From these profiles, three corresponding φ curves were subsequently created (not shown), and the ζ and φm values were determined (Figure 6). Normally, the absolute value of ζ increases with the decreasing [NaCl] in large channels (see the dashed line in Figure 6a) when EDL overlap can be neglectedsthe common ionic strength effect.21 To the contrary, it decreased with the decreasing [NaCl] from 3 to 1 mM (see the circular symbols in Figure 6a) as the Debye length increased from 5.5 to 9.5 nm in the 60-nm-deep channel. This was due to the EDL overlap that causes the reduction of the magnitude of the ζ, an effect that had been reported in the
literature.28 The results exhibited in Figure 6a were actually a combination of the above two effects. It should be noticed that the magnitude of the midplane potential (e.g., the data shown in Figure 6b) can be used as a parameter to express the degree of EDL overlap: the higher the magnitude, the more severe the EDL overlap. To generate the data points in Figure 2, we assumed that the reduction of the fluorescence intensity in the nanochannel was a result of a diminished [Fl2-]. Could the fluorescence signal decrease be caused by the pH change in the nanochannel solution? To test the effect of pH on fluorescein fluorescence intensity, we obtained a curve as presented in Figure 7. As can be seen, the fluorescence intensity of fluorescein remained almost a constant when pH was higher than 8.0. Referring back to the data presented in Figure 4c, [H+] is 8.4) in the nanochannel. These results suggested that the fluorescence intensity change was indeed a result of a diminished [Fl2-]. As mentioned earlier, the probing electrolyte should be at a concentration considerably lower than those of the dominant ions in the nanochannel to avoid causing significant variations of φ. Figure 8 presents the calculated effects of introducing an A+B--type and a C2+D2--type probing electrolyte to a dominant electrolyte on a potential profile. When an A+B--type electrolyte is added to a NaCl solution at a concentration of [NaCl] (where [NaCl] . [A+B-]). Because A+B- and NaCl are the same type of electrolytes, the resulting solution is equivalent to a pure NaCl solution with a concentration of [NaCl]′ ) [NaCl] + [A+B-].29 Figure 8a presents the potential profile calculated using equations described in the literature14,15 after assuming ζ ) -2(2kT/e). When a C2+D2--type electrolyte is introduced ([NaCl] . 2+ [C D2-]), the situation is more complicated because [C2+D2-] cannot be easily converted to an equivalent [NaCl]. Since the following equation exists,29
() dφ dy
2
)
2RT 0
∑i C0i exp
( ) -zieφ kT
+ constant
(6)
where R is the gas constant, is the relative dielectric constant of the solution, 0 is the permittivity of vacuum, C0i represents the concentration of ion i in the bulk solution, and zi is the charge on the ion, [C2+D2-] may be converted to [NaCl] using the following equation:
[NaCl]′′) [C2+D2-]‚exp
(-eφ kT )
(7)
Although [NaCl]′′ changes with φ in the above equation, it can be treated as a constant as long as [C2+D2-] is small. With this conversion plus the same assumptions made to generate Figure 8a, we calculated the potential profiles as exhibited in Figure 8b.
Probing Zeta Potential in Flat Nanochannels
J. Phys. Chem. C, Vol. 111, No. 29, 2007 10823 continuing to work on this project so that we can gain more insightful information on how ζ changes with channel depth and/or EDL overlap, and empirical relationships will be established between these parameters. Although only a flat nanochannel was tested in this report, the fundamental principle of the approach to measure ζ applies to other (e.g., round) nanochannels. When a probing electrolyte is used, a univalent tracer electrolyte is preferred because it will create less error compared to multivalent ones. Acknowledgment. This project is supported by NSF (CHE0514706) and the Texas Advanced Research Program. References and Notes
Figure 8. Calculated error on a potential curve as a probing electrolyte is introduced: (a) after an A+B--type probing electrolyte is added in the NaCl solution in which [AB]/[NaCl] ) 0.3%, and (b) after a C2+D2--type probing electrolyte is added in the NaCl solution in which [CD]/[NaCl] ) 0.3%. The dominant electrolyte was assumed to be NaCl. The thick line in each panel indicates the φ curve before the probing electrolyte is introduced.
The results shown in Figure 8 indicate that the absolute potential values decrease with the addition of the probing electrolyte. The maximum errors occurred at y ) 0: ∼1 and ∼10% when 0.3% A+B- and 0.3% C2+D2- were added. Apparently, the effect of adding a multivalent electrolyte on potential was much more significant than that of adding a univalent electrolyte. In this experiment, a divalent ion (fluorescein) was used as a probing ion because we have an LIF system that was ready for its detection at a low limit of detection. Since the probing electrolyte was Na2Fl, the results obtained in this work should be within 1-10%. Conclusions In summary, we have described a novel approach to measure ζ in nanochannels. To our knowledge, there are no suitable methods available to accurately evaluate ζ in nanochannels. Using this approach, ζ has been obtained in a 60-nm-deep flat nanochannel under various conditions. When the channel depthto-Debye length ratio is greater than 20, the ζ in the nanochannel is comparable to that in a large channel within the experimental uncertainties ((10%), and the effect of EDL overlap might be neglected. As the ratio decreases, the absolute value of the ζ in the nanochannel decreases significantly. For example, the ζ diminished from -124 mV in the 50-µm-deep channel to 90 mV in the 60-nm-deep channel when the ratio was ∼6. We are
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