Boundary Lubrication Mechanisms for High-Performance Friction

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Surfaces, Interfaces, and Applications

Boundary Lubrication Mechanisms for High-Performance Friction Modifiers Xingliang He, Jie Lu, Michael Desanker, Anna Magdalene Invergo, Tracy L. Lohr, Ning Ren, Frances E. Lockwood, Tobin J. Marks, Yip-Wah Chung, and Q. Jane Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b11075 • Publication Date (Web): 05 Nov 2018 Downloaded from http://pubs.acs.org on November 6, 2018

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ACS Applied Materials & Interfaces

Boundary Lubrication Mechanisms for High-Performance Friction Modifiers Xingliang He,a,§ Jie Lu,a,§ Michael Desanker,b Anna Magdalene Invergo,b Tracy Lynn Lohr,b Ning Ren,c Frances E. Lockwood,c Tobin J. Marks,b,* Yip-Wah Chung,d,* Q. Jane Wanga,* aDepartment

of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208-3113, USA bDepartment of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, USA cValvoline Inc., Lexington, Kentucky 40512, USA dDepartment of Material Science and Engineering, Northwestern University, Evanston, Illinois 60208-3113, USA §Both

*E-mails:

authors contributed equally to this work

(T.J.M.) [email protected]; (Y.-W.C.) [email protected]; and (Q. W.) [email protected]

Abstract. We recently reported a new molecular heterocyclic friction modifier (FM) that exhibits excellent friction and wear reduction in the boundary lubrication regime. This paper explores the mechanisms by which friction reduction occurs with heterocyclic alkyl-cyclen FM molecules. We find that these chelating molecules adsorb onto (oxidized) steel surfaces far more tenaciously than conventional FMs such as simple alkylamines. Molecular dynamics simulations argue that the surface coverage of our heterocyclic FM molecules remains close to 100% even at 200 °C. This thermal stability allows the FMs to firmly anchor on the surface, allowing the hydrocarbon chains of the molecules to interact and trap base oil molecules. This results in thicker boundary film thickness compared with conventional FMs, as shown by optical interferometry measurements. Keywords: Boundary lubrication film, surface adsorption, friction modifier, heterocyclic, elastohydrodynamic lubrication 1. Introduction Friction is inevitable in the operation of all machinery.1-6 Lubricants are used to minimize friction, protect surfaces from wear and corrosion, dissipate heat, provide hermetic sealing, carry away debris, buffer vibrations, and reduce the risk of failure.7-12 Under mild rolling or sliding conditions, friction modifier (FM) molecules in a formulated lubricant help mitigate friction and wear in the boundary lubrication regime.13-14 The chemical compositions and structures of organic FM molecules vary with applications, but they all consist of hydrocarbon chains attached to polar functional groups that allow FM molecules to form adsorbed layers on machine component surfaces through noncovalent and covalent intermolecular interactions with surface hydroxyl and oxo groups, and metal atoms. The hydrocarbon tails trap base oil molecules near the surface to increase asperity separation and thus lower surface shear.15-18 Unlike traditional anti-wear and extremepressure additives that chemisorb and react with surfaces, FMs typically physisorb onto the metal surfaces. As a result, most conventional FMs do not bind strongly to surfaces and thus provide only limited protection at elevated temperatures. FMs with stronger physisorption to the surface would 1 ACS Paragon Plus Environment

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form more resilient boundary lubrication films on mechanical surfaces, leading to reduced friction and wear. It is challenging to characterize ultra-thin physisorbed FM films on fluid-lubricated surfaces under contact and in motion using conventional materials and surface science spectroscopic techniques. Elastohydrodynamic lubrication (EHL) film thickness measurements provide accurate in-situ film thickness information for virtually all lubricants.19-26 This optical-interferometry-based method can measure lubricant film thickness from less than 1.0 nm to several µm as a function of speed, load, and temperature. When extrapolated to zero speed (at which the hydrodynamic effect vanishes), the measured film thickness represents the boundary lubrication film formed under the influence of the physisorbed FMs and other lubricant additives. Such measurements provide an easy comparison of the effectiveness of different FMs in forming protective boundary lubrication films at various temperatures. We previously reported the development of a class of alkyl-cyclen FMs. Using a Group III or PAO4 base oil as references, the friction reduction achieved using the alkyl-cyclen FMs is as large as 70% at 200 °C, while that achieved by the commercial alkylamine counterparts is no more than 40% under the same conditions. This manuscript is the second of a two-part study on the tribological/surface science properties of alkyl-cyclen FMs. In refs.27-28 we reported in detail the synthesis, characterization, surface science, and lubrication performance of these “tetradentate” tetramine heterocyclic FMs. In that work we also pointed out that it was the heterocyclic structure and tailored side chains that led to the low friction. The present manuscript details the mechanisms by which this molecular structure achieves low friction based on tribology experiments and MD simulations which reveal enhanced ultra-thin boundary lubrication films, enhanced surface adsorption, improved adsorption stability, and favorable thermodynamic conditions. We believe these mechanisms are important to lubrication scientists and engineers. The surface analysis tools we applied in our previous work included nitrogen X-ray photoelectron spectroscopy (XPS), aqueous contact angle goniometry, X-ray reflectivity (XRR), and a series of tribological tests over a wide range of conditions including variable-temperature sliding, linear speed ramping, reciprocating sliding, and rolling-sliding contacts. From this, we determined that the multiple nitrogen centers of the alkyl-cyclen FMs enabled cooperative binding to the surface, imparting strong surface adsorption and lubricant film durability in the boundary lubrication regime. These surface analysis measurements confirm that the tetradentate FMs are superior friction reducers compared to monodentate and bidentate FMs as a result of forming more strongly bound, more durable tribological interfaces. Equally important, the previous work set the stage for the present mechanistic study to better understand why alkyl-cyclen FMs exhibit such superior performance using the in-situ EHL experimental technique. The unique and insightful surface science provides that EHL studies are complementary to the previous static, ex-situ surface analyses. Reported in this paper are boundarylubrication film thickness measurements for lubricants containing various FM additives as a function of temperature, molecular dynamics (MD) simulations to estimate their adsorption strengths, and microscale scratch testing to evaluate the adhesion and durability of these adsorbed FM layers. The findings provide mechanistic insights underlying the exceptional boundary lubrication performances of alkyl-cyclen FMs at elevated temperature, which were not discussed in the aforementioned alkyl-cyclen synthetic, surface science, and initial tribological contributions. The significant extensions of that work reported here are additional EHL experiments and analysis on the new heterocyclic additives with varying alkyl substituents, the study of the temperature and concentration dependence, as well as the evaluation and analysis of cyclen boundary lubrication improvements by coupling in-situ EHL experimental results and the computational simulations of the surface adsorption processes. 2 ACS Paragon Plus Environment

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2. Experimental and Simulation Methods 2.1. Materials and test instrumentation FM additives, base oil, and test specimens. Three alkyl-cyclen FM additives with different side chain lengths, C6Cyc (508 g/mol), C12Cyc (844 g/mol), and C18Cyc (1,180 g/mol), were studied in this contribution. Detailed information on the synthesis and characterization of the heterocyclic FMs were reported elsewhere.27-28 Two commercial FMs, an alkylamine (Armeen T) and an alkyldiamine (Duomeen C) from AkzoNobel, were tested for comparison. They were chosen because their polar groups and those of the alkyl-cyclen FMs have the same nitrogen donor functionality. Figure 1 shows the structures of the FM molecules. The melting points of C18Cyc and Armeen T were determined to be 73 °C and 57 °C, respectively, using differential scanning calorimetry (DSC). A pure Group III oil containing no additives obtained from Valvoline Inc. was used as the base oil. Glass discs coated with a 20 nm thick Cr layer and a 500 nm thick SiO2 spacer layer were obtained from PCS Instruments. E52100 steel balls used in EHL experiments had typical chemical composition as follows: sulfur, ~ 0.025 wt. %; silicon, ~ 0.15 - 0.35 wt. %; phosphorus, ~ 0.025 wt. %; manganese, ~ 0.25 - 0.45 wt. %; chromium, ~ 1.30 - 1.60 wt. %; carbon, ~ 0.95 1.1 wt. %; and the balance iron.

Figure 1. Molecular structures of FMs studied in this research. Cn indicates the presence of alkyl chains between 12 - 18 carbons long. EHL apparatus and lubricant film measurements. A PCS EHD Ultra-Thin Film Measurement System was used to measure the lubricant film thickness of the Group III oils containing the various FM additives at 25 ºC and 125 ºC. This film thickness measurement system consists of a ball-ondisc tester and a white-light interferometer. The latter was used for in situ measurement of the central thickness of the lubricant film formed between the surfaces of the glass disc and the steel ball in circular contact. Under pure rolling conditions, the disc velocity was increased from ~ 1 mm/s to 3,500 mm/s while maintaining the load at 20 N (maximum Hertzian contact pressure ~ 540 MPa). Variation of lubricant film thickness versus the entraining speed was then recorded during EHL tests.

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Microscale scratching experiments. Microscale scratch testing was used to evaluate the adsorbed FM coatings on silicon surfaces (5 mm × 5 mm). Each tested FM was dip-coated onto the silicon wafer surface. Before coating, the silicon substrates were cleaned in an ultrasonic bath with hexane, isopropyl alcohol, and acetone in turn, followed by a 5 minute oxygen-plasma cleaning in a Harrick PDC-32G Plasma Cleaner. C18Cyc and commercial Armeen T were dip-coated onto the silicon substrate. The dip coating process was conducted by immersing the substrate in the respective pure FM liquid at 120 °C (above the FM melting point) from 30 sec to 24 h. The FM-coated silicon wafer was then withdrawn from the melted FM, and the excess FM liquid near the bottom edge was removed using Kimberly-Clark Kimtech Delicate Task Wipers. These FM-coated surfaces were then subjected to microscale scratching experiments at room temperature using a Micro Materials NanoTest system under different loads, 5 mN, 10 mN, 20 mN, 40 mN, and 60 mN. The scratching tests were conducted with a spherical steel tip (⌀ 2 mm) slid over the FM-coated specimen at 1 μm/s for 300 μm at room temperature. The lateral and normal forces were recorded simultaneously. The averaged coefficients of friction and standard deviations were then extracted from the measured data for further analyses. 2.2. MD simulation An MD model was built for simulating the adsorption and desorption of the pure FM molecules on a silica surface. Thus, a 54 Å × 54 Å × 70 Å hydrated silica surface was used in the MD simulation model, and the [001] direction was set as the z axis. The hydrated silica surface was selected because the structure of such a surface has previously been established,29 and a surface populated with OH groups mimicking the environment encountered by FM molecules in engines. Based on several previously reported studies, each silicon atom in the (001) surface plane was grafted with two hydroxyl groups, affording a number density of 8.05 OH per nm2. Periodic boundary conditions were applied in all three directions. A 10 nm high vacuum space above the surface was reserved for the motion of FM molecules. This is 10 times the cut-off distance of nonbounded interactions and is large enough to neglect the influence of the top image surface. Acquisition of precise partial charges is crucial for simulating an adsorption process. Thus, the Gaussian 09 software package at the 6-31G* level was used to optimize the structure of this model surface layer with a B3LYP function, while the Charge Equilibration (QEq) method was used to obtain partial charges of all the other atoms in the system.30 The Tersoff force field31 and the Consistent Valence Force field (CVFF)32 were used for the hydrated silica substrate29 and the FM molecules, respectively. The Tersoff potential is a widely used forcefield for materials containing silicon and/or carbon.33-34 The CVFF was used due to the fact that the FM systems simulated in this study were similar to those modeled for carbohydrate molecules35 and Langmuir–Blodgett monolayers of different carboxylic acids.36-37 Hexylamine (C6amine), dodecylamine (C12amine), and octadecylamine (C18amine) molecules (Figure 1) were modeled in MD simulations for side-by-side comparisons of the results with the corresponding alkyl-cyclen molecules. The number of nitrogen atoms in each FM system was held constant at 100, i.e., 25 alkyl-cyclen molecules versus 100 alkylamine molecules were simulated. The systems were modeled using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).38 Only the adsorption of pure FM molecules was considered in the simulation, and these molecules were initially placed and adsorbed uniformly near the surface.39-40 The initial molecular coverage of alkyl-cyclen and alkylamine molecules was set at 0.857 molecules/nm2 and 3.43 molecules/nm2, respectively. This ensures full surface coverage and is consistent with similar systems reported elsewhere.41 The total simulation time was 15 ns for stabilized systems. The Canonical (NVT) ensemble was used to simulate the surface adsorption, and the Nose-Hoover thermostat was used to control temperature. Interaction energy was calculated by summation of the 4 ACS Paragon Plus Environment

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Coulomb energy and the Lennard-Jones potential energy of all atoms or molecules of all hydroxyl groups and FM molecules. The random walk of one adsorbed FM molecule on the substrate was simulated by calculating the mean square displacement (MSD) using eq. (1),42-43 where N is the number of molecules

MSD 

1 N



N n 1

[ xn (t ) xn (0)]2

(1)

averaged, xn(t) is the position of the molecules at determined time t, and xn(0) is the reference position of the molecules. Random walk is used to reveal the surface diffusion kinetics and hence surface binding strength of different adsorbed FM molecules. A larger MSD means larger diffusivity and weaker binding of the FM molecule 3. Results and Discussion 3.1. Boundary film thickness Figure 2 shows the EHL film thickness of the base oil versus entrainment speed at different temperatures. In general, the film thickness measured follows the trend shown by the HamrockDowson eq. (2)44-47 before deviation at lower speeds, as the systems enters into the boundary lubrication regime. Here Hc is the central film thickness,  is the pressure-viscosity coefficient,

 

H c  2.69 E

' 0.53

 U0   '   E Re 

0.67

 F   ' 2   E Re 

0.067

1  0.61e

 0.73 k

R

e

(2)

E’ is the effective elastic modulus of the contacted solid bodies, U is the entrainment velocity, 0 is the lubricant viscosity under ambient condition, Re is the combined radius of curvature of the two surfaces in the direction of lubricant entrainment, F is the normal load, and k is the contact ellipticity parameter, which is 1 for the current case. Based on eq. (2), a log-log plot of film thickness versus entrainment speed should yield a straight line, as highlighted by the solid lines in Figure 2 for pure Group III oil. A critical entrainment speed can be defined, below which the film thickness does not follow the Hamrock-Dowson equation, as marked by the vertical dotted lines in Figure 2. This critical speed appears to increase with temperature. Extrapolation to zero entrainment speed gives approximately the thickness of a boundary lubrication film, about 5 nm at 25 °C and about 1 nm at 125 °C (Figure 2) for the present Group III base oil.

Figure 2. Lubricant film thickness of Group III oil as a function of entrainment speed at different temperatures. The EHL experimental results clearly show the experimental film thickness-speed 5 ACS Paragon Plus Environment


variation follows the Hamrock-Dowson equation in hydrodynamic lubrication regime. The straight lines serve to qualitatively indicate the linear variation in the log-log plots. Figure 3 presents the film thickness results obtained for Group III oil at different temperatures with five different FMs: C6Cyc, C12Cyc, C18Cyc, Armeen T, and Duomeen C. C18Cyc and Armeen T have poor oil solubility at room temperature. The thick films at low speeds in Figure 3a observed for these two FMs are due to building up of the insoluble additives in the ball-disc contact. C6Cyc, C12Cyc and Duomeen C in the Group III oil display no measurable improvement of the boundarylubrication film at 25 ºC. At 75 ºC, boundary lubrication film enhancement starts to show for alkylcyclen FMs and Armeen T (Figure 3b). Such boundary film improvement by alkyl-cyclen FMs is proportional to the chain length. The most notable lubricant film thickness enhancement in the boundary lubrication regime is observed in the presence of 1% alkyl-cyclen additives at 125 ºC. In Figure 3c, the boundary film thickness is about 6 nm with C18Cyc and about 2 nm with C12Cyc. This enhanced film thickness that provides physical separation between asperities is likely the key to the reduced friction in the boundary lubrication regime. The boundary film thickness scales with the carbon chain length. This suggests that the formation of this boundary film may be related to the entanglement between FM hydrocarbon chains and the base oil molecules, due to dispersive forces among alkyl chains.48-49 The film thickness of the lubricant drops precipitously with the addition of Armeen T or Duomeen C at 125 ºC. This suggests that the presence of amine-based FMs destabilizes the lubricant film at elevated temperature. Moreover, inferior EHL performance is found for the alkyldiamine (Duomeen C) over the alkylamine (Armeen T) in Figure 3. This poor lubricant film formation performance likely reflects the alkyl chain length differences, as well as impurities and low-molecular weight components.


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Figure 3. EHL film thickness versus entrainment speed for Group III oil with addition of different FMs at 25 ºC (a), 75 ºC (b), and 125 ºC (c). The EHL test results for Armeen T and Duomeen C shown in (c) is reprinted with a permission from "Alkyl-Cyclens as Effective Sulfur- and Phosphorus-Free Friction Modifiers for Boundary Lubrication" by M. Desanker and X. He, et al., ACS Appl. Mater. Interfaces, 2017, 9, 9118–9125. Copyright (2017) American Chemical Society. 7 ACS Paragon Plus Environment


Figure 4 shows how the film thickness is affected by the concentration of C12Cyc and C18Cyc dissolved in the Group III oil at 125 ºC. The boundary film thickness as the speed approaches zero is relatively insensitive to concentration: 2.0 ± 0.5 nm for C12Cyc between 0.1 and 1.0 wt.%, increasing to 6.0 ± 1.0 nm for C18Cyc between 0.1 and 1.0 wt.%.

Figure 4. EHL film thickness versus entrainment speed for Group III oil with addition of (a) C12Cyc and (b) C18Cyc at 125 ºC, at 0.1, 0.5, and 1.0 wt.% concentration. 3.2. MD simulation of surface adsorption of FM molecules MD simulations were conducted to gain further insight into the adsorption characteristics of the different FM molecules on the hydrated silica surface. Cyclen FMs are thermally stable with a decomposition onset temperature above 300 ºC. Within the temperature range simulated, the cyclen FM molecules could hardly be decomposed, and the four anchoring sites from the same heterocyclic core should act as a single entity during surface adsorption. Figure 5 plots the variation of interaction energy versus simulation time for different adsorbed alkyl-cyclen and alkylamine FM molecules at different temperatures. Higher interaction energy means stronger adsorption of FM molecules to the surface. There are three notable features shown in Figure 5. First, higher temperature results in weaker interaction between FM molecules and the surface, a result of increased adsorbate-surface separation due to thermal excitation. Second, C12Cyc and C18Cyc molecules always have higher interaction energies than C12amine and C18amine regardless of the temperature. As the same number of nitrogen atoms is simulated, the alkyl-cyclen FM system still have a higher interaction energy per nitrogen than does the alkyl amine system. The cooperative binding status of a multi-dentate molecule is also dependent on the density of available surface 8 ACS Paragon Plus Environment

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active sites, i.e., hydroxyl groups in the present research. An even greater interaction energy difference between the alkyl-cyclen and alkylamine molecules can be anticipated if the density of the surface active sites was greater. Third, alkyl-cyclen FM molecules with longer alkyl chains have higher interaction energies, suggesting the participation of their alkyl chains in surface interactions. Specifically, the analyses of short ethane (C2) and butane (C4) molecules demonstrate that the internal rotation of the terminal methyl groups with respect to their backbones induces an ineffective inter-chain cohesion due to the steric effects.50-53 The short alkyl chains of the C6Cyc molecules may undergo ineffective chain cohesions as well due to the internal rotation of the terminal methyl groups. A well-packed layer of the torsional short chains is not energetically favorable for surface adsorption. As a result, desorption of short-chain cyclen molecules occurs when the interaction energy decreases significantly with temperature.

Figure 5. Simulated interaction energies of adsorbed alkyl-cyclen (solid symbols) and alkylamine (open symbols) FM molecules at different temperatures. Comparisons of C6Cyc vs. C6amine, C12Cyc vs.C12amine, and C18Cyc vs.C18amine are shown in (a), (b), and (c), respectively. Figure 6 compares the mean-square-displacement (MSD) values of different adsorbed FM molecules at 120ºC. After 15 ns, the MSD values for C12Cyc and C18Cyc are about one order of magnitude lower than those for C12amine and C18amine. This indicates that these alkyl-cyclen 9 ACS Paragon Plus Environment


molecules are adsorbed more strongly than the corresponding alkylamine counterparts. The unexpectedly small MSD value for C6amine is an artifact, due to significant desorption in the course of the 15-ns simulation time.

Figure 6. MSD (mean-square-displacement) of alkyl-cyclen (solid symbols) and alkylamine (open symbols) FM molecules versus time at 120 ºC. Comparisons of C6Cyc vs. C6amine, C12Cyc vs.C12amine, and C18Cyc vs.C18amine are shown in (a), (b), and (c), respectively. Figure 7 shows the stronger adsorption of the C12 and C18 alkyl-cyclens compared to the analogous alkylamines, close to 100% at 200 °C over the simulation time of 15 ns. For C6Cyc, the surface coverage decreases from 100% at room temperature to 40% at 200 °C. As noted earlier, this suggests the importance of the alkyl chains in surface interactions. The shorter alkyl chain not only reduces the number of atoms participating in intermolecular interactions, but also may have more significant steric hindrance.


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Figure 7. MD simulation results of surface coverage of alkyl-cyclen (solid symbols, mostly overlapping with one other) and alkylamine (open symbols) FM molecules on hydrated silica substrates at different temperatures. Comparisons of C6Cyc vs. C6amine, C12Cyc vs. C12amine, and C18Cyc vs. C18amine are shown in (a), (b), and (c), respectively. The adsorption geometry of one single alkylamine or alkyl-cyclen molecule simulated at 120 ºC is shown in Figure 8. Multi-dentate adsorption configuration of the alkyl-cyclen molecule can be clearly seen. As alkyl chains of the cyclen molecules become longer, more prevalent interaction between them and the substrate surface is also demonstrated. All of the MD simulation results presented in this research suggest that the excellent boundary lubrication performance27-28 of alkylcyclen FMs stems from their stronger binding to the surface compared with conventional FMs such as alkylamines, especially at high temperatures. Both EHL experiments and MD simulation show that both the adsorption energy and boundary film thickness increase with the alkyl chain length of the cyclens: C18Cyc is the best boundary lubrication performer. In the following section, we compare the microscale scratching properties in the presence of C18Cyc and its linear commercial analog, Armeen T.



Figure 8. MD simulation snapshots of one single alkyl-cyclen or alkylamine molecule at 120 ºC for different times. 3.3. Microscale scratching experiments Samples of FM coatings on silicon were prepared by dip-coating at 120 °C for different times (30 secs – 24 h). The microscale scratch-friction results for different adsorbed FM layers on silicon are shown in Figure 9. Immediately after the dip-coating, the friction performance of C18Cyc is comparable to that of C18amine (Armeen T) (Figure 9a). The adsorption stability/effectiveness of the adsorbed FMs was evaluated and compared before and after the toluene rinse. Toluene could easily and quickly dissolve both FMs at 0.5 wt%. The surface analysis in ref. 27 previously showed that the toluene rinse after the dip coating removed most of the alkylamine FM from a steel substrate but not the alkyl-cyclen FM. The FM coatings prepared here for microscale scratch experiments were measured to be thinner than 10 nm. Given the very small amount of the materials adsorbed on a small silicon surface (5 mm × 5 mm), more than 100 mL toluene used for each ~1 minutelong rinse should effectively remove any weakly bonded FM molecules from the surface. After rinsing with toluene, the friction performance of C18Cyc is unaffected, while that of C18amine becomes essentially the same as bare silicon (Figure 9b). This indicates that C18Cyc forms a robust layer on the silicon surface and is not removed by the solvent. The MD simulation results and microscale scratching test data all indicate significantly enhanced surface adsorption of the heterocyclic alkyl-cyclen FM molecules, especially at high temperatures, which is believed to be a principal reason why such FMs could help reduce friction and wear significantly in the boundary lubrication regime at elevated temperatures.27-28


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Figure 9. Microscale scratching results of dip-coated FMs on silicon substrates (a) before and (b) after rinse with toluene. During the dip-coating process, the silicon substrates were immersed in the FM’s at 120°C for different times (30 seconds – 24 hours). 4.

Thermodynamic analysis of boundary lubrication film formation

A thermodynamic analysis was conducted to understand the physical nature of the MD simulation results. A boundary lubrication film enhancement process consists of two critical steps: surface adsorption by the polar groups, i.e. the nitrogen atoms or the heterocyclic ring in this study, and entanglement of the FM hydrocarbon chains with base oil molecules. The latter process requires the former. Our current solvent molecules-free simulation results can still be used to well understand the boundary lubrication film formation process. After the FM molecules are adsorbed onto the hydrated surface, their surface residence time (τ) largely depends on their enthalpy of adsorption and oscillating periods, as shown in eq. (3).

 ΔH ads   RT  

   0  exp 

or

 ΔH ads  ln ( )  ln ( 0 )     RT 

(3)

where τ is the surface residence time, τ0 is the oscillating period of the adsorbed molecule, ΔHads is the enthalpy of adsorption, R is the gas constant, and T is temperature. Figure 10a qualitatively plots the variations of surface residence time against the reciprocal of temperature for the two types 13 ACS Paragon Plus Environment


of FMs, whose slopes and intercepts with the vertical axis represent the enthalpy of adsorption (ΔHads) and oscillating period (τ0) of the adsorbed molecules, respectively. The chelate effect explains why the heterocyclic cyclen molecules exhibit greater adsorption energy and are more resistant to desorption than the linear amine or diamine FMs. The more sites at which a single molecule binds to a surface, the stronger its energy of adsorption. A single nitrogen atom desorbing is still held in close proximity to the surface by the other nitrogen atoms in the molecule, providing ample for re-adsorption. For a cyclen molecule to dissociate fully from the surface, multiple hydrogen bonding interactions need to be broken simultaneously. In the case of a monoamine, a single desorption results in the molecule drifting away from the surface. In order for re-adsorption to occur, the molecule must find a vacant coordination site on the surface, which can be limited by numerous factors such as mass transfer rates. The higher interaction energy of the alkyl-cyclen molecules, as shown in Figure 5, means a higher enthalpy of adsorption is needed for their adsorption. For each adsorbed FM molecule, the attempt frequency for overcoming the desorption energy barrier is proportional to MSD, while the oscillating period of the FM molecules on the surface is inversely proportional to MSD. A significantly smaller MSD is obtained for the C18Cyc molecules in comparison to the C18amine molecules, as shown in Figure 6. The adsorbed heterocyclic FM molecules therefore have longer oscillating periods than the simple alkylamine FM molecules. The variation of surface residence time versus the reciprocal of temperature for the alkyl-cyclen molecules is bound to have a steeper gradient and a greater vertical intercept than those for alkylamine molecules (Figure 10a). As a result, the adsorbed heterocyclic alkyl-cyclen molecules reside on the surface for a shorter period than do the adsorbed alkylamine molecules at low temperature, as shown by the right portion of Figure 10a. It is difficult for the heterocyclic FMs to effectively enhance the formation of boundary lubrication films at low temperature (Figure 3a). At elevated temperature (Figures 3b and 3c), the adsorbed heterocyclic alkyl-cyclen molecules reside on the surface much longer than the adsorbed alkylamine molecules, which enables their superior capabilities for effective reinforcement of boundary lubrication film at elevated temperature, as shown by the left portion of Figure 10a. This rationalizes the process of preheating the FM in the base oil to provide the necessary thermal energy for effective adsorption and coverage of the surface.

Figure 10. Qualitative view of the variation of surface residence time τ (a) and desorption rate Rdes (b) of the adsorbed molecules with respect to the reciprocal of temperature. The slope indicates 14 ACS Paragon Plus Environment

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ΔHads or Eades, and the vertical intercept indicates τ0 or ν. MD simulation snapshots of the C18amine (c) and C18Cyc (d) molecules at different temperatures. Likewise, desorption thermodynamics can also be analyzed. Desorption rate (Rdes) of the adsorbed FM molecules is also a function of the reciprocal of temperature, as expressed by eq. (4) and shown in Figure 10b.

Rdes  

dN  E   ν  N x  exp  ades  dt  RT 

E  ln ( Rdes )  ln ( ν )  ln ( N x )   ades   RT 

or

(4)

In the equation above, Rdes is desorption rate, N is the surface concentration of adsorbed molecules, t is time, ν is the attempt frequency for overcoming the desorption energy barrier, x is the kinetic order of desorption, Eades is the activation energy for desorption, R is the gas constant, and T is temperature. The attempt frequency of an adsorbed molecule to overcome the desorption energy barrier (ν) and the activation energy of desorption (Eades) are indicated by the intercept at the vertical axis and the slope in Figure 10b, respectively. The adsorbed multi-dentate FMs have to overcome a much steeper energy barrier in order for desorption to occur. This is also demonstrated by the consistently low MSD of the C12Cyc and C18Cyc molecules, as shown in Figure 6. Again, due to the chelate effect, alkyl-cyclen FMs require a greater activation energy (Eades) than do linear alkylamines to cause desorption. The significantly higher interaction energy of the alkyl-cyclen molecules than that of the alkylamine molecules, shown in Figure 5, is a clear indication of this high activation energy requirement. Consequently, the desorption-temperature plot for the alkylcyclen FM molecules has a steeper gradient and a lower intercept than should that of the alkylamine molecules (Figure 10b). The new heterocyclic FM molecules can achieve a notably slower desorption rate than do the alkylamine molecules regardless the surrounding temperatures, and this is another critical reason for the superb ability of the temperature-driven enhancement of boundary lubrication film for the former. Together with the surface coverage results shown in Figure 7 and the MD simulation snapshots in Figures 10c and 10d, eq. (4) describe how fast the alkylamine molecules would desorb from the surface and how stably the heterocyclic alkyl-cyclen molecules can adsorb on to the surface. 5. Conclusions This paper reports a study on the boundary lubrication mechanisms of new high-performance heterocyclic alkyl-cyclen friction modifiers (FMs). The research was conducted by means of boundary lubrication film analysis, molecular dynamics (MD) simulation, adsorption stability evaluation, and qualitative thermodynamic analysis. The alkyl-cyclen FM additives in Group III oil enable a significant enhancement in boundary-lubrication film thickness at elevated temperatures. MD simulations at selected temperatures demonstrates that, in comparison to conventional alkylamine molecules, the heterocyclic FM molecules exhibit increased surface interaction energies, decreased surface molecular diffusivities, and well-maintained surface coverage. The stability and durability of the adsorbed alkyl-cyclen FM molecules on hydrated silicon was substantiated by microscale scratching tests. The boundary lubrication film is reinforced by optimizing the surface adsorption processes. Altogether, the enhanced surface adsorption, prolonged surface residence, reduced desorption rate, and entanglement of the alkyl-cyclen FM alkyl chains with base oil molecules were found to be the essential mechanisms supporting the excellent boundary lubrication performance of the new alkyl-cyclen FMs.



Acknowledgements The authors gratefully acknowledge US Department of Energy for research support under contract DE-EE0006449 and sincerely thank AkzoNobel and Valvoline Inc for generous sample supplies. Dr. M. Desanker thanks the National Defense Science and Engineering Graduate Fellowship Program of the Department of Defense (DoD) for support. The authors also thank Drs. M. Delferro, A. Erdemir, and A. Greco at Argonne National Laboratory, Dr. Y. He of Sinopec Corp., and Dr. B. Johnson of Northwestern University for helpful discussions. Notes He, X. and Lu, J. contributed equally to this work. The authors declare the following competing financial interest(s): A patent application related to this work has been filed (US Patent Application PCT/US2016/031868). §

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Boundary Lubrication Mechanisms for High-Performance Friction

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