Building the bridge from atomistic to stochastic modelling of nanoscale friction phenomena

纳米尺度物体的直接分子动力学模拟涉及对其所有原子的运动方程进行数值积分。这种方法是精确的，但它有严重的规模和时间限制。随机建模通过只关注相关自由度的一个小子集（称为“系统”）来克服这些限制。其余大量不相关的，表示为“热浴”，没有明确模拟，但考虑到(i)重新规范化作用于系统坐标和系统坐标之间的力，（ii）包括描述从系统到热浴的能量传递的耗散力，以及（iii）引入描述热浴原子的热运动对系统的影响的随机力。随机建模需要近似的假设，因此，如何正确地将热浴效应(i)-(iii)纳入系统的运动方程并不总是很清楚。这个程序的目标是计算出允许人们从系统和浴原子之间作用的力的知识中获得成分(i)-(iii)的规则。第二个目标是应用这些规则来研究纳米级物体的动力学，如单原子、原子团簇和与固体表面接触的纳米颗粒。原子力显微镜是一种用于表面分析的标准实验工具，它的尖端是一个重要的纳米尺度物体。它的应用特别相关的程序是在纳米尺度上的摩擦现象的研究。宏观摩擦是由两个接触表面上的许多凹凸不平的复杂相互作用产生的，而纳米摩擦学的新兴研究领域集中在单个这样的凹凸不平-原子力显微镜尖端-与原子平面的相互作用上。宏观摩擦和纳米摩擦的共同特征是均表现出老化现象，即摩擦力随接触时间的延长而逐渐增大。虽然宏观摩擦中的老化问题已经研究了几十年，但其纳米尺度的对应物首次在实验中建立起来还不到十年。纳米尺度的摩擦已经用随机模型进行了理论研究，但大多数模型没有考虑接触老化的可能性。本计划的进一步目标是通过包括尖端-衬底接触老化的影响来改进现有的纳米尺度摩擦随机模型。该计划的预期结果是提高我们对纳米尺度自然规律的理解，并开发有效的数字工具来模拟固体表面上纳米尺度物体的动力学。这些工具应该在诸如纳米颗粒的操作、相互作用的研究和摩擦控制等领域找到许多科学和技术应用。

Direct molecular dynamic simulation of a nanoscale object involves numerical integration of the equations of motion for all its atoms. This approach is exact, but it has severe size and time-scale limitations. Stochastic modelling overcomes these limitations by focusing on only a small subset of the relevant degrees of freedom, termed "the system". The remaining large number of the irrelevant ones, denoted as "the heat bath", are not simulated explicitly, but taken into account by (i) renormalizing the forces acting on and between the system coordinates, (ii) including dissipative forces describing the energy transfer from the system into the heat bath, and (iii) introducing random forces describing the effect of thermal motion of the heat-bath atoms on the system.  Stochastic modelling requires approximative assumptions, and thus it is not always clear how to correctly incorporate the heat-bath effects (i)-(iii) into the system's equations of motion. The goal of this program is to work out the rules allowing one to obtain the ingredients (i)-(iii) from the knowledge of the forces acting between the system and the bath atoms. The second goal is to apply these rules to study the dynamics of nanoscale objects, such as single atoms, atomic clusters, and nanoparticles in contact with a solid surface.An important nanoscale object is the tip of an atomic force microscope, a standard experimental tool used for surface analysis. Its application particularly pertinent to this program is the study of friction phenomena at the nanoscale. While macroscopic friction results from complex interaction between many asperities on the two surfaces in contact, the newly emerging research field of nanotribology is focused on the interaction of a single such asperity - the atomic force microscope tip - with an atomically flat surface. The common feature of macro- and nanoscale friction is that both exhibit the phenomenon of aging, that is, gradual increase of friction force with contact duration. While aging in the macroscopic friction has been investigated for several decades, its nanoscale counterpart was first established experimentally less than a decade ago. Nanoscale friction has been studied theoretically using stochastic modelling, but the majority of such models do not consider the possibility of contact aging. The further goal of the present program is to improve the existing stochastic models of nanoscale friction by including the effect of aging of the tip-substrate contact.Theanticipated outcome of this program is improvement of our understanding of the laws of nature acting at the nanoscale, and development of efficient numericaltools to simulate the dynamics of nanoscale objects on solid surfaces. These tools should find a number of scientific and technological applications in such fields as manipulation of nanoparticles, investigation of their interactions, and control of friction.