Wrinkle development in graphene sheets with patterned nano-protrusions: A molecular dynamics study

Highlights

• Large-scale molecular dynamics to investigate wrinkling in graphene on nanoparticles.

• Strong adhesion to nanoparticles leads to specific wrinkle-branch emissions.

• Graphene pre-compression needed to induce predictable wrinkle patterns.

• Inter-particle distance and particle radius determine wrinkle dimensions.

• Asymmetric grain boundaries may alter the propagation of wrinkle lines.

Abstract

We perform large-scale molecular dynamics simulations to investigate wrinkling phenomena in uncompressed and pre-compressed graphene sheets with protrusions introduced by a hexagonal array of nanoparticles with varying spacing. The analysis includes the additional role of the nanoparticle size in conjunction with the cohesive energy between graphene and the particles in the formation of prominent adhesive profiles, or protrusions, in the sheets. The results throw new light on the underlying nucleation and propagation mechanisms of graphene wrinkles that emanate from equidistant, patterned protrusions. We find in the simulations that wrinkle morphology and the onset of wrinkling patterning are governed by a limited number of predominant factors that also determine the prominence of the protrusion profiles. The discussion provides a rationale to the development of wrinkle patterns with predictable geometry. We ascertain that the wrinkle topographies detected in our sheets are in good agreement with self-supported graphene experiments. The observed wrinkling mechanisms and the resulting patterning in our graphene simulations can pave the way to designing new tailor-made metamaterials based on suspended 2D materials.

Introduction

The susceptibility of graphene and other 2D materials to external stimuli is a crucial and integral property of these unique systems [1,2]. Lattice deformation comprises many various effects, which in turn influence the (opto)electronic structure of 2D materials—a process generally called the strain engineering [[3], [4], [5]]. Due to the intrinsic low bending rigidity, atomically thin materials react even to minuscule deformation by forming out-of-plane corrugations [[6], [7], [8], [9]]. Based on the dimensions and directions of spreading, the corrugations can be approximately divided into ripples (smaller than 1 nm), wrinkles (length/width aspect ratio usually larger than 1, length up to several μm), or crumples (with the dimensions of wrinkles but spreading isotropically) [7,10].

The control of lattice deformation and the out-of-plane corrugation is absolutely essential, both in studies and applications of 2D materials. Several ways exist to induce stable corrugations through substrate manipulation. Releasing a prestrained elastomer with a 2D material on top results in wrinkles or crumples delaminated from the substrate, depending on the straining directions [11]. Transferring graphene sheets using a polymer stamp with prefabricated ridges causes the formation of oriented sharp wrinkles [12], and heating a soft polymer with graphene creates supported wrinkle arrays with the orientation controlled by the flake aspect ratio [13].

However, a simple, passive approach can be taken, where no external stimuli is applied: substrate patterning. Nanopillar or nanoparticle (NP) arrays cause a (partial) delamination of the 2D materials from the flat substrate, and consequently, wrinkles spread from the nanopillar or NP tips [[14], [15], [16], [17], [18], [19]]. The dimensions and distribution of the pillars (or of NPs) determine—together with the processing conditions—the extent of delamination [19]. When large portions of the 2D material still adhere to the substrate between the pillars, a large strain on the lattice is built up on the top of the pillar. Such a system can in turn provide single photon emitters localized at these spots [20,21]. When the 2D material is delaminated, specific wrinkle topographies with varying characteristics (dimensions, orientation, density, etc.) are formed [16]. The wrinkles can be either discontinuous, spreading from individual pillars to different directions, mostly towards the nearest neighbor (NN) pillars [16], but not reaching them, or continuous in the sense of apparently connecting the NN pillars (further termed as directional wrinkling). The latter group can be divided into subgroups depending on the number of connected NN pillars and the presence of a prevalent wrinkling orientation [16,19]. The resulting control of the lattice strains and topography of suspended 2D materials can pave the way toward metamaterials with properties tailored to suit the needs of various applications ranging from photonics to sensing. However, the fabrication of such wrinkle arrays has been an experimental-based trial and error approach up to now. A smart design based on credible large-area simulations is needed to advance the field.

Recent investigations of monolayer graphene wrinkling using molecular dynamics (MD) simulations have provided fundamental insights into the developmental phases and propagation of small wrinkles in sheared freestanding [22,23] and in substrate-supported [24] sheets. Additional experimental and MD studies [25,26] have revealed the effect of distinct NP arrays on the formation of specific, stable wrinkle topographies in graphene-on-substrate systems in minute, nanoscopic sheets (of up to $\approx$ 40 $\times$ 20 nm). Under these conditions, the presence of NPs may generate prominent protrusion profiles in graphene sheets. Protrusions introducing sufficient levels of local lattice strains [27] may cause in turn the onset of out-of-plane wrinkle branches—due to dramatic wrinkle delamination—that emanate from the protruding zones in random directions. Although a common consensus suggests that wrinkling inception is attributed to the compressive strains in the graphene lattice [16,27,28], knowledge is still lacking in regard to the incipient mechanisms associated with wrinkle branch formation, which under a patterned distribution of protrusions, may lead to the development of directional wrinkling in monolayer graphene.

In this paper, we systematically investigate the factors influencing graphene wrinkling by conducting large-scale MD simulations of a specific graphene-NP system. The outcomes from these computations shed new light on the underlying mechanisms during early wrinkle formation in NP-supported sheets with patterned adhesive protrusions. A comparison to recent experimental wrinkle topographies in self-supported graphene enables us to validate the observed wrinkle mechanisms and the resulting wrinkling patterning obtained in the MD simulations. We explain the formation of salient protrusion profiles in graphene (including the role of NP size and the cohesive energy) and the rationale to the development of directional wrinkling with predictable geometry.