Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响

Effect of the substrate potential on the static friction force in the Frenkel-Kontorova model

用一维Frenkel-Kontorova模型,对相互接触的两个单原子分子链具有相对运动趋势时所产生的最大静摩擦力进行了研究.分别在相邻原子的距离与周期势场的周期比b/a为可公度(commensurate)、黄金分割(goldenmean)、螺旋分割(spiralmean)三种情况下,描述了特殊垫底势力的振幅A与分子链静摩擦力的关系,在特殊垫底势力的作用下上层原子链弹性系数K对静摩擦力的影响.研究表明,垫底势力的形式对静摩擦力的大小有很重要的影响.

By using the one-dimensional Frenkel-Kontorova（FK） model,we study the maximum static friction force between the two surface layers which are in contact.The relation between the substrate potential and the static friction force is studied in this paper.The effect of parameters of the upper layer such as the elastic coefficient K on the static friction force are also investigated.Results are obtained for three cases for which the ratio of the atomic distance to the period of potential field is commensurate,or equal to the golden mean,or the spiral mean respectively.The results show that both the form of the substrate potential and the commensurability have sigificant effect on the static friction force.