The performance of lubricant additives, such as organic friction modifiers (OFMs), depends critically on their ability to adsorb onto the surfaces of moving components and form protective self-assembled layers (SAMs). Therefore, understanding the relationship between the concentration of the additive in the base oil and the resulting surface coverage is extremely important for lubricant formulations, as well as many other surfactant applications. Here, we use molecular dynamics (MD) simulations to study the adsorption isotherms of three different OFMs, stearic acid (SA), glycerol monoostearate (GMS), and glycerol monooleate (GMO), onto a hematite surface from hydrocarbon solvents, n-hexadecane and poly-α-olefin (PAO). First, we calculate the potential of mean force (PMF) of the adsorption process using MD simulations with the adaptive biasing force (ABF) algorithm. Our MD simulations show that SA has the weakest adsorption energy on hematite, followed by GMS, and finally GMO, due to the increasing number of functional groups available to bind to the surface. We also estimate the area occupied by each OFM molecule on the surface in the high-coverage limit using MD simulations of the annealing of OFM films with different initial surface coverages. We obtain a similar hard-disk area for GMS and GMO, but a lower value for SA, which is due to its smaller headgroup size. Based on the adsorption energy and surface area, we determine the corresponding adsorption isotherms using the molecular thermodynamic theory (MTT), which agree well with one available experimental data-set for SA. Two other experimental data-sets for SA require lateral interactions between surfactant molecules to be accounted for. SA forms monolayers with lower surface coverage than GMO and GMS at low concentrations (due to a smaller adsorption energy), but also has the highest plateau coverage (due to a smaller hard-disk area). We validate the adsorption energies from the MD simulations using high frequency reciprocating rig (HFRR) friction experiments with different concentrations of the OFMs in PAO. We use the Jahanmir and Beltzer model to estimate the surface coverage at each concentration and the adsorption energy of each OFM from the HFRR friction data. For OFMs with saturated tailgroups (SA and GMS), we obtain good agreement between the predictions made by the simulations and the experiments. The MD simulation and experimental results deviate for OFMs containing Z-unsaturated tailgroups (GMO), with the former suggesting stronger adsorption for GMO than GMS, while the latter predicts the opposite trend. We suggest that this is can be attributed to the higher steric barrier of adsorption of the OFMs with kinked Z-unsaturated tailgroup through a partially formed monolayer, an aspect which was not captured in the current simulations. This study demonstrates that MD simulations with the ABF algorithm, alongside MTT, are an accurate and efficient tool to predict adsorption isotherms at solid-liquid interfaces.
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