NANO LETTERS
Ion-Enrichment and Ion-Depletion Effect of Nanochannel Structures
2004 Vol. 4, No. 6 1099-1103
Qiaosheng Pu,† Jongsin Yun,‡ Henryk Temkin,‡ and Shaorong Liu*,† Department of Chemistry and Biochemistry and Department of Electric Engineering and Computer Science, Texas Tech UniVersity, Lubbock, Texas 79409 Received April 6, 2004; Revised Manuscript Received April 29, 2004
ABSTRACT Unique properties exist in nanofluidic channels. In this paper, we report a new phenomenon, ion enrichment/depletion, associated with nanochannel structures. As a voltage is applied across a nanochannel, ions are rapidly enriched at one end and depleted at the other end of the nanochannel. The degree of this enrichment and depletion is directly related to the extent of double-layer overlap. A simple model is presented to qualitatively interpret this phenomenon.
Integrated microfluidic devices have opened new horizons and are expected to lead to revolutionary changes in bioanalytical sciences and separation technologies. Chemical analyses on microfluidic platforms can be highly automated and reduce the consumption of reagents by several orders of magnitude relative to current practice.1-7 Chemical separation on these devices can be completed on a submillisecond time scale.8 Large-scale integration (LSI) of microfluidic devices has recently been reported;9 highly integrated microfluidic devices require reduced channel dimensions. As the channel dimension goes down to the nm scale, fluids inside these channels exhibit properties different from the bulk, such as reduced electroosmotic flow10 and increased viscosity and decreased dielectric constants.11 Another interesting observation is the rapid current decrease after an electric field is applied across a nanochannel membrane.12-16 Recently, several new phenomena associated with nanochannel structures have been reported.17-19 These phenomena include the fast protein concentration,17 ultrafast mixing, and displacement of charged analytes.18,19 Some of the above phenomena10 are well investigated and understood, while clear explanations of the underlying principles are lacking for other observations.12-19 We have focused our efforts on the eletrophoretic transport of ionic species through nanochannels since it is one of the major mechanisms to move various substances around in nanofluidic devices. Many of the unusual properties associated with nanochannel structures are originated from the electric double layer. * Corresponding author. E-mail:
[email protected] † Department of Chemistry and Biochemistry. ‡ Department of Electric Engineering and Computer Science. 10.1021/nl0494811 CCC: $27.50 Published on Web 05/19/2004
© 2004 American Chemical Society
Herein, we report the observation of the ion-enrichment and ion-depletion effects inherent with nanochannel structures and attempt to give the phenomenon a qualitative interpretation. The experiment was performed using a device as depicted in Figure 1. Eight parallel 60-nm-deep nanochannels were fabricated in a glass chip. The ends of the nanchannels were connected to two 100-µm-deep large U-channels. After all the channels and the reservoirs were filled with a solution containing either fluorescein (negatively charged) or rhodamine 6G (positively charged) in a sodium tetraborate buffer solution, an electric field was applied across the nanochannels. Both fluorescein and rhodamine 6G were enriched at the cathode end and depleted at the anode end of the nanochannels (see Figure 2). This phenomenon is called the “ion-enrichment and ion-depletion effect” of nanochannels. If we describe the degree of ion-enrichment and iondepletion in terms of an enrichment factor (EF) and a depletion factor (DF) as defined by equations 1 and 2 below, an EF of ∼100 and a DF of ∼500 were attained after application of 1 kV for 30 s. EF )
Cfinal - Cinitial Cinitial
(1)
DF )
Cinitial - Cfinal Cfinal
(2)
where Cinitial and Cfinal are the fluorescein concentrations in the U-channels before and after an electric field was applied across the nanochannels.
inversely proportional to the square root of the electrolyte concentration,21 and that of a glass-aqueous solution interface ranges from 3 to 300 nm for electrolyte concentrations of 10-2 to 10-6 M.22 When double-layer overlap occurs inside the nanochannel, the cation concentration will be greater than the anion concentration inside the nanochannel. That is, [A+] ) R‚[B-]
(3)
where R > 1. Referring to Figure 3, X1 and Y1 are two cross-sectional planes in the vicinity of the cathode end and X2 and Y2 are two cross-sectional planes in the vicinity of the anode end of the nanochannel, with both X planes in the large channel and both Y planes in the nanochannel. Under the influence of an electric field, the ion fluxes (J) across the cross-section planes X1 and X2 can be expressed as
Figure 1. (a) Schematic diagram of two large U-channels connected by 8 nanochannels. Standard photolithographic technologies and borofloat glass wafers were used to make the chip device. The width and depth of the nanochannel were respectively 100 µm and 60 nm. In the finished chip device, the nanochannels overlapped partially with the two U-channels. The length of the nanochannel between the two U-channels was about 1 mm. The dimensions of the two U-channels were 750 µm (width) × 100 µm (depth) × 20 mm (from reservoir to the nanochannels). (b) Picture of the nanochannel device. Each reservoir had a volume of ∼300 µL. (c) Zoom-in view of the vicinity of the nanochannels. (d) SEM image showing the cross-section of a nanochannel. (e) SEM image showing the depth of a nanochannel.
The question is why both positively and negatively charged ions were enriched (and depleted) on the same side of the nanochannels. To explain, let us assume a most simplified case (see Figure 3) in which a nanochannel connects two large channels. Since the nanochannel is usually wide and shallow (e.g., 100 µm wide vs 60 nm deep in this report), it can be considered a nanogap between two parallel plates. We further assume that (i) the two large channels are identical, (ii) the depth of the large channels is many times greater than the thickness of the electric double-layer and, therefore, the double-layer overlap in the large channels is negligible, and (iii) all the channels are filled with a uniunivalent (A+B-) electrolyte solution. Because the nanochannels used in this experiment were fabricated using glass materials, nanochannel surfaces were negatively charged at the operating pH and the associated electric double layers were positively charged. The net charge distribution in a narrow flat channel can be mathematically described.20 As a qualitative expression, a positively charged double layer means that [A+] > [B-] in the double layer region. From the Gouy-Chapman model, the double layer thickness is 1100
JlA ) El‚Sl‚µA‚[A]l
(4)
JlB ) -El‚Sl‚µB‚[B]l
(5)
and those across Y1 and Y2 can be described as JnA ) En‚Sn‚µA‚[A]n
(6)
JnB ) -En‚Sn‚µB‚[B]n
(7)
where E is the electric field strength, S is the section area, µ is the electrophoretic mobility, and subscripts n and l designate the parameters in the nanochannel and large channel, respectively. The negative signs in equations 5 and 7 indicate that the fluxes of anions are in the opposite direction of the electric field. To maintain the continuity of the current, we have (this is equivalent to a statement of Kirchoff’s first law relating to the flow of electrical current that applies to the present situation) JlA - JlB ) JnA - JnB
(8)
After combination of all the above equations and consideration of the equal concentrations of [A]l ) [B]l, we have
Jl ) A
( (
µA +
) )
(
)
‚µ [A]n B µA + µB/R ‚JnA ) ‚JnA µA + µB µA + µB
[A]n ‚µ [B]n A µB + R‚µA ‚JnB ) ‚JnB µA + µB µA + µB
µB +
JlB )
[B]n
(
)
(9)
(10)
Nano Lett., Vol. 4, No. 6, 2004
Figure 2. Ion-enrichment and ion-depletion before and after an electric field was applied across the nanochannels. The image was collected using a CCD camera. The area included in each image was similar to that shown in Figure 1c. After the fluorescence dye was loaded in all of the channels, the fluorescence from the two U-channels was apparent. The florescence from the nanochannels was not obvious due to the extremely low volume of fluorescein solution in the nanochannels. The five images in each row respectively represented the fluorescence intensities in the two U-channels before any voltage was applied (a), and after a voltage of 1000 V was applied for 0.5 s (b), 5 s (c), 10 s (d), and 20 s (e). The anode was on the right-hand side and cathode on the left-hand side of the nanochannels. In row A: a solution used to fill all the channels contained 30 µM of fluorescein and 70 µM sodium tetraborate buffer (pH ) 8), and in row B: the solution contained 10 µM of rhodamine 6G in 100 µM phosphate buffer (pH ) 7).
Figure 3. Schematic illustration of ion-enrichment and iondepletion effect.
Based on equation 9, we have JlA < JnA because R > 1. On the anode side, JlA provides cations to the end region while JnA takes away cations from the end region of the nanochannel. The unbalanced fluxes (JlA < JnA) cause a depletion of A+ in this region. On the cathode side, JlA takes away cations from the end region while JnA provides cations to the end region of the nanochannel. The condition JlA < JnA results in an accumulation of A+ in this region. Likewise, JlB > JnB based on equation 10. On the anode side, JlB takes away anions from the end region while JnB provides anions to the end region of the nanochannel. The unbalanced fluxes (JlB > JnB) of B- force its depletion in this region. On the cathode side, JlB provides anions to the end region while JnB takes away anions from the end region of the nanochannel. The difference of JlB and JnB brings an accumulation of B- in Nano Lett., Vol. 4, No. 6, 2004
this region. That is, both positive and negative ions get depleted at the anode end and accumulated at the cathode end of the nanochannel. Figure 3 also presents a cartoon situation when a current of four unit charges passes through the nanochannel. In the two large channels, this current is carried by two cations migrating toward the cathode and two anions migrating toward the anode, assuming that the cation and anion have the same electrophoretic mobility. In the nanochannels, it is carried by three cations migrating toward the cathode and one anion migrating toward the anode, assuming R ) 3. Let us focus on the anode end region between X2 and Y2. Across X2, two cations enter this region and two anions leave this region. Across Y2, three cations leave this region and one anion enters this region. The net change in this region is a loss of one cation and one anion. Similarly between X1 and Y1, the net change is a gain of one cation and one anion. Ions (both negative and positive) are therefore enriched at the cathode end region and depleted at the anode end region of the nanochannel. The cartoon, of course, presents only one very specific case for equations 9 and 10, in which µA ) µB and R ) 3. Similarly, if the surfaces of the nanochannel are positively charged, the cation concentration will be lower than anion concentration. That is, R < 1. Equations 9 and 10 still apply. The difference is that the depletion will now occur on the cathode end region and enrichment on the anode end region of the nanochannels. Based on this model, the ion enrichment and depletion effect should be diminished at an elevated buffer concentration because the double-layer thickness (and thus the extent of double-layer overlap) decreases with the solution ionic strength. The experimental results presented in Figure 4 indeed show this behavior. A significant reduction in the rate with which the enriched/depleted zones 1101
Figure 4. Effect of buffer concentration on ion enrichment and ion depletion. The fluorescent dye solution contained the same concentration (30 µM fluorescein) with gradually increased buffer (sodium tetraborate) concentration, from 200 µM (row A), to 500 µM (row B), to 1 mM (row C), and finally to 3 mM (row D). The four images in each row represented the fluorescence intensities in the two U-channels before any voltage was applied (a), and after a voltage of 1000 V was applied for 5 s (b), 10 s (c), and 20 s (d). All other conditions were the same as those in Figure 2.
are formed occurs as the Na2B4O7 buffer concentration changed from 200 µM to 1 mM. By the time the buffer concentration was increased to 3 mM, no ion-enrichment/ depletion effect was observed, indicating that double-layer overlap was insignificant under these experimental conditions. It is worth pointing out that, based on the above model, tetraborate and sodium ions should have been enriched on the cathode side and depleted on the anode side of the nanochannel as well, although only the enrichment and depletion of fluorescein was seen in Figure 3. Our model is established based on a fundamental assumption that one kind of ions dominates the other due to the double layer overlap in the nanochannels. To test the validity of this assumption, we measured the extent of fluorescein depletion inside the nanochannel as a function of ionic strength. When a solution containing 30 µM of fluorescein and 30 mM of sodium tetraborate is in contact with a glass surface, the resulted double layer thickness is calculated to be about 1 nm.21 After this solution was filled in the 60-nm-deep nanochannels, the double layer overlap was negligible and fluorescein concentration inside the nanochannels should be the same as that in the bulk. When the double layer overlap occurred at reduced ionic 1102
strengths, the fluorescein was depleted. Figure 5 presents the fluorescein depletion in the nanochannel as a function of tetraborate concentration. Less than 10% (∼3 µM) of the fluorescein was present in the nanochannels when a solution of 30 µM of fluorescein and 30 µM of sodium tetraborate was filled in them. A laser-induced confocal fluorescence detector was used for this experiment. The fluorescence background was corrected and the effect of sodium tetraborate concentration on fluorescence intensity was considered when the fluorescein concentrations in the nanochannels were calculated. These results strongly suggested that positive ions were dominant over negative ions when double layers overlapped in the nanochannels, and hence demonstrated the validity of our fundamental assumption. In summary, we have observed an ion-enrichment and iondepletion effect that emerges as the dimension of a fluidic channel enters the nanometer regime. A simple model that invokes double-layer overlap is adequate to interpret this effect qualitatively. Although the model is not yet able to quantitatively describe the ion-enrichment and ion-depletion effect, it reveals the fundamental mechanisms of this effect. The basic principles can be helpful in understanding the previous observations12-19 and designing nanofluidic devices. Nano Lett., Vol. 4, No. 6, 2004
Figure 5. Effect of tetraborate concentration on fluorescein concentration in the nanochannels. The Y-axis is fluorescein concentration in the nanochannels and the X-axis is the concentration of sodium tetraborate of the test solution. All test solutions contained the same amount of fluorescein (30 µM) but different amounts of sodium tetraborate (30 µM, 100 µM, 300 µM, 1 mM, 3 mM, 10 mM, and 30 mM, respectively). After the solution containing 30 µM fluorescein and 30 mM sodium tetraborate was filled in the nanochannels, the fluorescein concentration in the nanochannels was considered to be 30 µM. The fluorescein concentrations at reduced ionic strengths were calculated based on their fluorescence intensities relative to that of the above solution. The effect of sodium tetraborate concentration on fluorescence intensity was considered and the background signal was corrected when the fluorescein concentrations were calculated. An Ar ion laser (488 nm and 10 mW) was used to excite the fluorescein. The fluorescence signal was collected by a PMT after passing through long pass filter (cutoff wavelength, 520 nm).
Acknowledgment. This project was supported by the Texas Excellence Funds. The authors have used the facilities of the Nano Tech Center at Texas Tech University to fabricate the nanochannel devices. References (1) Harrison, D. J.; Fluri, K.; Seiler, K.; Fan, Z.; Effenhauser C. S.; Manz, A. Science 1993, 261, 895-897. (2) van den Berg, A.; Lammerink, T. S. J. Top. Curr. Chem. 1997, 194, 21-49.
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