Adhesion and solvation forces between surfaces in liquids studied by


T. Kovács , F. C. Meldrum , and H. K. Christenson. The Journal of ... V. V. Yaminsky, B. W. Ninham, H. K. Christenson, and R. M. Pashley. Langmuir 19...
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Langmuir 1993,9, 2448-2454

2448

Adhesion and Solvation Forces between Surfaces in Liquids Studied by Vapor-Phase Experiments H. K. Christenson' and V. V. Yaminsky Experimental Surface Physics, Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 0200, Australia Received March 29,1993. In Final Form: July 6, 1999

We show how solvation forces in liquids can be measured by studying the interaction of surfaces in vapor. Thisis a convenientmethod of obtaining information on the inner part of the solvationforce,where the surfaces are separated by only a few molecular layers. In particular, the pull-off force between mica surfaces in contact in liquids may be determined easily and accurately this way. Results presented for odamethylcyclotetxasiloxane(OMCTS),cyclohexane,and n-pentanearelargely in agreementwithpublished data obtained by measurements in the liquid phase. Contrary to earlier results, the pull-off force (contact adhesion) is much larger than expected from extrapolationdown to contact of the minima of the solvation force. The large values (up to 100 mJ m-2) of the adhesion in nonpolar liquids illustrate how misleading it can be to use the Lifshitz theory to predict the contact adhesion of a polar solid.

Introduction When two surfaces are brought together in a condensable vapor near saturation a fmt-order phase transition from gas to liquid occurs at small gap widths, provided that the liquid wets the solid substrate (has a contact angle smaller than goo). The interaction between the surfaces changes from a van der Waals attraction across vapor before the transition to a solvation force (with a van der Waals contribution) across the liquid after the phase change.' In the vapor phase adsorption of moleculesto homogeneous, isolated surfaces occur in a stepwise fashion. Successive layers of molecules condense on the surfaces and the transitions between layers take place at Well-definedvalues of the vapor pressure, or chemical potential. Surface heterogeneities and the intrinsic roughness of the liquidvapour interface act to smear these layeringtransitions in most systems at normal temperatures.2 Only with very smooth and well-defined substrates such as alumina3and mica4have layering effectsbeen observed with a few vapors at room temperature. The solvation force found in the liquid phase arises from an enhancement of layering effects by two surfaces in proximity. The solvation force oscillates between attraction and repulsion as the surfaceseparation varies. The period of this oscillatory force is close to the mean molecular diameter for near-sphericalmolecules and the amplitude decreases exponentially with surface separation. Solvationforcesare expected between any smooth surfaces in simple liquids at room temperature^.^ Most experimental knowledge of solvationforces comes from measurements with the surface force This instrument allows measurement of the force between molecularly smooth sheets of mica in a crossed-cylinder e Abstract published in Advance ACS Abstracts, September 1, 1993. (1) ForanintroductiontothetopicseeEvans,R.InLiquidatInterfaces; Charvolin,J., Joanny, J. F., Zinn-Justin, J., Eds.; Elsevier: Amsterdam, 1990. (2) For a review see Sullivan,D. E.; Telo da Gama, M. M. In Fluid Interfacial Phenomena; Croxton, C. A., Ed.; Wiley: Chichester, U. K., 1986. (3) Blake, T. D.; Wade, W. H. J. Phys. Chem. 1972, 76,675. (4) Beaglehole,D.; Christenson, H. K. J. Phys. Chem. 1992,96,3395. (5) See Balbuena, P. B.; Berry, D.; Gubbins, K. E. J. Phys. Chem. 1993,97, 937, and references therein. (6) Israelachvili, J. N.; Adams, G. E. J . Chem. Soe., Faraday Tram. 1 1978, 74, 975. (7) Parker, J. L.; Christenson, H. K.; Ninham,B. W. Rev. Sci.Imtrum. 1989,60, 3135.

configuration. The surface separation is determined (to within 0.1-0.2nm) by monitoringthe shifts of interference fringesproduced by passing white light through the backsilvered mica sheets. The force is calculated from the deflection of a double-cantilever spring on which one of the surfaces is mounted. A number of papers dealiig with solvation forces in nonpolar, polar, and hydrogen-bonding liquids, as well as the effects of temperature, additives, and surface modifications, has been published.8 The surface force apparatus also permits the study of the firsborder gas-liquid transition in narrow gaps, or capillary conden~ation.~ (Most published work has dealt with the analogous case of a sparingly soluble solute such as water phase-separating from a nonpolar liquid).lOJ1As the surfaces are brought together the vapor-liquid transition leads to the formation of a curved liquid-vapor interface (most liquids wet or almost wet mica). The curvature of the interface is such that there is a negative Laplace pressure inside the liquid condensate and this pulls the surfaces into contact. At equilibrium there is an annular liquid condensate around the contact zone of the surfaces. The total (attractive) force F between the two surfaces in contact in an atmosphere of a condensable vapour near saturation is given by12J3 F = 41rR7,

+ F, + FY

(1) Here R is the mean radius of curvature of the surfaces (crossed cylinders or the equivalent sphere-on-a-flat)and the surface tension of the liquid condensed around the contact zone. The first term in the above equation is the Laplacepressure term, F, is the the solid+lid interaction acrossthe liquid in the condensate,and F, is a term related to the resolved component of the surface tension around the perimeter of the condensate. This last term is negligible for the experimental system considered here. When the mica surfaces are brought together in vapor, F, gives a comparatively small contribution to the adhesion because a few layers of molecules are trapped (8) For a review see Christenson, H. K. J. Dispersion Sci. Technol. 1988, 9, 171. (9) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981,80, 528. (10) Christenson, H. K.; Blom, C. E. J. Chem. Phye. 1987,86,419. (11) Christenson, H. K.; Fang J.; Israelachvili, J. N. Phye. Rev. 1989, B39, 11750. (12) Fisher, L. R.; Israelachvili, J. N. Colloids Surf. 1981,3, 303. (13) Christenson, H. K. J. Colloid Interface Sci. 1988, 121, 170.

0743-7463193124Q9-2448$Q4.QQ/Q 0 1993 American Chemical Society

Langmuir, Vol. 9, No. 9, 1993 2449

Solvation Forces in Liquids between the surfaces in contact.13 The solvation interaction at separations of a few molecular layers is usually negligibly small in comparison to the Laplace pressure term. The size of the annular capillary condensate is given by the radii of curvature rl, r2 of its interface and is related to the relative vapour pressure (=activity of an ideal gas) p l p , and the contact angle 8 of the liquid on the solid by the Kelvin equation, or l / r = l/r,

+ l/r2 = -RT ln[p/psl/yLVcos8

(2)

where Vis the molar volume of the liquid (assumed to be incompressible). In the experimental configuration l/r2 can be neglected compared to l/rl and cos 8 E 1(seefigures in refs 9, 12, and 13). The validity of eq 2 for nonpolar liquids on mica was establishedby Fisher and Israelachvili? The separation at which the surfaces are pulled together by the condensation of liquid has been quantitatively studied and compared to the predictions of a modified Kelvin equation for the case of a sparingly soluble solute (water) condensing from nonpolar liquids.ll The force measured between undeformed curved surfaces can be related to the free energy of interaction G between parallel, flat surfaces according to FIR = 2?rG (3) Applying this to the solid-solid contribution to the adhesion between surfaces in undersaturated vapor gives F,(O)/R

= Fa/R = 4*ys

(4)

The solid-solid adhesion force at contact Fais thus related to the interfacial (free) energy of the solid y, by a relationshipsimilar to that describingthe Laplace pressure in a condensed annulus (firstterm of eq 1)with the surface free energy of the liquid y~ replaced by the interfacial free energy of the solid y, (half the free energy of adhesion). In the surface force apparatus the mica sheets are mounted on supporting silica disks using a glue of a thickness comparableto or greater than the mica thickness (usually2-6 pm). Because of the large radius of curvature and the glue, which is softer than the mica, the composite mica-glue system deforms readily under the influence of only moderately strong forces between the mica sheets. The strongly attractive forces (FIR 1 100 mNIm) found between surfaces in gas or vapor give rise to substantial, flattened areas when the surfaces are in contact or close to contact. The deformations are relatively serious in the case of oscillatory solvation forces because of the steep gradient of the repulsive force barriers and the presence of an attractive minimum at separations immediately beyond the maximum. An applied force of only 2 mNIm is sufficient to cause noticeable deformation and the appearance of a flattened area of the surfaces,14even in the absence of an attractive meniscus force. The result is avery large overestimation of the height of the repulsive force barriers when the magnitude of the repulsion exceeds about 2 mN/m. The effect of surface flattening on the force-energy relationship of eq 3 has been a matter of great controversy. The Laplace pressure term in eq 1is not affectedby surface deformations for relative vapor pressures close to saturation @ / p a 1 0.9, at least), as has been shown both experimentally'3 and theoretically.ls According to the Johnson-Kendall-Roberts theory16 of elasticdeformations the relationship between the surface energy and pull-off (14) Christenson, H. K. J. Chem. Phys. 1983, 78,6906. (15) Fogden, A.; White, L. R. J. CoZloid Interface Sci. 1990,138,414. (16) Johnson, K. L.; Kendall, K.; Roberts, A. D. h o c . R. SOC.London 1971, A324, 301.

force (eq 4) changes to

Fa = 3?rRy,

(5)

Refinementsto the theory have proposed a gradual change from a factor of 4 to one of 3, depending on the range and strength of the interaction, the radius of curvature, and the modulus of compressibility.17 The validity of eq 5 for the layered mica-glue system is not obvious, even though the relevant parameters are such that the JKR theory should apply. Despite a great deal of experimental work convincing arguments for or against eq 5 for the miicaglue system are still l a ~ k i n g . ~ *Note J ~ that the same uncertainty regarding the use of eq 4 or 5 applies to the inner minima of the solvation force. This paper presents a synthesis of measurements of solvationforces and studies of capillary condensation and adhesion. We show how solvation forces can be conveniently and accurately measured with the surfaces surrounded by vapor only. This avoids most contamination problems from insufficient purification of the liquids and makes control of the water content of the liquids easy. This is particularly important for the measurement of the inner part of the solvation force. Indeed, only in one previous study has an attempt been made to measure the forces in a pure liquid at separations equivalent to less than two or three molecular layers.1° In particular, the technique allows accurate measurements of the contact adhesion between the surfaces in liquids. The extensive surface flattening on surmounting the inner barriers of an oscillatorysolvation force leads to greatly enhanced repulsive forces. It becomes almost impossible to bring the surfaces into molecular contactthe force required is so large that is causes (apparent) compression of the mica on a scale comparable to the molecular diameter of the liquid. Moreover, because of the limited lateral resolution, one cannot be certain that the last layer of molecules has been completely ejected from between the surfaces. Possible effects of contaminants on the adhesion are difficult to monitor. With the vapor technique it is an easy matter to bring the surfaces into contact in dry nitrogen and then introduce vapor at or close to saturation. On subsequent separation a pulloff force given by

F = 47rRyL+ F,(O)

(6)

where F,(O) =Fa,the contact adhesion in the condensate, is measured. If the surfaces are then brought together a second time, they will come into contact separated by a few layers of molecules. The Laplace pressure term is the same but the solid-solid interaction term in the pull-off force is now given by F,(n), the solvation force at the nth minimum from contact. For n 1 2 this is usually negligible compared to Fa. The difference between the two measurements thus gives the pull-off force at contact in the liquid, or Fa,provided the condensate is large enough that interactions outside the liquid-vapor interface can be neglected.

Materials and Methods The force measurements were carried out with a simplified version of the surface force apparatus Mark IV.' This modified instrument has no f i e mechanical control of the separation, i.e. no differential spring mechanism. The surface separation is (17) Muller, V. M.; Yushchenko, V. S.; Derjaguin, B. V. J. Colloid Interface Sci. 1983, 92,92. (18) Parker, J. L.; Attard, P. J. Phys. Chem. 1992,96,10398. (19) Chen, Y. L.; Helm, C. A.; Israelachvili, J. N. J.Phys. Chem. 1991, 95,10737.

2450 Langmuir, Vol. 9, No. 9,1993 controlled by a piezoelectric device (total range = 1.6 pm) and a dc motor controlling a translation stage directly. With this motor/stage combination it is possible to position the surfaces with an accuracy of 40 nm or better. A potentiometer on the shaft of the translation stage allows the load applied to the surfaces to be determined. Two types of force measuring spring were used a double-cantilever spring with a stiffness of 109 N m-l, and an almost completely rigid single-cantileversupport with an effectivespring constant of about 5 X lo" N m-l. With the weaker spring it is possible to accurately measure outward jumps corresponding to large or small forces whereas the rigid support permits the Surfaces to be separated and brought back into contact without the condensed bridge breaking or evaporating. The mica (from Mica Supplies Limited, U.K.) was cleaved in a normal laboratory atmosphere to yield sheets of uniform thickness (2-6pm). After cutting into 1 om2pieces with a white hot platinum wire the mica was protected from further exposure by storing the pieces in contact with a thicker sheet of freshly cleaved mica from the same crystal. The back-silvered mica sheets were glued to supporting silica disks with either of two thermosetting glues, an epoxy resin (Epon 1004,Shell Chemical Co.) or sym-diphenylcarbazide. During the gluing the mica was exposed to laboratory air for approximately 5 min and the total exposure time during both cleaving and gluing was of the order of 15 min. After the mica was mounted in the apparatus with PZOSas an in situ drying agent, the chamber was flushed out with nitrogen (evaporated from a liquid nitrogen tank) for at least half an hour. Measurements were carried out with the apparatus suspended from meter-long springs (the resonance frequency of the suspension was of the order of 1 Hz) to minimize the influence of external vibrations. All experiments were performed in a temperature-controlled laboratory (22 0.2 OC). After measurements of the pull-off force were carried out in dry nitrogen, the chamber was saturatedwith vapor by injectingexcess amounts of liquid onto the bottom, with the surfaces in contact or separated. The effective relative vapor pressure was slightly less than 1, due to a small heating effect from the light beam that passes through the surfaces and yields the interference fringes. The actual vapor pressure or degree of saturation was calculated from eq 2, using values for the equilibrium meniscus radius determined from the position of the discontinuity in the interference fringes at the location of the vapor-liquid interface. The uncertainty in this determination of the meniscus radius is less than lo%,leading to an uncertainty in the relative vapor pressure of a few tenths of a percent. When the condensates are large, it is not possible to accurately determine their Kelvin radii by the method used in ref 9, i.e. by determining the point at which the condensate neither grows nor evaporates with the surfaces separated (the relative vapor pressures in this study were higher than those in ref 9). The vapor was removed by flushing the chamber of the apparatus with nitrogen. Measurements of the surface separation, the meniscus radius, and the radius of curvature of the surfaces from the fringes of equal chromatic order were carried out either directly, with a movable eyepiece at the exit slit of the spectrometer, or with a video micrometer (Colorado, Model 305) using videotapes (recorded with a Videcon intensified video camera, DAGE MTI, Model 65)of the interference fringes. Three different vapors were studied octamethylcyclotetrasiloxane (OMCTS),cyclohexane, and n-pentane. The liquids were of analytical grade, used as received, or distilled under nitrogen (OMCTS). The largest errors in the measurements are in the determination of the radius of curvature of the mica surfaces (15%) and the spring constant (*2% for the double-cantilever spring, *lo% for the rigid support). Errors in the surface separation used to determine forces from outward jumps are small by comparison in the case of the double-cantileverspring (12% ). Note, however, that the minima of the solvation force are determined by the subtraction of two large numbers, and this source of error then becomes significant. The error in the minima thus determined is estimated to be *25%. With the rigid support, errors in the determination of the absolute surface separation (10.2nm) do become noticeable, as does the effect of thermal drifts on the measurements. For measurements with the same surfaces at

*

Christenson a n d Yaminsky 0.1

0

-.

-0.1

E

z. a

---

i i -0.2

-0.3 0

20

60 D (nm)

40

80

100

120

Figure 1. Force (normalized by mean radius of curvature) as a function of separation between mica surfaces in a simple vapor close to saturation. The f i i e illustrates the dependence of observations on the spring stiffness and the relative vapour pressure using results in octamethylcyclotetrasiloxane(OMCTS) vapor. On approach the surfaces are pulled together (fiied trianlge on x axis) from a separation of about 11 nm, independent of the spring comtant, indicating that the inward jump is caused by the condensation of liquid between the surfaces. The relative vapor pressure is deduced from the equilibrium size (and thereby meniscus curvature, see ref 9) of the annular OMCTS condensate with the surfaces in contact. Successive layers of OMCTS may be ejected from between the surfaces by applying a large compressive force. On separation, the surfaces jump out from one of the local minima in the oscillatory solvation force curve, along a line, the slope of which is equal to the spring constant (arrow). The force between the surfaces due to the negative Laplace pressure in the condensate has a distance dependence illustrated by the solid lines (constant Kelvin radius-implying thermodynamic equilibrium during the separation) or the dashed lines (constant volume). The actual distance dependence would lie somewhere between the dashed and dotted lines. The upper lines are for a Kelvin radius of 35nm @/p, = 0.936)and the lower lines for a Kelvin radius of 60 nm @ / p , = 0.962). For the weak spring k / R = 7 X lo" N m-2 and the outward jump occurs with the condensate snapping (dashed arrow). The rigid support is stiff enough ( k / R = 3 X 106 N m-2) that the surfaces will either jump out to a small separation (solid arrow) where they are still joined by the condensate (atp/pn= 0.936)or no jump due to the condensate occurs (at p/pn= 0.962). In the latter case the only observable jumps are due to the solvation force between the surfaces across the liquid condensate. Note that the surfaces undergo substantial flattening and that the magnitude of the repulsive maxima is greatly enhanced by this effect (see text). one and the same contact position the relative measurement error is very small with the double cantilever spring and any spread in values partly reflects genuine variations in the deformations that the surfaces experience during a contactseparation cycle.20

Results Figure 1 illustrates the general features of the force measurements in vapors close to saturation using data obtained with two mica surfaces in octamethylcyclotetrasiloxane (OMCTS) vapor @ips = 0.944.96). The differences between experiments with one of the surfaces mounted on a double cantilever spring of (normalized) stiffness klR = 7 X 104 N m-2 and when the surface is mounted on a rigid support (k/R = 3 X lo8 N m-2) are shown. In both cases the surfaces jump together from a separation of 11nm, and the surfaces come to a separation of about 2.5 nm. The surfaces flatten and around the (20) Christenson, H.K. Submitted for publication in J. Phys. Chem.

Langmuir, VoE. 9, No. 9, 1993 2461

Solvation Forces in Liquids

Table I. Pull-Off Forces in Saturated Vapors. contact vapor pull-off force se aration F/4rR = y~ y~ (lit.) pressure vapor F/R(mN/m) B(nm) (mN/m) (mN/m) PIP. n-pentane 213 f 4 0.7 (2) 17.0 16 0.993 n-pentane* 267 4 0.4 (1) 20.6 16 0.992 cyclohexane 309 f 8 1.2 (2) 24.6 26.3 0.983 cyclohexane 319 f 19 1.6 (2) 26.4 26.3 0.990 cyclohexane 323 f 4 1.0 (2) 26.7 26.3 0.993 cyclohexaneb 304 f 2 ? (2?) 24.2 26.3 0.989 cyclohexane 337 1.4 (2) 26.8 26.3 0.973 OMCTS OMCTS OMCTS -Oe8

-12 -1.6

I n 0

I 1

2

3 D (nm)

4

5

6

Figure 2. Solvation force measured between mica surfaces in OMCTS vapor at pip, = 0.96 with k/R = 6 X l(r N m-2. The open symbolsare forcesmeasured on approach, the filed trianglea are depths of adhesive minima calculated from outward jumps, note the very large contact adhesion (-1.5 N m-l). The filled circles show measurements of the minima only in a second experiment with OMCTS, with a muchsmaller contact adhesion. The dashed lime is the force due to the Laplace pressure in the OMCTS condensate. This is the zero force line for the solvation force component. The magnitude of the force barriers is significantly enhanced by surface deformations.

247-248 239 f 1 256 1

=3 (?) 2.8-2.9 (3) 2.4-2.9 (3)

19.6 19.0 20.3

18.4 18.4 18.4

0.964 0.969 0.96

p / p , calculated from the measured condensate radius and the Kelvin equation.9 T h e uncertainty in the Kelvin radius is 10%,the corresponding uncertainty in p l p . varies from 0.004 at p / p , = 0.95 to 0.001 at p / p l = 0.99. Errors in separations are A0.2 nm,errom in forces are *7 % ,due largely to uncertainties in the radium R and the spring stiffness (k = 1.1 X 109 N m-’). All measurementswere made at 22 “C. sym-Diphenylcarbazide glue, all others epoxy 1004 glue.

Table 11. Minima and Maxima of Solvation Force in OMCTS Force at Minima” (mN/m) minimum

from contact

0

1

2

3 ~

~~

-50 & 20 -25 & 10 ref 10 expt 1 -176 -(47 + f , & 12 -10 - 6 * (+ 2 f , 3 -fb -2 expt 32 (rigid spring) -80, -loo0-110 -40 -(36 i+10 f , 10 4 9 + f , 3 -fb

**

*

Force at Maxima (N/m)

contact zone there is a capillary-condensed annulus of OMCTS,the equilibrium size of which allows the effective vapor pressure of OMCTS to be calculated. The solid linesindicate the force due to the negative Laplace pressure in the annuluslbridge as a function of separation under constant Kelvin radius conditions (i.e. thermodynamic equilibrium at all separations see further ref 21, in particular Figure 7) for Kelvin radii and vapor pressures of 35 nm and 0.94 (upper line) and 60 nm and 0.96 (lower line), respectively. These values correspond to the limits of the actual values during the experimentswith OMCTS. At a separation of twice the Kelvin radius the bridge vanishes. The dashed lines are the corresponding force vs distance relationships for constant volume conditions, valid if the separation takes place so rapidly that the condensate does not have time to evaporate and adjust the Kelvin radius. If the surfaces are pulled apart, an outward jump occurs and the surfaces fly apart without any significant prior change in the surface separation. With the weaker spring the condensate snapslevaporates and there is alarge outwardjump (dashed arrow) from the size of which the force at the minimum may be calculated. With the rigid support there is either a short jump out (solid arrow) without the condensate breaking and evaporating @Ips = 0.94) or the surfaces may be moved in and out without any instabilities due to the condensate @Ips = 0.96). Only small outward or inward jumps due to the solvation force between the surfaces across the liquid in the condensate may be observed. If the surfaces are pushed together from the separation to which they jump in, several force barriers in the oscillatory solvation force curve can be surmounted, and if a rigid support is used, the surfaces may be forced into contact. Figure 2 shows the forces measured with a weak spring in OMCTS vapor. The filled circles are adhesive minima from a second experiment in OMCTS (experiment 2 in Table 111, with different surfaces. The dashed (nearly)

-

(21) Christenson,H. K. J. Colloid Interface Sci. 1985,104, 234.

maximum from contact

1

2

3

4

ref 10 8.0 2.0 0.4 0.04 expt 2 2.8-4.2 0.5 expt 3 (rigid spring) 8-14 2.4 0.8 n0.1 a The comparativelylarge errors in the determinationof the minima with the double cantilever spring are due to the subtraction of two large numbers. The depth of the outermost accessible minimum cannot be measured with a weak spring because it ie negligible compared to the Laplace pressure in the condensate. The depths of the inner minima are obtained relatiue to the outer minimum.

horizontal line is the Laplace pressure contribution to the force. This can be considered to be the zero force line of a renormalized force curve without the nearly constant Laplace pressure contribution and the results are then directly comparable to measurementsin the “bulk”. Three minima were invariably measured in all experimentswith OMCTS using a double-cantilever spring and the period of the oscillatory solvation force was 0.8-0.9 nm, as in previous experiments. Note also the very large variation in the contact adhesion between the two OMCTS experiments. This reflects a large difference in the pull-off forces measured in dry nitrogen at the beginning of the experiments (see all Table 11). Table I gives the pull-off forces (FIR) measured with a double-cantilever spring (k = 1.1X lo3N m-9, the surface tension of the condensed annulus deduced from this (FI 4?rR),the contact separation relative tothat in dry nitrogen (D)together with the inferred number of molecular layers between the surfaces (in brackets) for three different experiments with OMCTS, including the two shown in Figure 2. Ale0 listed are the literaturevalues of the surface tension and the calculated vapor pressure during the measurements. As can be seen, the pull-off force is given mainly by Laplace pressure in the condensed annulus. Table 11lists the magnitudes of the forces at the inner minima (including the contact adhesion) and maxima in three different experimentswith OMCTS, including those

Christenson and Yaminsky

2452 Langmuir, Vol. 9, No.9,1993 1

,,,

1

, /

1.2 120

0

o 0

1

2 3 D (nm)

4

5

6

Figure 3. Force (excluding the Laplace pressure contribution) between mica surfaces in cyclohexanevapor @ / p s = 0.99, spring constant k / R = 4 X 108 N m-2). The solid squares and diamonds are forces measured on approach of the surfaces; the triangles give locally adhesive miniia determined by measuring outward jumps. The fiied circle shows the adhesionmeasured after vapor was introduced with the surfaces in contact. The height of all the maxima is greatly enhanced by surface flattening. shown in Figure 2, and compares them with values published in ref 10. The outer minima cannot be accurately determined when a rigid support is used as the outward jumps are only of the order of 1 nm. Otherwise, the agreement between experiments is good and the maxima and minima determined here are within a factor of 2 of in magnitude of those found in ref 10, and quite possibly closer, given the comparatively large error. In cyclohexane two layers of molecules were always trapped between the surfaces when the double-cantilever spring was used, and the spacing of the layers was 0.5 f 0.1 nm (Table I). The pull-off force (measured with the double-cantilever spring) was in all cases within 6% of that expected from the Laplace pressure term alone. Figure 3 shows the force curve (excluding the Laplace pressure contribution) measured in cyclohexane vapor at pips = 0.987-0.990,using a rigid support of klR = 4 X lo6N m-z. There is an inward jump at 12-13 nm (not shown) and in this case it is possible to see up to five layers of molecules between the surfaces (if the surfaces are separated without breaking the condensate and then brought together again). The average period of the force curve is about 0.5 nm. The pull-off force from contact (excludingthe Laplace preasure contribution) varied from 0.38 N m-1 after introduction of vapor with the surfaces in contact, 4 h after gluing the mica, to 0.34 N m-l measured by forcing in after 24 h, and down to 0.15 N m-I after 2 days. In n-pentane usually only a single minimum could be measured, although on one occasion two were observed. The period was only about 0.4 nm, close to what has been found for n-hexane and other n-alkanes in 'bulk" experimenkZ2When onlyoneminimum was seen, the measured pull-off force (with k = 1.1 X lo3N m-l) was significantly greater than 47ry~,showing a large contribution, FH,from the solvation force at the first minimum (Table I). The contact adhesionin all the liquids, obtained by subtracting the Laplace pressure contribution (calculated using literature values of the surface tension) from the pull-off force measured between surfaces in molecular contact in saturated vapour (eq 61, is plotted as a function of the pull-off force measured immediatelybefore in dry nitrogen in Figure 4. The lower values of the adhesion in dry nitrogen were obtained several days after gluing the mica

0.4

0.8 1.2 F,/R (N/m)

1.6

Figure 4. Normalized adhesion in liquid F J R (calculatedfrom vapor phase measurements and eq 6, using literature values of the surface tension) as a function of the pull-off force FNIR in dry nitrogen,measured immediatelybeforeintroductionof vapor. The scale on the right-handside shows the interfacial free energy per surface calculated using JKR theory (eq 5). Squares are measurements in cyclohexane, triangles in n-pentane, and diamonds in OMCTS. Filled symbols are with epoxy 1004as the glue holding the mica to the silica supports, open symbols with eym-diphenylcarbazide. Surfaces and after repeated introduction and removal of vapor. The results show that, in general, the larger the adhesion in dry nitrogen the larger the value in any liquid.

Discussion The force curves in Figures 2 and 3 show that the shortrange part of the solvation interaction may be determined in the vapor phase with the same accuracy as in experiments either with the chamber filled or with amacroecopic droplet between the surfaces. The results for OMCTS are slightly different than the ones of ref 10, where the force was measured in a droplet of OMCTS (Table 11). The measured forces at the maxima are almost entirely due to the large deformations of the mica-glue system. The magnitudes do not necessarily scale with the radius and depend on the thickness ratio of the mica and glue, which is not controlled in the experiments. With these uncertainties in mind one cannot expect much better agreement. It is possible that the smaller amplitudes obtained previously were at least partly due to the adsorption of contaminants to the surfaces, from either the atmosphere or the liquid. If differences in surface adsorption affect the contact adhesion, as these results strongly suggest, they may well also influence the first few minima away from contact, albeit to a smaller extent. The difference between the magnitude of the minima at fiiite separations found here and in ref 10, if at all significant, is indeed much smaller than the difference between the contact adhesion found here and in ref 10. The fact that the chemical potential of the liquid condensate is slightly different from the bulk @ f p s= 1) is not likely to have any significant effect on the solvation force. No difference between the measurements with OMCTS at p f p 8= 0.94 and plp, = 0.96 was observed. The complete force curve in cyclohexane has not been published before. These results complement the ones published in ref 14, bearing in mind that the water content in that experiment was not controlled with drying agent in the chamber. The interaction between mica surfaces across n-pentane has not previously been studied, although it is likely that the force curve is similar to the one found

Solvation Forces in Liquids

Langmuir, Vol. 9, No.9,1993 2463 probably mainly due to the fact that the exposure of the mica to the laboratory air (during cleaving and gluing) as well as to dry nitrogen has been reduced as much as possible. Previous measurements (such as those in ref 13) were often carried out a day after mounting the mica in the apparatus, and recent work shows clearlythat adhedon decreaeea with time, even in dry nitrogen. Note that many of the lower values (with the epoxy glue) in Figure 4 were obtained after several days and repeated introductions and removals of vapor. The smaller adhesion often lheasured with the sym-diphenylcarbazideglue is almost certainly due to transfer of volatile components in the glue to the front surface of the mica, either through the atmosphere or by surface diffusiona20The many factors influencing the adhesion between mica surfaces in dry nitrogen will be fully considered in a forthcoming publication.20 At present we merely remark that the largest values of the adhesion measured here are in good agreement with direct measurementsof the energy required to cleave macroscopic mica sheets. Bailey and Kay26found an energy of 120 mJ m-2 for the cleavage of resealed and misaligned mica sheets in room air, which would most closely correspond to the conditions during the surface force measurements. The magnitude of the contact adhesion in the nonpolar liquids is also much larger than that found earlier. The largest values (for OMCTS) in Figure 4 correspond to surface energiesof over 100mJlm2,dependingon the exact relationship between the pull-off force and the surface energy. Published results for OMCTS have indicated values of 74 mN/m14and 50 f 20 mN/m.l0 Reference 14 also gave a value for the contact adhesion in benzene of 64 mN/m (obtained by filling the entire measuring chamber with benzene with the mica surfaces in contact). Given the low adhesion measured in dry nitrogen, the use of a shearing leaf spring in reference 14,and the fact that less attention was paid to time elapsed since the start of the experiment, these results are quite consistent with the present investigation. The decrease in the contact adhesion in cyclohexane with time after the start of the experiment found here shows the importance of timedependent effects, in liquids as well as in nitrogen. The decrease with time is presumably related to adsorption of contaminants to the surfaces. The dispersion force between curved surfaces is given by

with n-hexane or any of the other n-alkanes.22The spacing between contact and the first minimum (occasionallytwo minima) of the solvation force is consistent with a parallel orientation of the alkane chains, althoughthe short length of the pentane molecule makes this observation less certain than with the other alkanes. The fact that usually only one layer of n-pentane is trapped between the surfaces is in accord with the shorter range and smaller magnitude of the solvation forces measured in n-alkanes compared to those found in liquids like cyclohexane and OMCTS. When the surfaces are brought into contact in vapor close to saturation, the measured pull-off forces for cyclohexane and for OMCTS are completely dominated by the Laplace pressure contribution in a condensed annulus of liquid, despite the occurrence of extensive surface deformations. This conclusion was reached in ref 13 in a study of cyclohexane, n-hexane,and water. Fogden and White have recently analyzed the deformation of elastic surfaces in contact in the presence of capillary condensates and obtained this result theoretically.ls In the case of n-pentane, however,the measured pull-off force may be substantially larger than that predicted because the solvation force contribution (the solid-solid term) is significant by comparison. Compare for example the first two entries in Table I. From the figures and Table I an important difference between the vapors can be seen. The surfaces invariably come into contact in OMCTS near saturation separated by three molecular layers, in cyclohexane by two molecular layers, and in p-pentane usually only by one (out of a total of five experiments two layers were only seen once). The number of layers does not depend on the precise relative vapor pressure in the range 0.93-0.99, which supports the idea that the solvation force is not very sensitive to the precise value of the chemical potential. The number of layers trapped between the surfaces appears to be related to the range of the solvation force. This is to be expected, since the number of layers must be related to the height of the barriers compared to the magnitude of the capillary force. The contact adhesion in the liquids is obviously very much dependent on the pull-off force measured in dry nitrogen before the introduction of vapor (Figure 4). The adhesion in dry nitrogen was often much larger than previously found. This is not due to different batches of mica, as verified by comparison with results obtained with sheets cleaved from the remains of batches used in earlier work. The differences in the magnitude of the adhesion cannot be due to effects of the crystallographicorientation of the opposing mica sheets, such as those recently described by McGuiggan and Israelachvilifor mica sheets in aqueous solutions23(but not in humid air). They found very sharp maxima in the adhesion at relative crystallographic orientations of the two opposing mica sheets that were multiples of 60°. The lack of any correlation with the measured birefringence of the two mica sheets and the sharpness of these peaks (&lo) rule out such an effect here. Previously published values for the pull-off force in dry nitrogen were 509-754 mN m-l l3 and 603 & 75 mN m-1.24 An earlier publication from this laboratory gave even lower values of 200-300,12but this has been shown to be due largely to the use of a single cantilever spring in the earlier work.13 The greater adhesion sometimes found here is

FIR = -A/6D2 (7) With a "cut-off" distance26of 0.2 nm and a Hamaker constant of 1.4 X J,2' we find FIR = -58 mN/m. We are here measuring values that are up to 20 times larger! These larger values are more reasonable in view of the results of Bailey and Kay who also measured directly the energy needed to cleave sheets of mica in n-hexane.= Although the precise conditions during the surface force measurements were not mimicked, the important observation for our purposes was the relatively small reduction in cleavage energy (on initial cleavage) in n-hexane (255 mJ m-2) compared to dry air (308mJ m-2). Our results are similar in this regard and it is what is to be expected for an ionic solid where the adhesion is dominated by polar contributions not included in the Lifshitz theory of van der Waals force. The fact that the previous values were

(22) Christenson, H.K.; Gruen, D. W. R.; Horn,R. G.; Israelachvili, J. N. J . Chem. Phys. 1987,87,1834. (23) McGuiggan, P. M.; Israelachvili,J. N. J. Mater. Res. 1990,5,2232. (24) Horn, R. G.; Ieraelachvili, J. N.; Pribac, F. J . Colloid Interface Sei. 1987, 115, 480.

(26) Bailey, A. I.; Kay, M. K. h o c . R. SOC. London 1967, A301, 47. (26) Israelachvili,J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1991. (27) Christenson,H. K. Ph.D. Thesis, Australian National University 1983.

2464 Langmuir, Vol. 9, No. 9, 1993

in rough agreement with what would be expectad using the Lifshitz theory of van der Waals forces can only be taken as coincidental (see for example p 270-1 of ref 26). We conclude that the use of Lifshitz theory with a cut-off distance to interpret the adhesion between mica surfaces is not c o r r e ~ t . l ~With * ~ ~enough adsorption the surface energy is often reduced to values that appear to be close to what van der Waals interactions only would predict. It is uncertain whether or not the observed differences between the adhesion values for the three liquids y e significant. For a given pull-off force in dry nitrogen OMCTS does seem to show the largest adhesion, followed by cyclohexane and then n-pentane, which shows the smallest. Ionic contributions to the adhesion would be affected by the dielectricconstant, but since this is similar for all three liquids it is difficult to rationalize the differences suggested by the results of Figure 4. More work with different liquids is needed to explain these findings.

Christenson and Yaminsky

We have shown how measurements of the interaction of solid surfaces in vapor near saturation can yield information on the solvation forces between the surfaces in liquids. This method should have application to a number of liquids that have proven difficult to work with due to contaminationproblems. This is particularly true of many highly polar, nonaqueous liquids. The results highlight the very large contribution of solid-solid interactionsto the adhesion between smooth surfaces in vapor. The contact adhesion between mica surfaces (and presumably other polar solids) in simple liquids is very much larger than that predicted by Lifshitz theory using a "cutoff" distance. Short-range contributions (such as those due interactions between ionic lattices) to the adhesion and surface energy cannot always be ignored. Acknowledgment. H.K.C. thanks P. Attard for useful discussions. Miss E. Wanless is acknowledged for providing the distilled OMCTS and T. Sawkins and A. Hyde for technical assistance.