Thermal effects and spontaneous frictional relaxation in atomically thin layered materials

Abstract

We study the thermal effects on the frictional properties of atomically thin sheets. We simulate a simple model based on the Prandtl-Tomlinson model that reproduces the layer dependence of friction and strengthening effects seen in AFM experiments. We investigate sliding at constant speed as well as reversing direction. We also investigate contact aging: the changes that occur to the contact when the sliding stops completely. We compare the numerical results to analytical calculations based on Kramers rates. We find that there is a slower than exponential contact aging that weakens the contact and that we expect will be observable in experiments. We discuss the implications for sliding as well as aging experiments.

The Origin of Moiré‐Level Stick‐Slip Behavior on Graphene/h‐BN Heterostructures

“…This model is established based on the well‐known 1D PT model [ 57,58 ] by simplifying the MD system to a tip sliding against the graphene sheet with moiré‐level out‐of‐plane fluctuation supported by a rigid h ‐BN substrate, as shown in Figure a. Two extra degrees q x and q y are introduced to the PT model to describe the in‐plane deformation of graphene, [ 59,60 ] the equations of motion for the tip and graphene without considering the thermal effect can be written as $$\[\left\{ { \begin{array}{*{20}{c}}{{m_{{\rm{tip}}}}\ddot{x} = - \frac{{\partial U\left( {x,{q_x},{q_y},t} \right)}}{{\partial x}} - {m_{{\rm{tip}}}}{\gamma _x}\ddot{x}}\\{{m_{\rm{q}}}{{\ddot{q}}_x} = - \frac{{\partial U\left( {x,{q_x},{q_y},t} \right)}}{{\partial {q_x}}} - {m_{\rm{q}}}{\gamma _q}{{\dot{q}}_x}}\\{{m_{\rm{q}}}{{\ddot{q}}_y} = - \frac{{\partial U\left( {x,{q_x},{q_y},t} \right)}}{{\partial {q_y}}} - {m_{\rm{q}}}{\gamma _q}{{\dot{q}}_y}}\end{array} } \right.\]$$here, m tip and m q are the mass of tip and graphene sheet in the indentation region, respectively, and γ x and γ q are their corresponding damping coefficients. The total potential energy of the model system read as …”

“…This model is established based on the well-known 1D PT model [57,58] by simplifying the MD system to a tip sliding against the graphene sheet with moiré-level out-of-plane fluctuation supported by a rigid h-BN substrate, as shown in Figure 6a. Two extra degrees q x and q y are introduced to the PT model to describe the in-plane deformation of graphene, [59,60] the equations of motion for the tip and graphene without considering the thermal effect can be written as…”

Moiré superlattice effects on interfacial mechanical behavior: A concise review

“…When the periodicity of the moiré becomes smaller than the contact region between the AFM tip and the substrate, the long-range modulation becomes more uniform, leading to the disappearance of the stick-slip behaviors. [44][45][46] A deformation coupled (DC) PT model has been proposed to describe the moiré-level stick-slip behavior, [46,85,86]…”

“…When the periodicity of the moiré becomes smaller than the contact region between the AFM tip and the substrate, the long‐range modulation becomes more uniform, leading to the disappearance of the stick‐slip behaviors. [ 44‐46 ] A deformation coupled (DC) PT model has been proposed to describe the moiré‐level stick‐slip behavior, [ 46,85,86 ] $$$\left\{\begin{array}{c}{m}_{\text{tip}}\ddot{x}=-\frac{\partial U(x,{q}_{x},{q}_{y},t)}{\partial x}-{m}_{\text{tip}}{\gamma }_{x}\ddot{x}\\ {m}_{{\rm{q}}}{\ddot{q}}_{x}=-\frac{\partial U(x,{q}_{x},{q}_{y},t)}{\partial {q}_{x}}-{m}_{{\rm{q}}}{\gamma }_{{\rm{q}}}{\dot{q}}_{x}\\ {m}_{{\rm{q}}}{\ddot{q}}_{y}=-\frac{\partial U(x,{q}_{x},{q}_{y},t)}{\partial {q}_{y}}-{m}_{{\rm{q}}}{\gamma }_{{\rm{q}}}{\dot{q}}_{y}\end{array},\right.$$$where $${m}_{\text{tip}}$$ and $${m}_{{\rm{q}}}$$ are the mass of the AFM tip and the graphene substrate in the contact region, respectively, $${\gamma }_{x}$$ and $${\gamma }_{{\rm{q}}}$$ are their corresponding damping coefficients. The total potential en...…”