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Langmuir 2006, 22, 9784-9788
Fluidics of a Nanogap M. Brinkmann,#,† R. Blossey,*,† L. Marcon,‡ D. Stie´venard,‡ Y. F. Dufreˆne,§ and O. Melnyk¶ Biological Nanosystems Group, Interdisciplinary Research Institute c/o IEMN, Cite´ Scientifique BP 60069, F-59652 VilleneuVe d’Ascq, France, Institut d’Electronique, de Microe´ lectronique et de Nanotechnologie (IEMN), UMR 8520, Cite´ Scientifique BP 60069, F-59652 VilleneuVe d’Ascq, France, Unite´ de Chimie des Interfaces, UniVersite´ Catholique de LouVain, Croix du Sud 2/18, B-1348 LouVain-la-NeuVe, Belgium, and Institut de Biologie de Lille, UMR 8161, 1 rue du Professeur Calmette, 59021 Lille Cedex, France ReceiVed April 26, 2006. In Final Form: September 4, 2006 We have determined the filling properties of nanogaps with chemically heterogeneous walls. The quantitative criteria we present allow the prediction of the liquid loading of the nanostructure. They can easily be applied in combination with contact-angle measurements on planar substrates of the nanogap materials. We present an application of the theory to a recently developed nanogap biosensor. Chemical force microscopy (CFM) is employed to characterize the initial silanol properties of the gap. The functionality of the complex surface chemistry of the biosensor is demonstrated by the observation of functionalized nanoparticles in the gap with its resulting characteristic current -voltage relationship.
Introduction In the course of the miniaturization of lab-on-a-chip devices for applications in molecular biology and medicine,1-8 knowledge of fluid behavior in small confines becomes of utmost importance.9-12 There are at least two reasons for this; first, on nanometer scales, interactions of the liquids with the surfaces become increasingly important, and second, methods to visualize liquid behavior in such dimensions are lacking. The design and development of nanosize fluidic systems can thus be made difficult and costly since conceptual errors may be difficult to trace. Here, we fill this gap by a combination of theory and experiment. We first develop a basic analytical model for the invasion of a liquid in a chemically heterogeneous channel. The essential parameters in the model are the nanogap geometry, hence a variable under technical control, and the chemical properties of the surface leading to specific solid-liquid surface tensions. The model permits a comparison with contact angles measured on the corresponding planar surfaces, which is easy to achieve. The advantage of this model is thus its simplicity and ease of application in guiding device design. We apply the model # Present address: Max-Planck Institute of Dynamics and Self-Organization, Bunsenstr. 10, 37073 Go¨ttingen, Germany. † Interdisciplinary Research Institute at IEMN. ‡ IEMN. § Universite ´ Catholique de Louvain. ¶ Institut de Biologie de Lille.
(1) Weiss, S. Science 1999, 283, 1676. (2) Engval, E.; Perlman, P.; Immunochemistry 1971, 8, 871. (3) Homola, J.; Yee, S. S.; Gauglitz, G.; Sens. Actuators B 1999, 54, 3. (4) Sohn, L. L.; Saleh, O. A.; Facer, G. R.; Beavis, A. J.; Allan, R. S.; Nottermanet, D. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 10687. (5) Facer, G. R.; Notterman, D. A.; Sohn, L. L. Appl. Phys. Lett. 2001, 78, 996. (6) Kharitonov, A. B.; Wasserman, J.; Katz, E.; Willner, I. J. Phys. Chem. B 2001, 105, 4205. (7) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 3693. (8) Park, S. J.; T, Taton, A.; Mirkin, C. A. Science 2002, 295, 1503. (9) Dynamics in Small Confining Systems II; Drake, J. M., Klafter, J., Kopelman, R., Troian, S. M., Eds.; Material Research Society: Pittsburgh, PA, 1995; Vol. 366. (10) Cui, Y.; Wei, Q.; Park, H.; Lieber, C. M. Science 2001, 293, 1289. (11) Malaquin, L.; Vieu, C.; Martinez, C.; Steck, B.; Carcenac, F. Nanotechnology 2005, 16, S240. (12) Mijatovic, D.; Eijkel, J. C. T.; van den Berg, A. Lab on a Chip 2005, 5, 492.
to a recently developed nanogap biosensor.13 We carefully discuss the surface preparation of the nanogap sensor and its quantitative characterization by atomic force microscopy (AFM) and chemical force microscopy (CFM).
Results and Discussion Fluidics in the Gap: Theory. We evaluate the fluidic properties of a chemically heterogeneous nanogap with the theoretical setup described in Figure 1a. It shows a configuration in which a drop is placed atop two parallel gold beams of height L⊥ located at a distance L. A minimal condition of the functionality of the nanogap is its capacity to spontaneously imbibe the liquid. This can be quantified by calculating the work needed to advance the liquid channel by a length ∆L|. Although the loading of a gapbased sensor may in practice be performed in a different ways for example, by immersing the whole sensor in the liquidsit is to be expected that the capillary action of the channel will dominate the hydrodynamics of the gap. In other words, if a mesoscopic channel does not fill spontaneously by capillary action, it will not be functional. For the calculation of imbibition in the channel, we consider the groove as consisting of walls made of a solid phase δ (gold), which differs from the functionalized surface of the substrate γ; see Figure 1b. Assuming both as being chemically homogeneous, we can write down the interfacial free energy as the sum
FΣ ) ΣRβARβ + (Σβγ - ΣRγ)Aβγ + (Σβδ - ΣRδ)Aβδ (1) where Σij and Aij are the interfacial tensions and area, respectively, related to the interface between adjacent phases i, j which can take values R - δ. Note that the symbols R and β have been reserved for the vapor phase and the wetting liquid. In all what follows, we neglect dispersion forces. Their inclusion becomes important at scales below 10 nm, so that, within the philosophy of a minimal model we adopt here, they can be neglected. Evaporation effects are likewise neglected in our theory since in practice they can usually be controlled by sealing of the sensor in a box. (13) Haguet, V.; Martin, D.; Marcon, L.; Heim, T.; Stie´venard, D.; Olivier, C.; El-Mahdi, O.; Melnyk, O. Appl. Phys. Lett. 2004, 84, 1213.
10.1021/la0611357 CCC: $33.50 © 2006 American Chemical Society Published on Web 10/13/2006
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Figure 1. (a-d) From top left to bottom: (a) Geometry of the model used in the calculation; a drop is placed across the electrodes; for the explanation of the symbols, see text. (b) Profile of the nanogap as used in the model computation and the resulting liquid structures (I) and (II). (c) Channel filling diagram: liquid structures of type (I) or (II) develop in the channel. Gray-shaded areas indicate possible gap widths and the change in contact angles observed in our experiments on the nanogap before and after silanization in the case of surface A. Solid lines: contact angles on the electrodes of 60°. Dashed lines: contact angles on the electrodes of 30°. (d) Channel filling diagram in the case of tilted wall with a tilt angle of 60°.
Since R and β are both fluid phases, the Rβ interface has no preferred shape and orientation. Provided the liquid β is incompressible and an exchange of particles between both fluid phases is negligible, a droplet of β will assume a shape which minimizes its interfacial free energy under the constraint of a fixed volume. Then, the equilibrium contact angle θi at a threephase contact line on γ or δ has to fulfill the equation of YoungDupre´
ΣRβ cos θi ) ΣRi - Σβi
(2)
which can be read as a balance of forces acting on the threephase contact line induced by the interfacial tensions Σij. In addition, the equation of Laplace
2ΣRβM ) ∆P
(3)
relates the mean curvature M of the Rβ interface at mechanical equilibrium to its surface tension ΣRβ and the difference in bulk pressure ∆P ≡ Pβ - PR between the adjacent fluid phases. The mean curvature has to be constant at mechanical equilibrium provided that ∆P does not depend on the position of the Rβ interface. This holds to a good approximation whenever the height of the droplet is significantly smaller than the capillary length ξcap ≡ (ΣRβ/(a∆F)0.5, where a is the gravitational acceleration and ∆F is the density difference between the fluid phases R and β. For water under normal conditions, one finds ξcap ≈ 2 mm. Provided that the size of the droplet is much larger than the gap width L, we can assume that the mean curvature M of the Rβ interface is close to zero on length scales comparable to the transverse dimension of the sensor; that is 0 < M , L-1. A liquid column protruding into the gap will have a constant cross section along the groove, except for the regions near both ends. Since
the mean curvature of the Rβ interface of the liquid column is zero at equilibrium, we conclude that the cross section of the liquid phase is bounded by one or more straight lines. Thus we can solve our problem by finding all possibilities to draw one or more straight lines between either walls δ or a wall δ and the bottom γ of the grooves in accord with the equation of YoungDupre´. The two resulting cross sections are shown in Figure 1b. Further, we have to show whether these configurations are in mechanical equilibrium with respect to changes in their length L|. The contact angle θδ on the side wall has to be smaller than 90° to allow the formation of a cross section of type (I) at all. At larger values of θδ, the contact line cannot stay pinned to the upper edge of the gap. Liquid wedges (II) may occur whenever the inequality θγ < 90° - θδ holds. As outlined in the following, liquid wedges are absent if the aspect ratio l⊥ ≡ L⊥/L of the gap is sufficiently high. In this case, a complete filling of the gap takes place directly from the dry state. We now discuss the three different filling scenarios in more detail. The spontaneous formation of a certain type of liquid structure requires the work ∆W needed to prolong the liquid column (or columns) by an increment ∆L| to be less than zero. (1) If the gap is dry prior to filling with a column of type (I), one finds
∆W ) [(ΣRβ - Saγ)L - 2Saδ L⊥]∆L ||
(4)
Here, Sai < ΣRi - Σβi is the effective surface tension difference in case of an advancing contact line on i ) γ,δ. Its value can be determined from the relation
ΣRβ cos θai ) Sai
(5)
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in which θai > θi is the advancing contact angle on i ) γ,δ. Analogous relations (with inverted signs) apply to the case of receding contact lines. If we specialize to the advancing case, we find the condition for the dimensionless aspect ratio
l⊥ >
1 - cos θaγ
(6)
2 cos θaδ
valid for liquid columns of type (I) protruding into an initially dry gap. (2) Wetting of the bottom corners of the gap by liquid wedges (II) will occur whenever
∆W ) 2
(
)
Saγ - Saδ L⊥∆L || < 0 a a sin θγ tan θγ ΣRβ
(7)
holds, with the work ∆W gained by the system while the liquid wedges at either side of the gap are prolonged by the length ∆L|. With the application of the condition of Young-Dupre´, one finds a criterion of spontaneous wedge formation
θaγ < 90° - θaδ
(8)
(3) As a final case, we consider the situations in which the liquid had already formed liquid wedges (II) before the intrusion of a column of type (I) takes place. The work required for this process is now
[ (
∆W ) ΣRβ L -
2L⊥ sin
) (
θaγ
)]
2L⊥ - Saγ L ∆L || tan θaγ
(9) Figure 2. (a) Top: The nanogap sensor loaded with nanoparticles. (b) Bottom: A typical I-U curve of the loaded sensor. The flat curve is the current noise level of the unloaded sensor.
To achieve complete filling of the gap the condition
l⊥ >
1 - cos θaγ 2 sin θaγ
(10)
must be fulfilled, which does not depend on the wettability of the side walls δ. The results on the filling conditions of the gap are summarized in Figure 1c and d. The diagram in Figure 1d demonstrates the effect of a tilt angle F of the gap walls different to 90°. In this case, condition (6) for the filling of an initially dry gap by a single liquid column of type (I) needs to be generalized to
l⊥ >
(1 - cos θaγ)sin F 2(cos θaδ - cos θaγ cos F)
(11)
The formation of liquid wedges (II) in a dry gap requires θaγ < F - θaδ, while condition (10) for the transition from type (I) to type (II) stays valid. As Figure 3d clearly shows, a tilt of the walls disfavors liquid imbibition into the gap at low aspect ratios l⊥. Application to a Nanogap Sensor: Sensor Principle. We now apply our theoretical results to the biosensor described in ref 13, and first briefly recall its detection principle. Figure 2a shows a partial view of the sensor, which is made from two planar electrodes placed at a distance of 30 to 100-110 nm, with a thickness of 15 nm Au on 5 nm Ti. The electrodes reside on a functionalized surface designed to concentrate a ligand-receptor bound pair of biomolecules between the electrodes. In the study presented here, we chose protein A and immunoglobulin G (IgG). Protein A is a highly stable 42 kDa protein isolated from the cell wall of Staphylococcus aureus and is often used as a tool in immunological technologies because of its ability to interact
with immunoglobulins, mainly IgG from mammalian species through the Fc part of the immunoglobulin. Protein A is thus a good protein model to study the properties of novel biosensors. In this work, protein A was immobilized in the nanogap by adsorption on an amine-modified SiO2 surface. Incubation of the nanogap with diluted human sera led to the capture of IgG antibodies. The captured IgG molecules were further reacted with goat anti-human antibodies labeled with 25 nm gold nanoparticles. The incorporation of gold nanoparticles into the nanogap through this series of biomolecular interactions resulted in a change in the I(V) response curve compared to control experiments without diluted sera as shown in Figure 2b. It shows a typical I(V) response curve before and after incubation. After incubation, an average 105-fold current increase was observed, from 5 × 10-14 to 10-11 - 10-7 A, at V ) +5 V. The conduction mechanism is based on a multi-tunnel junction forming between each of the metal particles and the metallic surface of the electrodes. The particle density was evaluated as 200 particles/ µm2. We estimate the number of gold particles bridging the electrodes at ∼60. Further details on the conduction behavior of the nanogaps and the measurement setups can be found elsewhere.14-16 Surface Preparation: Materials and Methods/General. Chemical reagents were obtained from commercial suppliers and used without further purification. Water was deionized using a Milli-Q purification system (Millipore). Protein A and phosphate-buffered saline (PBS) were purchased from Sigma(14) Marcon, L.; The` se USTL 2005, unpublished. (15) Middleton, A. A.; Wingreen, N. S. Phys. ReV. Lett. 1993, 71, 3198. (16) Parthasarathy, R.; Liu, X. M.; Jaeger, H. M. Phys. ReV. Lett. 2001, 87, 186807.
Fluidics of a Nanogap
Aldrich (St. Louis, MO). Goat anti-human Ig(H+L) antibodies linked to 25 nm diameter gold nanoparticles were purchased from Electron Microscopy Science (Hatfield, PA). Human sera were collected from the clinical laboratory of the Centre Hospitalier Re´gional (Lille, France). PBS is 150 mM NaCl buffered at pH 7.2 with 10 mM potassium phosphate. Nanogap Preparation. The nanogap was prepared by electronbeam lithography on a Si substrate with a 200 nm thermal oxide (SiO2) first cleaned using a freshly prepared piranha solution (H2SO4/H2O, 1/1 by volume, 1 h). Amine functionalization was performed by subjecting the nanoelectrodes first to an oxygen plasma (0.1 T, 100 W, 50 s). The surface was then washed with water (3 × 3 min), methanol (3 min), and treated with 3% 3-aminopropyltrimethoxysilane in methanol/water, 95/5 by volume (30 min under sonication). Afterward, surfaces were washed with methanol, water (3 times) and again with methanol, and subsequently annealed for 20 min at 110 °C. Printing of Protein A in the Nanogaps. Protein A was dissolved in PBS at 1 mg/mL concentration, then printed onto the amino-activated gaps with a noncontact Biochip Arrayer (Perkin-Elmer Life Sciences, Meriden, CT). Three drops (1 nL) were deposited on each nanogap. The sample was placed overnight in a humid chamber (37 °C, 60% relative humidity). Capture of Antibodies from Human Serum. The sample was washed successively with PBS containing 0.05% of Tween 20 (by volume), water, and ethanol, and then incubated 2 h at 37 °C with a human serum diluted 1/20 with a PBS containing 0.05% Tween 20 and 2% of bovine serum albumin (BSA). The sample was washed several times with PBS containing 0.05% Tween 20 and incubated 1 h at 37 °C with anti-human secondary antibodies tagged with 25 nm gold nanoparticles. For this, the commercially available goat anti-human Ig(H+L) gold nanoparticles suspension was concentrated 10 times by centrifugation and redispersion in PBS containing 0.05% Tween 20 and 2% of BSA. Finally, the sample was washed with PBS containing 0.05% of Tween 20, water, and methanol and dried in vacuo. Surface Characterization. We have characterized the nonfunctionalized gap surfaces using AFM in air and CFM in aqueous solution (Nanoscope III, Digital Instruments, Santa Barbara, CA). Figure 3a shows an AFM topographic image of the gold electrodes recorded in air with a silicon nitride tip (Microlevers, ThermoMicroscopes, Sunnyvale, CA). It can be seen that the surface is fairly clean and that the two planar electrodes are ∼30 nm thick and separated by ∼125 nm. One difficulty is to know the nanogap surface chemistry properties. As a first step of the characterization, we check the silanol character of the nanogap by chemical force microscopy (CFM). We quantitatively mapped adhesion forces on the patterned samples, with the aim to reveal nanoscale variations of the surface hydrophilicity.17 To this end, AFM tips functionalized with alkanethiol self-assembled monolayers terminated with hydrophobic methyl groups18 were used to record adhesion force maps in deionized water on the patterned surfaces. Adhesion maps were obtained by recording 32 × 32 force-distance curves on areas of given size in the force-volume mode and calculating the pull-off force measured for each force curve.19 Figure 3b and c shows a typical topographic image and an adhesion map of the nanogap structure. Clearly, the adhesion map is highly contrasted, the adhesion force being much larger on the gold electrodes (∼8 nN) compared to the nanogap region (∼2 nN). These data, which (17) Frisbie, C. D.; Rosznyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071-2074. (18) Dufreˆne, Y. F.; Biophys. J. 2000, 78, 3286. (19) Denis, F. A.; Hanarp, P.; Sutherland, D. S.; Dufreˆne, Y. F. Langmuir 2004, 20, 9335.
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Figure 3. AFM characterization of the nanogap: (A) topographic image (2 µm × 2 µm) recorded in air, (B and C) adhesion force map (3 µm × 3 µm) recorded in aqueous solution using a hydrophobic tip. Brighter levels in the images correspond to higher height (B) and higher adhesion (C).
are consistent with the literature,19 demonstrate that the SiO2 nanogap is hydrophilic, while the Au electrodes are hydrophobic. At this step, the amine character of the gap is verified through the immobilization of protein A and the subsequent formation of protein A-IgG complexes detected by a secondary antibody labeled with gold particles. SEM observation, as shown in Figure 2a, provides evidence of the presence of nanoparticles in the gap, but also out of the gap, as is to be expected due to the size of the printed spots, which lies around 250 µm. Theory versus Experiment: Results. To apply the theoretical results to experiment after the precise characterization of the system, it suffices to determine advancing contact angle on planar substrates which are chemically identical to the surfaces γ and δ of the gap.20 For this, we performed contact angle measurements at 20 °C with a digidrop goniometer (GBX, Romans-sur-Ise´re, France) for two substrates, A ) Si/SiO2 and B ) Si/SiO2 + Au. The measurements were taken within 10 s after formation of a sessile droplet. At least 10 droplets of deionized water, as a reference liquid, were used for the determination of the angle (median, interquartile range). Prior to measurement of contact angles after each step of the process, the substrates were rinsed in deionized water and dried under a stream of N2. Silicon samples were cleaned by a plasma for 50 s and dried in a stream of high purity N2. This procedure generates a highly hydrophilic silicon oxide surface A with a low water contact angle of 6°. In contrast to the silicon oxide substrate, the sample B is slightly more hydrophobic and exhibited a contact angle close to 40°. After silanization, and before deposition of protein A, the contact angles were measured to be 25° for surface A and 46° for surface B. Some of the results of these measurements have been included into Figure 1c and 1d. The boundaries of the gray-shaded areas delimit the accessible parameter ranges for our system in case of surface A; the reasoning for surface B is analogous. The horizontal scale on the graph is given by the aspect ratio l⊥ of the gap we consider, while the vertical scale corresponds to the specific advancing contact angles we measured. Following the vertical boundary of the shaded area at l⊥ ) 0.2 from large to (20) Note that the theory neglects the effect of the additional Ti layer.
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small contact angles θaγ on the bottom surface, one sees that, for contact angles on the gold electrodes δ with roughly θaδ ≈ 30°, the gap will at least be filled by liquid wedges (II) if the advancing contact angle θaγ on the bottom surface γ of the gap has a value less than ∼60°. A further decrease of the contact angle on the gap bottom to θaγ j 30° leads to a spontaneous complete filling (I) of the gap. A slightly different scenario will be encountered if we assume the contact angle on the gold surface δ to be θaδ ≈ 60°. The range of advancing contact angle θaγ where liquid wedges (II) appear has now shrunk to smaller aspect ratios, while the range of contact angles θaγ of spontaneous complete filling (I) has hardly changed. Theoretical results, contact angle measurements, and AFM/CFM surface characterization for our nanogap sensor are well in accord with each other, and it is clear from Figure 1c that the wetting properties of the nanogap are critical for its operation.
Conclusions In this work, we have developed criteria for the liquid filling of nanogap structures. We have shown that the wetting properties can be computed in a simple way and related to advancing or equilibrium contact angles of liquids on the materials the structure is built from. As a general result from this study, we retain that the spontaneous imbibition of a liquid column which completely fills the gap is favored by low contact angles with both the electrodes and the substrate surface.
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Our theoretical results show that the geometry of the gap can limit the desired complete filling of the gap. Thin liquid wedges in both corners of the gap which partially wet the bottom surface of the gap are encountered whenever the chosen aspect ratio is too small. If the nanogap is not spontaneously filled by liquid during a wet surface preparation step or while applying a liquid sample to the gap surface, the gap may be clogged by small air bubbles, compromising its function. We have tested our model in an application to a nanosensor, for which it proved useful as an aid in the design of a functional nanogap-based sensor system. The developed methodology can directly be applied to similar configurations, but can also easily be extended to others. For example, an active control over the contact angle could open the possibility to select between liquid structures which partially or completely wet the gap bottom. Such a technique may be of great value for future applications since it allows one to selectively modify specific parts of the gap. Acknowledgment. Y.F.D. is a Research Associate of the National Foundation for Scientific Research (FNRS). Y.F.D. thanks the FNRS, the Universite´ Catholique de Louvain, and the Federal Office for Scientific, Technical and Cultural Affairs (Interuniversitary Poles of Attraction Program) for financial support. LA0611357
