Langmuir 2006, 22, 2399-2401 Reply to Comment on Reassessment of Solidification in Fluids Confined between Mica Sheets
Much of the current understanding about surface and intermolecular forces is based on experiments using the basal plane of cleaved muscovite mica. Much is qualitatively reproducible between different surface forces laboratories, but agreement is not quantitative. In this context, possible reasons may be of general interest. Readers should understand that our colleagues, who assert that they repeated our experiment, did not repeat two key aspects of our experimental protocol.1 First, they used a different method of surface preparation.2 Second, they did not repeat our use of equilibration time as a variable (more on this below). In the study criticized by our colleagues,1 as well as in a subsequent study on another confined liquid system,3 we distinguished between two states, high and low friction, depending on the history by which confined fluid films are formed. The significance of experimental history is confirmed by recent molecular dynamics simulations,4 yet our colleagues do not control this variable. Three figures presented below seek to respond constructively to our colleagues’ criticisms. Responding to their request to show error bars, Figure 1 goes beyond this to show histograms of raw data that went into the publication that our colleagues criticize. Responding to their claim that the OMCTS molecule is spherical (this concerns the comparison to computer simulations), Figure 2 shows the actual computed structure. Responding to their argument that linear-response experiments might give a flawed view of friction, Figure 3 shows how the friction of a molecularly thin film of OMCTS depends on sliding velocity in the equilibrated state. Readers should be aware that this general disagreement is not new. Our paper1 joined others that already reported the pivotal role of the method of mica preparation on findings using the surface forces apparatus.5 For perspective, readers may wish to view our related debate with Professor Israelachvili and coworkers about another confined fluid, in another journal.6,7 Oscillatory Force-Distance Relations in the OMCTS System. Surveying experiments on this system during the past 20 years, our colleagues’ Figure 1 reveals discrepancies too large to explain by any laboratory’s quoted experimental uncertainty. None of those studies agree quantitatively. †
University of Illinois. University of Notre Dame. § Iowa State University. ‡
(1) Zhu, Y; Granick, S. Langmuir 2003, 19, 8148. (2) Earlier drafts of our colleagues’ Comment explained that they did not employ the same mica preparation as we,1 but instead used a different Pt-free protocol of their own invention. It may be relevant that our colleagues’ protocol entails much longer exposure of the cleaved mica to laboratory air. Frantz and Salmeron showed5 that when mica was freshly cleaved in the manner that we employed, the adhesion between mica sheets was larger by 50% than when our colleagues’ method of using a “backing sheet” was employed. The difference is that, in our colleagues’ method, exposure to ambient atmosphere is longer, reducing the surface energy. (3) Zhu, Y.; Granick, S. Phys. ReV. Lett. 2004, 93, 096101. (4) Jabbarzadeh, A.; Harrowell, P.; Tanner, R. I. Phys. ReV. Lett. 2005, 94, 126103. (5) Frantz, P.; Salmeron, M. Tribol. Lett. 1998, 5, 151. Ohnishi, S.; Hato, M.; Tamada, K.; Christenson, H. K. Langmuir 1999, 15, 3312. Kohonen, M. M.; Meldrum, F. C.; Christenson, H. K. Langmuir 2003, 19, 975. Heuberger, M.; Zach, M. Langmuir 2003, 19, 1943. Lin, Z.; Granick, S. Langmuir 2003, 19, 7061. Becker, T.; Mugele, F. J. Phys.: Condens. Matter 2005, 17, S319. (6) Gourdon, D.; Israelachvili, J. N. Phys. ReV. Lett., in press. (7) Wong, J. S.; Bae, S. C.; Anthony, S.; Zhu, Y.; Granick, S. Phys. ReV. Lett., in press.
2399
Why are these data so inconsistent? As our colleagues criticize our technique, in footnotes we offer four technical remarks.8-11 As our colleagues criticize us for not presenting error bars, in Figure 1 we go beyond error bars to show the raw data that went into the publication that they criticize. For each pull-off force plotted in our original paper, we now show the histogram not only of force, but also of film thickness, whose averages we originally1 reported. Obviously, these raw data were more reproducible than the data surveyed by our colleagues. We suspect the time variable to be at the root of these discrepancies. When one considers that different friction states present themselves, depending on the rate at which the confined film was formed, to be molecularly thin,1,3 this suggests that the approach rate of the two confining surfaces can cause it to “jam” into alternative metastable states, depending on formation history. While our colleagues state that they observed no time dependence, unfortunately they provide no data about that. A recent AFM study of force-distance relations in the OMCTS system shows decided dependence, however.13 Indeed, Vanderlick, Scriven, and Davis concluded long ago that “solvation forces measured in OMCTS ... are not reproducible to within experimental error”.14 Presently, this laboratory is in the midst of systematically testing the hypothesis that just as the states of glasses and granular media depend on the history by which they were formed, and just as friction is known to depend on sample history,1,3,4 so too are oscillatory force-distance profiles obtained experimentally. Comparison to Computer Simulations. Our colleagues wish to quantitatively compare molecular dynamics simulations of Lennard-Jones spheres (ref 6 of our colleagues). The actual shape of the OMCTS molecule is instead like a hockey puck (oblate ellipsoid). Figure 2 shows the actual computed structure of this molecule. While it is true that nonspherical molecules are (8) Stepwise application of small force was employed, not the fixed drive speed our colleagues incorrectly claim. Force was applied by displacing the fulcrum of a spring, then waiting for confined fluid to drain to the new thickness that corresponded to this applied force. The equilibration times between the small increments of force (magnitude specified in the caption of Figure 1) eliminated hydrodynamic instability as a possible source of adhesion. (9) Our colleagues criticize us for using a “fixed speed motor”, but, as explained in footnote 8, the perturbation to the confined fluid was force, not distance traveled by a motor; the system equilibrated thickness in response to small steps of applied force. We fail to understand the relevance of our colleagues’ objection. (10) The two prior studies that employed Pt-free methods of mica preparation, cited by our colleagues, are not relevant to this argument. Specifically, regarding the private communication from Heuberger (ref 10 of our colleagues), one sole datum was measured in the separation direction; it is unclear whether this data was reproduced. Regarding our colleagues’ ref 14, compression was rapid (not quasi-static), and no attempt was made to measure attractive forces. (11) Our colleagues misrepresent the “as-received” purity of our OMCTS samples. In our experiments, moisture was removed by drying the sample over molecular sieves and placing phosphorus pentoxide, a highly hygroscopic chemical, within the sample chamber while experiments were performed. OMCTS is stable chemically; it will not oxidize or otherwise degrade during storage. The commercial OMCTS product was purified by its supplier by distillation (99+% pure); the predominant impurities should be linear siloxane oligomers with similar boiling point, and these would not be removed by the further distillation advocated by our colleagues. Mugele and co-workers found that molecular sieves reduce the moisture level in OMCTS to below the level detectable using the Karl Fischer technique.12 They also found that the as-received OMCTS samples contained no impurities above the limits detectable by NMR.12 For these reasons, we fail to understand what sample impurities concern our colleagues. (12) Mugele, F. University of Twente, The Netherlands. Private communication, July 22, 2005. (13) Patil, S.; Matei, G.; Oral, A.; Hoffmann, P. M. Cornell University Library, Condensed Matter Abstracts http://arxiv.org./abs/cond-mat/0512600 (accessed Jan 12, 2006). (14) Vanderlick, T. K.; Scriven, L. E.; Davis, H. T. Colloids Surf. 1991, 52, 9.
10.1021/la052372x CCC: $33.50 © 2006 American Chemical Society Published on Web 01/26/2006
2400 Langmuir, Vol. 22, No. 5, 2006
Comments
Figure 1. Examples of the raw data that went into the averages quoted in the original1 publication. (a) Pull-off adhesive force F, normalized by the mean radius of curvature R between the crossed cylinder surfaces, is plotted against surface separation on semilogarithmic scales. Error bars show the standard deviation in repeated experiments, derived from the raw data summarized in panels b and c. Retractive forces were applied stepwise with 60-150 s equilibration close to the pull-off point. (b) Histogram of thickness, measured in repeated experiments, for the data in panel a. (c) Histogram of force, measured in repeated experiments, for the data in panel a. Because these histograms from repeated experiments refer to confined films of several different thickness, colors are used in panels b and c to distinguish the layers of different thickness.
often treated as spheres with minor error, this becomes a serious error when the problem is how molecules pack. Why is this significant? It is known that when temperature or pressure goes beyond the glass transition point, molecules fail to equilibrate thermally. The effect of confinement can be analogous.15,16 Provocatively, the friction of confined fluids then resembles that of granular materials. In the field of granular materials, it is known that ellipsoids can pack to much higher density than spheres; this was shown recently by two different groups.17 More complex arrangements form than is possible for spheres, and if the unit cell involves several elementary units, this might result in different nucleation barriers between discrete values of film thickness. The mistake that our colleagues have made, in considering the OMCTS molecule to be spherical, highlights the opportunity for advance in this field, if one seeks to theoretically explore the role of shape on molecular packing on fluids in confined geometry. Our colleagues also appeal to the Derjaguin approximation, which relates the force between curved surfaces to the energy of interaction between flat plates, assuming that the curved surfaces are rigid. However, mica sheets in the surface forces apparatus are mounted on glue, which is compliant; in response to interaction forces, the curved mica sheets deform. The conditions assumed by the Derjaguin approximation fail.18 However, observing this experimentally requires higher image solution than is customary in a surface forces experiment.7 Friction of OMCTS Confined between the (001) Planes of Muscovite Mica. Careful readers will notice that, in Figure 2 of their critique, our colleagues report friction for just two values (15) Demirel, A. L.; Granick, S. Phys. ReV. Lett. 1996, 77, 2261. (16) Demirel, A. L.; Granick, S. J. Chem. Phys. 2002, 117, 7745. (17) Donev, A.; Cisse, I.; Sachs, D.; Variano, E.; Stillinger, F. H.; Connelly, R.; Torquato, S.; Chaikin, P. M. Science 2004, 303, 990; Johnson, P. M.; van Kats, C. M.; van Blaaderen, A. Langmuir 2005, 21, 11510. (18) Parker, J. L.; Attard, P. J. Phys. Chem. 1992, 96, 10398. Vinogradova, O. I.; Feuillebois, F. Langmuir 2002, 18, 5126. Vinogradova, O. I.; Feuillebois, F. J. Colloid Interface Sci. 2003, 268, 464.
Figure 2. Structural representation of the OMCTS (octamethylcyclotetrasiloxane) molecule from two perspectives: side view (a) and top view (b). This ring-shaped molecule, the cyclic tetramer of dimethylsiloxane, is shaped like a hockey puck, approximately 7.3 × 7.3 × 4.3 Å. The structure shown here was reproducibly generated using either molecular mechanics (MM+ with bond dipole electrostatics) or semiempirical (AM1 or PM3) geometry optimizations in the commercially available HyperChem software package, which is a popular software package for calculations of this sort.
Comments
Figure 3. Friction force plotted against root-mean-square (rms) sliding velocity for an OMCTS film with measured thickness 1.0 nm (n ) 1) after forming the film by quasi-static compression as described earlier.1 The crystallographic axes of the two mica sheets were not aligned. The oscillation frequency was 200 Hz, and the sliding amplitude was varied from angstroms (linear response) up to 1 µm. The maximum strain amplitude of 1 µm much exceeded the film thickness of 1 nm, resulting in very large strain (their quotient). Up to 5 µm sec-1 (shear rate ≈ 5000 sec-1), friction force increased in direct proportion to sliding velocity (solid line). Velocity was raised and subsequently lowered, confirming reversibility. Because this experiment was performed by a fresh researcher (Z.L.) who was uninvolved in the original experiments, this figure further shows the repeatability of our findings when an independent researcher was involved.
of OMCTS thickness, the thinnest films at n ) 1 and n ) 2. For thickness n ) 3, they plot just one datum above the noise level, yet through one datum they draw a curved line! For thickness n ) 4 they plot data points indistinguishable from zero. In other words, friction was large enough to measure only for the very thinnest films. This is significant because earlier work had concluded that “confinement-induced solidification” in this fluid occurs precisely at n ) 6 molecular layers.19,20 It is appropriate to reassess those earlier conclusions19,20 because neither our colleagues’ experiments nor ours confirm them. Our colleagues also confirm (inset of their Figure 2) that friction depended on the relative orientation of confining crystal lattices and was highest when the lattices were crystallographically aligned. In related systems, we found the same.21,22 Also concerning this point, earlier reports of confinement-induced solidification need to be reassessed because, in those studies, this parameter was not controlled. Our original publication reported two distinct patterns of friction: low friction when films were produced by quasi-static compression, and friction larger by orders of magnitude (quantized with film thickness, extending to thicker films).1 Our colleagues’ data (their Figure 2) appears to lie between the two limiting extremes. Apparently, in their friction measurements, our colleagues did not test for dependence on sample history, although this was a key conclusion of our study. Rapid Sliding versus Linear Responses. We are criticized because the original publication, which dealt with linear viscoelastic response,1 involved shear deformation amplitudes smaller than the dimension of the fluid molecules. Since receiving our colleagues’ criticism, we extended this by 3 orders of (19) Kumacheva, E.; Klein, J. Science 1995, 269, 5225. (20) Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108, 6996. (21) Zhu, Y.; Granick, S. Phys. ReV. Lett. 2001, 87, 096104. (22) Ruths, M.; Granick, S. Langmuir 2000, 16, 8368 and references therein.
Langmuir, Vol. 22, No. 5, 2006 2401
magnitude. After forming the thin film quasi-statically, friction was measured with a range of amplitudes from sub-nanometer to 1 µm, resulting in very large strain (the quotient of amplitude and film thickness). The experimental method, described elsewhere in detail, is summarized in footnote 23. In Figure 3, friction force is plotted against velocity for the thinnest film, n ) 1. It is worth emphasizing that, in our experiments, friction increased monotonically with increasing sliding velocity and that these measurements were reversible. Curiously, our colleagues report a negative friction-velocity relation (their Figure 2). Since a negative friction-velocity relation is usually thought to be mechanically unstable, we consider this to be an odd finding. Outlook. When investigating how molecules order, it is helpful that the experimental probe involve more than force measurement. Integrated platforms now exist to augment force and friction studies using Raman, visible, and photoluminescence spectroscopy to measure how molecules orient;24,25 fluorescence spectroscopy with single-molecule resolution to study how molecules diffuse;26-28 and synchrotron X-ray radiation to study structure.29 Looking to the future, we exhort this community to not just adopt a uniform protocol to prepare mica, but to also augment force and friction measurements with even more direct measurements of how molecules actually pack and diffuse in thin films. The research agenda of this field is an excellent position to move on to fresher questions. Acknowledgment. This work was supported by the U.S. Department of Energy, Division of Materials Science under Award Number DEFG02-91ER45439. Steve Granick,*,† Yingxi Zhu,‡ Zhiqun Lin,§ Sung Chul Bae,† Janet S. Wong,† and Jeff Turner†
Departments of Materials Science, Chemistry, and Physics, UniVersity of Illinois, Urbana, Illinois 61801, Department of Chemical and Biomolecular Engineering, UniVersity of Notre Dame, Notre Dame, Indiana 46556, and Department of Materials Science and Engineering, Iowa State UniVersity, Ames, Iowa 50011 ReceiVed August 30, 2005 In Final Form: December 15, 2005 LA052372X (23) Briefly, the bottom mica surface was fixed in place, and the top surface was hung from two symmetrically placed piezoelectric bimorphs. Sinusoidal shear forces were applied to one bimorph, the “sender”, but displacement was resisted by friction [Van Alsten, G.; Granick, S. Phys. ReV. Lett. 1988, 61, 2570. Peachey, J.; Van Alsten, J.; Granick, S. ReV. Sci. Inst. 1991, 62, 463]. The actual amplitude and phase of displacement were detected from the voltage induced in the other “receiver” bimorph. The idea is standard in rheology and has been so for many years [J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980]. Nonlinearities and apparatus compliance were quantified [Reiter, G.; Demirel, A. L.; Granick, S. Science 1994, 263, 1741. Reiter, G.; Demirel, A. L.; Peanasky, J.; Cai, LL.; Granick, S. J. Chem. Phys. 1994, 101, 2606]. Quantitative comparison of the actual motion to calibrated motion in the absence of confined fluid [Bae, S. C.; Granick, S. ReV. Sci. Instrum. 2000, 71, 3955] allows one to infer the out-of-phase (dissipative) response, that is, friction. For reasons discussed elsewhere [Granick, S. Science 1991, 253, 1374], peak velocity is defined as the product of oscillation amplitude and frequency in Figure 2. (24) Bae, S. C.; Lee, H.; Lin, Z.; Granick, S. Langmuir 2005, 21, 5685. (25) Bae, S. C.; Lin, Z.; Granick, S. Macromolecules 2005, 38, 9275. (26) Mukhopadyay, A.; Zhao, J.; Bae, S. C.; Granick, S. Phys. ReV. Lett. 2002, 89, 13610. (27) Mukhopadyay, A.; Zhao, J.; Bae, S. C.; Granick, S. ReV. Sci. Instrum. 2003, 74, 3067. (28) Mukhophadyay, A.; Bae, S. C.; Zhao, J.; Granick, S. Phys. ReV. Lett. 2004, 93, 236105. (29) Seeck, O. H.; Kim, H.; Lee, D. R.; Shu, D.; Kaendler, I. D.; Basu, J. K.; Sinha, S. K. Europhys. Lett. 2002, 60, 376.
