Bui Anna T, Cox Stephen J
Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom.
J Chem Phys. 2024 Nov 28;161(20). doi: 10.1063/5.0238363.
A central aim of statistical mechanics is to establish connections between a system's microscopic fluctuations and its macroscopic response to a perturbation. For non-equilibrium transport properties, this amounts to establishing Green-Kubo (GK) relationships. In hydrodynamics, relating such GK expressions for liquid-solid friction to macroscopic slip boundary conditions has remained a long-standing problem due to two challenges: (i) The GK running integral of the force autocorrelation function decays to zero rather than reaching a well-defined plateau value, and (ii) debates persist on whether such a transport coefficient measures an intrinsic interfacial friction or an effective friction in the system. Inspired by ideas from the coarse-graining community, we derive a GK relation for liquid-solid friction where the force autocorrelation is sampled with a constraint of momentum conservation in the liquid. Our expression does not suffer from the "plateau problem" and unambiguously measures an effective friction coefficient, in an analogous manner to Stokes' law. We further establish a link between the derived friction coefficient and the hydrodynamic slip length, enabling a straightforward assessment of continuum hydrodynamics across length scales. We find that continuum hydrodynamics describes the simulation results quantitatively for confinement length scales all the way down to 1 nm. Our approach amounts to a straightforward modification to the present standard method of quantifying interfacial friction from molecular simulations, making possible a sensible comparison between surfaces of vastly different slippage.
统计力学的一个核心目标是建立系统微观涨落与其对微扰的宏观响应之间的联系。对于非平衡输运性质而言，这相当于建立格林 - 久保（GK）关系。在流体动力学中，由于两个挑战，将液体 - 固体摩擦的此类GK表达式与宏观滑移边界条件联系起来一直是一个长期存在的问题：（i）力自相关函数的GK运行积分衰减至零，而非达到一个明确定义的平台值；（ii）关于这样一个输运系数是测量系统中的固有界面摩擦还是有效摩擦，争论一直存在。受粗粒化领域思想的启发，我们推导了一种用于液体 - 固体摩擦的GK关系，其中在液体中通过动量守恒约束对力自相关进行采样。我们的表达式不存在“平台问题”，并且以类似于斯托克斯定律的方式明确测量了一个有效摩擦系数。我们进一步在推导的摩擦系数与流体动力学滑移长度之间建立了联系，从而能够对跨长度尺度的连续介质流体动力学进行直接评估。我们发现，对于小至1纳米的限制长度尺度，连续介质流体动力学能够定量描述模拟结果。我们的方法相当于对目前从分子模拟量化界面摩擦的标准方法进行直接修改，使得能够对具有极大不同滑移率的表面进行合理比较。
