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Nanorheology of Poly Isoprene Solutions Confined Between Two Solid Surfaces
Tribology for Energy Conservation / D. Dowson et al. (Editors) 1998 Elsevier Science B.V.
51
NANORItEOLOGY OF POLY ISOPRENE SOLUTIONS CONFINED BETWEEN T W O SOLID SURFACES J-M. Georges a, S. MilloP, A. Toncld, R.C. Coy u, A.G. Schlijper u and B.P. WiUiamson b a Laboratoire de Tribologie et Dynamique des Syst6mes F.cole Centrale de Lyon, 69131 Ecully- France ~' SHELL Research Ltd, Thornton Research Centre Chester CH 1 3SH - England The rheology of dilute polyisoprene solutions and a formulated oil confined between two metallic surfaces was investigated by means of a Surface Force Apparatus. Experiments have been conducted to a large number of fluids, which had different concentrations and different molecular weights of polymer. By comparison between SFA measurements and the modelling of the rheological behaviour of these fluids, we showed that the structure of molecular layers near the solid surface is heterogeneous. According to their rheotogical behaviours, three, types of layer (A,B,C) have been determined. They all include an elastic layer near the solid surfaces and the viscous fluid. This viscous fluid can have an uniform viscosity (A) or be composed of a viscous layer whose viscosity is hi~er (B) or lower (C) than the bulk viscosity. Case C is found for a formulated oil. The mechanical properties of the layer B has been determined and confirmed by EHD measurements. KEYWORDS: Surface Force Apparatus, rheology, hydrodynamic layer, viscous layer, layer thickness, molecular structure, EHD, thin film, polymer solution, formulated oil
I INTRODUCTION The rheological properties of surfaces coated with adsorbed polymers control phenomena such as colloidal stability, fluid flow near surfaces and different regimes of lubrication (I) (2) (3) (4). For instance, polymer-modified lubricants have been used extensively as engine oil since the 1950's, because the main role of the polymer is to increase the viscosity of the lubricant and thus increase the hydrodynamic (EHD) film thickness (5). Many researchers have examined the effect of dissolved polymers on the rheology of lubricants and thus their hydrodynamic film formation. It has also been suggested that polymers may influence film formation in elastohydrodynamic (EHD) contacts by forming boundary lubricating films (6). Recent observations have also shown that some polymers dissolved in lubricating base fluids form boundary lubricating films up to 30 nm thick, under slow speed rolling in a concentrated contact. These boundary films may result from the presence of viscous layers of adsorbed concentrated polymer on the solid surfaces (7). A good description of the polymer layer adsorbed on a solid surface can be obtained by calculating on the basis of a porous layer model using segment density profiles (8) (9) (10) The roles of mils, loops and trains have been analysed and compared to different experimental data. This type of description assumes that the adsorption of the polymer is homogeneous on the solid surface. But as described
in figure 1, some "mushrooms" of polymers (height L) are in equilibrium with coils of the polymer solution (diameter 2RH). On the other hand . , "an hydrodynamic" thickness I.~ can be measured (11). This thickness characterises the distance between the metallic surface and the mean shear plane of the liquid, where the flow speed is zero. Comparison between theoretical and experimental data are not always possible because the amount of adsorbed polymer is not precisely known.
1 .~ .......
~.
"
"
i
----~.'
Some "mushrooms" of polymer are adsorbed on solid surface. Coils of polymer (diameter 2RH) are in the solution. An "hydrodynamic" thickness L. and a total thickness L can be measured.
This paper is mainly concerned with the rheological properties of the polymer layers near a metallic
52
dD + i~oI')" . ~.~._..~
J _ _ ._
~
___._..---1 ~
/*,"
/ i
' .
i''t'
,
i dD/d,~
T
~......
~'
6 ' t r ~ -" = .
~
,,R'3 - D. 2 L.
r,
n
Squeeze flow
I.
~,(D) Static force
surface. Here, the polymer layers are due to the adsorption of a relatively simple flexible polymer molecule (polyisoprene) of low and high molecular weights. These layer thicknesses are compared with those obtained with a commercial formulated oil containing polymer. Three types of rheological behaviour of polymer layers are detected using a Surface Force Apparatus (SFA). The structure of this paper is as follows. First the experimental method summarises the experimental approach. Second, the main experimental results are presented for one example of a layer (type B). Third, two models are presented for the study of the layer structure. Fourth, the comparison of the three types of layer are summarised and explained on the basis of their structures. Fifth, the relationship between SFA and EHD data are presented. II EXPERIMENTAL METHODS The Surface Force Apparatus (SFA) The SFA used in this study has already been described in detail in previous work (12) (13)). The general principle of the system (figure2), is that a sphere of radius R can be moved towards and away from (in the direction Oz) a plane using the expansion and the vibration of a piezoelectric crystal. During the normal squeeze of the sphere, in the inward and outward normal approach, the sphere-plane displacement D is monitored with two speed components. One is a steady ramp, which gives a constant approach speed dD/dt of 0.2 nm/s. This speed has a low value, therefore a quasistatic situation can be studied. Superimposed on this, is a small amplitude oscillatory motion of about 0.1 nm RMS, with a frequency of co = 2 . 4 . 102 rad/s. The following measurements are simultaneously recorded : the sphere-plane capacitance C and the mechanical transfer function. From this complex transfer function, only the imaginary part is used in this paper. This component, which is the dynamic
EJgllr£~ Principle of the experiment using a Surface Force Apparatus (SFA). During the normal squeeze of the sphere, in the inward and outward normal approach, the sphere-plane displacement D is monitored with two speed components. The vibrating speed too D permits to measure the squeeze flow.* and therefore the "hydrodynamic layer" thickness LH. The low speed dD/dt ~0, gives the static force Fs, which permits to measure the thickness L of the polymer layer on each solid surface. force in quadrature with respect to the oscillatory motion gives the damping function A. The resulting force F is decomposed into an hydrodynamic component F, and a static component F s , thus F = F, + Fs (Figure 2) The dynamic contribution F,, corresponds to the rheology of the fluid in the interface (figure 2). For a newtonian fluid, the hydrodynamic force is given by Reynolds lubrication theory and can be written : A = FH----:- - 6rtrlBR------~-" [ 1] imD D It should be noted that, if the bulk viscosity of the fluid rls and R remain constant, the inverse of the damping function (l/A)is proportional to D. When a layer is adsorbed on the solid surfaces, the dynamic contribution is well described by equation [ I ], after correcting D, by an "hydrodynamic layer" thickness LH : 6nR 2 D-2L H ~ = 12] A rib Therefore the plot of the function 6rtR-~/A versus D gives the bulk viscosity rib and the hydrodynamic layer thickness L~, for a mean shear rate dy ldt range of I0 - 100 (l/s). As a matter of fact, the maximum shear rate is given by (13). R 0.5 dy / dt = 1.4. (dD: dt) 13 1 (D - 2L H )15 The static contribution Fs is defined as the force measured at low speed, when the equilibrium is reached (figure2). For D < 2L, the static force increases as D decreases revealing a repulsive force due to the matching of the two polymer layers. In conclusion, simultaneous static and dynamic measurements of normal forces present during the drainage of the sphere-plane interface can characterise the interface.
53
Solutions
ij
i j|
ill
~
Mw g/mole
,
PAO + PAO + PAO + PAO +
,,
Pl 19 PI 44 PI 475 Pl 1056
_ . . . . . . . . . . . . . .
V at 3o,,c mm2ts
2R~
nm _
n
1310 3030 32400" 71950
i
, ,
c=O.5
1,5 2,2 7,i" 10.6
............
...
c=2O
24.57 24.64 24,88 25.1'8 .... . . . . . . . . . . . . . . . .
24.73 24.93 26.24... 27.83
_- . . . . . . . . . .
•
nm
.........c = 5 O 1.6 2,6 I0,4 16.6
25.36 26.43 32.34 f 40.09 ,
Materials
21~
,
,1
Table I. dilute polymer solutions in good solvent. The solvent is a synthetic hydrocarbon poly- alphaolefin (PAO). The polymer used is cis 1,4 polyisoprene (-CH2-C-(CH3)=CH-CHz)N. N is the monomer number. These polymers are designed "P! N". v is the kinematic viscosity, I ~ is the calculated gyration radius. RR is the hydrodynamic radius of the coil polymer in solution. The gyration radius RG is calculated from the Wall
Solid Surfaces The sphere and the plane used consists of metallic cobalt coatings on fused borosilicate glass, whose Poisson's ratio is 0.22 and Young's modulus E=65GPa. This cobalt layer was deposited under a low argon pressure (5.10 .6 Pa), using cathodic sputtering. AFM examinations of the sputtered surfaces show that, the surfaces consist of irregular connected clusters producing a gently bumpy corrugation with a peak to valley roughness of 1 nm. The corrugation diameter is about 50 am. The low amplitude of the surface roughness is therefore negligible compared with the thickness of polymer layers. Liquid
Experiments were carried out with dilute polymer solutions in good solvent and formulated oil. The solvent is a synthetic hydrocarbon base fluid, SHF4 I, a polyalphaolefm (PAO). Its bulk kinematic viscosity is 24.56 at 30°C. The polymer used is the cis !,4 polyisoprene (-CH2-C-(CH3)=CH-CH2) N, and N is the monomer number. These polymers will be designed "PIN". The weight average molecular weight, Mw, of the polymer has been measured by gel permeation chromatography (Polymer Laboratories). The corresponding polydispersity index Ip varies between 1.03 and 1.05. Different molecular weights (Mw= 1310, 3030, 32400, 71950) and different concentrations (0.5 %, 2 %, 5 % w/w) of polyisoprene in solution have been tested. Their molecular weights are lower and higher than the critical mass Mc (Mc=I0tX~ (15)). They correspond to polymer solutions of low (Mw Mc) molecular weight.
formula as RG = 0,0 I98. M 0~5. The values are given in table I. Measurements of the kinematic viscosities at 30 °C of the polymer solutions for three solution concentrations give the intrinsic viscosity [1"1]for each molecular weight. [rl] : tim c ~ o \ - - q ~ 0 J - lime*0
v0
Experimental values leads to [q ] = 0,18. M 0.5 W
"
The knowledge of the intrinsic viscosity, gives an indication of the hydrodynamic radius R, of the coil polymer in solution. According to the Einstein law [1"I] is related to RH by the relation : R3 0"0955x [rl] x MW [4] H = NA where N^ s the Avogadro number. Therefore values of R, are reported in table I. It is found found that R, is larger than RG, this suggests that PAO is a good solvent of polyisoprene polymers. A set of solid samples (sphere and plane) is prepared for each experiment. Specimens are mounted on the SFA. Then the fluid droplet which is fdtered with a Nalgene 0.2 t~m + syringe filter, is deposited between the two surfaces. Experiments were performed in dry air in the presence of the drying agent P,_O5. The temperature was about 23.5 °C. The stabitisation time for adsorption requires between a few minutes for the pure solvent to some hours for the polymer solutions. The EHI) measurements
Elastohydrodynamic EHD, film thickness measurements have been made at Shell Research Thornton using a thin film optical rheometer developed from the ultrathin film technique described by the Imperial College Group (3)(7).
54 Experimental fluids consisted of the PAO containing mono dispersed polyisoprene polymers, in varying molecular weights and concentrations. Details of the fluids are given in Table I. The rheometer generates a roiling EHD point contact between a super finished (~, 7nm CLA) tungsten carbide ball and a ( ~ 4 n m CLA) glass disc. CLA is centre line average, taken in this case over a 0.8mm cut off length. An optical interference technique was used to resolve fluid film thicknesses down to 5nm. Randomised measurements of fluid film thickness were taken over a range of low roiling speeds. (0.0003m/s to 0.0500m/s). Bulk temperature (30 °C) and contact load (14.7N) were held constant throughout the measurements. Ill FIRST EXPERIMENTAL RESULTS The results presented in this section concern the comparison of pure PAO, a polyisoprene solution of 0
I0
20
30
40
50
60
70
80
25 PaO pure
.,,'~. "
"~,,'"'.~.'"1
...--'.i:;-'". . . . . 2 Ltl = 9 4 ~ill
2 LII ~" ]9 rlli~i
I000
IOO
Z
low molecular weight (PA0+2% Pl 44) and a polyisprene solution of high molecular weight (PA0 + 2 % PI 1056). The inverse of the damping function (I/A) profile in dynamic mode and the normal force profile F, (D) in the "quasi static" mode are simultaneously determined (figure3). The plot of I/A (figure3a). versus D again reveals a linear variation for lathe D. For instance, for PA0+2% PI 1056, it is for D > 60 nm. The measured viscosity is riB=35 + 4 mPa.s, which corresponds to the bulk viscosity since a value of 33 mPa.s is found for the same solution with a capillary viscometer. The intercept of the extrapolation I/A with the surface separation axis is D=2L.= 39 nm. This corresponds to an "hydrodynamic" layer thickness on each surface equal to ~ . Consequently LH- 2R,, a value in good agreement with the data of the literature (I 1) (17). Similar results are obtained for pure PAO and Pa0+2% PI 44. Figure3b shows Fs plotted against closest sphereplane distance D. Repulsive interactions for the uncompressed layer starts at D = 2 L - - 4 nm for pure Pa0, at D = 2 L - - 1 2 nm for PA0+2% PI 44, and at D = 2 L - - 4 0 rim for PA0+2% P! 1056 This corresponds to the beginning of interpenetrating adsorbed layers. For these two polymer films, L=I.~, which can be attributed to the presence of an homogeneous layer coverage. The contact of two bearing surfaces covered by polymer is analysed by the Alexander-de Gennes theory [26]. Chains are attached to the solid surface. The force H(D), per unit surface between two parallel plates separated by a distance D can be ] ()().()4)
~o
i:
',,k.
•:!~
-
20
2 L ~- 40nm
J0
40
50
~.,q
!i :l I.(X) ]+
=
+[
§
i
2 L = 12nm I0
il,a~¢ o,I I
~. . . . . . .
~. . . . . . . .
~
i
3(>.1~)
kl.
0
m. . . . . . . . . . . . . . . . . . . . . . . .
60
70
l0
Sphere-plane distance D nm
|"o ' .v' ,+,,' 1'l".-'il,+ ()(-p
P\IA
il i,~;ii.i;~,7.,7<:~ ""
:i "'
;i •I ll.!)l
-~
solulie.n
ii . . . .
~ su,:ci,~i,u,d,: I -L-_
-"~ . . . . . .if.. . . . . . . . . . . . .
1
Figure 3 a e t 3b. SFA experiments with pure PaO, and two polyisoprene solutions: low molecular weight (PA0+2% PI 44) and high molecular weight (PA0+ 2% PI 1056). ~re 3 a , The inverse of the damping function (l/A) versus D reveals a linear variation for large D. The extrapolation gives L,. Figure 3 b. Variations of the quasi-static force/radius measurement during upward displacement D. Its starts for 2L.
,oI~......
t
Plil :
high \1,,
q[ - ~
Io
Sphete-I)lan¢
d~,d,Jnce ( r i m
Figure 4 The evolution of the pressure H(D) in the sphere plane contact (cobalt surfaces) versus the sphere plane distance D. Data for the base oil PAO, and for low and high molecular weight polyisoprene in PAO solution. Data are compared with other data obtained with the same surfaces. PIB succinimide solution in hydrocarbon (PIB), OCP and PMA in hydrocarbon solution (31) (32).
55 obtained for the experiments presented in figure 4. According to the Derjaguin approximation, the pressure I-I(D) or force per unit surface between two parallel plates of separation D, is related to the force F on the sphere-plane interface: 1 dF H(D) = [5] 2rtR dD Figure 4 shows the evolution of pressure H(D) in the sphere plane contact versus the sphere plane distance D, for different solutions. The pressure profile depends on the quality of polymer adsorption on solid surfaces. It is, in particular, clear that high molecular weight polymer gives thicker layers. But the layer coverage is not always homogeneous as it is in the case of polyisoprene. For instance, for PMA and OCP solutions, the layers are not homogeneous and correspond to the mushroom description of figure l (31) (32). The resistance to pressure of such polymer layers is low, and is due to the low compressibility, the layers not resisting to a pressure higher than 100MPa. AN
IV ANNULAR MODELS OF HETERGENEOUS VISCOUS LAYER
aB =
/
/
/
/
/
/
-
"/,,-
-.
- -
, /-. - -
~ ~ " ~ , .........
-
-
.- / /
,-
....- "
," . . / . , . ' , . , /
,, ..-',,,/ /,,,"
•
(H-2LH)
.
/
•
A=6nrlBR2[
6nrt L R ( )rdr 4Lv H - L H
oc
fi H 2
dH - , [6] x ( l - I / B)(L'~! - LHH )
+4
6nrlB R2 H
. Therefore
oo dH ACB) = r ! _ E = H x j .....21............................ 2 . . . . . . . . A(B=I) riB HH +4x(l-I/B)(L H LHH) It is interesting to plot the ratio rldrtB (figure6) where tie is the effective viscosity calculated in the case of a viscous layer model and rib is the effective viscosity of sphere-plane distance where a layer is not taken into account. For H > > 2L., the calculation of the total damping 6rcR2riB
function is : A =
( H - 2 L v x (I- 1/13)) This damping function can be compared to the damping
>,
function
previously
described
1,,~.... 1-. . . . . . . . . . . . . '
1
~1 l] '" • 2 ' , . i ' i
/
in
I::~+i
41
,
IV"
<:
"I.Ii
A I ~_]gurc 5 Model ! with a viscous layer only
aL =
This damping function varies with B=rhJriB and 2L,. If the viscous layer is homogeneous, fl = I, we
................... +
,,(p
2rdr
2I.,, and H correspond respectively to the thickness of the viscous layer and the heterogeneous viscous layer. Using the usual variable change r -~ H, (r.dr=R.dH), the total damping of the structure is:
> v
6xrl B R
fred A(B = !)=
The purpose of this part is to give a mechanical description of the surface layer obtained with adsorbed polymers. In the experiment PA0+2% PI 1056, presented in figure3, the function I/A versus D is no longer linear with D lower than 60 nm. Its curvature at lower distances can be interpreted as an effect of the mechanical properties of the surface layers. An elastic effect due to the deformations of the solids or of the surface layer itself cannot explain this important sagging, which is consequently attributed to a surface viscosity effect. The function I/A is in fact a total measurement, which integrates the squeeze phenomena on a large range of distances. So, a model based on a single viscosity step at the surface is first presented (model I). Then a more complex structure, which includes viscous and elastic layer is presented (model II). The damping between a rigid sphere and a plane
+
covered by a viscous layers is presented in figure 5. To simplify the understanding of this figure, no layer has been represented on the sphere, but the layer thickness has been doubled on the plane. The calculation of the damping can be approached by a rheological model assuming simply, that structural damping results from the combination of two dashpots representing respectively the bulk fluid (as) and the viscous layer (at.), whose viscosity's are respectively riB, qL- It has been shown that the expressions of the damping coefficients are respectively :
~,.t+ - 3',: ~ n m
!! . . . . . . . . . . . . . l+;fi
15~+
"~,:
" .:,..,
~<~,,
,Sphere-plane distance (nm)
/ /
Figure 6 .Application of the model I presented in figure 4 for 2% PI 1056 in solution in PAO
56
61tR 2TJB equation[2] A = _ _...:..:::_ D-2LH In the central zone, D = H + 2LH In the case of 2% PI 1056 in solution in PAO, a fit is found if fi-10, 2LH=39nm, Figure 6. The comparison between the experimental data and those obtained with the model with a viscous layer is not adequate. Therefore, a second model is proposed in figure 7. It represents an heterogeneous structure. Moving away from the surface, the interface is composed of firstly a solid layer, which has elastic properties, then a viscous layer TlL· The thickness of the solid layer, L, and its compressibility modulus is K.
Figure 7 Model II with an elastic layer covered by an viscous layer. It allows an approximate quantification of the increase of surface viscosity T](D), where this phenomenon takes place. The lower limit defines the thickness of the solid layer whose elastic properties have been estimated using the elastic part of the
measured transfer function (not shown in this paper,[19]. Three examples of application of the model II are now presented. An example of this simple modelling is given in figures 7, 8, 9. • First, in the case of 2% PI 1056 in solution in PAO using model II,_ a constant value of the viscosity is given for"' the layer, T], =6.7 T], 2Lv=32nm. An elastic layer is taken with 2L,=l0nm, and an elastic modulus K=30-50MPa. With these parameters the viscosity profile T](D) is plotted. The results obtained with SFA measurements and model are in good agreement while for lower sphere-plane distances, some variations are observed. They are due to the fact that the elastic deformation of the solids and the elastic layer are not taken into account. Moreover, the viscosity increase near the surface is probably not a "squared" function but increases progressively when the sphere-plane distance decreases as Kong et al. [18] have observed in dissipative particle dynamics simulations. Though this model can be improved [ 19] the results obtained from SFA measurements and from the model are in relatively good agreement and confirm the heterogeneity of the interface thickness structure. • Second, in the case of 2% PI 44 in solution in PAO using model II, no viscous layer is detected. But an elastic layer is taken with 24 = 1Onm, and an elastic modulus K=20-30MPa.
1 : b4
SHF41+2%P••IY44 .
Elastic layer
:-~
,.....
·;;;;,j 8 9 .::!2 3
;r
/
relative viscositie ~ , from model II / ~ 2 " i~rom SFA easurement
(:Z
50
100
150
200
250
300
Sphere-plane distance(nm)
Figure 8 Relative viscosity versus the sphere plane distance D, for 2% PI 1056 in solution in PAO. From the SFA measurements, at each distanceD, the slope of the curve 1/A(D), gives a viscosity profile T](D), which is compared to the bulk viscosity Tl· Using model II, a constant value of the viscosity is given for the layer, T], =6.7 T], 2L.=32nm. An elastic layer is taken with 2L,=10nm, and an elastic modulus K=30-50MPa. With these parameters the viscosity profile TJ(D) is plotted. Good agreement between the two viscosity profiles is obtained.
\(··~--
SFA measurement
0~--------~----+-------------~ 0 50 100 ISO 200 250 300 2LH
Sphere-plane distance (nm)
Figure 9 Relative viscosity versus the sphere plane distance D, for 2% PI 44 in solution in PAO. From the SFA measurements, at each distanceD, the slope of the curve 1/A(D), gives a viscosity profile TJ(D), which is compared to the bulk viscosity 11· Using model II, no viscous layer is detected. The elastic layer is taken with 2L,=l0nm, and an elastic modulus K=20-30MPa. With these parameters the viscosity profile T](D) is plotted. Good agreement between the two viscosity profiles is obtained.
57
• Third, in the case of a formulated oil containing polymer package but also small molecules such as antiwear additive (ZDTP). The behaviour is different, figure I0. An elastic layer is detected with 2Ls = 10nm, and an elastic modulus K =50-70MPa. But the viscous surface layer has a viscosity less than that of the bulk fluid qs =0.8 ri. This suggests the presence of a depleted layer of polymer near the solid surface.
i :il/Y
w
* Layer type A On each solid surface, a thin purely elastic layer L, is covered by a purely viscous liquid. The layers are approximatively the same thickness, L , - L a - L . This type of layer corresponds to the situation of the pure base oil PAO and for the low molecular weight polymer in solution (Mw=1180,1310,3030). We found that for thefrange of low molecular weight polyisoprenes tested, the ratio L./2RH is in the range of 1.5 - 2 , the compressibility modulus Ks - 30 MPa. This value of compressibility modulus is high in comparison to the rubber modulus of a pure polyisoprene melt which is equal to 0.44MPa. Therefore, we can assume that a layer of randomly flat molecules stay on the surface giving a thickness in the range of L~---LH- L - 5 n m . We notice that the pure base oil PAO presents the same behaviour with an immobile layer of molecules, L -- L, -- L - 2.5nm ).
o
m
• . . , _ ~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
•
,
•
•
•
.~
-:
i:..~
-.i :. :
: : ' : : ~
....
:. = . : :
~ .....
" . :
.'.,. ....
Layer type B
..:
- - ~ , . . ' . , , . , _ . " .~ . . . .. . . . . .
~)
.
.
..~, .
.
.
.
.
.
-.::..: ~..
, ,....
,-.,.
Figure I0 Relative viscosity versus the sphere plane distance D, for a formulated oil. The inverse of the damping function (l/A) versus D reveals'a linear variation for large D. The extrapolation gives L , = - 14nm, a negative value. From the SFA measurements, at each distance D, the slope of the curve I/A(D), gives a viscosity profile ri(D), which is compared to the bulk viscosity rl. Using model !I, a constant value of the viscosity is given for the layer, rls =0.8 rl 2L~=75nm. An elastic layer is taken with 2Ls = 10nm, and an elastic modulus K=50-70MPa. With these parameters the viscosity profile rl(D) is plotted. Good agreement between the two viscosity profiles is obtained
V MECHANICAL CHARACTERISTICS OF POLYMER LAYERS From the SFA data obtained on the different solutions studied, the pure base stock (solvent PAO), low molecular weight polymers in PAO solution, high molecular weight polymers in solution and formulated oils containing polymer, three types of layer were detected. Their main characteristics are summarised in table II.
On each solid surface, two layers are detected between the solid and the bulk fluid. Near the surface, the first layer has a purely elastic behaviour similar to type A and above this there is a second highly viscous layer. This type of layer corresponds to high molecular weight polymer solutions in good solvents. The results presented here correspond to dilute polymer solutions c/c* < 1. ), where c is the weight polymer concentration and c* the critical concentration. The bulk property of the solution is that of a liquid with a viscosity fla. The "hydrodynamic" thickness LH is lower than the thickness of the layer detected by the static force L~ < L. The compressibility modulus of the solid layer is K~---30-50 MPa suggesting a high concentration of monomers near the surface. This modulus value is intermediate between the rubber (0.44 MPa) and the glassy (I03MPa) modulus of po!yisoprene. This behaviour has already been found for compressed and uncompressed polymer layers in the literature. Similar results have been obtained by Hu and Granick (21) with unentangled conf'med polymer melts. For very low thickness corresponding to 4-5 Rg, they have measured a plateau modulus which is about twice the rubber like plateau modulus. They suggested that the elastic effects observed can usefully be viewed as an entanglement phenomenon. According to the scaling theory of polymers (22)(23), the rubbery plateau modulus of the polymer network is related to the entanglement distance ~ which is the order of the mesh size of the
58
temporary network formed by the chains and is defined by the relation : kBT K ~ ~ [7]
The ratio La/2R, is found close to 1 in accordance with previous results presented in literature (I 1). The fact that L is different from Lu (L>I.~) suggests that the layer is non-homogeneous in the xy plane. The mechanical information obtained with the SFA comes from a circular area of contact with a radius (RD) °'s- 10/zm). Consequently, over this large surface area, the polymer does not homogeneously cover the'surface). We may assume that the layer is formed by some "mushrooms" of polymer. The enhancement of the viscosity is due to the polymer coils attached to the surface and to coils trapped in the vicinity of the layer. The ratio LH/2Ra obtained for different molecular weight polyisoprenes are given in figure I 1.
~3
According to Rault [24] for polyisoprene melts, K=0.44 MPa and ~ = 8.2 nm. Therefore, for K--30 MPa, the correlation length ~, of the compressed polymer is evaluated to be 2 nm. This value of the correlation length ~ is very small and could be due to the applied external pressure. The polymer did not escape from the contact volume and hence the "mesh" size of the polymer layer will be reduced. For overlapping polymer layers (D<2L) Fredrickson and Pincus (8) assigned the viscosity term to the draining of solvent molecules from the network made of grafted chains. They use Brinkmann's equation to describe the solvent velocity field by means of a hydrodynamic screening length {H and predict a viscosity coefficient in the form
.".
.__..
=
~ ......... . ,
2
,,. .
.
.
.
.
~
.~
.
•
.
.
.
-~
...,
•
5 1
Previous results have shown that for a sphere-plane distance D---10nm, the relative effective viscosity could vary between 5 and 10. For the polymer solution of 2% PI 1056 in PAO, rlr/rla-6.7. In this case the mesh size {H is about to 1.8 nm. The value of the ratio ~,a/{ " 1. I is in good agreement with the literature data.
0 - 1
t ........
1000
.
.
. . . . . . ... . . . . . . . ... . . . . . .,. .
.
•
.,
.
.
.
10000
.
"t
.................
.
T
100000
Figure 11 Evolution of Ln/2R., versus the molecular weight of the polyisoprene.
Table H Main characteristics of the polymers layers type
......
Fluids
2R. nm
.................
.......
L i t
PAO _
i
pure
iiiii iiiiiii i i
!
. . . . . . . . . . . . . . . . . . . .
PAO+0.5% •-
A
PII9
PI
B
lilllll
ii i
1,6
I
II
IIIII |
MPa
i,5±o.5'
I
1,o
. . . . . . . . . . . . . . . . . . . . . . .
3'6_+0.5
4,0~0.5
0.90-
2.25.......... ,20'30-
.... ;i,7 +0.5
0.77
2.25
1,6
3.65:0.5
......P 1 4 4 ........
2,6
4.0+0.5
5.2 5:0.5 ........0.77 ........... i.53"
20-30
2.6
4.7+_0.5
6,0±0.5
0.78
i is0
1o-30
I0,4
13.2:£1.0
14.0_+1,0
i~25
30-50-
PAO +2,0% PI,475
10,4
16.0_+1.0
17.05:1.0
0.94
1.53
30-50
PAO + 0.5% PI 1056
I6,6
19.0+_2.0
20.0±2.0
0,.95 ......
1.~4
3040
PAO
llm
+
PI44 ....
iii
0.5% Vi 475
i
|mlllllll n
PAO +2,0% Pi 1056 C
Ill
2.55:0.5 i
'Ks
19
+ 2,0%
PAO + 2'0% -
i
!ii i
l..m/2Rn
~,
PA0÷0.5%
---
1
=
PAO
i
~,/L"
nm
nm .
I'_'
Formulated Oil
16,6 i
i
i
...1
19.0:!:2.0 . . . . .
i
. . . . . . . . . . . . . . . . . . .
..
.
.
.
20.0:t:5.0
•
4-1-1.0 .
ii
.
.
0.94 .....
.
.
i
.
.
15:t:!.0 .
............
|. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
0.95 i
<0 '
'
20-30
1.14
.
.
.
ii
.
.
. iiiiii
i . . . . . . . .
30-50 11 _ t
.
.
.
.
.
.
.
.
.
50-70
59
•
Layer type C
On each surface, two layers are detected between the solid surface and the bulk fluid . Near the surface, the first thin layer has a purely elastic behaviour and then a "low" viscous layer is found. This type of layer corresponds to a formulated oil containing polymer and other additives (small molecules). The main effect of the drainage measurement is a negative value for the "hydrodynamic" layer thickness I.~. The extrapolated 1/A function versus D gives I..,= -4 nm. A more complete analysis similar to that conducted for layer type B, detects the presence of two successive layers. The solid layer has a thickness L , - 4 - 5 nm with a compressibility modulus of about 50 MPa. This suggests the presence of some molecules which do not participate in the flow and which are compacted on the surface. A second layer of "low" viscosity (hL=0.8ha) is observed in the vicinity of the surfaces. An hypothetical explanation can be found in the fact that the small molecules present in the solution are more strongly adsorbed on the cobalt surface than the polymer molecules. Consequently, the layer is non homogeneous. During the drainage, the free coils of polymer coming from the bulk cannot penetrate into the layer as readily as the solvent (base) which can more easily flow in the layer rather than in the bulk. More analysis has to be done with known solutions in order to explain this important difference in the flow behaviour.
polymers above 32400 molecular weight diverge from the theoretical line to form a plateau region at approximately l0nm. As already explained by Guanteng et a1.(29 ], the film thickness in an EHD contact is determined by the viscosity of the material
rlb
. i :
rli
,
.....
I i | ii
IIII
.....
i
ii iiill
I
•
..........
~, III
..................................
*
T
U/2 00 ..................................................................................................................... E o,J
o 10 E
,,,.,_ t~
1
i ........
I
L .. , j
~ l!,,
I
. . . . . . . .
~
. . . . .
I0 I00 Rolling speed U (x 10-4 m/s)
=L
!
1000
ILl
CI
Vl RELATIONS BETWEEN MEASUREMENTS
SFA
and
EHD
ta~ O td~
•-
;>
EHD experiments with polyisoprene solutions were conducted. Figure 12 presents the results with two characteristic products, a low and a high molecular weight polymer. These experiments show that the polymer additives form quite mobile viscous surface layers on solid surfaces. The viscous layer has an important effect because it is well known that the film thickness in a rolling EHD contact is mainly determined by the inlet zone [6]. If the viscosity of the fluid is increased or if the boundary conditions are changed in this zone then an increase in film thickness h may now be observed. This was observed with polymer solutions where type B layers ( high molecular weight as Pii056). An example figure 12b presents a log (film thickness h) versus log (rolling speed u) plot. classical EHD theory, assuming base fluid bulk viscosity, was used to generate the "theory" line of gradient 0.67. For polymer solutions it is found that at high, thickness / speed, theory is followed. However, as speed is reduced, It is detectable with this technique ul,~,
0".
5
D
txl
a~
o .... [Z_
0
O'
'~.
' 0
10 20 30 EHD film thickness (nm)
40
Figure 12 a,b,c. EHD experiments with polyisoprene solutions in polyalphao!efin PAO. • Pure PAO x 2% 44PI in PAO 2% 1056 in PAO Figure 12 a Schematic aspect of the inlet contact region. Figure 12 b. Film thickness h versus rolling speed
Figure ..... 12 ..... c
Relative viscosity between the viscosity in the inlet for a given film thickness and the bulk viscosity versus E H D film thickness h. deduced
60
in the immediate contact inlet, figure 12a, primarily within an inlet zone whose thickness is only one to two times the central film thickness. It is therefore possible to determine the effective mean viscosity in the inlet by using the Hamrock Dowson equation (30), where The theoretical film thickness 1% is related to the rolling speed U, by the relation ' h t oc U 0.67 x r 10.67 x tx 0.57
[9]
Indeed, as the pressure viscosity coefficient, a, of the solution is almost constant, the measured film thickness h m is such that hm= hi
(~)
rli
0.67
[1t3t]
where h~ is the viscosity in the inlet. Figure 12c shows the relative viscosity (rli/rlB). It is found that (rltrl0 starts to rise when the central film thickness, hm, is about 20 nm. This corresponds to an interface thickness in the inlet zone of about 40nm (1 to 3 hm). Agreement between these data and data presented in figure 3 and figure8 are relatively good. The hm versus U evolution for a layer of type A is quite different since hm/h,= 1 for low rolling speed. The low polymer molecular weight does not improve the lubrication. Agreement between these data and that presented in figure 3 are relatively good Figure 13 presents two different rheological experiments with adsorbed layers of the same polyisoprene solutions PI 1056.
S~,d
1000
/,~j.,,I,'X~_, h
molecular tribometer
ultra thin film interferomctry
v C d~ °..
.~
CONCLUSIONS
,
,/a
t00 /~A
• e
oe
10 /,/
"13
=,.
Als
I pm/s
First, EHD film thickness h measurements are reported as in figure!2b. Second, on the same graph are reported the rheology of adsorbed layers of poly-isoprene between two cobalt surfaces, investigated with the SFA tribometer. The two layers of poly-isoprene are compressed between the smooth sphere and a plane. During the compression process, the solvent molecules are repelled ~om the polymer network and formed a compressed polymer "mesh" which is not connected. The mean "mesh" size is lower than the one corresponding to the "rubber" plateau of a polyisoprene melt. The contact pressure is 107Pa, and the film thickness of the two compressed layers is in the range of D=19.3nm. A sliding experiment is conducted, and the variations of D, accurately measured. The film thickness variations follow those of the friction force and are the sum of two contributions (20). One is a thickness decrease due to creep of the layers themselves. Another is a very small increase of the interfacial thickness between the two layers, which was found to be dependent on the sliding speed. This interfacial thickness is that of the shear band. Its value is reported as a function of the sliding speed (20). It is interesting to note, that over 8 speed decades, two major processes control the sheared zone. At low speeds, movements of molecular groups are responsible for the lift of the two compressed layers. It is the consequence of best trajectories taken by the molecular groups during the sliding as also described by Harrison's simulations (33). At higher speeds, the global increase of the viscosity in the inlet zone provokes the lift.
Speed I mm/s
Figure 13; Two different rheological experiments with adsorbed layers of poly-isoprene solutions. On the right part, elastohydrodynamic, film thickness D measurements using a thin film optical rheometer. On the left part, rheology of adsorbed layers of polyisoprene between two cobalt surfaces, investigated with a molecular tribometer (20).
. The Surface Force Apparatus can detect two parameters simultaneously which characterise the presence of an adsorbed polymer layer: the "hydrodynamic" film thickness L, and the beginning of the repulsive force which gives an indication of the total thickness L. . The ratio I_~ / L gives an indication of the quality of the polymer coverage. When LH / L = I, the coverage is good as it is in the case for polyisoprene solution on cobalt surfaces. But it is not always the case for all the polymer solutions (31). * The ratio I.~ / 2 RH varies between 1 and 2. ,, The mechanical properties of the layers has been analysed. Comparison of different polymer solutions were undertaken and three types of layer are detected. For pure polymer solutions, two cases are presented. In the situation of low molecular weight, a thin elastic layer covers the solid. In the case of
61 high molecular weight, the solid is covered by two layers, one elastic layer and one viscous layer. • The layer is effective, when a low contact pressure is applied (p < I00MPa). • A formulated oil presents the same properties as the second case but with some important differences, in particular a negative value is found for LH. • The viscous layers detected with the Surface Force Apparatus are also found in EHD measurements. Agreement between the thickness and increase of viscosity are relatively good. • The elastic and enhanced viscosity layers on the contact surface may explain the ability of adsorbed polymer layers to reduce wear. REFERENCES (I) Briscoe, B.J. and Evans, D.C.B., Proc. Roy. Soc. (London), A 380, 99-105, (I973). (2) Cann, P.M. and Spikes, H.A. STLE/ASME, 93-TC-IB-I, (1993). (3) Smeeth, M., Gunsel, S. and Spikes, H.A. "Performance of Viscosity Index Improvers in lubricated contacts", Langmuir, 12, 4, 4594-4598, (1996). (4) Klein,J., Kamiyama, Y., Yoshizawa,H., Israelachvili,J.N., Fredrickson, G.H., Pincus,P., Fetters, L.J., Macromolecu!es, 26, 5552-5560, (!993). (5) Hutton, J.F., Jackson, K.P. and Williamson, B.P. "The Effect of Lubricant Rheology on the Performance of Journal Bearings", ASLE Trans., 29,52-60, (1986). (6) Spikes, H.A., Cann, P.M., Coy, R.C. and Wardle, R.W.M. "An 'In Lubro' Study of VI Improvers in EHD Contacts." Lub. Science 3, pp. 45-62, (1990). (7) Smeeth, M., Gunsel, S. and Spikes, H.A. "The Formation of Viscous Surface Films by Polymer Solutions : Boundary or Elastohydrodynamic Lubrication', STLE Meeting, 95,TC 3C- 1. (1995). (8) Fredrickson, G. H., Pincus, P., Langmuir, "Drainage of Compressed Polymer Layers : Dynamics of a Squeezed Sponge",7,786-795, (1991). (9) Sens,P. Marques, C.M., Joarmy. J.F., "Viscoelasticity of Adsorbed Polymer Layers ",Macromolecules, 27,3812 (I 994). (10) Klein, J. Perahia, D. and Warburg, S., Nature, "Forces between polymer-bearing surfaces undergoing shear, 352, 143-145, (1991). (11) Cohen-Stuart, M. A., Waajen, F.H., Cosgrove, T. Vincent, B., and Crowley T.L., "Hydrodynamic Thickness of Adsorbed Polymer Layers", Macromolecules, 17,1825- ! 830, (1984).
(12) Tonck, A. Gcorges, J.M. and Loubet, J.L., Measurements of Imermolecular Forces and the Rheology of Dodecanc between Alumina Surfaces", J. of Colloid and Inter. Sci., 126,1,1540-1563, (1988). (13) Georges, J-M., Millot, S., Loubet, J-L. and Tonck, A., J. Chem. Phys., "Drainage of thin liquid films between relatively smooth solid surfaces', 98,8, 7345-73~), (1993). (14) Derjaguin, B.V., Kolloidn. Zh., 69,155, (1934). (15) Ferry J.D., "Viscoelastic properties of polymers", Second Ed., John Willey Sons, 406, (1970). (16) Stockmayer W., "Dynamics of Chain Molecules," in Fluides Mol6culaires, R Balian and G Weills, Eds., Gordon & Breach, New York, (1976). (17) Millot S., Loubet J-L., Georges J-M., "Variation of the hydrodynamic layer thickness on solid surfaces with molecular weight and concentration", Adsorption Science & Technology, 3,12, (1995). (18) Kong, Y., Manke, C.W., Madden, W.G. and Schlijper, A.G., "Simulation of a confined polymer in solution using the dissipative particle dynamics method", International Jounal of Thermophysics. (19) Sidoroff, F., Tonck, A., Auslender F., Georges, J-M, article in preparation (20) Georges, J-M., Tonck, A., Loubet, J-L, Mazuyer, D., Georges, E., Sidoroff, F.,'Rheology and Friction of Compressed Polymer Layers Adsorbed on Solid Surfaces" J.Phys., II, France, 6, 57-76 (1996). (21) Hu, H.W. and Granick, S., "Viscoelastic Dynamics of Confined Polymer Melts", Science, 258,1339-1342, (1992). (22) de Gennes, P.G. " Scaling Concepts in Polymer Physics", Corneil Univ. Press, (I979). (23) Brandrup, J. and Immergut, E.H. edits. "Polymer Handbook", second edition, J. Wiley, (1975). (24) Rault, J. C.R. Acad. Sc. Paris, "Conjecture sur la distance entre enchev~trement dans les polym~res fondus',300,ll 10,433-436, (1985). (25) !sraelachvili, J.N., Kott, S.J. and Fetters, L.J., "Measurements of Dynamic Interactions in Thin Films of Polymer Melts : The Transition from Simple to Complex Behaviour", J. Polym. Sci., 27, 489-502, (I 989). (26) de Gennes, P.G., "Polymers and interfaces" Macromolecules, 14,6, 1639-1644, 1981. (27) Spikes, H.A. "Boundary Lubrication and Boundary Films." Proc. 19th Leeds-Lyon Symposium on Tribology, Leeds, Sept I992, "Thin Films in Tribology". Publ. Elsevier 1993.
62
(28) Cann, P.M. and Spikes, H.A. "The Behavior of Polymer Solutions in Concentrated Contacts : Immobile Surface Layer Formation." Trib. Trans. 37, 580-586, (1994). (29) Guangteng, G., Smeeth, M. and Spikes, H.A. "Measurement and Modelling of the Boundary Film Properties of Polymeric Lubricant Additives, To be published Proc. l.Mech. E. 1995. (30) Hamrock, B.T. and Dowson, D. "Ball Bearing Lubrication : the Elastohydrodynamics of Elliptical Contacts", Publ. J. Wiley, New York, (1981). (31) Georges, E., Georges, J.M. Diraison, C. "Rheology of Olefinic Copolymer layers adsorbed on solid surfaces" STLE Tribology trans. 39, 3, 563575, (1996). 1997. (32) Georges, E., Georges, unpublished data (33) Harrison, J.A.; Brenner, D.W.d.Am.Chem.Soc., 116, 10399, 1994. Harrison, J.A.; White, C.T. Colton, R.J.; Brenner, D.W. Thin Solid Films, 260, 205, 1995.
51
NANORItEOLOGY OF POLY ISOPRENE SOLUTIONS CONFINED BETWEEN T W O SOLID SURFACES J-M. Georges a, S. MilloP, A. Toncld, R.C. Coy u, A.G. Schlijper u and B.P. WiUiamson b a Laboratoire de Tribologie et Dynamique des Syst6mes F.cole Centrale de Lyon, 69131 Ecully- France ~' SHELL Research Ltd, Thornton Research Centre Chester CH 1 3SH - England The rheology of dilute polyisoprene solutions and a formulated oil confined between two metallic surfaces was investigated by means of a Surface Force Apparatus. Experiments have been conducted to a large number of fluids, which had different concentrations and different molecular weights of polymer. By comparison between SFA measurements and the modelling of the rheological behaviour of these fluids, we showed that the structure of molecular layers near the solid surface is heterogeneous. According to their rheotogical behaviours, three, types of layer (A,B,C) have been determined. They all include an elastic layer near the solid surfaces and the viscous fluid. This viscous fluid can have an uniform viscosity (A) or be composed of a viscous layer whose viscosity is hi~er (B) or lower (C) than the bulk viscosity. Case C is found for a formulated oil. The mechanical properties of the layer B has been determined and confirmed by EHD measurements. KEYWORDS: Surface Force Apparatus, rheology, hydrodynamic layer, viscous layer, layer thickness, molecular structure, EHD, thin film, polymer solution, formulated oil
I INTRODUCTION The rheological properties of surfaces coated with adsorbed polymers control phenomena such as colloidal stability, fluid flow near surfaces and different regimes of lubrication (I) (2) (3) (4). For instance, polymer-modified lubricants have been used extensively as engine oil since the 1950's, because the main role of the polymer is to increase the viscosity of the lubricant and thus increase the hydrodynamic (EHD) film thickness (5). Many researchers have examined the effect of dissolved polymers on the rheology of lubricants and thus their hydrodynamic film formation. It has also been suggested that polymers may influence film formation in elastohydrodynamic (EHD) contacts by forming boundary lubricating films (6). Recent observations have also shown that some polymers dissolved in lubricating base fluids form boundary lubricating films up to 30 nm thick, under slow speed rolling in a concentrated contact. These boundary films may result from the presence of viscous layers of adsorbed concentrated polymer on the solid surfaces (7). A good description of the polymer layer adsorbed on a solid surface can be obtained by calculating on the basis of a porous layer model using segment density profiles (8) (9) (10) The roles of mils, loops and trains have been analysed and compared to different experimental data. This type of description assumes that the adsorption of the polymer is homogeneous on the solid surface. But as described
in figure 1, some "mushrooms" of polymers (height L) are in equilibrium with coils of the polymer solution (diameter 2RH). On the other hand . , "an hydrodynamic" thickness I.~ can be measured (11). This thickness characterises the distance between the metallic surface and the mean shear plane of the liquid, where the flow speed is zero. Comparison between theoretical and experimental data are not always possible because the amount of adsorbed polymer is not precisely known.
1 .~ .......
~.
"
"
i
----~.'
Some "mushrooms" of polymer are adsorbed on solid surface. Coils of polymer (diameter 2RH) are in the solution. An "hydrodynamic" thickness L. and a total thickness L can be measured.
This paper is mainly concerned with the rheological properties of the polymer layers near a metallic
52
dD + i~oI')" . ~.~._..~
J _ _ ._
~
___._..---1 ~
/*,"
/ i
' .
i''t'
,
i dD/d,~
T
~......
~'
6 ' t r ~ -" = .
~
,,R'3 - D. 2 L.
r,
n
Squeeze flow
I.
~,(D) Static force
surface. Here, the polymer layers are due to the adsorption of a relatively simple flexible polymer molecule (polyisoprene) of low and high molecular weights. These layer thicknesses are compared with those obtained with a commercial formulated oil containing polymer. Three types of rheological behaviour of polymer layers are detected using a Surface Force Apparatus (SFA). The structure of this paper is as follows. First the experimental method summarises the experimental approach. Second, the main experimental results are presented for one example of a layer (type B). Third, two models are presented for the study of the layer structure. Fourth, the comparison of the three types of layer are summarised and explained on the basis of their structures. Fifth, the relationship between SFA and EHD data are presented. II EXPERIMENTAL METHODS The Surface Force Apparatus (SFA) The SFA used in this study has already been described in detail in previous work (12) (13)). The general principle of the system (figure2), is that a sphere of radius R can be moved towards and away from (in the direction Oz) a plane using the expansion and the vibration of a piezoelectric crystal. During the normal squeeze of the sphere, in the inward and outward normal approach, the sphere-plane displacement D is monitored with two speed components. One is a steady ramp, which gives a constant approach speed dD/dt of 0.2 nm/s. This speed has a low value, therefore a quasistatic situation can be studied. Superimposed on this, is a small amplitude oscillatory motion of about 0.1 nm RMS, with a frequency of co = 2 . 4 . 102 rad/s. The following measurements are simultaneously recorded : the sphere-plane capacitance C and the mechanical transfer function. From this complex transfer function, only the imaginary part is used in this paper. This component, which is the dynamic
EJgllr£~ Principle of the experiment using a Surface Force Apparatus (SFA). During the normal squeeze of the sphere, in the inward and outward normal approach, the sphere-plane displacement D is monitored with two speed components. The vibrating speed too D permits to measure the squeeze flow.* and therefore the "hydrodynamic layer" thickness LH. The low speed dD/dt ~0, gives the static force Fs, which permits to measure the thickness L of the polymer layer on each solid surface. force in quadrature with respect to the oscillatory motion gives the damping function A. The resulting force F is decomposed into an hydrodynamic component F, and a static component F s , thus F = F, + Fs (Figure 2) The dynamic contribution F,, corresponds to the rheology of the fluid in the interface (figure 2). For a newtonian fluid, the hydrodynamic force is given by Reynolds lubrication theory and can be written : A = FH----:- - 6rtrlBR------~-" [ 1] imD D It should be noted that, if the bulk viscosity of the fluid rls and R remain constant, the inverse of the damping function (l/A)is proportional to D. When a layer is adsorbed on the solid surfaces, the dynamic contribution is well described by equation [ I ], after correcting D, by an "hydrodynamic layer" thickness LH : 6nR 2 D-2L H ~ = 12] A rib Therefore the plot of the function 6rtR-~/A versus D gives the bulk viscosity rib and the hydrodynamic layer thickness L~, for a mean shear rate dy ldt range of I0 - 100 (l/s). As a matter of fact, the maximum shear rate is given by (13). R 0.5 dy / dt = 1.4. (dD: dt) 13 1 (D - 2L H )15 The static contribution Fs is defined as the force measured at low speed, when the equilibrium is reached (figure2). For D < 2L, the static force increases as D decreases revealing a repulsive force due to the matching of the two polymer layers. In conclusion, simultaneous static and dynamic measurements of normal forces present during the drainage of the sphere-plane interface can characterise the interface.
53
Solutions
ij
i j|
ill
~
Mw g/mole
,
PAO + PAO + PAO + PAO +
,,
Pl 19 PI 44 PI 475 Pl 1056
_ . . . . . . . . . . . . . .
V at 3o,,c mm2ts
2R~
nm _
n
1310 3030 32400" 71950
i
, ,
c=O.5
1,5 2,2 7,i" 10.6
............
...
c=2O
24.57 24.64 24,88 25.1'8 .... . . . . . . . . . . . . . . . .
24.73 24.93 26.24... 27.83
_- . . . . . . . . . .
•
nm
.........c = 5 O 1.6 2,6 I0,4 16.6
25.36 26.43 32.34 f 40.09 ,
Materials
21~
,
,1
Table I. dilute polymer solutions in good solvent. The solvent is a synthetic hydrocarbon poly- alphaolefin (PAO). The polymer used is cis 1,4 polyisoprene (-CH2-C-(CH3)=CH-CHz)N. N is the monomer number. These polymers are designed "P! N". v is the kinematic viscosity, I ~ is the calculated gyration radius. RR is the hydrodynamic radius of the coil polymer in solution. The gyration radius RG is calculated from the Wall
Solid Surfaces The sphere and the plane used consists of metallic cobalt coatings on fused borosilicate glass, whose Poisson's ratio is 0.22 and Young's modulus E=65GPa. This cobalt layer was deposited under a low argon pressure (5.10 .6 Pa), using cathodic sputtering. AFM examinations of the sputtered surfaces show that, the surfaces consist of irregular connected clusters producing a gently bumpy corrugation with a peak to valley roughness of 1 nm. The corrugation diameter is about 50 am. The low amplitude of the surface roughness is therefore negligible compared with the thickness of polymer layers. Liquid
Experiments were carried out with dilute polymer solutions in good solvent and formulated oil. The solvent is a synthetic hydrocarbon base fluid, SHF4 I, a polyalphaolefm (PAO). Its bulk kinematic viscosity is 24.56 at 30°C. The polymer used is the cis !,4 polyisoprene (-CH2-C-(CH3)=CH-CH2) N, and N is the monomer number. These polymers will be designed "PIN". The weight average molecular weight, Mw, of the polymer has been measured by gel permeation chromatography (Polymer Laboratories). The corresponding polydispersity index Ip varies between 1.03 and 1.05. Different molecular weights (Mw= 1310, 3030, 32400, 71950) and different concentrations (0.5 %, 2 %, 5 % w/w) of polyisoprene in solution have been tested. Their molecular weights are lower and higher than the critical mass Mc (Mc=I0tX~ (15)). They correspond to polymer solutions of low (Mw
formula as RG = 0,0 I98. M 0~5. The values are given in table I. Measurements of the kinematic viscosities at 30 °C of the polymer solutions for three solution concentrations give the intrinsic viscosity [1"1]for each molecular weight. [rl] : tim c ~ o \ - - q ~ 0 J - lime*0
v0
Experimental values leads to [q ] = 0,18. M 0.5 W
"
The knowledge of the intrinsic viscosity, gives an indication of the hydrodynamic radius R, of the coil polymer in solution. According to the Einstein law [1"I] is related to RH by the relation : R3 0"0955x [rl] x MW [4] H = NA where N^ s the Avogadro number. Therefore values of R, are reported in table I. It is found found that R, is larger than RG, this suggests that PAO is a good solvent of polyisoprene polymers. A set of solid samples (sphere and plane) is prepared for each experiment. Specimens are mounted on the SFA. Then the fluid droplet which is fdtered with a Nalgene 0.2 t~m + syringe filter, is deposited between the two surfaces. Experiments were performed in dry air in the presence of the drying agent P,_O5. The temperature was about 23.5 °C. The stabitisation time for adsorption requires between a few minutes for the pure solvent to some hours for the polymer solutions. The EHI) measurements
Elastohydrodynamic EHD, film thickness measurements have been made at Shell Research Thornton using a thin film optical rheometer developed from the ultrathin film technique described by the Imperial College Group (3)(7).
54 Experimental fluids consisted of the PAO containing mono dispersed polyisoprene polymers, in varying molecular weights and concentrations. Details of the fluids are given in Table I. The rheometer generates a roiling EHD point contact between a super finished (~, 7nm CLA) tungsten carbide ball and a ( ~ 4 n m CLA) glass disc. CLA is centre line average, taken in this case over a 0.8mm cut off length. An optical interference technique was used to resolve fluid film thicknesses down to 5nm. Randomised measurements of fluid film thickness were taken over a range of low roiling speeds. (0.0003m/s to 0.0500m/s). Bulk temperature (30 °C) and contact load (14.7N) were held constant throughout the measurements. Ill FIRST EXPERIMENTAL RESULTS The results presented in this section concern the comparison of pure PAO, a polyisoprene solution of 0
I0
20
30
40
50
60
70
80
25 PaO pure
.,,'~. "
"~,,'"'.~.'"1
...--'.i:;-'". . . . . 2 Ltl = 9 4 ~ill
2 LII ~" ]9 rlli~i
I000
IOO
Z
low molecular weight (PA0+2% Pl 44) and a polyisprene solution of high molecular weight (PA0 + 2 % PI 1056). The inverse of the damping function (I/A) profile in dynamic mode and the normal force profile F, (D) in the "quasi static" mode are simultaneously determined (figure3). The plot of I/A (figure3a). versus D again reveals a linear variation for lathe D. For instance, for PA0+2% PI 1056, it is for D > 60 nm. The measured viscosity is riB=35 + 4 mPa.s, which corresponds to the bulk viscosity since a value of 33 mPa.s is found for the same solution with a capillary viscometer. The intercept of the extrapolation I/A with the surface separation axis is D=2L.= 39 nm. This corresponds to an "hydrodynamic" layer thickness on each surface equal to ~ . Consequently LH- 2R,, a value in good agreement with the data of the literature (I 1) (17). Similar results are obtained for pure PAO and Pa0+2% PI 44. Figure3b shows Fs plotted against closest sphereplane distance D. Repulsive interactions for the uncompressed layer starts at D = 2 L - - 4 nm for pure Pa0, at D = 2 L - - 1 2 nm for PA0+2% PI 44, and at D = 2 L - - 4 0 rim for PA0+2% P! 1056 This corresponds to the beginning of interpenetrating adsorbed layers. For these two polymer films, L=I.~, which can be attributed to the presence of an homogeneous layer coverage. The contact of two bearing surfaces covered by polymer is analysed by the Alexander-de Gennes theory [26]. Chains are attached to the solid surface. The force H(D), per unit surface between two parallel plates separated by a distance D can be ] ()().()4)
~o
i:
',,k.
•:!~
-
20
2 L ~- 40nm
J0
40
50
~.,q
!i :l I.(X) ]+
=
+[
§
i
2 L = 12nm I0
il,a~¢ o,I I
~. . . . . . .
~. . . . . . . .
~
i
3(>.1~)
kl.
0
m. . . . . . . . . . . . . . . . . . . . . . . .
60
70
l0
Sphere-plane distance D nm
|"o ' .v' ,+,,' 1'l".-'il,+ ()(-p
P\IA
il i,~;ii.i;~,7.,7<:~ ""
:i "'
;i •I ll.!)l
-~
solulie.n
ii . . . .
~ su,:ci,~i,u,d,: I -L-_
-"~ . . . . . .if.. . . . . . . . . . . . .
1
Figure 3 a e t 3b. SFA experiments with pure PaO, and two polyisoprene solutions: low molecular weight (PA0+2% PI 44) and high molecular weight (PA0+ 2% PI 1056). ~re 3 a , The inverse of the damping function (l/A) versus D reveals a linear variation for large D. The extrapolation gives L,. Figure 3 b. Variations of the quasi-static force/radius measurement during upward displacement D. Its starts for 2L.
,oI~......
t
Plil :
high \1,,
q[ - ~
Io
Sphete-I)lan¢
d~,d,Jnce ( r i m
Figure 4 The evolution of the pressure H(D) in the sphere plane contact (cobalt surfaces) versus the sphere plane distance D. Data for the base oil PAO, and for low and high molecular weight polyisoprene in PAO solution. Data are compared with other data obtained with the same surfaces. PIB succinimide solution in hydrocarbon (PIB), OCP and PMA in hydrocarbon solution (31) (32).
55 obtained for the experiments presented in figure 4. According to the Derjaguin approximation, the pressure I-I(D) or force per unit surface between two parallel plates of separation D, is related to the force F on the sphere-plane interface: 1 dF H(D) = [5] 2rtR dD Figure 4 shows the evolution of pressure H(D) in the sphere plane contact versus the sphere plane distance D, for different solutions. The pressure profile depends on the quality of polymer adsorption on solid surfaces. It is, in particular, clear that high molecular weight polymer gives thicker layers. But the layer coverage is not always homogeneous as it is in the case of polyisoprene. For instance, for PMA and OCP solutions, the layers are not homogeneous and correspond to the mushroom description of figure l (31) (32). The resistance to pressure of such polymer layers is low, and is due to the low compressibility, the layers not resisting to a pressure higher than 100MPa. AN
IV ANNULAR MODELS OF HETERGENEOUS VISCOUS LAYER
aB =
/
/
/
/
/
/
-
"/,,-
-.
- -
, /-. - -
~ ~ " ~ , .........
-
-
.- / /
,-
....- "
," . . / . , . ' , . , /
,, ..-',,,/ /,,,"
•
(H-2LH)
.
/
•
A=6nrlBR2[
6nrt L R ( )rdr 4Lv H - L H
oc
fi H 2
dH - , [6] x ( l - I / B)(L'~! - LHH )
+4
6nrlB R2 H
. Therefore
oo dH ACB) = r ! _ E = H x j .....21............................ 2 . . . . . . . . A(B=I) riB HH +4x(l-I/B)(L H LHH) It is interesting to plot the ratio rldrtB (figure6) where tie is the effective viscosity calculated in the case of a viscous layer model and rib is the effective viscosity of sphere-plane distance where a layer is not taken into account. For H > > 2L., the calculation of the total damping 6rcR2riB
function is : A =
( H - 2 L v x (I- 1/13)) This damping function can be compared to the damping
>,
function
previously
described
1,,~.... 1-. . . . . . . . . . . . . '
1
~1 l] '" • 2 ' , . i ' i
/
in
I::~+i
41
,
IV"
<:
"I.Ii
A I ~_]gurc 5 Model ! with a viscous layer only
aL =
This damping function varies with B=rhJriB and 2L,. If the viscous layer is homogeneous, fl = I, we
................... +
,,(p
2rdr
2I.,, and H correspond respectively to the thickness of the viscous layer and the heterogeneous viscous layer. Using the usual variable change r -~ H, (r.dr=R.dH), the total damping of the structure is:
> v
6xrl B R
fred A(B = !)=
The purpose of this part is to give a mechanical description of the surface layer obtained with adsorbed polymers. In the experiment PA0+2% PI 1056, presented in figure3, the function I/A versus D is no longer linear with D lower than 60 nm. Its curvature at lower distances can be interpreted as an effect of the mechanical properties of the surface layers. An elastic effect due to the deformations of the solids or of the surface layer itself cannot explain this important sagging, which is consequently attributed to a surface viscosity effect. The function I/A is in fact a total measurement, which integrates the squeeze phenomena on a large range of distances. So, a model based on a single viscosity step at the surface is first presented (model I). Then a more complex structure, which includes viscous and elastic layer is presented (model II). The damping between a rigid sphere and a plane
+
covered by a viscous layers is presented in figure 5. To simplify the understanding of this figure, no layer has been represented on the sphere, but the layer thickness has been doubled on the plane. The calculation of the damping can be approached by a rheological model assuming simply, that structural damping results from the combination of two dashpots representing respectively the bulk fluid (as) and the viscous layer (at.), whose viscosity's are respectively riB, qL- It has been shown that the expressions of the damping coefficients are respectively :
~,.t+ - 3',: ~ n m
!! . . . . . . . . . . . . . l+;fi
15~+
"~,:
" .:,..,
~<~,,
,Sphere-plane distance (nm)
/ /
Figure 6 .Application of the model I presented in figure 4 for 2% PI 1056 in solution in PAO
56
61tR 2TJB equation[2] A = _ _...:..:::_ D-2LH In the central zone, D = H + 2LH In the case of 2% PI 1056 in solution in PAO, a fit is found if fi-10, 2LH=39nm, Figure 6. The comparison between the experimental data and those obtained with the model with a viscous layer is not adequate. Therefore, a second model is proposed in figure 7. It represents an heterogeneous structure. Moving away from the surface, the interface is composed of firstly a solid layer, which has elastic properties, then a viscous layer TlL· The thickness of the solid layer, L, and its compressibility modulus is K.
Figure 7 Model II with an elastic layer covered by an viscous layer. It allows an approximate quantification of the increase of surface viscosity T](D), where this phenomenon takes place. The lower limit defines the thickness of the solid layer whose elastic properties have been estimated using the elastic part of the
measured transfer function (not shown in this paper,[19]. Three examples of application of the model II are now presented. An example of this simple modelling is given in figures 7, 8, 9. • First, in the case of 2% PI 1056 in solution in PAO using model II,_ a constant value of the viscosity is given for"' the layer, T], =6.7 T], 2Lv=32nm. An elastic layer is taken with 2L,=l0nm, and an elastic modulus K=30-50MPa. With these parameters the viscosity profile T](D) is plotted. The results obtained with SFA measurements and model are in good agreement while for lower sphere-plane distances, some variations are observed. They are due to the fact that the elastic deformation of the solids and the elastic layer are not taken into account. Moreover, the viscosity increase near the surface is probably not a "squared" function but increases progressively when the sphere-plane distance decreases as Kong et al. [18] have observed in dissipative particle dynamics simulations. Though this model can be improved [ 19] the results obtained from SFA measurements and from the model are in relatively good agreement and confirm the heterogeneity of the interface thickness structure. • Second, in the case of 2% PI 44 in solution in PAO using model II, no viscous layer is detected. But an elastic layer is taken with 24 = 1Onm, and an elastic modulus K=20-30MPa.
1 : b4
SHF41+2%P••IY44 .
Elastic layer
:-~
,.....
·;;;;,j 8 9 .::!2 3
;r
/
relative viscositie ~ , from model II / ~ 2 " i~rom SFA easurement
(:Z
50
100
150
200
250
300
Sphere-plane distance(nm)
Figure 8 Relative viscosity versus the sphere plane distance D, for 2% PI 1056 in solution in PAO. From the SFA measurements, at each distanceD, the slope of the curve 1/A(D), gives a viscosity profile T](D), which is compared to the bulk viscosity Tl· Using model II, a constant value of the viscosity is given for the layer, T], =6.7 T], 2L.=32nm. An elastic layer is taken with 2L,=10nm, and an elastic modulus K=30-50MPa. With these parameters the viscosity profile TJ(D) is plotted. Good agreement between the two viscosity profiles is obtained.
\(··~--
SFA measurement
0~--------~----+-------------~ 0 50 100 ISO 200 250 300 2LH
Sphere-plane distance (nm)
Figure 9 Relative viscosity versus the sphere plane distance D, for 2% PI 44 in solution in PAO. From the SFA measurements, at each distanceD, the slope of the curve 1/A(D), gives a viscosity profile TJ(D), which is compared to the bulk viscosity 11· Using model II, no viscous layer is detected. The elastic layer is taken with 2L,=l0nm, and an elastic modulus K=20-30MPa. With these parameters the viscosity profile T](D) is plotted. Good agreement between the two viscosity profiles is obtained.
57
• Third, in the case of a formulated oil containing polymer package but also small molecules such as antiwear additive (ZDTP). The behaviour is different, figure I0. An elastic layer is detected with 2Ls = 10nm, and an elastic modulus K =50-70MPa. But the viscous surface layer has a viscosity less than that of the bulk fluid qs =0.8 ri. This suggests the presence of a depleted layer of polymer near the solid surface.
i :il/Y
w
* Layer type A On each solid surface, a thin purely elastic layer L, is covered by a purely viscous liquid. The layers are approximatively the same thickness, L , - L a - L . This type of layer corresponds to the situation of the pure base oil PAO and for the low molecular weight polymer in solution (Mw=1180,1310,3030). We found that for thefrange of low molecular weight polyisoprenes tested, the ratio L./2RH is in the range of 1.5 - 2 , the compressibility modulus Ks - 30 MPa. This value of compressibility modulus is high in comparison to the rubber modulus of a pure polyisoprene melt which is equal to 0.44MPa. Therefore, we can assume that a layer of randomly flat molecules stay on the surface giving a thickness in the range of L~---LH- L - 5 n m . We notice that the pure base oil PAO presents the same behaviour with an immobile layer of molecules, L -- L, -- L - 2.5nm ).
o
m
• . . , _ ~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
•
,
•
•
•
.~
-:
i:..~
-.i :. :
: : ' : : ~
....
:. = . : :
~ .....
" . :
.'.,. ....
Layer type B
..:
- - ~ , . . ' . , , . , _ . " .~ . . . .. . . . . .
~)
.
.
..~, .
.
.
.
.
.
-.::..: ~..
, ,....
,-.,.
Figure I0 Relative viscosity versus the sphere plane distance D, for a formulated oil. The inverse of the damping function (l/A) versus D reveals'a linear variation for large D. The extrapolation gives L , = - 14nm, a negative value. From the SFA measurements, at each distance D, the slope of the curve I/A(D), gives a viscosity profile ri(D), which is compared to the bulk viscosity rl. Using model !I, a constant value of the viscosity is given for the layer, rls =0.8 rl 2L~=75nm. An elastic layer is taken with 2Ls = 10nm, and an elastic modulus K=50-70MPa. With these parameters the viscosity profile rl(D) is plotted. Good agreement between the two viscosity profiles is obtained
V MECHANICAL CHARACTERISTICS OF POLYMER LAYERS From the SFA data obtained on the different solutions studied, the pure base stock (solvent PAO), low molecular weight polymers in PAO solution, high molecular weight polymers in solution and formulated oils containing polymer, three types of layer were detected. Their main characteristics are summarised in table II.
On each solid surface, two layers are detected between the solid and the bulk fluid. Near the surface, the first layer has a purely elastic behaviour similar to type A and above this there is a second highly viscous layer. This type of layer corresponds to high molecular weight polymer solutions in good solvents. The results presented here correspond to dilute polymer solutions c/c* < 1. ), where c is the weight polymer concentration and c* the critical concentration. The bulk property of the solution is that of a liquid with a viscosity fla. The "hydrodynamic" thickness LH is lower than the thickness of the layer detected by the static force L~ < L. The compressibility modulus of the solid layer is K~---30-50 MPa suggesting a high concentration of monomers near the surface. This modulus value is intermediate between the rubber (0.44 MPa) and the glassy (I03MPa) modulus of po!yisoprene. This behaviour has already been found for compressed and uncompressed polymer layers in the literature. Similar results have been obtained by Hu and Granick (21) with unentangled conf'med polymer melts. For very low thickness corresponding to 4-5 Rg, they have measured a plateau modulus which is about twice the rubber like plateau modulus. They suggested that the elastic effects observed can usefully be viewed as an entanglement phenomenon. According to the scaling theory of polymers (22)(23), the rubbery plateau modulus of the polymer network is related to the entanglement distance ~ which is the order of the mesh size of the
58
temporary network formed by the chains and is defined by the relation : kBT K ~ ~ [7]
The ratio La/2R, is found close to 1 in accordance with previous results presented in literature (I 1). The fact that L is different from Lu (L>I.~) suggests that the layer is non-homogeneous in the xy plane. The mechanical information obtained with the SFA comes from a circular area of contact with a radius (RD) °'s- 10/zm). Consequently, over this large surface area, the polymer does not homogeneously cover the'surface). We may assume that the layer is formed by some "mushrooms" of polymer. The enhancement of the viscosity is due to the polymer coils attached to the surface and to coils trapped in the vicinity of the layer. The ratio LH/2Ra obtained for different molecular weight polyisoprenes are given in figure I 1.
~3
According to Rault [24] for polyisoprene melts, K=0.44 MPa and ~ = 8.2 nm. Therefore, for K--30 MPa, the correlation length ~, of the compressed polymer is evaluated to be 2 nm. This value of the correlation length ~ is very small and could be due to the applied external pressure. The polymer did not escape from the contact volume and hence the "mesh" size of the polymer layer will be reduced. For overlapping polymer layers (D<2L) Fredrickson and Pincus (8) assigned the viscosity term to the draining of solvent molecules from the network made of grafted chains. They use Brinkmann's equation to describe the solvent velocity field by means of a hydrodynamic screening length {H and predict a viscosity coefficient in the form
.".
.__..
=
~ ......... . ,
2
,,. .
.
.
.
.
~
.~
.
•
.
.
.
-~
...,
•
5 1
Previous results have shown that for a sphere-plane distance D---10nm, the relative effective viscosity could vary between 5 and 10. For the polymer solution of 2% PI 1056 in PAO, rlr/rla-6.7. In this case the mesh size {H is about to 1.8 nm. The value of the ratio ~,a/{ " 1. I is in good agreement with the literature data.
0 - 1
t ........
1000
.
.
. . . . . . ... . . . . . . . ... . . . . . .,. .
.
•
.,
.
.
.
10000
.
"t
.................
.
T
100000
Figure 11 Evolution of Ln/2R., versus the molecular weight of the polyisoprene.
Table H Main characteristics of the polymers layers type
......
Fluids
2R. nm
.................
.......
L i t
PAO _
i
pure
iiiii iiiiiii i i
!
. . . . . . . . . . . . . . . . . . . .
PAO+0.5% •-
A
PII9
PI
B
lilllll
ii i
1,6
I
II
IIIII |
MPa
i,5±o.5'
I
1,o
. . . . . . . . . . . . . . . . . . . . . . .
3'6_+0.5
4,0~0.5
0.90-
2.25.......... ,20'30-
.... ;i,7 +0.5
0.77
2.25
1,6
3.65:0.5
......P 1 4 4 ........
2,6
4.0+0.5
5.2 5:0.5 ........0.77 ........... i.53"
20-30
2.6
4.7+_0.5
6,0±0.5
0.78
i is0
1o-30
I0,4
13.2:£1.0
14.0_+1,0
i~25
30-50-
PAO +2,0% PI,475
10,4
16.0_+1.0
17.05:1.0
0.94
1.53
30-50
PAO + 0.5% PI 1056
I6,6
19.0+_2.0
20.0±2.0
0,.95 ......
1.~4
3040
PAO
llm
+
PI44 ....
iii
0.5% Vi 475
i
|mlllllll n
PAO +2,0% Pi 1056 C
Ill
2.55:0.5 i
'Ks
19
+ 2,0%
PAO + 2'0% -
i
!ii i
l..m/2Rn
~,
PA0÷0.5%
---
1
=
PAO
i
~,/L"
nm
nm .
I'_'
Formulated Oil
16,6 i
i
i
...1
19.0:!:2.0 . . . . .
i
. . . . . . . . . . . . . . . . . . .
..
.
.
.
20.0:t:5.0
•
4-1-1.0 .
ii
.
.
0.94 .....
.
.
i
.
.
15:t:!.0 .
............
|. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
0.95 i
<0 '
'
20-30
1.14
.
.
.
ii
.
.
. iiiiii
i . . . . . . . .
30-50 11 _ t
.
.
.
.
.
.
.
.
.
50-70
59
•
Layer type C
On each surface, two layers are detected between the solid surface and the bulk fluid . Near the surface, the first thin layer has a purely elastic behaviour and then a "low" viscous layer is found. This type of layer corresponds to a formulated oil containing polymer and other additives (small molecules). The main effect of the drainage measurement is a negative value for the "hydrodynamic" layer thickness I.~. The extrapolated 1/A function versus D gives I..,= -4 nm. A more complete analysis similar to that conducted for layer type B, detects the presence of two successive layers. The solid layer has a thickness L , - 4 - 5 nm with a compressibility modulus of about 50 MPa. This suggests the presence of some molecules which do not participate in the flow and which are compacted on the surface. A second layer of "low" viscosity (hL=0.8ha) is observed in the vicinity of the surfaces. An hypothetical explanation can be found in the fact that the small molecules present in the solution are more strongly adsorbed on the cobalt surface than the polymer molecules. Consequently, the layer is non homogeneous. During the drainage, the free coils of polymer coming from the bulk cannot penetrate into the layer as readily as the solvent (base) which can more easily flow in the layer rather than in the bulk. More analysis has to be done with known solutions in order to explain this important difference in the flow behaviour.
polymers above 32400 molecular weight diverge from the theoretical line to form a plateau region at approximately l0nm. As already explained by Guanteng et a1.(29 ], the film thickness in an EHD contact is determined by the viscosity of the material
rlb
. i :
rli
,
.....
I i | ii
IIII
.....
i
ii iiill
I
•
..........
~, III
..................................
*
T
U/2 00 ..................................................................................................................... E o,J
o 10 E
,,,.,_ t~
1
i ........
I
L .. , j
~ l!,,
I
. . . . . . . .
~
. . . . .
I0 I00 Rolling speed U (x 10-4 m/s)
=L
!
1000
ILl
CI
Vl RELATIONS BETWEEN MEASUREMENTS
SFA
and
EHD
ta~ O td~
•-
;>
EHD experiments with polyisoprene solutions were conducted. Figure 12 presents the results with two characteristic products, a low and a high molecular weight polymer. These experiments show that the polymer additives form quite mobile viscous surface layers on solid surfaces. The viscous layer has an important effect because it is well known that the film thickness in a rolling EHD contact is mainly determined by the inlet zone [6]. If the viscosity of the fluid is increased or if the boundary conditions are changed in this zone then an increase in film thickness h may now be observed. This was observed with polymer solutions where type B layers ( high molecular weight as Pii056). An example figure 12b presents a log (film thickness h) versus log (rolling speed u) plot. classical EHD theory, assuming base fluid bulk viscosity, was used to generate the "theory" line of gradient 0.67. For polymer solutions it is found that at high, thickness / speed, theory is followed. However, as speed is reduced, It is detectable with this technique ul,~,
0".
5
D
txl
a~
o .... [Z_
0
O'
'~.
' 0
10 20 30 EHD film thickness (nm)
40
Figure 12 a,b,c. EHD experiments with polyisoprene solutions in polyalphao!efin PAO. • Pure PAO x 2% 44PI in PAO 2% 1056 in PAO Figure 12 a Schematic aspect of the inlet contact region. Figure 12 b. Film thickness h versus rolling speed
Figure ..... 12 ..... c
Relative viscosity between the viscosity in the inlet for a given film thickness and the bulk viscosity versus E H D film thickness h. deduced
60
in the immediate contact inlet, figure 12a, primarily within an inlet zone whose thickness is only one to two times the central film thickness. It is therefore possible to determine the effective mean viscosity in the inlet by using the Hamrock Dowson equation (30), where The theoretical film thickness 1% is related to the rolling speed U, by the relation ' h t oc U 0.67 x r 10.67 x tx 0.57
[9]
Indeed, as the pressure viscosity coefficient, a, of the solution is almost constant, the measured film thickness h m is such that hm= hi
(~)
rli
0.67
[1t3t]
where h~ is the viscosity in the inlet. Figure 12c shows the relative viscosity (rli/rlB). It is found that (rltrl0 starts to rise when the central film thickness, hm, is about 20 nm. This corresponds to an interface thickness in the inlet zone of about 40nm (1 to 3 hm). Agreement between these data and data presented in figure 3 and figure8 are relatively good. The hm versus U evolution for a layer of type A is quite different since hm/h,= 1 for low rolling speed. The low polymer molecular weight does not improve the lubrication. Agreement between these data and that presented in figure 3 are relatively good Figure 13 presents two different rheological experiments with adsorbed layers of the same polyisoprene solutions PI 1056.
S~,d
1000
/,~j.,,I,'X~_, h
molecular tribometer
ultra thin film interferomctry
v C d~ °..
.~
CONCLUSIONS
,
,/a
t00 /~A
• e
oe
10 /,/
"13
=,.
Als
I pm/s
First, EHD film thickness h measurements are reported as in figure!2b. Second, on the same graph are reported the rheology of adsorbed layers of poly-isoprene between two cobalt surfaces, investigated with the SFA tribometer. The two layers of poly-isoprene are compressed between the smooth sphere and a plane. During the compression process, the solvent molecules are repelled ~om the polymer network and formed a compressed polymer "mesh" which is not connected. The mean "mesh" size is lower than the one corresponding to the "rubber" plateau of a polyisoprene melt. The contact pressure is 107Pa, and the film thickness of the two compressed layers is in the range of D=19.3nm. A sliding experiment is conducted, and the variations of D, accurately measured. The film thickness variations follow those of the friction force and are the sum of two contributions (20). One is a thickness decrease due to creep of the layers themselves. Another is a very small increase of the interfacial thickness between the two layers, which was found to be dependent on the sliding speed. This interfacial thickness is that of the shear band. Its value is reported as a function of the sliding speed (20). It is interesting to note, that over 8 speed decades, two major processes control the sheared zone. At low speeds, movements of molecular groups are responsible for the lift of the two compressed layers. It is the consequence of best trajectories taken by the molecular groups during the sliding as also described by Harrison's simulations (33). At higher speeds, the global increase of the viscosity in the inlet zone provokes the lift.
Speed I mm/s
Figure 13; Two different rheological experiments with adsorbed layers of poly-isoprene solutions. On the right part, elastohydrodynamic, film thickness D measurements using a thin film optical rheometer. On the left part, rheology of adsorbed layers of polyisoprene between two cobalt surfaces, investigated with a molecular tribometer (20).
. The Surface Force Apparatus can detect two parameters simultaneously which characterise the presence of an adsorbed polymer layer: the "hydrodynamic" film thickness L, and the beginning of the repulsive force which gives an indication of the total thickness L. . The ratio I_~ / L gives an indication of the quality of the polymer coverage. When LH / L = I, the coverage is good as it is in the case for polyisoprene solution on cobalt surfaces. But it is not always the case for all the polymer solutions (31). * The ratio I.~ / 2 RH varies between 1 and 2. ,, The mechanical properties of the layers has been analysed. Comparison of different polymer solutions were undertaken and three types of layer are detected. For pure polymer solutions, two cases are presented. In the situation of low molecular weight, a thin elastic layer covers the solid. In the case of
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