Effect of Surface Chemistry on the Squeeze-Thin Film and Friction of Boundary Films

Abstract

An approach combining adsorption characterization and lubricity effectiveness of amine-based friction modifier molecules has been performed using chemically controlled surfaces, coated either with cobalt or carbon, while keeping the surface roughness constant and sub-nanometric. Through squeeze measurements and numerical modeling, we have identified the mechanical properties of both adsorbed amine films, as a function of the surface on which they were formed. On the one hand, we were able to evidence that the fluid structuring at the vicinity of the adsorbed boundary film differed as a function of the latter mechanical properties, directly resulting from its molecular organization. On the other hand, we showed that the coverage ratio of the monolayer associated with the shear elastic modulus of the boundary film governed the friction level. Changing the surface chemistry while keeping the roughness constant controls the final organization in the boundary layer, the correlated mechanical properties, and the level of friction dissipation.

Introduction

In lubrication, especially in thin-film lubrication with low viscosity fluid, the two antagonistic surfaces in contact are separated by a fluid film whose thickness is lower than hundreds of nanometers. This means that locally due to the surface roughness asperities from both surfaces might also interact. When sliding is introduced between the two surfaces, friction dissipation results from a combination of the shear of the thin film under pressure, shear of the adsorbed layers on the surfaces, and shear of the interacting asperities. Therefore, surfaces play a key role in governing friction dissipation. Surface properties directly derive from their manufacturing processes, and their reactivity differs from one another, according to their chemistry. To better understand friction dissipation mechanisms, it is necessary to investigate the role of surface roughness and also to identify the organization and the mechanical properties of the adsorbed layers on the surfaces, forming the so-called boundary film.

On metallic surfaces, pioneering studies¹ showed the influence of the formation of a boundary layer on surfaces to reduce friction. This formation depends on various parameters, such as, for instance, the concentration,² the molecular structure,³⁻¹⁰ the role of the anchor,^5,11,12 the surface roughness,¹³ etc. Surface chemistry was also investigated by Bowden and Tabor¹⁴ using metallic surfaces with different reactivities. For low reactive metals, such as nickel, chromium, platinum, or silver, hardly any friction reduction was measured by adding dodecanoic acid in paraffin oil. On more reactive metal surfaces, i.e., copper, cadmium, zinc, or magnesium, friction reduction of an order of magnitude was obtained. This was interpreted as a reaction between the additive and the surface. More recently, Ratoi et al.^15,16 evidenced the presence of a nanometer-thick film of carboxylic acid on bearing steel compared to stainless steel at low entrainment velocity under pure rolling conditions, suggesting the preponderance of oxide layers on the additive film formation. The role of amine-based friction modifier molecules was also studied by Nalam et al.:¹⁷ they showed that a high number of amine functional groups in the anchor part of fatty amines lead to a slow self-assembly kinetics associated with higher adsorbed masses on steel surfaces while maintaining friction reduction.

On nonmetallic surfaces, Hutchinson and Rideal analyzed the lubricated friction response of ceramics, and they highlighted a friction reduction in the presence of long hydrocarbon chains surfactants.¹⁴ Carbon in its graphitic form is also known for its low friction dissipation due to its lamellar structure and the presence of adsorbed water molecules on the surface.¹⁸ For nongraphitic carbon surfaces, such as diamond-like-carbon (DLC) coatings that offer the advantage of a low surface energy, inferior to 50 mJ/m^219,20 while combining high mechanical resistance, friction was also reduced in the presence of lubricant.²¹ This interest in carbon surfaces lead to development of the so-called DLC surfaces, and extensive literature can be found on the interactions between additives and carbon^22,23 and DLC surfaces.²⁴⁻²⁶ For instance,²² Georges et al. showed that polymeric additives formed homogeneous adsorbed films of thickness of a few tens of nanometers, exhibiting a macroscopic elastic behavior under squeeze and confinement. The role of fatty acids was also investigated by Simič and Kalin²⁴ who confirmed the formation of self-assembled monolayers of palmitic acid on DLC surfaces, with a coverage ratio similar to the one measured for steel surfaces but lower friction dissipation. These examples show the growing interest in understanding the effect of surface chemistry on boundary film formation and friction reduction. Nevertheless, as the surface morphology varies with the chemistry, although it fully governs the friction mechanisms,²⁷ it is usually difficult to separate both contributions, i.e., morphology and chemistry.

The goal of this paper is to analyze the role of surface chemistry, while keeping the roughness constant and sub-nanometric, on the formation of amine-based friction modifier self-assembled monolayers. We also aimed to identify the mechanical properties of these viscoelastic layers. The surfaces have been coated with cobalt and/or carbon to mimic metallic and/or nonmetallic surfaces, respectively, in order to modify the surface chemistry while ensuring a similar roughness of highly smooth surfaces. Using the ATLAS molecular tribometer, an approach was implemented coupling the characterization of the molecular organization of the adsorbed layers to the analysis of the interfacial behavior during the squeeze of the two surfaces. The friction response of the two boundary films resulting from the adsorption of amine-based friction modifier molecules was also investigated.

Experimental Section

Fluids

The amine solution was prepared at a concentration of 1% w/w in a group III base oil. This low concentration ensured that no micelles were present to disturb the film formation. The solution was provided by TotalEnergies. The viscosity of the solution was measured using a TA2000 rheometer in a cone/plane configuration at 24 °C and a shear rate of 1 s^–1. Under such conditions, the measured viscosity was about η = 28 ± 1 mPa·s.

The amine-based friction modifiers were derived from a fatty amine. It was mainly present in the form of a triamine at 80% (N-aminopropyl-N-tallowalkyl trimethylenediamine)²⁸ (see Figure 1a) and the remaining 20% was composed of diamine (N-tallowalkyl-1,3-propanediamine) (see Figure 1b). The alkyl chains were obtained from Tallow glycerides with a combination of saturated and unsaturated chains of C16 to C18. The solutions were filtered with a nucleopore filter of 200 nm. This filtration step allowed one to eliminate the aggregates and dusts likely to disturb the boundary film formation on the surface and therefore the forces and distance measurements.

Figure 1.

Chemical structure of the amine-based molecule (a,b) and (c) schematic of the experiment.

The triamine molecule has a length, L_TA, ranging from 2.5 to 2.7 nm¹⁷ according to numerical simulations with Avogadro, and the surface occupied by one molecule once adsorbed is between 0.38 and 0.55 nm²,²⁸ corresponding to a diameter of 0.6–0.8 nm if one assumes a circular area. All of these data are reported in Table 1.

Table 1. Experimental Details—Molecular Structure and Viscosity.

LTA (nm)	area/mol (nm2)	diameter ϕ (nm)	viscosity η (mPa·s)
2.5–2.7	0.38–0.55	0.6–0.8	28 ± 1 at 24°C

Solids

Following the procedure already detailed in refs (9, 29, and 30), a fused-silicate glass sphere of radius, R (values reported in Table 2), and a (111) silicon wafer of 1/2 in. diameter and 1 mm thickness, were both cleaned with isopropanol followed by a cathodic sputtering cobalt coating deposition of a 5 nm layer. The coating on both surfaces was made simultaneously, under low argon pressure (3.4 × 10^–3 mbar), in order to obtain chemically symmetrical metallic surfaces. X-ray photoelectron spectroscopy showed the existence of a cobalt oxide layer of a few tenths of nanometers, composed of CoO, Co₂O₃, and Co₃O₄.²⁹ This conductive cobalt coating allows one to determine the absolute origin of distance, as explained in the literature,^29,30 by means of sphere/plane capacitance measurements. For the carbon surfaces, an additional 3 nm thick amorphous carbon layer was deposited on top of the cobalt coating. Due to the carbon chemical neutrality, no oxide layer was measured: C–C bonds were detected, as well as traces of argon.²³ Using carbon surfaces allowed one to mimic nonmetallic surfaces such as DLC coatings frequently used in tribological applications. The deposition process was developed and explained in detail in ref (30). Full coverage of the coating had been ensured by observations, chemical analysis, surface energy measurements, and capacitive measurements. The thin layer of carbon was chosen to modify the surface chemistry without changing the roughness. In the remainder of the text, the indications (Co) and (CoC) will be used to refer to the measurements obtained on cobalt surfaces and carbon surfaces, respectively.

Table 2. Surface Characterization—Sphere Radii (R), Surface Energy Components (Dispersive γ^d_SV and Non-dispersive γ^nd_SV), and Wetting Angle with Dodecane (θ).

surfaces	R (mm)	γdSV (mJ/m2)	γndSV (mJ/m2) water	γndSV (mJ/m2) diiodomethane	θ (deg)
cobalt (Co)	2.3 ± 0.1				9 ± 3
carbon (CoC)	2.2 ± 0.1	≈25.4	≈11.9	≈30.6	≈0

Due to this thin coating deposition procedure, one could expect the roughness to be unmodified. This was confirmed by multiscale topography measurements using a Brüker Contour GT interferometry profilometer in phase shift interferometry mode over 47 × 63 μm² and a Park NX10 atomic force microscope (AFM) over 5 × 5 and 1 × 1 μm². The root mean square roughness was measured, with both the interferometer and the AFM, at 0.5 ± 0.3 nm for all the considered surfaces at each step of the deposition process (before deposition, after deposition of cobalt coating, and after deposition of carbon coating).⁹

Surface energy measurements were carried out using different solvents, such as water, diiodomethane, and dodecane, on carbon surfaces using the Fowkes method³¹ at 24 °C. The value of surface tension, resulting from the sum of dispersive and nondispersive components, is about 47 mN/m for the carbon surfaces. This value is close to the one measured in a previous study²³ for similarly produced surfaces and using the same measurement method. In the case of cobalt surfaces, the fast formation of the oxide makes the measurements more difficult and unreliable. Due to this time evolution, the values were not reported in Table 2. However, fresh cobalt surface energy would reach 2.5 J/m².³²

The silicon wafer plane has a Young’s modulus of 187 GPa for a Poisson’s ratio of 0.25 in the ⟨111⟩ directions. The shear elastic modulus was taken as 58 GPa according to ref (9). The silica sphere Young’s modulus is equal to 70 GPa for a Poisson’s ratio of 0.17. The shear elastic modulus of the isotropic silica was calculated from the latter values at about 30 GPa.

ATLAS Tribometer

The principle of the ATLAS molecular tribometer is described in detail in refs (29 and 30). Developed in Laboratoire de Tribologie et Dynamique des Systèmes (LTDS),³³ this tribometer realizes a contact between a sphere and a plane. It allows the simultaneous analysis of the interfacial mechanics (tribological response included) and the rheology of the confined fluid and/or the adsorbed layers on the surfaces, by means of the measurements of the displacements and the interaction forces, in both directions (normal z and tangential x) (see Figure 1c) using high-resolution capacitive sensors^30,33 in quasi-static and dynamic modes. In the dynamic mode, oscillations of small amplitudes of ±0.35 and ±0.15 nm at 38 and 70 Hz in the z and x directions, respectively, were superimposed to quasi-static sphere displacements. From these dynamic force and displacement measurements, the interfacial film rheology, that is, the viscoelasticity in terms of elastic stiffness and viscous damping, was deduced as detailed in ref (30). This analysis was performed independently in both directions, normal (z) and tangential (x), as shown in Figure 1c. A set of fresh and clean surfaces was prepared for each experiment. The time of transfer between the deposition chamber and the ATLAS chamber was optimized and carefully monitored to ensure “freshness” of the cobalt surfaces. A droplet of solution was deposited between the two surfaces.

Squeeze experiments were carried out for a closing speed, V_z, of 0.1 nm/s, while the progressive increase in normal force was measured. This choice of very slow normal velocity permitted to maintain quasi-static conditions and to avoid a viscous contribution to the squeeze. Steady-state friction experiments were realized at an imposed normal force, F_z = 1000 μN, at a sliding velocity, V_x = 1 nm/s. The confined film thickness and its variations were simultaneously measured during all tests thanks to in situ capacitive measurements between surfaces.

Experiments were performed between 24 and 26 ± 0.5 °C under 1 bar of argon. The relative humidity in the test chamber was 1–3%. Experiments were performed seven times, and three successive approach/retraction cycles were performed at the same position.

Results and Discussion

Interfacial Fluid Structuring

The viscoelasticity properties of the interface, that is, the elastic stiffness and the viscous damping, were characterized in both normal (z) and tangential (x) directions during approach and retraction. Figure 2 presents the corresponding experimental data of stiffness and damping values in normal and tangential directions (respectively, K_z, Im_z, K_x, and Im_x) for both interfaces. K_z is defined as the elastic stiffness of the interface in the normal direction, z, and Im_z corresponds to the viscous damping of the interface in the normal direction, z. Similar definitions are valid in the tangential direction, x. These data were obtained using superimposed dynamic measurements during squeeze. The evolution of these data was similar for both surfaces. It can be seen that values in the normal direction are much larger than those in the tangential direction. In addition, at large distance, the normal damping is larger than the normal stiffness, indicating a viscous regime, while, at short distance, an elastic regime dominates. It is worth noticing that the transition between an overall viscous to elastic behavior in the normal direction, Im_z∼K_z, happened at shorter separation distance for cobalt surfaces than carbon surfaces. In addition, in the tangential direction, the sudden increase in elastic stiffness K_x and viscous damping Im_x at a non-null separation distance is the signature of the presence of a tangentially stiff adsorbed layer on each surface.

Figure 2.

Superimposed approach and retraction curves showing the elastic tiffness, K, and viscous damping, Im, in both directions, normal z and tangential x, versus the separation distance, Z, for both interfaces; (a) cobalt surfaces and (b) carbon surfaces.

These observations were consistent with previous ones measured on various interfaces, from fatty acid to polymeric solutions between cobalt surfaces.^{5,7,10,12,34−38} In addition, data from approach and retraction were quasi-superimposed: a very small hysteresis was observed.

At large separation distances, the lubricated interface can be considered as a compressible fluid (the solvent) interacting with the substrates and the adsorbed layers, both assumed as rigid materials. According to Lai et al.,³⁹ the normal stiffness, K_z, can be theoretically approximated at large distance as follows

1

where K_f is the fluid compressibility and L₀ is the thickness of the adsorbed layer on each surface. The normal damping, Im_z, can be calculated following the classical Stokes’ law

2

Figure 3a,b shows the evolution of the normal stiffness and normal damping in logarithmic scale as a function of the distance Z, for the cobalt and the carbon surfaces, respectively. L₀ was equal to 2.2 ± 0.2 nm for the cobalt surfaces and 2.5 ± 0.2 nm for the carbon surfaces, respectively. These values were adjusted from the evolution of the damping function Im_z, and the viscosity value was equal to η = 28 mPa·s, as measured with the rheometer. Then the only adjustable parameter in the evolution of the stiffness K_z was the fluid compressibility, K_f, equal here to 92 ± 3 and 45 ± 2 MPa, respectively.

Figure 3.

Dynamic experimental measurements of normal stiffness, K_z, and damping, Im_z, as a function of the separation distance, Z, for the cobalt surfaces (a) and the carbon surfaces (b) with a schematic of the interface (inset in a). The theoretically calculated values were also plotted as a dashed line for a viscosity, η = 28 mPa·s. The confrontation to experimental data provided a value of fluid compressibility, K_f, that depends on the surface: K_f = 92 ± 3 MPa for the cobalt surfaces and 45 ± 2 MPa for the carbon surfaces, respectively (also in the dashed line). The values of 2L₀ are also indicated (a,b), corresponding to the thickness of the immobile layer schematically represented in the inset (a). The solution provided by the full numerical modeling is represented in the continuous line with the values indicated in Table 3.

The good agreement between the experimental and theoretical data confirms the existence of an adsorbed layer on the surfaces. This thickness L₀ on each surface corresponds to an immobile layer which does not participate to the hydrodynamic flow.^30,35 It is an average value measured over an area of characteristic dimension of √(R.Z) ∼ 4 μm.^29,33Z is the separation distance corresponding to 50–100 nm, as the immobile layer is obtained from dynamic measurements at a large separation distance. It is most likely composed of amine-based friction modifier molecules. However, some base oil molecules also compose this layer.

This agreement also indicates that the chemistry of the surface modified the fluid structuring at the solid interface, as shown by the significant variations of the fluid compressibility measured between cobalt and carbon surfaces.

Adsorption and Boundary Film Formation

Figure 4a presents the evolution of the normal force, F_z/R, as a function of the separation distance, D, taking the surface compliance and deformation into account,^30,35 for both cobalt and carbon surfaces separated by the amine solution during approach and retraction of a quasi-static squeeze experiment. Hysteresis was observed for the cobalt surfaces between approach and retraction, suggesting a viscoelastic behavior of the confined layer, although the approach–retraction curves were superimposed for the carbon surfaces. A zoom shown in Figure 4b indicated a repulsive force at relatively large distance, around 2L ≈ 14 nm, much larger than the size of the amine molecules, for the cobalt interface, and an attractive force followed by a repulsive force at shorter separation distance (about 8 nm, still larger than the amine molecule size) for the carbon interface. In this latter case, the measured attractive force was fitted using van der Waals force for a sphere/plane configuration, F_vdw = −H.R/6D², with H being the Hamaker constant and R being the sphere radius. The fit provided an average value of the Hamaker constant, H, of the heterogeneous interface consisting of cobalt/carbon/amine/carbon/cobalt. The value was equal to 34 × 10^–20 J for a separation distance of the same order of magnitude as the carbon thickness. This value can be compared to that of carbon surfaces separated by a hydrocarbon base oil at 1.17 × 10^–20 J²³ or to similar values measured in the case of cobalt coated surfaces separated with oleic or elaidic acid complete monolayers.⁷ This seems to indicate that despite a clear influence of the carbon surfaces on the amine adsorption and the existence of van der Waals interactions, the constant H that was fitted here was not a characteristic of the carbon/amine layer/carbon interface only but an average value of the whole interface.

Figure 4.

a) Normal force evolution as a function of the separation distance, D (a). This separation distance was calculated by taking the surface compliance and deformation into account, for both sets of surfaces. The cobalt surfaces are represented in gray squares, and the carbon surfaces with black circles. (b) Zoom in on the attractive and/or repulsive force at the onset of contact. The dashed line in (b) corresponds to the fit of van der Waals force with an average Hamaker constant of 34 × 10^–20 J. The meaning of this value is discussed in the text.

Following the first repulsion, the normal force increased as the separation distance, D, remained more or less constant, reaching the elastic wall of thickness 2L_c, as presented in Figure 4a. Both solid and adsorbed layers may deform elastically. The value of 2L_c was measured at a normal force of 1 mN. For both cobalt and carbon surfaces, this value was equal to 2L_c(Co) = 5.4 nm ± 0.5 nm and 2L_c(CoC) = 5.2 nm ± 0.5 nm, respectively, very close to the value of 2L_TA.

A hysteretic/nonhysteretic behavior was also observed for the evolution of the tangential stiffness, K_x, between cobalt and carbon surfaces, respectively: a zoom presented in Figure 5a,b highlights the difference, especially at the onset of contact between the two adsorbed layers. This behavior was reproducible for three successive experiments at the same position. This seems to indicate that no adsorbed amines were displaced from the surface.

Figure 5.

Zoom on the tangential stiffness, K_x, evolution as a function of the separation distance, D, for cobalt (a) and carbon (b) surfaces. The arrows indicate the approach/retraction. The hysteresis observed in the case of cobalt surfaces was quantified by a 0.7 nm difference in the distance from which the tangential stiffness starts increasing.

This force-thickness-tangential stiffness characterization allowed us to discuss the boundary film formation and to try to describe schematically the different molecular organizations on both surfaces. The polar function of the anchors of the friction modifier molecules, here an amine group, tends to indicate that the molecules are physically attracted to the cobalt metallic surfaces: the sub-nanometric oxide layer²⁹ at the extreme surface creates an oxygen-induced chemical potential that increases the amine affinity with the surface.²⁴ The molecules are supposed to adsorb more or less vertically^17,35 by replacing/exchanging with the nonpolar solvent molecules. However, the surface occupied by a triamine molecule was calculated using a projection of the anchor on the surface: it was between 0.38 and 0.55 nm².²⁸ Due to this rather large value combined with the complex molecular architecture of this friction modifier, one could expect a nondense or incomplete adsorbed layer. For the sake of comparison, a monolayer of elaidic acid with a 94% surface coverage ratio was associated with 0.22 nm² occupied surface/molecule.⁷

In addition, the ratio between L₀ (measured at large distance) and L_c (confined thickness) in both cases is an indication of the surface coverage:^5,7,35L₀/L_c(Co) = 0.8 < L₀/L_c(CoC) = 0.9. This ratio seems to indicate that the exchange process between amine molecules and nonpolar solvent molecules at the vicinity of the surface is enhanced for the carbon surfaces.

This ratio is in good agreement with the force–distance curve evolution observed for the cobalt surfaces. The repulsive force measured at a large distance, 2L ≈ 14 nm, for the cobalt surfaces could be due to the presence of multiple layers locally on the surfaces. However, the immobile layer has a thickness of the same order of magnitude as the molecule length. The latter being an average value, multiple layers would not be predominant on the surfaces. Another explanation relies on the presence of solvent molecules being transiently trapped within the interface during squeeze. A less dense monolayer on cobalt surfaces would favor the presence of some solvent molecules. The low quasi-static approach velocity, here 0.1 nm/s, allowed most of these large solvent molecules to be removed from the interface, and as the confinement increased, the film thickness reached the elastic wall value of 2L_c ≈ 2L_TA. The increase of the tangential stiffness, K_x, for separation distance smaller than 2L_x ≈ 6 nm, would favor this interpretation as well as the hysteresis measured both on the normal force, F_z, and the tangential stiffness, K_x, during loading/unloading. A schematic description of the molecular organization is proposed as a function of the separation distance in Figure 6.

Figure 6.

Schematic of the molecular organization on cobalt and carbon surfaces at a large distance (a) and for a separation distance equal to 2L_c ≈ 2L_TA (b). The molecule and its characteristic dimensions are also represented. For the sake of clarity, the base oil molecules were not drawn in (a) but only drawn in (b) represented by yellow coils.

In the case of the carbon surfaces, the force and tangential stiffness evolution, which are both nonhysteretic during approach/retraction, associated with the existence of van der Waals interaction at approach and a larger value of tangential stiffness seem to indicate that the monolayers on carbon are denser, i.e., more complete than the one on cobalt surfaces and that no solvent molecules remained trapped during approach. The corresponding schematic description is presented in Figure 6.

Mechanical Characterization of the Boundary Film

From Figures 2 and 4, an elastic shear modulus, G, of the adsorbed layer can be calculated for both surfaces^29,35

3

where a_c is the contact radius, calculated either with Hertz theory or DMT theory. This equation assumed that the amplitude of the dynamic oscillations was small enough to avoid any sliding and that the substrates were much more rigid than the boundary layers. For a normal force of 1 mN, the application of this equation gives G(Co) = 19 ± 3 and G(CoC) = 23 ± 3 MPa.

Taking the substrate rigidity into account, Gacoin et al.⁴⁰ proposed the following equation for the shear elastic modulus of the adsorbed layer, G_c

4

where is the reduced elastic shear modulus of the dry sphere/plane contact, here equal to 11 GPa. Corresponding G_c values for both surfaces were equal to G_c(Co) = 30 ± 4 and G_c(CoC) = 40 ± 2 MPa.

The comparison of G and G_c shows that G < G_c, meaning that the coupling between the adsorbed layers and the substrates must be considered. The values of the elastic shear modulus for both surfaces are reported in Table 3. It is noteworthy that eqs 3 and 4 remain valid for such thin films, as shown by previous studies.^39,40

Table 3. Mechanical Properties of the Adsorbed Layer and Separating Fluid as a Function of the Surface Chemistry.

surfaces	thickness of adsorbed layer L0 (nm)	fluid compressibility Kf (MPa)	adsorbed layer shear modulus Gc (MPa)	adsorbed layer elastic modulus Kc′ (MPa)	adsorbed layer viscous modulus Kc″ (MPa)
cobalt (Co)	2.2 ± 0.2	92 ± 3	30 ± 4	1000 ± 50	800 ± 50
carbon (CoC)	2.5 ± 0.2	45 ± 2	40 ± 2	500 ± 50	400 ± 40

The full numerical modeling of the squeeze response was performed according to previous literature,³⁹ and the results were plotted in a continuous line, as shown in Figure 3. This was carried out by solving the generalized oedometric Reynolds equations under harmonic solicitation and in the presence of an adsorbed layer of thickness L₀ on each surface.³⁹ Compared to previous experimental data,^7,39 in the case analyzed here, the viscoelasticity of the adsorbed layers had to be integrated in order to reproduce the values of normal stiffness K_z and normal damping Im_z evolution at short distances. This was realized using a complex modulus, such as K_c = K_c^′ + i K_c^″, for the adsorbed layer where K_c^′ represents the elastic part and K_c^″ the viscous part, respectively. This analysis provided a value of the elastic modulus of the adsorbed layer, K_c^′, equal to 1000 ± 50 MPa for the cobalt surfaces and 500 ± 50 MPa for the carbon surfaces, with a comparatively large viscous contribution at K_c^″, equal to 800 ± 50 MPa for the cobalt surfaces and 400 ± 40 MPa for the carbon surfaces. All of the values are reported in Table 3.

It is noteworthy that the fit quality was lower for the adsorbed layers on cobalt surfaces, indicating the probable presence of base oil molecules mixed in the adsorbed amine layer and disturbing the molecular organization: in the mechanical modeling, the adsorbed layer was indeed considered homogeneous. The presence of base oil molecules would explain the repulsive normal force measured at large distance, and it would also confirm the hypothesis of an incomplete amine monolayer on cobalt surfaces.

Even though the ratio between K_c^″ and K_c^′ is similar in both cases, the value of the viscous contribution of the adsorbed layer on the cobalt surfaces K_c^″(Co) is twice as much as the one for carbon surfaces, K_c^″(CoC): this could explain the hysteretic behavior observed during approach/retraction for the cobalt surfaces.

Finally, the values of the elastic modulus K_c and shear modulus G_c allowed us to estimate the Poisson ratio, ν, of the adsorbed layers following

5

and providing ν(Co) = 0.485 > ν(CoC) = 0.469, that is, the adsorbed layer on cobalt surfaces is more incompressible than the one on carbon surfaces.

Friction Response of the Boundary Film

Finally, Figure 7 reports the steady-state friction as a function of the sliding distance for two monolayers in contact for both surfaces, under a constant normal force, F_z = 1 mN and a constant sliding velocity, V_x = 1 nm/s. The sliding distance was about 40–60 nm, much larger than the molecule size (nanometers) and smaller than the contact diameter (few micrometers). This value of sliding distance was chosen to ensure that steady-state friction was reached. Three phases can be distinguished: a linear reversible phase in which the friction force increased with the sliding distance due to the elastic deformation of the interface with a characteristic tangential stiffness K_x, a nonlinear phase in which the tangential force increased until an equilibrium steady-state value F_x (surface), and the phase where the tangential force remained constant at its steady-state value.

Figure 7.

Friction force, F_x, vs the sliding distance X under constant normal force, F_z = 1 mN and a constant sliding velocity, V_x = 1 nm/s for cobalt (gray square) and carbon (black circle) surfaces. The film thickness is equal to 2L_c corresponding to two adsorbed layers sliding against each other. The tangential stiffness, K_x, is indicated showing that K_x(CoC) > K_x(Co). The values of tangential stiffness K_x calculated from the slope of the F_x–X curves are identical with the ones measured using dynamic measurements. The friction forces depend on the chemistry of the surfaces. The threshold distance X* = F_{x,steady-state}/K_x, is also shown for both cases: X*(CoC) ≈ 2 nm < X*(Co) ≈ 5 nm.

Thanks to our independent measurements of the friction force and the tangential stiffness, the origin of friction can be discussed. As well-established, the level of steady-state friction results from the product between the tangential stiffness and the critical threshold.³⁵ Here, despite a slightly lower tangential stiffness K_x(Co) = 105,400 N/m < K_x(CoC) = 118,200 N/m, the tangential force F_x(Co) reached in the case of the cobalt surfaces is larger than the one measured for the carbon surfaces. This difference of behavior was attributed to the threshold distance X* = F_x/K_x that is smaller for the monolayers adsorbed onto the carbon surfaces: X*(CoC) ≈ 2 nm < X*(Co) ≈ 5 nm. This distance X* corresponds to the distance beyond which the interface is no longer elastically deformed and starts sliding.³⁵ This smaller threshold distance in the case of carbon surfaces could be related to more complete monolayers.

If the friction mechanisms remain similar for both surfaces, the effect of surface chemistry was clearly visible in the level of friction that resulted from the monolayer surface coverage and the tangential mechanical properties of the adsorbed layers: the molecular organization governed by the interactions between the surface chemistry and the molecule anchor led to a tangentially stiffer and more complete layer on carbon surfaces.

Conclusions

We showed that surface chemistry strongly contributes to the molecular organization of amine-based friction modifier monolayers, regardless of their roughness. This molecular organization was identified thanks to force and displacement measurements and was also correlated to the viscoelasticity of the resulting boundary layers and to their friction response.

Even though surface energies of carbon and oxidized cobalt surfaces were similar, the molecular organization of the adsorbed boundary layers was impacted by the chemical modification of the surfaces while keeping the roughness constant and sub-nanometric.

Confined characteristic thickness measurements for the amine-based friction modifier boundary films were similar. However, an attractive force during approach at a short separation distance was observed on the carbon surfaces. Conversely, the organization on cobalt surfaces resulted in a longer range of repulsion. We also assessed the mechanical properties of both boundary films in both directions. In the normal direction, the boundary films exhibited highly viscoelastic behavior. The analysis of this behavior indicated that the film on cobalt surfaces consisted of an incomplete amine monolayer mixed with base oil molecules while the film on carbon surfaces was made of a more complete amine monolayer. In the tangential direction, the film on the carbon surfaces was stiffer.

This variation in the molecular organization of the adsorbed layers resulted in two changes. For large separation distances, we showed that bulk fluid structuring in the vicinity of the surface was modified, resulting in a strong variation of the fluid compressibility. When these boundary layers were in contact, we measured a lower friction dissipation for the layers adsorbed on carbon surfaces, which was attributed to variations in the tangential elastic stiffness and coverage ratio.

Glossary

Nomenclature

a_c

contact radius according to Hertz or DMT theory (m)

D

separation distance integrating the elastic deformation of the sphere and the plane (m)

F_x

friction or tangential force (N)

F_z

normal force (N)

F_vdw

van der Waals force (N)

G

G_c shear elastic modulus of the adsorbed layer calculated with eqs 3 and 4 (Pa)

H

Hamaker constant

Im_x

viscous damping in the tangential direction (N/m)

Im_z

viscous damping in the normal direction (N/m)

K_f

bulk fluid compressibility (Pa)

K_c

mechanical modulus of the adsorbed layer, K_c = K_c^′ + i·K_c^″, where K_c^′ is the elastic component and K″_c is the viscous component

K_x

elastic stiffness in the tangential direction (N/m)

K_z

elastic stiffness in the normal direction (N/m)

L₀

thickness of the immobile layer (m)

L

separation distance of onset of normal force (m)

L_c

confined thickness (m)

L_TA

length of the molecule (m)

L_x

separation distance of onset in increase in K_x (m)

R

sphere radius (m)

V_x

sliding velocity (m/s)

V_z

normal velocity during approach/retraction (m/s)

X*

threshold distance during sliding (m)

ϕ

diameter of the area occupied by a molecule adsorbed on the surface (m)

γ^d_SV

dispersive component of the surface energy (J/m²)

γ^nd_SV

nondispersive component of the surface energy (J/m²)

η

bulk fluid viscosity (Pa·s)

θ

wetting angle with dodecane (deg)

υ

Poisson ratio of the adsorbed layer

ω_z

pulsation of the oscillation in the normal direction (rad/s)

Author Contributions

All authors contributed equally. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.

Special Issue

Published as part of Langmuirvirtual special issue“2023 Pioneers in Applied and Fundamental Interfacial Chemistry: Nicholas D. Spencer”.