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

纳米级物体的直接分子动力学模拟涉及其所有原子的运动方程的数值积分。这种方法是精确的，但它有严重的大小和时间尺度限制。随机建模克服了这些限制，只关注一个小的子集的相关自由度，称为“系统”。其余大量的不相关的，表示为“热浴”，没有明确模拟，但考虑到（i）重新正规化的力作用在系统坐标和之间，（ii）包括耗散力描述的能量转移从系统到热浴，和（iii）引入随机力描述热浴原子的热运动对系统的影响。 随机建模需要近似假设，因此并不总是清楚如何正确地将热浴效应（i）-（iii）纳入系统的运动方程。这个程序的目标是制定规则，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）。第二个目标是应用这些规则来研究纳米级物体的动力学，例如与固体表面接触的单个原子，原子团簇和纳米颗粒。 一个重要的纳米级物体是原子力显微镜的尖端，这是一种用于表面分析的标准实验工具。它的应用特别相关的这个程序是在纳米级的摩擦现象的研究。虽然宏观摩擦的结果，从复杂的相互作用的两个表面上接触的许多粗糙，纳米摩擦学的新兴研究领域是集中在一个单一的这样的粗糙-原子力显微镜的尖端-与原子平面的相互作用。宏观和纳米摩擦的共同特点是都表现出老化现象，即摩擦力随着接触时间的延长而逐渐增大。虽然宏观摩擦中的老化已经研究了几十年，但其纳米级对应物在不到十年前首次通过实验建立。 纳米尺度的摩擦已经在理论上使用随机建模进行了研究，但大多数这样的模型不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-衬底接触的老化效应来改进现有的纳米级摩擦的随机模型。 的 该计划的预期成果是提高我们对纳米尺度下自然规律的理解，并开发有效的数值计算方法。 工具来模拟固体表面上纳米级物体的动力学。这些工具应该在纳米粒子的操纵，它们的相互作用的研究和摩擦控制等领域找到一些科学和技术应用。

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. The anticipated outcome of this program is improvement of our understanding of the laws of nature acting at the nanoscale, and development of efficient numerical tools 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.