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Nanofluidics: Structural Forces, Density Anomalies, and the Pivotal Role of Nanoparticles M. Heuberger* and M. Za¨ch† Laboratory for Surface Science and Technology, Department of Materials, ETH Zu¨ rich, ETH Zentrum, CH-8092 Zu¨ rich, Switzerland Received October 2, 2002. In Final Form: November 29, 2002 Cyclohexane is confined between two surfaces. Different types of confinement geometries are realized using different preparation protocols for mica surfaces. We profile thickness and refractive index of a nanometer-thin liquid film at high resolution with a newly developed three-dimensional scanning technique in the extended surface forces apparatus. We propose that the recently reported density anomalies in the thin liquid film are intimately coupled to the presence of local surface nonparallelism and nanoparticles that are produced during a widely used mica-cutting procedure. Measurements of cyclohexane confined between near parallel, nanoparticle-free mica surfaces contrast markedly with those reported in earlier studies.
1. Introduction When a fluid is confined to nanometer dimensions, its noncontinuum, molecular nature can become apparent. Fluids in such tight situations are to be found in living organisms, porous materials, capillaries, thin-film lubrication systems, or microfluidic networks. Some two decades ago, so-called structural forces were discovered in cyclohexane.1 Later, an apparent solidification was reported in conjunction with lateral shearing of such nanometer-thin films.2,3 In these experiments, the liquid medium was slowly squeezed out of the gap formed between two cylindrically curved mica surfaces in the surface forces apparatus.4 An alternative experimental approach to studying confined liquids is to adsorb them into porous materials. Such experiments have revealed significant confinement-induced shifts of thermodynamic quantities, including a reduction of transition enthalpies and a depression of phase-transition temperatures.5-7 For comparison, the confinement realized in a surface forces apparatus is locally equivalent to a nominally parallel single-slit pore. Recently, we have reported the existence of liquiddensity anomalies in such surface forces apparatus experiments.8 Film-thickness fluctuations and plasticity effects related to film-thickness transitions accompanied these unprecedented findings. Assuming ideal surfaces, the observed effects were discussed in terms of known thermodynamic effects that are also found in porous materials. In this letter, we demonstrate the occurrence of a confinement-induced densification and the absence of the above density anomalies when the confining surfaces * To whom correspondence should be addressed. E-mail:
[email protected]. † Current address: Chalmers University of Technology, Department of Applied Physics, Fysikgra¨nd 3, Go¨teborg, Sweden. (1) Christenson, H. K.; Horn, R. G.; Israelachvili, J. N. J. Colloid Interface Sci. 1982, 88, 79-88. (2) Kumacheva, E. Prog. Surf. Sci. 1998, 58, 75-120. (3) Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108, 7010-7021. (4) Heuberger, M. In Encyclopedia of Chemical Physics and Physical Chemistry; Moore, J. H., Spencer, N. D., Eds.; Institute of Physics Publishing: Bristol, 2001; Vol. II, pp 1517-1536. (5) Faivre, C.; Bellet, D.; Dolino, G. Eur. Phys. J. B 1999, 7, 19-36. (6) Dore, J. C.; Dunn, M.; Hasebe, T.; Strange, J. H. Colloids Surf. 1989, 36, 199-207. (7) Aksnes, D. W.; Gjerdåker, L. J. Mol. Struct. 1999, 475, 27-34. (8) Heuberger, M.; Za¨ch, M.; Spencer, N. D. Science 2001, 292, 905908.
are free of nanoparticles. This is achieved by an unconventional mica surface preparation procedure, which prevents the deposition of unwanted nanoparticles on the surface.9 With particle-free surfaces, cyclohexane is found to grow a high-density film, which is comparable to the known SI plastic-crystalline phase of frozen cyclohexane.10 Load-induced deformations of this high-density film appear as discrete film-thickness transitions of molecular size 0.55(2) nm that are of longer range and associated with much larger forces than reported hitherto. 2. Materials and Methods 2.1. The Extended Surface Forces Apparatus. We confined a thin film of cyclohexane between two surfaces of mica in the extended surface forces apparatus (eSFA). The eSFA is a modified version of the SFA 3.11,12 Modifications include drift control,13 temperature control,14 and automated acquisition and evaluation of thin-film interference spectra using fast spectral correlation (FSC).15 2.2. Mica Surface Preparation. Two cylindrically curved (R1 ≈ R2 ≈ 20 mm) mica sheets were brought into proximity in a crossed-cylinder arrangement. In this study, two different micacutting procedures are compared: Cutting procedure A corresponds to the widely used, traditional mica-cutting process16-18 employing a hot Pt wire to melt through the thin mica piece. In contrast, cutting procedure B corresponds to a cold-cutting approach using precision surgical scissors.9 Care was taken that the airflow of the laminar-flow cabinet pointed away from the cutting edge during mechanical cutting. For protection and intermediate storage, the cut mica sheets were collected and laid down onto a freshly cleaved mica surface. A distinct support (9) Za¨ch, M. PhD Thesis, Department of Materials, Swiss Federal Institute of Technology (ETH), Zu¨rich, March 2002; p 206. http://ecollection.ethbib.ethz.ch/cgi-bin/show.pl?type)diss&nr)14560. (10) Wisotzki, K. D.; Wu¨rflinger, A. J. Phys. Chem. Solids 1982, 43, 13-20. (11) Israelachvili, J. N.; McGuiggan, P. M. J. Mater. Res. 1990, 5, 2223-2231. (12) Israelachvili, J. N. U.S. Patent 5,861,954, 1999; p 25. (13) Heuberger, M.; Za¨ch, M.; Spencer, N. D. Rev. Sci. Instrum. 2000, 71, 4502-4508. (14) Heuberger, M.; Vanicek, J.; Za¨ch, M. Rev. Sci. Instrum. 2001, 72, 3556-3560. (15) Heuberger, M. Rev. Sci. Instrum. 2001, 72, 1700-1707. (16) Israelachvili, J. N.; Tabor, D. Nat. Phys. Sci. 1972, 236, 106108. (17) Tabor, D.; Winterton, R. H. S. Proc. R. Soc. London 1969, A312, 435-450. (18) Israelachvili, J. N. J. Colloid Interface Sci. 1973, 44, 259-271.
10.1021/la026645p CCC: $25.00 © 2003 American Chemical Society Published on Web 02/08/2003
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Figure 1. Topography of (A) melt-cut (type A) mica and (B) mechanically cut (type B) mica sheets, measured with an AFM in contact mode. Nanoparticles are reproducibly found on type A surfaces. Type B surfaces are largely particle-free. The deposition of nanoparticles during hot-wire cutting has previously been reported by Ohnishi et al. (ref 22). AFM parameters: contact mode; set-point, 5 nN; tip radius, 20-60 nm. Image treatment: second-order flattening and contrast enhancement. The small surface waviness could be due to the standard gluing of these thin mica sheets and is a subject of further investigations. was used for each cutting type. In the case of cold-cut mica (type B), the sheets were laid down with one edge overlapping a band of clean poly(tetrafluoroethylene) (PTFE). This measure was necessary to ensure lift-off after thermal evaporation of a 40 nm silver mirror. Prior to the eSFA experiment, the silver-coated mica sheets were glued onto cylindrical lenses with the silvered face against the glue and one chosen optical axis parallel to the cylinder axis. The glue was a 1:1 mixture of D-(+)-glucose and D-(+)-galactose that melted on a temperature-controlled heating plate. 2.3. Methodology. All eSFA experiments were carried out in a temperature-controlled environment of stability (2 mK/h, or (5 mK/day.14 Thermal and nonthermal drifts of the instrument amounted to less than 0.5 pm/s.13,14 The eSFA and all optical parts are operated on a pressurized antivibration table. One surface was mounted on a double-cantilever spring,11,12,19 which can deflect under the action of surface forces. A precision ((2 nm), dc-motor-driven actuator12 was used to vary the surface separation at controlled velocities ranging from 0.01 to 5 nm/s. The integral force, F, across the curved interface is inferred from the difference between the calibrated actuator position, M, and the locally measured surface separation, D, using the simple relation F ) k(D - M), where k is the spring constant of the force-measuring spring. For the experiments presented here, the spring constant was fixed at either k1 ) 108 ( 14 N/m or k2 ) 1002 ( 23 N/m. Larger spring constants were not used to avoid unwanted errors.20 The transmission spectrum of the multilayer interference filter formed between the silver mirrors is evaluated using the FSC method, which was described in detail elsewhere.15 Using FSC, we can simultaneously determine thickness and refractive index of the liquid film between the mica surfaces at high precision. A laterally resolved measurement of these quantities was implemented using a new optical scanning technique.15 This allows one to assess the behavior of confined liquids throughout the macroscopic contact zone, at scan sizes reaching some 200 µm × 200 µm at roughly 1 µm lateral resolution.
3. Results 3.1. Characterization of Mica Surfaces. In Figure 1A,B, the surface topography of mica of type A and type B is compared as measured using an atomic force microscope (AFM). The AFM was operated at 5 nN constant force mode. We used standard silicon nitride tips with a manufacturer-specified radius of 20-60 nm. We always observe a dense carpet of nanoparticles on surfaces of type A, which is not present on surfaces of type (19) Israelachvili, J. N. Chemtracts: Anal. Phys. Chem. 1989, 1, 1-12. (20) Za¨ch, M.; Heuberger, M. Langmuir 2000, 16, 7309-7314.
B. This finding strongly suggests the deposition of nanoparticles on the mica surface by the established hotcutting procedure, since all other steps of the surface preparation were identical. The nanoparticle height distribution is 8 ( 2 nm. The apparent in-plane diameter of the particles is between 100 and 250 nm, which may, however, be significantly overestimated due to the finite diameter of the AFM tip. The number density varies between 0.1 and 1 µm-2. When two such mica surfaces are brought into contact in the SFA, the particle concentration is effectively doubled at the interface. Under the external load, the mica sheets mechanically deform around each nanoparticle. Using plate mechanics21 and reasonable parameter values, one can show that such deformation around one single particle would extend over a lateral distance of 7-10 µm and mainly depend on the mica thickness. However, due to the small distance between particles (Figure 1A), these mica deformations never decay and thus are effectively so small that they cannot be detected via manual inspection of interference fringes. Nevertheless, the existence of nanoparticles has been reported previously by Ohnishi et al.22 A potentially detrimental effect of such nanoparticles on the fast drainage of confined liquids was briefly discussed by Mugele et al.,23 and more correct mica preparation procedures have been proposed.23,24 In agreement with Ohnishi et al.,22 we found that scanning at higher loads (AFM) can displace the particles, which suggests the presence of adhesive bonding. However, attempts to remove the particles by rinsing of mica with cyclohexane or saltwater were not successful.9 Nanoparticles change the local confinement geometry and the local force distribution at the interface and therefore should be taken into account for the interpretation of direct surface force measurements whenever the surface separation is less than some 20 nm. Earlier results should thus be reinterpreted in terms of a complex multiasperity contact (e.g., Figure 2A, inset). 3.2. Confined Fluid Properties. Figure 2 compares film thickness and refractive index of confined cyclohexane (21) Johnson, K. L. Private communication. (22) Ohnishi, S.; Hato, M.; Tamada, T.; Christenson, H. K. Langmuir 1999, 15, 3312-3316. (23) Mugele, F.; Becker, T.; Klingner, A.; Salmeron, M. Colloids Surf. 2002, 206, 105-113. (24) Frantz, P.; Salmeron, M. Tribol. Lett. 1998, 5, 151-153.
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Figure 2. Structural forces and refractive index measurement in surface-confined cyclohexane: (A) for mica surfaces of type A and (B) for mica surfaces of type B. The data shown in (A) are adopted from ref 8 and obtained using a spring constant of k2 ) 1002 ( 23 N/m. The spring constant for the measurement shown in (B) was k1 ) 108 ( 14 N/m. As a visual aid to distinguish fluctuations from errors, light gray areas have been added to specify the expected three-sigma error regime for the measurement of refractive index using FSC (ref 15), assuming a constant refractive index of cyclohexane (n ) 1.427). The statistical errors associated with film thickness (x-axis) are smaller than the symbol size in all cases. The insets schematically cartoon snapshots of plausible molecular arrangements in the presence of nanoparticles (A) and in the absence of nanoparticles (B) without claiming geometrical or physical authenticity.
between mica surfaces of types A and B. The top portion of the graph shows the normalized force, F/R, where the effective radius R ) (R1R2)0.5 is used to normalize the force. Ri are the undeformed cylinder radii. 3.2.1. Confinement Geometry with Nanoparticles. When mica of type A is used, one can observe the familiar film-thickness transitions, oftentimes referred to as oscillatory forces. As the external pressure on the surfaces is increased, the film thickness is decreased stepwise. The effective range of this structural force is in the order of 2-4 nm. The shape of the measured curve is highly reproducible when the loading-unloading cycle is carried out multiple times on the exact same lateral surface location. On the other hand, we observed a notable deviation between different surface locations.8 Between discrete film-thickness transitions, we observe fluctuations of the film thickness. The amplitude of this fine structure is in the order of (0.2 nm and has a characteristic time constant of a few seconds. These fluctuations of film thickness are linked with density fluctuations in the liquid, as deduced from the remarkable changes in the refractive index. There is a correlation between these two types of fluctuations, and a nonrandom statistics involving multiple modes was reported.8 Moreover, there is a remarkable decrease of space- and time-averaged density with decreasing film thickness, which can go as low as 50% of the bulk liquid density. It is important to note here that there is most likely a systematic error due to the presence of nanoparticles during the determination of the optical zero (i.e., nanoparticles preventing true mica-mica contact). Since nanoparticles can be considerably deformed under the high local pressures, the reference measurement of the optical zero can also become a function of applied load or time in contact as illustrated in Figure 6a,b of ref 15. This systematic error of film-thickness measurement could lead to an offset in the order of a few nanometers on type A mica. Principally, such systematic error could also be present for type B surfaces (e.g., organic contaminants),
but it is expected that the error would be at least 1 order of magnitude smaller. Depending on the optical properties of the nanoparticle carpet, we also expect systematic errors for the subsequent measurement of the refractive index of liquids confined between such surfaces. 3.2.2. Confinement Geometry without Nanoparticles. The use of particle-free mica of type B produces qualitatively similar film-thickness transitions of approximately one molecular diameter as seen with type A (Figure 2B). However, the absolute thickness of the cyclohexane film can become more than twice as large, while the first transitions occur at comparable external loads. Accounting for the molecular diameter of cyclohexane (0.55 nm), we thus observe a film of altered properties up to 22 molecular diameters in thickness. We have carried out measurement series using two different spring constants (k1 ) 108 ( 14 N/m or k2 ) 1002 ( 23 N/m) and different mica surfaces. Fluctuations of the film thickness are still visible in these measurements, however at significantly smaller amplitudes. Interestingly, the time-averaged film density no longer decreases; it consistently increases to 10-15% above the bulk liquid density. We also find that the previously seen density fluctuations have vanished within the precision of FSC (gray areas in Figure 2). In contrast to measurements obtained on type A mica, repeated loading-unloading cycles on a fixed surface location reveal significant time effects over periods of minutes and hours, generally leading to an increased thickness of the high-density film with time under confinement and repeated loading cycles (seen as an increased range of the repulsive forces). Such film growth, which can start at an initial film thickness of 2 nm, quickly growing to 4-6 nm after the first loading cycle, can finally reach some 10 nm (Figure 2B). This new finding strongly suggests that the observed densification is a rate-limited process, enhanced or even initiated by confinement. Furthermore, we have also found a dependence of the maximal film thickness on the force-measuring spring
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Figure 3. This three-dimensional measurement of the confined film was obtained using the new scanning feature of the eSFA (ref 15). The image consists of 61 × 61 points measured over an area of 60 µm × 60 µm around the contact. A 3 × 3 median filter was applied to reduce point-to-point jitter in the data. All measurements were obtained with a spring constant of k2 ) 1002 ( 23 N/m. The thickness profiles (A) with type A mica and (B) with type B mica are shown. The color scale corresponds to the refractive index of the confined liquid. (C) and (D) illustrate the corresponding refractive index profiles, which are a measure for the effective film density, as pointed out by the density scale in percent (refs 27 and 28), where 100% corresponds to the density of bulk liquid cyclohexane.
constant, k, and the associated loading rate dF/dt ) kv. Stiffer springs and higher motor speeds, v, both result in higher loading rates, which tend to decrease the maximal range of the observed film-thickness transitions. This agrees with the previous finding that the molecular ordering occurs over measurable time scales. A detailed discussion of these time effects lies outside the scope of this letter. The data shown in Figure 2B represent a measurement obtained with a small spring constant of k1 ) 108 ( 14 N/m and thus illustrate the maximal extent of film thickness under low-rate conditions. The mica surface deformation was barely noticeable in these measurements; however, the local radius of surface curvature was relatively large, R ) 26 mm. 3.3. The Role of Confinement Geometry. In our instrument, the interference spectrum analysis is performed on a small spot of approximately 1 µm diameter; we like to call it the optical probe. To assess the lateral aspect throughout the confined liquid, we use calibrated actuation of optical elements to laterally displace that optical probe in a scanning pattern.15 The result of such a scanning measurement is a three-dimensional representation showing film thickness and refractive index of the confined liquid throughout the entire contact zone as shown in Figure 3. At a typical acquisition rate of 1 Hz, it takes about 60 min to obtain a complete image of 60 × 60 points. Figure 3D illustrates the extent of the densification in the center of the contact, suggesting confinement-induced solidification.10 The spring constant used in this experiment was k2 ) 1002 ( 23 N/m, and the external load during scanning was unchanged, F/R )
1.8 mN/m. No substantial surface flattening was observed in this case, and the film thickness in the point of closest approach (PCA) was 3.5 nm. We have also performed loading-unloading cycles and three-dimensional scans (not shown) at much higher final loads, which were accompanied by substantial surface deformations. In these cases, it was found that film-thickness transitions can be observed down to a film thickness of about 2 nm in the PCA, if the external load was increased to F/R ) 350 mN/m, which represents a very high external load. The magnitude of the external load required to produce film-thickness transitions increases roughly exponentially with decreasing film thickness. The previously seen density reduction does not occur even when the film is compressed down to 2 nm at these very high loads. 4. Discussion Fluid densities exceeding bulk liquid density have already been reported as fluctuations in the presence of nanoparticles and were consistently linked to the occurrence of repulsive forces.8 The core region of the contact zone shown in Figure 3D exhibits a density 10-15% above that of the bulk liquid. Such a large-scale increase of density must be accompanied by substantial molecular ordering in the liquid, which takes a certain amount of time to proceed, as we have seen above. The fact that this high-density film can organize itself and grow under confinement suggests that there is a significant, confinement-induced reduction of entropy in the system, which drives this molecular ordering. There is an outer anus of slightly reduced (ca. 5%) density around the center of the contact zone (Figure 3D).
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Inside that anus, cyclohexane is confined by slightly nonparallel walls (slope < 0.1%). A small density reduction in nonparallel confinement is in agreement with recent computer simulations that suggest the occurrence of fluid density reduction in such situations.25 The extraordinary magnitude of the density anomalies observed in the presence of nanoparticles must be corrected due to a systematic error in the presence of nanoparticles during the optical measurement of the mica thickness. The real extent of these density anomalies is probably smaller and could be understood in terms of surface nonparallelism. It has been shown that the pressure in a confined liquid is anisotropic and, in the direction perpendicular to the surfaces, a sinusoidal function of the surface separation.26 In nonparallel confinement, liquids are thus expected to preferably condense in regions where the surface distance is favorable. Regions of unfavorable surface separation could thus contain a considerable number of packing defects in the film, which lower the average density measured using interferometry. Subnanometer variations of the surface separation should thus be sufficient to move high-density condensates in the lateral direction. For the stationary optical probe of the eSFA, this would cause temporal density fluctuations. The inverse correlation between film-thickness fluctuations and density fluctuations8 suggests that the pressure in such condensed regions is less than in the vapor voids. As the external pressure on the mica plates is continuously increased, surface nonparallelism, due to surface deformation around nanoparticles, is amplified and even lower density is recorded. Several modes of distinct film thickness may thus coexist and shift laterally, which can be detected by our stationary optical probe. These effects were indeed observed as multiple thickness modes8 in fluctuation statistics. Figure 3B,D shows that despite the absence of nanoparticle-induced nonparallelism, cyclo(25) Porcheron, F.; Schoen, M.; Fuchs, A. H. J. Chem. Phys. 2002, 116, 5816-5824. (26) Wang, J. C.; Fichthorn, K. A. J. Chem. Phys. 2002, 116, 410417. (27) Gladstone, J. H.; Dale, J. Philos. Trans. 1863, 153, 317. (28) Godbout, G.; Sicotte, Y. J. Chim. Phys. 1968, 65, 1944-1948.
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hexane does not condense perfectly homogeneously throughout the macroscopic contact. A residual plate nonparallelism can be found when profiling the film at high resolution. We are currently investigating if residual nanometer waviness of the thin mica sheets after gluing (Figure 1B) could be responsible for this secondary effect. 5. Conclusion In conclusion, we have confirmed the presence of nanoparticles on mica when prepared according to the widely used hot-wire cutting process. Nanoparticles are shown to significantly alter the mechanics of direct force measurement and, more importantly, the behavior of confined fluids. Comparison with measurements on particle-free mica suggests that the fluid density, especially in very thin films, can be significantly reduced under nonparallel confinement. This finding is consistent with recent computer simulations25 and supports the finding that oscillatory forces between parallel surfaces could in reality be much stronger than measured experimentally.26 Since the first particles are expected to engage at surface separations below 20 nm, several different types of SFA measurements are potentially affected. A consistent densification of cyclohexane comparable to the plastic crystalline state is a new finding, but in agreement with the high-density spikes observed earlier in the presence of nanoparticles.8 It is desirable to further study confined liquids between both perfectly parallel and nonparallel surfaces. The possibility to locally influence entropy and to displace and densify liquids under confinement by actively controlling surface parallelism at the subnanometer scale could become a basis for future nanofluidics experiments. Acknowledgment. We acknowledge N. D. Spencer for his financial and scientific support, S. Lee, K. Feldman, and J. Manojlovic for their help in obtaining the AFM data, and M. Elsener and J. Vanicek for their excellent technical support in connection with the eSFA. Financial support was provided by the Swiss National Science Foundation (M.Z., J.M.). LA026645P
