Rigorous derivation of diffusion equation for submonolayer lubricant film

In magnetic hard disk drives, it is important to secure the stability and durability of head–disk interface in relation to a submonolayer lubricant film because the spacing between a head and lubricant surface has to be reduced to ~0.5 nm to achieve a high density recording far beyond 2 Tb/in2. As a succeeding paper of the newly proposed diffusion equation for a submonolayer liquid film, this paper presents a rigorous derivation of the disjoining pressure (DP) from the Lennard–Jones potential (LJP) and formulated the rigorous diffusion equation incorporating the DP. The flow equation for a submonolayer film and viscosity model are the same as in the previous paper. The difference of the rigorous DP and diffusion equation from the previous ones are not significant except in a small thickness regime less than the van der Walls (vdW) distance. Theoretical relationship between the vdW distance in DP and the molecular force equilibrium distance in LJP is elucidated. Rigorous expressions of the conventional DP and diffusion equation for multilayer film are shown. Superiority of the submonolayer diffusion theories to the conventional theory are demonstrated by comparing their theoretical diffusion coefficients with Waltman’s experimental data.