Friction of adsorbed layers of poly-isoprene between two cobalt surfaces

Lubricants and Lubrication / D. Dowson et a]. (Editors) 1995 Elsevier Science B.V.

467

Friction of adsorbed layers of poly-isoprene between two cobalt surfaces J.-M. Georges, A. Tonck, D. Mazuyer, J.-L.Loubet, E. Georges Laboratoire de Tribologie et de Dynamique des Systemes. U.R.A. C.N.R.S. 855 Ecole Centrale de Lyon, B. P. 163, F49131 Ecully Cedex, France. The friction of adsorbed layers of poly-isoprene between two cobalt surfaces were investigated using a recently developed molecular tribometer (1).Each poly-isoprene layer is obtained by adsorption of the polymer from a semidilute solution of cis 1-4 poly-isoprene (Pis) in 2,4, dicyclohexyl-2-methylpentane,(DCHPM),which is a small hydrocarbon molecule and a good solvent of the poly-isoprene at 23°C. During friction testing, the film thickness was accurately measured by variations of the sphere-plane capacitance. The film thickness variations follow those of the friction force and is the sum of two contributions. One is a thickness decrease due to creep of the layers themselves. Another is a very small increase of the interface between the two layers, which was found to be dependent of the sliding speed. A "pinning" regime, where the application of a shear results in ordered polymer chains and reduced friction, is found for high pressure and low speed. 1. INTRODUCTION

The polymer-modified lubricants have been used extensively as engine oils since the 1950's, to increase viscosity and thus lubricant film thickness (2). Surfaces, covered with adsorbed polymer, can bear the contact of two solid surfaces, as shown in comprehensive experimental (3114) and theoretical (5)(6) studies conducted over the past decade. However, little is known about the shear behaviour of such layers {7), due to experimental difficulty of carrying out both normal and shear characterisation of such layers. A better understanding of mechanisms of adhesion and friction is now possible with the recent development of new instruments such as the surface force apparatus, the molecular tribometer (8)(9)(10)(11)(12) (16)(17), the atomic force microscope (13)(14){15), which make it feasible to measure, at a molecular scale, the normal and tangential forces between two surfaces. The interesting aspect of sliding experiments with long chain polymer molecules is also the possibility of orienta-

Velocitv X

Load

Frictim force

6 h e a r band

Figure 1 Schematic geometry of the contacting solids separated by thin compressed layers. This is also the geomety adopted in the experiments with :he molecular tribometer described here. The two solid surfaces are covered with an adsorbed polymer of thickness L , and an "hydrodynamic" layer LH. They are pressed against each other with a normal load F,. Opposed to a applied relative speed X, a tangential force is detected and thickness D. The understanding of the mechanisms, which control the tangential force T, is related with the knowledge of three points: the area of the contact zone, the properties of the interfacial film, the thin shear band.

468 -tion of the molecules by the applied shear force. In the presence of such shear force, long chains molecules will become preferentially aligned in the sliding direction, and evidence for shear-induced orientation has been observed in number previous experiments t361137){381. In another paper {l), we have recently presented the rheological behaviour of adsorbed layers of the solution of 9% w/w Pis in DCHPM, (same solution presented here), with the normal approach of a smooth sphere on a plane. When the normal distance between sphere and plane D varies, an “hydrodynamic layer” LH = 9 nm, is detected on each surface, whose thickness is smaller than the thickness of each polymer layer (L=70 nm) adsorbed on the cobalt surface. This result is explained by the presence of large extended trains of polymer in which the solvent can flow. During the compression process, the solvent molecules are partially repelled from the polymer network. When the separation distance D becomes very small, the layers are formed by a compressed polymer “mesh” not interconnected. The mean “mesh” size is lower than the one corresponding to the ”rubber” plateau of a poly-isoprene melt. This paper is mainly concerned the shearing behaviour of the highly compressed layers as shown schematically in Figure 1. The two solid surfaces are each covered with an adsorbed polymer layer of thickness L, and are pressed against each other with a normal load F,. Opposed to an applied relative speed

X, a tangential force is detected and related

to the friction force T generated along the area of contact of radius a and at the boundary of the interface of thickness D. An understanding of the mechanisms which control the tangential force T, implies a knowledge of three points. First, the area of the contact zone is influenced by both the mechanical and adhesive properties of the solids in contact and of the interfacial film. Second, the viscoelastic properties of the interfacial film, which is related to its structure, influences, in particular the interfacial thickness. Third, the very thin shear band is where the sliding

occurs. The poor definition of the position and the thickness of these shear band is a key unknown. The analysis of these three points clearly shows how it is important to fully characterise the geometrical and mechanical properties of the adsorbed films used in these experiments. These three factors can be analysed with the same instrument: the molecular tribometer

2.1 The molecular tribometer The molecular tribometer, designed for friction studies, was used i n these experiments; it has the main principle of the surface force apparatus (S.F.A), previously described (17)(18). The general principle of the system (Figure 2), is that a macroscopic spherical body can be moved towards and away, in the three directions Oxyz, from a planar one using the expansion and the vibration of a piezoelectric crystal. A sphere of radius R is firmly fixed to the three axial piezoelectric translator. The plane specimen of mass m is supported by double force (F,T) sensors AIZl A2X. Each of them is equipped with a capacitive measurement and a double cantilever spring. The sensor’s high resolution allows a very low compliance to be used for the force measurement (25.10-6 m/N), which increases the measurement ability without instability. A drop of liquid to be tested is introduced between the plane and the sphere to form a meniscus. The first capacitive sensor AIZ measures the elastic deformation of the cantilever and thus the force P transmitted through the liquid to the plane in the normal direction Oz; the second capacitive sensor AzX measures the elastic deformation of the second cantilever and thus the tangential force T transmitted in the tangential direction Ox. The force sensors F, T are characterised by a spring compliance of 25 10-6 N/m, and a resonance period of 8ms. A triple sensor (A3X, A~Y,ACJ~) is designed to measure relative displacements in the three directions between

469

Approach micrometer

I

'Ihree-axial piezoelectric translator

I

'Ihree-axial Y z $,A~A~ capacitive displacement Sensor

Figure 2 Schematic representation of a molecular tribometer, which is a surface force apparatus CS.F.A) modified for friction studies supports of the two solids, with a displacement resolution of O.lnm in each direction. Generally specimens are metallic, and the capacitive sensor Cmeasures the electrical capacitance of the sphere-plane interface and then the sphere-plane interface closest distance D. Each capacitance of the capacitive sensor (AlZ, A2X, A3x, A3Y, A3Z, C), is determined by incorporating it in a LC oscillator acting in the range 5 to 12MHz. Each resulting frequency is measured by two ways: first by use of a frequency counter and second by use of a low noise discriminator, which directly gives a voltage function of the frequency measured. Three feedback loops control the relative displacements between the holders of the sphere and the plane, in the three axes oxyz. These displacements can be automatically selected under computer control. Each displacement signal is compared with an imposed signal using a negative proportional integral (P.I.) feedback loop acting on each piezoelectric crystal (Af, A3Y, A3Z) via an high voltage amplifier. For instance, X and Y displacements can be maintained constant and the feedback process regulates the

displacement Z between the sphere and the plane outside of the contact region. The sphere-plane distance, in the contact region, D Wig measured by the capacitive sensor C. 2.2 Materials.

2.21 Solid Surfaces. The sphere used consists of metallic cobalt coatings on fused borosilicate glass, whose Poisson's ratio v l is 0.22 and Young's modulus E l = 65 GPa, ( glass 732-01, Sovirel Corp.). The plane used consists of metallic cobalt coatings on a silicon wafer (E2= 166GPa, v2=0.23). This cobalt layer was deposited under a low argon pressure (5.104 Pa), using cathodic sputtering. Atomic force microscopy (AFM) and scanning tunneling microscopy examinations of the sputtered surfaces show that, the surfaces consist of irregular connected clusters producing a gently bumpy corrugation with a "blackberry" like roughness; (peak to valley lnm, measured with a scan length of lpm). 'he corrugation diameter is about 5onm. X.P.S. analysis of these surfaces confirm the presence of metallic cobalt on the glass, and show an oxide layer of thickness less than lnm

470 (18). The low amplitude of the surface roughness is therefore negligible compared with the thickness of polymer layers considered in this study. Dust minimisation is one key to experimental success. The use of a laminar flow bench was sufficient to reduce dust when coupled with a good inspection system, such as dark field optical microscopy.

according our experimental results presented in (1).

2.2.2 Liquids

Experiments were carried out with pure solvent and polymer solution. The solvent is 2,4, dicyclohexyl-2-methylpentane (DCHPM), (Santotrac 40 from Shell Research, Thornton, U.K). The polymer used is the cis. 1,4, poly-isoprene (-CH2-C-(CH3)=CHC H 2 ) ~ ,designated Pis, (Polymer Laboratories). The weight average molecular weight of the liquid polymer Mw, measured by gel permeation chromatography is 62800, which corresponds to a monomer number N=922. The polydispersity index is 1.03. The bulk viscosity of the pure polymer is 2900Pa.s (18). Its radius of gyration is given by: & = ~ N 0 * 5 with , the length of the

i?i

monomer estimated to be(19) 5=0.46nm, then RG= 5.7nm; the molecule length is I= 424nm. The concentration of the cispolyisoprene in solution with DCHPM, studied here, is 9% w/w or c = S0.10-3g/cm3. Since the number of polymers in a unit volume is c NA /Mw (where NA is the Avogadro number), the concentration c* at wich the overlap of the polymer starts is estimated, in the case of good solvents, as

c*=

1 %

4, 3

k3N A

The critical concentration is theoretically found to be c*=134 xlO-3 g/cm3. The experiments data will show, that at the experimental temperature of 23.5"C, DCHPM is a good solvent of cis-polyisoprene. Therefore the concentration c is less than c*, and corresponds to the semi-dilute regime (20). Figure 3 presents a schematic representation of the interface, before contact with molecules of polyisoprene adsorbed

Rc= 5.7nm4i" 9nm L =70nm s =7nm

Figure 3 Schematic representation of the interface, with molecules of polyisoprene adsorbed according our experimental results presented in Ill. 3 FRICTIONAL B E H A V I O U R

OE

The analysis of the behaviour in friction of highly compressed polyisoprene films can be considered, because we have a relatively good description of the interface. In the contact area, one "mesh of polyisoprene molecules covers each solid surface in contact. The adhesion between the two "meshes" is negligible, indicating that no molecule diffuse in the opposite "mesh"(1).Consequently, it is possible to deduce that the shear plane occurs between these two "meshes", and not between each layer and the substrate, where an irreversible adsorption is produced, or in the interior of one on the layer. Friction is studied for different sliding speeds and different contact pressures, in order to describe the friction behaviour. 3.1 Initial friction process of very compressed films. The sphere and the plane are pressed with during the test (Fs =508flpN Figure 4a). The sphere indentation in the two adsorbed films of thickness 2L, makes circular contact area of radius af = 23pm. In the middle of the contact is disposed the circular Hertzian contact area of radius a=2.4p. This corresponds to cobaltglass substrate deformations 6 equal to 3.3nm

47 1

and an Hertzian pressure evaluated to 28MPa . The tangential piezoelectric transducer permits a relative sliding displacement X between the sphere and the plane. X is also measured with a resolution better than O.lnm.

It is important to note, that all the sliding displacements, realised in the experiments reported in this paper, are small i n comparison with the Hertzian contact radius. The variations of the tangential force T and those of the film thickness AD, as measured by the electric capacitance of the

tangential compliance of the thin film pressed in the Hertzian contact:

(dX/dT)(D=const, X=O) = C i + C,H. + C i 111 The three first values of compliance are h w h

X

8

sphere-plane interface, are studied as a function of time or displacement X. Figure 4b shows the simultaneous variations of T and AD versus time, when a constant sliding speed of X=o.hm/s is applied.

Fsl

L

c$

I

Sliding speed 0.2 nm/s

120

8

0 a

Figure 4a The sphere nnd the plane are pressed with a constant normal compression (Fs =508pN) The sphere indentation in the two adsorbed films of thickness 2L, realises a circular contact area of radius af = 23pm . In the middle of the contact is disposed the circular Hertzian contact area a=2.4pm. Notice that a is smaller than af. 3.1.1 The tangential force

force detected is

for the following argument. The measured tangential compliance (dX/dT)(D, const, ~ 4can ) be considered in two ways. First, the measured tangential compliance is the sum of the tangential compliance of the apparatus C i , of the tangential compliance of the Hertzian contact Cp, and of the

1.6

0 Time Figure 4b Initial jriction process of very compressed layers. The tangential force detected increases non-linearly with the displacement. The film thickness, which is initially equal to D=19.3nm, decreases.

472

Their values are respectively, (dX/dT) (D= const, x=o)= 26x10'6 m /N; c i =2x10'6m/N; the normal and tangential compliances of the Hertzian contact being related(31){32): C p 4 . 1 5 C p [2], therefore = 8 ~ 1 0 m/N. ' ~ The tangential compliance of the film can be determined with a good accuracy with the equation [20] and is =16x1@ m/N. Second, the measured tangential compliance is the sum of the tangential compliance of the apparatus and of the tangential compliance of the thin film situated in all the contact, whose radius is af (Figure 4). In this case, the maximum relative displacement due to the elastic shear will be 26 x 10 -6 N/mx508 x lod N = 13nm.We do not detect such an elastic displacement. We conclude, first, that the mechanical behaviour of compressed films in the Hertzian contact controls the tangential force The shear modulus Gf of the compressed films is obtained with the relation {W):

cp ci

Gr =

xa2 C&

PI,

and found to be equal to 18f2 MPa. Consequently the compressive modulus is Ef = 54f6 MPa, and therefore this test is conducted with a pressure ratio p/Ef = 0.52. According to the scaling theory of polymer (20), the shear elastic modulus of the polymer network is related to the correlation length 4, which is of the order of the mesh size of the temporary network formed by the chains, by the relation :

Gf

(11

+ 5 kT

141

According to Rault (21), for the cispolyisoprene in melt 5 = 8.2 nm and Gf= 0.44 MPa; therefore, for Gf = 18f2 MPa,' the correlation length 5 of the compressed polymer is evaluated to be 2.4nm. Due to applied external pressure, because the polymer does not escape from the contact area, the "mesh' size of the polymer layer is reduced. We note that a value of 5 = 2.4nm is larger than the

DCHPM molecule size (lnm)(18).Therefore, in the thickness of the interface (D=19.3nm), each "mesh" layer contains between 5 to 20 polymer molecules, (20, if the polymer molecules are in contact). At this compression rate, layers behave as a solid in the rubbery state. The glass transition temperature for pure polyisoprene is Tg-73OC. The constant of compressibility dTg/dp 12.4 x 10 -7OC/Pa. Therefore an applied pressure of 28MPa will shift the transition temperature by 7.2"C, and will give Tg=-66OC. We conclude at the experiment temperature (235"C), the glassy state is not reached, and that the friction study is therefore dominated by the behaviour of the highly compressed polyisoprene layers, which are in the rubbery state.. Figure 4b shows also that, the tangential force detected increases non-linearly with the displacement. A relative displacement evaluated between 50 to lOOnm is needed for the tangential force to reach the "stabilised" friction force TL. At this level, the shear stress of the film, assumed uniformly distributed on the indented film area, is T =TL/ 1~ a* = 7.6MPa, and the friction coefficient ~ = T L / F is ~found in the range of p= 0.27. 3.1.2 The decrease of the film thicknessAD. The film thickness, which is initially

equal to D=193nm, decreases, as X increases. This decrease ,canbe followed accurately by variations of the sphere-plane capacitance C or less accurately, by the capacitive transducer A3=. For this initial sliding experiment, the decrease is extended with a distance of 80nm. When, after sliding at a speed of 0.2nm/s, the sliding is stopped, the tangential force and the film thickness does not relax immediately and completely. Film thickness variations follow those of the friction force variations and can be considered as the s u m of two contributions AD1 and AD2, as described in Figure 5. It will be shown, that variations of the thickness AD1 are attributed to the decrease of film

413

f

D

i

-1 D - AD2

1 Figure 5 : Durng the sliding process, film thickness variations are considered as the sum of two contributions AD1 and AD2. Variations of the thickness AD1 are attributed to the decrease of films thickness D, due to the creep of layers itself. AD1 is negative and essentially dependant of the sliding distance X and of the normal applied pressure p . Variation of the thickness AD2 is positive and is an increase of the intwface between the two layers due to the sliding speed. not time, but sliding distance, evaluated thickness D, due to the creep of the layers between 50 to 100nm. This distance, which is themselves. AD1 is negative and essentially roughly of the same order that the length of dependant on the sliding distance X and the the long compressed tails. normal applied pressure p. AD1 decreases, when the sliding distance X increases. The We note also that TLdecreases as the variation of the thickness AD2 is positive and speed increases. Similar results where found in is an increase of the interface between the two the dry friction regime (24). layers due to the sliding speed. AD2 increases Film thickness variations AD follows when the sliding speed increases. Therefore those of friction force variations and can be AD can be written as: interpreted as follows. AD= ADl(X,p, )+AD& ). 3.2.1 The creep of the layer. Effects of sliding speeds are considered During the initial friction process, as before the interpretation of changes of AD. shown in Figure 4b or 6, the polymer layer is first sheared at constant thickness D ( index 3.2 Effect of the sliding speed. af3 in Figure 4b), then the shear produces a Figure 6 shows the frictional force T and creep of the layer, and therefore a decreases fluctuations of the film thickness AD of the ADI.( index f36e in Figure 4b). The absolute same experiment as in Figure 4b, but for value of AD 1, is of the same order of different sliding speeds. During the sliding magnitude than the size of few monomers size. process, the speed is increased by steps ( 0.2; The decrease of the thickness is probably due 2.5; and Unm/s). The frictional force T and the to alignment of the polymer chains and may fluctuations of the film thickness AD are correspond to molecular orientation due to simultaneously found dependent on the sliding sliding. Experimental results given in Figure 4 speed X. The “stabilised” friction force TL, and 6 indicates that AD is proportional to the obtained for each speed, is reached more and square of the shear stress ‘5 : more rapidly, as the sliding speed increases. f2= 3. AD [q This suggests that the relevant parameter is

474

3.22 Film thickness variations ADZ.

The Fs(Z) curves realised after friction test not reported here does not detect any appreciable increase of the adhesive force.

-

-

sliding speed dX/dt (nm/s) 2 I 2.51 25 I

1.

a

0

#

,

I

.

p,

I I

100 200 300 Slidingdistance X (nm)

Figure 6 Frictional force T and fluctuations of the film thickness A D of the same experiment as in Figure 4b but for different sliding speeds. During the sliding process, the speed is increased by steps ( .2; 2.5; 25nm/s).

Therefore, adhesion of the two compressed adsorbed layers is negligible the sliding tests, the shear plane occurs between the two "mesh layers. Therefore the sliding dissipation is dominated by the small zone at the contact between the two compressed layers, where they "gently" interpenetrate. In these experiments, the direct measurement of the interpenetration zone is not possible. But, the thickness ADZ, which is an increase of the interface between two layers, is found to be dependent of the sliding speed and is related to the thickness of the interpenetration zone between the two sliding layers. I h e absolute value of ADZ, is of the same order of the size of a lateral group of the polymer (0.05-0.3nm). It is small in comparison with the absolute value of creep change AD1. Similar results have been obtained with the friction of "solid" state stearic acid monolayers (12). In this case, the friction force was also found to decrease (as in the present experiments) as the speed increases. Because the creep change thickness AD1 was negligible ( the compressive modulus of stearic acid monolayer is much higher that of layers studied here), the thickness AD-AD2 was found to increases as the speed increased. These results suggest that the sliding force T, which is dependant of the thickness of the interpenetration zone, is related to the thickness ADZ. T decreases when AD2 increases. Taking into account Harrison et al. results(22)(23},it is possible to interpret the fluctuations of the thickness AD2 as due to the "levitation", a consequence of best trajectories taking by the molecular groups during the sliding. As a matter of fact, recently, Harrison, White, Colton and Brenner have simulated the friction of methyl-,ethyl-, and propyl- terminated surfaces placed in sliding contact with an hydrogenated surface. Their studies show that depending on the applied loads, the trajectories of the opposite atoms CM differ. For instance, at low loads, the ethyl molecule bends over, lies down and is dragged almost straight across the repulsive potential, like the trajectory a chain would

-

475

have if one end were tied to the upper surface. At high load, however the ethyl molecule uses its flexibility and length to "snake" (detour) around high potential energy barriers; this trajectory spends less energy and produces a lower friction at higher loads. An important result of these simulations is that the friction coefficient for methyl-,ethyl-, and propyl- terminated surfaces is equal to 0.2 and found to be independant of the contact pressure. This value corresponds to the situation where the molecular group snakes. We think that these simulations explain ours experiments. At high pressure and low speed, the molecular groups use their flexibility to "snake" around the potential barrier and in this case AD2 is small. A pinning state is reached. At high speed, groups are dragged almost in straight line and therefore AD2 is more important. Therefore, because the sliding process is a dynamic one, it is tempting to relate variations of film thickness AD2, with a characteristic time. The time, ta, it takes one surface to traverse a characteristic polymer dimension such the monomer breath (OSnm). Times are found in the range of 10s to 0.lms. These results indicate that, when the two opposite mesh pass each other, depending on the sliding speed, interpenetration can take place and the thickness AD2 is a measurement that detects this process. 3 3 Effect of the contact pressure.

The compressed layer was characterised with three constant normal loads leading to different Hertzian applied pressures p : Fs =52M.3pNI p/Ef = 0.25; Fs = 2222flpN, p/Ef = 0.85.In each experiment, "stabilised" friction forces TL, were detected for each sliding speed. Figure 7 shows the "stabilised" friction coefficient p~ = TL/FS versus the transit time ta For these three series of experiments, two sliding regimes occur: (i) the "pinning" regime corresponds to ta > 0.025s or X < 20nm/s; in this regime, pLvaries with p; (ii) the "non-pinning" regime corresponds to ta < 0.025s , and is characterised by a constant friction coefficient p~= 0.18f0.01.This regime

.

responds to the classical Amonton's law, which is followed when the adhesion is low. The dissipation of the sliding energy, in the non-pinning" regime, is d u e to the

"

f l

-

pinning

I

I

10

-1

10

I non-pinning

I

I

10

I

I

-1

lkansit time (s) 10

10

10

-3

I

3

Sliding speed (nm/s) Figure 7 Stabilized friction coefficient p L, versus the transit time.The compressed layer is characterised with three different Hertzian applied pressures p : p/Ef = 0.25, p/Ef = 0.85. In each experiment, "stabilised" friction forces TL, were detected for each sliding speed. vibrations of the groups at a time scale much less than the transit time ta. We expect that the groups flexibility allows their travels in potential energy valleys of the interface. Added to these dissipation energy, in the "pinning" regime another dissipation is found. It is realised at a transit time of 1 to lOs, and can correspond to the movement of some monomers. Experimentally, the friction coefficient is found - for high transit time (Figure 7)to be very dependent on the contact pressure.

476

To explain this, the limiting friction coefficient can be written as the following: p ~ and l TLlcorrespond to-the end groups contributions acting in both "pinning" and "non-pinning"regimes. pu and T L correspond ~ to monomer-monomer interactions. The forceTu can be given as the product of the local force on micro contact times the surface density of micro contact times the surface area:

T== f . 1 . z a 2 [q

k2

where k is a constant. Because for a compressed layer the correlation length 6 of the compressed polymer is constant:

T La ~ f a2[8]

According Hertz theory, the normal

force is:

F, a

a3 [9] therefore the friction coefficient is

llL2

a fp 1

But the Hertzian pressure p is proportional to a, therefore the friction coefficient is: PL2

p1.

a f

We experimentally found that, at small sliding speed, the stabilised friction coefficient p ~ is2 proportional to the pressure p, therefore according equations [lo], f a P2[U But p is also proportional to the squeeze deformation of the layer . Equation [12] suggests that the force f is proportional to the cross section of the part of the molecule in contact. In conclusion, a t low speed interpenetration of the molecules leads to an increase of the friction force and consequently to a shear alignment. 4 CONCLUSIONS

The following conclusions can be drawn from this study: (i) Molecularly smooth metal films sputtered on glass surfaces allows the study of

the rheology and the friction with a molecular tribometer. (ii) During the sliding process the film thickness follows the friction force variations and is the s u m of two contributions. One is a thickness decrease due to the creep of the layers themselves. Another is an increase of the interface between two layers, which found to be dependent on the sliding speed and is related to the interpenetration thickness between the two layers. (iii) Application of shear results in ordering of the polymer chains and decreases the friction. (iv) Friction coefficients are found dependent on the state of "pinning" of the two "mesh layers. 5 ACKNOWLEDGEMENTS

The authors are grateful to A. Schlijper and R. Coy for their help during the preparation of the manuscript. They are indebted to Shell Research Limited for financial assistance and for providing chemical products. We also thank the French CNRS and all the members of the GDR 936 "mesures des forces de surfaces en milieux liquides", and in particular J.F. Joanny. 6 REFERENCES (11 Georges, J.M., Tonck,A., Mazuyer,

(21

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I41 I5t I61

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(21) (22) (23) (24)