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Phosphorus-based lubricant additives on iron with Machine Learning Interatomic Potentials

Paolo Restuccia, Enrico Pedretti, Francesca Benini, Sophie Loehlé, M. Clelia Righi

TL;DR

This study addresses the molecular origins of friction reduction by phosphorus-based lubricant additives on iron under boundary lubrication. It uses machine-learning interatomic potentials trained via active learning (Smart Configuration Sampling) to perform large-scale MD of DBHP, OAP, and MPEG-P additives at Fe interfaces, linking molecular architecture (esterification degree and chain length) to adsorption behavior, tribofilm formation, and interfacial separation. Key findings show DBHP achieves the lowest friction and the largest interfacial distance due to steric hindrance and reactive P--O chemistry; by contrast, OAP and mPEG-P exhibit higher friction with thinner films, though within mPEG-P, more esters and longer chains reduce friction via steric effects, sometimes outweighing adsorption strength. The work provides atomistic design principles for phosphorus-based additives, advocating a balance between reactive anchoring and molecular bulk to sustain low-friction, durable interfaces under severe confinement, enabled by an MLIP framework that captures bond-breaking and adsorption processes at realistic timescales.

Abstract

Phosphorus-based lubricant additives are used for protecting metallic contacts under boundary lubrication by forming surface films that reduce wear and friction. Despite their importance, the molecular mechanisms driving their friction-reducing effects remain unclear, especially for phosphate esters, whose molecular structure critically impact tribological behavior. In this study, we use machine learning-based molecular dynamics simulations to investigate the tribological performance of three representative phosphorus-based additives, Dibutyl Hydrogen Phosphite (DBHP), Octyl Acid Phosphate (OAP), and Methyl Polyethylene Glycol Phosphate (mPEG-P), on iron surfaces. The mPEG-P family is further analyzed by varying esterification degree and chain length. DBHP exhibits the lowest friction and largest interfacial separation, resulting from steric hindrance and tribochemical reactivity, as indicated by P-O bond cleavage and enhanced O-Fe interactions. In contrast, OAP and mPEG-P monoesters produce higher friction due to limited steric protection and reduced resistance to shear, leading to partial loss of surface coverage under extreme conditions. Within the mPEG-P family, multi-ester and longer-chain molecules significantly lower friction by maintaining larger separations, demonstrating that steric effects can outweigh surface reactivity under severe confinement. Overall, these results provide atomistic insights into how molecular architecture controls additive performance and support the design of phosphorus-based lubricants combining reactive anchoring with optimized steric structures for durable, low-friction interfaces.

Phosphorus-based lubricant additives on iron with Machine Learning Interatomic Potentials

TL;DR

This study addresses the molecular origins of friction reduction by phosphorus-based lubricant additives on iron under boundary lubrication. It uses machine-learning interatomic potentials trained via active learning (Smart Configuration Sampling) to perform large-scale MD of DBHP, OAP, and MPEG-P additives at Fe interfaces, linking molecular architecture (esterification degree and chain length) to adsorption behavior, tribofilm formation, and interfacial separation. Key findings show DBHP achieves the lowest friction and the largest interfacial distance due to steric hindrance and reactive P--O chemistry; by contrast, OAP and mPEG-P exhibit higher friction with thinner films, though within mPEG-P, more esters and longer chains reduce friction via steric effects, sometimes outweighing adsorption strength. The work provides atomistic design principles for phosphorus-based additives, advocating a balance between reactive anchoring and molecular bulk to sustain low-friction, durable interfaces under severe confinement, enabled by an MLIP framework that captures bond-breaking and adsorption processes at realistic timescales.

Abstract

Phosphorus-based lubricant additives are used for protecting metallic contacts under boundary lubrication by forming surface films that reduce wear and friction. Despite their importance, the molecular mechanisms driving their friction-reducing effects remain unclear, especially for phosphate esters, whose molecular structure critically impact tribological behavior. In this study, we use machine learning-based molecular dynamics simulations to investigate the tribological performance of three representative phosphorus-based additives, Dibutyl Hydrogen Phosphite (DBHP), Octyl Acid Phosphate (OAP), and Methyl Polyethylene Glycol Phosphate (mPEG-P), on iron surfaces. The mPEG-P family is further analyzed by varying esterification degree and chain length. DBHP exhibits the lowest friction and largest interfacial separation, resulting from steric hindrance and tribochemical reactivity, as indicated by P-O bond cleavage and enhanced O-Fe interactions. In contrast, OAP and mPEG-P monoesters produce higher friction due to limited steric protection and reduced resistance to shear, leading to partial loss of surface coverage under extreme conditions. Within the mPEG-P family, multi-ester and longer-chain molecules significantly lower friction by maintaining larger separations, demonstrating that steric effects can outweigh surface reactivity under severe confinement. Overall, these results provide atomistic insights into how molecular architecture controls additive performance and support the design of phosphorus-based lubricants combining reactive anchoring with optimized steric structures for durable, low-friction interfaces.
Paper Structure (10 sections, 1 equation, 7 figures)

This paper contains 10 sections, 1 equation, 7 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Training machine learning interatomic potentials
  4. Set up ab initio calculations
  5. Molecular systems and large-scale simulations set up
  6. Number of bonds per molecule (NBM) definition
  7. Results and discussion
  8. Difference between phosphites and phosphates as friction modifiers
  9. Different number of ester groups and chain length in mPEG-P
  10. Conclusions

Figures (7)

  • Figure 1: Ball-and-stick representation of the molecules studied in this work. From now on, white atoms represent H, grey C, yellow P and red O, respectively. In the lower panels, mPEG-P molecules with different number of esters and glycol units are shown. We modelled mPEG-P monoester with 4 glycol units (label A in red), mPEG-P diester with 4 glycol units (label B), mPEG-P triester with 4 glycol units (label C), mPEG-P monoester with 8 glycol units (label D), and mPEG-P diester with 8 glycol units (label E).
  • Figure 2: Parity plot for the DeePMD model evaluated on the complete dataset, comparing predicted atomic forces from the MLIP (y-axis) with reference DFT values. (x-axis). The colour scale indicates the density of data points, with warmer (cooler) colours representing higher (lower) counts of occurrences at specific force values. The overall RMSE is also reported in the plot.
  • Figure 3: Ball-and-stick representation of the computational setup for the system containing DBHP molecules confined within the iron interface (represented in blue). The black solid line represents the adopted simulation cell size. The red solid box represents the top-most iron layer where the normal load and the sliding velocity are applied, while the bottom-most black solid box identifies the reference iron layer, with fixed atomic positions.
  • Figure 4: Friction vs distance for the systems containing mPEG-P monoester (n=4), mPEG-P monoester (n=8), OAP and DBHP.
  • Figure 5: Ball-and-stick representation of the iron asperity containing DBHP (upper panel), OAP (central) and mPEG-P monoester with 4 glycol units (lower) additives at the end of the sliding simulations (19.5 ns). The dimension of Fe atoms has been reduced to make more visible the interaction of the P-based additives.
  • ...and 2 more figures