NANO LETTERS
Ionic Transport Phenomena in Nanofluidics: Experimental and Theoretical Study of the Exclusion-Enrichment Effect on a Chip
2005 Vol. 5, No. 6 1147-1155
Adrien Plecis,* Reto B. Schoch, and Philippe Renaud Microsystems Laboratory, STI-LMIS, EPFL, CH-1015 Lausanne, Switzerland Received February 10, 2005; Revised Manuscript Received April 8, 2005
ABSTRACT In nanometer-sized apertures with charged surfaces, the extension of the electrical double layer results in the electrostatic exclusion of co-ions and enrichment in counterions, which affects the permselectivity of such structures. A modeling of this phenomenon is proposed and is compared with quantitative measurements of the ionic permeability change of a Pyrex nanoslit at low ionic strength. The comparison of experimental results with theoretical predictions justifies that electrostatic forces are the governing forces in nanofluidics.
As the surface-to-volume ratio is increasing with miniaturization, interfacial effects are becoming more and more important. Among them, the electrical double layer (EDL) is a specific charge distribution at the liquid-solid interface: the fixed surface charges on the solid are compensated by mobile counterions in solution. The thickness of this electrostatic screening zone depends on ionic concentration and can vary from less than 1 nm at high ionic strength to a few tens of nanometers at low ionic strength. In the case of nanometer-sized apertures, the EDL can represent a significant fraction of the total volume and as its ionic composition can be highly unsymmetrical, EDL extension results in a difference in the overall cationic and anionic concentrations in the opening. In the present work, the counterion enrichment and the exclusion of co-ions due to electrostatic interactions with surface charges is called the exclusion-enrichment effect (EEE). The charge-selectivity induced by surface charges in nanopores has first been observed in biological ionic channels. Among the mechanisms responsible for the permselectivity of such structures1 are the electrostatic interactions of ions with charged amino acid residues presented in the lumen of these biopores. Eisenberg and co-workers developed the theory of a charge selectivity induced by a specific charge distribution in open ionic channels,2 and compared their theoretical results with conductance measurements. Recent work3-5 performed on the structure of passive ionic channels further validates the assumption that the charge selectivity was due to the presence of the ionic residues. * Corresponding author. E-mail:
[email protected]. 10.1021/nl050265h CCC: $30.25 Published on Web 04/29/2005
© 2005 American Chemical Society
The permselectivity induced by the EEE in nonbiological structures was first experimentally investigated with the advent of nanoporous membranes. Many groups established the possibility to modulate the transport of charged species through such synthetic sieves. Martin et al.6-8 developed a gold-plating technique that allowed them to control both size and surface chemistry of pores on polycarbonate track etched (PCTE) membranes. Further transport studies highlighted a growing permselectivity of these membranes on anions or cations when EDL thickness was in the order of the pore radius. The ionic permselectivity was also shown to depend on the surface charge: positively charged pores showed an increased anion flux compared to negatively charged pores, and inversely for cations. This legitimates the idea that the EEE was responsible for the permselectivity. Numerical resolutions of the fundamental flux equations by Ramirez et al.9,10 for such membranes were compared with experimental results and could explain qualitatively the observed permselectivity. Such permselective membranes can have practical applications in several fields. Bluhm et al.11 investigated cation transport across positively charged porous alumina membranes for the separation of radioactive and hazardous metal cations from contaminated water. Separation of proteins of similar size has recently been carried out by Stroeve et al.12,13 for a proteomic purpose, showing that electrostatic effects enabled transport only if the proteins were at their point of zero charge. Biotechnological applications have also been investigated14 for bioseparation and drug delivery applications. However, all these experiments deal with macroscopic
Figure 1. Schematic sketch of the exclusion effect on the anionic transport. At high ionic strength, there are a lot of counterions (cations) in solution, and the negative surface charge of the Pyrex is immediately shielded so that anions (co-ions) can freely diffuse in the whole geometrical section S* of the slit. The instantaneous flux without electrostatic interactions φ* is proportional to S*. At low ionic strength, counterions are less numerous and less effective to shield the negative surface charge. EDL thickness λD increases (eq 11) and as it is mainly composed of cations, the effective section Seff (through which anions can diffuse) decreases. This results in a lower effective flux φeff.
setup and samples and require several hours of experimentation. As micro- and nanofluidic developments offer the possibility to precisely control the size and geometry of nanoscaled structures, these phenomena can be investigated and used with a higher efficiency in micro-total-analysis systems (µ-TAS). So, Kuo et al.15 introduced these nanoscaled structures in the microfluidic field by connecting polydimethyl-siloxane channels through a PCTE membrane and demonstrated some interesting applications as molecular gates in such microfluidic devices. Recently, Pu et al.16 filled a microfabricated nanochannel in Pyrex with aqueous solutions containing fluorescent anionic dyes. A dramatic change in the electrophoretic transport of these dyes through the nanochannels was observed when the EEE discriminates ionic population in the nanochannel at low ionic strength. In this latter case, as the electrophoretic current is mainly due to the cationic species in excess in the nanoslits, anionic dyes accumulate at the nanochannel entrance and a depletion in their concentration is observed at the nanochannel exit. The present study investigates the consequences of the EEE on the passive transport of charged species through a Pyrex nanoslit: by measuring the flux of charged fluorescent dyes through the slit, it is possible to investigate the quantitative changes in the nanoslit permeability when EDL thickness increases. For anions, the decrease in nanoslit permeability at low ionic strength is schematically described in Figure 1 as the electrostatic “narrowing” of the slit. At high ionic strength, the instantaneous flux φ* is proportional to the geometrical section S*. When EDL gets larger at low ionic strength, the effective section Seff through which anions can diffuse is reduced, resulting in a lower effective flux φeff. For cationic species, the enrichment effect at low ionic strength increases the number of cations in the nanoslit that can be transported by diffusion. This results in a higher effective flux. 1148
Figure 2. Concentration profile of diffusing species across the nanoslit. The dotted line represents the linear concentration profile for noninteracting diffusing species, whereas plain lines show the concentration profile change in the nanoslit. At the nanoslit entrances, charged species are discriminated by the electrostatic potential in the nanoslit. The EEE also results in a flux increase for counterions (represented by the black line) and a flux decrease for co-ions (represented by the gray line), as this flux is proportional to the local gradient of concentration (the slope of the concentration profile in the nanoslit).
First of all, a mathematical description of the problem has to be made. In the following developments, x is defining the direction parallel to the flux and z represents the direction perpendicular to this flux (see Figure 1). The reference parameter for diffusion experiments is the permeability P, which is the constant that links the instantaneous flux φ to the concentration difference ∆C before and after the nanoslits: φ ) P∆C
(1)
The geometrical permeability P* and the geometrical section S* are characterizing the nanoslit when electrostatic interactions are negligible on transport rate (high ionic concentration), whereas the terms of effective permeability Peff and effective section Seff are used when the transport of charged species is affected by electrostatic forces. When there are no electrostatic interactions, the concentration C*(x) in the slit is homogeneous in the whole section and does not depend on z. By considering the steady-state approximation, the instantaneous flux φ* is constant in the whole nanoslits, which leads to a linear concentration profile (see Figure 2) and the following expression of the flux: ∂C*(x) ∆C ) S*D ∂x L
φ* ) S*D
(2)
where L is the length of the nanoslit and D is the diffusion coefficient of the solute inside (which can be different from the bulk diffusion coefficient because of hydrodynamic restrictions of the nanoslit). With eq 1 and eq 2, we can determine the geometrical permeability of the nanoslit P*: P* )
S*D L
(3)
When EEE occurs at low ionic strength, the local concentration of charged species is no longer homogeneous in the section of the slit as the EDL extension increases the Nano Lett., Vol. 5, No. 6, 2005
counterion concentration near the charged surface. So the z profile of the local concentration C(x, z) (calculated in Figure 7) must be averaged in order to determine the effective concentration Ceff(x) in the nanoslit in the presence of electrostatic forces. The ratio between Ceff(x) and C*(x) defines the exclusion-enrichment coefficient β which is constant in the whole nanoslit, as will be shown further down. This coefficient quantifies the EEE: β)
Ceff(x)
)
C*(x)
〈C(x, z)〉z C*(x)
(4)
It is superior to unity in the case of enrichment and inferior to unity in the case of exclusion. So, the effective flux φeff can be deduced fom eq 2 and eq 4: ∂Ceff(x) ∂C(x) ∆C ) βS*D ) S* Dβ ∂x L ∂(x)
φeff ) S* D
(5)
If the effective section Seff is introduced as the product βS*, eq 5 leads to an expression of the effective permeability Peff, which can be formulated in the general form Peff )
SeffD L
(6)
The introduction of an effective section makes the expression of the permeability to be very similar in eq 3 and eq 6, which is convenient and legitimates the idea that the EEE can induce an electrostatic “narrowing” or “widening” of the nanoslit. However, even if this schematic description is very intuitive in the case of the anionic transport illustrated in Figure 1, the image of an increase in the effective section is perhaps less obvious in the case of cations. Figure 2 gives a more accurate description of the exclusion-enrichment effect on the instantaneous flux for both anions and cations compared to neutral diffusing species. The main consequence of the EEE is to create an overconcentration of cations (respectively a subconcentration of anions) in the nanoslit. This induces an increase (respectively a decrease) in the concentration profile slope that is proportional to the flux, so a higher (respectively a lower) effective permeability. Finally, as the exclusion enrichment coefficient β is now clearly defined as well as the permeability model of the nanoslit, a quantitative relation between Peff an P* can easily be deduced from eq 3 and eq 6: Peff/P* ) β
(7)
Thus, the proposed model for the description of the diffusive transport of charged species leads to a simple quantitative relation between the slit permeability and the EEE. For a nanoslit, it is possible both to accurately measure Peff/P* and to give an analytical expression of β. Then, a quantitative discussion on the validity of this model and on its limitations is possible. Nano Lett., Vol. 5, No. 6, 2005
Figure 3. Geometrical description of the system. The SEM picture in (a) shows the cross section of our system. The nanoslits height h is 50 nm in the z direction, its length L varies from 2 to 6 µm in the x direction and its width is in the order of the mm in the y direction, which justifies that the diffusion problem can be considered as invariant in this direction. The nanoslit was realized using a 50 nm high layer of amorphous silicon, which serves as a spacer as shown in (b). The fluidic connections were made on the upper wafer, whereas the transport of fluorescent dye from one microchannel to the other was recorded through the lower Pyrex wafer. The fluidic network allowed to alternate dynamic conditions during which a laminar flow filled the two microchannels with new solutions, with static flow conditions where the diffusion of fluorescent dyes from one microchannel to the other could be investigated. In (c), a top view of these two experimental phases is represented.
In this paragraph, the system is presented and a methodology that allows measuring Peff/P* on a chip by fluorescence detection is introduced. The chip used for this diffusion experiment consists of two parallel microchannels linked by a nanoslit of 50 nm in height (Figure 3a). The microchannels were chemically etched in Pyrex with HF. The spacing between the two channels defines the length L of the nanoslits, varying from 2 to 6 µm. The nanoslit was formed by sputtering a layer of amorphous silicon (aSi) on the Pyrex wafer except in the nanoslit region and in the microchannels. When the upper wafer is sealed on the previous wafer by anodic field assisted bonding, a 50 nm high nanoslit is created in the region free of aSi (Figure 3b). The width of the nanoslit was a few mm, which is much larger than its length, and justifies considering the system as invariant in the y direction. That is why the representation in Figure 1 is planar and the following mathematical developments will only consider x and z directions. All the parameters that could depend on the width of the nanoslit will implicitly be considered as linear. The fluidic network made it possible to alternate dynamic flow conditions, during which time the fluid in both microchannels was changed (only one microchannel was filled with buffer solution containing fluorescent dyes) and stationary conditions during which the diffusion of fluorescent solutes from one microchannel to the other through the nanoslit was investigated (Figure 3c). During the diffusion 1149
phase, the change in concentration difference can be derived from the flux and the volume V of the microchannel, leading to the following first-order differential equation ∂∆C V ) -2φ ) -2P∆C ∂t
(8)
where P is either the effective or geometrical permeability of the nanoslit. Equation 8 can easily be solved for the exponential time dependence ∆C ) ∆C0e-t/τdiff τdiff )
V 2P
(9) (10)
where ∆C0 is the initial concentration difference between the microchannels. Here, the typical diffusion time τdiff is introduced and is inversely proportional to the permeability: the more permeable the nanoslit is, the faster the diffusion process is taking place. So, by experimentally determining τdiff, which represents the typical time needed for equilibrating the concentrations of both microchannels, we can deduce the nanoslit permeability that varies with ionic strength. During the experiments, KCl concentrations c from 1 to 10-5 M were used to fix the ionic strength of the solutions. These concentrations correspond to EDL thicknesses from 3 Å up to 100 nm, which was sufficient to observe the overlapping of the electrical double layers in 50 nm high slits. For an infinite flat plate, the thickness of these layers depends on counterion concentration and has the following expression for a 1:1 electrolyte like KCl:17
λD )
x
0rRT 2F2c
(11)
λD is also known as the Debye screening length, F is the Faraday constant, R is the molar gas constant, 0 is the permettivity of vacuum, r is the dielectric constant of medium, and T is the temperature in Kelvin. No buffering of the pH was intended but it was measured to remain close to 7.5 for all solutions. As glass dissolution and ion exchange between solution and Pyrex18 can rapidly change solution composition in microscale structures, all diffusion experiments were executed immediately after filling up the channels with new solution (significant changes in transport behavior could be seen at very low salt concentrations after 30 min). To stabilize the surface charge and reduce glass dissolution, the chip was filled with 18 MΩ cm water for at least 24 h before experimental studies. This treatment results in a rapid dissolution of Si(OH)4 in water until saturation. A dynamical exchange between the solution and Pyrex is taking place, which results in a reorganization of the silicon skeleton at the surface.19 The silica-rich region that is formed is known to dissolve slowly,20 which allows to get similar results with 1150
Figure 4. Experimental determination of the typical diffusion time during diffusion phase. (a) Pictures of the diffusion phase were taken at different times (0, 4, 8, and 12 s) for rhodamine B at 1 M KCl. The intensity in both microchannels was averaged in the regions represented by the gray and white rectangles. The fluorescent probe concentrations in the microchannels are equilibrating in a few seconds. (b) The typical diffusion time τdiff (τdiff ) τexp ) 7.2 s in this example - no bleaching correction) for rhodamine B was obtained by fitting the exponential decay of the intensity difference ∆I ) 〈I+〉 - 〈I_〉. (c) For all the fluorophores, the residuals of this fitting curve showed a good monoexponential decay.
different chips. Filling the microchannels with a 1 M KOH solution was also used as pretreatment in order to etch the superficial layer of Pyrex and increase its negative surface charge. As we wanted to keep the slit nanometer-sized, the chips were washed in a continuous flow for only 10 min at room temperature. Finally, a similar washing with aqueous 0.1 M AlCl3 was performed at 80 °C in order to inverse the zeta potential of Pyrex. After each pretreatment, and before filling the chip with the experimental solutions described above, the chip was rinsed in a laminar flow of DI water for approximately 10 minutes. For consecutive experiments with solutions of different ionic strength, lower KCl concentrations were always first investigated. Fluorophores with different net charges were used as diffusing species. Fluorophore concentrations of 30 µM for fluorescein salt (used as a dianion), 10 µM for rhodamineB (used as neutral probe), and 10 µM for rhodamine 6G (cation) were used in order to get a sufficient signal in the microchannels. These concentrations are not negligible anymore for KCl concentrations below 10-4 M, which was a problem for investigating lowest ionic strengths as will be discussed in the results section. The fluorescence intensity I is related to the local concentration of fluorescent probes by the following relation: I ) Ae-t/τbleach C
(12)
where A is a constant depending on fluorophores efficiency and optical parameters and τbleach is the inverse bleach rate of the fluorophore. At t ) 0, when the flux is stopped in the microchannel to monitor the diffusion of fluorescent molecules, a first-order photochemical reaction renders the Nano Lett., Vol. 5, No. 6, 2005
Figure 5. Typical diffusion time for fluorescein at different ionic strengths for a 3 µm long nanoslit. The increase in τdiff at low concentrations is due to the electrostatic narrowing of the slit when EDL expansion is reducing the effective section of the slit. The results are also plotted as the change in relative permeability Peff/ P*, which does not depend on geometrical parameters of our system. The permeability is inversely proportional to τdiff: the less permeable the nanoslit is, the more time it needs to equilibrate the concentrations. Experimental data are represented by circles and triangles; dotted lines are plotted by interpolating these data in order to guide the eye of the reader. The EEE is already significant before the EDL overlap (when the Debye screening length becomes larger than half the height of the nanoslits), which occurs at concentration between 10-4 M and 10-3 M in the 50 nm high nanoslits. This makes the use of such nanoslit relevant for biotechnological applications in the range of mM salt concentrations.
molecules irreversibly nonfluorescent.21 This results in a monoexponential decay of the total intensity with time. The bleaching time τbleach is proportional to the excitation intensity and was calibrated in our system by filling both channels with fluorescent solutions and recording the fluorescence intensity decrease when the flow was stopped. No significant change in rhodamine dye intensity was observed during diffusion experiments, whereas fluorescein showed a nonnegligible bleaching rate. Intensities I+ and I- were respectively measured in the microchannel originally filled with fluorophores and the dye-free microchannel (Figure 4). Considering the bleaching process, the total exponential decay of the intensity difference ∆I between the microchannels can be derived from eq 9 and eq 12: ∆I ) 〈I+〉 - 〈I-〉 ) A′e(-t/τexp)
(13)
A′ ) A∆C0
(14)
1 1 1 ) + τexp τdiff τbleach
(15)
where
To determine τdiff, the exponential fitting of ∆I was done using a least-squares method, and τexp was obtained from the monoexponential decay. In the case of rhodamine dyes Nano Lett., Vol. 5, No. 6, 2005
Figure 6. Variation of the relative permeability of a 3 µm long nanoslit versus ionic strength for different probe charges. Marks represent experimental measurements whereas dotted lines are theoretical fittings obtained with eq 20. Native Pyrex surface is negatively charged which excludes anions when EDLO occurs at low KCl concentrations. On the contrary, cations are attracted in the slit, which enhances their transport to the other microchannel.
where τbleach is much greater than τdiff, τexp is equal to τdiff and no correction was necessary. For fluorescein, the experimental exponential time τexp had to be corrected using eq 15 in order to give the typical diffusion time τdiff presented in the following paragraphs. The fluorescence signal was recorded using a charge coupled device digital camera and averaged in the middle of the nanoslit width in order to avoid boundary effects, which could affect the diffusion dynamics. A 10× objective with a 0.25 numerical aperture was used. The first experiment presented in Figure 5 investigates the diffusion of the fluorescein dianions through the nanoslit. The experimental τdiff is reported for different ionic strengths. The relative permeability Peff/P* was deduced from eq 10 and plotted on the same figure in order to give an experimental variation of the nanoslit permeability that does not depend on geometrical parameters (P* is referring to the permeability measured at 1 M KCl). As expected, the measured τdiff is increasing at low ionic strength, as the electrostatic exclusion increases. In our system, EDL overlap (EDLO) occurs when the Debye screening length λD is 25 nm at KCl concentrations between 10-3 M and 10-4 M. However, the change in permeability for the fluorescein already gets important before the overlap, which means that the electrostatic interaction between charged species and the walls are already important. Moreover, the permeability is not zero at very low concentrations, which shows that EDLO does not mean a total obstruction of the nanoslit for anions, as one could suppose from Figure 1. The role of EDLO in the EEE will be discussed with the theoretical determination of the exclusion-enrichment coefficient β. As this phenomenon also depends on the net charge of the diffusing analyte, the relative permeability Peff/P* of the nanoslit was measured for different probes. The experimental points in Figure 6 show both the effects of the exclusion 1151
plates. In this case, the electrical potential ψ(z) only depends on z and can be numerically calculated considering the PB differential equation and the zeta potential ξ of Pyrex as boundary condition for the system ∂2ψ 2Fc ) sinh(F/ψ/RT) ∂z2 0r
(16)
ψ(z ) 0) ) ψ(z ) h) ) ξ
(17)
To get an analytical expression of the potential, the system has to be linearized. In this latter case, the Debye-Hu¨ckel approximation leads to a more convenient expression of the potential between two infinite parallel plates17 Figure 7. Concentrations and potential profiles in the nanoslit for two ionic strengths. At high ionic strength (KCl concentration ) 0.1 M), the potential decays fast compared with low ionic strength (KCl concentration ) 0.001 M) where the potential remains quite high in the whole section. No significant difference was observed between the numerical solution of eq 16 (dotted black line) and the approximated analytical expression of the electrical potential ψ(z) issued from eq 18 (gray solid line). The concentration profiles of charged species are determined by a Boltzmann equilibrium (eq 19). When electrostatic shielding is less efficient at low ionic strength, one can see a enrichment in cationic species (black solid line calculated with a net charge q ) +1 eV) and the exclusion of the anionic species (gray solid line calculated with a net charge q ) -1 eV).
(anions) and enrichment effect (cations) on relative permeability changes, whereas no change in the permeability was observed for the neutral probes. Qualitatively, these results are in accordance with the main hypothesis that EDL extension results in a higher permeability for counterions and a lower permeability for co-ions. Before any quantitative discussion of these results is given, the second term in eq 7 has to be calculated. The exclusion-enrichment coefficient β was defined in eq 4 as the ratio between the concentration of charged species without electrostatic interaction and the concentration when a residual electrostatic potential discriminates ionic populations in the nanoslit. So, the electrostatic potential in the nanoslit, which generates the EEE, can be calculated using different approximations. The Donnan equilibrium, which consists of using a constant potential throughout the nanochannel, has often been used in previous theoretical work on nanofiltration (NF) membranes.22,23 This approximation is only valid when the Debye screening length λD is larger than pore radius, which is not the case in our system. In intermediary systems, where λD is in the order of pore radius, a radial dependence in the electrostatic potential is introduced and solved using the Poisson-Boltzmann (PB) equations as in the space-charge model proposed by Gross and Osterle24 and developed by Wang et al.25 However, our problem is less difficult as no ionic flux has to considered (the potential is only determined by KCl repartition at the equilibrium, the ionic current due to fluorescent probe diffusion remains negligible) and as the geometry is simpler: the height h of the nanoslit is very small compared to its width and length, so the nanoslit can be considered as 2D infinite parallel 1152
ψ(z) )
ξcosh((h/2 - z)/λD)
(18)
cosh(h/2λD)
The numerical solution of eq 16 and the approximated potential presented in eq 18 are compared in Figure 7 for different ionic strengths. It is known that the Debye-Hu¨ckel approximation generally overestimates the electrical potential. To achieve a better precision, one should use the numerical solution of the Poisson-Boltzmann equation. However, when considering experimental incertitude on permeability measurements, the difference between the two predicted potentials remains small and the Debye Hu¨ckel approximation is satisfying. Then, the local concentration C(x, z) of ionic species depends both on the net charge q of the diffusing ion and on the local potential ψ(z) through a Boltzmann equilibrium: C(x, z) ) C*(x) exp(-qψ(z)/KT)
(19)
Figure 7 shows that when the ionic strength is high and the potential is zero in most of the nanoslit, no significant change in concentration is observed and Ceff(x) is equal to C*, except from a negligible region near the surface. At low ionic strength, as the electrical potential remains high in the whole slit, exclusion of ionic species and enrichment of cationic species becomes important. Finally, to determine Ceff(x) and β defined in eq 4, this local concentration must be averaged over the whole height of the nanoslit, which leads to the following analytical expression of the exclusion-enrichment effect: β)
(
)
ξcosh((h/2 - z)/λD) /kT dz cosh(h/2λD)
∫0h exp -q
1 h
(20)
In eq 20, β does not depend on x, which legitimates the image of a global effective section change in the whole nanoslit as our former developments implicitly suggested. Moreover, with this analytical expression of the EEE, EDLO (represented by the Debye screening length λD) is shown to be necessary but not sufficient. Indeed, the net charge q of the diffusing species and the ξ-potential of the surface are Nano Lett., Vol. 5, No. 6, 2005
also important parameters in the quantification of the EEE. So, to compare this expression with experimental data, the ξ-potential has to be determined. For a 1-1 inorganic electrolyte, the ξ-potential of glass is known to vary linearly with the logarithm of the bulk concentration,26 leading to the following expression of ξ ξ ) a0 + a1 log(C)
(21)
where a0 and a1 are two constants depending on surface properties and the solution composition. Experimental studies reported by Kirby et al.26 have shown that for Pyrex and KCl solutions, a0 can be taken as 0 mV and a1 depends on bulk pH, surface pretreatments, and adsorbing ionic species in solution. In Figure 5, a1 was taken as the only fitting parameter in order to determine the theoretical curves compared with experimental results. For fluorescein, the fitting of the experimental points resulted in a value of a1 ) 16 mV, which is a reasonable value compared with literature (Revil et al.27 showed that a1 ≈ 20 mV for a pure 1:1 electrolyte in contact with silica). In the case of rhodamine 6G, the a1 factor was only found to be 9 mV. We guess that the main reason was the specific adsorption of rhodamine 6G observed during the experiments. Indeed, whereas fluorescein is negatively charged, which prevents its adsorption on the Pyrex surface, the positive net charge of rhodamine enhances its adsorption, which reduces the surface charge of the nanoslits and the ξ-potential. In both cases, the model leading to eq 7 and eq 20 appears quite satisfying. The determination of the ξ-potential by other experiments (as streaming potential measurements) should further confirm its validity. However, some restrictions of this model already appear in Figure 6, as the comparison of predicted permeabilities with experimental data becomes more critical for very low KCl concentrations. Indeed, the permselectivity observed at 10-5 M KCl was lower than the one predicted by the theory. This can be explained by three important approximations that were made in the modeling of the problem proposed before. The first assumption implicitly formulated was that the transport of charged species through the nanoslit was exclusively due to diffusion, and no transverse potential in the x direction that could affect their Brownian motion was taken into account. This assumption is no longer true when the difference in ionic composition of the two channels becomes too large (due to the fluorophore concentration in one channel), which is the case in our system at 10-5 M of KCl. The permselectivity creates a charge separation when ionic species are transported at different rates through the nanoslit, which results in a transverse potential. This reverse potential was well investigated for all permselective membranes and ionic channels. For a couple of ionic diffusing molecules (the fluorescent probes and their ions), this effect slows down fast diffusing ions which cannot enrich the second microchannel without their counterions and accelerates the transport of slow diffusing molecules thanks to the electrostatic field generated by charge separation. This Nano Lett., Vol. 5, No. 6, 2005
Figure 8. Evolution of τdiff for a 6 µm long nanoslit as function of chemical pretreatments. After the reference measurement in water, KOH pretreatment was executed. This pretreatment results in higher τdiff at low KCl concentration, which is in accordance with an increased surface charge for Pyrex. Al pretreatment inverts the zeta potential of Pyrex, which results in an enrichment effect at low ionic strength for fluorescein (instead of the exclusion effect observed with the native negatively charged surface of Pyrex). With these pretreatments, the dependence of the nanoslit permeability on the zeta potential formulated in eq 20 is qualitatively demonstrated.
phenomenon can be treated with the Nernst-Planck flux equations, but leads to a more complex problem, which is out of the focus of this work. Indeed, the fact that the concentration of diffusing fluorophores is no more negligible at low KCl concentration remains an experimental problem to solve. A second assumption that is not sustainable anymore when a very high enrichment of cations occurs is the idea that the concentration can be considered as homogeneous in the whole microchannel. In the case of a very high transport rate in the nanoslit, a diffusionnal limit at the nanoslit entrance and exit emerges, which reduces the predicted permeability. Finally, a third assumption made in the permeability model could have quantitative consequences on measured permeabilities. It is the dynamical diffusion coefficient of fluorescent dyes D in the nanoslit that was considered as constant, whereas it can vary when electrostatic interactions with walls are increasing. So it should be advisable to consider an effective diffusion coefficient Deff in the model presented above. However, the last two phenomena described can be considered as refinements. Their effects on the nanoslit permeability can be neglected as long as some other experimental parameters such as the surface potential are very sensitive to experimental conditions and can have greater effects on the nanoslit permeability. In the last paragraph, the influence of the ξ-potential on the permselectivity of the nanoslit will be illustrated through the chemical modulation of the Pyrex surface. In addition to the classical preparation of the Pyrex surface with a 24 h water bath, two pretreatments were performed on samples before diffusion experiments and compared with the water pretreatment. The results are summarized in Figure 8. All fluorescein diffusion experiments were made with the same chip. The typical diffusion time τdiff was systematically measured just after each pretreatment for three different molarities. The reference water treatment was first performed, followed by the KOH and the Al pretreatment. 1153
The general consequence of the KOH pretreatment was a dramatic increase in τdiff at low ionic strength. The etching properties of KOH on Pyrex can explain this result: KOH does not attack the Si-skeleton homogeneously, which increases simultaneously surface roughness and surface charge (more SiOH groups are in contact with the solution). This results in a higher permselectivity, which reduces fluorescein transport. No significant change in τdiff was observed at high ionic strength when the pretreatment was performed for 10 min. For longer pretreatment a slight decrease could be measured, which is attributed to the geometrical widening of the slit as a result of KOH etching. The Al pretreatment reversed the permselectivity of the slit for fluorescein. Al adsorption on Pyrex surface is known to inverse the zeta potential,28,29 but had not yet been investigated for microfluidic applications. This effect was so strong that it was difficult to measure τdiff at low ionic strength. The effective permeability was measured to be 6 times higher at very low KCl concentration, which is certainly due to the net charge of fluorescein (|q| ) 2), which makes it more sensitive to the enrichment effect than rhodamine 6G (|q| ) 1). The value of τdiff for the 1 M KCl after inversing the zeta potential was found to be slightly higher than the value measured with a negative surface charge. This is explained by the electrostatic adsorption of fluorescein on the positively charged surface of the Pyrex that slows down probe diffusion in the slit. This adsorption was strongly observed in the microchannels. Finally, the long-term effects of these pretreatment were observed to decrease with time and the number of experiments, which implies that the stability of the Pyrex surface state has to be further investigated in order to use these pretreatments for µ-TAS applications. Nevertheless, the chemical investigation of the Pyrex-water interface can be performed in less complex systems than the nanoslit presented in this paper. The main purpose of all the pretreatments presented here was to verify the qualitative influence of surface charge variations on the EEE and its consequences on the nanoslit permselectivity formulated in eq 20. The last parameter in this equation that could be varied is the height h of the slit: thinner slits should enable to reach higher permselectivity for moderate ionic strength, which is both an experimental challenge for nanoslit fabrication and a theoretical one for the validation of the model presented here. In conclusion, this work provides the first quantitative study of the EEE and its consequences on the permselectivity of integrated nanoslits. The experimental method described above allows to monitor the permselectivity change on a wide range of KCl concentrations and to observe the growing of the exclusion-enrichment effect at low ionic strength. The controllable size and geometry of our nanoslits made it possible to develop a simple model of the EEE as well as the quantitative interpretation of experimental results. Moreover, the geometry of such nanoslits takes both advantage of EDLO and large transport flux compared to cylindrical pores, which makes them very interesting for potential µ-TAS applications. Concerning the possibility to chemically modulate the permselectivity of Pyrex nanoslits through surface 1154
pretreatments, the stability of the water-glass interface have to be further investigated. The Al pretreatment presented in this paper showed good potentialities for microfluidic applications where an inversion of the surface charge of Pyrex is needed. Many technologies have recently been developed to exploit the EEE in microfabricated systems,30 particularly for biotechnological applications, but no quantitative study of the diffusion through such artificial structures had yet been proposed. It was shown in this work that a simple model based on the PB equation could describe the diffusive transport of charged species as long as the concentration of these is low compared to the bulk concentration, which is generally the case for a wide range of biological applications. The permselectivity observed in our nanoslit was measured to be significant at mM concentrations, which should allow us to work with biological samples. The EEE can prove to be very useful for many on-chip separation processes, and applying a transverse potential in addition to the EEE can lead to very interesting applications as the protein preconcentration performed on a chip by Foote et al.31 for proteomic purposes. The tuneable ionic transport has also been achieved recently by Schmuhl et al.32 All these applications imply that simple models and quantitative studies of this phenomenon are necessary in order to better understand and control the permselectivity of these nanostructures. The exclusionenrichment coefficient β defined in this work for our nanoslits belongs to a class of parameters specific at the nanoscale, which have both a physical significance and an important role in transport phenomena. There is no doubt that it will be of great interest for further nanofluidic applications. References (1) Hille, B. Ionic channels of excitable membranes; Sinauer Associates: Sunderland, MA, 1984. (2) Eisenberg, R. S. J. Membrane Biol. 1999, 171, 1-24. (3) Gu, L. Q.; Dalla Serra, M.; Vincent, J. B.; Vigh, G.; Cheley, S.; Braha, O.; Bayley, H. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 39593964. (4) Zeth, K.; Diederichs, K.; Welte, W.; Engelhardt, H. Structure 2000, 8, 981-992. (5) Colegio, O. R.; Van Itallie, C. M.; McCrea, H. J.; Rahner, C.; Anderson, J. M. Am. J. Physiol. 2002, 283, C142-C147. (6) Martin, C. R.; Nishizawa, M.; Jirage, K.; Kang, M. S.; Lee, S. B. AdV. Mater. 2001, 13, 1351-1362. (7) Lee, S. B.; Martin, C. R. Anal. Chem. 2001, 73, 768-775. (8) Nishizawa, M.; Menon, V. P.; Martin, C. R. Science 1995, 268, 700702. (9) Ramirez, P.; Mafe, S.; Aguilella, V. M.; Alcaraz, A. Phys. ReV. E 2003, 68, Art. No. 011910. (10) Ramirez, P.; Mafe, S.; Alcaraz, A.; Cervera, J. J. Phys. Chem. B 2003, 107, 13178-13187. (11) Bluhm, E. A.; Bauer, E.; Chamberlin, R. M.; Abney, K. D.; Young, J. S.; Jarvinen, G. D. Langmuir 1999, 15, 8668-8672. (12) Ku, J. R.; Stroeve, P. Langmuir 2004, 20, 2030-2032. (13) Chun, K. Y.; Stroeve, P. Langmuir 2002, 18, 4653-4658. (14) Jimbo, T.; Ramirez, P.; Tanioka, A.; Mafe, S.; Minoura, N. J. Colloid Interface Sci. 2000, 225, 447-454. (15) Kuo, T. C.; Cannon, D. M.; Chen, Y. N.; Tulock, J. J.; Shannon, M. A.; Sweedler, J. V.; Bohn, P. W. Anal. Chem. 2003, 75, 1861-1867. (16) Pu, Q. S.; Yun, J. S.; Temkin, H.; Liu, S. R. Nano Lett. 2004, 4, 1099-1103. (17) Hunter, R. J. Zeta potential in colloid science principles and applications; Academic Press: London, 1981. (18) Doremus, R. H. Glass science, 2nd ed.; Wiley: New York, 1994.
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(19) Devreux, F.; Barboux, P.; Filoche, M.; Sapoval, B. J. Mater. Sci. 2001, 36, 1331-1341. (20) Hench, L. L.; Clark, D. E. J. Non-Cryst. Solids 1978, 28, 83-105. (21) Rettig, W. Applied fluorescence in chemistry, biology and medicine; Springer: Berlin, 1999. (22) Bowen, W. R.; Welfoot, J. S. Chem. Eng. Sci. 2002, 57, 11211137. (23) Garcia-Aleman, J.; Dickson, J. M. J. Membrane Sci. 2004, 235, 1-13. (24) Gross, R. J.; Osterle, J. F. J. Chem. Phys. 1968, 49, 228-234. (25) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membrane Sci. 1995, 103, 117-133. (26) Kirby, B. J.; Hasselbrink, E. F. Electrophoresis 2004, 25, 187202.
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