Calculating shear viscosity with confined non-equilibrium molecular dynamics: a case study on hematite - PAO-2 lubricant

The behaviour of confined lubricants at the atomic scale as affected by the interactions at the surface-lubricant interface is relevant in a range of technological applications in areas such as the automotive industry. In this paper, by performing fully atomistic molecular dynamics, we investigate the regime where the viscosity starts to deviate from the bulk behaviour, a topic of great practical and scientific relevance. The simulations consist of setting up a shear flow by confining the lubricant between iron oxide surfaces. By using confined Non-Equilibrium Molecular Dynamics (NEMD) simulations at a pressure range of 0.1-1.0 GPa at 100 °C, we demonstrate that the film thickness of the fluid affects the behaviour of viscosity. We find that by increasing the number of lubricant molecules, we approach the viscosity value of the bulk fluid derived from previously published NEMD simulations for the same system. These changes in viscosity occurred at film thicknesses ranging from 10.12 to 55.93 Å. The viscosity deviations at different pressures between the system with the greatest number of lubricant molecules and the bulk simulations varied from -16% to 41%. The choice of the utilized force field for treating the atomic interactions was also investigated.

Investigating the Behavior of Various Lubrication Regimes under Dynamic Conditions Using Nonequilibrium Molecular Dynamics

It is crucial to comprehend how the oil film varies under dynamic operating conditions and the accompanying friction properties to better grasp the friction mechanism and control friction behavior. To model the friction characteristics under boundary lubrication (BL) and elastohydrodynamic lubrication (EHL), nonequilibrium molecular dynamics simulations with various numbers of hexadecane molecules as lubricating oil were conducted in this research under the conditions of dynamic speed and dynamic load. All the dynamic operating conditions have the form of sine waves, with various frequencies and amplitudes. According to the findings, the friction force is strongly connected with interfaces where relative sliding takes place, whose number, velocity difference, and the degree of solidification have significant influences. The variation of amplitude under dynamic load can cause a regular change in the density of the lubricating layer, while the variation of frequency can cause a change in molecular layer's range of motion. Both effects are crucial for friction. The structure of the lubricating layer with lower friction varies with various frequencies for dynamic velocity. Both high and small amplitudes of velocity offer advantages to form a stable film structure at low frequencies in the BL and EHL regions, while the amplitude in the BL area has minimal association with friction at high frequencies. At high frequencies in the EHL region, the friction rises as the amplitude of velocity grows and the lubricating layer becomes more unstable.

Rheological Properties of Small-Molecular Liquids at High Shear Strain Rates

Molecular-scale understanding of rheological properties of small-molecular liquids and polymers is critical to optimizing their performance in practical applications such as lubrication and hydraulic fracking. We combine nonequilibrium molecular dynamics simulations with two unsupervised machine learning methods: principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), to extract the correlation between the rheological properties and molecular structure of squalane sheared at high strain rates (106-1010s-1) for which substantial shear thinning is observed under pressures P∈0.1-955 MPa at 293 K. Intramolecular atom pair orientation tensors of 435×6 dimensions and the intermolecular atom pair orientation tensors of 61×6 dimensions are reduced and visualized using PCA and t-SNE to assess the changes in the orientation order during the shear thinning of squalane. Dimension reduction of intramolecular orientation tensors at low pressures P=0.1,100 MPa reveals a strong correlation between changes in strain rate and the orientation of the side-backbone atom pairs, end-backbone atom pairs, short backbone-backbone atom pairs, and long backbone-backbone atom pairs associated with a squalane molecule. At high pressures P≥400 MPa, the orientation tensors are better classified by these different pair types rather than strain rate, signaling an overall limited evolution of intramolecular orientation with changes in strain rate. Dimension reduction also finds no clear evidence of the link between shear thinning at high pressures and changes in the intermolecular orientation. The alignment of squalane molecules is found to be saturated over the entire range of rates during which squalane exhibits substantial shear thinning at high pressures.

Computing Viscosities of Mixtures of Ester-Based Lubricants at Different Temperatures

Synthetic esters are used as lubricants for applications at high temperatures, but their development can be a trial and error process. In this context, molecular dynamics simulations could be used as a tool to investigate the properties of new lubricants, in particular viscosity. We employ nonequilibrium molecular dynamics (NEMD) simulations to predict bulk Newtonian viscosities of a set of mixtures of two esters, di(2-ethylhexyl) sebacate (DEHS) and di(2-ethylhexyl) adipate (DEHA) at 293 and 343 K as well as equilibrium molecular dynamics (EMD) and NEMD at 393 K and compare these to experimental measurements. The simulations predict mixture densities within 5% of the experimental values, and we are able to retrieve between 99% and 75% of the experimental viscosities for all ranges of temperature. Experimental viscosities show a linear trend which we are able to capture using NEMD at low temperature and EMD at high temperature. Our work shows that, using EMD and NEMD simulations, and the workflows we developed, we can obtain reliable estimates of the viscosities of mixtures of industrially relevant ester-based lubricants at different temperatures.

Combining Molecular Dynamics and Machine Learning to Analyze Shear Thinning for Alkane and Globular Lubricants in the Low Shear Regime

Lubricants with desirable frictional properties are important in achieving an energy-saving society. Lubricants at the interfaces of mechanical components are confined under high shear rates and pressures and behave quite differently from the bulk material. Computational approaches such as nonequilibrium molecular dynamics (NEMD) simulations have been performed to probe the molecular behavior of lubricants. However, the low-shear-velocity regions of the materials have rarely been simulated owing to the expensive calculations necessary to do so, and the molecular dynamics under shear velocities comparable with that in the experiments are not clearly understood. In this study, we performed NEMD simulations of extremely confined lubricants, i.e., two molecular layers for four types of lubricants confined in mica walls, under shear velocities from 0.001 to 1 m/s. While we confirmed shear thinning, the velocity profiles could not show the flow behavior when the shear velocity was much slower than thermal fluctuations. Therefore, we used an unsupervised machine learning approach to detect molecular movements that contribute to shear thinning. First, we extracted the simple features of molecular movements from large amounts of MD data, which were found to correlate with the effective viscosity. Subsequently, the extracted features were interpreted by examining the trajectories contributing to these features. The magnitude of diffusion corresponded to the viscosity, and the location of slips that varied depending on the spherical and chain lubricants was irrelevant. Finally, we attempted to apply a modified Stokes-Einstein relation at equilibrium to the nonequilibrium and confined systems. While systems with low shear rates obeyed the relation sufficiently, large deviations were observed under large shear rates.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Correlation between ordering and shear thinning in confined OMCTS liquids

Despite the extensive research that has been conducted for decades on the behavior of confined liquids, detailed knowledge of this phenomenon, particularly in the mixed/boundary lubrication regime, remains limited. This can be attributed to several factors including the difficulty of direct experimental observations of the behavior of lubricant molecules under non-equilibrium conditions, the high computational cost of molecular simulations to reach steady state, and the low signal-to-noise ratio at extremely low shear rates corresponding to actual operating conditions. To this end, we studied the correlation between the structure formation and shear viscosity of octamethylcyclotetrasiloxane confined between two mica surfaces in a mixed/boundary lubrication regime. Three different surface separations corresponding to two-, three-, and five-layered structures were considered to analyze the effect of confinement. The orientational distributions with one specific peak for n=2 and two distributions, including a parallel orientation with the surface normal for n>2, were observed at rest. The confined liquids exhibited a distinct shear-thinning behavior independent of surface separations for a relatively low shear rate, \dot{\gamma}<10^{8} s^{-1}. However, the shear viscosities at \dot{\gamma}<10^{8} s^{-1} depended on the number of layered structures. Newtonian behavior was observed with a further increase in the shear rate. Furthermore, we found a strong correlation between the degree of molecular orientation and the shear viscosity of the confined liquids. The magnitude of the shear viscosity of the confined liquids can primarily be determined by the degree of molecular orientation, and shear-thinning originates from the vanishing of specific orientational distributions with increasing shear rate.

Slip and stress from low shear rate nonequilibrium molecular dynamics: The transient-time correlation function technique

We derive the transient-time correlation function (TTCF) expression for the computation of phase variables of inhomogenous confined atomistic fluids undergoing boundary-driven planar shear (Couette) flow at constant pressure. Using nonequilibrium molecular dynamics simulations, we then apply the TTCF formalism to the computation of the shear stress and the slip velocity for atomistic fluids at realistic low shear rates, in systems under constant pressure and constant volume. We show that, compared to direct averaging of multiple trajectories, the TTCF method dramatically improves the accuracy of the results at low shear rates and that it is suitable to investigate the tribology and rheology of atomistically detailed confined fluids at realistic flow rates.

Structures of Nanoconfined Liquids Determined by Synchrotron X-ray Diffraction

We have successfully performed X-ray diffraction measurements of the liquids octamethylcyclotetrasiloxane (OMCTS, a quasi-spherical-shaped molecule) and n-hexadecane (a normal alkane) confined between mica surfaces at surface separation distances (D's) from 500 nm to the hard-wall thickness (1.9 nm for OMCTS and 1.0 nm for hexadecane). At all of the studied D's, we observed diffraction peaks corresponding to their mean intermolecular spacing at q = 8.6 nm^-1 (d = 0.73 nm) for OMCTS and q = 13.6 nm^-1 (d = 0.45 nm) for n-hexadecane. The peak intensity increased at D < ca. 50 nm for OMCTS even with the decreasing distance and exhibited a local maximum at D = 17-13 nm, indicating the sharp increase in the molecular order in this distance range. The peak intensities normalized by the D and I_normalized values of OMCTS and n-hexadecane were nearly constant at D's greater than 100 nm, though they appeared to increase slightly. The increase then became more significant with decreasing D below 100 nm, and finally the I_normalized values became 120 (for OMCTS) and 160 (for n-hexadecane) at the hard wall. These results clearly demonstrated the significant increase in the structural order of OMCTS and n-hexadecane under nanoconfinement, especially below 100 nm. The fwhm values of the peaks of OMCTS and n-hexadecane showed no significant change until small distances when the confinement effect was significant. These results indicated that the increase in the structural order should be mainly ascribed to the ordering of the molecules in the parallel plane in the enhanced layered structure formed under the confinement. The viscous parameters (b₂) of OMCTS and n-hexadecane obtained from the resonance shear measurement showed no increase at D's down to ca. 7 nm. This indicated that a certain ordering of the confined molecules was required for the observable increase in the viscosity.

Transport Phenomena in Nano/Molecular Confinements

The transport of fluid and ions in nano/molecular confinements is the governing physics of a myriad of embodiments in nature and technology including human physiology, plants, energy modules, water collection and treatment systems, chemical processes, materials synthesis, and medicine. At nano/molecular scales, the confinement dimension approaches the molecular size and the transport characteristics deviates significantly from that at macro/micro scales. A thorough understanding of physics of transport at these scales and associated fluid properties is undoubtedly critical for future technologies. This compressive review provides an elaborate picture on the promising future applications of nano/molecular transport, highlights experimental and simulation metrologies to probe and comprehend this transport phenomenon, discusses the physics of fluid transport, tunable flow by orders of magnitude, and gating mechanisms at these scales, and lists the advancement in the fabrication methodologies to turn these transport concepts into reality. Properties such as chain-like liquid transport, confined gas transport, surface charge-driven ion transport, physical/chemical ion gates, and ion diodes will provide avenues to devise technologies with enhanced performance inaccessible through macro/micro systems. This review aims to provide a consolidated body of knowledge to accelerate innovation and breakthrough in the above fields.

Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes

In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.

Unraveling and Mapping the Mechanisms for Near-Surface Microstructure Evolution in CuNi Alloys under Sliding

The origin of friction and wear in polycrystalline materials is intimately connected with their microstructural response to interfacial stresses. Although many mechanisms that govern microstructure evolution in sliding contacts are generally understood, it is still a challenge to ascertain which mechanisms matter under what conditions, which limits the development of tailor-made microstructures for reducing friction and wear. Here, we shed light on the circumstances that promote plastic deformation and surface damage by studying several face-centered cubic CuNi alloys subjected to sliding with molecular dynamics simulations featuring tens of millions of atoms. By analyzing the depth- and time-dependent evolution of the grain size, twinning, shear, and stresses in the aggregate, we derive a deformation mechanism map for CuNi alloys. We verify the predictions of this map against focused ion beam images of the near-surface regions of CuNi alloys that were experimentally subjected to similar loading conditions. Our results may serve as a tool for finding optimum material compositions within a specified operating range.

Transport coefficients of model lubricants up to 400 MPa from molecular dynamics

In this paper, the predictive power of molecular dynamics methods is demonstrated for the cases of model paraffinic and aromatic lubricant liquids at pressures up to 400 MPa. The shear viscosity and self-diffusion coefficients are calculated for 2,2,4-trimethylpentane (C₈H₁₈) at 298 K and 1,1-diphenylethane (C₁₄H₁₄) at 333 K. Three force fields with different levels of accuracy are compared by the ability to predict the experimental data. The Stokes-Einstein correlation between viscosity and self-diffusion is demonstrated for both compounds.

Mechanochemistry of Zinc Dialkyldithiophosphate on Steel Surfaces under Elastohydrodynamic Lubrication Conditions

Zinc dialkyldithiophosphate (ZDDP) is added to engine lubricants to reduce wear and ensure reliable operation. ZDDP reacts under rubbing conditions to form protective zinc/iron phosphate tribofilms on steel surfaces. Recently, it has been demonstrated that this process can be promoted by applied stresses in lubricated contacts, as well as temperature, and is thus mechanochemical in origin. In this study, a tribology test rig, capable of applying very high loads, has been developed to generate ZDDP tribofilms under full-film elastohydrodynamic lubrication (EHL) conditions in steel/steel ball-on-disk contacts. This provides a well-defined temperature and stress environment with negligible direct asperity contact in which to study mechanochemical processes. ZDDPs with branched primary and secondary alkyl substituents have been studied in three base oils, two with high EHL friction and one with low EHL friction. In the high EHL friction base oils, the tribofilm growth rate increases exponentially with shear stress and temperature for both ZDDPs, as predicted by a stress-augmented thermal activation model. Conversely, under otherwise identical conditions, negligible ZDDP tribofilm formation takes place in the low EHL friction base oil. This confirms that the ZDDP reaction is driven by macroscopic shear stress rather than hydrostatic pressure. The secondary ZDDP forms tribofilms considerably faster than the primary ZDDP under equivalent conditions, suggesting that the initial decomposition reaction is the rate-determining step for tribofilm formation. The rate of tribofilm growth is independent of ZDDP concentration over the range studied, indicating that this process follows zero-order kinetics. Under full-film EHL conditions, ZDDP tribofilm formation is promoted by macroscopic shear stress applied through the base oil molecules, which induces asymmetric stress on adsorbed ZDDP molecules to promote their decomposition and initiate rapid phosphate polymerization.

The Influence of Lubrication and the Solid-Fluid Interaction on Thermodynamic Properties in a Nanoscopic Scratching Process

Liquid lubricants play an important role in contact processes; for example, they reduce friction and cool the contact zone. To gain better understanding of the influence of lubrication on the nanoscale, both dry and lubricated scratching processes in a model system are compared in the present work using molecular dynamics simulations. The entire range between total dewetting and total wetting is investigated by tuning the solid-fluid interaction energy. The investigated scratching process consists of three sequential movements: A cylindrical indenter penetrates an initially flat substrate, then scratches in the lateral direction, and is finally retracted out of the contact with the substrate. The indenter is fully submersed in the fluid in the lubricated cases. The substrate, the indenter, and the fluid are described by suitably parametrized Lennard-Jones model potentials. The presence of the lubricant is found to have a significant influence on the friction and on the energy balance of the process. The thermodynamic properties of the lubricant are evaluated in detail. A correlation of the simulation results for the profiles of the temperature, density, and pressure of the fluid in the vicinity of the chip is developed. The work done by the indenter is found to mainly dissipate and thereby heat up the substrate and eventually the fluid. Only a minor part of the work causes plastic deformation of the substrate.

Effect of Ambient Chemistry on Friction at the Basal Plane of Graphite

Graphite is widely used as a solid lubricant due to its layered structure, which enables ultralow friction. However, the lubricity of graphite is affected by ambient conditions and previous studies have shown a sharp contrast between frictional behavior in vacuum or dry environments compared to humid air. Here, we studied the effect of organic gaseous species in the environment, specifically comparing the adsorption of phenol and pentanol vapor. Atomic force microscopy experiments and reactive molecular dynamics simulations showed that friction was larger with phenol than with pentanol. The simulation results were analyzed to test multiple hypotheses to explain the friction difference, and it was found that mechanically driven chemical bonding between the tip and phenol molecules plays a critical role. Bonding increases the number of phenol molecules in the contact, which increases the adhesion as well as the number of atoms in registry with the topmost graphene layer acting as a pinning site to resist sliding. The findings of this research provide insight into how the chemistry of the operating environment can affect the frictional behavior of graphite and layered materials more generally.

Tuning Water Slip Behavior in Nanochannels Using Self-Assembled Monolayers

Water slip at solid surfaces is important for a wide range of micro-/nanofluidic applications. While it is known that water slip behavior depends on surface functionalization, how it impacts the molecular level dynamics and mass transport at the interface is still not thoroughly understood. In this paper, we use nonequilibrium molecular dynamics simulations to investigate the slip behavior of water confined between gold surfaces functionalized by self-assembled monolayer (SAM) molecules with different polar functional groups. We observe a positive-to-negative slip transition from hydrophobic to hydrophilic SAM functionalizations, which is found to be related to the stronger interfacial interaction between water molecules and more hydrophilic SAM molecules. The stronger interaction increases the surface friction and local viscosity, making water slip more difficult. More hydrophilic functionalization also slows down the interfacial water relaxation and leads to more pronounced water trapping inside the SAM layer, both of which impede water slip. The results from this work will provide useful insights into the understanding of the water slip at functionalized surfaces and design guidelines for various applications.

Shear heating, flow, and friction of confined molecular fluids at high pressure

Understanding the molecular-scale behavior of fluids confined and sheared between solid surfaces is important for many applications, particularly tribology where this often governs the macroscopic frictional response. In this study, nonequilibrium molecular dynamics simulations are performed to investigate the effects of fluid and surface properties on the spatially resolved temperature and flow profiles, as well as friction. The severe pressure and shear rate conditions studied are representative of the elastohydrodynamic lubrication regime. In agreement with tribology experiments, flexible lubricant molecules give low friction, which increases linearly with logarithmic shear rate, while bulky traction fluids show higher friction, but a weaker shear rate dependence. Compared to lubricants, traction fluids show more significant shear heating and stronger shear localization. Models developed for macroscopic systems can be used to describe both the spatially resolved temperature profile shape and the mean film temperature rise. The thermal conductivity of the fluids increases with pressure and is significantly higher for lubricants compared to traction fluids, in agreement with experimental results. In a subset of simulations, the efficiency of the thermostat in one of the surfaces is reduced to represent surfaces with lower thermal conductivity. For these unsymmetrical systems, the flow and the temperature profiles become strongly asymmetric and some thermal slip can occur at the solid-fluid interface, despite the absence of velocity slip. The larger temperature rises and steeper velocity gradients in these cases lead to large reductions in friction, particularly at high pressure and shear rate.

Elastohydrodynamic lubricant flow with nanoparticle tracking

Lubricants operating in elastohydrodynamic (EHD) contacts exhibit local variations in rheological properties when the contact pressure rises.

Comparing the molecular and global rheology of a fluid under high pressures

The viscosity of liquids is a strong function of pressure. While viscosity is relatively easy to measure at low pressure, high-pressure rheology presents significant experimental challenges. As a result, rheological models are often used to extrapolate viscosity from low pressure measurements to higher pressures. Techniques to obtain data over a wide range of pressures and shear rates, as well as understanding the validity and limitations of methods to fill the gaps in the available data, are therefore of crucial practical and theoretical importance. This work examines the viscosity of polyalphaolefin (PAO) by combining average global area averaged measurements at high pressure and local molecular viscosity measurements at moderate pressures. Viscosities spanning five orders of magnitude are examined at pressures up to 720 MPa. High pressure results were obtained with friction measurements where the fluid is sheared between two surfaces in a loaded point contact. The local molecular microviscosity at medium and low pressures was measured by applying a technique based on fluorescence anisotropy, which probes the rotational motion of dye molecules in a nanoscale film under shear. Both sets of measurements are taken in the same configuration, an elastohydrodynamic (EHD) contact. This is the first set of quantitative local viscosity measurements that have been verified against both friction and high pressure rheometry measurements. Commonly used rheological models were compared to experimental results. Our work shows that fluorescence anisotropy and friction measurements can be used to determine the viscosity of liquids over a wide range of conditions from a single experimental setup. The results obtained match results from low- and high-pressure rheometry for PAO. The importance of correcting friction data for pressure non-uniformity, temperature and shear thinning is also highlighted.

Independence between friction and velocity distribution in fluids subjected to severe shearing and confinement

Lubricated friction at high shear and high enough pressure becomes saturated, independently of the velocity profile in the lubricant thickness.