- Email: [email protected]
Shear properties and structure of simple liquids in molecularly thin films: The transition from bulk (continuum) to molecular behavior with decreasing film thickness
Shear Properties and Structure of Simple Liquids in Molecularly Thin Films: The Transition from Bulk (Continuum) to Molecular Behavior with Decreasing Film Thickness JACOB N. ISRAELACHVILI 1 AND STEPHEN J. KOTT Department of Chemical and Nuclear Engineering and Materials Department, University of California, Santa Barbara, California 93106
Received April 22, 1988;acceptedJuly 11, 1988 A new dynamic technique for use with the surface forces apparatus allows the viscosity of thin films to be measured at very high shear rates. The results show that the shear viscosity of a thin film of the simple Newtonian liquid n-tetradecane between two molecularly smooth mica surfaces is the same, within 10%, as the bulk value down to film thicknesses as small as lO molecular diameters and at shear rates up to lO 5 s - l . This indicates that the nonslip plane, or "shear" plane, is located within less than 1 molecular diameter of the solid-liquid interface so long as the film thickness is greater than about 10 molecular diameters. Only for thinner films does the viscosity increase markedly from that expected from c o n t i n u u m behavior. This effect correlates with deviations seen in the c o n t i n u u m van der Waals interactions between surfaces at very small separations (again less than about lO molecular diameters). We conclude that it is not so m u c h the liquid structuring at isolated surfaces that leads to deviations from c o n t i n u u m behavior in both static and dynamic interactions, but rather the close approach of two surfaces which modifies the liquid structure between the surfaces that leads to these effects. A further conclusion is that the structure, interactions, and mobility of liquid molecules adjacent to one surface are not additive properties on approach of a second surface. © 1989AcademicPress,Inc. INTRODUCTION
Certain properties of liquids confined within very small spaces, such as narrow pores or thin films, can be quite different from their bulk, or continuum, properties (1-9). These deviations may be specific--depending on the particular liquid and its interactions with the confining surfaces--for example, when strong hydrogen bonds are involved as occurs between water and silica (10). But there are also deviations that are quite general (i.e., not specific) which arise whenever the pore dimensions or film thickness approach the size of the liquid molecules ( 1-9 ). For example, it is now well established that the equilibrium liquid density between two solid walls is not uniform across the film but has an oscillatory profile, where the periodicity of the oscillations is close to the diameter of the liquid molecules (3-9). To w h o m correspondence should be addressed.
This phenomenon occurs even for noninteracting hard-sphere molecules confined between two inert walls irrespective of the particular type of molecule-molecule or molecule-wall interaction potential. The closer two solid surfaces approach each other the more pronounced do these density oscillations become, reflecting the increasing force experienced by the liquid molecules inducing them to order into quasi-discrete layers between the two surfaces (3, 8). Closely related to this phenomenon is the oscillatory "structural" or "solvation" force experienced by two surfaces as they approach each other in liquids (4, 5, 8, 9 ). These forces have been much studied experimentally in recent years with a great variety of different liquids, and they have been found to occur in all cases where liquids are trapped between two molecularly smooth surfaces (5, 11). The theoretical basis of solvation forces is well un-
461
Journal of Colloid and Interface Science, Vol. 129,No. 2, May 1989
0021-9797/89 $3.00 Copyright© 1989by AcademicPress,Inc. All rightsof reproductionin any formreserved.
462
ISRAELACHVILIAND KOTT
derstood (8), and recent theoretical computations of the oscillatory force-laws agree very well with those measured between mica surfaces across both a simple nonpolar liquid and an aqueous salt solution (9). More generally, both theory and experiment show that these interactions begin to dominate over the continuum forces (e.g., the monotonically attractive van der Waals forces) at surface separations below 5-10 molecular diameters (4, 5, 9, 11, 12). These oscillatory forces were originally thought to reflect some "intrinsic" structuring/ ordering of molecules into layers at isolated surfaces, i.e., without the need of a second surface. It is worth stressing that this is not strictly correct: solvation forces arise from the change, or enhancement, in the local structure (e.g., density, layering, or orientation) induced by the close approach of a second surface. If there were no change in the molecular structure there would be no solvation force. So far the above discussion has dealt mainly with the static, or equilibrium, interactions across thin films or between two surfaces in liquids. It is the aim of this paper to explore whether similar effects also occur for certain dynamic properties, e.g., the viscosity of liquids in very thin films, and, if so, how these effects manifest themselves and how they are related to the liquid Stlnacture and the static interactions. A number of experiments have recently been made on the shear viscosity of some simple Newtonian liquids in very thin films between atomically smooth mica surfaces (7, 13, 14). Two techniques were employed: the first (13, 14) involved oscillating the two surfaces relative to each other; the second (7) involved driving them together at a steady rate. The accuracy of these experiments was such that the position of the non-slip plane, or shear plane, relative to the physical solid-liquid interface could be established to within 1-2 ~,, i.e., within 1 molecular diameter. In the first of these studies, using the "oscillatory" method (13, 14) with water, tetradecane, and cyclohexane, it was found that for film thicknesses Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
down to 10 molecular diameters the viscosity is the same as the bulk value, indicating that the shear plane coincides exactly with the solid-liquid interface and that at most one layer of liquid molecules is immobilized at each surface. By contrast, in a series of "drainage" experiments, Chan and Horn (7) forced two mica surfaces towards each other at a steady rate down to much smaller separations (2-3 molecular diameters). To fit their data they found that the position of the shear plane would have to be shifted significantly out from the solid-liquid interface, indicating that about two layers of molecules were effectively immobilized at each surface. Chan and Horn discussed possible reasons for this discrepancy with the results of the oscillatory experiments (13), and noted (7, p. 5320) that in their drainage experiments the maximum shear rate was about six times higher than that in the oscillatory experiment; but they considered it unlikely that immobile regions should appear by increasing the shear rate by a factor of only 6. Another, hitherto unmentioned, possibility is that the position of the shear plane at one surface is not an intrinsic property of that surface but depends on the proximity of the second surfacemmoving outward as two surfaces approach each other below about 10 molecular diameters. This novel and so far unexplored phenomenon would reconcile the "discrepancies" in the two studies and account for the deviations observed at smaller separations in the drainage experiments (7). Such an explanation would also be consistent with, and conceptuaily very similar to, the mechanism by which a second surface affects the equilibrium structure and interaction forces across thin liquid films (as described above). Our first aim in this paper was to eliminate the possibility that the discrepancy could arise from the higher shear rates used in the drainage experiments than those used in the oscillatory experiments, e.g., 1200 s-~ compared to 200 s -1 , respectively, for tetradecane in 5-nm-thick films (7). Accordingly, we describe a new
463
SHEAR PROPERTIES OF T H I N L I Q U I D FILMS
(third) technique
for measuring the shear viscosity at shear rates up to > 105 s-l. We also describe the results of a new frictional sliding experiment, in which two surfaces can be moved laterally past each other in liquids, and which has recently provided new data on the shear properties o f discrete molecular films exactly one, two, three, or four molecular diameters thick (6). Taken together, the results o f these four different types of experiments can be reconciled and provide a consistent and totally new way of looking at the fundamental mechanisms associated with the dynamic interactions and especially the shear flow of liquids in very thin films and near surfaces. E X P E R I M E N T S A N D RESULTS
A new attachment has been developed for use with the surface forces apparatus which allows the viscosity o f thin liquid films to be directly measured at high shear rates (15 ). In previous experiments (7, 13) only relatively low shear rates could be used. In these, one of the surfaces (the upper) is moved toward or away from the other surface either sinusoidally or linearly with time (these being the oscillatory (13) and drainage (7) experiments, respectively). The response of the lower surface is monitored by recording the moving interference fringe pattern produced by the light passing through the two surfaces using a video camera. The recorded data are later analyzed and provide all the information needed to compute both the shear viscosity of the liquid between the two surfaces and the position of the shear plane. In the new experimental setup (Fig. 1) the spring supporting the lower surface was replaced by a piezoelectric "bimorph" strip (Vernitron piezoelectric ceramic PZT-5B) which acts both as a spring and as a displacement strain gauge (a clamped bimorph develops a voltage across its exposed surfaces proportional to the displacement of the unclamped end). Feeding the sinusoidal input voltage to the piezoelectric tube supporting the upper surface and the output voltage from the bimorph into a lock-in amplifier (Stanford
PIEZOELECTRIC
LIGHT TO
LIGHT IN
,f
i
5 cM
FIG. 1. Schematicdiagram of new experimentalsetup showingmodificationsmadeto the surfaceforcesapparatus for measuring dynamic propertiesin thin liquid films at high shear rates 05 ). In these experiments, rather than the wholechamber beingfilledwith liquid, a macroscopic dropletofliquid tetradecanewas injectedbetweenthe surfaces, which also minimizes inertial effectsof the liquid [from Ref. (15)]. Research Systems, Model SR 530) allowed measurement of both the relative amplitude and the phase ~b of the u p p e r and lower surfaces at any driving frequency v and mean surface separation D. This attachment therefore allows much higher frequencies to be used than is possible with the video camera-recorder system, which is limited to studying relatively slow motions and low frequencies (<5 Hz) because of its 50 frames per second recording speed. By contrast, the oscillatory technique using the bimorph and lock-in amplifier system is not limited to low frequencies and, in addition, can also be used to measure amplitudes and especially phases accurately when only very small amplitudes of vibration are being u s e d - - o f order 0.1 n m or less-which are well beyond the resolution attainable with the video and recorder system used in the earlier studies. The general equations of motion of the surfaces have been solved in a number of previous papers (7, 13, 15 ). For two curved mica surfaces of radius R separated by distance D, if the upper surface is driven at a sinusoidal amplitude Ao and frequency u causing the lower Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
464
ISRAELACHVILI AND KOTT
to oscillate at amplitude AI a n d phase ~b (relative to the u p p e r ) , the viscosity o f the fluid between them, ~/, is given by
KD = 12r2R2~, tan
[1 -(~/~o)2],
[1]
8OO
4OO
vtQn¢ 1-(V/Vo)~ (s-~) 5O
where K is the stiffness (spring constant) o f the spring supporting the lower surface and Z,o the natural frequency o f the lower support. Thus, for a N e w t o n i a n liquid, a plot o f v tan 0 20 40 60 80 100 ~b/[1 - 0,/v0) 2] against D should yield a Distance, D (nm) straight line whose inverse slope gives the visFIG. 2. Plot of v tan ~/[1 - v2/~02]against D for ncosity a n d where the effective position o f the shear plane relative to the solid-liquid inter- tetradecane at 22°C. In this case K = 4.9 × 103 N/m, v0 face (at D = 0) is given by the intercept o f this = 285 Hz, R = 0.46 cm, and two different driving frequencies ~ and three different amplitudes A0 were used, line extrapolated t h r o u g h the distance axis. viz. v = 100 Hz., Ao = 8.5 nm (A); u = 100 Hz, A0 A n o t h e r useful equation is that giving the = 17.0 nm (O); and v = 200 Hz, Ao = 21.2 nm (e). In each case measurements were made to distances of about m a x i m u m shear rate (7, 15), 1500 nm (1.5 um) although results are shown only for "/'max = O.073AoK/~R3/2DW2 s -~, [2] points below 120 nm, except for the highest frequency (and shear rate) used which are shown in the inset. In which is valid at high driving frequencies (high each case the points fall on a straight line with an inverse "rrnax) where A0 ~ A and where ~b is small. In slope equal to the bulk liquid viscosityof 2.2-2.3 cP (calorder to attain the highest shear rates possible culated using Eq. [1]), and when extrapolated below 10 with any particular liquid, we therefore require nm the three lines pass through the D-axis at a mean distance of D = -0.2 + 0.6 nm (computed from a leasta large stiffness K (short b i m o r p h clamping squares fit to all the data points out to D = 1.5 ~tm). length), small radius R , large driving amplitude A0, and a liquid o f low viscosity 7. In these experiments all these parameters were distance axis at D = - 0 . 2 ___ 0.6 n m , correoptimized accordingly, so that typical values sponding to a shear plane at D = - 0 . 1 _ 0.3 n m per surface. were K = 5 × 10 3 N / m , R = 0.5 cm, a n d A 0 Thus, so long as two surfaces are farther > 10 nm. The liquid used was n-tetradecane, as in the previous experiments (7, 13 ), which apart t h a n 5 - 1 0 n m (i.e., about 10 molecular diameters) the liquid in the gap retains its bulk has a bulk shear viscosity o f 2.3 cP at 22°C. Measurements were m a d e at a n u m b e r o f N e w t o n i a n behavior even at the highest shear driving frequencies ( u p to 200 H z ) and a range rate studied, which was "/'max> 105 S-I in this experiment. Further, the shear plane remains o f driving amplitudes Ao ( u p to 20 n m ) . T h e coincident with the solid-liquid interface, as distance regime studied was f r o m D = 4 n m up to D = 1500 n m (1.5 # m ) . In a / / c a s e s a previously obtained with n-tetradecane, water, and cyclohexane at lower shear rates ( 13, 14). plot o f v tan ~b/[1 - (~/v0) 2] against D produced a straight line passing through the origin T h u s a higher shear rate c a n n o t explain the (at D = 0) within a few angstroms. Figure 2 (apparent) discrepancy between the earlier m e a s u r e m e n t s o f Israelachvili (13) and those shows the results obtained at the highest shear rates studied. A least-squares fit to each set o f o f C h a n and H o r n (7), and we m u s t look elsedata points (including points at larger dis- where for its origin. First we m a y note that at separations below tances up to 1.5 # m ) p r o d u c e d a straight line 10 n m there do appear to be some small dewhich when extrapolated below 10 molecular diameters ( D < 10 n m ) passes through the viations from the straight line (cf. points falling Journal of Colloid and lnteOCace Science, Vol. 129, No. 2, May 1989
SHEAR
PROPERTIES
OF
below the straight line in Fig. 2) indicating an effectively increased viscosity, but only for these very thin films. This is consistent and reconcilable with the observations of Chan and Horn (7) if one assumes that the viscosity and/ or the position of the shear plane at one surface is a function of its proximity to a second surface. However, these dynamic techniques do not allow one to make sufficiently accurate measurements at these very small separations that would be needed to obtain this more detailed and quantitative insight into this phenomenon. To get this insight we require a way of sliding two surfaces laterally past each other, i.e., at some constant surface separation, rather than moving them normally toward or away from each other. The recently developed lateral sliding mechanism, described in Ref. (6), has enabled us to make such measurements, where it is now possible to slide (shear) two flattened surfaces past each other at a fixed surface separation, D, sliding speed, v, and normal compressive load, Fn, while simultaneously monitoring the exact molecular contact area, A, and the lateral shear (or frictional) force, Fs. The effective viscosity of these thin films is therefore given by the normal expression for Couette flow, n = FsD/Av,
[3]
and the shear rate is simply ~'=v/D
s -1.
[4]
In experiments with cyclohexane (6) and tetradecane (to be published) it was found that when sliding occurs with only one layer of liquid molecules between the surfaces (D ~ 5A) the viscosity is five to seven orders of magnitude higher than the bulk value. This falls by almost an order of magnitude on going from one layer to two layers. Table 1 shows the resuits obtained for the effective viscosity of cyclohexane films one, two, three, and four molecular layers thick. It is clear that for such molecularly thin films the "trapped" molecules are effectively immobilized by the close
THIN
LIQUID
465
FILMS TABLE
I
Effective Viscosity of Cyclohexane Films between Two Molecularly Smooth Mica Surfaces Sliding Laterally Past Each Other (6)° Film thickness, D (nm). and number of layers (n)
Effective viscosity, ~/(D) (P)
7/(D)
0.6 (1) 1.2 (2) 1.8 (3) 2.4 (4)
1.4 X 105 1.2 X 104 7.7 X l0s 4.8 X 102
2 X 107 2 X 106 1 X 106 7 X 10~
~b.lk
Typical contact areas were A = 10 -4-10 -5 cm 2, typical sliding velocities were v = 1-4 ~m/s. The shear viscosity was calculated using Eq. [3] although it was noted that for the first four layers the shear stress FdA was largely independent of velocity v, indicating that the whole concept of viscosity does not strictly apply to such molecularly thin liquid films. Qualitatively similar results have been obtained with n-tetradecane, where with four molecular layers (chain widths) the effective viscosity was about 106 times the bulk value.
proximity of the two solid surfaces. This effect could not be attributed to a high shear rate, which from Eq. [4] was "/'max = ( 1 - - 5 ) X 10 3 S-1 in these experiments, i.e., much lower than the value of l0 s s -i used to obtain the data of Fig. 2. By extrapolation of the data of Table I one would also conclude that only for films about 10 layers thick (D > 5 n m ) would the viscosity approach the bulk value. Thus once again we arrive at the same number of layers needed before a simple liquid film trapped between two solid surfaces can be treated as having b u l k / c o n t i n u u m shear properties. SUMMARY
AND
CONCLUSIONS
The results of four different types of dynamic measurements, as well as earlier measurements of the static forces between two surfaces in liquids, indicate that certain liquid properties can no longer be described by their bulk (continuum) properties once the number of molecular layers in the gap falls below about 10. This applies to the local density, molecular orientation, and general structuring of liquids in molecularly thin films between two solid Journal of Colloid and Interface Science, Vol. t 29, No. 2, May 1989
466
ISRAELACHVILI AND KOTT
surfaces. This phenomenon affects both the equilibrium interaction forces (leading to solvation forces) and certain dynamic interactions such as the mobility of molecules, the viscosity, the location of the shear plane, andmmost likely--all other rheological properties of very thin liquid films. Indeed, the resuits suggest that the enhanced resistance to shear flow is so marked that the whole concept of a shear viscosity and shear plane breaks down for films less than 5-10 layers thick (cf. Table I), becoming replaced by a critical shear stress instead (6). This is in marked contrast to what happens at a single, isolated, surface, or when two surfaces are far apart, where there are no signs of any significant deviations from bulk continuum properties beyond the first layer of liquid molecules adjacent to the surfaces. Thus a further conclusion is that the static and dynamic properties cannot be considered additive when two surfaces approach each other. These conclusions apply both to simple liquids, made up of spherical molecules, and to liquids composed of linear chain molecules such as alkanes, and are illustrated schematically in Fig. 3. To date there is little theoretical work with which these dynamic results can be compared. As mentioned in the Introduction, much theoretical work has already been done on static interactions, using Monte Carlo, molecular dynamics, and analytical (integral equa-
tion) techniques, which compares very well with experimental results on a variety of equilibrium oscillatory force measurements (9). It is fair to say that the origin and theoretical basis of these equilibrium interactions are now well understood. The same cannot be said for dynamic interactions. Only two theoretical papers have so far addressed this matter, these being the recent theoretical analyses of flow in narrow pores and thin films by Bitsanis et al. and by Vanderlick et al. (3), who found that fluids form into discrete layers when bounded by totally smooth surfaces and that the diffusivity deviates significantly below l0 molecular diameters. It was also found that the oscillatory liquid density profile remains unchanged during flow even at very high shear rates. This is certainly consistent with our experimental findings; but we must await more detailed simulations, especially with more realistic surfaces that include the granularity of surface atoms (i.e., that do not treat the surfaces as being perfectly smooth) before any quantitative comparisons can be made. ACKNOWLEDGMENTS We are thankful to the Department of Energy (DOE) for financial support to carry out this research project under DOE Grant DE-FG03-87ER 45331, although this support does not constitute an endorsement by DOE of the views expressed in this article. We also thank Patty McGuiggan and Michelle Gee for their constructive comments on this manuscript.
REFERENCES
FIG. 3. Schematic illustration of the way two approaching surfaces induce or enhance the layering of liquid molecules between them, for both simple spherical molecules (left) and short linear chain molecules such as tetradecane (right).
Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
1. Evans, R., and Marini Bettolo Marconi, U., J. Chem. Phys. 86, 7138 (1987). 2. Peterson, B. K., Walton, J. P. R. B., and Gubbins, K. E., J. Chem. Soc. Faraday Trans 2 82, 1789 (1986). 3. Bitsanis, I., Magda, J. J., Tirrell, M., and Davis, H. T., J. Chem. Phys. 87, 1733 (1987); Vanderlick, T. K., and Davis, H. T., J. Chem. Phys. 87, 1791 (1988). 4. Israelachvili, J. N., "Intermolecular and Surface Forces." Academic Press, New York/London, 1985. 5. Israelachvili, J. N., Acc. Chem. Res. 20, 415 (1987).
SHEAR PROPERTIES OF THIN LIQUID FILMS 6. Israelachvili, J. N., McGuiggan, P. M., and Hornola, A. M., Science 240, 189 (1988). 7. Chan, D. Y. C., and Horn, R. G., J. Chem. Phys. 83, 5311 (1985). 8. Van Megen, W., and Snook, I. K., J. Chem. Soc. Faraday Trans 2 75, 1095 (1979); J. Chem. Phys. 74, 1409 (1981). 9. Henderson, D., and Lozada-Cassou, M., J. Colloid Interface Sci. 114, 180 (1986). 10. Derjaguin, B. V., Karasev, V. V., and Khromova, E. N., Y. Colloid Interface Sci. 109, 586 (1986) and references therein; Fisher, L. R., Gamble,
11. 12. 13. 14. 15.
467
R. A., and Middlehurst, J., Nature (London) 290, 575 (1981). Christenson, H. K., and Horn, R. G., Chem. Scr. 25, 37 (1985). Christenson, H. K., J. Phys. Chem. 90, 4 (1986). Israelachvili, J. N., J, Colloid Interface Sci. 110, 263 (1986). Israelachvili, J. N., Colloid Polym. Sci. 264, 1060 (1986). Israelachvili, J. N., Kott, S. J., and Fetters, L. J., J. Polym. Sci. Phys. in press; Montfort, J. P., and Hadziioannou, G., 3". Chem. Phys. 88, 7187 (1988).
Journal of ColloM and Interface Science, VoL 129, No. 2, May 1989
Received April 22, 1988;acceptedJuly 11, 1988 A new dynamic technique for use with the surface forces apparatus allows the viscosity of thin films to be measured at very high shear rates. The results show that the shear viscosity of a thin film of the simple Newtonian liquid n-tetradecane between two molecularly smooth mica surfaces is the same, within 10%, as the bulk value down to film thicknesses as small as lO molecular diameters and at shear rates up to lO 5 s - l . This indicates that the nonslip plane, or "shear" plane, is located within less than 1 molecular diameter of the solid-liquid interface so long as the film thickness is greater than about 10 molecular diameters. Only for thinner films does the viscosity increase markedly from that expected from c o n t i n u u m behavior. This effect correlates with deviations seen in the c o n t i n u u m van der Waals interactions between surfaces at very small separations (again less than about lO molecular diameters). We conclude that it is not so m u c h the liquid structuring at isolated surfaces that leads to deviations from c o n t i n u u m behavior in both static and dynamic interactions, but rather the close approach of two surfaces which modifies the liquid structure between the surfaces that leads to these effects. A further conclusion is that the structure, interactions, and mobility of liquid molecules adjacent to one surface are not additive properties on approach of a second surface. © 1989AcademicPress,Inc. INTRODUCTION
Certain properties of liquids confined within very small spaces, such as narrow pores or thin films, can be quite different from their bulk, or continuum, properties (1-9). These deviations may be specific--depending on the particular liquid and its interactions with the confining surfaces--for example, when strong hydrogen bonds are involved as occurs between water and silica (10). But there are also deviations that are quite general (i.e., not specific) which arise whenever the pore dimensions or film thickness approach the size of the liquid molecules ( 1-9 ). For example, it is now well established that the equilibrium liquid density between two solid walls is not uniform across the film but has an oscillatory profile, where the periodicity of the oscillations is close to the diameter of the liquid molecules (3-9). To w h o m correspondence should be addressed.
This phenomenon occurs even for noninteracting hard-sphere molecules confined between two inert walls irrespective of the particular type of molecule-molecule or molecule-wall interaction potential. The closer two solid surfaces approach each other the more pronounced do these density oscillations become, reflecting the increasing force experienced by the liquid molecules inducing them to order into quasi-discrete layers between the two surfaces (3, 8). Closely related to this phenomenon is the oscillatory "structural" or "solvation" force experienced by two surfaces as they approach each other in liquids (4, 5, 8, 9 ). These forces have been much studied experimentally in recent years with a great variety of different liquids, and they have been found to occur in all cases where liquids are trapped between two molecularly smooth surfaces (5, 11). The theoretical basis of solvation forces is well un-
461
Journal of Colloid and Interface Science, Vol. 129,No. 2, May 1989
0021-9797/89 $3.00 Copyright© 1989by AcademicPress,Inc. All rightsof reproductionin any formreserved.
462
ISRAELACHVILIAND KOTT
derstood (8), and recent theoretical computations of the oscillatory force-laws agree very well with those measured between mica surfaces across both a simple nonpolar liquid and an aqueous salt solution (9). More generally, both theory and experiment show that these interactions begin to dominate over the continuum forces (e.g., the monotonically attractive van der Waals forces) at surface separations below 5-10 molecular diameters (4, 5, 9, 11, 12). These oscillatory forces were originally thought to reflect some "intrinsic" structuring/ ordering of molecules into layers at isolated surfaces, i.e., without the need of a second surface. It is worth stressing that this is not strictly correct: solvation forces arise from the change, or enhancement, in the local structure (e.g., density, layering, or orientation) induced by the close approach of a second surface. If there were no change in the molecular structure there would be no solvation force. So far the above discussion has dealt mainly with the static, or equilibrium, interactions across thin films or between two surfaces in liquids. It is the aim of this paper to explore whether similar effects also occur for certain dynamic properties, e.g., the viscosity of liquids in very thin films, and, if so, how these effects manifest themselves and how they are related to the liquid Stlnacture and the static interactions. A number of experiments have recently been made on the shear viscosity of some simple Newtonian liquids in very thin films between atomically smooth mica surfaces (7, 13, 14). Two techniques were employed: the first (13, 14) involved oscillating the two surfaces relative to each other; the second (7) involved driving them together at a steady rate. The accuracy of these experiments was such that the position of the non-slip plane, or shear plane, relative to the physical solid-liquid interface could be established to within 1-2 ~,, i.e., within 1 molecular diameter. In the first of these studies, using the "oscillatory" method (13, 14) with water, tetradecane, and cyclohexane, it was found that for film thicknesses Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
down to 10 molecular diameters the viscosity is the same as the bulk value, indicating that the shear plane coincides exactly with the solid-liquid interface and that at most one layer of liquid molecules is immobilized at each surface. By contrast, in a series of "drainage" experiments, Chan and Horn (7) forced two mica surfaces towards each other at a steady rate down to much smaller separations (2-3 molecular diameters). To fit their data they found that the position of the shear plane would have to be shifted significantly out from the solid-liquid interface, indicating that about two layers of molecules were effectively immobilized at each surface. Chan and Horn discussed possible reasons for this discrepancy with the results of the oscillatory experiments (13), and noted (7, p. 5320) that in their drainage experiments the maximum shear rate was about six times higher than that in the oscillatory experiment; but they considered it unlikely that immobile regions should appear by increasing the shear rate by a factor of only 6. Another, hitherto unmentioned, possibility is that the position of the shear plane at one surface is not an intrinsic property of that surface but depends on the proximity of the second surfacemmoving outward as two surfaces approach each other below about 10 molecular diameters. This novel and so far unexplored phenomenon would reconcile the "discrepancies" in the two studies and account for the deviations observed at smaller separations in the drainage experiments (7). Such an explanation would also be consistent with, and conceptuaily very similar to, the mechanism by which a second surface affects the equilibrium structure and interaction forces across thin liquid films (as described above). Our first aim in this paper was to eliminate the possibility that the discrepancy could arise from the higher shear rates used in the drainage experiments than those used in the oscillatory experiments, e.g., 1200 s-~ compared to 200 s -1 , respectively, for tetradecane in 5-nm-thick films (7). Accordingly, we describe a new
463
SHEAR PROPERTIES OF T H I N L I Q U I D FILMS
(third) technique
for measuring the shear viscosity at shear rates up to > 105 s-l. We also describe the results of a new frictional sliding experiment, in which two surfaces can be moved laterally past each other in liquids, and which has recently provided new data on the shear properties o f discrete molecular films exactly one, two, three, or four molecular diameters thick (6). Taken together, the results o f these four different types of experiments can be reconciled and provide a consistent and totally new way of looking at the fundamental mechanisms associated with the dynamic interactions and especially the shear flow of liquids in very thin films and near surfaces. E X P E R I M E N T S A N D RESULTS
A new attachment has been developed for use with the surface forces apparatus which allows the viscosity o f thin liquid films to be directly measured at high shear rates (15 ). In previous experiments (7, 13) only relatively low shear rates could be used. In these, one of the surfaces (the upper) is moved toward or away from the other surface either sinusoidally or linearly with time (these being the oscillatory (13) and drainage (7) experiments, respectively). The response of the lower surface is monitored by recording the moving interference fringe pattern produced by the light passing through the two surfaces using a video camera. The recorded data are later analyzed and provide all the information needed to compute both the shear viscosity of the liquid between the two surfaces and the position of the shear plane. In the new experimental setup (Fig. 1) the spring supporting the lower surface was replaced by a piezoelectric "bimorph" strip (Vernitron piezoelectric ceramic PZT-5B) which acts both as a spring and as a displacement strain gauge (a clamped bimorph develops a voltage across its exposed surfaces proportional to the displacement of the unclamped end). Feeding the sinusoidal input voltage to the piezoelectric tube supporting the upper surface and the output voltage from the bimorph into a lock-in amplifier (Stanford
PIEZOELECTRIC
LIGHT TO
LIGHT IN
,f
i
5 cM
FIG. 1. Schematicdiagram of new experimentalsetup showingmodificationsmadeto the surfaceforcesapparatus for measuring dynamic propertiesin thin liquid films at high shear rates 05 ). In these experiments, rather than the wholechamber beingfilledwith liquid, a macroscopic dropletofliquid tetradecanewas injectedbetweenthe surfaces, which also minimizes inertial effectsof the liquid [from Ref. (15)]. Research Systems, Model SR 530) allowed measurement of both the relative amplitude and the phase ~b of the u p p e r and lower surfaces at any driving frequency v and mean surface separation D. This attachment therefore allows much higher frequencies to be used than is possible with the video camera-recorder system, which is limited to studying relatively slow motions and low frequencies (<5 Hz) because of its 50 frames per second recording speed. By contrast, the oscillatory technique using the bimorph and lock-in amplifier system is not limited to low frequencies and, in addition, can also be used to measure amplitudes and especially phases accurately when only very small amplitudes of vibration are being u s e d - - o f order 0.1 n m or less-which are well beyond the resolution attainable with the video and recorder system used in the earlier studies. The general equations of motion of the surfaces have been solved in a number of previous papers (7, 13, 15 ). For two curved mica surfaces of radius R separated by distance D, if the upper surface is driven at a sinusoidal amplitude Ao and frequency u causing the lower Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
464
ISRAELACHVILI AND KOTT
to oscillate at amplitude AI a n d phase ~b (relative to the u p p e r ) , the viscosity o f the fluid between them, ~/, is given by
KD = 12r2R2~, tan
[1 -(~/~o)2],
[1]
8OO
4OO
vtQn¢ 1-(V/Vo)~ (s-~) 5O
where K is the stiffness (spring constant) o f the spring supporting the lower surface and Z,o the natural frequency o f the lower support. Thus, for a N e w t o n i a n liquid, a plot o f v tan 0 20 40 60 80 100 ~b/[1 - 0,/v0) 2] against D should yield a Distance, D (nm) straight line whose inverse slope gives the visFIG. 2. Plot of v tan ~/[1 - v2/~02]against D for ncosity a n d where the effective position o f the shear plane relative to the solid-liquid inter- tetradecane at 22°C. In this case K = 4.9 × 103 N/m, v0 face (at D = 0) is given by the intercept o f this = 285 Hz, R = 0.46 cm, and two different driving frequencies ~ and three different amplitudes A0 were used, line extrapolated t h r o u g h the distance axis. viz. v = 100 Hz., Ao = 8.5 nm (A); u = 100 Hz, A0 A n o t h e r useful equation is that giving the = 17.0 nm (O); and v = 200 Hz, Ao = 21.2 nm (e). In each case measurements were made to distances of about m a x i m u m shear rate (7, 15), 1500 nm (1.5 um) although results are shown only for "/'max = O.073AoK/~R3/2DW2 s -~, [2] points below 120 nm, except for the highest frequency (and shear rate) used which are shown in the inset. In which is valid at high driving frequencies (high each case the points fall on a straight line with an inverse "rrnax) where A0 ~ A and where ~b is small. In slope equal to the bulk liquid viscosityof 2.2-2.3 cP (calorder to attain the highest shear rates possible culated using Eq. [1]), and when extrapolated below 10 with any particular liquid, we therefore require nm the three lines pass through the D-axis at a mean distance of D = -0.2 + 0.6 nm (computed from a leasta large stiffness K (short b i m o r p h clamping squares fit to all the data points out to D = 1.5 ~tm). length), small radius R , large driving amplitude A0, and a liquid o f low viscosity 7. In these experiments all these parameters were distance axis at D = - 0 . 2 ___ 0.6 n m , correoptimized accordingly, so that typical values sponding to a shear plane at D = - 0 . 1 _ 0.3 n m per surface. were K = 5 × 10 3 N / m , R = 0.5 cm, a n d A 0 Thus, so long as two surfaces are farther > 10 nm. The liquid used was n-tetradecane, as in the previous experiments (7, 13 ), which apart t h a n 5 - 1 0 n m (i.e., about 10 molecular diameters) the liquid in the gap retains its bulk has a bulk shear viscosity o f 2.3 cP at 22°C. Measurements were m a d e at a n u m b e r o f N e w t o n i a n behavior even at the highest shear driving frequencies ( u p to 200 H z ) and a range rate studied, which was "/'max> 105 S-I in this experiment. Further, the shear plane remains o f driving amplitudes Ao ( u p to 20 n m ) . T h e coincident with the solid-liquid interface, as distance regime studied was f r o m D = 4 n m up to D = 1500 n m (1.5 # m ) . In a / / c a s e s a previously obtained with n-tetradecane, water, and cyclohexane at lower shear rates ( 13, 14). plot o f v tan ~b/[1 - (~/v0) 2] against D produced a straight line passing through the origin T h u s a higher shear rate c a n n o t explain the (at D = 0) within a few angstroms. Figure 2 (apparent) discrepancy between the earlier m e a s u r e m e n t s o f Israelachvili (13) and those shows the results obtained at the highest shear rates studied. A least-squares fit to each set o f o f C h a n and H o r n (7), and we m u s t look elsedata points (including points at larger dis- where for its origin. First we m a y note that at separations below tances up to 1.5 # m ) p r o d u c e d a straight line 10 n m there do appear to be some small dewhich when extrapolated below 10 molecular diameters ( D < 10 n m ) passes through the viations from the straight line (cf. points falling Journal of Colloid and lnteOCace Science, Vol. 129, No. 2, May 1989
SHEAR
PROPERTIES
OF
below the straight line in Fig. 2) indicating an effectively increased viscosity, but only for these very thin films. This is consistent and reconcilable with the observations of Chan and Horn (7) if one assumes that the viscosity and/ or the position of the shear plane at one surface is a function of its proximity to a second surface. However, these dynamic techniques do not allow one to make sufficiently accurate measurements at these very small separations that would be needed to obtain this more detailed and quantitative insight into this phenomenon. To get this insight we require a way of sliding two surfaces laterally past each other, i.e., at some constant surface separation, rather than moving them normally toward or away from each other. The recently developed lateral sliding mechanism, described in Ref. (6), has enabled us to make such measurements, where it is now possible to slide (shear) two flattened surfaces past each other at a fixed surface separation, D, sliding speed, v, and normal compressive load, Fn, while simultaneously monitoring the exact molecular contact area, A, and the lateral shear (or frictional) force, Fs. The effective viscosity of these thin films is therefore given by the normal expression for Couette flow, n = FsD/Av,
[3]
and the shear rate is simply ~'=v/D
s -1.
[4]
In experiments with cyclohexane (6) and tetradecane (to be published) it was found that when sliding occurs with only one layer of liquid molecules between the surfaces (D ~ 5A) the viscosity is five to seven orders of magnitude higher than the bulk value. This falls by almost an order of magnitude on going from one layer to two layers. Table 1 shows the resuits obtained for the effective viscosity of cyclohexane films one, two, three, and four molecular layers thick. It is clear that for such molecularly thin films the "trapped" molecules are effectively immobilized by the close
THIN
LIQUID
465
FILMS TABLE
I
Effective Viscosity of Cyclohexane Films between Two Molecularly Smooth Mica Surfaces Sliding Laterally Past Each Other (6)° Film thickness, D (nm). and number of layers (n)
Effective viscosity, ~/(D) (P)
7/(D)
0.6 (1) 1.2 (2) 1.8 (3) 2.4 (4)
1.4 X 105 1.2 X 104 7.7 X l0s 4.8 X 102
2 X 107 2 X 106 1 X 106 7 X 10~
~b.lk
Typical contact areas were A = 10 -4-10 -5 cm 2, typical sliding velocities were v = 1-4 ~m/s. The shear viscosity was calculated using Eq. [3] although it was noted that for the first four layers the shear stress FdA was largely independent of velocity v, indicating that the whole concept of viscosity does not strictly apply to such molecularly thin liquid films. Qualitatively similar results have been obtained with n-tetradecane, where with four molecular layers (chain widths) the effective viscosity was about 106 times the bulk value.
proximity of the two solid surfaces. This effect could not be attributed to a high shear rate, which from Eq. [4] was "/'max = ( 1 - - 5 ) X 10 3 S-1 in these experiments, i.e., much lower than the value of l0 s s -i used to obtain the data of Fig. 2. By extrapolation of the data of Table I one would also conclude that only for films about 10 layers thick (D > 5 n m ) would the viscosity approach the bulk value. Thus once again we arrive at the same number of layers needed before a simple liquid film trapped between two solid surfaces can be treated as having b u l k / c o n t i n u u m shear properties. SUMMARY
AND
CONCLUSIONS
The results of four different types of dynamic measurements, as well as earlier measurements of the static forces between two surfaces in liquids, indicate that certain liquid properties can no longer be described by their bulk (continuum) properties once the number of molecular layers in the gap falls below about 10. This applies to the local density, molecular orientation, and general structuring of liquids in molecularly thin films between two solid Journal of Colloid and Interface Science, Vol. t 29, No. 2, May 1989
466
ISRAELACHVILI AND KOTT
surfaces. This phenomenon affects both the equilibrium interaction forces (leading to solvation forces) and certain dynamic interactions such as the mobility of molecules, the viscosity, the location of the shear plane, andmmost likely--all other rheological properties of very thin liquid films. Indeed, the resuits suggest that the enhanced resistance to shear flow is so marked that the whole concept of a shear viscosity and shear plane breaks down for films less than 5-10 layers thick (cf. Table I), becoming replaced by a critical shear stress instead (6). This is in marked contrast to what happens at a single, isolated, surface, or when two surfaces are far apart, where there are no signs of any significant deviations from bulk continuum properties beyond the first layer of liquid molecules adjacent to the surfaces. Thus a further conclusion is that the static and dynamic properties cannot be considered additive when two surfaces approach each other. These conclusions apply both to simple liquids, made up of spherical molecules, and to liquids composed of linear chain molecules such as alkanes, and are illustrated schematically in Fig. 3. To date there is little theoretical work with which these dynamic results can be compared. As mentioned in the Introduction, much theoretical work has already been done on static interactions, using Monte Carlo, molecular dynamics, and analytical (integral equa-
tion) techniques, which compares very well with experimental results on a variety of equilibrium oscillatory force measurements (9). It is fair to say that the origin and theoretical basis of these equilibrium interactions are now well understood. The same cannot be said for dynamic interactions. Only two theoretical papers have so far addressed this matter, these being the recent theoretical analyses of flow in narrow pores and thin films by Bitsanis et al. and by Vanderlick et al. (3), who found that fluids form into discrete layers when bounded by totally smooth surfaces and that the diffusivity deviates significantly below l0 molecular diameters. It was also found that the oscillatory liquid density profile remains unchanged during flow even at very high shear rates. This is certainly consistent with our experimental findings; but we must await more detailed simulations, especially with more realistic surfaces that include the granularity of surface atoms (i.e., that do not treat the surfaces as being perfectly smooth) before any quantitative comparisons can be made. ACKNOWLEDGMENTS We are thankful to the Department of Energy (DOE) for financial support to carry out this research project under DOE Grant DE-FG03-87ER 45331, although this support does not constitute an endorsement by DOE of the views expressed in this article. We also thank Patty McGuiggan and Michelle Gee for their constructive comments on this manuscript.
REFERENCES
FIG. 3. Schematic illustration of the way two approaching surfaces induce or enhance the layering of liquid molecules between them, for both simple spherical molecules (left) and short linear chain molecules such as tetradecane (right).
Journal of Colloid and Interface Science, Vol. 129, No. 2, May 1989
1. Evans, R., and Marini Bettolo Marconi, U., J. Chem. Phys. 86, 7138 (1987). 2. Peterson, B. K., Walton, J. P. R. B., and Gubbins, K. E., J. Chem. Soc. Faraday Trans 2 82, 1789 (1986). 3. Bitsanis, I., Magda, J. J., Tirrell, M., and Davis, H. T., J. Chem. Phys. 87, 1733 (1987); Vanderlick, T. K., and Davis, H. T., J. Chem. Phys. 87, 1791 (1988). 4. Israelachvili, J. N., "Intermolecular and Surface Forces." Academic Press, New York/London, 1985. 5. Israelachvili, J. N., Acc. Chem. Res. 20, 415 (1987).
SHEAR PROPERTIES OF THIN LIQUID FILMS 6. Israelachvili, J. N., McGuiggan, P. M., and Hornola, A. M., Science 240, 189 (1988). 7. Chan, D. Y. C., and Horn, R. G., J. Chem. Phys. 83, 5311 (1985). 8. Van Megen, W., and Snook, I. K., J. Chem. Soc. Faraday Trans 2 75, 1095 (1979); J. Chem. Phys. 74, 1409 (1981). 9. Henderson, D., and Lozada-Cassou, M., J. Colloid Interface Sci. 114, 180 (1986). 10. Derjaguin, B. V., Karasev, V. V., and Khromova, E. N., Y. Colloid Interface Sci. 109, 586 (1986) and references therein; Fisher, L. R., Gamble,
11. 12. 13. 14. 15.
467
R. A., and Middlehurst, J., Nature (London) 290, 575 (1981). Christenson, H. K., and Horn, R. G., Chem. Scr. 25, 37 (1985). Christenson, H. K., J. Phys. Chem. 90, 4 (1986). Israelachvili, J. N., J, Colloid Interface Sci. 110, 263 (1986). Israelachvili, J. N., Colloid Polym. Sci. 264, 1060 (1986). Israelachvili, J. N., Kott, S. J., and Fetters, L. J., J. Polym. Sci. Phys. in press; Montfort, J. P., and Hadziioannou, G., 3". Chem. Phys. 88, 7187 (1988).
Journal of ColloM and Interface Science, VoL 129, No. 2, May 1989