pubs.acs.org/Langmuir © 2009 American Chemical Society
Frictional Rheology of a Confined Adsorbed Polymer Layer Juliette Cayer-Barrioz,*,† Denis Mazuyer,† Andre Tonck,† and Elaine Yamaguchi‡ †
Laboratoire de Tribologie et Dynamique des Syst emes-UMR 5513 CNRS/Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France, and ‡CHEVRON-ORONITE Company LLC, P.O. Box 1627, Richmond, California 94802-0627 Received April 16, 2009. Revised Manuscript Received June 5, 2009 The sliding dynamics of a confined adsorbed polymer layer is investigated at the nanoscale. A combined mechanical and physical approach is used to model the rheology and structure of the adsorbed layer. The confinement at short distances governs the nanotribological behavior of the polymer layer formed close to the surface. It appears that the Amontons’ proportionality between frictional and normal stresses does not hold here: the higher the contact pressure, the lower the friction. Besides, the sliding stress is strongly dependent on the velocity: it increases with the sliding velocity. Using a model based on the kinetics of formation and rupture of adhesive bonds between the two shearing surfaces theoretically accounts for the behavior of this system. This approach allows us to correlate the frictional properties to the molecular organization on the surfaces.
Introduction Soluble polymers, known as viscosity modifiers, are currently added to almost all multigrade engine oils where their main role is to modify the bulk rheological properties of the fluids with which they are blended. These additives typically reduce the extent of the decrease in viscosity as the temperature is increased, increase the viscosity as the temperature is decreased, or both. Viscosity modifiers are usually high-molecular weight polymers that modify the viscosity-temperature response of a base oil to increase the viscosity index of the oil.1 On the other hand, dispersants are employed in lubricants because of their ability to interact with surfaces and other polar substances and to keep impurities in suspension. Mixtures of conventional dispersants with polymeric viscosity improvers are often used, but such combinations are costly and may adversely affect low-temperature viscometric performance due to competitive or synergetic interactions. Therefore, multifunctional additives that provide both viscosity improving properties and dispersant properties, i.e., dispersant viscosity modifier (DVM), are generally prepared by functionalizing highmolecular weight hydrocarbon polymers. In addition to the above, it also appears that some polymers may act as effective friction modifiers2 by forming a nanometer thick boundary film on polar surfaces. For various DVMs in rolling concentrated contacts, Smeeth et al.3 proposed the following mechanisms of boundary film formation: at high speeds, thick film conditions persist and the bulk polymer solution is entrained into the contact and thus forms an elastohydrodynamic film consistent with the high shear rate viscosity of the blend; at low speed where film thickness is significantly reduced, the contact inlet is filled with the adsorbed polymer layer. The localized concentration of the adsorbed polymer layer creates a higher surface viscosity relative to the bulk, and that results in a thicker than expected film. These adsorbed layers result in a decrease in friction. On the other hand, some polymers exhibit a reduction in film thickness at low speeds, *To whom correspondence should be addressed. Telephone: þ33 4 72 18 62 84. Fax: þ33 4 78 43 33 83. E-mail:
[email protected]. (1) Stachowiak, G. W.; Batchelor, A. W. Engineering Tribology, 2nd ed.; Butterworth Heinemann: Boston, 2001. (2) Fan, J.; M€uller, M.; Stohr, T.; Spikes, H. A. Tribol. Lett. 2007, 28, 287–298. (3) Smeeth, M.; Gunsel, S.; Spikes, H. A. Tribol. Trans. 1996, 39, 726–734.
10802 DOI: 10.1021/la9013398
and this was ascribed to polymer depletion.4 It is therefore clear from the above that the ability of polymers to be entrained into the contact and form boundary films depends strongly on their affinity for the surface, relative to the interaction of the base oil with the surface. Consequently, the performance of a lubricant depends upon its dynamic properties and interaction forces with the shearing surfaces.5 Extensive previous experimental6-11 and theoretical work12,13 has focused on the organization of various molecules onto the surfaces and their response under confinement. The friction response of a simple liquid or liquid-like lubricant squeezed in a low-pressure contact (300 nm) according to eq 5. It is equal to 0.28 Pa/s, which is consistent with the value obtained with a capillary viscometer. The hydrodynamic thickness LH is measured from the intercept of the distance axis with the fit of the curve at large distances. Since this value is much higher than the radius of gyration of the molecule, a mechanical modeling of the interface can be applied, and this gives a corrected hydrodynamic thickness LH0 of 8 nm for a higherviscosity η0 layer with a thickness of h0 on each surface. Table 1. Thicknesses of the Adsorbed Surface Layer under Various Confinements, Surface Coverage Ratios, and Bulk Viscosities 2L (nm)
2LH (nm)
2LC (nm at 0.1 mN)
2LC (nm at 1 mN)
LH/L
η (Pa/s)
80
55
11
6
0.68
0.28
contact pressure of ∼13106 Pa (or 34 106 Pa) and is ∼5.5 ( 0.4 nm (or 3 ( 0.4 nm). In the dynamic mode, via superimposition of an oscillatory motion of given amplitude and pulsation ω, the viscous damping Az(ω) of the interface is measured. The plot of 1/ωzAz as a function of D, at a frequency of 38 Hz and oscillatory amplitude of 0.1 nm, is also presented in Figure 2b. At large distances (>300 nm), according to Stokes’ law, the slope of the curve gives the bulk viscosity η of the lubricant. This value of 0.28 Pa/s, reported in Table 1, is consistent with the value determined with a capillary viscometer (0.27 Pa/s). Moreover, the best fit of the curve at large distances intercepts the distance axis at 2LH, which defines the hydrodynamic thickness: 2LH is ∼55 ( 0.4 nm. This demonstrates the occurrence of adsorption of DOCP molecules on the surfaces. The thicknesses characteristic of the interface and the oil viscosity are reported in Table 1. The ratio between LH and L is representative of the surface coverage ratio. From the values of Table 1, the following can be deduced. L . Lc exposes that the confinement is progressive and slow. The thickness of each adsorbed layer before confinement L=40 nm is much larger than the radius of gyration Rg of the DOCP Langmuir 2009, 25(18), 10802–10810
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Figure 3. Modeling of the interface using two layers of viscosity η and η0 > η with a hydrodynamic layer of thickness LH0 on each surface. Each viscosity layer is represented by a dashpot of damping function ai in a ring of thickness dr. The integration of the resulting damping function, a, over the contact allows us to simulate the existence of a layer of higher viscosity at the vicinity of the surfaces.
molecules that has been estimated at 23 C to be ∼6 nm. It can be assumed that at low confinement, the solvent molecules remain within the contact. As confinement increases, the distance L reaches the value of Lc=5.5 ( 0.4 nm at Fz=0.1 mN and then the value of Lc=3 ( 0.4 nm at Fz=1 mN. One may suppose that the solvent molecules are finally squeezed out at severe confinement. The hydrodynamic layer LH on each surface is measured as 27.5 nm. It appears to be much larger than the diameter of the free coil. The surface coverage ratio LH/L is rather low, ∼0.68. This preliminary description of the interface seems insufficient: in particular, the high value of hydrodynamic thickness LH is inconsistent with the diameter of the coil. Therefore, a simple modeling of the contact has been proposed:16,35 the confined interface is made of a bulk viscosity fluid film squeezed between two thin viscous layers close to the immobile hydrodynamic layer LH0 adsorbed on each solid. Their total thickness is 2h0, and their viscosity, η0, is greater than that of the bulk lubricant, η. The interface is modeled using two dashpots in series as depicted in Figure 3, and the damping function, a1 (or a2), of dashpot 1 (or dashpot 2) is35 6πηR a1 ¼ r dr ð2Þ ðz -2h0 Þ2 a2 ¼
6πη0 R r dr 2h0 ð2z -2h0 Þ
ð3Þ
where h0 is the thickness of the layer with enhanced viscosity on each solid surface. The equivalent dashpot is 6πRηr dr az ¼ ð4Þ 2 z - z 4h0 ð1- η=η0 Þ þ 4h0 2 ð1- η=η0 Þ When the existence of the hydrodynamic layer of thickness LH0 and D . h0 are taken into account, the damping function Az which results from the integration of the elementary dashpot, az, over the whole contact becomes35 Z þ¥ 1 2 Az ¼ 6πηR dz 0 ½z -2h ð1- η=η Þ2 D - 2LH 0 0 ¼
6πηR2 D -2LH 0 - 2h0 ð1- η=η0 Þ
ð5Þ
Equation 5 is used to fit data in Figure 2b. This allows us to estimate η, η0, and LH0 . At large distances, far from the surfaces, (35) Tonck, A. Developpement d’un appareil de mesure de forces de surface et de nanorheologie. Ph.D. Dissertation, Ecole Centrale de Lyon, Lyon, France, 1989.
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the viscosity η of the lubricant is equal to that of the bulk; i.e., η= 0.28 Pa/s. At the vicinity of the surfaces, a homogeneous layer of enhanced viscosity (η0=0.50 Pa/s) can be defined from the slope of the curve 1/(ωzAz)=f (D) at small distances by using the largest linear fit for the viscosity. The thickness of the immobile hydrodynamic layer LH0 is deduced from the intercept of this slope with the axis, as reported in Figure 2b. Derived from eq 5, the thickness of the higher-viscosity layer, h0, can be calculated: h0 ¼
LH -LH 0 1- η=η0
ð6Þ
where LH=27.5 nm, LH0 =8 nm, η=0.28 Pa/s, and η0=0.50 Pa/s. It is noteworthy that LH0 is of the same order of magnitude as the diameter of the coil.34 This gives an h0 of 44 nm. Considering the interface as a multilayer medium from the surface to the bulk allows us to model the whole experimental curve 1/(ωzAz)=f (D) (see Figure 2b). Even if the former model allows us to simulate accurately the variation of the damping function with the sphere-plane distance, questions regarding the origin of the molecular adsorption at the vicinity of the solid surfaces and the way it controls the properties of the confined interface remain unanswered. It is wellknown that when a fluid separating two solids contains highmolecular weight polymer molecules, these molecules may be adsorbed on the metallic surfaces. De Gennes12 describes the adsorption layer for a semidilute polymer solution near a solid wall using a free sticking energy, γ1, which is positive in the case of an attractive wall. This approach is based upon the construction of concentration profiles which divides the adsorbed polymer layer into three regions.12 The proximal region close to the surface and where the effects of short-range forces between a monomer and the wall are important has a thickness e given by 1 kT 3=2 ð7Þ e¼ 2 a jγ1 j where a is the diameter of one monomer assumed to be equal to 0.2 nm. In this region, the concentration is higher than the bulk and the monomer volume fraction near the wall, φs, is given by 4=3 a φs ¼ . φb ð8Þ e The central region which has a thickness equal to that of the adsorption layer extends to a distance ξb from the wall. ξb is the correlation length of the polymer solution such as ξb ¼ aðφb Þ -3=4 DOI: 10.1021/la9013398
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Figure 4. Quantitative plot of the monomer volume fraction φ vs distance D from the surface. There are three distinct regions: the proximal region where D < e = 2 nm, the central region where eξb from the wall, in the distal zone, the solution can be pictured as a random network of mesh ξb; for D
