Abstract
In magnetic hard disk drives, it is important to evaluate the replenishment effect of a submonolayer lubricant film under a more severe condition that the head–disk spacing has to be reduced from the current 0.7 nm to ~0.5 nm. In contrast to the prevailing conventional diffusion equation validated for multilayer liquid film, the author has already proposed a new diffusion equation more suitable for submonolayer film by intuitively incorporating the density reduction effect in the submonolayer liquid film. This paper presents a rigorous derivation of the disjoining pressure (DP) from Lennard–Jones potential (LJP) and formulated the diffusion equation incorporating the DP. The difference in the rigorous DP and diffusion equation from the previous versions is negligibly small except in a small film thickness less than the van der Waals (vdW) distance. The theoretical relationship between the vdW distance in the DP and the molecular force equilibrium distance in the LJP is elucidated. Rigorous derivations of the DP and diffusion equation for multilayer liquid film from the LJP are also presented. The superiority of the submonolayer diffusion equation over the conventional equation in the submonolayer film regime is demonstrated by comparing their theoretical diffusion coefficients with Waltman’s experimental data.
Highlights
In the field of micro- and nanotribology, evaluating the boundary lubrication and replenishment effect of a submonolayer liquid film is becoming increasingly important
This study aims to provide a scientific foundation to the disjoining pressures for both submonolayer and multilayer films by rigorous derivation from the Lennard–Jones potential (LJP)
The derivation process of the conventional disjoining pressure Πc1 is not clear to the best of the author’s knowledge, the present author thought that the validity of Πc1 is not appropriate for submonolayer lubricant film [17]
Summary
In the field of micro- and nanotribology, evaluating the boundary lubrication and replenishment effect of a submonolayer liquid film is becoming increasingly important. Mate [14] investigated the spreading kinetics of PFPE lubricant nanodroplets with 0–8 hydroxyl functional groups on a carbon-coated magnetic disk surface He found that when the central droplet dissipates into a pancake-shaped film, the spreading profile is well described by a diffusion equation derived from the Poiseuille flow model with zero slip for Fomblin-Z and Z-dol lubricants if the unknown viscosity is identified experimentally. Incorporating the new disjoining pressure and mass flow equation with film-thickness-dependent viscosity function, a new diffusion equation that is more valid for the submonolayer film was formulated [17] From this theory, it was found that the experimental replenishment profile could be calculated from the bulk viscosity if the effective viscosity is assumed to linearly increase to a few times larger than the bulk viscosity at the boundary of the bonded layer; approximately 30% of the depleted scar after 96 h was caused by wear of the bonded layer. The superiority of this submonolayer diffusion theory is demonstrated by comparing the theoretical diffusion coefficient with Waltman’s experimental results [18]
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