Fluidity of Water Confined Down to Subnanometer Films - American

stress can be sustained by water (within our resolution and shear rates) down to films of thickness D ). D0 ) 0.0 ( 0.3 nm. At short range (D < 3.5 ( ...
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Fluidity of Water Confined Down to Subnanometer Films Uri Raviv,†,‡ Susan Perkin,§ Pierre Laurat,†,| and Jacob Klein*,†,§ Weizmann Institute of Science, Rehovot 76100, Israel, and Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K. Received November 17, 2003. In Final Form: March 24, 2004 A surface force balance with extremely high sensitivity and resolution for measuring shear forces across thin films has been used to investigate directly the dynamic properties of salt-free water (so-called conductivity water) in a gap between two atomically smooth solid surfaces. Our results reveal that no shear stress can be sustained by water (within our resolution and shear rates) down to films of thickness D ) D0 ) 0.0 ( 0.3 nm. At short range (D < 3.5 ( 1 nm), an attractive van der Waals (vdW) force between the surfaces causes a jump into a flat adhesive contact at D0, at which the surfaces rigidly couple. Analysis of the jump behavior reveals that the viscosity of water remains within a factor of 3 or so of its bulk value down to D0. This contrasts sharply with the case of confined nonassociating liquids, whose effective viscosity increases by many orders of magnitude at film thicknesses lower than about five to eight monolayers. We attribute this to the fundamentally different mechanisms of solidification of organic liquids and of water. In the former case, the density increase induced in the films by the confinement promotes solidification, while, in the case of water, such densification (due to vdW attraction between the liquid molecules and the confining walls), in agreement with bulk behavior, suppresses the tendency of the water to solidify.

Introduction Understanding the fluidity of water in the vicinity of solid surfaces and particularly under confinement is fundamental to the quantitative understanding of many processes in cell biology and living tissues. It clearly influences the rates and effectiveness of processes such as the transport of materials and energy in the cell, the enzymatic activity of proteins, biochemical reactions, and the function of membranes, as well as the final rate of approach of interacting molecular species (e.g., ligandreceptor). It is also important in technological problems including oil recovery from natural reservoirs, mining, catalysis, and corrosion inhibition. Water is found in confined geometries in porous materials such as Vycor glass, silica gel, and zeolites as well as in polymer gels, clays, rocks, sandstones, micelles, vesicles, and microemulsions. The properties of water confined in pores or between surfaces have been studied extensively using NMR,1,2 dielectric relaxation spectroscopy,3 neutron diffraction,4 neutron scattering,2,5 and simulations.2,6 It has been reported that, near surfaces of pores of diameters of 1-5 * To whom correspondence should be addressed. E-mail: [email protected] or [email protected]. † Weizmann Institute of Science. ‡ Current address: Materials Research Laboratory, University of California, Santa Barbara, CA 93106. § Physical and Theoretical Chemistry Laboratory. | Current address: Service Recherche Technologies Systems, LEGRAND SA 128, avenue de Lattre de Tassigny, 87045 Limoges Cedex, France. (1) Chen, S.-H.; Bellissent-Funel, M.-C. In Hydrogen Bond networks; Bellissent-Funel, M.-C., Dore, J. C., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994; Vol. 435, p 307. (2) Clifford, J. In Water in Disperse Systems; Franks, F., Ed.; Plenum Press: New York, 1975; Vol. 5, p 75. (3) Pissis, P.; Laudat, J.; Daoukaki-Diamanti, D.; Kyritsis, A. In Hydrogen Bond networks; Bellissent-Funel, M.-C., Dore, J. C., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994; Vol. 435, p 425. (4) Ricci, M. A.; Bruni, F.; Gallo, P.; Rovere, M.; Soper, A. K. J. Phys.: Condens. Matter 2000, 12, A345. (5) Bellissent-Funel, M. C.; Lal, J.; Bosio, L. J. Chem. Phys. 1993, 98 (5), 4246.

nm, the molecular motion of water in the first one to three layers is very restricted and is significantly slower than that of bulk water. The reduction reported is within a factor of 2-1001,2,4-7 for pores of diameters of 2-5 nm and up to a solidlike2,3,8 or glasslike9 behavior for pores of diameters of 1 nm or slightly smaller. Its particular dynamic behavior and structure are determined by the interactions with the surfaces10 and are entirely different from those of bulk water, and they are accompanied by a distortion of the hydrogen bond network.2,4 It is also clear that, if water layers thicker than 2-3 nm are being considered, their properties are close to those of bulk liquid.1,2,5,7-9,11-15 Simulations, neutron scattering experiments, and O17 NMR measurements of water between clay or mica platelets separated by 1.5 nm or in Vycor glass pores of diameters of 2-5 nm showed that the residence times of water in the first hydration layer are of the order of tens of picoseconds.1,2,4,7,9 The smaller the pore size, the larger the residence time,16 and at lower temperatures, the confinement effects are enhanced.13 A reduction in the mobility of water in the first one to three layers was reported also near a single surface of various types (metallic,17,18 hydrophobic,19 or hydrophilic16). Scanning (6) Rossky, P. J. In Hydrogen Bond networks; Bellissent-Funel, M.C., Dore, J. C., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994; Vol. 435, p 337. (7) Bellissent-Funel, M.-C.; Chen, S. H.; Zanotti, J. M. Phys. Rev. E 1995, 51 (5), 4558. (8) Bruni, F.; Ricci, M. A.; Soper, A. K. J. Chem. Phys. 1998, 109 (4), 1478. (9) Gallo, P.; Rovere, M.; Ricci, M.; Hartnig, C.; Spohr, E. Europhys. Lett. 2000, 49 (2), 183. (10) Cui, S. T.; Cummings, P. T.; Cochran, H. D. J. Chem. Phys. 2001, 114 (16), 7189. (11) Bluhm, H.; Salmeron, M. J. Chem. Phys. 1999, 111 (15), 6947. Hu, J.; Xiao, X. D.; Ogletree, D. F.; Salmeron, M. Science 1995, 268, 267. Hu, J.; Xiao, X. D.; Ogletree, D. F.; Salmeron, M. Surf. Sci. 1995, 344, 221. (12) Borzsak, I.; Cummings, P. T. Phys. Rev. E 1997, 56 (6), R6279. (13) Crupi, V.; Magazu, S.; Majolino, D.; Migliardo, P.; Venuti, V.; Bellissent-Funel, M. C. J. Phys.: Condens. Matter 2000, 12, 3625. (14) Horn, R. G.; Smith, D. T.; Haller, W. Chem. Phys. Lett. 1989, 162 (4-5), 404. (15) Israelachvili, J. N. J. Colloid Interface Sci. 1986, 110 (1), 263.

10.1021/la030419d CCC: $27.50 © 2004 American Chemical Society Published on Web 05/20/2004

Fluidity of Water Confined to Subnanometer Films

polarization force microscopy (SPFM) studies,11 at room temperature and humidity up to 40-50%, and detailed molecular dynamics simulations20 of water adsorption at the surface of muscovite mica [KAl2(AlSi3)O10(OH)2] showed that at monolayer coverage water condenses into a fully connected, two dimensional ordered and stable hydrogen bond network, which was described as two dimensional (2D) ice. On average, the dipole moment of the water molecules points toward the surface (in contrast to the case of neutral17 and positively charged metal surfaces21). At higher humidity (∼80%), the first monolayer reaches saturation and the second and successive layers of water start to condense, forming a fluid film on top of the ice layer. The surface force balance (SFB) technique has been used to probe both dynamic and structural properties of ultrathin aqueous films confined between two atomically smooth solid surfaces. Normal forces between two curved mica surfaces, immersed in purified water with no added salt (so-called conductivity water), were measured as a function of the separation between the surfaces.22 Long range repulsive double layer forces were measured, due to the osmotic pressure of the ions in the water (these arise from trace ions leached from the glassware, from CO2 dissolved from the atmosphere, and from hydrated protons (or hydroxonium ions) in the water). Those forces are in agreement with the so-called Derjaguin-LandauVerwey-Overbeek (DLVO) theory23,24 down to a separation of D ) 3.3 ( 0.2 nm, from which there is a jump into strongly adhesive mica-mica contact. The conclusion from the force measurements at different salt concentrations and pH values is that most of the potassium ions are exchanged with hydroxonium ions, which are at least 10 times more mobile than potassium ions.22,25 It is this exchange which means that, unlike at high salt concentration,22,26-28 no additional repulsive hydration forces are observed in conductivity water. Dynamic SFB studies have been performed for aqueous salt solutions, and they suggest that the viscosity of very thin aqueous salt solution films is similar to that of bulk water down to a separation of 2 nm and that the slip plane is at D ) 0.2 ( 0.3 nm.15 A similar result was obtained by observing the rate of thinning of an aqueous electrolyte film (thickness of g2 nm) between silica surfaces.14 These SFB methods rely on hydration repulsion, resulting from the tenaciously bound hydration sheaths about the counterions trapped between the confining surfaces, to prevent the surfaces from approaching adhesive contact. In the absence of hydration forces, where the surfaces can (16) Takahara, S.; Nakano, M.; Kittaka, S.; Kuroda, Y.; Mori, T.; Hamano, H.; Yamaguchi, T. J. Phys. Chem. B 1999, 103, 5814. (17) Porter, J. D.; Zinn, A. S. J. Phys. Chem. 1993, 97, 1190. (18) Porter, J. D.; Zinn-Warner, A. S. Phys. Rev. Lett. 1994, 73 (21), 2879. Xia, X.; Perera, L.; Essmann, U.; Berkowitz, M. L. Surf. Sci. 1995, 335, 401. (19) Meyer, M.; Stanley, H. E. J. Phys. Chem. B 1999, 103, 9728. (20) Miranda, P. B.; Xu, L.; Shen, Y. R.; Salmeron, M. Phys. Rev. Lett. 1998, 81 (26), 5876. (21) Toney, M. F.; Howard, J. N.; Richer, J.; Borges, G. L.; Gordon, J. G.; Yee, D.; Sorensen, L. B. Nature 1994, 368, 444. (22) Pashley, R. M. J. Colloid Interface Sci. 1980, 80 (1), 153. Quirk, J. P.; Pashley, R. M. J. Phys. Chem. 1991, 95, 3300. (23) Derjaguin, B. V.; Landau, L. Acta Phys. Chem. 1941, 14, 633. Derjaguin, B. V.; Landau, L. JETP Lett. 1945, 15, 633. Verwey, E. J. W.; Overbeek, J. T. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam, The Netherlands, 1948. (24) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Plenum Publishing Corporation: New York, 1987. (25) Xu, L.; Salmeron, M. Langmuir 1998, 14, 5841. (26) Pashley, R. M. J. Colloid Interface Sci. 1981, 83 (2), 531. (27) Pashley, R. M.; Israelachvili, J. N. J. Colloid Interface Sci. 1984, 101 (2), 511. (28) Raviv, U.; Klein, J. Science 2002, 297, 1540.

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jump into contact, only films thicker than ∼5 nm have been investigated with the dynamic SFB approach. Recently, we have shown28 that 0.1 M NaCl solutions retain the shear fluidity characteristic of the bulk liquid, even when compressed (between mica surfaces) down to films 1.0 ( 0.3 nm thick. The fluidity of subnanometer salt-free water films has not previously to our knowledge been studied directly; mostly, indirect spectroscopic methods or simulations were utilized, as noted earlier.2,3,8,9 Recently, using a SFB with a uniquely high resolution for measuring shear forces across thin films, we investigated directly the dynamic behavior of conductivity water confined between atomically smooth mica surfaces to progressively thinner films, down to adhesive mica-mica contact.39-41 We found that confined water is unable to sustain shear stress (within our sensitivity) and retains its bulk viscosity (within a factor of 3), down to mica-mica contact, unlike the cases of nonassociative liquids.29-31 In this paper, we extend our earlier short reports32-34 (including new data using mica prepared in different ways) to provide a comprehensive account of this behavior. Experimental Section Methods. The SFB technique and detailed experimental procedures for the normal force and shear measurements have been described in detail elsewhere.29,35,36 The force balance used here is shown schematically in the inset to Figure 1A. Briefly, two half-silvered mica sheets (thickness of ∼1-2 µm and atomically smooth on both sides) are mounted facing each other on cylindrical lenses in a crossed-cylinder configuration at a closest distance of D apart and can be moved both in a normal and in a lateral direction relative to each other via a sectored piezoelectric tube (PZT). The normal and shear forces between them are measured by monitoring the bending of two orthogonal springs (inset to Figure 1A) with an accuracy of ∼ (2 Å using multiple beam interferometry and capacitance changes, respectively. The noise level before signal processing of the shear measurements is of the order of (1-2 µΝ, due to ambient vibrations that are transmitted despite the electronic vibration isolation system (this is larger than the optimal noise levels reported earlier in nonaqueous solvents29). The circuitry of the air gap capacitor may also introduce some high-frequency electronic noise. To obtain optimal sensitivity in the shear measurement, the shear traces measured across conductivity water at different separations, as illustrated in Figure 1, were processed. The raw data traces (Figure 1A) were Fourier transformed, and the amplitude Fs(ω0) at the applied frequency ω0 was measured (Figure 1B). The applied motion is a triangular function and not a sinusoidal one, so we had to take into account that it has components at frequencies other than ω0, which in total (as shown in calibration measurements) sum up to ∼10% of its amplitude. To correct (29) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108 (16), 6996. (30) Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108 (16), 7010. (31) Klein, J.; Kumacheva, E. Science 1995, 269, 816. (32) Raviv, U.; Laurat, P.; Klein, J. Nature 2001, 413, 51-54. (33) Raviv, U.; Giasson, S.; Frey, J.; Klein, J. J. Phys.: Condens. Matter 2002, 14, 9275-9283. (34) Raviv, U.; Kampf, N.; Klein, J. In Dynamics and friction at submicron confining systems; Braiman, Y., Drake, M., Family, F., Klafter, J. American Chemical Society: Washington, DC; in press. (35) Klein, J. J. Chem. Soc., Faraday Trans. 1 1983, 79, 99. (36) Raviv, U.; Frey, J.; Sak, R.; Laurat, P.; Tadmor, R.; Klein, J. Langmuir 2002, 18, 7482. (37) Israelachvili, J. N.; Alcantar, N. A.; Mates, M. N. T.; Ruths, M. Langmuir, to be published, 2003. (38) Ohnishsi, S.; Hato, M.; Tamada, K.; Christenson, H. K. Langmuir 1999, 15, 3312. (39) Kohonen, M. M.; Meldrum, F. C.; Christenson, H. K. Langmuir 2003, 19, 975-976. (40) Heuberger, M.; Zach, M. Langmuir 2003, 19, 1943. Lin, Z.; Granick, S. Langmuir 2003, 19, 7061. (41) Derjaguin, B. V. Kolloidn. Zh. 1934, 69, 155.

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Figure 1. (A) Shear forces, Fs ) ks∆x, as a function of time between mica surfaces across water. The top trace is the uniform back-and-forth motion, at a frequency of 0.5 Hz, applied to the top mica surface. The lower traces are the direct recordings of the shear forces transmitted to the lower surface taken from the same experiment at different separations, as indicated in the figure. Inset: Schematic illustration of the surface force balance (SFB) used in the experiments. The two mica sheets are mounted on cylindrical quartz lenses in a crossed-cylinder configuration. The distance D between the surfaces is measured (to (2 Å) using optical interference fringes. The top lens is mounted on a sectored piezoelectric tube (PZT), enabling controlled motion both in the normal direction (D) and laterally (∆x0). The lower surface is coupled to a set of orthogonal springs. The bending of the vertical spring (with the spring constant, kn) is measured by interferometery and yields the normal forces. The bending, ∆x, of the horizontal spring (ks) is measured by an air gap capacitor (to (2-3 Å) and yields the shear force transmitted to the lower surface.29 (B) The Fourier transform of the shear response traces shown in part A. The inset shows the range that includes the frequency of the applied lateral motion in more detail. this, 10% was added to the amplitudes of the shear response measured at the applied frequency. When measuring Fs between the laterally sliding surfaces, it was found that, even at large D values where no shear forces should be measurable, a small systematic shear force was nonetheless observed and was attributed to the shear coupling of the two surfaces via the thin wires connecting the PZT. After allowing for this systematic effect, the scatter δFs ≈ 20 nN (within each experiment) of the shear responses at the applied frequency determines the actual sensitivity of the shear force measurements (for each experiment, the systematic error obtained from the large D response is slightly different due to differences in the wire coupling arising from the mounting of the apparatus). This value of δFs ultimately determines our sensitivity and resolution in measuring shear forces across the water films. The separation can be changed either by applying normal motion, using a driven differential spring or the PZT, or by allowing the slow approach of the surfaces as a result of dimensional changes of the box due to thermal drift. The latter motion, in the range 0.03-0.1 nm/s at D > 400 nm, was utilized to bring the two surfaces, in conductivity water, very slowly into contact while shear motion was being applied.

Raviv et al. Procedure. Mica surfaces were freshly cleaved, and large thin pieces of areas in the range 2-10 cm2 were melt-cut using a hot Pt wire (∼1 cm long, diameter of 0.25 mm), laid onto a freshly cleaved mica base sheet, and coated with silver. Before mounting, ∼1 cm2 pieces needed for the experiment were cut from the larger pieces using a scalpel. In this way, the proximity of molten edges to the central region of each mica surface was minimized. We note that under these conditions (see ref 37, and especially for the thin mica sheets used, with a thickness of 1-2 µm, see ref 38), platinum nanoparticles, which are ejected from the hot Pt wire during cutting39 and have recently been reported to contaminate melt-cut mica sheets in a number of laboratories,40 are absent from the mutual interaction areas (the central regions) of the surfaces. The absence of any nanoparticles in the central region of such melt-cut mica sheets is directly revealed by atomic force microscopy (AFM) measurements (a comprehensive report on this by S. Perkin et al. is to be published). To confirm this unambiguously, we also carried out additional separate experiments for both the normal and shear forces, where, instead of the melt-cut sheets, we used mica sheets that were “torn-off” from a cleaved larger sheet using only tweezers (prior to being laid on the base sheet and silvered). These measurements are included and identified in the Results section. Such torn-off (i.e., non-melt-cut) sheets can have no Pt nanoparticles on them, as confirmed also by AFM micrographs. Before every experiment, glassware was cleaned by immersion for 50-60 min in a fresh mixture of hydrogen peroxide (H2O2, 30% solution) and sulfuric acid (H2SO4, 95-97%, solution) in a ratio of 3:7. The glassware was then rinsed first with deionized water and then with conductivity water, sonicated in conductivity water, rinsed with filtered ethanol (0.22 µm, Fluoropore), and dried in a laminar flow hood. Tools and all the parts of the SFB in direct contact with the solvent were sonicated for 10-20 min in toluene, rinsed with filtered ethanol, and air-dried. This was followed by sonication in ethanol, then sonication in conductivity water, rinsing with filterd ethanol, and air-drying in a laminar flow hood. After the apparatus was cleaned and the mica sheets were mounted, the first stage of each experiment was to bring the surfaces into adhesive air contact in order to determine the position of air contact. The shear response and the variation in time of the ambient noise were measured in air from large separations to rigid coupling at contact, utilizing both applied normal motion and the “thermal-drift-in” approach. The surfaces were then separated (by ∼2 mm), and the cell was filled with conductivity water, using a glass syringe, as described elsewhere.36 After 1 h was allowed for thermal equilibration, the normal forces were measured as a function of the distance between the surfaces. Uniform back-and-forth shear motion was then applied to the top surface, and the shear responses as well as the noise level of the lower surface were recorded, at progressively smaller separations. Over the final 10 nm, the thermal drift of the box was utilized to approach very slowly, while the shear motion was being applied, to final adhesive contact. Materials. Highly pure conductivity water was obtained by treating tap water with activated charcoal followed by a Millipore water purification system, consisting of a RiOs and a Milli-Q Gradient (A10) stage. The specific resistivity of the water was >18.2 MΩ cm, which corresponds to an ion concentration of kn, the constant of the leaf spring supporting the lower mica surface. A good estimate for the attractive force is given by the theoretical vdW force expected between two crossed cylinders of radius of curvature R, at the closest distance D, F(D) ) -AR/6D2, where A is the Hamaker constant of two mica surfaces across water (A ) 2 × 10-20 J). The condition for a jump in is thus ∂Fn/∂D ) AR/3D3 > kn ) 150 N/m, from which we obtain the maximum distance, Dj, from which jump in can occur to be Dj < (AR/3kn)1/3 ) 6-7.6 nm, for R ) 0.5-1 cm. The jump in observed upon first compression was from distances of 3.5 ( 1.0 nm, because in addition to the vdW attractive force there was a repulsive double layer force, which decreased the distance from which the jump in occurred (see also ref 47). Considering the hydrodynamic factors limiting the rate of approach of two surfaces in a fluid medium, where D is the surface-surface separation, we can estimate the expected duration of this jump, applying an approach used in an earlier study35 to analyze the jump from Dj to D0. The equation of motion for a smooth sphere approaching a smooth flat (equivalent to our experimental geometry) across the gap Dj < D < D0 subjected to a force, F(D), is determined by

M(dD2/dt2) + 6πR2ηeff[(dD/dt)/D] ) F(D) - kn(Dj - D) (5) where M () ∼3 × 10-3 kg) is the mass of the lower lens moving to contact with the upper one and ηeff is the effective viscosity of the medium. The first term on the left-hand side is the inertial term, the second term on the left-hand side is the Reynolds lubrication force50 opposing the (50) Reynold, O. Philos. Trans. R. Soc. London 1886, 177, 157.

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Figure 7. The illustration at the top right illustrates the jump in driven by van der Waals attraction and opposed by the hydrodynamic force resulting from the expulsion of the viscous liquid from between the surfaces. The inset (lower right) shows how, for an effective viscosity ηeff ) ηbulk ) 0.86 mPa s (the viscosity of bulk water at 23 °C), the jump time, τj, varies with the distance jumped for a jump commencing at Dj ) 3.5 nm and ending at D0, according to eq 7. The main part of this figure shows the effective viscosity, ηeff, of the liquid being squeezed out of the gap corresponding to the jump time to contact, τj, for three values of the jump distance, Dj: the midrange value 3.5 nm (solid line) and the two extremes from which jumps occurred, Dj ) 2.5 and 4.5 nm (broken lines). The shaded vertical band is the range of experimentally determined τj values, so that the range of effective viscosity, ηeff, of the confined water films in the thickness interval {3.5 ( 1 nm, 0}, which corresponds to the experiments, is defined (horizontal dotted lines) by the overlap of the broken lines with the shaded band. This possible range of values is within a factor of 3 or so to either side of ηbulk; its midrange value with respect to Dj and τj, indicated as a solid square, is close to ηbulk itself.

approach (due to the need to squeeze out the viscous liquid from between the surfaces) for R . D, and the right-hand side is the net force on the sphere at a separation of D. It can be readily shown that the inertial and the spring terms are negligible (see Appendix I). The change in the double layer repulsive force over the jump distance was neglected too, as it is very small compared to the change in vdW force over this range. Upon substituting for F(D), we obtain

6πR2ηeff[(dD/dt)/D] ) -AR/6D2

(6)

that upon integration leads to a jump time, τj, for spontaneous motion of the surfaces from Dj to D0:

τj(ηeff, Dj, D0) ) (18πRηeff/A)[(Dj)2 - (D0)2]

(7)

This variation is indicated in the inset to Figure 7 for Dj ) 3.5 nm and ηeff ) ηbulk ) 0.86 × 10-3 Pa s, the viscosity of bulk water at 23 °C. The vertical shaded band in Figure 7 shows the range (0.2-0.5 s) of experimental τj values. The solid straight line crossing the shaded band is the implicit relation from eq 7 between the jump time, τj (from Dj ) 3.5 nm to D0 ) 0), and the effective viscosity, ηeff; also shown as diagonal broken lines are the implicit τj variations for the limits Dj ) 2.5 and 4.5 nm of the jump distances. The range of ηeff where τj(ηeff, Dj, 0) overlaps the shaded band, shown by horizontal dotted lines, thus defines the range of effective viscosities that correspond to the experimental jump times. This shows that the viscosity of water confined to films of thickness in the

range 3.5 ( 1 nm down to D0 is within a factor of 3 or so in either direction of the viscosity of bulk water, ηbulk (arrow). The uncertainty arises from the scatter in the values of the jump distance, Dj, and the jump time, τj. It is of interest that the viscosity corresponding to the midrange of both Dj (3.5 nm) and the experimental τj value (0.35 s), indicated as the solid square in Figure 7, is rather close to that of bulk water. Although the above analysis suggests that the viscosity of the water being squeezed out of the gap is close to that of bulk water, there remain three issues that merit consideration. The first concerns the Reynolds term in eqs 5 and 6; this relates to the squeeze-out of liquid across the entire gap, and it is conceivable that within a small region about the point of closest approach the actual viscosity of the confined water is much higher. In Appendix II, this question is treated in detail, and we conclude that such an effect would not be consistent with our results, since it would lead to jump-in times significantly longer than those that we actually observe. We may confidently conclude therefore that the viscosity of water confined between solid walls to films in the range (3-0) ( 0.3 nm is indeed close to that of bulk water, as indicated in Figure 7. The second point concerns the nature of the confining mica surfaces, which are formed by the cleavage of the mica sheets and whose laterally macroscopic atomic smoothness is a central assumption when discussing confinement to subnanometer films. Recent reports suggest that, in a number of laboratories carrying out surface force measurements using SFBs, the interacting (central) regions of the melt-cut mica sheets are contaminated with Pt nanoparticles during the melt-cutting process.40 Such contamination can readily be avoided by proper procedure and safeguards (as clearly described in ref 37), and in our experiments, both here and in earlier studies, we have consistently adopted such a procedure as that described in the Experimental Section. In particular, we ensured reproducibility of earlier literature results as controls, in terms of the force profiles (Figure 2), the jump into micamica contact across conductivity water, and the surface energies evaluated from pull-off forces. We have moreover checked our melt-cut mica samples as prepared for the present study, and AFM micrographs reveal them to be quite free of nanoparticles over the entire region of interest (S. Perkin et al., to be published). However, to ensure unambiguously that the interactions reported are indeed characteristic of atomically smooth confining surfaces, we have carried out new experiments since our earlier brief report,32 using torn-off mica sheets (atomically smooth on both sides, as revealed in the usual way by interference colors and the shape of the interference fringes) rather than melt-cut mica (to be published), since such torn-off sheets clearly can carry no Pt nanoparticles. The results with the torn-off mica sheets are quite identical to the results using melt-cut sheets, in terms of the forcedistance profiles (Figure 2), the jump into contact (Figure 5, especially part D), and the surface energies deduced from the pull-off forces (Table 1). We conclude from this identity that all our results, using melt-cut as well as torn-off mica sheets, are indeed characteristic of surfaces that are atomically smooth and contaminant-free over the entire region of interest. The third point concerns the issue of water slip at the mica surface. In eqs 5 and 6, we assume stick boundary conditions because the mica surfaces are hydrophilic.51 Recent experiments (see ref 52 and references therein) (51) Vinogradova, O. I. Langmuir 1995, 11, 2213.

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Figure 8. The calculated53 maximal shear rate, γmax, due to water squeeze-out during the jump in (solid line), occurring at a distance of r away from the point of closest approach of the surfaces (broken line), as a function of D.

suggest that at sufficiently high shear rates some slip of liquid may occur even past smooth solid surfaces which are wetted by the liquid; slip lengths of ∼8-9 nm were indicated for shear rates larger than ∼104 s-1. Recently, we performed the same analysis as that above (eqs 5-7) for the case of slip boundary conditions33 and found that, even when such slip lengths were taken into account in solving these equations, the effect on the viscosity deduced from the jump time is rather small (up to a factor of 5-10). In practice, as explained below, the dominant shear rates affecting the approach of our surfaces are much less than 104 s-1, so that slip-length considerations are unlikely to modify our conclusions even by this small factor. We can identify different shear rates relevant to this study. In the absence of applied lateral motion (Figure 3), the shear is due to ambient vibrations at the instrument characteristic frequency, which yields shear rates of up to ∼150 s-1 for D values down to ∼2 nm, just prior to the jump in. When lateral motion is applied (e.g., at 500 nm/ s), the shear rate due to this motion varies between ∼200 s-1 at D ) 2.5 nm and ∼1000 s-1 at D ) 0.5 nm. Finally, using expressions developed by Chan and Horn,53 we may also estimate the maximal shear rate, γmax, values due to water squeeze-out during the jump in:

γmax ) (1/2)(3/2)5/2(R1/2/D3/2)(dD/dt)

(8)

This variation is plotted in Figure 8. Using the variation of D with t from the inset to Figure 7, we find that γmax ) ∼5 × 103 s-1 at D ) 1 nm and ∼4 × 104 s-1 at D ) 0.5 nm. However, these maximal rates occur (as plotted in Figure 8, broken line) at a distance of r ) (2RD/3)1/2 ) ∼2.6 and ∼1.8 µm, respectively, away from the point of closest approach of the surfaces;53 nearer the point of closest approach, the shear rates are substantially smaller. Since the Reynolds force is greatest at the lowest D values, it is therefore not likely that slip effects modify our conclusions above concerning the water viscosity to any significant effect. We note also that, despite these substantial variations in shear rate (∼102-104), our results do not (within our resolution) exhibit any apparent variation in the effective viscosity of the confined water. For this reason, we believe the behavior of the confined water is Newtonian within the range of our parameters. (52) Bonaccurso, E.; Butt, H. J.; Craig, V. S. Phys. Rev. Lett. 2003, 90, 144501. (53) Chan, D. Y. C.; Horn, R. G. J. Chem. Phys. 1985, 83 (10), 5311.

We come finally to the issue of why the confined water films in our study behave so differently compared to the case of nonassociating liquids confined to nanometricthickness films.29,31,49 We should first note the case of water confined to nanometer-sized pores, as studied by various spectroscopic and scattering methods.1,2,4,7,9,13,16 These show considerable suppression of the mobility of the water molecules in the smallest (e ∼1 nm) pores. This may be due to some complexation of the confined water with the pore walls (via hydrogen bonding) or with ions leached out of the pore material, possibly forming a material similar to the thin (∼5 Å) water-based film on the mica surfaces in air (discussed earlier), which has rather solidlike properties but which is mostly water42 and is washed off by addition of the bulk water. We cannot however attribute these differences more precisely, as the nature of the confining surfaces in the porous materials and their topography is not sufficiently characterized for comparison with the present configuration. The most striking difference arises when comparing simple (i.e., small and quasi-spherical) nonassociative liquids such as cyclohexane, OMCTS, and toluene under progressive confinement: as the two confining surfaces approach each other from large separation, such liquids retain their bulk fluidity across the entire gap until at a critical spacing, which is characteristic of each liquid, the entire film appears to undergo a liquid-to-solid transition or has a diverging viscosity29 (in the sense that at lower film thicknesses the confined material exhibits a yield stress at zero frequency). One may understand this at several levels. Most generally, it is because, as confinement increases, the translational entropy available to these nonassociating molecules decreases to the point at which it becomes thermodynamically favorable for them to condense as a solid. For the case of water, given that the confining mica surfaces must suppress the translational freedom of the water molecules just as they do in the case of organic solvents and that in addition mica is hydrophilic and has a surface lattice structure quite commensurate with water,54 one might have expected that solidification would be promoted also in confined water films.10 The fact that it clearly does not indicates we must seek a solidification mechanism which differentiates between water and nonaqueous solvents. As has been explained elsewhere,40,41 since we find similar behavior also with hydrophobic surfaces, we attribute its persistent fluidity under confinement to the properties of the water itself, not the nature of the confining surfaces. Insight into the origin of the different behaviors in water may be obtained from the following considerations. It appears that the presence of the confining surfaces inhibits the formation of the highly directional hydrogen bond network necessary for water solidification.1,2,7 Such inhibition of the network formation by the confinement may be related to the well-known anomalous density decrease of ice upon melting as well as to the massive supercooling of water near surfaces and in small droplets.2,55 More explicitly, consider the effect that the van der Waals fields of the confining walls exert on the molecules in their vicinity. The attractive van der Waals forces are equivalent to a pressure on the liquid molecules near to and in the direction of the walls, which will lead to a densification of the liquid in the near-wall region. When two such solid confining surfaces approach, the liquid-filled region in the gap between them will have a higher mean density than that of bulk liquid. Indeed, (54) Ravina, I.; Low, P. F. Clays Clay Miner. 1972, 20, 109. (55) Errington, J. R.; Debenedetti, P. G. Nature 2001, 409, 318.

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unlike the nonassociating liquids where densification promotes solidification. These findings have interesting implications for understanding the behavior of living and other naturally occurring systems as well as for technology, where water is often forced to flow and diffuse in highly confined films and pores.

Figure 9. Illustrating schematically the proposed origin for the persistent fluidity of highly confined water in contrast to nonassociating liquids. At large separations, the molecules in the central region of the gap are at their liquidlike density, while the molecules in the near-surface regions (bracketed) are attracted to the respective surfaces by van der Waals forces, equivalent to an effective pressure, and are therefore densified. As the surfaces approach, the two densified (bracketed) regions overlap and the mean density in the gap increases: This promotes solidification for nonassociating liquids (see also ref 10), but it tends to suppress it for the water, in agreement with the different phase behavior of the latter, since liquid water is denser than ice.

recent detailed computer simulations by Cummings and co-workers10 have shown explicitly that, for the case of nonassociating alkane-type molecules confined between mica-like surfaces, the mean density in the gap equals or exceeds that of the solid phase (due to the densification effect noted above) as the surface separation decreases from seven to six molecular layers. They identified this with the previously observed liquid-to-solid transition at this confinement,29 as it is well-known that densification promotes solidification in nonassociating liquids. For water too, one expects such an increase in the mean density of the water in the gap to occur as the surfaces approach closely, but in the case of water, its anomalous phase behavior suggests that densification acts to keep it in the liquid phase (which is why ice floats) and therefore actually suppresses its tendency to solidify. This is schematically illustrated in Figure 9. At the simplest level, we believe the very different behavior, under extreme confinement, of water compared to nonassociating liquids may be attributed to this effect. An alternative way of looking at this is to consider that the solid confining surfaces prefer the denser liquid phase in their immediate vicinity, as the overall van der Waals interaction energy can then be minimized. Very recently,56 a computer simulation of a liquid which dilates upon solidifying (much as water does) indicated that such a liquid remains fluid under all compressions between two solid walls, in agreement with our findings.

Acknowledgment. We thank D. Chandler, J. Israelachvili, S. Safran, and S. Titmuss for comments and discussions. We thank the Eshkol Foundation (Israel) for a studentship (U.R.), the EPSRC (U.K.) for a studentship (S.P.), and the US-Israel Binational Science Foundation, the Deutsche-Israelische Program (DIP), and the Minerva Foundation for their support of this work. Appendix I Justification for Dropping Inertial and Spring Terms from the Equation of Motion. The equation of motion is

M(d2D/dt2) + 6πR2ηeff[(dD/dt)/D] ) FvdW(D) - Kn(Dj - D) where FvdW(D) ) -AR/6D2 (R ) 10-2 m, A ) 2 × 10-20 J) and M ) ∼3 × 10-3 kg is the mass of the lower lens moving to contact with the upper one. The inertial and the spring term can be shown to be negligible as follows. First, the spring term is ∼100 nN/nm × 1 nm ) O(10-7 N) (Kn ) 150 nN/nm, (Dj - D) ) ∼1 nm). The vdW term equals ∼2 × 10-20.10-2/6.(10-9)2 ) O(10-5 N). Taking the jump time from Dj ) 3 nm as being of the order of 0.5 s gives a mean value for (dD/dt) ) ∼6 nm/s, giving (for ηeff ) 10-3 Pa s) the Reynolds term 6πR2ηeff[(dD/dt)/D] ) O(10-5 N). d2D/ dt2 can be estimated from the duration of the jump time, τj, and the jump distance (∼3 nm), assuming it is constant over the jump, from the following relation: Dj ) 0.5(d2D/ dt2)(τj)2 ) 3 nm, giving d2D/dt2 ) 24 nm/s2, so the inertial term M(d2D/dt2) is of the order of 10-11 N, that is, completely negligible, which would hold even if our assumption concerning constant (d2D/dt2) was not quite right. Thus, the Reynolds term and the vdW term are ∼100 times greater than the spring term and ∼106 times greater than the inertial term. Indeed, a numerical solution of the full equation yields an essentially identical τj versus D curve to that shown in the lower inset to Figure 7. Appendix II Analysis of the Jump in of the Sphere onto the Flat across the Liquid. Assume the geometry of the system to be as follows:

Conclusions We have found that purified, salt-free (conductivity) water remains fluid under confinement by solid surfaces, down to film thicknesses in the range (3-0) ( 0.3 nm, retaining a viscosity within a factor of 3 or so to either side of its bulk value. This behavior is in sharp contrast to that of nonassociating liquids, whose viscosity increases by many orders of magnitude when confined to films of less than about five to eight molecular layers. We attribute this to the very different phase behavior of water, whose densification in the vicinity of the confining walls (due to van der Waals forces) suppresses its tendency to solidify, (56) Jagla, E. A. Phys. Rev. Lett. 2002, 88, 245504.

where the water in the gap in the region between D and D + δ (shaded, δ being roughly a water molecule size of ∼0.3 nm) is highly viscous, with the viscosity ηhigh, while the region at all higher D values (outside the radius r) has the low viscosity of bulk water, ηbulk. We now apply the Reynolds formula50 for the normal stress, P, between a

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Raviv et al.

flat circular disk of radius r approaching a rigid flat of a distance of D apart across a fluid with the viscosity ηhigh. 2

3

P ) ∼[ηhighr /D ](dD/dt)

τj ) (24πRηhigh/A){[δ2 + 2δDj +Dj2] ln(Dj/D0) + [(1/2)(Dj2 - D02) - 2δ(Dj - D0) - 2Dj(Dj - D0)]} +

(A1)

(18πRηbulk/A)(Dj2 - D02) (A5)

Since this is the pressure, the total force on the disk will be πr2P ) [πηhighr4/D3](dD/dt). Ignoring the inertial and spring terms as before, the equation of motion becomes

By having D0 ) 0.3 nm (i.e., taking the size of a water molecule as the final contact separation in order to avoid the logarithmic divergence) and with δ ) 0.3 nm, we found that the dominant term in the braces is that in Dj2, and to a very good approximation

6πR2ηbulk[(dD/dt)/D] + [πηhighr4/D3](dD/dt) ) FvdW(D) ) -AR/6D2 (A2)

τj ) (24πRηhigh/A)Dj2 + (18πRηbulk/A)(Dj2 - D02) (A6)

where the first two terms are the usual Reynolds term for the hydrodynamic force between a curved surface and a flat (now with the bulk viscosity of water, since that is what we assume for all of the gap that is outside the shaded region) and the new term representing the effect of the highly viscous region, for example, within a radius r of the point of closest approach, which for that region dominates the Reynolds term. This radius r, which defines the area of the gap within which the water is confined to 3 nm or less, is not constant but must increase as Dj decreases to D. At the separation Dj shown in the above graphic, we have r2 ) 2Rδ, from the geometry, but as the surfaces approach, the effective δ f [δ + (Dj - D)], where δ retains its incremental value of 0.3 nm. Thus, from the geometry in the above graphic, r now increases as D decreases, as r2 ) 2R[δ + (Dj - D)], and the equation of motion now becomes (replacing for r in eq 2)

where the first term is the contribution of the high viscosity region and the second is that due to the rest of the gap at the viscosity of bulk water. Rearranging and dropping D02 relative to Dj2, we have

6πR2ηeff[(dD/dt)/D] + {4πR2[δ + (Dj - D)]2ηhigh/D3}(dD/dt) ) -AR/6D2 (A3) This readily rearranges to give for the jump time

τj )

∫(24πRηhigh/A){[δ + (Dj - D)]2/D} dD + ∫[(36πRηbulk/A)D] dD

(A4)

with lower and upper integration limits D0 and Dj. The first integral is the effect of the assumed high viscosity region, and the second integral is the Reynolds term. Both integrals are elementary, and the solution is

τj ) (18πRDj2/A)[ηbulk + (4/3)ηhigh]

(A7)

This is the result we have been seeking, and it gives the effect of a region of high viscosity on the overall jump time. We know that using ηbulk alone in eq 7, with the mean value of Dj, would yield a jump time of 0.24 s. However, since we actually measure a jump time in the range 0.2-0.5 s, this is telling us that water in gaps confined to 3 nm or less cannot have a viscosity significantly higher than that evaluated from our approach using only the Reynolds equation. This is an important conclusion for our experiments, showing that our analysis is valid and that the deductions about the magnitude of the viscosity of water in confined subnanometer films are correct. [Note that our conclusion applies even if one were considering just the final 0.7 nm, for example, as having a high viscosity, ηhigh, with the region from 3 to 0.7 nm having a low viscosity. In that case, the jump time from 3 to 0.7 nm would take ∼0.2 s, and the final 0.7 nm, assumed to be dominated by the high viscosity, would take (24πRηhigh/A)(0.7 nm)2 ≈ (20 ηhigh) s. If this final jump time from 0.7 nm to contact is, for example, 0.05 s (so that the overall jump time remains 0.25 s in all, in agreement with our observations), this could make ηhigh ≈ 2.5 × 10-3 Pa s, i.e., ∼3 times larger than the viscosity of bulk water, which does not really alter our conclusions about water viscosity in subnanometer gaps.] LA030419D