Interlayer Friction and Adhesion Effects in Penta-PdSe2-Based van der Waals Heterostructures

Abstract

Due to their inherent lattice mismatch characteristics, 2D heterostructure interfaces are considered ideal for achieving stable and sustained ultralow friction (superlubricity). Despite extensive research, the current understanding of how interface adhesion affects interlayer friction remains limited. This study focused on graphene/MoS₂ and graphene/PdSe₂ heterostructure interfaces, where extremely low friction coefficients of ≈10^-3 are observed. In contrast, the MoS₂/PdSe₂ heterostructure interfaces exhibit higher friction coefficients, ≈0.02, primarily due to significant interfacial interactions driven by interlayer charge transfer, which is closely related to the ionic nature of 2D material crystals. These findings indicate that the greater the difference in ionicity between the two 2D materials comprising the sliding interfaces is, the lower the interlayer friction, providing key criteria for designing ultralow friction pairs. Moreover, the experimental results demonstrate that interlayer friction in heterostructure systems is closely associated with the material thickness and interface adhesion strength. These experimental findings are supported by molecular dynamics simulations, further validating the observed friction behavior. By integrating experimental observations with simulation analyses, this study reveals the pivotal role of interface adhesion in regulating interlayer friction and offers new insights into understanding and optimizing the frictional performance of layered solid lubricants.

Keywords: 2D heterostructure; interlayer friction; superlubricity; van der Waals interaction.

Figure 1

Gold‐assisted exfoliation and characterization of large‐scale 2D PdSe₂ materials. a) Schematic representation of gold‐assisted mechanical exfoliation utilized to obtain large‐area monolayer and few‐layer PdSe₂ materials. b) Bright‐field image showcasing few‐layer 2D PdSe₂ on a porous carbon microgrid. c) High‐resolution transmission electron microscopy (HRTEM) image of few‐layer 2D PdSe₂, with an inset depicting an atomic‐resolution STEM image in the upper left corner. d) Fast Fourier transform (FFT) image of few‐layer 2D PdSe₂. e) Raman spectroscopy of 2D PdSe₂ materials with varying thicknesses. f,g) Imagery from energy dispersive spectroscopy (EDS) reveals the spatial arrangement of Pd and Se within few‐layer 2D PdSe₂.

Figure 2

Characterization of interlayer superlubricity in heterostructure systems. a) The experimental arrangement, depicted in a schematic diagram, demonstrates the methodology for measuring the friction between heterostructure layers. The setup involves a substrate securely mounted on an AFM stage, which incorporates a piezoelectric ceramic transducer (PZT) and a Si/SiO₂ surface. The frictional characteristics of 2D material layers under an applied load are quantified using a custom‐made AFM colloidal probe that exerts a normal force. Furthermore, an objective lens is attached to the AFM head, enabling in situ tracking of the motion of the microsphere probe relative to the substrate. b) SEM top view of the homemade colloidal probe. c) AFM image of PdSe₂ flakes on a Si/SiO₂ substrate. The inset depicts the height profile. d) Corresponding optical image in c. e) An AFM image showing MoS₂ flakes positioned on a Si/SiO₂ substrate is presented. The accompanying inset illustrates the height profile. f) Corresponding optical image in e. g–i) Three different heterostructure combinations, namely, G/MoS₂ g), G/PdSe₂ h), and MoS₂/PdSe₂ i), were studied with friction as a function of the applied normal load. The figure includes a green dashed line, which serves as the fitting line. The slope of this line signifies the friction coefficient of the respective heterostructure. The illustration represents the associated structural model. Standard deviations define the error bars in this context.

Figure 3

Measurements of the interlayer cohesive force. a–c) The adhesive force histograms between the tip and the 2D materials were measured for the G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c) heterostructure systems. The red dashed line represents the Gaussian fitting curve. d–f) Typical force‒distance curves (sometimes known as F‒D curves) recorded on the complete heterostructure interfaces of G/MoS₂ d), G/PdSe₂ e), and MoS₂/PdSe₂ f) crystals.

Figure 4

Variational trends of interfacial friction and adhesion forces with layer thickness. a–c) The evolution trend of the interlayer frictional force with respect to the substrate thickness in heterostructure systems G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c). d–f) The trend of the interfacial adhesion force with respect to the substrate thickness in heterostructure systems G/MoS₂ d), G/PdSe₂ e), and MoS₂/PdSe₂ f).

Figure 5

The measured friction of heterostructures exhibits rotational anisotropy. a–c) The evolution of interlayer friction in heterostructure systems G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c) with stacking angle, as measured by AFM. d–f) The evolution of the interlayer adhesion force in heterostructure systems G/MoS₂ d), G/PdSe₂ e), and MoS₂/PdSe₂ f) as a function of stacking angle.

Figure 6

The velocity‐dependent nature of the interfacial friction force. a–c) The variation in interlayer friction in the heterostructure systems G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c) as a function of scanning speed, measured using AFM.

Figure 7

Training process for the NEP machine‐learned potential. a) The evolution of the loss function concerning the training dataset throughout the generative process. b,c) A comparison is made between the predictions derived from the NEP and the reference data from DFT for energy and virial properties in the test datasets. d–f) An evaluation is performed to assess the agreement between the NEP predictions and DFT reference data for the testing dataset along the x‐, y‐, and z‐axes.

Figure 8

Precise validation of the NEP machine learning potential. a–c) An assessment of the phonon spectra of graphene a), MoS₂ b), and PdSe₂ c) materials involving a comparison between the predictions obtained from the NEP and the reference data derived from DFT. d–f) An examination of the energy evolution with interlayer spacing in the three heterostructure systems, namely, G/MoS₂ d), G/PdSe₂ e), and MoS₂/PdSe₂ f).

Figure 9

MD simulations of interlayer friction performance. a–c) Frictional force as a function of normal force for G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c). The corresponding friction coefficients, μ, are indicated. d–f) Adhesion force profiles against separation distance, with peak forces, F_ad, highlighted. g–i) PES for each heterostructure system, with color gradients signifying energy variations from low (blue) to high (red).

Figure 10

Variation in friction with substrate layer thickness. a–c) Variation in frictional force with layer number in heterostructure systems G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c).

Figure 11

Interlayer friction and adhesion force as a function of stacking angle. a–c) Variation in frictional force as a function of stacking angle in heterostructure systems G/MoS₂ a), G/PdSe₂ b), and MoS₂/PdSe₂ c). d) Trend of adhesive force with changes in stacking angle.