Boundary Lubrication Performance of Polyelectrolyte-Surfactant Complexes on Biomimetic Surfaces.

Aqueous mixtures of oppositely charged polyelectrolytes and surfactants are useful in many industrial applications, such as shampoos and hair conditioners. In this work, we investigate the friction between biomimetic hair surfaces in the presence of adsorbed complexes formed from cationic polyelectrolytes and anionic surfactants in an aqueous solution. We apply nonequilibrium molecular dynamics (NEMD) simulations using the coarse-grained MARTINI model. We first developed new MARTINI parameters for cationic guar gum (CGG), a functionalized, plant-derived polysaccharide. The complexation of CGG and the anionic surfactant sodium dodecyl sulfate (SDS) on virgin and chemically damaged biomimetic hair surfaces was studied using a sequential adsorption approach. We then carried out squeeze-out and sliding NEMD simulations to assess the boundary lubrication performance of the CGG-SDS complex compressed between two hair surfaces. At low pressure, we observe a synergistic friction behavior for the CGG-SDS complex, which gives lower shear stress than either pure CGG or SDS. Here, friction is dominated by viscous dissipation in an interfacial layer comprising SDS and water. At higher pressures, which are probably beyond those usually experienced during hair manipulation, SDS and water are squeezed out, and friction increases due to interdigitation. The outcomes of this work are expected to be beneficial to fine-tune and screen sustainable hair care formulations to provide low friction and therefore a smooth feel and reduced entanglement.

Effects of surface chemistry on the mechanochemical decomposition of tricresyl phosphate.

The growth of protective tribofilms from lubricant antiwear additives on rubbing surfaces is initiated by mechanochemically promoted dissociation reactions. These processes are not well understood at the molecular scale for many important additives, such as tricresyl phosphate (TCP). One aspect that needs further clarification is the extent to which the surface properties affect the mechanochemical decomposition. Here, we use nonequilibrium molecular dynamics (NEMD) simulations with a reactive force field (ReaxFF) to study the decomposition of TCP molecules confined and pressurised between sliding ferrous surfaces at a range of temperatures. We compare the decomposition of TCP on native iron, iron carbide, and iron oxide surfaces. We show that the decomposition rate of TCP molecules on all the surfaces increases exponentially with temperature and shear stress, implying that this is a stress-augmented thermally activated (SATA) process. The presence of base oil molecules in the NEMD simulations decreases the shear stress, which in turn reduces the rate constant for TCP decomposition. The decomposition is much faster on iron surfaces than iron carbide, and particularly iron oxide. The activation energy, activation volume, and pre-exponential factor from the Bell model are similar on iron and iron carbide surfaces, but significantly differ for iron oxide surfaces. These findings provide new insights into the mechanochemical decomposition of TCP and have important implications for the design of novel lubricant additives for use in high-temperature and high-pressure environments.

Effects of surfactant adsorption on the wettability and friction of biomimetic surfaces.

The properties of solid-liquid interfaces can be markedly altered by surfactant adsorption. Here, we use molecular dynamics (MD) simulations to study the adsorption of ionic surfactants at the interface between water and heterogeneous solid surfaces with randomly arranged hydrophilic and hydrophobic regions, which mimic the surface properties of human hair. We use the coarse-grained MARTINI model to describe both the hair surfaces and surfactant solutions. We consider negatively-charged virgin and bleached hair surface models with different grafting densities of neutral octadecyl and anionic sulfonate groups. The adsorption of cationic cetrimonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS) surfactants from water are studied above the critical micelle concentration. The simulated adsorption isotherms suggest that cationic surfactants adsorb to the surfaces via a two-stage process, initially forming monolayers and then bilayers at high concentrations, which is consistent with previous experiments. Anionic surfactants weakly adsorb via hydrophobic interactions, forming only monolayers on both virgin and medium bleached hair surfaces. We also conduct non-equilibrium molecular dynamics simulations, which show that applying cationic surfactant solutions to bleached hair successfully restores the low friction seen with virgin hair. Friction is controlled by the combined surface coverage of the grafted lipids and the adsorbed CTAB molecules. Treated surfaces containing monolayers and bilayers both show similar friction, since the latter are easily removed by compression and shear. Further wetting MD simulations show that bleached hair treated with CTAB increases the hydrophobicity to similar levels seen for virgin hair. Treated surfaces containing CTAB monolayers with the tailgroups pointing predominantly away from the surface are more hydrophobic than bilayers due to the electrostatic interactions between water molecules and the exposed cationic headgroups.

Non-equilibrium molecular simulations of thin film rupture.

The retraction of thin films, as described by the Taylor-Culick (TC) theory, is subject to widespread debate, particularly for films at the nanoscale. We use non-equilibrium molecular dynamics simulations to explore the validity of the assumptions used in continuum models by tracking the evolution of holes in a film. By deriving a new mathematical form for the surface shape and considering a locally varying surface tension at the front of the retracting film, we reconcile the original theory with our simulation to recover a corrected TC speed valid at the nanoscale.

The Intrinsic Fragility of the Liquid-Vapor Interface: A Stress Network Perspective.

The evolution of the liquid-vapor interface of a Lennard-Jones fluid is examined with molecular dynamics simulations using the intrinsic sampling method. Results suggest clear damping of the intrinsic profiles with increasing temperature. Investigating the surface stress distribution, we have identified a linear variation of the space-filling nature (fractal dimension) of the stress clusters at the intrinsic surface with increasing surface tension or, equivalently, with decreasing temperature. A percolation analysis of these stress networks indicates that the stress field is more disjointed at higher temperatures. This leads to more fragile (or poorly connected) interfaces which result in a reduction in surface tension.

Coarse-grained molecular models of the surface of hair.

We present a coarse-grained molecular model of the surface of human hair, which consists of a supported lipid monolayer, in the MARTINI framework. Using coarse-grained molecular dynamics (MD) simulations, we identify a lipid grafting distance that yields a monolayer thickness consistent with both atomistic MD simulations and experimental measurements of the hair surface. Coarse-grained models for fully-functionalised, partially damaged, and fully damaged hair surfaces are created by randomly replacing neutral thioesters with anionic sulfonate groups. This mimics the progressive removal of fatty acids from the hair surface by bleaching and leads to chemically heterogeneous surfaces. Using molecular dynamics (MD) simulations, we study the island structures formed by the lipid monolayers at different degrees of damage in vacuum and in the presence of polar (water) and non-polar (n-hexadecane) solvents. We also use MD simulations to compare the wetting behaviour of water and n-hexadecane droplets on the model surfaces through contact angle measurements, which are compared to experiments using virgin and bleached hair. The model surfaces capture the experimentally-observed transition of the hair surface from hydrophobic (and oleophilic) to hydrophilic (and oleophobic) as the level of bleaching damage increases. By selecting surfaces with specific damage ratios, we obtain contact angles from the MD simulations that are in good agreement with experiments for both solvents on virgin and bleached human hairs. To negate the possible effects of microscale curvature and roughness of real hairs on wetting, we also conduct additional experiments using biomimetic surfaces that are co-functionalised with fatty acids and sulfonate groups. In both the MD simulations and experiments, the cosine of the water contact angle increases linearly with the sulfonate group surface coverage with a similar slope. We expect that the proposed systems will be useful for future molecular dynamics simulations of the adsorption and tribological behaviour of hair, as well as other chemically heterogeneous surfaces.

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.

Scale-Dependent Friction-Coverage Relations and Nonlocal Dissipation in Surfactant Monolayers.

Surfactant molecules, known as organic friction modifiers (OFMs), are routinely added to lubricants to reduce friction and wear between sliding surfaces. In macroscale experiments, friction generally decreases as the coverage of OFM molecules on the sliding surfaces increases; however, recent nanoscale experiments with sharp atomic force microscopy (AFM) tips have shown increasing friction. To elucidate the origin of these opposite trends, we use nonequilibrium molecular dynamics (NEMD) simulations and study kinetic friction between OFM monolayers and an indenting nanoscale asperity. For this purpose, we investigate various coverages of stearamide OFMs on iron oxide surfaces and silica AFM tips with different radii of curvature. We show that the differences between the friction-coverage relations from macroscale and nanoscale experiments are due to molecular plowing in the latter. For our small tip radii, the friction coefficient and indentation depth both have a nonmonotonic dependence on OFM surface coverage, with maxima occurring at intermediate coverage. We rationalize the nonmonotonic relations through a competition of two effects (confinement and packing density) that varying the surface coverage has on the effective stiffness of the OFM monolayers. We also show that kinetic friction is not very sensitive to the sliding velocity in the range studied, indicating that it originates from instabilities. Indeed, we find that friction predominately originates from plowing of the monolayers by the leading edge of the tip, where gauche defects are created, while thermal dissipation is mostly localized in molecules toward the trailing edge of the tip, where the chains return to a more extended conformation.

Molecular Simulations of Surfactant Adsorption on Iron Oxide from Hydrocarbon Solvents.

The performance of organic friction modifiers (OFMs) depends on their ability to adsorb onto surfaces and form protective monolayers. Understanding the relationship between OFM concentration in the base oil and the resulting surface coverage is important for improving lubricant formulations. Here, we use molecular dynamics (MD) simulations to study the adsorption of three OFMs─stearic acid (SA), glycerol monoostearate (GMS), and glycerol monooleate (GMO)─onto a hematite surface from two hydrocarbon solvents─n-hexadecane and poly(α-olefin) (PAO). We calculate the potential of mean force of the adsorption process using the adaptive biasing force algorithm, and the adsorption strength increases in the order SA < GMS < GMO. We estimate the minimum area occupied by OFM molecules on the surface using annealing MD simulations and obtained a similar hard-disk area for GMS and GMO but a lower value for SA. Using the MD results, we determine the adsorption isotherms using the molecular thermodynamic theory (MTT), which agree well with one previous experimental data set for SA on hematite. For two other experimental data sets for SA, lateral interactions between surfactant molecules need to be accounted for within the MTT framework. SA forms monolayers with lower surface coverage than GMO and GMS at low concentrations but also has the highest plateau coverage. We validate the adsorption energies from the MD simulations using high-frequency reciprocating rig friction experiments with different concentrations of the OFMs in PAO. For OFMs with saturated tailgroups (SA and GMS), we obtain good agreement between the simulations and the experiments. The results deviate for OFMs containing Z-unsaturated tailgroups (GMO) due to the additional steric hindrance, which is not accounted for in the current simulation framework. This study demonstrates that MD simulations, alongside MTT, are an accurate and efficient tool to predict adsorption isotherms at solid-liquid interfaces.

Probing the high-pressure viscosity of hydrocarbon mixtures using molecular dynamics simulations.

Computational predictions of the high-pressure viscosity of hydrocarbon mixtures could help to accelerate the development of fuels and lubricants with improved performance. In this study, we use molecular dynamics simulations to study the viscosity and density of methylcyclohexane, 1-methylnaphthalene, and their binary mixtures at 323 K and pressures of up to 500 MPa. The simulation results are in excellent agreement with previous experiments available up to 100 MPa for both pure compounds (200 MPa for 1-methylnaphthalene) and the binary mixtures. For 1-methylnaphthalene, the viscosity initially increases slower-than-exponential with pressure before it reaches an inflection point and then increases faster-than-exponential. The inflection point (300 MPa) occurs at a pressure slightly below the one at which 1-methylnaphthalene is expected to enter the supercooled phase (400 MPa). For methylcyclohexane, the increase in viscosity with pressure is slower-than-exponential over the entire pressure range studied. The binary mixtures show intermediate pressure-viscosity responses between the two pure cases. The applicability of equations commonly used to describe the pressure dependence of viscosity, as well as the viscosity of binary mixtures, is evaluated against the computational predictions.

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.

Slip of Alkanes Confined between Surfactant Monolayers Adsorbed on Solid Surfaces.

The slip and friction behavior of n-hexadecane, confined between organic friction modifier surfactant films adsorbed on hematite surfaces, has been studied using nonequilibrium molecular dynamics simulations. The influence of the surfactant type and coverage, as well as the applied shear rate and pressure, has been investigated. A measurable slip length is only observed for surfactant films with a high surface coverage, which provide smooth interfaces between well-defined surfactant and hexadecane layers. Slip commences above a critical shear rate, beyond which the slip length first increases with increasing shear rate and then asymptotes toward a constant value. The maximum slip length increases significantly with increasing pressure. Systems and conditions which show a larger slip length typically give a lower friction coefficient. Generally, the friction coefficient increases linearly with logarithmic shear rate; however, it shows a much stronger shear rate dependency at low pressure than at high pressure. Relating slip and friction, slip only occurs above a critical shear stress, after which the slip length first increases linearly with increasing shear stress and then asymptotes. This behavior is well-described using previously proposed slip models. This study provides a more detailed understanding of the slip of alkanes on surfactant monolayers. It also suggests that high coverage surfactant films can significantly reduce friction by promoting slip, even when the surfaces are well-separated by a lubricant.

Nonequilibrium Molecular Dynamics Simulations of Organic Friction Modifiers Adsorbed on Iron Oxide Surfaces.

For the successful development and application of lubricants, a full understanding of the nanoscale behavior of complex tribological systems is required, but this is difficult to obtain experimentally. In this study, we use nonequilibrium molecular dynamics (NEMD) simulations to examine the atomistic structure and friction properties of commercially relevant organic friction modifier (OFM) monolayers adsorbed on iron oxide surfaces and lubricated by a thin, separating layer of hexadecane. Specifically, acid, amide, and glyceride OFMs, with saturated and Z-unsaturated hydrocarbon tail groups, are simulated at various surface coverages and sliding velocities. At low and medium coverage, the OFMs form liquidlike and amorphous monolayers, respectively, which are significantly interdigitated with the hexadecane lubricant, resulting in relatively high friction coefficients. At high coverage, solidlike monolayers are formed for all of the OFMs, which, during sliding, results in slip planes between well-defined OFM and hexadecane layers, yielding a marked reduction in the friction coefficient. When present at equal surface coverage, OFMs with saturated and Z-unsaturated tail groups are found to yield similar structure and friction behavior. OFMs with glyceride head groups yield significantly lower friction coefficients than amide and particularly carboxylic acid head groups. For all of the OFMs and coverages simulated, the friction coefficient is found to increase linearly with the logarithm of sliding velocity; however, the gradient of this increase depends on the coverage. The structure and friction details obtained from these simulations agree well with experimental results and also shed light on the relative tribological performance of these OFMs through nanoscale structural variations. This has important implications in terms of the applicability of NEMD to aid the development of new formulations to control friction.

Polymer brushes for friction control: Contributions of molecular simulations.

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Nanoscale friction of biomimetic hair surfaces.

We investigate the nanoscale friction between biomimetic hair surfaces using chemical colloidal probe atomic force microscopy experiments and nonequilibrium molecular dynamics simulations. In the experiments, friction is measured between water-lubricated silica surfaces functionalised with monolayers formed from either octadecyl or sulfonate groups, which are representative of the surfaces of virgin and ultimately bleached hair, respectively. In the simulations, friction is monitored between coarse-grained model hair surfaces with different levels of chemical damage, where a specified amount of grafted octadecyl groups are randomly replaced with sulfonate groups. The sliding velocity dependence of friction in the simulations can be described using an extended stress-augmented thermally activation model. As the damage level increases in the simulations, the friction coefficient generally increases, but its sliding velocity-dependence decreases. At low sliding velocities, which are closer to those encountered experimentally and physiologically, we observe a monotonic increase of the friction coefficient with damage ratio, which is consistent with our new experiments using biomimetic surfaces and previous ones using real hair. This observation demonstrates that modified surface chemistry, rather than roughness changes or subsurface damage, control the increase in nanoscale friction of bleached or chemically damaged hair. We expect the methods and biomimetic surfaces proposed here to be useful to screen the tribological performance of hair care formulations both experimentally and computationally.

Macroscale Superlubricity and Polymorphism of Long-Chain n-Alcohols.

Simple n-alcohols, such as 1-dodecanol, show anomalous film-forming and friction behaviors under elastohydrodynamic lubrication (EHL) conditions, as found inside bearings and gears. Using tribometer, diamond anvil cell (DAC), and differential scanning calorimetry (DSC) experiments, we show that liquid 1-dodecanol undergoes a pressure-induced solidification when entrained into EHL contacts. Different solid polymorphs are formed inside the contact depending on the temperature and pressure conditions. Surprisingly, at a moderate temperature and pressure, 1-dodecanol forms a polymorph that exhibits robust macroscale superlubricity. The DAC and DSC experiments show that superlubricity is facilitated by the formation of lamellar, hydrogen-bonded structures of hexagonally close-packed molecules, which promote interlayer sliding. This novel superlubricity mechanism is similar to that proposed for the two-dimensional materials commonly employed as solid lubricants, but it also enables the practical advantages of liquid lubricants to be maintained. When the pressure is increased, 1-dodecanol undergoes a polymorphic transformation into a phase that gives a higher friction. The DAC and DSC experiments indicate that the high-friction polymorph is an orthorhombic crystal. The polymorphic transformation pressure coincides with the onset of a dimple formation in the EHL films, revealing that the anomalous film shapes are caused by the formation of rigid orthorhombic crystals inside the contact. This is the first demonstration of a macroscale superlubricity in an EHL contact lubricated by a nonaqueous liquid that arises from bulk effects rather than tribochemical transformations at the surfaces. Since the superlubricity observed here results from phase transformations, it is continuously self-replenishing and is insensitive to surface chemistry and topology. This discovery creates the possibility of implementing superlubricity in a wide range of machine components, which would result in enormous improvements in efficiency and durability.

Mechanochemistry of phosphate esters confined between sliding iron surfaces.

The molecular structure of lubricant additives controls not only their adsorption and dissociation behaviour at the nanoscale, but also their ability to reduce friction and wear at the macroscale. Here, we show using nonequilibrium molecular dynamics simulations with a reactive force field that tri(s-butyl)phosphate dissociates much faster than tri(n-butyl)phosphate when heated and compressed between sliding iron surfaces. For both molecules, dissociative chemisorption proceeds through cleavage of carbon-oxygen bonds. The dissociation rate increases exponentially with temperature and stress. When the rate-temperature-stress data are fitted with the Bell model, both molecules have similar activation energies and activation volumes and the higher reactivity of tri(s-butyl)phosphate is due to a larger pre-exponential factor. These observations are consistent with experiments using the antiwear additive zinc dialkyldithiophosphate. This study represents a crucial step towards the virtual screening of lubricant additives with different substituents to optimise tribological performance.

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.

Simulating Surfactant-Iron Oxide Interfaces: From Density Functional Theory to Molecular Dynamics.

Understanding the behavior of surfactant molecules on iron oxide surfaces is important for many industrial applications. Molecular dynamics (MD) simulations of such systems have been limited by the absence of a force field (FF), which accurately describes the molecule-surface interactions. In this study, interaction energies from density functional theory (DFT) + U calculations with a van der Waals functional are used to parameterize a classical FF for MD simulations of amide surfactants on iron oxide surfaces. The original FF, which was derived using mixing rules and surface Lennard-Jones (LJ) parameters developed for nonpolar molecules, was shown to significantly underestimate the adsorption energy and overestimate the equilibrium adsorption distance compared to DFT. Conversely, the optimized FF showed excellent agreement with the interaction energies obtained from DFT calculations for a wide range of surface coverages and molecular conformations near to and adsorbed on α-Fe2O3(0001). This was facilitated through the use of a Morse potential for strong chemisorption interactions, modified LJ parameters for weaker physisorption interactions, and adjusted partial charges for the electrostatic interactions. The original FF and optimized FF were compared in classical nonequilibrium molecular dynamics simulations of amide molecules confined between iron oxide surfaces. When the optimized FF was employed, the amide molecules were pulled closer to the surface and the orientation of the headgroups was more similar to that observed in the DFT calculations. The optimized FF proposed here facilitates classical MD simulations of anhydrous amide-iron oxide interfaces in which the interactions are representative of accurate DFT calculations.