Confined Lubricant Layering — Nanotribology Squeeze-Film Simulator

Squeeze the Film

Plate gap D 3.20 nm

Molecule diameter σ 0.55 nm

Sliding speed 1.0×

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Liquid-like film

Confined layers n

Solvation force F_N

0.00

Friction force F_L

0.00

Friction coeff. μ(n)

0.00

How it works

When a liquid is confined between two atomically smooth surfaces to within a few molecular diameters, it can no longer be treated as a continuum. It orders itself into discrete parallel layers, and the force needed to squeeze the surfaces together oscillates as each layer is expelled — the classic result measured with a Surface Forces Apparatus (Israelachvili & Horn):

F(D)/R ≈ F₀ · e^(−D/ξ) · cos(2πD/σ)
n(D) = round(D / σ)   ← number of confined layers
ξ ≈ 3σ                 ← structural decay length

Each local minimum of that oscillation is a mechanically stable gap where an integer number of layers fits exactly; the region between minima is unstable, so as you squeeze D down, the film jumps from n layers to n−1 the instant it crosses an instability point — a real "layering transition", not a smooth compression.

Shearing the top plate sideways then probes friction in two very different regimes:

n ≥ 4 (liquid-like): the film still flows, shearing smoothly layer over layer. Friction coefficient stays low, μ(n) → μ_min.
n ≤ 2 (boundary lubrication): too few layers remain to flow as a liquid — molecules lock into the two solid surfaces' potential and must hop over each other to slide, exactly the stick-slip regime measured for confined OMCTS, water and alkanes. Friction rises sharply:

μ(n) = μ_min + (μ_max − μ_min) · e^(−(n−1)/1.2)

This is the microscopic origin of boundary lubrication: once a lubricant film thins to one or two molecular layers — inside a MEMS/NEMS hinge, a disk-drive head/slider gap, or a rubbing biomedical implant surface — friction and wear jump by an order of magnitude, which is exactly why nanotribologists design coatings and additives to keep at least a few ordered layers in place under load.

Rigid plates Lubricant layers Boundary layer (n≤2)

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