| In recent years, nano-tribology has been developping rapidly. In many theoretical research on the nano-tribology, the method of the molecular dynamics has been usually used. One of the simple but very useful model is the Frenkel-Kontorova (FK) model which has been used in the nano-tribology extensively.In chapter I, a brief review of the development of nano-tribology and research works are introduced. In chapter II, the effects of the particles number to the static friction force are investigated based on the two-dimensional FK model. In the case of commensurate, the static friction force is independent of the number of the particles when misfit angle . The static friction force increases while the number of the particles decreases when . In chapter III, the microcosmic mechanism of the dynamical friction force and static friction force are investigated. In the depinning process, two critical points Fs1 and Fs2 are found. In the pinning process, two critical points Fb1 and Fb2 are also found. The dependence of four critical forces Fs1, Fs2, and on the system parameters such as external driving force, misfit angle, winding number, interatomic strength are investigated. The analytical results of four critical points Fs1, Fs2,Fb1 and Fb2 are obtained which are in good agreements with the numerical results. The dependence of both and on the misfit angleθis not in fractal structure which is different from the depinning force Fs1. |
