Stability of Planar Slits in Multilayer Graphite Crystals

TL;DR

The paper addresses the stability of planar slits formed in multilayer graphite when capped by multilayer graphene sheets. It develops a 2D coarse-grained chain model to quantify open versus closed slit states, revealing that the maximum open width $L_o$ grows with the covering-layer count $K$ and exhibits distinct behavior for single-, double-, and triple-layer cavities. Inside the crystal, two-layer slits can remain open at any width, while wider slits may adopt a closed state; the stability is modulated by temperature via Langevin dynamics. All-atom simulations using LJ and KC potentials validate the coarse-grained predictions, with KC offering results in good agreement with DFT pinning energies, thereby supporting the model's relevance for designing nanoscale graphite/multilayer graphene pores and understanding their thermal robustness.

Abstract

Using a two-dimensional coarse-grained chain model, planar slits in multilayer graphite crystals are simulated. It is shown that when covering a linear cavity on the flat surface of a graphite crystal with a multilayer graphene sheet, an open (unfilled slit) can form only if the cavity width does not exceed a critical value L_o (for width L>L_o, only a closed state of the slit is formed, with the cavity space filled by the covering sheet). The critical width of the open slit L_o increases monotonically with the number of layers K in the covering sheet. For a single-layer cavity, there is a finite critical value of its width L_o<3nm, while for two- and three-layer cavities, the maximum width of the open slit increases infinitely with increasing K as a power function K^αwith exponent 0<α<1. Inside the crystal, two- and three-layer slits can have stable open states at any width. For a slit with width L>7.6nm, a stationary closed state is also possible, in which its lower and upper surfaces adhere to each other. Simulation of thermal oscillations showed that open states of two-layer slits with width L<15nm are always stable against thermal oscillations, while wider slits at T>400K transition from the open to the closed state. Open states of three-layer slits are always stable against thermal oscillations.

Figures (11)

• Figure 1: Schematic of the two-dimensional chain model construction for (a) a flat graphene sheet lying in the $xy$ plane (${\bf u}_n$ is the coordinate vector of the $n$-th carbon atom). Chain model (b) with period $a=a_x$ and (c) $a=2a_x$ ($n$ is the bead index, $M_c$ is the carbon atom mass, $M=2M_c$ is the bead mass).
• Figure 2: Chain model of a multilayer graphene sheet, $k$ is the index of chain (or sheet layer), $n$ is the bead index (vector ${\bf u}_{n,k}$ gives the coordinates of bead $n,k$), $M$ is the bead mass. Potential $V(r)$ describes the longitudinal stiffness, and $U(\theta)$ describes the bending stiffness of the chain. Gray circles show the van der Waals radii of the beads.
• Figure 3: Stationary state of a two-layer slit ($K_g=2$) of width $L_x=(N_g+1)a$, covered by a $K$-layer graphene sheet for (a) $N_g=15$, $K=1$; (b) $N_g=16$, $K=1$, (c) $N_g=22$, $K=3$, (d) $N_g=23$, $K=3$, (e) $N_g=29$, $K=6$, (f) $N_g=30$, $K=6$. The upper graphene sheet is shown in red, the substrate sheets participating in the slit formation are shown in green, the remaining substrate layers are shown in blue. The chain model with discretization parameter $d=2$ (chain period $a=2a_x=2.456$Å) is used. Only the top 8 layers of the substrate out of $K_s=50$ layers are shown (number of beads in the chain $N_s=200$, $N=180$).
• Figure 4: The dependence of the maximum width of the open state of the slit $L_o$ on the number of layers of the covering sheet $K$. Within the framework of various models, these dependencies were calculated for a gap with a height of one, two and three layers. Panel (a) compares the results of the initial two-dimensional model (discreteness parameter $d$=1, curves 1, 2, 3) with the all-atomic LJ-model (curves 10, 11, 12). Panel (b) shows the values of the maximum width in the two-dimensional model at $d$=2 (curves 4, 5, 6), with $d$=2.129 (curves 7, 8, 9), as well as within the framework of a three-dimensional KC-model (curves 13, 14, 15). Curves 1, 4, 7, 10, 13 give the dependence for a single-layer gap ($K_g=1$), curves 2, 5, 8, 11, 14 -- for a two-layer gap ($K_g=2$), and 3, 6, 9, 12, 15 -- for a three-layer slit ($K_g=3$). Logarithmic axes are used, dotted lines show the power-law dependencies of $K^\alpha$.
• Figure 5: View of the stationary state of a single-layer slit in a multilayer crystal with width $L_x=aN_g$ for $N_g=10$, 11, 12, 13 (a, b, c, d). Chain period $a=2a_x$ (chain discreteness $d=2$).